%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWW473+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n028.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 : 600s
% DateTime : Thu Jul 21 00:30:04 EDT 2022
% Result : Theorem 172.85s 173.49s
% Output : CNFRefutation 172.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 170
% Syntax : Number of formulae : 1308 ( 407 unt; 0 def)
% Number of atoms : 2779 ( 679 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 2575 (1104 ~;1168 |; 59 &)
% ( 38 <=>; 206 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 15 con; 0-5 aty)
% Number of variables : 3563 ( 141 sgn1250 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X2,X1,X12,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)))
=> ? [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
& ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X8))),hAPP(X2,fun(X1,bool),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),hAPP(fun(X1,X2),fun(X1,fun(X2,bool)),hAPP(fun(X2,fun(X2,bool)),fun(fun(X1,X2),fun(X1,fun(X2,bool))),combb(X2,fun(X2,bool),X1),fequal(X2)),X12)),hAPP(X1,X2,X12,X33)))))) ) ) ),
file('<stdin>',fact_49_pigeonhole__infinite) ).
fof(c_0_1,axiom,
! [X1,X16,X15] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X16)),X15))))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X15))) ) ),
file('<stdin>',fact_26_finite__Collect__disjI) ).
fof(c_0_2,axiom,
! [X1,X11,X16] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fimplies),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11)))),X16)),
file('<stdin>',fact_57_insert__Collect) ).
fof(c_0_3,axiom,
! [X1,X15,X16] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X15))) )
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X16)),X15)))) ),
file('<stdin>',fact_10_finite__Collect__conjI) ).
fof(c_0_4,axiom,
! [X2,X1,X12,X13,X8] :
( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X33)),X13)) )
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)),X13)) ),
file('<stdin>',fact_96_image__subsetI) ).
fof(c_0_5,axiom,
! [X1,X33,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X40) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X33))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X40))),
file('<stdin>',fact_80_insert__compr__raw) ).
fof(c_0_6,axiom,
! [X1,X11,X13] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X13))),
file('<stdin>',fact_56_insert__compr) ).
fof(c_0_7,axiom,
! [X1] :
( order(X1)
=> ! [X20,X31,X12] :
( ! [X32] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X12,X32)),hAPP(nat,X1,X12,hAPP(nat,nat,suc,X32))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X12,X20)),hAPP(nat,X1,X12,X31))) ) ) ),
file('<stdin>',fact_48_lift__Suc__mono__le) ).
fof(c_0_8,axiom,
! [X2,X1,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))),hAPP(fun(X1,bool),nat,finite_card(X1),X8))) ),
file('<stdin>',fact_4_card__image__le) ).
fof(c_0_9,axiom,
! [X20,X19,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X19)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ) ) ),
file('<stdin>',fact_39_le__diff__iff) ).
fof(c_0_10,axiom,
! [X2,X1,X12,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
=> ? [X30] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X30),X8))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X30))
& ti(fun(X1,bool),X13) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X30) ) ) ),
file('<stdin>',fact_47_finite__subset__image) ).
fof(c_0_11,axiom,
! [X1,X2,X13,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
<=> ? [X44] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X44),X8))
& ti(fun(X1,bool),X13) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X44) ) ),
file('<stdin>',fact_90_subset__image__iff) ).
fof(c_0_12,axiom,
! [X1,X2,X34,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
=> ~ ! [X33] :
( ti(X1,X34) = hAPP(X2,X1,X12,X33)
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X33),X8)) ) ),
file('<stdin>',fact_92_imageE) ).
fof(c_0_13,axiom,
! [X1,X2,X39,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X39),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
<=> ? [X33] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X33),X8))
& ti(X1,X39) = hAPP(X2,X1,X12,X33) ) ),
file('<stdin>',fact_77_image__iff) ).
fof(c_0_14,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X8)))) ),
file('<stdin>',fact_1_finite__Collect__subsets) ).
fof(c_0_15,axiom,
! [X2,X1,X12,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X13))) ),
file('<stdin>',fact_91_image__mono) ).
fof(c_0_16,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ),
file('<stdin>',fact_84_insert__subset) ).
fof(c_0_17,axiom,
! [X1,X11,X37,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X37),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X37)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X43))) ),
file('<stdin>',fact_87_insert__mono) ).
fof(c_0_18,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)))) ),
file('<stdin>',fact_7_card__insert__le) ).
fof(c_0_19,axiom,
! [X1,X13,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X13)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ),
file('<stdin>',fact_85_subset__insert) ).
fof(c_0_20,axiom,
! [X29,X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X18))) ),
file('<stdin>',fact_44_diff__le__mono2) ).
fof(c_0_21,axiom,
! [X29,X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X29)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X29))) ),
file('<stdin>',fact_43_diff__le__mono) ).
fof(c_0_22,axiom,
! [X18,X17,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X18)),X17)),hAPP(nat,nat,suc,X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X25),
file('<stdin>',fact_37_Suc__diff__diff) ).
fof(c_0_23,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X13)),hAPP(fun(X1,bool),nat,finite_card(X1),X8)))
=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ) ),
file('<stdin>',fact_6_card__seteq) ).
fof(c_0_24,axiom,
! [X2,X1,X13,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X13),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13)) ) ),
file('<stdin>',fact_46_finite__surj) ).
fof(c_0_25,axiom,
! [X19] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X19)))),
file('<stdin>',fact_12_finite__Collect__le__nat) ).
fof(c_0_26,axiom,
! [X1,X11,X34,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X8)))
<=> ( ti(X1,X11) = ti(X1,X34)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ) ),
file('<stdin>',fact_60_insert__iff) ).
fof(c_0_27,axiom,
! [X1,X11,X34,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X8)))
=> ( ti(X1,X11) != ti(X1,X34)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ) ),
file('<stdin>',fact_54_insertE) ).
fof(c_0_28,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ),
file('<stdin>',fact_78_imageI) ).
fof(c_0_29,axiom,
! [X17,X25,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X18))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17) ) ),
file('<stdin>',fact_40_Nat_Odiff__diff__eq) ).
fof(c_0_30,axiom,
! [X2,X1,X41,X12,X38,X8] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),hAPP(fun(X41,bool),fun(X2,bool),hAPP(fun(X41,X2),fun(fun(X41,bool),fun(X2,bool)),image(X41,X2),X38),X8)) = hAPP(fun(X41,bool),fun(X1,bool),hAPP(fun(X41,X1),fun(fun(X41,bool),fun(X1,bool)),image(X41,X1),hAPP(fun(X41,X2),fun(X41,X1),hAPP(fun(X2,X1),fun(fun(X41,X2),fun(X41,X1)),combb(X2,X1,X41),X12),X38)),X8),
file('<stdin>',fact_81_image__image) ).
fof(c_0_31,axiom,
! [X2,X1,X34,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( ti(X2,X34) = hAPP(X1,X2,X12,X14)
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X34),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ) ),
file('<stdin>',fact_79_rev__image__eqI) ).
fof(c_0_32,axiom,
! [X1,X2,X8,X34,X12,X14] :
( ti(X1,X34) = hAPP(X2,X1,X12,X14)
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8))) ) ),
file('<stdin>',fact_50_image__eqI) ).
fof(c_0_33,axiom,
! [X1,X34,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
file('<stdin>',fact_86_subset__insertI2) ).
fof(c_0_34,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),X13))) ) ),
file('<stdin>',fact_5_card__mono) ).
fof(c_0_35,axiom,
! [X1,X34,X11,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
file('<stdin>',fact_63_insertI2) ).
fof(c_0_36,axiom,
! [X1,X34,X11,X13] :
( ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> ti(X1,X11) = ti(X1,X34) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
file('<stdin>',fact_53_insertCI) ).
fof(c_0_37,axiom,
! [X1,X37,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X37))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X37)) ) ),
file('<stdin>',fact_72_subset__trans) ).
fof(c_0_38,axiom,
! [X20,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X20)),hAPP(nat,nat,suc,X28)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X28)) ),
file('<stdin>',fact_33_Suc__le__mono) ).
fof(c_0_39,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8) ),
file('<stdin>',fact_89_insert__image) ).
fof(c_0_40,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
file('<stdin>',fact_71_set__mp) ).
fof(c_0_41,axiom,
! [X1,X13,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
file('<stdin>',fact_70_set__rev__mp) ).
fof(c_0_42,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
file('<stdin>',fact_69_in__mono) ).
fof(c_0_43,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X13)) ) ),
file('<stdin>',fact_52_subsetD) ).
fof(c_0_44,axiom,
! [X28,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X20)),X28)) ),
file('<stdin>',fact_35_not__less__eq__eq) ).
fof(c_0_45,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8)))
<=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('<stdin>',fact_27_finite__insert) ).
fof(c_0_46,axiom,
! [X18,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X18)),
file('<stdin>',fact_45_diff__le__self) ).
fof(c_0_47,axiom,
! [X26,X27,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X27)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X25)),X27),
file('<stdin>',fact_25_diff__commute) ).
fof(c_0_48,axiom,
! [X1,X36,X8,X14] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X36),X8),X14))
<=> ( ti(X1,X36) = ti(X1,X14)
| hBOOL(hAPP(X1,bool,X8,X14)) ) ),
file('<stdin>',fact_61_insert__code) ).
fof(c_0_49,axiom,
! [X2,X1,X12,X11,X13] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X11),X13)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X2,X1,X12,X11)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X13)),
file('<stdin>',fact_88_image__insert) ).
fof(c_0_50,axiom,
! [X20,X19,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X19) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X19)
<=> X28 = X20 ) ) ),
file('<stdin>',fact_41_eq__diff__iff) ).
fof(c_0_51,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X18)),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
file('<stdin>',fact_30_Suc__leD) ).
fof(c_0_52,axiom,
! [X1,X13,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13))
=> ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X13)
<=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ) ),
file('<stdin>',fact_62_insert__ident) ).
fof(c_0_53,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ) ),
file('<stdin>',fact_66_set__eq__subset) ).
fof(c_0_54,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8))
=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ),
file('<stdin>',fact_51_equalityI) ).
fof(c_0_55,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X25)) ) ),
file('<stdin>',fact_21_le__trans) ).
fof(c_0_56,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(fun(X1,bool),nat,finite_card(X1),X8) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X8)) ) ) ),
file('<stdin>',fact_8_card__insert__if) ).
fof(c_0_57,axiom,
! [X45,X16,X19] :
( hBOOL(hAPP(nat,bool,X16,X19))
=> ( ! [X32] :
( hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,suc,X32)))
=> hBOOL(hAPP(nat,bool,X16,X32)) )
=> hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X19),X45))) ) ),
file('<stdin>',fact_94_zero__induct__lemma) ).
fof(c_0_58,axiom,
! [X1,X13,X11] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))),
file('<stdin>',fact_83_subset__insertI) ).
fof(c_0_59,axiom,
! [X1,X14,X36,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X36),X8)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X36),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),
file('<stdin>',fact_59_insert__commute) ).
fof(c_0_60,axiom,
! [X17,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X18)),X17) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) ),
file('<stdin>',fact_11_Suc__diff__le) ).
fof(c_0_61,axiom,
! [X1,X11,X13] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))),
file('<stdin>',fact_55_insertI1) ).
fof(c_0_62,axiom,
! [X20] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X20))) = hAPP(nat,nat,suc,X20),
file('<stdin>',fact_13_card__Collect__le__nat) ).
fof(c_0_63,axiom,
! [X2,X1,X9,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X9),X10))) ),
file('<stdin>',fact_2_finite__imageI) ).
fof(c_0_64,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X8)) ) ),
file('<stdin>',fact_9_card__insert__disjoint) ).
fof(c_0_65,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),hAPP(nat,nat,suc,X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
| X28 = hAPP(nat,nat,suc,X20) ) ),
file('<stdin>',fact_34_le__Suc__eq) ).
fof(c_0_66,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,suc,X17)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> X18 = hAPP(nat,nat,suc,X17) ) ),
file('<stdin>',fact_31_le__SucE) ).
fof(c_0_67,axiom,
! [X17,X46] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X46))
=> ? [X47] : X46 = hAPP(nat,nat,suc,X47) ),
file('<stdin>',fact_95_Suc__le__D) ).
fof(c_0_68,axiom,
! [X1,X13,X8] :
( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X13)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ),
file('<stdin>',fact_93_subsetI) ).
fof(c_0_69,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8))) ),
file('<stdin>',fact_3_finite_OinsertI) ).
fof(c_0_70,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X17)),
file('<stdin>',fact_36_Suc__n__not__le__n) ).
fof(c_0_71,axiom,
! [X48] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X48))
<=> ? [X47] :
! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X48))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X47)) ) ),
file('<stdin>',fact_98_finite__nat__set__iff__bounded__le) ).
fof(c_0_72,axiom,
! [X6,X7] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X6),X7))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X7),X6)) ),
file('<stdin>',fact_0_assms_I1_J) ).
fof(c_0_73,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,suc,X17))) ),
file('<stdin>',fact_32_le__SucI) ).
fof(c_0_74,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18))
=> X18 = X17 ) ),
file('<stdin>',fact_20_le__antisym) ).
fof(c_0_75,axiom,
! [X26,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X26)) = X26 ),
file('<stdin>',fact_42_diff__diff__cancel) ).
fof(c_0_76,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
file('<stdin>',fact_29_rev__finite__subset) ).
fof(c_0_77,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
file('<stdin>',fact_28_finite__subset) ).
fof(c_0_78,axiom,
! [X3,X2,X1,X53,X54,X55] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2)),combs(X3,X1,X2),X53),X54),X55) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X53,X55),hAPP(X3,X1,X54,X55)),
file('<stdin>',help_COMBS_1_1_U) ).
fof(c_0_79,axiom,
! [X1,X14,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8),
file('<stdin>',fact_58_insert__absorb2) ).
fof(c_0_80,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8) = ti(fun(X1,bool),X8) ),
file('<stdin>',fact_64_insert__absorb) ).
fof(c_0_81,axiom,
! [X3,X2,X1,X53,X54,X55] : hAPP(X3,X2,hAPP(X1,fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2)),combc(X3,X1,X2),X53),X54),X55) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X53,X55),X54),
file('<stdin>',help_COMBC_1_1_U) ).
fof(c_0_82,axiom,
! [X3,X2,X1,X53,X54,X55] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),combb(X1,X2,X3),X53),X54),X55) = hAPP(X1,X2,X53,hAPP(X3,X1,X54,X55)),
file('<stdin>',help_COMBB_1_1_U) ).
fof(c_0_83,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
<=> hBOOL(hAPP(X1,bool,X8,X14)) ),
file('<stdin>',fact_75_mem__def) ).
fof(c_0_84,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18)) ),
file('<stdin>',fact_23_nat__le__linear) ).
fof(c_0_85,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X18)),hAPP(nat,nat,suc,X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17),
file('<stdin>',fact_38_diff__Suc__Suc) ).
fof(c_0_86,axiom,
! [X3,X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22))
| ti(X3,X21) = ti(X3,X22) ),
file('<stdin>',help_fequal_1_1_T) ).
fof(c_0_87,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54))
| ~ hBOOL(X53)
| hBOOL(X54) ),
file('<stdin>',help_fimplies_3_1_U) ).
fof(c_0_88,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54))
| hBOOL(X53)
| hBOOL(X54) ),
file('<stdin>',help_fdisj_3_1_U) ).
fof(c_0_89,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X54) ),
file('<stdin>',help_fconj_3_1_U) ).
fof(c_0_90,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X53) ),
file('<stdin>',help_fconj_2_1_U) ).
fof(c_0_91,axiom,
! [X1,X2,X12,X38] :
( ! [X33] : hAPP(X1,X2,X12,X33) = hAPP(X1,X2,X38,X33)
=> ti(fun(X1,X2),X12) = ti(fun(X1,X2),X38) ),
file('<stdin>',fact_74_ext) ).
fof(c_0_92,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ) ),
file('<stdin>',fact_73_equalityE) ).
fof(c_0_93,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ),
file('<stdin>',fact_68_equalityD2) ).
fof(c_0_94,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ),
file('<stdin>',fact_67_equalityD1) ).
fof(c_0_95,axiom,
! [X1,X8] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X8)),
file('<stdin>',fact_65_subset__refl) ).
fof(c_0_96,axiom,
! [X3,X21,X22] :
( ti(X3,X21) != ti(X3,X22)
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22)) ),
file('<stdin>',help_fequal_2_1_T) ).
fof(c_0_97,axiom,
! [X3] :
( preorder(X3)
=> ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X21)) ),
file('<stdin>',fact_97_order__refl) ).
fof(c_0_98,axiom,
! [X18,X17] :
( X18 = X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
file('<stdin>',fact_22_eq__imp__le) ).
fof(c_0_99,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X17)),
file('<stdin>',fact_24_le__refl) ).
fof(c_0_100,axiom,
! [X54,X53] :
( ~ hBOOL(X53)
| ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54)) ),
file('<stdin>',help_fconj_1_1_U) ).
fof(c_0_101,axiom,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54)) ),
file('<stdin>',help_fimplies_2_1_U) ).
fof(c_0_102,axiom,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
file('<stdin>',help_fdisj_2_1_U) ).
fof(c_0_103,axiom,
! [X54,X53] :
( ~ hBOOL(X53)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
file('<stdin>',help_fdisj_1_1_U) ).
fof(c_0_104,axiom,
! [X54,X53] :
( hBOOL(X53)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54)) ),
file('<stdin>',help_fimplies_1_1_U) ).
fof(c_0_105,axiom,
! [X1,X42] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X42) = ti(fun(X1,bool),X42),
file('<stdin>',fact_82_image__ident) ).
fof(c_0_106,axiom,
! [X53] :
( ~ hBOOL(hAPP(bool,bool,fNot,X53))
| ~ hBOOL(X53) ),
file('<stdin>',help_fNot_1_1_U) ).
fof(c_0_107,axiom,
! [X23,X24] :
( hAPP(nat,nat,suc,X23) = hAPP(nat,nat,suc,X24)
<=> X23 = X24 ),
file('<stdin>',fact_17_nat_Oinject) ).
fof(c_0_108,axiom,
! [X21,X22] :
( hAPP(nat,nat,suc,X21) = hAPP(nat,nat,suc,X22)
=> X21 = X22 ),
file('<stdin>',fact_16_Suc__inject) ).
fof(c_0_109,axiom,
! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
file('<stdin>',tsy_c_hAPP_res) ).
fof(c_0_110,axiom,
! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2))),combs(X3,X1,X2)) = combs(X3,X1,X2),
file('<stdin>',tsy_c_COMBS_res) ).
fof(c_0_111,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
file('<stdin>',tsy_c_hAPP_arg1) ).
fof(c_0_112,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('<stdin>',fact_15_finite) ).
fof(c_0_113,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('<stdin>',fact_14_finite__code) ).
fof(c_0_114,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,X4,ti(X3,X5)) = hAPP(X3,X2,X4,X5),
file('<stdin>',tsy_c_hAPP_arg2) ).
fof(c_0_115,axiom,
! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2))),combc(X3,X1,X2)) = combc(X3,X1,X2),
file('<stdin>',tsy_c_COMBC_res) ).
fof(c_0_116,axiom,
! [X1,X2,X3] : ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
file('<stdin>',tsy_c_COMBB_res) ).
fof(c_0_117,axiom,
! [X53] :
( hBOOL(X53)
| hBOOL(hAPP(bool,bool,fNot,X53)) ),
file('<stdin>',help_fNot_2_1_U) ).
fof(c_0_118,axiom,
! [X17] : X17 != hAPP(nat,nat,suc,X17),
file('<stdin>',fact_19_n__not__Suc__n) ).
fof(c_0_119,axiom,
! [X17] : hAPP(nat,nat,suc,X17) != X17,
file('<stdin>',fact_18_Suc__n__not__n) ).
fof(c_0_120,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
file('<stdin>',tsy_c_Set_Oimage_res) ).
fof(c_0_121,axiom,
! [X1,X16] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = ti(fun(X1,bool),X16),
file('<stdin>',fact_76_Collect__def) ).
fof(c_0_122,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
file('<stdin>',tsy_c_Set_Oinsert_res) ).
fof(c_0_123,axiom,
! [X3,X53] : hAPP(X3,X3,combi(X3),X53) = ti(X3,X53),
file('<stdin>',help_COMBI_1_1_U) ).
fof(c_0_124,axiom,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
file('<stdin>',tsy_v_P_res) ).
fof(c_0_125,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
file('<stdin>',tsy_c_member_res) ).
fof(c_0_126,axiom,
! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
file('<stdin>',tsy_c_Set_OCollect_res) ).
fof(c_0_127,axiom,
! [X3] :
( preorder(X3)
=> ti(fun(X3,fun(X3,bool)),ord_less_eq(X3)) = ord_less_eq(X3) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(c_0_128,axiom,
! [X3] : ti(fun(X3,fun(X3,bool)),fequal(X3)) = fequal(X3),
file('<stdin>',tsy_c_fequal_res) ).
fof(c_0_129,axiom,
! [X1] : ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
file('<stdin>',tsy_c_Finite__Set_Ofinite_res) ).
fof(c_0_130,axiom,
! [X2] : ti(fun(fun(X2,bool),nat),finite_card(X2)) = finite_card(X2),
file('<stdin>',tsy_c_Finite__Set_Ocard_res) ).
fof(c_0_131,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
file('<stdin>',tsy_c_fimplies_res) ).
fof(c_0_132,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
file('<stdin>',tsy_c_fdisj_res) ).
fof(c_0_133,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
file('<stdin>',tsy_c_fconj_res) ).
fof(c_0_134,axiom,
! [X51,X52] : ti(X51,ti(X51,X52)) = ti(X51,X52),
file('<stdin>',help_ti_idem) ).
fof(c_0_135,axiom,
! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
file('<stdin>',tsy_c_COMBI_res) ).
fof(c_0_136,axiom,
! [X49,X50] :
( ( finite_finite_1(X50)
& finite_finite_1(X49) )
=> finite_finite_1(fun(X49,X50)) ),
file('<stdin>',arity_fun___Finite__Set_Ofinite) ).
fof(c_0_137,axiom,
! [X49,X50] :
( order(X50)
=> order(fun(X49,X50)) ),
file('<stdin>',arity_fun___Orderings_Oorder) ).
fof(c_0_138,axiom,
! [X49,X50] :
( preorder(X50)
=> preorder(fun(X49,X50)) ),
file('<stdin>',arity_fun___Orderings_Opreorder) ).
fof(c_0_139,axiom,
ti(fun(bool,bool),fNot) = fNot,
file('<stdin>',tsy_c_fNot_res) ).
fof(c_0_140,axiom,
! [X3] : ti(X3,undefined(X3)) = undefined(X3),
file('<stdin>',tsy_c_HOL_Oundefined_res) ).
fof(c_0_141,axiom,
order(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Oorder) ).
fof(c_0_142,axiom,
finite_finite_1(bool),
file('<stdin>',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(c_0_143,axiom,
preorder(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Opreorder) ).
fof(c_0_144,axiom,
order(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Oorder) ).
fof(c_0_145,axiom,
preorder(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Opreorder) ).
fof(c_0_146,plain,
! [X2,X1,X12,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)))
=> ? [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
& ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X8))),hAPP(X2,fun(X1,bool),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),hAPP(fun(X1,X2),fun(X1,fun(X2,bool)),hAPP(fun(X2,fun(X2,bool)),fun(fun(X1,X2),fun(X1,fun(X2,bool))),combb(X2,fun(X2,bool),X1),fequal(X2)),X12)),hAPP(X1,X2,X12,X33)))))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_147,axiom,
! [X1,X16,X15] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X16)),X15))))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X15))) ) ),
c_0_1 ).
fof(c_0_148,axiom,
! [X1,X11,X16] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fimplies),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11)))),X16)),
c_0_2 ).
fof(c_0_149,axiom,
! [X1,X15,X16] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X15))) )
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X16)),X15)))) ),
c_0_3 ).
fof(c_0_150,axiom,
! [X2,X1,X12,X13,X8] :
( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X33)),X13)) )
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)),X13)) ),
c_0_4 ).
fof(c_0_151,axiom,
! [X1,X33,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X40) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X33))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X40))),
c_0_5 ).
fof(c_0_152,axiom,
! [X1,X11,X13] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X13))),
c_0_6 ).
fof(c_0_153,axiom,
! [X1] :
( order(X1)
=> ! [X20,X31,X12] :
( ! [X32] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X12,X32)),hAPP(nat,X1,X12,hAPP(nat,nat,suc,X32))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X12,X20)),hAPP(nat,X1,X12,X31))) ) ) ),
c_0_7 ).
fof(c_0_154,axiom,
! [X2,X1,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))),hAPP(fun(X1,bool),nat,finite_card(X1),X8))) ),
c_0_8 ).
fof(c_0_155,axiom,
! [X20,X19,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X19)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ) ) ),
c_0_9 ).
fof(c_0_156,axiom,
! [X2,X1,X12,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
=> ? [X30] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X30),X8))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X30))
& ti(fun(X1,bool),X13) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X30) ) ) ),
c_0_10 ).
fof(c_0_157,axiom,
! [X1,X2,X13,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
<=> ? [X44] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X44),X8))
& ti(fun(X1,bool),X13) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X44) ) ),
c_0_11 ).
fof(c_0_158,plain,
! [X1,X2,X34,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
=> ~ ! [X33] :
( ti(X1,X34) = hAPP(X2,X1,X12,X33)
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X33),X8)) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_159,axiom,
! [X1,X2,X39,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X39),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
<=> ? [X33] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X33),X8))
& ti(X1,X39) = hAPP(X2,X1,X12,X33) ) ),
c_0_13 ).
fof(c_0_160,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X8)))) ),
c_0_14 ).
fof(c_0_161,axiom,
! [X2,X1,X12,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X13))) ),
c_0_15 ).
fof(c_0_162,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ),
c_0_16 ).
fof(c_0_163,axiom,
! [X1,X11,X37,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X37),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X37)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X43))) ),
c_0_17 ).
fof(c_0_164,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)))) ),
c_0_18 ).
fof(c_0_165,plain,
! [X1,X13,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X13)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_166,axiom,
! [X29,X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X18))) ),
c_0_20 ).
fof(c_0_167,axiom,
! [X29,X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X29)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X29))) ),
c_0_21 ).
fof(c_0_168,axiom,
! [X18,X17,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X18)),X17)),hAPP(nat,nat,suc,X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X25),
c_0_22 ).
fof(c_0_169,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X13)),hAPP(fun(X1,bool),nat,finite_card(X1),X8)))
=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ) ),
c_0_23 ).
fof(c_0_170,axiom,
! [X2,X1,X13,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X13),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13)) ) ),
c_0_24 ).
fof(c_0_171,axiom,
! [X19] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X19)))),
c_0_25 ).
fof(c_0_172,axiom,
! [X1,X11,X34,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X8)))
<=> ( ti(X1,X11) = ti(X1,X34)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ) ),
c_0_26 ).
fof(c_0_173,axiom,
! [X1,X11,X34,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X8)))
=> ( ti(X1,X11) != ti(X1,X34)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ) ),
c_0_27 ).
fof(c_0_174,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ),
c_0_28 ).
fof(c_0_175,axiom,
! [X17,X25,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X18))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17) ) ),
c_0_29 ).
fof(c_0_176,axiom,
! [X2,X1,X41,X12,X38,X8] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),hAPP(fun(X41,bool),fun(X2,bool),hAPP(fun(X41,X2),fun(fun(X41,bool),fun(X2,bool)),image(X41,X2),X38),X8)) = hAPP(fun(X41,bool),fun(X1,bool),hAPP(fun(X41,X1),fun(fun(X41,bool),fun(X1,bool)),image(X41,X1),hAPP(fun(X41,X2),fun(X41,X1),hAPP(fun(X2,X1),fun(fun(X41,X2),fun(X41,X1)),combb(X2,X1,X41),X12),X38)),X8),
c_0_30 ).
fof(c_0_177,axiom,
! [X2,X1,X34,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( ti(X2,X34) = hAPP(X1,X2,X12,X14)
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X34),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ) ),
c_0_31 ).
fof(c_0_178,axiom,
! [X1,X2,X8,X34,X12,X14] :
( ti(X1,X34) = hAPP(X2,X1,X12,X14)
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8))) ) ),
c_0_32 ).
fof(c_0_179,axiom,
! [X1,X34,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
c_0_33 ).
fof(c_0_180,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),X13))) ) ),
c_0_34 ).
fof(c_0_181,axiom,
! [X1,X34,X11,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
c_0_35 ).
fof(c_0_182,plain,
! [X1,X34,X11,X13] :
( ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> ti(X1,X11) = ti(X1,X34) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_183,axiom,
! [X1,X37,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X37))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X37)) ) ),
c_0_37 ).
fof(c_0_184,axiom,
! [X20,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X20)),hAPP(nat,nat,suc,X28)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X28)) ),
c_0_38 ).
fof(c_0_185,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8) ),
c_0_39 ).
fof(c_0_186,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
c_0_40 ).
fof(c_0_187,axiom,
! [X1,X13,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
c_0_41 ).
fof(c_0_188,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
c_0_42 ).
fof(c_0_189,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X13)) ) ),
c_0_43 ).
fof(c_0_190,plain,
! [X28,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X20)),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_191,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8)))
<=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
c_0_45 ).
fof(c_0_192,axiom,
! [X18,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X18)),
c_0_46 ).
fof(c_0_193,axiom,
! [X26,X27,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X27)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X25)),X27),
c_0_47 ).
fof(c_0_194,axiom,
! [X1,X36,X8,X14] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X36),X8),X14))
<=> ( ti(X1,X36) = ti(X1,X14)
| hBOOL(hAPP(X1,bool,X8,X14)) ) ),
c_0_48 ).
fof(c_0_195,axiom,
! [X2,X1,X12,X11,X13] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X11),X13)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X2,X1,X12,X11)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X13)),
c_0_49 ).
fof(c_0_196,axiom,
! [X20,X19,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X19) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X19)
<=> X28 = X20 ) ) ),
c_0_50 ).
fof(c_0_197,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X18)),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
c_0_51 ).
fof(c_0_198,plain,
! [X1,X13,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13))
=> ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X13)
<=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_199,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ) ),
c_0_53 ).
fof(c_0_200,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8))
=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ),
c_0_54 ).
fof(c_0_201,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X25)) ) ),
c_0_55 ).
fof(c_0_202,plain,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(fun(X1,bool),nat,finite_card(X1),X8) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X8)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_203,axiom,
! [X45,X16,X19] :
( hBOOL(hAPP(nat,bool,X16,X19))
=> ( ! [X32] :
( hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,suc,X32)))
=> hBOOL(hAPP(nat,bool,X16,X32)) )
=> hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X19),X45))) ) ),
c_0_57 ).
fof(c_0_204,axiom,
! [X1,X13,X11] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))),
c_0_58 ).
fof(c_0_205,axiom,
! [X1,X14,X36,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X36),X8)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X36),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),
c_0_59 ).
fof(c_0_206,axiom,
! [X17,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X18)),X17) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) ),
c_0_60 ).
fof(c_0_207,axiom,
! [X1,X11,X13] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))),
c_0_61 ).
fof(c_0_208,axiom,
! [X20] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X20))) = hAPP(nat,nat,suc,X20),
c_0_62 ).
fof(c_0_209,axiom,
! [X2,X1,X9,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X9),X10))) ),
c_0_63 ).
fof(c_0_210,plain,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X8)) ) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_211,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),hAPP(nat,nat,suc,X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
| X28 = hAPP(nat,nat,suc,X20) ) ),
c_0_65 ).
fof(c_0_212,plain,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,suc,X17)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> X18 = hAPP(nat,nat,suc,X17) ) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_213,axiom,
! [X17,X46] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X46))
=> ? [X47] : X46 = hAPP(nat,nat,suc,X47) ),
c_0_67 ).
fof(c_0_214,axiom,
! [X1,X13,X8] :
( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X13)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ),
c_0_68 ).
fof(c_0_215,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8))) ),
c_0_69 ).
fof(c_0_216,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X17)),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_217,axiom,
! [X48] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X48))
<=> ? [X47] :
! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X48))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X47)) ) ),
c_0_71 ).
fof(c_0_218,axiom,
! [X6,X7] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X6),X7))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X7),X6)) ),
c_0_72 ).
fof(c_0_219,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,suc,X17))) ),
c_0_73 ).
fof(c_0_220,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18))
=> X18 = X17 ) ),
c_0_74 ).
fof(c_0_221,axiom,
! [X26,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X26)) = X26 ),
c_0_75 ).
fof(c_0_222,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
c_0_76 ).
fof(c_0_223,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
c_0_77 ).
fof(c_0_224,axiom,
! [X3,X2,X1,X53,X54,X55] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2)),combs(X3,X1,X2),X53),X54),X55) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X53,X55),hAPP(X3,X1,X54,X55)),
c_0_78 ).
fof(c_0_225,axiom,
! [X1,X14,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8),
c_0_79 ).
fof(c_0_226,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8) = ti(fun(X1,bool),X8) ),
c_0_80 ).
fof(c_0_227,axiom,
! [X3,X2,X1,X53,X54,X55] : hAPP(X3,X2,hAPP(X1,fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2)),combc(X3,X1,X2),X53),X54),X55) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X53,X55),X54),
c_0_81 ).
fof(c_0_228,axiom,
! [X3,X2,X1,X53,X54,X55] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),combb(X1,X2,X3),X53),X54),X55) = hAPP(X1,X2,X53,hAPP(X3,X1,X54,X55)),
c_0_82 ).
fof(c_0_229,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
<=> hBOOL(hAPP(X1,bool,X8,X14)) ),
c_0_83 ).
fof(c_0_230,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18)) ),
c_0_84 ).
fof(c_0_231,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X18)),hAPP(nat,nat,suc,X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17),
c_0_85 ).
fof(c_0_232,plain,
! [X3,X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22))
| ti(X3,X21) = ti(X3,X22) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_233,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54))
| ~ hBOOL(X53)
| hBOOL(X54) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_234,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54))
| hBOOL(X53)
| hBOOL(X54) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_235,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X54) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_236,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X53) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_237,axiom,
! [X1,X2,X12,X38] :
( ! [X33] : hAPP(X1,X2,X12,X33) = hAPP(X1,X2,X38,X33)
=> ti(fun(X1,X2),X12) = ti(fun(X1,X2),X38) ),
c_0_91 ).
fof(c_0_238,plain,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_239,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ),
c_0_93 ).
fof(c_0_240,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ),
c_0_94 ).
fof(c_0_241,axiom,
! [X1,X8] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X8)),
c_0_95 ).
fof(c_0_242,axiom,
! [X3,X21,X22] :
( ti(X3,X21) != ti(X3,X22)
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22)) ),
c_0_96 ).
fof(c_0_243,axiom,
! [X3] :
( preorder(X3)
=> ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X21)) ),
c_0_97 ).
fof(c_0_244,axiom,
! [X18,X17] :
( X18 = X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
c_0_98 ).
fof(c_0_245,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X17)),
c_0_99 ).
fof(c_0_246,plain,
! [X54,X53] :
( ~ hBOOL(X53)
| ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_247,plain,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54)) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_248,plain,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_249,plain,
! [X54,X53] :
( ~ hBOOL(X53)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_250,axiom,
! [X54,X53] :
( hBOOL(X53)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54)) ),
c_0_104 ).
fof(c_0_251,axiom,
! [X1,X42] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X42) = ti(fun(X1,bool),X42),
c_0_105 ).
fof(c_0_252,plain,
! [X53] :
( ~ hBOOL(hAPP(bool,bool,fNot,X53))
| ~ hBOOL(X53) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_253,axiom,
! [X23,X24] :
( hAPP(nat,nat,suc,X23) = hAPP(nat,nat,suc,X24)
<=> X23 = X24 ),
c_0_107 ).
fof(c_0_254,axiom,
! [X21,X22] :
( hAPP(nat,nat,suc,X21) = hAPP(nat,nat,suc,X22)
=> X21 = X22 ),
c_0_108 ).
fof(c_0_255,axiom,
! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
c_0_109 ).
fof(c_0_256,axiom,
! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2))),combs(X3,X1,X2)) = combs(X3,X1,X2),
c_0_110 ).
fof(c_0_257,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
c_0_111 ).
fof(c_0_258,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
c_0_112 ).
fof(c_0_259,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
c_0_113 ).
fof(c_0_260,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,X4,ti(X3,X5)) = hAPP(X3,X2,X4,X5),
c_0_114 ).
fof(c_0_261,axiom,
! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2))),combc(X3,X1,X2)) = combc(X3,X1,X2),
c_0_115 ).
fof(c_0_262,axiom,
! [X1,X2,X3] : ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
c_0_116 ).
fof(c_0_263,axiom,
! [X53] :
( hBOOL(X53)
| hBOOL(hAPP(bool,bool,fNot,X53)) ),
c_0_117 ).
fof(c_0_264,axiom,
! [X17] : X17 != hAPP(nat,nat,suc,X17),
c_0_118 ).
fof(c_0_265,axiom,
! [X17] : hAPP(nat,nat,suc,X17) != X17,
c_0_119 ).
fof(c_0_266,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
c_0_120 ).
fof(c_0_267,axiom,
! [X1,X16] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = ti(fun(X1,bool),X16),
c_0_121 ).
fof(c_0_268,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
c_0_122 ).
fof(c_0_269,axiom,
! [X3,X53] : hAPP(X3,X3,combi(X3),X53) = ti(X3,X53),
c_0_123 ).
fof(c_0_270,axiom,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
c_0_124 ).
fof(c_0_271,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
c_0_125 ).
fof(c_0_272,axiom,
! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
c_0_126 ).
fof(c_0_273,axiom,
! [X3] :
( preorder(X3)
=> ti(fun(X3,fun(X3,bool)),ord_less_eq(X3)) = ord_less_eq(X3) ),
c_0_127 ).
fof(c_0_274,axiom,
! [X3] : ti(fun(X3,fun(X3,bool)),fequal(X3)) = fequal(X3),
c_0_128 ).
fof(c_0_275,axiom,
! [X1] : ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
c_0_129 ).
fof(c_0_276,axiom,
! [X2] : ti(fun(fun(X2,bool),nat),finite_card(X2)) = finite_card(X2),
c_0_130 ).
fof(c_0_277,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
c_0_131 ).
fof(c_0_278,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
c_0_132 ).
fof(c_0_279,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
c_0_133 ).
fof(c_0_280,axiom,
! [X51,X52] : ti(X51,ti(X51,X52)) = ti(X51,X52),
c_0_134 ).
fof(c_0_281,axiom,
! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
c_0_135 ).
fof(c_0_282,axiom,
! [X49,X50] :
( ( finite_finite_1(X50)
& finite_finite_1(X49) )
=> finite_finite_1(fun(X49,X50)) ),
c_0_136 ).
fof(c_0_283,axiom,
! [X49,X50] :
( order(X50)
=> order(fun(X49,X50)) ),
c_0_137 ).
fof(c_0_284,axiom,
! [X49,X50] :
( preorder(X50)
=> preorder(fun(X49,X50)) ),
c_0_138 ).
fof(c_0_285,axiom,
ti(fun(bool,bool),fNot) = fNot,
c_0_139 ).
fof(c_0_286,axiom,
! [X3] : ti(X3,undefined(X3)) = undefined(X3),
c_0_140 ).
fof(c_0_287,axiom,
order(bool),
c_0_141 ).
fof(c_0_288,axiom,
finite_finite_1(bool),
c_0_142 ).
fof(c_0_289,axiom,
preorder(bool),
c_0_143 ).
fof(c_0_290,axiom,
order(nat),
c_0_144 ).
fof(c_0_291,axiom,
preorder(nat),
c_0_145 ).
fof(c_0_292,plain,
! [X34,X35,X36,X37] :
( ( hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),esk3_4(X34,X35,X36,X37)),X37))
| ~ hBOOL(hAPP(fun(X34,bool),bool,finite_finite(X34),hAPP(fun(X35,bool),fun(X34,bool),hAPP(fun(X35,X34),fun(fun(X35,bool),fun(X34,bool)),image(X35,X34),X36),X37)))
| hBOOL(hAPP(fun(X35,bool),bool,finite_finite(X35),X37)) )
& ( ~ hBOOL(hAPP(fun(X35,bool),bool,finite_finite(X35),hAPP(fun(X35,bool),fun(X35,bool),collect(X35),hAPP(fun(X35,bool),fun(X35,bool),hAPP(fun(X35,fun(bool,bool)),fun(fun(X35,bool),fun(X35,bool)),combs(X35,bool,bool),hAPP(fun(X35,bool),fun(X35,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X35,bool),fun(X35,fun(bool,bool))),combb(bool,fun(bool,bool),X35),fconj),hAPP(fun(X35,bool),fun(X35,bool),hAPP(fun(X35,fun(fun(X35,bool),bool)),fun(fun(X35,bool),fun(X35,bool)),combc(X35,fun(X35,bool),bool),member(X35)),X37))),hAPP(X34,fun(X35,bool),hAPP(fun(X35,fun(X34,bool)),fun(X34,fun(X35,bool)),combc(X35,X34,bool),hAPP(fun(X35,X34),fun(X35,fun(X34,bool)),hAPP(fun(X34,fun(X34,bool)),fun(fun(X35,X34),fun(X35,fun(X34,bool))),combb(X34,fun(X34,bool),X35),fequal(X34)),X36)),hAPP(X35,X34,X36,esk3_4(X34,X35,X36,X37)))))))
| ~ hBOOL(hAPP(fun(X34,bool),bool,finite_finite(X34),hAPP(fun(X35,bool),fun(X34,bool),hAPP(fun(X35,X34),fun(fun(X35,bool),fun(X34,bool)),image(X35,X34),X36),X37)))
| hBOOL(hAPP(fun(X35,bool),bool,finite_finite(X35),X37)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])])])]) ).
fof(c_0_293,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),X18)))
| ~ hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),hAPP(fun(X17,bool),fun(X17,bool),hAPP(fun(X17,fun(bool,bool)),fun(fun(X17,bool),fun(X17,bool)),combs(X17,bool,bool),hAPP(fun(X17,bool),fun(X17,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X17,bool),fun(X17,fun(bool,bool))),combb(bool,fun(bool,bool),X17),fdisj),X18)),X19)))) )
& ( hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),X19)))
| ~ hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),hAPP(fun(X17,bool),fun(X17,bool),hAPP(fun(X17,fun(bool,bool)),fun(fun(X17,bool),fun(X17,bool)),combs(X17,bool,bool),hAPP(fun(X17,bool),fun(X17,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X17,bool),fun(X17,fun(bool,bool))),combb(bool,fun(bool,bool),X17),fdisj),X18)),X19)))) )
& ( ~ hBOOL(hAPP(fun(X20,bool),bool,finite_finite(X20),hAPP(fun(X20,bool),fun(X20,bool),collect(X20),X21)))
| ~ hBOOL(hAPP(fun(X20,bool),bool,finite_finite(X20),hAPP(fun(X20,bool),fun(X20,bool),collect(X20),X22)))
| hBOOL(hAPP(fun(X20,bool),bool,finite_finite(X20),hAPP(fun(X20,bool),fun(X20,bool),collect(X20),hAPP(fun(X20,bool),fun(X20,bool),hAPP(fun(X20,fun(bool,bool)),fun(fun(X20,bool),fun(X20,bool)),combs(X20,bool,bool),hAPP(fun(X20,bool),fun(X20,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X20,bool),fun(X20,fun(bool,bool))),combb(bool,fun(bool,bool),X20),fdisj),X21)),X22)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])])])])]) ).
fof(c_0_294,plain,
! [X17,X18,X19] : hAPP(fun(X17,bool),fun(X17,bool),hAPP(X17,fun(fun(X17,bool),fun(X17,bool)),insert(X17),X18),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),X19)) = hAPP(fun(X17,bool),fun(X17,bool),collect(X17),hAPP(fun(X17,bool),fun(X17,bool),hAPP(fun(X17,fun(bool,bool)),fun(fun(X17,bool),fun(X17,bool)),combs(X17,bool,bool),hAPP(fun(X17,bool),fun(X17,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X17,bool),fun(X17,fun(bool,bool))),combb(bool,fun(bool,bool),X17),fimplies),hAPP(fun(X17,bool),fun(X17,bool),hAPP(fun(bool,bool),fun(fun(X17,bool),fun(X17,bool)),combb(bool,bool,X17),fNot),hAPP(X17,fun(X17,bool),hAPP(fun(X17,fun(X17,bool)),fun(X17,fun(X17,bool)),combc(X17,X17,bool),fequal(X17)),X18)))),X19)),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_295,plain,
! [X17,X18,X19] :
( ( ~ hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),X19)))
| hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),hAPP(fun(X17,bool),fun(X17,bool),hAPP(fun(X17,fun(bool,bool)),fun(fun(X17,bool),fun(X17,bool)),combs(X17,bool,bool),hAPP(fun(X17,bool),fun(X17,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X17,bool),fun(X17,fun(bool,bool))),combb(bool,fun(bool,bool),X17),fconj),X19)),X18)))) )
& ( ~ hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),X18)))
| hBOOL(hAPP(fun(X17,bool),bool,finite_finite(X17),hAPP(fun(X17,bool),fun(X17,bool),collect(X17),hAPP(fun(X17,bool),fun(X17,bool),hAPP(fun(X17,fun(bool,bool)),fun(fun(X17,bool),fun(X17,bool)),combs(X17,bool,bool),hAPP(fun(X17,bool),fun(X17,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X17,bool),fun(X17,fun(bool,bool))),combb(bool,fun(bool,bool),X17),fconj),X19)),X18)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])]) ).
fof(c_0_296,plain,
! [X34,X35,X36,X37,X38] :
( ( hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),esk11_5(X34,X35,X36,X37,X38)),X38))
| hBOOL(hAPP(fun(X34,bool),bool,hAPP(fun(X34,bool),fun(fun(X34,bool),bool),ord_less_eq(fun(X34,bool)),hAPP(fun(X35,bool),fun(X34,bool),hAPP(fun(X35,X34),fun(fun(X35,bool),fun(X34,bool)),image(X35,X34),X36),X38)),X37)) )
& ( ~ hBOOL(hAPP(fun(X34,bool),bool,hAPP(X34,fun(fun(X34,bool),bool),member(X34),hAPP(X35,X34,X36,esk11_5(X34,X35,X36,X37,X38))),X37))
| hBOOL(hAPP(fun(X34,bool),bool,hAPP(fun(X34,bool),fun(fun(X34,bool),bool),ord_less_eq(fun(X34,bool)),hAPP(fun(X35,bool),fun(X34,bool),hAPP(fun(X35,X34),fun(fun(X35,bool),fun(X34,bool)),image(X35,X34),X36),X38)),X37)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])])]) ).
fof(c_0_297,plain,
! [X41,X42,X43] : hAPP(fun(X41,bool),fun(X41,bool),hAPP(X41,fun(fun(X41,bool),fun(X41,bool)),insert(X41),X42),X43) = hAPP(fun(X41,bool),fun(X41,bool),collect(X41),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,fun(bool,bool)),fun(fun(X41,bool),fun(X41,bool)),combs(X41,bool,bool),hAPP(fun(X41,bool),fun(X41,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X41,bool),fun(X41,fun(bool,bool))),combb(bool,fun(bool,bool),X41),fdisj),hAPP(X41,fun(X41,bool),hAPP(fun(X41,fun(X41,bool)),fun(X41,fun(X41,bool)),combc(X41,X41,bool),fequal(X41)),X42))),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,fun(fun(X41,bool),bool)),fun(fun(X41,bool),fun(X41,bool)),combc(X41,fun(X41,bool),bool),member(X41)),X43))),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_298,plain,
! [X14,X15,X16] : hAPP(fun(X14,bool),fun(X14,bool),hAPP(X14,fun(fun(X14,bool),fun(X14,bool)),insert(X14),X15),X16) = hAPP(fun(X14,bool),fun(X14,bool),collect(X14),hAPP(fun(X14,bool),fun(X14,bool),hAPP(fun(X14,fun(bool,bool)),fun(fun(X14,bool),fun(X14,bool)),combs(X14,bool,bool),hAPP(fun(X14,bool),fun(X14,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X14,bool),fun(X14,fun(bool,bool))),combb(bool,fun(bool,bool),X14),fdisj),hAPP(X14,fun(X14,bool),hAPP(fun(X14,fun(X14,bool)),fun(X14,fun(X14,bool)),combc(X14,X14,bool),fequal(X14)),X15))),hAPP(fun(X14,bool),fun(X14,bool),hAPP(fun(X14,fun(fun(X14,bool),bool)),fun(fun(X14,bool),fun(X14,bool)),combc(X14,fun(X14,bool),bool),member(X14)),X16))),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_299,plain,
! [X33,X34,X35,X36] :
( ~ order(X33)
| ~ hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less_eq(X33),hAPP(nat,X33,X36,esk2_4(X33,X34,X35,X36))),hAPP(nat,X33,X36,hAPP(nat,nat,suc,esk2_4(X33,X34,X35,X36)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X35))
| hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less_eq(X33),hAPP(nat,X33,X36,X34)),hAPP(nat,X33,X36,X35))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])])])]) ).
fof(c_0_300,plain,
! [X13,X14,X15,X16] :
( ~ hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X16))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X13,bool),nat,finite_card(X13),hAPP(fun(X14,bool),fun(X13,bool),hAPP(fun(X14,X13),fun(fun(X14,bool),fun(X13,bool)),image(X14,X13),X15),X16))),hAPP(fun(X14,bool),nat,finite_card(X14),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_154])]) ).
fof(c_0_301,plain,
! [X29,X30,X31] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X31),X30)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X30)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X29))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X29))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X31)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X29))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X31),X30)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X30)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X29))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X31)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])])]) ).
fof(c_0_302,plain,
! [X31,X32,X33,X34,X35] :
( ( hBOOL(hAPP(fun(X31,bool),bool,hAPP(fun(X31,bool),fun(fun(X31,bool),bool),ord_less_eq(fun(X31,bool)),esk1_5(X31,X32,X33,X34,X35)),X34))
| ~ hBOOL(hAPP(fun(X32,bool),bool,hAPP(fun(X32,bool),fun(fun(X32,bool),bool),ord_less_eq(fun(X32,bool)),X35),hAPP(fun(X31,bool),fun(X32,bool),hAPP(fun(X31,X32),fun(fun(X31,bool),fun(X32,bool)),image(X31,X32),X33),X34)))
| ~ hBOOL(hAPP(fun(X32,bool),bool,finite_finite(X32),X35)) )
& ( hBOOL(hAPP(fun(X31,bool),bool,finite_finite(X31),esk1_5(X31,X32,X33,X34,X35)))
| ~ hBOOL(hAPP(fun(X32,bool),bool,hAPP(fun(X32,bool),fun(fun(X32,bool),bool),ord_less_eq(fun(X32,bool)),X35),hAPP(fun(X31,bool),fun(X32,bool),hAPP(fun(X31,X32),fun(fun(X31,bool),fun(X32,bool)),image(X31,X32),X33),X34)))
| ~ hBOOL(hAPP(fun(X32,bool),bool,finite_finite(X32),X35)) )
& ( ti(fun(X32,bool),X35) = hAPP(fun(X31,bool),fun(X32,bool),hAPP(fun(X31,X32),fun(fun(X31,bool),fun(X32,bool)),image(X31,X32),X33),esk1_5(X31,X32,X33,X34,X35))
| ~ hBOOL(hAPP(fun(X32,bool),bool,hAPP(fun(X32,bool),fun(fun(X32,bool),bool),ord_less_eq(fun(X32,bool)),X35),hAPP(fun(X31,bool),fun(X32,bool),hAPP(fun(X31,X32),fun(fun(X31,bool),fun(X32,bool)),image(X31,X32),X33),X34)))
| ~ hBOOL(hAPP(fun(X32,bool),bool,finite_finite(X32),X35)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])])]) ).
fof(c_0_303,plain,
! [X45,X46,X47,X48,X49,X51,X52,X53,X54,X55,X56] :
( ( hBOOL(hAPP(fun(X46,bool),bool,hAPP(fun(X46,bool),fun(fun(X46,bool),bool),ord_less_eq(fun(X46,bool)),esk6_5(X45,X46,X47,X48,X49)),X49))
| ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),X47),hAPP(fun(X46,bool),fun(X45,bool),hAPP(fun(X46,X45),fun(fun(X46,bool),fun(X45,bool)),image(X46,X45),X48),X49))) )
& ( ti(fun(X45,bool),X47) = hAPP(fun(X46,bool),fun(X45,bool),hAPP(fun(X46,X45),fun(fun(X46,bool),fun(X45,bool)),image(X46,X45),X48),esk6_5(X45,X46,X47,X48,X49))
| ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),X47),hAPP(fun(X46,bool),fun(X45,bool),hAPP(fun(X46,X45),fun(fun(X46,bool),fun(X45,bool)),image(X46,X45),X48),X49))) )
& ( ~ hBOOL(hAPP(fun(X52,bool),bool,hAPP(fun(X52,bool),fun(fun(X52,bool),bool),ord_less_eq(fun(X52,bool)),X56),X55))
| ti(fun(X51,bool),X53) != hAPP(fun(X52,bool),fun(X51,bool),hAPP(fun(X52,X51),fun(fun(X52,bool),fun(X51,bool)),image(X52,X51),X54),X56)
| hBOOL(hAPP(fun(X51,bool),bool,hAPP(fun(X51,bool),fun(fun(X51,bool),bool),ord_less_eq(fun(X51,bool)),X53),hAPP(fun(X52,bool),fun(X51,bool),hAPP(fun(X52,X51),fun(fun(X52,bool),fun(X51,bool)),image(X52,X51),X54),X55))) ) ),
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)],[c_0_157])])])])])]) ).
fof(c_0_304,plain,
! [X35,X36,X37,X38,X39] :
( ( ti(X35,X37) = hAPP(X36,X35,X38,esk7_5(X35,X36,X37,X38,X39))
| ~ hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),hAPP(fun(X36,bool),fun(X35,bool),hAPP(fun(X36,X35),fun(fun(X36,bool),fun(X35,bool)),image(X36,X35),X38),X39))) )
& ( hBOOL(hAPP(fun(X36,bool),bool,hAPP(X36,fun(fun(X36,bool),bool),member(X36),esk7_5(X35,X36,X37,X38,X39)),X39))
| ~ hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),hAPP(fun(X36,bool),fun(X35,bool),hAPP(fun(X36,X35),fun(fun(X36,bool),fun(X35,bool)),image(X36,X35),X38),X39))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])])])]) ).
fof(c_0_305,plain,
! [X40,X41,X42,X43,X44,X46,X47,X48,X49,X50,X51] :
( ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk5_5(X40,X41,X42,X43,X44)),X44))
| ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X44))) )
& ( ti(X40,X42) = hAPP(X41,X40,X43,esk5_5(X40,X41,X42,X43,X44))
| ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X44))) )
& ( ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(X47,fun(fun(X47,bool),bool),member(X47),X51),X50))
| ti(X46,X48) != hAPP(X47,X46,X49,X51)
| hBOOL(hAPP(fun(X46,bool),bool,hAPP(X46,fun(fun(X46,bool),bool),member(X46),X48),hAPP(fun(X47,bool),fun(X46,bool),hAPP(fun(X47,X46),fun(fun(X47,bool),fun(X46,bool)),image(X47,X46),X49),X50))) ) ),
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)],[c_0_159])])])])])]) ).
fof(c_0_306,plain,
! [X9,X10] :
( ~ hBOOL(hAPP(fun(X9,bool),bool,finite_finite(X9),X10))
| hBOOL(hAPP(fun(fun(X9,bool),bool),bool,finite_finite(fun(X9,bool)),hAPP(fun(fun(X9,bool),bool),fun(fun(X9,bool),bool),collect(fun(X9,bool)),hAPP(fun(X9,bool),fun(fun(X9,bool),bool),hAPP(fun(fun(X9,bool),fun(fun(X9,bool),bool)),fun(fun(X9,bool),fun(fun(X9,bool),bool)),combc(fun(X9,bool),fun(X9,bool),bool),ord_less_eq(fun(X9,bool))),X10)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_160])]) ).
fof(c_0_307,plain,
! [X14,X15,X16,X17,X18] :
( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X17),X18))
| hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),hAPP(fun(X15,bool),fun(X14,bool),hAPP(fun(X15,X14),fun(fun(X15,bool),fun(X14,bool)),image(X15,X14),X16),X17)),hAPP(fun(X15,bool),fun(X14,bool),hAPP(fun(X15,X14),fun(fun(X15,bool),fun(X14,bool)),image(X15,X14),X16),X18))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])]) ).
fof(c_0_308,plain,
! [X15,X16,X17,X18,X19,X20,X21,X22] :
( ( hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X18))
| ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17)),X18)) )
& ( hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X17),X18))
| ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17)),X18)) )
& ( ~ hBOOL(hAPP(fun(X19,bool),bool,hAPP(X19,fun(fun(X19,bool),bool),member(X19),X20),X22))
| ~ hBOOL(hAPP(fun(X19,bool),bool,hAPP(fun(X19,bool),fun(fun(X19,bool),bool),ord_less_eq(fun(X19,bool)),X21),X22))
| hBOOL(hAPP(fun(X19,bool),bool,hAPP(fun(X19,bool),fun(fun(X19,bool),bool),ord_less_eq(fun(X19,bool)),hAPP(fun(X19,bool),fun(X19,bool),hAPP(X19,fun(fun(X19,bool),fun(X19,bool)),insert(X19),X20),X21)),X22)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])])])])]) ).
fof(c_0_309,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X47))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(X44,fun(fun(X44,bool),fun(X44,bool)),insert(X44),X45),X46)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(X44,fun(fun(X44,bool),fun(X44,bool)),insert(X44),X45),X47))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])]) ).
fof(c_0_310,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(fun(X15,bool),bool,finite_finite(X15),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X15,bool),nat,finite_card(X15),X17)),hAPP(fun(X15,bool),nat,finite_card(X15),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_164])]) ).
fof(c_0_311,plain,
! [X15,X16,X17,X18] :
( ( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X18),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X17),X16)))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X18),X16))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X18)) )
& ( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X18),X16))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X18),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X17),X16)))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X18)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_165])])]) ).
fof(c_0_312,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X30),X32)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X30),X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_166])]) ).
fof(c_0_313,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X31),X30)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X32),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_167])]) ).
fof(c_0_314,plain,
! [X26,X27,X28] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X26)),X27)),hAPP(nat,nat,suc,X28)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X27)),X28),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_315,plain,
! [X14,X15,X16] :
( ~ hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X16))
| ~ hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X14,bool),nat,finite_card(X14),X16)),hAPP(fun(X14,bool),nat,finite_card(X14),X15)))
| ti(fun(X14,bool),X15) = ti(fun(X14,bool),X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_169])]) ).
fof(c_0_316,plain,
! [X14,X15,X16,X17,X18] :
( ~ hBOOL(hAPP(fun(X15,bool),bool,finite_finite(X15),X18))
| ~ hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X16),hAPP(fun(X15,bool),fun(X14,bool),hAPP(fun(X15,X14),fun(fun(X15,bool),fun(X14,bool)),image(X15,X14),X17),X18)))
| hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_170])]) ).
fof(c_0_317,plain,
! [X20] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X20)))),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_318,plain,
! [X35,X36,X37,X38,X39,X40,X41,X42] :
( ( ~ hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X36),hAPP(fun(X35,bool),fun(X35,bool),hAPP(X35,fun(fun(X35,bool),fun(X35,bool)),insert(X35),X37),X38)))
| ti(X35,X36) = ti(X35,X37)
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X36),X38)) )
& ( ti(X39,X40) != ti(X39,X41)
| hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),X40),hAPP(fun(X39,bool),fun(X39,bool),hAPP(X39,fun(fun(X39,bool),fun(X39,bool)),insert(X39),X41),X42))) )
& ( ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),X40),X42))
| hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),X40),hAPP(fun(X39,bool),fun(X39,bool),hAPP(X39,fun(fun(X39,bool),fun(X39,bool)),insert(X39),X41),X42))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_172])])])])]) ).
fof(c_0_319,plain,
! [X35,X36,X37,X38] :
( ~ hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X36),hAPP(fun(X35,bool),fun(X35,bool),hAPP(X35,fun(fun(X35,bool),fun(X35,bool)),insert(X35),X37),X38)))
| ti(X35,X36) = ti(X35,X37)
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X36),X38)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_173])]) ).
fof(c_0_320,plain,
! [X15,X16,X17,X18,X19] :
( ~ hBOOL(hAPP(fun(X16,bool),bool,hAPP(X16,fun(fun(X16,bool),bool),member(X16),X18),X19))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),hAPP(X16,X15,X17,X18)),hAPP(fun(X16,bool),fun(X15,bool),hAPP(fun(X16,X15),fun(fun(X16,bool),fun(X15,bool)),image(X16,X15),X17),X19))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_174])]) ).
fof(c_0_321,plain,
! [X26,X27,X28] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X28))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X26))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X27)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X27)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_175])]) ).
fof(c_0_322,plain,
! [X42,X43,X44,X45,X46,X47] : hAPP(fun(X42,bool),fun(X43,bool),hAPP(fun(X42,X43),fun(fun(X42,bool),fun(X43,bool)),image(X42,X43),X45),hAPP(fun(X44,bool),fun(X42,bool),hAPP(fun(X44,X42),fun(fun(X44,bool),fun(X42,bool)),image(X44,X42),X46),X47)) = hAPP(fun(X44,bool),fun(X43,bool),hAPP(fun(X44,X43),fun(fun(X44,bool),fun(X43,bool)),image(X44,X43),hAPP(fun(X44,X42),fun(X44,X43),hAPP(fun(X42,X43),fun(fun(X44,X42),fun(X44,X43)),combb(X42,X43,X44),X45),X46)),X47),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_323,plain,
! [X35,X36,X37,X38,X39,X40] :
( ~ hBOOL(hAPP(fun(X36,bool),bool,hAPP(X36,fun(fun(X36,bool),bool),member(X36),X39),X40))
| ti(X35,X37) != hAPP(X36,X35,X38,X39)
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),hAPP(fun(X36,bool),fun(X35,bool),hAPP(fun(X36,X35),fun(fun(X36,bool),fun(X35,bool)),image(X36,X35),X38),X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_177])]) ).
fof(c_0_324,plain,
! [X35,X36,X37,X38,X39,X40] :
( ti(X35,X38) != hAPP(X36,X35,X39,X40)
| ~ hBOOL(hAPP(fun(X36,bool),bool,hAPP(X36,fun(fun(X36,bool),bool),member(X36),X40),X37))
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X38),hAPP(fun(X36,bool),fun(X35,bool),hAPP(fun(X36,X35),fun(fun(X36,bool),fun(X35,bool)),image(X36,X35),X39),X37))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_178])]) ).
fof(c_0_325,plain,
! [X35,X36,X37,X38] :
( ~ hBOOL(hAPP(fun(X35,bool),bool,hAPP(fun(X35,bool),fun(fun(X35,bool),bool),ord_less_eq(fun(X35,bool)),X37),X38))
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(fun(X35,bool),fun(fun(X35,bool),bool),ord_less_eq(fun(X35,bool)),X37),hAPP(fun(X35,bool),fun(X35,bool),hAPP(X35,fun(fun(X35,bool),fun(X35,bool)),insert(X35),X36),X38))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_179])]) ).
fof(c_0_326,plain,
! [X14,X15,X16] :
( ~ hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X16))
| ~ hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X14,bool),nat,finite_card(X14),X15)),hAPP(fun(X14,bool),nat,finite_card(X14),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_180])]) ).
fof(c_0_327,plain,
! [X35,X36,X37,X38] :
( ~ hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),X38))
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),hAPP(fun(X35,bool),fun(X35,bool),hAPP(X35,fun(fun(X35,bool),fun(X35,bool)),insert(X35),X36),X38))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])]) ).
fof(c_0_328,plain,
! [X35,X36,X37,X38] :
( ( ~ hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),X38))
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),hAPP(fun(X35,bool),fun(X35,bool),hAPP(X35,fun(fun(X35,bool),fun(X35,bool)),insert(X35),X36),X38))) )
& ( ti(X35,X37) != ti(X35,X36)
| hBOOL(hAPP(fun(X35,bool),bool,hAPP(X35,fun(fun(X35,bool),bool),member(X35),X37),hAPP(fun(X35,bool),fun(X35,bool),hAPP(X35,fun(fun(X35,bool),fun(X35,bool)),insert(X35),X36),X38))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_182])])]) ).
fof(c_0_329,plain,
! [X38,X39,X40,X41] :
( ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,bool),fun(fun(X38,bool),bool),ord_less_eq(fun(X38,bool)),X40),X41))
| ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,bool),fun(fun(X38,bool),bool),ord_less_eq(fun(X38,bool)),X41),X39))
| hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,bool),fun(fun(X38,bool),bool),ord_less_eq(fun(X38,bool)),X40),X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])]) ).
fof(c_0_330,plain,
! [X29,X30,X31,X32] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X30)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X30)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X31)),hAPP(nat,nat,suc,X32))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_184])])])]) ).
fof(c_0_331,plain,
! [X15,X16,X17,X18,X19] :
( ~ hBOOL(hAPP(fun(X16,bool),bool,hAPP(X16,fun(fun(X16,bool),bool),member(X16),X18),X19))
| hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),hAPP(X16,X15,X17,X18)),hAPP(fun(X16,bool),fun(X15,bool),hAPP(fun(X16,X15),fun(fun(X16,bool),fun(X15,bool)),image(X16,X15),X17),X19)) = hAPP(fun(X16,bool),fun(X15,bool),hAPP(fun(X16,X15),fun(fun(X16,bool),fun(X15,bool)),image(X16,X15),X17),X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_185])]) ).
fof(c_0_332,plain,
! [X15,X16,X17,X18] :
( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X17),X18))
| ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X17))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])]) ).
fof(c_0_333,plain,
! [X15,X16,X17,X18] :
( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X18))
| ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X18),X16))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])]) ).
fof(c_0_334,plain,
! [X15,X16,X17,X18] :
( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(fun(X15,bool),fun(fun(X15,bool),bool),ord_less_eq(fun(X15,bool)),X17),X18))
| ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X17))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])]) ).
fof(c_0_335,plain,
! [X36,X37,X38,X39] :
( ~ hBOOL(hAPP(fun(X36,bool),bool,hAPP(fun(X36,bool),fun(fun(X36,bool),bool),ord_less_eq(fun(X36,bool)),X38),X39))
| ~ hBOOL(hAPP(fun(X36,bool),bool,hAPP(X36,fun(fun(X36,bool),bool),member(X36),X37),X38))
| hBOOL(hAPP(fun(X36,bool),bool,hAPP(X36,fun(fun(X36,bool),bool),member(X36),X37),X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_189])]) ).
fof(c_0_336,plain,
! [X29,X30,X31,X32] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X30))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X29)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X32)),X31))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])])])]) ).
fof(c_0_337,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(fun(X12,bool),bool,finite_finite(X12),hAPP(fun(X12,bool),fun(X12,bool),hAPP(X12,fun(fun(X12,bool),fun(X12,bool)),insert(X12),X13),X14)))
| hBOOL(hAPP(fun(X12,bool),bool,finite_finite(X12),X14)) )
& ( ~ hBOOL(hAPP(fun(X15,bool),bool,finite_finite(X15),X17))
| hBOOL(hAPP(fun(X15,bool),bool,finite_finite(X15),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_191])])])]) ).
fof(c_0_338,plain,
! [X19,X20] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X19),X20)),X19)),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_339,plain,
! [X28,X29,X30] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X29)),X30) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X30)),X29),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_340,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44] :
( ( ~ hBOOL(hAPP(X37,bool,hAPP(fun(X37,bool),fun(X37,bool),hAPP(X37,fun(fun(X37,bool),fun(X37,bool)),insert(X37),X38),X39),X40))
| ti(X37,X38) = ti(X37,X40)
| hBOOL(hAPP(X37,bool,X39,X40)) )
& ( ti(X41,X42) != ti(X41,X44)
| hBOOL(hAPP(X41,bool,hAPP(fun(X41,bool),fun(X41,bool),hAPP(X41,fun(fun(X41,bool),fun(X41,bool)),insert(X41),X42),X43),X44)) )
& ( ~ hBOOL(hAPP(X41,bool,X43,X44))
| hBOOL(hAPP(X41,bool,hAPP(fun(X41,bool),fun(X41,bool),hAPP(X41,fun(fun(X41,bool),fun(X41,bool)),insert(X41),X42),X43),X44)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_194])])])])]) ).
fof(c_0_341,plain,
! [X14,X15,X16,X17,X18] : hAPP(fun(X14,bool),fun(X15,bool),hAPP(fun(X14,X15),fun(fun(X14,bool),fun(X15,bool)),image(X14,X15),X16),hAPP(fun(X14,bool),fun(X14,bool),hAPP(X14,fun(fun(X14,bool),fun(X14,bool)),insert(X14),X17),X18)) = hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),hAPP(X14,X15,X16,X17)),hAPP(fun(X14,bool),fun(X15,bool),hAPP(fun(X14,X15),fun(fun(X14,bool),fun(X15,bool)),image(X14,X15),X16),X18)),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_342,plain,
! [X29,X30,X31] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X31),X30) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X30)
| X31 = X29
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X29))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X31)) )
& ( X31 != X29
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X31),X30) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X30)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X29))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X31)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_196])])]) ).
fof(c_0_343,plain,
! [X19,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X19)),X20))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])]) ).
fof(c_0_344,plain,
! [X15,X16,X17,X18] :
( ( hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X17),X18) != hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X17),X16)
| ti(fun(X15,bool),X18) = ti(fun(X15,bool),X16)
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X16))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X18)) )
& ( ti(fun(X15,bool),X18) != ti(fun(X15,bool),X16)
| hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X17),X18) = hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X17),X16)
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X16))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X17),X18)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_198])])]) ).
fof(c_0_345,plain,
! [X14,X15,X16,X17,X18,X19] :
( ( hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16))
| ti(fun(X14,bool),X15) != ti(fun(X14,bool),X16) )
& ( hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X16),X15))
| ti(fun(X14,bool),X15) != ti(fun(X14,bool),X16) )
& ( ~ hBOOL(hAPP(fun(X17,bool),bool,hAPP(fun(X17,bool),fun(fun(X17,bool),bool),ord_less_eq(fun(X17,bool)),X18),X19))
| ~ hBOOL(hAPP(fun(X17,bool),bool,hAPP(fun(X17,bool),fun(fun(X17,bool),bool),ord_less_eq(fun(X17,bool)),X19),X18))
| ti(fun(X17,bool),X18) = ti(fun(X17,bool),X19) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_199])])])])]) ).
fof(c_0_346,plain,
! [X14,X15,X16] :
( ~ hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16))
| ~ hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X16),X15))
| ti(fun(X14,bool),X15) = ti(fun(X14,bool),X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])]) ).
fof(c_0_347,plain,
! [X28,X29,X30] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X30))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X28))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])]) ).
fof(c_0_348,plain,
! [X15,X16,X17] :
( ( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X17))
| hAPP(fun(X15,bool),nat,finite_card(X15),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17)) = hAPP(fun(X15,bool),nat,finite_card(X15),X17)
| ~ hBOOL(hAPP(fun(X15,bool),bool,finite_finite(X15),X17)) )
& ( hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X17))
| hAPP(fun(X15,bool),nat,finite_card(X15),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17)) = hAPP(nat,nat,suc,hAPP(fun(X15,bool),nat,finite_card(X15),X17))
| ~ hBOOL(hAPP(fun(X15,bool),bool,finite_finite(X15),X17)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])])]) ).
fof(c_0_349,plain,
! [X46,X47,X48] :
( ( hBOOL(hAPP(nat,bool,X47,hAPP(nat,nat,suc,esk9_3(X46,X47,X48))))
| hBOOL(hAPP(nat,bool,X47,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X48),X46)))
| ~ hBOOL(hAPP(nat,bool,X47,X48)) )
& ( ~ hBOOL(hAPP(nat,bool,X47,esk9_3(X46,X47,X48)))
| hBOOL(hAPP(nat,bool,X47,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X48),X46)))
| ~ hBOOL(hAPP(nat,bool,X47,X48)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_203])])])]) ).
fof(c_0_350,plain,
! [X14,X15,X16] : hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),hAPP(fun(X14,bool),fun(X14,bool),hAPP(X14,fun(fun(X14,bool),fun(X14,bool)),insert(X14),X16),X15))),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_351,plain,
! [X37,X38,X39,X40] : hAPP(fun(X37,bool),fun(X37,bool),hAPP(X37,fun(fun(X37,bool),fun(X37,bool)),insert(X37),X38),hAPP(fun(X37,bool),fun(X37,bool),hAPP(X37,fun(fun(X37,bool),fun(X37,bool)),insert(X37),X39),X40)) = hAPP(fun(X37,bool),fun(X37,bool),hAPP(X37,fun(fun(X37,bool),fun(X37,bool)),insert(X37),X39),hAPP(fun(X37,bool),fun(X37,bool),hAPP(X37,fun(fun(X37,bool),fun(X37,bool)),insert(X37),X38),X40)),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_352,plain,
! [X19,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X20)),X19) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_206])]) ).
fof(c_0_353,plain,
! [X14,X15,X16] : hBOOL(hAPP(fun(X14,bool),bool,hAPP(X14,fun(fun(X14,bool),bool),member(X14),X15),hAPP(fun(X14,bool),fun(X14,bool),hAPP(X14,fun(fun(X14,bool),fun(X14,bool)),insert(X14),X15),X16))),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_354,plain,
! [X21] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X21))) = hAPP(nat,nat,suc,X21),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_355,plain,
! [X11,X12,X13,X14] :
( ~ hBOOL(hAPP(fun(X12,bool),bool,finite_finite(X12),X14))
| hBOOL(hAPP(fun(X11,bool),bool,finite_finite(X11),hAPP(fun(X12,bool),fun(X11,bool),hAPP(fun(X12,X11),fun(fun(X12,bool),fun(X11,bool)),image(X12,X11),X13),X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_209])]) ).
fof(c_0_356,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(fun(X15,bool),bool,finite_finite(X15),X17))
| hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X17))
| hAPP(fun(X15,bool),nat,finite_card(X15),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17)) = hAPP(nat,nat,suc,hAPP(fun(X15,bool),nat,finite_card(X15),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_210])]) ).
fof(c_0_357,plain,
! [X29,X30,X31,X32] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),hAPP(nat,nat,suc,X30)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X30))
| X29 = hAPP(nat,nat,suc,X30) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),hAPP(nat,nat,suc,X32))) )
& ( X31 != hAPP(nat,nat,suc,X32)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),hAPP(nat,nat,suc,X32))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_211])])])])]) ).
fof(c_0_358,plain,
! [X19,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),hAPP(nat,nat,suc,X20)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
| X19 = hAPP(nat,nat,suc,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_212])]) ).
fof(c_0_359,plain,
! [X48,X49] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X48)),X49))
| X49 = hAPP(nat,nat,suc,esk10_2(X48,X49)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_213])])]) ).
fof(c_0_360,plain,
! [X34,X35,X36] :
( ( hBOOL(hAPP(fun(X34,bool),bool,hAPP(X34,fun(fun(X34,bool),bool),member(X34),esk8_3(X34,X35,X36)),X36))
| hBOOL(hAPP(fun(X34,bool),bool,hAPP(fun(X34,bool),fun(fun(X34,bool),bool),ord_less_eq(fun(X34,bool)),X36),X35)) )
& ( ~ hBOOL(hAPP(fun(X34,bool),bool,hAPP(X34,fun(fun(X34,bool),bool),member(X34),esk8_3(X34,X35,X36)),X35))
| hBOOL(hAPP(fun(X34,bool),bool,hAPP(fun(X34,bool),fun(fun(X34,bool),bool),ord_less_eq(fun(X34,bool)),X36),X35)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_214])])])]) ).
fof(c_0_361,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP(fun(X12,bool),bool,finite_finite(X12),X14))
| hBOOL(hAPP(fun(X12,bool),bool,finite_finite(X12),hAPP(fun(X12,bool),fun(X12,bool),hAPP(X12,fun(fun(X12,bool),fun(X12,bool)),insert(X12),X13),X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_215])]) ).
fof(c_0_362,plain,
! [X18] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X18)),X18)),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_363,plain,
! [X49,X51,X52,X53] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X49))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X51),X49))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),esk12_1(X49))) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk13_2(X52,X53)),X52))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X52)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk13_2(X52,X53)),X53))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X52)) ) ),
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)],[c_0_217])])])])])]) ).
fof(c_0_364,plain,
! [X8,X9] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X8),X9))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X9),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_218])]) ).
fof(c_0_365,plain,
! [X19,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),hAPP(nat,nat,suc,X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_219])]) ).
fof(c_0_366,plain,
! [X19,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X19))
| X19 = X20 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_220])]) ).
fof(c_0_367,plain,
! [X27,X28] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X28))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X27)) = X27 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_221])]) ).
fof(c_0_368,plain,
! [X14,X15,X16] :
( ~ hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X16))
| ~ hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16))
| hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_222])]) ).
fof(c_0_369,plain,
! [X14,X15,X16] :
( ~ hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16))
| ~ hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X16))
| hBOOL(hAPP(fun(X14,bool),bool,finite_finite(X14),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_223])]) ).
fof(c_0_370,plain,
! [X56,X57,X58,X59,X60,X61] : hAPP(X56,X57,hAPP(fun(X56,X58),fun(X56,X57),hAPP(fun(X56,fun(X58,X57)),fun(fun(X56,X58),fun(X56,X57)),combs(X56,X58,X57),X59),X60),X61) = hAPP(X58,X57,hAPP(X56,fun(X58,X57),X59,X61),hAPP(X56,X58,X60,X61)),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_371,plain,
! [X15,X16,X17] : hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17)) = hAPP(fun(X15,bool),fun(X15,bool),hAPP(X15,fun(fun(X15,bool),fun(X15,bool)),insert(X15),X16),X17),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_372,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP(fun(X12,bool),bool,hAPP(X12,fun(fun(X12,bool),bool),member(X12),X13),X14))
| hAPP(fun(X12,bool),fun(X12,bool),hAPP(X12,fun(fun(X12,bool),fun(X12,bool)),insert(X12),X13),X14) = ti(fun(X12,bool),X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_226])]) ).
fof(c_0_373,plain,
! [X56,X57,X58,X59,X60,X61] : hAPP(X56,X57,hAPP(X58,fun(X56,X57),hAPP(fun(X56,fun(X58,X57)),fun(X58,fun(X56,X57)),combc(X56,X58,X57),X59),X60),X61) = hAPP(X58,X57,hAPP(X56,fun(X58,X57),X59,X61),X60),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_374,plain,
! [X56,X57,X58,X59,X60,X61] : hAPP(X56,X57,hAPP(fun(X56,X58),fun(X56,X57),hAPP(fun(X58,X57),fun(fun(X56,X58),fun(X56,X57)),combb(X58,X57,X56),X59),X60),X61) = hAPP(X58,X57,X59,hAPP(X56,X58,X60,X61)),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_375,plain,
! [X15,X16,X17,X18,X19,X20] :
( ( ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),X17))
| hBOOL(hAPP(X15,bool,X17,X16)) )
& ( ~ hBOOL(hAPP(X18,bool,X20,X19))
| hBOOL(hAPP(fun(X18,bool),bool,hAPP(X18,fun(fun(X18,bool),bool),member(X18),X19),X20)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_229])])])]) ).
fof(c_0_376,plain,
! [X19,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X19)) ),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_377,plain,
! [X19,X20] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X19)),hAPP(nat,nat,suc,X20)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X19),X20),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_378,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),fequal(X23),X24),X25))
| ti(X23,X24) = ti(X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_379,plain,
! [X55,X56] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X55),X56))
| ~ hBOOL(X55)
| hBOOL(X56) ),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_380,plain,
! [X55,X56] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X55),X56))
| hBOOL(X55)
| hBOOL(X56) ),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_381,plain,
! [X55,X56] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X55),X56))
| hBOOL(X56) ),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_382,plain,
! [X55,X56] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X55),X56))
| hBOOL(X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_236])])]) ).
fof(c_0_383,plain,
! [X39,X40,X41,X42] :
( hAPP(X39,X40,X41,esk4_4(X39,X40,X41,X42)) != hAPP(X39,X40,X42,esk4_4(X39,X40,X41,X42))
| ti(fun(X39,X40),X41) = ti(fun(X39,X40),X42) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_237])])]) ).
fof(c_0_384,plain,
! [X14,X15,X16] :
( ( hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16))
| ti(fun(X14,bool),X15) != ti(fun(X14,bool),X16) )
& ( hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X16),X15))
| ti(fun(X14,bool),X15) != ti(fun(X14,bool),X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_238])])]) ).
fof(c_0_385,plain,
! [X14,X15,X16] :
( ti(fun(X14,bool),X15) != ti(fun(X14,bool),X16)
| hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X16),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_239])]) ).
fof(c_0_386,plain,
! [X14,X15,X16] :
( ti(fun(X14,bool),X15) != ti(fun(X14,bool),X16)
| hBOOL(hAPP(fun(X14,bool),bool,hAPP(fun(X14,bool),fun(fun(X14,bool),bool),ord_less_eq(fun(X14,bool)),X15),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_240])]) ).
fof(c_0_387,plain,
! [X9,X10] : hBOOL(hAPP(fun(X9,bool),bool,hAPP(fun(X9,bool),fun(fun(X9,bool),bool),ord_less_eq(fun(X9,bool)),X10),X10)),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_388,plain,
! [X23,X24,X25] :
( ti(X23,X24) != ti(X23,X25)
| hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),fequal(X23),X24),X25)) ),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_389,plain,
! [X22,X23] :
( ~ preorder(X22)
| hBOOL(hAPP(X22,bool,hAPP(X22,fun(X22,bool),ord_less_eq(X22),X23),X23)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_243])])]) ).
fof(c_0_390,plain,
! [X19,X20] :
( X19 != X20
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_244])]) ).
fof(c_0_391,plain,
! [X18] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X18)),
inference(variable_rename,[status(thm)],[c_0_245]) ).
fof(c_0_392,plain,
! [X55,X56] :
( ~ hBOOL(X56)
| ~ hBOOL(X55)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X56),X55)) ),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_393,plain,
! [X55,X56] :
( ~ hBOOL(X56)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X55),X56)) ),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_394,plain,
! [X55,X56] :
( ~ hBOOL(X56)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X55),X56)) ),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_395,plain,
! [X55,X56] :
( ~ hBOOL(X56)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X56),X55)) ),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_396,plain,
! [X55,X56] :
( hBOOL(X56)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X56),X55)) ),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_397,plain,
! [X43,X44] : hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,X43),fun(fun(X43,bool),fun(X43,bool)),image(X43,X43),combi(X43)),X44) = ti(fun(X43,bool),X44),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_398,plain,
! [X54] :
( ~ hBOOL(hAPP(bool,bool,fNot,X54))
| ~ hBOOL(X54) ),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_399,plain,
! [X25,X26,X27,X28] :
( ( hAPP(nat,nat,suc,X25) != hAPP(nat,nat,suc,X26)
| X25 = X26 )
& ( X27 != X28
| hAPP(nat,nat,suc,X27) = hAPP(nat,nat,suc,X28) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_253])])])]) ).
fof(c_0_400,plain,
! [X23,X24] :
( hAPP(nat,nat,suc,X23) != hAPP(nat,nat,suc,X24)
| X23 = X24 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_254])]) ).
fof(c_0_401,plain,
! [X6,X7,X8,X9] : ti(X6,hAPP(X7,X6,X8,X9)) = hAPP(X7,X6,X8,X9),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_402,plain,
! [X4,X5,X6] : ti(fun(fun(X4,fun(X5,X6)),fun(fun(X4,X5),fun(X4,X6))),combs(X4,X5,X6)) = combs(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_403,plain,
! [X6,X7,X8,X9] : hAPP(X6,X7,ti(fun(X6,X7),X8),X9) = hAPP(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_404,plain,
! [X9,X10] :
( ~ finite_finite_1(X9)
| hBOOL(hAPP(fun(X9,bool),bool,finite_finite(X9),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_258])])]) ).
fof(c_0_405,plain,
! [X9,X10] :
( ~ finite_finite_1(X9)
| hBOOL(hAPP(fun(X9,bool),bool,finite_finite(X9),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_259])])]) ).
fof(c_0_406,plain,
! [X6,X7,X8,X9] : hAPP(X6,X7,X8,ti(X6,X9)) = hAPP(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_407,plain,
! [X4,X5,X6] : ti(fun(fun(X4,fun(X5,X6)),fun(X5,fun(X4,X6))),combc(X4,X5,X6)) = combc(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_408,plain,
! [X4,X5,X6] : ti(fun(fun(X4,X5),fun(fun(X6,X4),fun(X6,X5))),combb(X4,X5,X6)) = combb(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_409,plain,
! [X54] :
( hBOOL(X54)
| hBOOL(hAPP(bool,bool,fNot,X54)) ),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_410,plain,
! [X18] : X18 != hAPP(nat,nat,suc,X18),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_411,plain,
! [X18] : hAPP(nat,nat,suc,X18) != X18,
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_412,plain,
! [X3,X4] : ti(fun(fun(X3,X4),fun(fun(X3,bool),fun(X4,bool))),image(X3,X4)) = image(X3,X4),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_413,plain,
! [X17,X18] : hAPP(fun(X17,bool),fun(X17,bool),collect(X17),X18) = ti(fun(X17,bool),X18),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_414,plain,
! [X2] : ti(fun(X2,fun(fun(X2,bool),fun(X2,bool))),insert(X2)) = insert(X2),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_415,plain,
! [X54,X55] : hAPP(X54,X54,combi(X54),X55) = ti(X54,X55),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_416,axiom,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
c_0_270 ).
fof(c_0_417,plain,
! [X2] : ti(fun(X2,fun(fun(X2,bool),bool)),member(X2)) = member(X2),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_418,plain,
! [X2] : ti(fun(fun(X2,bool),fun(X2,bool)),collect(X2)) = collect(X2),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_419,plain,
! [X4] :
( ~ preorder(X4)
| ti(fun(X4,fun(X4,bool)),ord_less_eq(X4)) = ord_less_eq(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_273])]) ).
fof(c_0_420,plain,
! [X4] : ti(fun(X4,fun(X4,bool)),fequal(X4)) = fequal(X4),
inference(variable_rename,[status(thm)],[c_0_274]) ).
fof(c_0_421,plain,
! [X2] : ti(fun(fun(X2,bool),bool),finite_finite(X2)) = finite_finite(X2),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_422,plain,
! [X3] : ti(fun(fun(X3,bool),nat),finite_card(X3)) = finite_card(X3),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_423,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
c_0_277 ).
fof(c_0_424,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
c_0_278 ).
fof(c_0_425,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
c_0_279 ).
fof(c_0_426,plain,
! [X53,X54] : ti(X53,ti(X53,X54)) = ti(X53,X54),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_427,plain,
! [X4] : ti(fun(X4,X4),combi(X4)) = combi(X4),
inference(variable_rename,[status(thm)],[c_0_281]) ).
fof(c_0_428,plain,
! [X51,X52] :
( ~ finite_finite_1(X52)
| ~ finite_finite_1(X51)
| finite_finite_1(fun(X51,X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_282])]) ).
fof(c_0_429,plain,
! [X51,X52] :
( ~ order(X52)
| order(fun(X51,X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_283])]) ).
fof(c_0_430,plain,
! [X51,X52] :
( ~ preorder(X52)
| preorder(fun(X51,X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_284])]) ).
fof(c_0_431,axiom,
ti(fun(bool,bool),fNot) = fNot,
c_0_285 ).
fof(c_0_432,plain,
! [X4] : ti(X4,undefined(X4)) = undefined(X4),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_433,axiom,
order(bool),
c_0_287 ).
fof(c_0_434,axiom,
finite_finite_1(bool),
c_0_288 ).
fof(c_0_435,axiom,
preorder(bool),
c_0_289 ).
fof(c_0_436,axiom,
order(nat),
c_0_290 ).
fof(c_0_437,axiom,
preorder(nat),
c_0_291 ).
cnf(c_0_438,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2))),hAPP(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,esk3_4(X3,X1,X4,X2))))))) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_439,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_440,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_441,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fimplies),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2)))),X3)),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_442,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_443,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_444,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_445,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk11_5(X1,X2,X3,X5,X4))),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_446,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_447,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_448,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,esk2_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk2_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_449,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_450,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_451,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk1_5(X3,X1,X4,X5,X2)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_452,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk11_5(X1,X2,X3,X5,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_453,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk6_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_454,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk7_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_455,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk5_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_456,plain,
( hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_457,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_458,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_459,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_460,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_461,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_462,plain,
( hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),esk1_5(X3,X1,X4,X5,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_463,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_464,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk1_5(X3,X1,X4,X5,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_465,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_466,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk6_5(X1,X3,X2,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_467,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_468,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_469,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_470,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk7_5(X1,X3,X2,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_471,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk5_5(X1,X3,X2,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_472,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk3_4(X3,X1,X4,X2)),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_473,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,suc,X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_474,plain,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_475,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_476,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_477,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1)))),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_478,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_479,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X1,X2) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_480,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X1,X2) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_481,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_482,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_483,plain,
hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)) = hAPP(fun(X4,bool),fun(X2,bool),hAPP(fun(X4,X2),fun(fun(X4,bool),fun(X2,bool)),image(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),combb(X1,X2,X4),X3),X5)),X6),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_484,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_485,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_486,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
| ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_487,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_488,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_489,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_490,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_491,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_492,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_493,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_494,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_495,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_496,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_497,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_498,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_499,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_500,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_501,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_502,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)),X2),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_503,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ti(X1,X4) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_504,plain,
hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),hAPP(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_505,plain,
( X2 = X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_506,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_507,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ti(fun(X1,bool),X3) = ti(fun(X1,bool),X4)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_508,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_509,plain,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_510,plain,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_511,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_512,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_513,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_514,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk9_3(X3,X1,X2))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_515,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_516,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_517,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_518,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_519,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_520,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3))),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_521,plain,
hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1))) = hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_522,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_523,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X4) ),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_524,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_525,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_526,plain,
( X1 = hAPP(nat,nat,suc,X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_527,plain,
( X1 = hAPP(nat,nat,suc,X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_528,plain,
( X1 = hAPP(nat,nat,suc,esk10_2(X2,X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_529,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk8_3(X1,X3,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_530,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_531,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_532,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_533,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,esk9_3(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_534,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_535,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk12_1(X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_536,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_537,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X2))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_538,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_539,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_540,plain,
( X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_541,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_542,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_543,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_544,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4))
| ti(X1,X2) != ti(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_545,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,X3),fun(X1,X2)),combs(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),hAPP(X1,X3,X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_546,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk8_3(X1,X3,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_547,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_548,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_549,plain,
hAPP(X1,X2,hAPP(X3,fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_550,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_551,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_552,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk13_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_553,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_554,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_555,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_556,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_557,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_558,plain,
( hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_559,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_560,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_561,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_562,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk13_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_563,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,esk4_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk4_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_564,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_565,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_566,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_567,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_568,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_569,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_570,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_571,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_572,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_573,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_574,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_575,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_576,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_577,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_578,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_579,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_580,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_581,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_582,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_583,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_584,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_585,plain,
ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_586,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_587,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_588,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_589,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_590,plain,
ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_591,plain,
ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_592,plain,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_593,plain,
( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_594,plain,
X1 != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_595,plain,
hAPP(nat,nat,suc,X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_596,plain,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_597,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_598,plain,
ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_599,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_600,plain,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_601,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_602,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_603,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_604,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_605,plain,
ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_606,plain,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_607,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_608,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_609,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_610,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_611,plain,
ti(fun(X1,X1),combi(X1)) = combi(X1),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_612,plain,
( finite_finite_1(fun(X1,X2))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_613,plain,
( order(fun(X1,X2))
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_614,plain,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_615,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_616,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_617,plain,
order(bool),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_618,plain,
finite_finite_1(bool),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_619,plain,
preorder(bool),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_620,plain,
order(nat),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_621,plain,
preorder(nat),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_622,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2))),hAPP(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,esk3_4(X3,X1,X4,X2))))))) ),
c_0_438,
[final] ).
cnf(c_0_623,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
c_0_439,
[final] ).
cnf(c_0_624,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
c_0_440,
[final] ).
cnf(c_0_625,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fimplies),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2)))),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
c_0_441,
[final] ).
cnf(c_0_626,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
c_0_442,
[final] ).
cnf(c_0_627,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
c_0_443,
[final] ).
cnf(c_0_628,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
c_0_444,
[final] ).
cnf(c_0_629,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk11_5(X1,X2,X3,X5,X4))),X5)) ),
c_0_445,
[final] ).
cnf(c_0_630,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),
c_0_446,
[final] ).
cnf(c_0_631,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),
c_0_447,
[final] ).
cnf(c_0_632,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,esk2_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk2_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
c_0_448,
[final] ).
cnf(c_0_633,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4)) ),
c_0_449,
[final] ).
cnf(c_0_634,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1))) ),
c_0_450,
[final] ).
cnf(c_0_635,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk1_5(X3,X1,X4,X5,X2)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_451,
[final] ).
cnf(c_0_636,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk11_5(X1,X2,X3,X5,X4)),X4)) ),
c_0_452,
[final] ).
cnf(c_0_637,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk6_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_453,
[final] ).
cnf(c_0_638,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk7_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_454,
[final] ).
cnf(c_0_639,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk5_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_455,
[final] ).
cnf(c_0_640,plain,
( hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
c_0_456,
[final] ).
cnf(c_0_641,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5)) ),
c_0_457,
[final] ).
cnf(c_0_642,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4)) ),
c_0_458,
[final] ).
cnf(c_0_643,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_459,
[final] ).
cnf(c_0_644,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4)) ),
c_0_460,
[final] ).
cnf(c_0_645,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
c_0_461,
[final] ).
cnf(c_0_646,plain,
( hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),esk1_5(X3,X1,X4,X5,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_462,
[final] ).
cnf(c_0_647,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_463,
[final] ).
cnf(c_0_648,plain,
( hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk1_5(X3,X1,X4,X5,X2)) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_464,
[final] ).
cnf(c_0_649,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
c_0_465,
[final] ).
cnf(c_0_650,plain,
( hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk6_5(X1,X3,X2,X4,X5)) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_466,
[final] ).
cnf(c_0_651,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
c_0_467,
[final] ).
cnf(c_0_652,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
c_0_468,
[final] ).
cnf(c_0_653,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_469,
[final] ).
cnf(c_0_654,plain,
( hAPP(X3,X1,X4,esk7_5(X1,X3,X2,X4,X5)) = ti(X1,X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_470,
[final] ).
cnf(c_0_655,plain,
( hAPP(X3,X1,X4,esk5_5(X1,X3,X2,X4,X5)) = ti(X1,X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
c_0_471,
[final] ).
cnf(c_0_656,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk3_4(X3,X1,X4,X2)),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2))) ),
c_0_472,
[final] ).
cnf(c_0_657,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,suc,X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3),
c_0_473,
[final] ).
cnf(c_0_658,plain,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
c_0_474,
[final] ).
cnf(c_0_659,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X5)) ),
c_0_475,
[final] ).
cnf(c_0_660,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
c_0_476,
[final] ).
cnf(c_0_661,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1)))),
c_0_477,
[final] ).
cnf(c_0_662,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
c_0_478,
[final] ).
cnf(c_0_663,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X1,X2) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
c_0_479,
[final] ).
cnf(c_0_664,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X1,X2) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
c_0_480,
[final] ).
cnf(c_0_665,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
c_0_481,
[final] ).
cnf(c_0_666,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_482,
[final] ).
cnf(c_0_667,plain,
hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)) = hAPP(fun(X4,bool),fun(X2,bool),hAPP(fun(X4,X2),fun(fun(X4,bool),fun(X2,bool)),image(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),combb(X1,X2,X4),X3),X5)),X6),
c_0_483,
[final] ).
cnf(c_0_668,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
c_0_484,
[final] ).
cnf(c_0_669,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
c_0_485,
[final] ).
cnf(c_0_670,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
| ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
c_0_486,
[final] ).
cnf(c_0_671,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
c_0_487,
[final] ).
cnf(c_0_672,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
c_0_488,
[final] ).
cnf(c_0_673,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_489,
[final] ).
cnf(c_0_674,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_490,
[final] ).
cnf(c_0_675,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_491,
[final] ).
cnf(c_0_676,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
c_0_492,
[final] ).
cnf(c_0_677,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
c_0_493,
[final] ).
cnf(c_0_678,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
c_0_494,
[final] ).
cnf(c_0_679,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
c_0_495,
[final] ).
cnf(c_0_680,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_496,
[final] ).
cnf(c_0_681,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
c_0_497,
[final] ).
cnf(c_0_682,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
c_0_498,
[final] ).
cnf(c_0_683,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
c_0_499,
[final] ).
cnf(c_0_684,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))) ),
c_0_500,
[final] ).
cnf(c_0_685,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X1)),
c_0_501,
[final] ).
cnf(c_0_686,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)),X2),
c_0_502,
[final] ).
cnf(c_0_687,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ti(X1,X4) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2),X3)) ),
c_0_503,
[final] ).
cnf(c_0_688,plain,
hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),hAPP(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)),
c_0_504,
[final] ).
cnf(c_0_689,plain,
( X2 = X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1) ),
c_0_505,
[final] ).
cnf(c_0_690,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
c_0_506,
[final] ).
cnf(c_0_691,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ti(fun(X1,bool),X3) = ti(fun(X1,bool),X4)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4) ),
c_0_507,
[final] ).
cnf(c_0_692,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_508,
[final] ).
cnf(c_0_693,plain,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
c_0_509,
[final] ).
cnf(c_0_694,plain,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
c_0_510,
[final] ).
cnf(c_0_695,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| X2 != X3 ),
c_0_511,
[final] ).
cnf(c_0_696,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_512,
[final] ).
cnf(c_0_697,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
c_0_513,
[final] ).
cnf(c_0_698,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk9_3(X3,X1,X2))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_514,
[final] ).
cnf(c_0_699,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))),
c_0_515,
[final] ).
cnf(c_0_700,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),
c_0_516,
[final] ).
cnf(c_0_701,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_517,
[final] ).
cnf(c_0_702,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ti(X1,X2) != ti(X1,X3) ),
c_0_518,
[final] ).
cnf(c_0_703,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ti(X1,X2) != ti(X1,X3) ),
c_0_519,
[final] ).
cnf(c_0_704,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3))),
c_0_520,
[final] ).
cnf(c_0_705,plain,
hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1))) = hAPP(nat,nat,suc,X1),
c_0_521,
[final] ).
cnf(c_0_706,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4)) ),
c_0_522,
[final] ).
cnf(c_0_707,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X4) ),
c_0_523,
[final] ).
cnf(c_0_708,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
c_0_524,
[final] ).
cnf(c_0_709,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
c_0_525,
[final] ).
cnf(c_0_710,plain,
( X1 = hAPP(nat,nat,suc,X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
c_0_526,
[final] ).
cnf(c_0_711,plain,
( X1 = hAPP(nat,nat,suc,X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
c_0_527,
[final] ).
cnf(c_0_712,plain,
( hAPP(nat,nat,suc,esk10_2(X2,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
c_0_528,
[final] ).
cnf(c_0_713,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk8_3(X1,X3,X2)),X3)) ),
c_0_529,
[final] ).
cnf(c_0_714,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
c_0_530,
[final] ).
cnf(c_0_715,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
c_0_531,
[final] ).
cnf(c_0_716,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
c_0_532,
[final] ).
cnf(c_0_717,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,esk9_3(X3,X1,X2))) ),
c_0_533,
[final] ).
cnf(c_0_718,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
c_0_534,
[final] ).
cnf(c_0_719,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk12_1(X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2)) ),
c_0_535,
[final] ).
cnf(c_0_720,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_536,
[final] ).
cnf(c_0_721,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X2))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X2),X1)) ),
c_0_537,
[final] ).
cnf(c_0_722,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_538,
[final] ).
cnf(c_0_723,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_539,
[final] ).
cnf(c_0_724,plain,
( X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_540,
[final] ).
cnf(c_0_725,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_541,
[final] ).
cnf(c_0_726,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
c_0_542,
[final] ).
cnf(c_0_727,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
c_0_543,
[final] ).
cnf(c_0_728,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4))
| ti(X1,X2) != ti(X1,X4) ),
c_0_544,
[final] ).
cnf(c_0_729,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,X3),fun(X1,X2)),combs(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),hAPP(X1,X3,X5,X6)),
c_0_545,
[final] ).
cnf(c_0_730,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk8_3(X1,X3,X2)),X2)) ),
c_0_546,
[final] ).
cnf(c_0_731,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),
c_0_547,
[final] ).
cnf(c_0_732,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
c_0_548,
[final] ).
cnf(c_0_733,plain,
hAPP(X1,X2,hAPP(X3,fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),X5),
c_0_549,
[final] ).
cnf(c_0_734,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
c_0_550,
[final] ).
cnf(c_0_735,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
c_0_551,
[final] ).
cnf(c_0_736,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk13_2(X1,X2)),X2)) ),
c_0_552,
[final] ).
cnf(c_0_737,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_553,
[final] ).
cnf(c_0_738,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2),
c_0_554,
[final] ).
cnf(c_0_739,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != hAPP(nat,nat,suc,X2) ),
c_0_555,
[final] ).
cnf(c_0_740,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
c_0_556,
[final] ).
cnf(c_0_741,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
c_0_557,
[final] ).
cnf(c_0_742,plain,
( hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1)) ),
c_0_558,
[final] ).
cnf(c_0_743,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
c_0_559,
[final] ).
cnf(c_0_744,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
c_0_560,
[final] ).
cnf(c_0_745,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
c_0_561,
[final] ).
cnf(c_0_746,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk13_2(X1,X2)),X1)) ),
c_0_562,
[final] ).
cnf(c_0_747,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,esk4_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk4_4(X1,X2,X3,X4)) ),
c_0_563,
[final] ).
cnf(c_0_748,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
c_0_564,
[final] ).
cnf(c_0_749,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
c_0_565,
[final] ).
cnf(c_0_750,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
c_0_566,
[final] ).
cnf(c_0_751,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
c_0_567,
[final] ).
cnf(c_0_752,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
c_0_568,
[final] ).
cnf(c_0_753,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
c_0_569,
[final] ).
cnf(c_0_754,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
c_0_570,
[final] ).
cnf(c_0_755,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
c_0_571,
[final] ).
cnf(c_0_756,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
c_0_572,
[final] ).
cnf(c_0_757,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
c_0_573,
[final] ).
cnf(c_0_758,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
c_0_574,
[final] ).
cnf(c_0_759,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
c_0_575,
[final] ).
cnf(c_0_760,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| ~ hBOOL(X2) ),
c_0_576,
[final] ).
cnf(c_0_761,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X2) ),
c_0_577,
[final] ).
cnf(c_0_762,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
c_0_578,
[final] ).
cnf(c_0_763,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| hBOOL(X1) ),
c_0_579,
[final] ).
cnf(c_0_764,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = ti(fun(X1,bool),X2),
c_0_580,
[final] ).
cnf(c_0_765,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
c_0_581,
[final] ).
cnf(c_0_766,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
c_0_582,
[final] ).
cnf(c_0_767,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
c_0_583,
[final] ).
cnf(c_0_768,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
c_0_584,
[final] ).
cnf(c_0_769,plain,
ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
c_0_585,
[final] ).
cnf(c_0_770,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
c_0_586,
[final] ).
cnf(c_0_771,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
c_0_587,
[final] ).
cnf(c_0_772,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
c_0_588,
[final] ).
cnf(c_0_773,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
c_0_589,
[final] ).
cnf(c_0_774,plain,
ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
c_0_590,
[final] ).
cnf(c_0_775,plain,
ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
c_0_591,
[final] ).
cnf(c_0_776,plain,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
c_0_592,
[final] ).
cnf(c_0_777,plain,
( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
| X1 != X2 ),
c_0_593,
[final] ).
cnf(c_0_778,plain,
hAPP(nat,nat,suc,X1) != X1,
c_0_594,
[final] ).
cnf(c_0_779,plain,
hAPP(nat,nat,suc,X1) != X1,
c_0_595,
[final] ).
cnf(c_0_780,plain,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
c_0_596,
[final] ).
cnf(c_0_781,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
c_0_597,
[final] ).
cnf(c_0_782,plain,
ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
c_0_598,
[final] ).
cnf(c_0_783,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
c_0_599,
[final] ).
cnf(c_0_784,plain,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
c_0_600,
[final] ).
cnf(c_0_785,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
c_0_601,
[final] ).
cnf(c_0_786,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
c_0_602,
[final] ).
cnf(c_0_787,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ preorder(X1) ),
c_0_603,
[final] ).
cnf(c_0_788,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
c_0_604,
[final] ).
cnf(c_0_789,plain,
ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
c_0_605,
[final] ).
cnf(c_0_790,plain,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
c_0_606,
[final] ).
cnf(c_0_791,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
c_0_607,
[final] ).
cnf(c_0_792,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
c_0_608,
[final] ).
cnf(c_0_793,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
c_0_609,
[final] ).
cnf(c_0_794,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
c_0_610,
[final] ).
cnf(c_0_795,plain,
ti(fun(X1,X1),combi(X1)) = combi(X1),
c_0_611,
[final] ).
cnf(c_0_796,plain,
( finite_finite_1(fun(X1,X2))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
c_0_612,
[final] ).
cnf(c_0_797,plain,
( order(fun(X1,X2))
| ~ order(X2) ),
c_0_613,
[final] ).
cnf(c_0_798,plain,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
c_0_614,
[final] ).
cnf(c_0_799,plain,
ti(fun(bool,bool),fNot) = fNot,
c_0_615,
[final] ).
cnf(c_0_800,plain,
ti(X1,undefined(X1)) = undefined(X1),
c_0_616,
[final] ).
cnf(c_0_801,plain,
order(bool),
c_0_617,
[final] ).
cnf(c_0_802,plain,
finite_finite_1(bool),
c_0_618,
[final] ).
cnf(c_0_803,plain,
preorder(bool),
c_0_619,
[final] ).
cnf(c_0_804,plain,
order(nat),
c_0_620,
[final] ).
cnf(c_0_805,plain,
preorder(nat),
c_0_621,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_622_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2))),hAPP(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,sk1_esk3_4(X3,X1,X4,X2))))))) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_1,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2))),hAPP(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,sk1_esk3_4(X3,X1,X4,X2))))))) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2))),hAPP(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,sk1_esk3_4(X3,X1,X4,X2)))))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_623_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_623_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_624_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_624_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_626_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_627_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_628_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_629_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,sk1_esk11_5(X1,X2,X3,X5,X4))),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_629_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,sk1_esk11_5(X1,X2,X3,X5,X4))),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_632_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk2_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk2_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk2_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk2_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk2_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk2_4(X1,X3,X4,X2)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk2_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk2_4(X1,X3,X4,X2)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_633_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_633_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_634_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_635_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk1_5(X3,X1,X4,X5,X2)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk1_5(X3,X1,X4,X5,X2)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk1_5(X3,X1,X4,X5,X2)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_636_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk11_5(X1,X2,X3,X5,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_636_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk11_5(X1,X2,X3,X5,X4)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_637_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk6_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_637_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk6_5(X1,X3,X2,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_638_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk7_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk7_5(X1,X3,X2,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_639_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk5_5(X1,X3,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_639_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk5_5(X1,X3,X2,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_640_0,axiom,
( hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_640_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_641_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_641_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_642_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_643_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_644_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_645_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_646_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),sk1_esk1_5(X3,X1,X4,X5,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),sk1_esk1_5(X3,X1,X4,X5,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),sk1_esk1_5(X3,X1,X4,X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_647_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_648_0,axiom,
( hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk1_5(X3,X1,X4,X5,X2)) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk1_5(X3,X1,X4,X5,X2)) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk1_5(X3,X1,X4,X5,X2)) = ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_649_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_649_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_650_0,axiom,
( hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk6_5(X1,X3,X2,X4,X5)) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk6_5(X1,X3,X2,X4,X5)) = ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_651_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_651_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_651_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_652_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_652_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_653_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_653_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_654_0,axiom,
( hAPP(X3,X1,X4,sk1_esk7_5(X1,X3,X2,X4,X5)) = ti(X1,X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_654_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hAPP(X3,X1,X4,sk1_esk7_5(X1,X3,X2,X4,X5)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_655_0,axiom,
( hAPP(X3,X1,X4,sk1_esk5_5(X1,X3,X2,X4,X5)) = ti(X1,X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_655_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hAPP(X3,X1,X4,sk1_esk5_5(X1,X3,X2,X4,X5)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_656_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk3_4(X3,X1,X4,X2)),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk3_4(X3,X1,X4,X2)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk3_4(X3,X1,X4,X2)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_658_0,axiom,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_659_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_659_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_659_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_660_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_660_1,axiom,
( ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_660_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5))
| ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_662_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_663_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X1,X2) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_663_1,axiom,
( ti(X1,X2) = ti(X1,X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_663_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3)))
| ti(X1,X2) = ti(X1,X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_664_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X1,X2) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_1,axiom,
( ti(X1,X2) = ti(X1,X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3)))
| ti(X1,X2) = ti(X1,X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_665_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_665_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_666_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_666_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_666_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_668_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_668_1,axiom,
( ti(X1,X2) != hAPP(X3,X1,X4,X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_668_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_669_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_669_1,axiom,
( ti(X1,X2) != hAPP(X3,X1,X4,X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_669_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
| ti(X1,X2) != hAPP(X3,X1,X4,X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_670_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
| ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_670_1,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
| ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_670_2,axiom,
( ti(X1,X2) != hAPP(X3,X1,X4,X6)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_671_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_671_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_672_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_672_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_672_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_673_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_673_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_674_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_674_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_675_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_675_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_676_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_676_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_676_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_677_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_678_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_679_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_680_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_681_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_682_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_683_0,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_684_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_687_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| ti(X1,X4) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_1,axiom,
( ti(X1,X4) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2),X3))
| ti(X1,X4) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_689_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 = X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_3,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_690_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_691_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ti(fun(X1,bool),X3) = ti(fun(X1,bool),X4)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(fun(X1,bool),X3) = ti(fun(X1,bool),X4)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_2,axiom,
( ti(fun(X1,bool),X3) = ti(fun(X1,bool),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_3,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)
| ti(fun(X1,bool),X3) = ti(fun(X1,bool),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_692_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_693_0,axiom,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_694_0,axiom,
( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_695_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_3,axiom,
( X2 != X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_696_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_696_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_696_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_697_0,axiom,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_698_0,axiom,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk9_3(X3,X1,X2))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_1,axiom,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk9_3(X3,X1,X2))))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk9_3(X3,X1,X2))))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_701_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_701_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_702_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_702_1,axiom,
( ti(X1,X2) != ti(X1,X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_703_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_1,axiom,
( ti(X1,X2) != ti(X1,X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_706_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_706_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_707_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X4) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X4) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_2,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X4) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_3,axiom,
( ti(fun(X1,bool),X3) != ti(fun(X1,bool),X4)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_708_0,axiom,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_709_0,axiom,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_710_0,axiom,
( X1 = hAPP(nat,nat,suc,X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 = hAPP(nat,nat,suc,X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 = hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_711_0,axiom,
( X1 = hAPP(nat,nat,suc,X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 = hAPP(nat,nat,suc,X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 = hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_712_0,axiom,
( hAPP(nat,nat,suc,sk1_esk10_2(X2,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1))
| hAPP(nat,nat,suc,sk1_esk10_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_713_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk8_3(X1,X3,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_713_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk8_3(X1,X3,X2)),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_714_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_714_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_715_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_715_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_717_0,axiom,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk9_3(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_717_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk9_3(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_717_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,sk1_esk9_3(X3,X1,X2)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_718_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_718_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X3,X4))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_719_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk12_1(X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_1,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk12_1(X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_2,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk12_1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_720_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_720_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_721_0,axiom,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X2))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_721_1,axiom,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X2),X1))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_722_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_722_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_723_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_723_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_724_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_724_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_724_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_725_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_725_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_726_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_726_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_726_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_727_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_727_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_727_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_728_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4))
| ti(X1,X2) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_728]) ).
cnf(c_0_728_1,axiom,
( ti(X1,X2) != ti(X1,X4)
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_728]) ).
cnf(c_0_730_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk8_3(X1,X3,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_730_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk8_3(X1,X3,X2)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_732_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) = ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_735_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_735_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_736_0,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk13_2(X1,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_736_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk13_2(X1,X2)),X2))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_737_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_737]) ).
cnf(c_0_737_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_737]) ).
cnf(c_0_739_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_739_1,axiom,
( X1 != hAPP(nat,nat,suc,X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_740_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_740_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X3,X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_741_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_741_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_742_0,axiom,
( hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_1,axiom,
( ~ hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_2,axiom,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1))
| ~ hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_743_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_743_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_743_2,axiom,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1))
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_744_0,axiom,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_744_1,axiom,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_745_0,axiom,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_745]) ).
cnf(c_0_745_1,axiom,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_745]) ).
cnf(c_0_746_0,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk13_2(X1,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_746_1,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk13_2(X1,X2)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_747_0,axiom,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,sk1_esk4_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,sk1_esk4_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_747_1,axiom,
( hAPP(X1,X2,X3,sk1_esk4_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,sk1_esk4_4(X1,X2,X3,X4))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_748_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_748_1,axiom,
( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_749_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_749_1,axiom,
( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_750_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_750]) ).
cnf(c_0_750_1,axiom,
( ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_750]) ).
cnf(c_0_751_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_1,axiom,
( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_752_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_752_1,axiom,
( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_753_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_753_1,axiom,
( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_755_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_755]) ).
cnf(c_0_755_1,axiom,
( ti(X1,X2) != ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_755]) ).
cnf(c_0_756_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_756_1,axiom,
( ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_757_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_757_1,axiom,
( X1 != X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_759_0,axiom,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_759_1,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_759_2,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_760_0,axiom,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_760_1,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_761_0,axiom,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_761_1,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_762_0,axiom,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_762_1,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_763_0,axiom,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_763]) ).
cnf(c_0_763_1,axiom,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_763]) ).
cnf(c_0_765_0,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_765_1,axiom,
( ~ hBOOL(hAPP(bool,bool,fNot,X1))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_766_0,axiom,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_766_1,axiom,
( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_767_0,axiom,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_767]) ).
cnf(c_0_767_1,axiom,
( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_767]) ).
cnf(c_0_771_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_771]) ).
cnf(c_0_771_1,axiom,
( ~ finite_finite_1(X1)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_771]) ).
cnf(c_0_772_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_772]) ).
cnf(c_0_772_1,axiom,
( ~ finite_finite_1(X1)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_772]) ).
cnf(c_0_776_0,axiom,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_776]) ).
cnf(c_0_776_1,axiom,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_776]) ).
cnf(c_0_777_0,axiom,
( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_777]) ).
cnf(c_0_777_1,axiom,
( X1 != X2
| hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_777]) ).
cnf(c_0_787_0,axiom,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_787]) ).
cnf(c_0_787_1,axiom,
( ~ preorder(X1)
| ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_787]) ).
cnf(c_0_796_0,axiom,
( finite_finite_1(fun(X1,X2))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_796]) ).
cnf(c_0_796_1,axiom,
( ~ finite_finite_1(X1)
| finite_finite_1(fun(X1,X2))
| ~ finite_finite_1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_796]) ).
cnf(c_0_796_2,axiom,
( ~ finite_finite_1(X2)
| ~ finite_finite_1(X1)
| finite_finite_1(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_796]) ).
cnf(c_0_797_0,axiom,
( order(fun(X1,X2))
| ~ order(X2) ),
inference(literals_permutation,[status(thm)],[c_0_797]) ).
cnf(c_0_797_1,axiom,
( ~ order(X2)
| order(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_797]) ).
cnf(c_0_798_0,axiom,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_798]) ).
cnf(c_0_798_1,axiom,
( ~ preorder(X2)
| preorder(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_798]) ).
cnf(c_0_716_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_778_0,axiom,
hAPP(nat,nat,suc,X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_778]) ).
cnf(c_0_779_0,axiom,
hAPP(nat,nat,suc,X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_779]) ).
cnf(c_0_625_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fimplies),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2)))),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_630_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_631_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_657_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,suc,X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_661_0,axiom,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1)))),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_667_0,axiom,
hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)) = hAPP(fun(X4,bool),fun(X2,bool),hAPP(fun(X4,X2),fun(fun(X4,bool),fun(X2,bool)),image(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),combb(X1,X2,X4),X3),X5)),X6),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_685_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_686_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)),X2),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_688_0,axiom,
hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),hAPP(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_699_0,axiom,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2))),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_700_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_704_0,axiom,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3))),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_705_0,axiom,
hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1))) = hAPP(nat,nat,suc,X1),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_729_0,axiom,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,X3),fun(X1,X2)),combs(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),hAPP(X1,X3,X5,X6)),
inference(literals_permutation,[status(thm)],[c_0_729]) ).
cnf(c_0_731_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_733_0,axiom,
hAPP(X1,X2,hAPP(X3,fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),X5),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_734_0,axiom,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_738_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_754_0,axiom,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_758_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_764_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = ti(fun(X1,bool),X2),
inference(literals_permutation,[status(thm)],[c_0_764]) ).
cnf(c_0_768_0,axiom,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_768]) ).
cnf(c_0_769_0,axiom,
ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_769]) ).
cnf(c_0_770_0,axiom,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_770]) ).
cnf(c_0_773_0,axiom,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_773]) ).
cnf(c_0_774_0,axiom,
ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_774]) ).
cnf(c_0_775_0,axiom,
ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_775]) ).
cnf(c_0_780_0,axiom,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_780]) ).
cnf(c_0_781_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(literals_permutation,[status(thm)],[c_0_781]) ).
cnf(c_0_782_0,axiom,
ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
inference(literals_permutation,[status(thm)],[c_0_782]) ).
cnf(c_0_783_0,axiom,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_783]) ).
cnf(c_0_784_0,axiom,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
inference(literals_permutation,[status(thm)],[c_0_784]) ).
cnf(c_0_785_0,axiom,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(literals_permutation,[status(thm)],[c_0_785]) ).
cnf(c_0_786_0,axiom,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(literals_permutation,[status(thm)],[c_0_786]) ).
cnf(c_0_788_0,axiom,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(literals_permutation,[status(thm)],[c_0_788]) ).
cnf(c_0_789_0,axiom,
ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
inference(literals_permutation,[status(thm)],[c_0_789]) ).
cnf(c_0_790_0,axiom,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
inference(literals_permutation,[status(thm)],[c_0_790]) ).
cnf(c_0_791_0,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(literals_permutation,[status(thm)],[c_0_791]) ).
cnf(c_0_792_0,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(literals_permutation,[status(thm)],[c_0_792]) ).
cnf(c_0_793_0,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(literals_permutation,[status(thm)],[c_0_793]) ).
cnf(c_0_794_0,axiom,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_794]) ).
cnf(c_0_795_0,axiom,
ti(fun(X1,X1),combi(X1)) = combi(X1),
inference(literals_permutation,[status(thm)],[c_0_795]) ).
cnf(c_0_799_0,axiom,
ti(fun(bool,bool),fNot) = fNot,
inference(literals_permutation,[status(thm)],[c_0_799]) ).
cnf(c_0_800_0,axiom,
ti(X1,undefined(X1)) = undefined(X1),
inference(literals_permutation,[status(thm)],[c_0_800]) ).
cnf(c_0_801_0,axiom,
order(bool),
inference(literals_permutation,[status(thm)],[c_0_801]) ).
cnf(c_0_802_0,axiom,
finite_finite_1(bool),
inference(literals_permutation,[status(thm)],[c_0_802]) ).
cnf(c_0_803_0,axiom,
preorder(bool),
inference(literals_permutation,[status(thm)],[c_0_803]) ).
cnf(c_0_804_0,axiom,
order(nat),
inference(literals_permutation,[status(thm)],[c_0_804]) ).
cnf(c_0_805_0,axiom,
preorder(nat),
inference(literals_permutation,[status(thm)],[c_0_805]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('<stdin>',conj_6) ).
fof(c_0_1_002,hypothesis,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
file('<stdin>',conj_2) ).
fof(c_0_2_003,hypothesis,
hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
file('<stdin>',conj_3) ).
fof(c_0_3_004,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('<stdin>',conj_1) ).
fof(c_0_4_005,hypothesis,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
file('<stdin>',conj_5) ).
fof(c_0_5_006,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('<stdin>',conj_4) ).
fof(c_0_6_007,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
file('<stdin>',conj_0) ).
fof(c_0_7_008,hypothesis,
ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
file('<stdin>',tsy_c_Groups_Ominus__class_Ominus_res) ).
fof(c_0_8_009,hypothesis,
! [X1] :
( hBOOL(ti(bool,X1))
<=> hBOOL(X1) ),
file('<stdin>',tsy_c_hBOOL_arg1) ).
fof(c_0_9_010,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
file('<stdin>',tsy_v_mgt__call_res) ).
fof(c_0_10_011,hypothesis,
ti(fun(pname,bool),u) = u,
file('<stdin>',tsy_v_U_res) ).
fof(c_0_11_012,hypothesis,
ti(fun(x_a,bool),g) = g,
file('<stdin>',tsy_v_G_res) ).
fof(c_0_12_013,hypothesis,
ti(fun(nat,nat),suc) = suc,
file('<stdin>',tsy_c_Nat_OSuc_res) ).
fof(c_0_13_014,hypothesis,
ti(pname,pn) = pn,
file('<stdin>',tsy_v_pn_res) ).
fof(c_0_14_015,hypothesis,
ti(nat,na) = na,
file('<stdin>',tsy_v_na_res) ).
fof(c_0_15_016,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_16_017,hypothesis,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
c_0_1 ).
fof(c_0_17_018,hypothesis,
hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
c_0_2 ).
fof(c_0_18_019,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
c_0_3 ).
fof(c_0_19_020,hypothesis,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_20_021,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
c_0_5 ).
fof(c_0_21_022,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
c_0_6 ).
fof(c_0_22_023,hypothesis,
ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
c_0_7 ).
fof(c_0_23_024,hypothesis,
! [X1] :
( hBOOL(ti(bool,X1))
<=> hBOOL(X1) ),
c_0_8 ).
fof(c_0_24_025,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
c_0_9 ).
fof(c_0_25_026,hypothesis,
ti(fun(pname,bool),u) = u,
c_0_10 ).
fof(c_0_26_027,hypothesis,
ti(fun(x_a,bool),g) = g,
c_0_11 ).
fof(c_0_27_028,hypothesis,
ti(fun(nat,nat),suc) = suc,
c_0_12 ).
fof(c_0_28_029,hypothesis,
ti(pname,pn) = pn,
c_0_13 ).
fof(c_0_29_030,hypothesis,
ti(nat,na) = na,
c_0_14 ).
fof(c_0_30_031,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
c_0_15 ).
fof(c_0_31_032,hypothesis,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
c_0_16 ).
fof(c_0_32_033,hypothesis,
hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
c_0_17 ).
fof(c_0_33_034,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
c_0_18 ).
fof(c_0_34_035,hypothesis,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
c_0_19 ).
fof(c_0_35_036,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
c_0_20 ).
fof(c_0_36_037,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
c_0_21 ).
fof(c_0_37_038,hypothesis,
ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
c_0_22 ).
fof(c_0_38_039,hypothesis,
! [X2,X3] :
( ( ~ hBOOL(ti(bool,X2))
| hBOOL(X2) )
& ( ~ hBOOL(X3)
| hBOOL(ti(bool,X3)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_39_040,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
c_0_24 ).
fof(c_0_40_041,hypothesis,
ti(fun(pname,bool),u) = u,
c_0_25 ).
fof(c_0_41_042,hypothesis,
ti(fun(x_a,bool),g) = g,
c_0_26 ).
fof(c_0_42_043,hypothesis,
ti(fun(nat,nat),suc) = suc,
c_0_27 ).
fof(c_0_43_044,hypothesis,
ti(pname,pn) = pn,
c_0_28 ).
fof(c_0_44_045,hypothesis,
ti(nat,na) = na,
c_0_29 ).
cnf(c_0_45_046,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46_047,hypothesis,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47_048,hypothesis,
hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_48_049,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_49_050,hypothesis,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_50_051,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51_052,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52_053,hypothesis,
ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_53_054,hypothesis,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_54_055,hypothesis,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55_056,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_56_057,hypothesis,
ti(fun(pname,bool),u) = u,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_57_058,hypothesis,
ti(fun(x_a,bool),g) = g,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_58_059,hypothesis,
ti(fun(nat,nat),suc) = suc,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_59_060,hypothesis,
ti(pname,pn) = pn,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_60_061,hypothesis,
ti(nat,na) = na,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_61_062,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
c_0_45,
[final] ).
cnf(c_0_62_063,hypothesis,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
c_0_46,
[final] ).
cnf(c_0_63_064,hypothesis,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)) = hAPP(fun(x_a,bool),nat,finite_card(x_a),g),
c_0_47,
[final] ).
cnf(c_0_64_065,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
c_0_48,
[final] ).
cnf(c_0_65_066,hypothesis,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
c_0_49,
[final] ).
cnf(c_0_66_067,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
c_0_50,
[final] ).
cnf(c_0_67_068,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
c_0_51,
[final] ).
cnf(c_0_68_069,hypothesis,
ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
c_0_52,
[final] ).
cnf(c_0_69_070,hypothesis,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
c_0_53,
[final] ).
cnf(c_0_70_071,hypothesis,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
c_0_54,
[final] ).
cnf(c_0_71_072,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
c_0_55,
[final] ).
cnf(c_0_72_073,hypothesis,
ti(fun(pname,bool),u) = u,
c_0_56,
[final] ).
cnf(c_0_73_074,hypothesis,
ti(fun(x_a,bool),g) = g,
c_0_57,
[final] ).
cnf(c_0_74_075,hypothesis,
ti(fun(nat,nat),suc) = suc,
c_0_58,
[final] ).
cnf(c_0_75_076,hypothesis,
ti(pname,pn) = pn,
c_0_59,
[final] ).
cnf(c_0_76_077,hypothesis,
ti(nat,na) = na,
c_0_60,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_381,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_66) ).
cnf(c_539,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(copy,[status(esa)],[c_381]) ).
cnf(c_568,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(copy,[status(esa)],[c_539]) ).
cnf(c_585,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(copy,[status(esa)],[c_568]) ).
cnf(c_608,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(copy,[status(esa)],[c_585]) ).
cnf(c_1741,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(copy,[status(esa)],[c_608]) ).
cnf(c_275,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_665_1) ).
cnf(c_1513,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(copy,[status(esa)],[c_275]) ).
cnf(c_2687,plain,
hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(pname,X0,X1,pn)),hAPP(fun(pname,bool),fun(X0,bool),hAPP(fun(pname,X0),fun(fun(pname,bool),fun(X0,bool)),image(pname,X0),X1),u))),
inference(resolution,[status(thm)],[c_1741,c_1513]) ).
cnf(c_2690,plain,
hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(pname,X0,X1,pn)),hAPP(fun(pname,bool),fun(X0,bool),hAPP(fun(pname,X0),fun(fun(pname,bool),fun(X0,bool)),image(pname,X0),X1),u))),
inference(rewriting,[status(thm)],[c_2687]) ).
cnf(c_317,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_647_2) ).
cnf(c_1597,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ),
inference(copy,[status(esa)],[c_317]) ).
cnf(c_7403,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(pname,X0,X1,pn)),X2)),hAPP(fun(pname,bool),fun(X0,bool),hAPP(fun(pname,X0),fun(fun(pname,bool),fun(X0,bool)),image(pname,X0),X1),u)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(pname,bool),fun(X0,bool),hAPP(fun(pname,X0),fun(fun(pname,bool),fun(X0,bool)),image(pname,X0),X1),u))) ),
inference(resolution,[status(thm)],[c_2690,c_1597]) ).
cnf(c_7406,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(pname,X0,X1,pn)),X2)),hAPP(fun(pname,bool),fun(X0,bool),hAPP(fun(pname,X0),fun(fun(pname,bool),fun(X0,bool)),image(pname,X0),X1),u)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(pname,bool),fun(X0,bool),hAPP(fun(pname,X0),fun(fun(pname,bool),fun(X0,bool)),image(pname,X0),X1),u))) ),
inference(rewriting,[status(thm)],[c_7403]) ).
cnf(c_380,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_64) ).
cnf(c_537,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_380]) ).
cnf(c_567,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_537]) ).
cnf(c_586,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_567]) ).
cnf(c_607,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_586]) ).
cnf(c_1739,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_607]) ).
cnf(c_250,plain,
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_676_1) ).
cnf(c_1463,plain,
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(copy,[status(esa)],[c_250]) ).
cnf(c_2736,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),g)) ),
inference(resolution,[status(thm)],[c_1739,c_1463]) ).
cnf(c_2737,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),g)) ),
inference(rewriting,[status(thm)],[c_2736]) ).
cnf(c_323,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_645_1) ).
cnf(c_1609,plain,
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(copy,[status(esa)],[c_323]) ).
cnf(c_9386,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X1),g)) ),
inference(resolution,[status(thm)],[c_2737,c_1609]) ).
cnf(c_9389,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X1),g)) ),
inference(rewriting,[status(thm)],[c_9386]) ).
cnf(c_376,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_61) ).
cnf(c_557,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_376]) ).
cnf(c_563,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_557]) ).
cnf(c_590,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_563]) ).
cnf(c_603,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_590]) ).
cnf(c_1731,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(copy,[status(esa)],[c_603]) ).
cnf(c_251,plain,
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_676_0) ).
cnf(c_1465,plain,
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3)) ),
inference(copy,[status(esa)],[c_251]) ).
cnf(c_1753,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),X0))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(resolution,[status(thm)],[c_1731,c_1465]) ).
cnf(c_1754,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),X0))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(rewriting,[status(thm)],[c_1753]) ).
cnf(c_1833,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),X0))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X1),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),X1)) ),
inference(resolution,[status(thm)],[c_1754,c_1465]) ).
cnf(c_1834,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),X0))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X1),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),X1)) ),
inference(rewriting,[status(thm)],[c_1833]) ).
cnf(c_117096,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),X1)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X1),g)) ),
inference(resolution,[status(thm)],[c_9389,c_1834]) ).
cnf(c_117097,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),X1)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),X0),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X1),g)) ),
inference(rewriting,[status(thm)],[c_117096]) ).
cnf(c_122332,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),X0)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),g)) ),
inference(resolution,[status(thm)],[c_7406,c_117097]) ).
cnf(c_122335,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),X0)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),g)) ),
inference(rewriting,[status(thm)],[c_122332]) ).
cnf(c_30,plain,
hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p',c_0_754_0) ).
cnf(c_1035,plain,
hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)),
inference(copy,[status(esa)],[c_30]) ).
cnf(c_123365,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),X0)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),g)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122335,c_1035]) ).
cnf(c_123366,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),X0)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),g)) ),
inference(rewriting,[status(thm)],[c_123365]) ).
cnf(c_123369,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),g)),
inference(resolution,[status(thm)],[c_123366,c_1035]) ).
cnf(c_123370,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),g)),
inference(rewriting,[status(thm)],[c_123369]) ).
cnf(c_124234,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_123370,c_1035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW473+5 : TPTP v8.1.0. Released v5.3.0.
% 0.04/0.13 % Command : iprover_modulo %s %d
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 5 10:00:27 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Running in mono-core mode
% 0.20/0.45 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.45 % FOF problem with conjecture
% 0.20/0.45 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8e2efe.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_c2f252 | grep -v "SZS"
% 0.20/0.47
% 0.20/0.47 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.47
% 0.20/0.47 %
% 0.20/0.47 % ------ iProver source info
% 0.20/0.47
% 0.20/0.47 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.47 % git: non_committed_changes: true
% 0.20/0.47 % git: last_make_outside_of_git: true
% 0.20/0.47
% 0.20/0.47 %
% 0.20/0.47 % ------ Input Options
% 0.20/0.47
% 0.20/0.47 % --out_options all
% 0.20/0.47 % --tptp_safe_out true
% 0.20/0.47 % --problem_path ""
% 0.20/0.47 % --include_path ""
% 0.20/0.47 % --clausifier .//eprover
% 0.20/0.47 % --clausifier_options --tstp-format
% 0.20/0.47 % --stdin false
% 0.20/0.47 % --dbg_backtrace false
% 0.20/0.47 % --dbg_dump_prop_clauses false
% 0.20/0.47 % --dbg_dump_prop_clauses_file -
% 0.20/0.47 % --dbg_out_stat false
% 0.20/0.47
% 0.20/0.47 % ------ General Options
% 0.20/0.47
% 0.20/0.47 % --fof false
% 0.20/0.47 % --time_out_real 150.
% 0.20/0.47 % --time_out_prep_mult 0.2
% 0.20/0.47 % --time_out_virtual -1.
% 0.20/0.47 % --schedule none
% 0.20/0.47 % --ground_splitting input
% 0.20/0.47 % --splitting_nvd 16
% 0.20/0.47 % --non_eq_to_eq false
% 0.20/0.47 % --prep_gs_sim true
% 0.20/0.47 % --prep_unflatten false
% 0.20/0.47 % --prep_res_sim true
% 0.20/0.47 % --prep_upred true
% 0.20/0.47 % --res_sim_input true
% 0.20/0.47 % --clause_weak_htbl true
% 0.20/0.47 % --gc_record_bc_elim false
% 0.20/0.47 % --symbol_type_check false
% 0.20/0.47 % --clausify_out false
% 0.20/0.47 % --large_theory_mode false
% 0.20/0.47 % --prep_sem_filter none
% 0.20/0.47 % --prep_sem_filter_out false
% 0.20/0.47 % --preprocessed_out false
% 0.20/0.47 % --sub_typing false
% 0.20/0.47 % --brand_transform false
% 0.20/0.47 % --pure_diseq_elim true
% 0.20/0.47 % --min_unsat_core false
% 0.20/0.47 % --pred_elim true
% 0.20/0.47 % --add_important_lit false
% 0.20/0.47 % --soft_assumptions false
% 0.20/0.47 % --reset_solvers false
% 0.20/0.47 % --bc_imp_inh []
% 0.20/0.47 % --conj_cone_tolerance 1.5
% 0.20/0.47 % --prolific_symb_bound 500
% 0.20/0.47 % --lt_threshold 2000
% 0.20/0.47
% 0.20/0.47 % ------ SAT Options
% 0.20/0.47
% 0.20/0.47 % --sat_mode false
% 0.20/0.47 % --sat_fm_restart_options ""
% 0.20/0.47 % --sat_gr_def false
% 0.20/0.47 % --sat_epr_types true
% 0.20/0.47 % --sat_non_cyclic_types false
% 0.20/0.47 % --sat_finite_models false
% 0.20/0.47 % --sat_fm_lemmas false
% 0.20/0.47 % --sat_fm_prep false
% 0.20/0.47 % --sat_fm_uc_incr true
% 0.20/0.47 % --sat_out_model small
% 0.20/0.47 % --sat_out_clauses false
% 0.20/0.47
% 0.20/0.47 % ------ QBF Options
% 0.20/0.47
% 0.20/0.47 % --qbf_mode false
% 0.20/0.47 % --qbf_elim_univ true
% 0.20/0.47 % --qbf_sk_in true
% 0.20/0.47 % --qbf_pred_elim true
% 0.20/0.47 % --qbf_split 32
% 0.20/0.47
% 0.20/0.47 % ------ BMC1 Options
% 0.20/0.47
% 0.20/0.47 % --bmc1_incremental false
% 0.20/0.47 % --bmc1_axioms reachable_all
% 0.20/0.47 % --bmc1_min_bound 0
% 0.20/0.47 % --bmc1_max_bound -1
% 0.20/0.47 % --bmc1_max_bound_default -1
% 0.20/0.47 % --bmc1_symbol_reachability true
% 0.20/0.47 % --bmc1_property_lemmas false
% 0.20/0.47 % --bmc1_k_induction false
% 0.20/0.47 % --bmc1_non_equiv_states false
% 0.20/0.47 % --bmc1_deadlock false
% 0.20/0.47 % --bmc1_ucm false
% 0.20/0.47 % --bmc1_add_unsat_core none
% 0.20/0.47 % --bmc1_unsat_core_children false
% 0.20/0.47 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.47 % --bmc1_out_stat full
% 0.20/0.47 % --bmc1_ground_init false
% 0.20/0.47 % --bmc1_pre_inst_next_state false
% 0.20/0.47 % --bmc1_pre_inst_state false
% 0.20/0.47 % --bmc1_pre_inst_reach_state false
% 0.20/0.47 % --bmc1_out_unsat_core false
% 0.20/0.47 % --bmc1_aig_witness_out false
% 0.20/0.47 % --bmc1_verbose false
% 0.20/0.47 % --bmc1_dump_clauses_tptp false
% 6.78/7.40 % --bmc1_dump_unsat_core_tptp false
% 6.78/7.40 % --bmc1_dump_file -
% 6.78/7.40 % --bmc1_ucm_expand_uc_limit 128
% 6.78/7.40 % --bmc1_ucm_n_expand_iterations 6
% 6.78/7.40 % --bmc1_ucm_extend_mode 1
% 6.78/7.40 % --bmc1_ucm_init_mode 2
% 6.78/7.40 % --bmc1_ucm_cone_mode none
% 6.78/7.40 % --bmc1_ucm_reduced_relation_type 0
% 6.78/7.40 % --bmc1_ucm_relax_model 4
% 6.78/7.40 % --bmc1_ucm_full_tr_after_sat true
% 6.78/7.40 % --bmc1_ucm_expand_neg_assumptions false
% 6.78/7.40 % --bmc1_ucm_layered_model none
% 6.78/7.40 % --bmc1_ucm_max_lemma_size 10
% 6.78/7.40
% 6.78/7.40 % ------ AIG Options
% 6.78/7.40
% 6.78/7.40 % --aig_mode false
% 6.78/7.40
% 6.78/7.40 % ------ Instantiation Options
% 6.78/7.40
% 6.78/7.40 % --instantiation_flag true
% 6.78/7.40 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 6.78/7.40 % --inst_solver_per_active 750
% 6.78/7.40 % --inst_solver_calls_frac 0.5
% 6.78/7.40 % --inst_passive_queue_type priority_queues
% 6.78/7.40 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 6.78/7.40 % --inst_passive_queues_freq [25;2]
% 6.78/7.40 % --inst_dismatching true
% 6.78/7.40 % --inst_eager_unprocessed_to_passive true
% 6.78/7.40 % --inst_prop_sim_given true
% 6.78/7.40 % --inst_prop_sim_new false
% 6.78/7.40 % --inst_orphan_elimination true
% 6.78/7.40 % --inst_learning_loop_flag true
% 6.78/7.40 % --inst_learning_start 3000
% 6.78/7.40 % --inst_learning_factor 2
% 6.78/7.40 % --inst_start_prop_sim_after_learn 3
% 6.78/7.40 % --inst_sel_renew solver
% 6.78/7.40 % --inst_lit_activity_flag true
% 6.78/7.40 % --inst_out_proof true
% 6.78/7.40
% 6.78/7.40 % ------ Resolution Options
% 6.78/7.40
% 6.78/7.40 % --resolution_flag true
% 6.78/7.40 % --res_lit_sel kbo_max
% 6.78/7.40 % --res_to_prop_solver none
% 6.78/7.40 % --res_prop_simpl_new false
% 6.78/7.40 % --res_prop_simpl_given false
% 6.78/7.40 % --res_passive_queue_type priority_queues
% 6.78/7.40 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 6.78/7.40 % --res_passive_queues_freq [15;5]
% 6.78/7.40 % --res_forward_subs full
% 6.78/7.40 % --res_backward_subs full
% 6.78/7.40 % --res_forward_subs_resolution true
% 6.78/7.40 % --res_backward_subs_resolution true
% 6.78/7.40 % --res_orphan_elimination false
% 6.78/7.40 % --res_time_limit 1000.
% 6.78/7.40 % --res_out_proof true
% 6.78/7.40 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8e2efe.s
% 6.78/7.40 % --modulo true
% 6.78/7.40
% 6.78/7.40 % ------ Combination Options
% 6.78/7.40
% 6.78/7.40 % --comb_res_mult 1000
% 6.78/7.40 % --comb_inst_mult 300
% 6.78/7.40 % ------
% 6.78/7.40
% 6.78/7.40 % ------ Parsing...% successful
% 6.78/7.40
% 6.78/7.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 6.78/7.40
% 6.78/7.40 % ------ Proving...
% 6.78/7.40 % ------ Problem Properties
% 6.78/7.40
% 6.78/7.40 %
% 6.78/7.40 % EPR false
% 6.78/7.40 % Horn false
% 6.78/7.40 % Has equality true
% 6.78/7.40
% 6.78/7.40 % % ------ Input Options Time Limit: Unbounded
% 6.78/7.40
% 6.78/7.40
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 Compiling...
% 6.78/7.40 Loading plugin: done.
% 6.78/7.40 % % ------ Current options:
% 6.78/7.40
% 6.78/7.40 % ------ Input Options
% 6.78/7.40
% 6.78/7.40 % --out_options all
% 6.78/7.40 % --tptp_safe_out true
% 6.78/7.40 % --problem_path ""
% 6.78/7.40 % --include_path ""
% 6.78/7.40 % --clausifier .//eprover
% 6.78/7.40 % --clausifier_options --tstp-format
% 6.78/7.40 % --stdin false
% 6.78/7.40 % --dbg_backtrace false
% 6.78/7.40 % --dbg_dump_prop_clauses false
% 6.78/7.40 % --dbg_dump_prop_clauses_file -
% 6.78/7.40 % --dbg_out_stat false
% 6.78/7.40
% 6.78/7.40 % ------ General Options
% 6.78/7.40
% 6.78/7.40 % --fof false
% 6.78/7.40 % --time_out_real 150.
% 6.78/7.40 % --time_out_prep_mult 0.2
% 6.78/7.40 % --time_out_virtual -1.
% 6.78/7.40 % --schedule none
% 6.78/7.40 % --ground_splitting input
% 6.78/7.40 % --splitting_nvd 16
% 6.78/7.40 % --non_eq_to_eq false
% 6.78/7.40 % --prep_gs_sim true
% 6.78/7.40 % --prep_unflatten false
% 6.78/7.40 % --prep_res_sim true
% 6.78/7.40 % --prep_upred true
% 6.78/7.40 % --res_sim_input true
% 6.78/7.40 % --clause_weak_htbl true
% 6.78/7.40 % --gc_record_bc_elim false
% 6.78/7.40 % --symbol_type_check false
% 6.78/7.40 % --clausify_out false
% 6.78/7.40 % --large_theory_mode false
% 6.78/7.40 % --prep_sem_filter none
% 6.78/7.40 % --prep_sem_filter_out false
% 6.78/7.40 % --preprocessed_out false
% 6.78/7.40 % --sub_typing false
% 6.78/7.40 % --brand_transform false
% 6.78/7.40 % --pure_diseq_elim true
% 6.78/7.40 % --min_unsat_core false
% 6.78/7.40 % --pred_elim true
% 6.78/7.40 % --add_important_lit false
% 6.78/7.40 % --soft_assumptions false
% 6.78/7.40 % --reset_solvers false
% 6.78/7.40 % --bc_imp_inh []
% 6.78/7.40 % --conj_cone_tolerance 1.5
% 6.78/7.40 % --prolific_symb_bound 500
% 6.78/7.40 % --lt_threshold 2000
% 6.78/7.40
% 6.78/7.40 % ------ SAT Options
% 6.78/7.40
% 6.78/7.40 % --sat_mode false
% 6.78/7.40 % --sat_fm_restart_options ""
% 6.78/7.40 % --sat_gr_def false
% 6.78/7.40 % --sat_epr_types true
% 6.78/7.40 % --sat_non_cyclic_types false
% 6.78/7.40 % --sat_finite_models false
% 6.78/7.40 % --sat_fm_lemmas false
% 6.78/7.40 % --sat_fm_prep false
% 6.78/7.40 % --sat_fm_uc_incr true
% 6.78/7.40 % --sat_out_model small
% 6.78/7.40 % --sat_out_clauses false
% 6.78/7.40
% 6.78/7.40 % ------ QBF Options
% 6.78/7.40
% 6.78/7.40 % --qbf_mode false
% 6.78/7.40 % --qbf_elim_univ true
% 6.78/7.40 % --qbf_sk_in true
% 6.78/7.40 % --qbf_pred_elim true
% 6.78/7.40 % --qbf_split 32
% 6.78/7.40
% 6.78/7.40 % ------ BMC1 Options
% 6.78/7.40
% 6.78/7.40 % --bmc1_incremental false
% 6.78/7.40 % --bmc1_axioms reachable_all
% 6.78/7.40 % --bmc1_min_bound 0
% 6.78/7.40 % --bmc1_max_bound -1
% 6.78/7.40 % --bmc1_max_bound_default -1
% 6.78/7.40 % --bmc1_symbol_reachability true
% 6.78/7.40 % --bmc1_property_lemmas false
% 6.78/7.40 % --bmc1_k_induction false
% 6.78/7.40 % --bmc1_non_equiv_states false
% 6.78/7.40 % --bmc1_deadlock false
% 6.78/7.40 % --bmc1_ucm false
% 6.78/7.40 % --bmc1_add_unsat_core none
% 6.78/7.40 % --bmc1_unsat_core_children false
% 6.78/7.40 % --bmc1_unsat_core_extrapolate_axioms false
% 6.78/7.40 % --bmc1_out_stat full
% 6.78/7.40 % --bmc1_ground_init false
% 6.78/7.40 % --bmc1_pre_inst_next_state false
% 6.78/7.40 % --bmc1_pre_inst_state false
% 6.78/7.40 % --bmc1_pre_inst_reach_state false
% 6.78/7.40 % --bmc1_out_unsat_core false
% 6.78/7.40 % --bmc1_aig_witness_out false
% 6.78/7.40 % --bmc1_verbose false
% 6.78/7.40 % --bmc1_dump_clauses_tptp false
% 6.78/7.40 % --bmc1_dump_unsat_core_tptp false
% 6.78/7.40 % --bmc1_dump_file -
% 6.78/7.40 % --bmc1_ucm_expand_uc_limit 128
% 6.78/7.40 % --bmc1_ucm_n_expand_iterations 6
% 6.78/7.40 % --bmc1_ucm_extend_mode 1
% 6.78/7.40 % --bmc1_ucm_init_mode 2
% 6.78/7.40 % --bmc1_ucm_cone_mode none
% 6.78/7.40 % --bmc1_ucm_reduced_relation_type 0
% 6.78/7.40 % --bmc1_ucm_relax_model 4
% 6.78/7.40 % --bmc1_ucm_full_tr_after_sat true
% 6.78/7.40 % --bmc1_ucm_expand_neg_assumptions false
% 6.78/7.40 % --bmc1_ucm_layered_model none
% 6.78/7.40 % --bmc1_ucm_max_lemma_size 10
% 6.78/7.40
% 6.78/7.40 % ------ AIG Options
% 6.78/7.40
% 6.78/7.40 % --aig_mode false
% 6.78/7.40
% 6.78/7.40 % ------ Instantiation Options
% 6.78/7.40
% 6.78/7.40 % --instantiation_flag true
% 6.78/7.40 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 6.78/7.40 % --inst_solver_per_active 750
% 6.78/7.40 % --inst_solver_calls_frac 0.5
% 149.89/150.47 % --inst_passive_queue_type priority_queues
% 149.89/150.47 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 149.89/150.47 % --inst_passive_queues_freq [25;2]
% 149.89/150.47 % --inst_dismatching true
% 149.89/150.47 % --inst_eager_unprocessed_to_passive true
% 149.89/150.47 % --inst_prop_sim_given true
% 149.89/150.47 % --inst_prop_sim_new false
% 149.89/150.47 % --inst_orphan_elimination true
% 149.89/150.47 % --inst_learning_loop_flag true
% 149.89/150.47 % --inst_learning_start 3000
% 149.89/150.47 % --inst_learning_factor 2
% 149.89/150.47 % --inst_start_prop_sim_after_learn 3
% 149.89/150.47 % --inst_sel_renew solver
% 149.89/150.47 % --inst_lit_activity_flag true
% 149.89/150.47 % --inst_out_proof true
% 149.89/150.47
% 149.89/150.47 % ------ Resolution Options
% 149.89/150.47
% 149.89/150.47 % --resolution_flag true
% 149.89/150.47 % --res_lit_sel kbo_max
% 149.89/150.47 % --res_to_prop_solver none
% 149.89/150.47 % --res_prop_simpl_new false
% 149.89/150.47 % --res_prop_simpl_given false
% 149.89/150.47 % --res_passive_queue_type priority_queues
% 149.89/150.47 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 149.89/150.47 % --res_passive_queues_freq [15;5]
% 149.89/150.47 % --res_forward_subs full
% 149.89/150.47 % --res_backward_subs full
% 149.89/150.47 % --res_forward_subs_resolution true
% 149.89/150.47 % --res_backward_subs_resolution true
% 149.89/150.47 % --res_orphan_elimination false
% 149.89/150.47 % --res_time_limit 1000.
% 149.89/150.47 % --res_out_proof true
% 149.89/150.47 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8e2efe.s
% 149.89/150.47 % --modulo true
% 149.89/150.47
% 149.89/150.47 % ------ Combination Options
% 149.89/150.47
% 149.89/150.47 % --comb_res_mult 1000
% 149.89/150.47 % --comb_inst_mult 300
% 149.89/150.47 % ------
% 149.89/150.47
% 149.89/150.47
% 149.89/150.47
% 149.89/150.47 % ------ Proving...
% 149.89/150.47 %
% 149.89/150.47
% 149.89/150.47
% 149.89/150.47 % Time Out Real
% 149.89/150.47
% 149.89/150.47 % ------ Statistics
% 149.89/150.47
% 149.89/150.47 % ------ General
% 149.89/150.47
% 149.89/150.47 % num_of_input_clauses: 217
% 149.89/150.47 % num_of_input_neg_conjectures: 1
% 149.89/150.47 % num_of_splits: 0
% 149.89/150.47 % num_of_split_atoms: 0
% 149.89/150.47 % num_of_sem_filtered_clauses: 0
% 149.89/150.47 % num_of_subtypes: 0
% 149.89/150.47 % monotx_restored_types: 0
% 149.89/150.47 % sat_num_of_epr_types: 0
% 149.89/150.47 % sat_num_of_non_cyclic_types: 0
% 149.89/150.47 % sat_guarded_non_collapsed_types: 0
% 149.89/150.47 % is_epr: 0
% 149.89/150.47 % is_horn: 0
% 149.89/150.47 % has_eq: 1
% 149.89/150.47 % num_pure_diseq_elim: 0
% 149.89/150.47 % simp_replaced_by: 0
% 149.89/150.47 % res_preprocessed: 17
% 149.89/150.47 % prep_upred: 0
% 149.89/150.47 % prep_unflattend: 0
% 149.89/150.47 % pred_elim_cands: 0
% 149.89/150.47 % pred_elim: 0
% 149.89/150.47 % pred_elim_cl: 0
% 149.89/150.47 % pred_elim_cycles: 0
% 149.89/150.47 % forced_gc_time: 0
% 149.89/150.47 % gc_basic_clause_elim: 0
% 149.89/150.47 % parsing_time: 0.024
% 149.89/150.47 % sem_filter_time: 0.
% 149.89/150.47 % pred_elim_time: 0.
% 149.89/150.47 % out_proof_time: 0.
% 149.89/150.47 % monotx_time: 0.
% 149.89/150.47 % subtype_inf_time: 0.
% 149.89/150.47 % unif_index_cands_time: 0.52
% 149.89/150.47 % unif_index_add_time: 0.088
% 149.89/150.47 % total_time: 150.016
% 149.89/150.47 % num_of_symbols: 74
% 149.89/150.47 % num_of_terms: 360804
% 149.89/150.47
% 149.89/150.47 % ------ Propositional Solver
% 149.89/150.47
% 149.89/150.47 % prop_solver_calls: 19
% 149.89/150.47 % prop_fast_solver_calls: 37
% 149.89/150.47 % prop_num_of_clauses: 11116
% 149.89/150.47 % prop_preprocess_simplified: 14213
% 149.89/150.47 % prop_fo_subsumed: 0
% 149.89/150.47 % prop_solver_time: 0.003
% 149.89/150.47 % prop_fast_solver_time: 0.
% 149.89/150.47 % prop_unsat_core_time: 0.
% 149.89/150.47
% 149.89/150.47 % ------ QBF
% 149.89/150.47
% 149.89/150.47 % qbf_q_res: 0
% 149.89/150.47 % qbf_num_tautologies: 0
% 149.89/150.47 % qbf_prep_cycles: 0
% 149.89/150.47
% 149.89/150.47 % ------ BMC1
% 149.89/150.47
% 149.89/150.47 % bmc1_current_bound: -1
% 149.89/150.47 % bmc1_last_solved_bound: -1
% 149.89/150.47 % bmc1_unsat_core_size: -1
% 149.89/150.47 % bmc1_unsat_core_parents_size: -1
% 149.89/150.48 % bmc1_merge_next_fun: 0
% 149.89/150.48 % bmc1_unsat_core_clauses_time: 0.
% 149.89/150.48
% 149.89/150.48 % ------ Instantiation
% 149.89/150.48
% 149.89/150.48 % inst_num_of_clauses: 1580
% 149.89/150.48 % inst_num_in_passive: 804
% 149.89/150.48 % inst_num_in_active: 298
% 149.89/150.48 % inst_num_in_unprocessed: 478
% 149.89/150.48 % inst_num_of_loops: 299
% 149.89/150.48 % inst_num_of_learning_restarts: 1
% 149.89/150.48 % inst_num_moves_active_passive: 0
% 149.89/150.48 % inst_lit_activity: 980
% 149.89/150.48 % inst_lit_activity_moves: 0
% 149.89/150.48 % inst_num_tautologies: 0
% 149.89/150.48 % inst_num_prop_implied: 0
% 149.89/150.48 % inst_num_existing_simplified: 0
% 149.89/150.48 % inst_num_eq_res_simplified: 0
% 149.89/150.48 % inst_num_child_elim: 0
% 149.89/150.48 % inst_num_of_dismatching_blockings: 358
% 149.89/150.48 % inst_num_of_non_proper_insts: 923
% 149.89/150.48 % inst_num_of_duplicates: 893
% 149.89/150.48 % inst_inst_num_from_inst_to_res: 0
% 149.89/150.48 % inst_dismatching_checking_time: 0.299
% 149.89/150.48
% 149.89/150.48 % ------ Resolution
% 149.89/150.48
% 149.89/150.48 % res_num_of_clauses: 172298
% 149.89/150.48 % res_num_in_passive: 165258
% 149.89/150.48 % res_num_in_active: 7278
% 149.89/150.48 % res_num_of_loops: 11210
% 149.89/150.48 % res_forward_subset_subsumed: 161041
% 149.89/150.48 % res_backward_subset_subsumed: 406
% 149.89/150.48 % res_forward_subsumed: 4025
% 149.89/150.48 % res_backward_subsumed: 17
% 149.89/150.48 % res_forward_subsumption_resolution: 52
% 149.89/150.48 % res_backward_subsumption_resolution: 1
% 149.89/150.48 % res_clause_to_clause_subsumption: 142284
% 149.89/150.48 % res_orphan_elimination: 0
% 149.89/150.48 % res_tautology_del: 3130
% 149.89/150.48 % res_num_eq_res_simplified: 4
% 149.89/150.48 % res_num_sel_changes: 0
% 149.89/150.48 % res_moves_from_active_to_pass: 0
% 149.89/150.48
% 149.89/150.48 % Status Unknown
% 149.95/150.58 % Orienting using strategy ClausalAll
% 149.95/150.58 % FOF problem with conjecture
% 149.95/150.58 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8e2efe.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_7aa767.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_327b96 | grep -v "SZS"
% 149.95/150.60
% 149.95/150.60 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 149.95/150.60
% 149.95/150.60 %
% 149.95/150.60 % ------ iProver source info
% 149.95/150.60
% 149.95/150.60 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 149.95/150.60 % git: non_committed_changes: true
% 149.95/150.60 % git: last_make_outside_of_git: true
% 149.95/150.60
% 149.95/150.60 %
% 149.95/150.60 % ------ Input Options
% 149.95/150.60
% 149.95/150.60 % --out_options all
% 149.95/150.60 % --tptp_safe_out true
% 149.95/150.60 % --problem_path ""
% 149.95/150.60 % --include_path ""
% 149.95/150.60 % --clausifier .//eprover
% 149.95/150.60 % --clausifier_options --tstp-format
% 149.95/150.60 % --stdin false
% 149.95/150.60 % --dbg_backtrace false
% 149.95/150.60 % --dbg_dump_prop_clauses false
% 149.95/150.60 % --dbg_dump_prop_clauses_file -
% 149.95/150.60 % --dbg_out_stat false
% 149.95/150.60
% 149.95/150.60 % ------ General Options
% 149.95/150.60
% 149.95/150.60 % --fof false
% 149.95/150.60 % --time_out_real 150.
% 149.95/150.60 % --time_out_prep_mult 0.2
% 149.95/150.60 % --time_out_virtual -1.
% 149.95/150.60 % --schedule none
% 149.95/150.60 % --ground_splitting input
% 149.95/150.60 % --splitting_nvd 16
% 149.95/150.60 % --non_eq_to_eq false
% 149.95/150.60 % --prep_gs_sim true
% 149.95/150.60 % --prep_unflatten false
% 149.95/150.60 % --prep_res_sim true
% 149.95/150.60 % --prep_upred true
% 149.95/150.60 % --res_sim_input true
% 149.95/150.60 % --clause_weak_htbl true
% 149.95/150.60 % --gc_record_bc_elim false
% 149.95/150.60 % --symbol_type_check false
% 149.95/150.60 % --clausify_out false
% 149.95/150.60 % --large_theory_mode false
% 149.95/150.60 % --prep_sem_filter none
% 149.95/150.60 % --prep_sem_filter_out false
% 149.95/150.60 % --preprocessed_out false
% 149.95/150.60 % --sub_typing false
% 149.95/150.60 % --brand_transform false
% 149.95/150.60 % --pure_diseq_elim true
% 149.95/150.60 % --min_unsat_core false
% 149.95/150.60 % --pred_elim true
% 149.95/150.60 % --add_important_lit false
% 149.95/150.60 % --soft_assumptions false
% 149.95/150.60 % --reset_solvers false
% 149.95/150.60 % --bc_imp_inh []
% 149.95/150.60 % --conj_cone_tolerance 1.5
% 149.95/150.60 % --prolific_symb_bound 500
% 149.95/150.60 % --lt_threshold 2000
% 149.95/150.60
% 149.95/150.60 % ------ SAT Options
% 149.95/150.60
% 149.95/150.60 % --sat_mode false
% 149.95/150.60 % --sat_fm_restart_options ""
% 149.95/150.60 % --sat_gr_def false
% 149.95/150.60 % --sat_epr_types true
% 149.95/150.60 % --sat_non_cyclic_types false
% 149.95/150.60 % --sat_finite_models false
% 149.95/150.60 % --sat_fm_lemmas false
% 149.95/150.60 % --sat_fm_prep false
% 149.95/150.60 % --sat_fm_uc_incr true
% 149.95/150.60 % --sat_out_model small
% 149.95/150.60 % --sat_out_clauses false
% 149.95/150.60
% 149.95/150.60 % ------ QBF Options
% 149.95/150.60
% 149.95/150.60 % --qbf_mode false
% 149.95/150.60 % --qbf_elim_univ true
% 149.95/150.60 % --qbf_sk_in true
% 149.95/150.60 % --qbf_pred_elim true
% 149.95/150.60 % --qbf_split 32
% 149.95/150.60
% 149.95/150.60 % ------ BMC1 Options
% 149.95/150.60
% 149.95/150.60 % --bmc1_incremental false
% 149.95/150.60 % --bmc1_axioms reachable_all
% 149.95/150.60 % --bmc1_min_bound 0
% 149.95/150.60 % --bmc1_max_bound -1
% 149.95/150.60 % --bmc1_max_bound_default -1
% 149.95/150.60 % --bmc1_symbol_reachability true
% 149.95/150.60 % --bmc1_property_lemmas false
% 149.95/150.60 % --bmc1_k_induction false
% 149.95/150.60 % --bmc1_non_equiv_states false
% 149.95/150.60 % --bmc1_deadlock false
% 149.95/150.60 % --bmc1_ucm false
% 149.95/150.60 % --bmc1_add_unsat_core none
% 149.95/150.60 % --bmc1_unsat_core_children false
% 149.95/150.60 % --bmc1_unsat_core_extrapolate_axioms false
% 149.95/150.60 % --bmc1_out_stat full
% 149.95/150.60 % --bmc1_ground_init false
% 149.95/150.60 % --bmc1_pre_inst_next_state false
% 149.95/150.60 % --bmc1_pre_inst_state false
% 149.95/150.60 % --bmc1_pre_inst_reach_state false
% 149.95/150.60 % --bmc1_out_unsat_core false
% 149.95/150.60 % --bmc1_aig_witness_out false
% 149.95/150.60 % --bmc1_verbose false
% 149.95/150.60 % --bmc1_dump_clauses_tptp false
% 158.82/159.45 % --bmc1_dump_unsat_core_tptp false
% 158.82/159.45 % --bmc1_dump_file -
% 158.82/159.45 % --bmc1_ucm_expand_uc_limit 128
% 158.82/159.45 % --bmc1_ucm_n_expand_iterations 6
% 158.82/159.45 % --bmc1_ucm_extend_mode 1
% 158.82/159.45 % --bmc1_ucm_init_mode 2
% 158.82/159.45 % --bmc1_ucm_cone_mode none
% 158.82/159.45 % --bmc1_ucm_reduced_relation_type 0
% 158.82/159.45 % --bmc1_ucm_relax_model 4
% 158.82/159.45 % --bmc1_ucm_full_tr_after_sat true
% 158.82/159.45 % --bmc1_ucm_expand_neg_assumptions false
% 158.82/159.45 % --bmc1_ucm_layered_model none
% 158.82/159.45 % --bmc1_ucm_max_lemma_size 10
% 158.82/159.45
% 158.82/159.45 % ------ AIG Options
% 158.82/159.45
% 158.82/159.45 % --aig_mode false
% 158.82/159.45
% 158.82/159.45 % ------ Instantiation Options
% 158.82/159.45
% 158.82/159.45 % --instantiation_flag true
% 158.82/159.45 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 158.82/159.45 % --inst_solver_per_active 750
% 158.82/159.45 % --inst_solver_calls_frac 0.5
% 158.82/159.45 % --inst_passive_queue_type priority_queues
% 158.82/159.45 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 158.82/159.45 % --inst_passive_queues_freq [25;2]
% 158.82/159.45 % --inst_dismatching true
% 158.82/159.45 % --inst_eager_unprocessed_to_passive true
% 158.82/159.45 % --inst_prop_sim_given true
% 158.82/159.45 % --inst_prop_sim_new false
% 158.82/159.45 % --inst_orphan_elimination true
% 158.82/159.45 % --inst_learning_loop_flag true
% 158.82/159.45 % --inst_learning_start 3000
% 158.82/159.45 % --inst_learning_factor 2
% 158.82/159.45 % --inst_start_prop_sim_after_learn 3
% 158.82/159.45 % --inst_sel_renew solver
% 158.82/159.45 % --inst_lit_activity_flag true
% 158.82/159.45 % --inst_out_proof true
% 158.82/159.45
% 158.82/159.45 % ------ Resolution Options
% 158.82/159.45
% 158.82/159.45 % --resolution_flag true
% 158.82/159.45 % --res_lit_sel kbo_max
% 158.82/159.45 % --res_to_prop_solver none
% 158.82/159.45 % --res_prop_simpl_new false
% 158.82/159.45 % --res_prop_simpl_given false
% 158.82/159.45 % --res_passive_queue_type priority_queues
% 158.82/159.45 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 158.82/159.45 % --res_passive_queues_freq [15;5]
% 158.82/159.45 % --res_forward_subs full
% 158.82/159.45 % --res_backward_subs full
% 158.82/159.45 % --res_forward_subs_resolution true
% 158.82/159.45 % --res_backward_subs_resolution true
% 158.82/159.45 % --res_orphan_elimination false
% 158.82/159.45 % --res_time_limit 1000.
% 158.82/159.45 % --res_out_proof true
% 158.82/159.45 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8e2efe.s
% 158.82/159.45 % --modulo true
% 158.82/159.45
% 158.82/159.45 % ------ Combination Options
% 158.82/159.45
% 158.82/159.45 % --comb_res_mult 1000
% 158.82/159.45 % --comb_inst_mult 300
% 158.82/159.45 % ------
% 158.82/159.45
% 158.82/159.45 % ------ Parsing...% successful
% 158.82/159.45
% 158.82/159.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 158.82/159.45
% 158.82/159.45 % ------ Proving...
% 158.82/159.45 % ------ Problem Properties
% 158.82/159.45
% 158.82/159.45 %
% 158.82/159.45 % EPR false
% 158.82/159.45 % Horn false
% 158.82/159.45 % Has equality true
% 158.82/159.45
% 158.82/159.45 % % ------ Input Options Time Limit: Unbounded
% 158.82/159.45
% 158.82/159.45
% 158.82/159.45 Compiling...
% 158.82/159.45 Loading plugin: done.
% 158.82/159.45 Compiling...
% 158.82/159.45 Loading plugin: done.
% 158.82/159.45 Compiling...
% 158.82/159.45 Loading plugin: done.
% 158.82/159.45 Compiling...
% 158.82/159.45 Loading plugin: done.
% 158.82/159.45 Compiling...
% 158.82/159.45 Loading plugin: done.
% 158.82/159.45 % % ------ Current options:
% 158.82/159.45
% 158.82/159.45 % ------ Input Options
% 158.82/159.45
% 158.82/159.45 % --out_options all
% 158.82/159.45 % --tptp_safe_out true
% 158.82/159.45 % --problem_path ""
% 158.82/159.45 % --include_path ""
% 158.82/159.45 % --clausifier .//eprover
% 158.82/159.45 % --clausifier_options --tstp-format
% 158.82/159.45 % --stdin false
% 158.82/159.45 % --dbg_backtrace false
% 158.82/159.45 % --dbg_dump_prop_clauses false
% 158.82/159.45 % --dbg_dump_prop_clauses_file -
% 158.82/159.45 % --dbg_out_stat false
% 158.82/159.45
% 158.82/159.45 % ------ General Options
% 158.82/159.45
% 158.82/159.45 % --fof false
% 158.82/159.45 % --time_out_real 150.
% 158.82/159.45 % --time_out_prep_mult 0.2
% 158.82/159.45 % --time_out_virtual -1.
% 158.82/159.45 % --schedule none
% 158.82/159.45 % --ground_splitting input
% 158.82/159.45 % --splitting_nvd 16
% 158.82/159.45 % --non_eq_to_eq false
% 158.82/159.45 % --prep_gs_sim true
% 158.82/159.45 % --prep_unflatten false
% 158.82/159.45 % --prep_res_sim true
% 158.82/159.45 % --prep_upred true
% 158.82/159.45 % --res_sim_input true
% 158.82/159.45 % --clause_weak_htbl true
% 158.82/159.45 % --gc_record_bc_elim false
% 158.82/159.45 % --symbol_type_check false
% 158.82/159.45 % --clausify_out false
% 158.82/159.45 % --large_theory_mode false
% 158.82/159.45 % --prep_sem_filter none
% 158.82/159.45 % --prep_sem_filter_out false
% 158.82/159.45 % --preprocessed_out false
% 158.82/159.45 % --sub_typing false
% 158.82/159.45 % --brand_transform false
% 158.82/159.45 % --pure_diseq_elim true
% 158.82/159.45 % --min_unsat_core false
% 158.82/159.45 % --pred_elim true
% 158.82/159.45 % --add_important_lit false
% 158.82/159.45 % --soft_assumptions false
% 158.82/159.45 % --reset_solvers false
% 158.82/159.45 % --bc_imp_inh []
% 158.82/159.45 % --conj_cone_tolerance 1.5
% 158.82/159.45 % --prolific_symb_bound 500
% 158.82/159.45 % --lt_threshold 2000
% 158.82/159.45
% 158.82/159.45 % ------ SAT Options
% 158.82/159.45
% 158.82/159.45 % --sat_mode false
% 158.82/159.45 % --sat_fm_restart_options ""
% 158.82/159.45 % --sat_gr_def false
% 158.82/159.45 % --sat_epr_types true
% 158.82/159.45 % --sat_non_cyclic_types false
% 158.82/159.45 % --sat_finite_models false
% 158.82/159.45 % --sat_fm_lemmas false
% 158.82/159.45 % --sat_fm_prep false
% 158.82/159.45 % --sat_fm_uc_incr true
% 158.82/159.45 % --sat_out_model small
% 158.82/159.45 % --sat_out_clauses false
% 158.82/159.45
% 158.82/159.45 % ------ QBF Options
% 158.82/159.45
% 158.82/159.45 % --qbf_mode false
% 158.82/159.45 % --qbf_elim_univ true
% 158.82/159.45 % --qbf_sk_in true
% 158.82/159.45 % --qbf_pred_elim true
% 158.82/159.45 % --qbf_split 32
% 158.82/159.45
% 158.82/159.45 % ------ BMC1 Options
% 158.82/159.45
% 158.82/159.45 % --bmc1_incremental false
% 158.82/159.45 % --bmc1_axioms reachable_all
% 158.82/159.45 % --bmc1_min_bound 0
% 158.82/159.45 % --bmc1_max_bound -1
% 158.82/159.45 % --bmc1_max_bound_default -1
% 158.82/159.45 % --bmc1_symbol_reachability true
% 158.82/159.45 % --bmc1_property_lemmas false
% 158.82/159.45 % --bmc1_k_induction false
% 158.82/159.45 % --bmc1_non_equiv_states false
% 158.82/159.45 % --bmc1_deadlock false
% 158.82/159.45 % --bmc1_ucm false
% 158.82/159.45 % --bmc1_add_unsat_core none
% 158.82/159.45 % --bmc1_unsat_core_children false
% 158.82/159.45 % --bmc1_unsat_core_extrapolate_axioms false
% 158.82/159.45 % --bmc1_out_stat full
% 158.82/159.45 % --bmc1_ground_init false
% 158.82/159.45 % --bmc1_pre_inst_next_state false
% 158.82/159.45 % --bmc1_pre_inst_state false
% 158.82/159.45 % --bmc1_pre_inst_reach_state false
% 158.82/159.45 % --bmc1_out_unsat_core false
% 158.82/159.45 % --bmc1_aig_witness_out false
% 158.82/159.45 % --bmc1_verbose false
% 158.82/159.45 % --bmc1_dump_clauses_tptp false
% 158.82/159.45 % --bmc1_dump_unsat_core_tptp false
% 158.82/159.45 % --bmc1_dump_file -
% 158.82/159.45 % --bmc1_ucm_expand_uc_limit 128
% 158.82/159.45 % --bmc1_ucm_n_expand_iterations 6
% 158.82/159.45 % --bmc1_ucm_extend_mode 1
% 158.82/159.45 % --bmc1_ucm_init_mode 2
% 158.82/159.45 % --bmc1_ucm_cone_mode none
% 158.82/159.45 % --bmc1_ucm_reduced_relation_type 0
% 158.82/159.45 % --bmc1_ucm_relax_model 4
% 158.82/159.45 % --bmc1_ucm_full_tr_after_sat true
% 158.82/159.45 % --bmc1_ucm_expand_neg_assumptions false
% 158.82/159.45 % --bmc1_ucm_layered_model none
% 158.82/159.45 % --bmc1_ucm_max_lemma_size 10
% 158.82/159.45
% 158.82/159.45 % ------ AIG Options
% 158.82/159.45
% 158.82/159.45 % --aig_mode false
% 158.82/159.45
% 158.82/159.45 % ------ Instantiation Options
% 158.82/159.45
% 158.82/159.45 % --instantiation_flag true
% 158.82/159.45 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 158.82/159.45 % --inst_solver_per_active 750
% 158.82/159.45 % --inst_solver_calls_frac 0.5
% 158.82/159.45 % --inst_passive_queue_type priority_queues
% 158.82/159.45 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 172.85/173.49 % --inst_passive_queues_freq [25;2]
% 172.85/173.49 % --inst_dismatching true
% 172.85/173.49 % --inst_eager_unprocessed_to_passive true
% 172.85/173.49 % --inst_prop_sim_given true
% 172.85/173.49 % --inst_prop_sim_new false
% 172.85/173.49 % --inst_orphan_elimination true
% 172.85/173.49 % --inst_learning_loop_flag true
% 172.85/173.49 % --inst_learning_start 3000
% 172.85/173.49 % --inst_learning_factor 2
% 172.85/173.49 % --inst_start_prop_sim_after_learn 3
% 172.85/173.49 % --inst_sel_renew solver
% 172.85/173.49 % --inst_lit_activity_flag true
% 172.85/173.49 % --inst_out_proof true
% 172.85/173.49
% 172.85/173.49 % ------ Resolution Options
% 172.85/173.49
% 172.85/173.49 % --resolution_flag true
% 172.85/173.49 % --res_lit_sel kbo_max
% 172.85/173.49 % --res_to_prop_solver none
% 172.85/173.49 % --res_prop_simpl_new false
% 172.85/173.49 % --res_prop_simpl_given false
% 172.85/173.49 % --res_passive_queue_type priority_queues
% 172.85/173.49 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 172.85/173.49 % --res_passive_queues_freq [15;5]
% 172.85/173.49 % --res_forward_subs full
% 172.85/173.49 % --res_backward_subs full
% 172.85/173.49 % --res_forward_subs_resolution true
% 172.85/173.49 % --res_backward_subs_resolution true
% 172.85/173.49 % --res_orphan_elimination false
% 172.85/173.49 % --res_time_limit 1000.
% 172.85/173.49 % --res_out_proof true
% 172.85/173.49 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8e2efe.s
% 172.85/173.49 % --modulo true
% 172.85/173.49
% 172.85/173.49 % ------ Combination Options
% 172.85/173.49
% 172.85/173.49 % --comb_res_mult 1000
% 172.85/173.49 % --comb_inst_mult 300
% 172.85/173.49 % ------
% 172.85/173.49
% 172.85/173.49
% 172.85/173.49
% 172.85/173.49 % ------ Proving...
% 172.85/173.49 %
% 172.85/173.49
% 172.85/173.49
% 172.85/173.49 % Resolution empty clause
% 172.85/173.49
% 172.85/173.49 % ------ Statistics
% 172.85/173.49
% 172.85/173.49 % ------ General
% 172.85/173.49
% 172.85/173.49 % num_of_input_clauses: 390
% 172.85/173.49 % num_of_input_neg_conjectures: 1
% 172.85/173.49 % num_of_splits: 0
% 172.85/173.49 % num_of_split_atoms: 0
% 172.85/173.49 % num_of_sem_filtered_clauses: 0
% 172.85/173.49 % num_of_subtypes: 0
% 172.85/173.49 % monotx_restored_types: 0
% 172.85/173.49 % sat_num_of_epr_types: 0
% 172.85/173.49 % sat_num_of_non_cyclic_types: 0
% 172.85/173.49 % sat_guarded_non_collapsed_types: 0
% 172.85/173.49 % is_epr: 0
% 172.85/173.49 % is_horn: 0
% 172.85/173.49 % has_eq: 1
% 172.85/173.49 % num_pure_diseq_elim: 0
% 172.85/173.49 % simp_replaced_by: 0
% 172.85/173.49 % res_preprocessed: 17
% 172.85/173.49 % prep_upred: 0
% 172.85/173.49 % prep_unflattend: 0
% 172.85/173.49 % pred_elim_cands: 0
% 172.85/173.49 % pred_elim: 0
% 172.85/173.49 % pred_elim_cl: 0
% 172.85/173.49 % pred_elim_cycles: 0
% 172.85/173.49 % forced_gc_time: 0
% 172.85/173.49 % gc_basic_clause_elim: 0
% 172.85/173.49 % parsing_time: 0.024
% 172.85/173.49 % sem_filter_time: 0.
% 172.85/173.49 % pred_elim_time: 0.
% 172.85/173.49 % out_proof_time: 0.003
% 172.85/173.49 % monotx_time: 0.
% 172.85/173.49 % subtype_inf_time: 0.
% 172.85/173.49 % unif_index_cands_time: 0.075
% 172.85/173.49 % unif_index_add_time: 0.034
% 172.85/173.49 % total_time: 22.905
% 172.85/173.49 % num_of_symbols: 74
% 172.85/173.49 % num_of_terms: 107409
% 172.85/173.49
% 172.85/173.49 % ------ Propositional Solver
% 172.85/173.49
% 172.85/173.49 % prop_solver_calls: 6
% 172.85/173.49 % prop_fast_solver_calls: 37
% 172.85/173.49 % prop_num_of_clauses: 3812
% 172.85/173.49 % prop_preprocess_simplified: 5224
% 172.85/173.49 % prop_fo_subsumed: 0
% 172.85/173.49 % prop_solver_time: 0.
% 172.85/173.49 % prop_fast_solver_time: 0.
% 172.85/173.49 % prop_unsat_core_time: 0.
% 172.85/173.49
% 172.85/173.49 % ------ QBF
% 172.85/173.49
% 172.85/173.49 % qbf_q_res: 0
% 172.85/173.49 % qbf_num_tautologies: 0
% 172.85/173.49 % qbf_prep_cycles: 0
% 172.85/173.49
% 172.85/173.49 % ------ BMC1
% 172.85/173.49
% 172.85/173.49 % bmc1_current_bound: -1
% 172.85/173.49 % bmc1_last_solved_bound: -1
% 172.85/173.49 % bmc1_unsat_core_size: -1
% 172.85/173.49 % bmc1_unsat_core_parents_size: -1
% 172.85/173.49 % bmc1_merge_next_fun: 0
% 172.85/173.49 % bmc1_unsat_core_clauses_time: 0.
% 172.85/173.49
% 172.85/173.49 % ------ Instantiation
% 172.85/173.49
% 172.85/173.49 % inst_num_of_clauses: 2344
% 172.85/173.49 % inst_num_in_passive: 969
% 172.85/173.49 % inst_num_in_active: 817
% 172.85/173.49 % inst_num_in_unprocessed: 554
% 172.85/173.49 % inst_num_of_loops: 900
% 172.85/173.49 % inst_num_of_learning_restarts: 0
% 172.85/173.49 % inst_num_moves_active_passive: 78
% 172.85/173.49 % inst_lit_activity: 181
% 172.85/173.49 % inst_lit_activity_moves: 0
% 172.85/173.49 % inst_num_tautologies: 4
% 172.85/173.49 % inst_num_prop_implied: 0
% 172.85/173.49 % inst_num_existing_simplified: 0
% 172.85/173.49 % inst_num_eq_res_simplified: 0
% 172.85/173.49 % inst_num_child_elim: 0
% 172.85/173.49 % inst_num_of_dismatching_blockings: 6344
% 172.85/173.49 % inst_num_of_non_proper_insts: 3615
% 172.85/173.49 % inst_num_of_duplicates: 2552
% 172.85/173.49 % inst_inst_num_from_inst_to_res: 0
% 172.85/173.49 % inst_dismatching_checking_time: 0.018
% 172.85/173.49
% 172.85/173.49 % ------ Resolution
% 172.85/173.49
% 172.85/173.49 % res_num_of_clauses: 30916
% 172.85/173.49 % res_num_in_passive: 28094
% 172.85/173.49 % res_num_in_active: 2667
% 172.85/173.49 % res_num_of_loops: 3548
% 172.85/173.49 % res_forward_subset_subsumed: 17883
% 172.85/173.49 % res_backward_subset_subsumed: 88
% 172.85/173.49 % res_forward_subsumed: 1020
% 172.85/173.49 % res_backward_subsumed: 3
% 172.85/173.49 % res_forward_subsumption_resolution: 14
% 172.85/173.49 % res_backward_subsumption_resolution: 0
% 172.85/173.49 % res_clause_to_clause_subsumption: 9805
% 172.85/173.49 % res_orphan_elimination: 0
% 172.85/173.49 % res_tautology_del: 460
% 172.85/173.49 % res_num_eq_res_simplified: 0
% 172.85/173.49 % res_num_sel_changes: 0
% 172.85/173.49 % res_moves_from_active_to_pass: 0
% 172.85/173.49
% 172.85/173.49 % Status Unsatisfiable
% 172.85/173.49 % SZS status Theorem
% 172.85/173.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------