%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW473+5 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:32:34 PM UTC 2026
% Result : Theorem 1.06s 1.66s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_240)
% Comments :
%------------------------------------------------------------------------------
fof(fact_92_imageE,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_imageE) ).
fof(fact_62_insert__ident,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_insert__ident) ).
fof(fact_53_insertCI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insertCI) ).
fof(fact_73_equalityE,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_equalityE) ).
fof(help_fequal_1_1_T,axiom,
! [X3,X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22))
| ti(X3,X21) = ti(X3,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
fof(fact_49_pigeonhole__infinite,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pigeonhole__infinite) ).
fof(fact_47_finite__subset__image,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite__subset__image) ).
fof(help_COMBI_1_1_U,axiom,
! [X3,X53] : hAPP(X3,X3,combi(X3),X53) = ti(X3,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(fact_90_subset__image__iff,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_subset__image__iff) ).
fof(fact_85_subset__insert,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subset__insert) ).
fof(fact_77_image__iff,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_image__iff) ).
fof(fact_6_card__seteq,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_card__seteq) ).
fof(fact_60_insert__iff,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_insert__iff) ).
fof(fact_54_insertE,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_insertE) ).
fof(fact_50_image__eqI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_image__eqI) ).
fof(fact_79_rev__image__eqI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_rev__image__eqI) ).
fof(fact_61_insert__code,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_insert__code) ).
fof(fact_35_not__less__eq__eq,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_not__less__eq__eq) ).
fof(fact_66_set__eq__subset,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_set__eq__subset) ).
fof(fact_51_equalityI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_equalityI) ).
fof(fact_8_card__insert__if,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_card__insert__if) ).
fof(fact_9_card__insert__disjoint,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_card__insert__disjoint) ).
fof(fact_31_le__SucE,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__SucE) ).
fof(fact_36_Suc__n__not__le__n,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Suc__n__not__le__n) ).
fof(fact_64_insert__absorb,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_insert__absorb) ).
fof(fact_67_equalityD1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_equalityD1) ).
fof(fact_68_equalityD2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_equalityD2) ).
fof(fact_74_ext,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
fof(help_fimplies_3_1_U,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54))
| ~ hBOOL(X53)
| hBOOL(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(help_fdisj_3_1_U,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54))
| hBOOL(X53)
| hBOOL(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
fof(help_fequal_2_1_T,axiom,
! [X3,X21,X22] :
( ti(X3,X21) != ti(X3,X22)
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
fof(tsy_c_COMBS_res,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('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
fof(tsy_c_COMBC_res,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('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
fof(tsy_c_COMBB_res,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('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
fof(help_fconj_1_1_U,axiom,
! [X54,X53] :
( ~ hBOOL(X53)
| ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fimplies_2_1_U,axiom,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(help_fdisj_1_1_U,axiom,
! [X54,X53] :
( ~ hBOOL(X53)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(help_fdisj_2_1_U,axiom,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
fof(tsy_c_Set_Oimage_res,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
fof(fact_82_image__ident,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_image__ident) ).
fof(tsy_c_Set_Oinsert_res,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
fof(tsy_c_hAPP_arg1,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(help_ti_idem,axiom,
! [X51,X52] : ti(X51,ti(X51,X52)) = ti(X51,X52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
fof(tsy_c_hAPP_arg2,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,X4,ti(X3,X5)) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(tsy_c_hAPP_res,axiom,
! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(tsy_c_member_res,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [X4] :
( hBOOL(ti(bool,X4))
<=> hBOOL(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(help_fNot_1_1_U,axiom,
! [X53] :
( ~ hBOOL(hAPP(bool,bool,fNot,X53))
| ~ hBOOL(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(tsy_c_Set_OCollect_res,axiom,
! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
fof(fact_76_Collect__def,axiom,
! [X1,X16] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = ti(fun(X1,bool),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
! [X3] :
( preorder(X3)
=> ti(fun(X3,fun(X3,bool)),ord_less_eq(X3)) = ord_less_eq(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(tsy_c_fequal_res,axiom,
! [X3] : ti(fun(X3,fun(X3,bool)),fequal(X3)) = fequal(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
fof(tsy_c_Finite__Set_Ocard_res,axiom,
! [X2] : ti(fun(fun(X2,bool),nat),finite_card(X2)) = finite_card(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).
fof(tsy_c_Finite__Set_Ofinite_res,axiom,
! [X1] : ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
fof(tsy_c_COMBI_res,axiom,
! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
fof(tsy_c_HOL_Oundefined_res,axiom,
! [X3] : ti(X3,undefined(X3)) = undefined(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(fact_26_finite__Collect__disjI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__Collect__disjI) ).
fof(fact_57_insert__Collect,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_insert__Collect) ).
fof(fact_10_finite__Collect__conjI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Collect__conjI) ).
fof(fact_96_image__subsetI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_image__subsetI) ).
fof(fact_80_insert__compr__raw,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_insert__compr__raw) ).
fof(fact_56_insert__compr,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_insert__compr) ).
fof(conj_6,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/sandbox/benchmark/theBenchmark.p',conj_6) ).
fof(fact_48_lift__Suc__mono__le,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lift__Suc__mono__le) ).
fof(fact_4_card__image__le,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_card__image__le) ).
fof(fact_39_le__diff__iff,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__diff__iff) ).
fof(fact_1_finite__Collect__subsets,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
fof(fact_91_image__mono,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_image__mono) ).
fof(fact_84_insert__subset,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__subset) ).
fof(fact_87_insert__mono,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_insert__mono) ).
fof(fact_7_card__insert__le,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_card__insert__le) ).
fof(fact_43_diff__le__mono,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_diff__le__mono) ).
fof(fact_44_diff__le__mono2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_diff__le__mono2) ).
fof(fact_37_Suc__diff__diff,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Suc__diff__diff) ).
fof(fact_46_finite__surj,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_finite__surj) ).
fof(fact_12_finite__Collect__le__nat,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__le__nat) ).
fof(fact_78_imageI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_imageI) ).
fof(fact_40_Nat_Odiff__diff__eq,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).
fof(fact_81_image__image,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_image__image) ).
fof(fact_86_subset__insertI2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_subset__insertI2) ).
fof(fact_5_card__mono,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_card__mono) ).
fof(fact_63_insertI2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_insertI2) ).
fof(fact_72_subset__trans,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_subset__trans) ).
fof(fact_33_Suc__le__mono,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Suc__le__mono) ).
fof(fact_89_insert__image,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__image) ).
fof(fact_70_set__rev__mp,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_set__rev__mp) ).
fof(fact_71_set__mp,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_set__mp) ).
fof(fact_69_in__mono,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_in__mono) ).
fof(fact_52_subsetD,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subsetD) ).
fof(fact_27_finite__insert,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite__insert) ).
fof(fact_45_diff__le__self,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_diff__le__self) ).
fof(fact_25_diff__commute,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_diff__commute) ).
fof(fact_88_image__insert,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_image__insert) ).
fof(fact_41_eq__diff__iff,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_eq__diff__iff) ).
fof(fact_30_Suc__leD,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Suc__leD) ).
fof(fact_21_le__trans,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_le__trans) ).
fof(fact_94_zero__induct__lemma,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__induct__lemma) ).
fof(fact_83_subset__insertI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_subset__insertI) ).
fof(fact_59_insert__commute,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_insert__commute) ).
fof(fact_11_Suc__diff__le,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Suc__diff__le) ).
fof(fact_55_insertI1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_insertI1) ).
fof(fact_13_card__Collect__le__nat,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_card__Collect__le__nat) ).
fof(fact_2_finite__imageI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__imageI) ).
fof(conj_5,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('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
fof(fact_34_le__Suc__eq,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_le__Suc__eq) ).
fof(fact_95_Suc__le__D,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Suc__le__D) ).
fof(fact_93_subsetI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_subsetI) ).
fof(fact_3_finite_OinsertI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite_OinsertI) ).
fof(fact_98_finite__nat__set__iff__bounded__le,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).
fof(fact_0_assms_I1_J,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
fof(fact_32_le__SucI,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_le__SucI) ).
fof(fact_20_le__antisym,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_le__antisym) ).
fof(fact_42_diff__diff__cancel,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_diff__diff__cancel) ).
fof(fact_28_finite__subset,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite__subset) ).
fof(fact_29_rev__finite__subset,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
fof(help_COMBS_1_1_U,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('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
fof(fact_58_insert__absorb2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_insert__absorb2) ).
fof(help_COMBB_1_1_U,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('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
fof(help_COMBC_1_1_U,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('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
fof(fact_75_mem__def,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
fof(fact_23_nat__le__linear,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nat__le__linear) ).
fof(fact_38_diff__Suc__Suc,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_diff__Suc__Suc) ).
fof(fact_65_subset__refl,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_subset__refl) ).
fof(fact_97_order__refl,axiom,
! [X3] :
( preorder(X3)
=> ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_order__refl) ).
fof(fact_22_eq__imp__le,axiom,
! [X18,X17] :
( X18 = X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_eq__imp__le) ).
fof(fact_24_le__refl,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_le__refl) ).
fof(help_fimplies_1_1_U,axiom,
! [X54,X53] :
( hBOOL(X53)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(tsy_v_P_res,axiom,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_P_res) ).
fof(fact_17_nat_Oinject,axiom,
! [X23,X24] :
( hAPP(nat,nat,suc,X23) = hAPP(nat,nat,suc,X24)
<=> X23 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
fof(fact_16_Suc__inject,axiom,
! [X21,X22] :
( hAPP(nat,nat,suc,X21) = hAPP(nat,nat,suc,X22)
=> X21 = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Suc__inject) ).
fof(fact_15_finite,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite) ).
fof(fact_14_finite__code,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__code) ).
fof(tsy_c_Groups_Ominus__class_Ominus_res,hypothesis,
ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
fof(tsy_c_fimplies_res,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
fof(tsy_c_fdisj_res,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
fof(tsy_c_fconj_res,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
fof(help_fNot_2_1_U,axiom,
! [X53] :
( hBOOL(X53)
| hBOOL(hAPP(bool,bool,fNot,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(fact_18_Suc__n__not__n,axiom,
! [X17] : hAPP(nat,nat,suc,X17) != X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Suc__n__not__n) ).
fof(fact_19_n__not__Suc__n,axiom,
! [X17] : X17 != hAPP(nat,nat,suc,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n__not__Suc__n) ).
fof(tsy_v_mgt__call_res,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_mgt__call_res) ).
fof(tsy_v_U_res,hypothesis,
ti(fun(pname,bool),u) = u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_U_res) ).
fof(tsy_v_G_res,hypothesis,
ti(fun(x_a,bool),g) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_G_res) ).
fof(tsy_c_Nat_OSuc_res,hypothesis,
ti(fun(nat,nat),suc) = suc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).
fof(tsy_c_fNot_res,axiom,
ti(fun(bool,bool),fNot) = fNot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
fof(tsy_v_pn_res,hypothesis,
ti(pname,pn) = pn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_pn_res) ).
fof(tsy_v_na_res,hypothesis,
ti(nat,na) = na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_na_res) ).
fof(arity_fun___Finite__Set_Ofinite,axiom,
! [X49,X50] :
( ( finite_finite_1(X50)
& finite_finite_1(X49) )
=> finite_finite_1(fun(X49,X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
fof(arity_fun___Orderings_Oorder,axiom,
! [X49,X50] :
( order(X50)
=> order(fun(X49,X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
fof(arity_fun___Orderings_Opreorder,axiom,
! [X49,X50] :
( preorder(X50)
=> preorder(fun(X49,X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
fof(conj_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(conj_3,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('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(conj_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(conj_4,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(conj_0,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(arity_Nat_Onat___Orderings_Oorder,axiom,
order(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
fof(arity_HOL_Obool___Orderings_Oorder,axiom,
order(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
finite_finite_1(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(arity_Nat_Onat___Orderings_Opreorder,axiom,
preorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
fof(arity_HOL_Obool___Orderings_Opreorder,axiom,
preorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
fof(i_0_161,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)],[fact_92_imageE]) ).
fof(i_0_162,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)],[fact_62_insert__ident]) ).
fof(i_0_163,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)],[fact_53_insertCI]) ).
fof(i_0_164,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)],[fact_73_equalityE]) ).
fof(i_0_165,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)],[help_fequal_1_1_T]) ).
fof(i_0_166,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)],[fact_49_pigeonhole__infinite]) ).
fof(i_0_167,plain,
! [X612,X613,X614,X615,X616] :
( ( hBOOL(hAPP(fun(X612,bool),bool,hAPP(fun(X612,bool),fun(fun(X612,bool),bool),ord_less_eq(fun(X612,bool)),esk1_5(X612,X613,X614,X615,X616)),X615))
| ~ hBOOL(hAPP(fun(X613,bool),bool,hAPP(fun(X613,bool),fun(fun(X613,bool),bool),ord_less_eq(fun(X613,bool)),X616),hAPP(fun(X612,bool),fun(X613,bool),hAPP(fun(X612,X613),fun(fun(X612,bool),fun(X613,bool)),image(X612,X613),X614),X615)))
| ~ hBOOL(hAPP(fun(X613,bool),bool,finite_finite(X613),X616)) )
& ( hBOOL(hAPP(fun(X612,bool),bool,finite_finite(X612),esk1_5(X612,X613,X614,X615,X616)))
| ~ hBOOL(hAPP(fun(X613,bool),bool,hAPP(fun(X613,bool),fun(fun(X613,bool),bool),ord_less_eq(fun(X613,bool)),X616),hAPP(fun(X612,bool),fun(X613,bool),hAPP(fun(X612,X613),fun(fun(X612,bool),fun(X613,bool)),image(X612,X613),X614),X615)))
| ~ hBOOL(hAPP(fun(X613,bool),bool,finite_finite(X613),X616)) )
& ( ti(fun(X613,bool),X616) = hAPP(fun(X612,bool),fun(X613,bool),hAPP(fun(X612,X613),fun(fun(X612,bool),fun(X613,bool)),image(X612,X613),X614),esk1_5(X612,X613,X614,X615,X616))
| ~ hBOOL(hAPP(fun(X613,bool),bool,hAPP(fun(X613,bool),fun(fun(X613,bool),bool),ord_less_eq(fun(X613,bool)),X616),hAPP(fun(X612,bool),fun(X613,bool),hAPP(fun(X612,X613),fun(fun(X612,bool),fun(X613,bool)),image(X612,X613),X614),X615)))
| ~ hBOOL(hAPP(fun(X613,bool),bool,finite_finite(X613),X616)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_47_finite__subset__image])])])]) ).
fof(i_0_168,plain,
! [X857,X858] : hAPP(X857,X857,combi(X857),X858) = ti(X857,X858),
inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).
fof(i_0_169,plain,
! [X787,X788,X789,X790,X791,X793,X794,X795,X796,X797,X798] :
( ( hBOOL(hAPP(fun(X788,bool),bool,hAPP(fun(X788,bool),fun(fun(X788,bool),bool),ord_less_eq(fun(X788,bool)),esk6_5(X787,X788,X789,X790,X791)),X791))
| ~ hBOOL(hAPP(fun(X787,bool),bool,hAPP(fun(X787,bool),fun(fun(X787,bool),bool),ord_less_eq(fun(X787,bool)),X789),hAPP(fun(X788,bool),fun(X787,bool),hAPP(fun(X788,X787),fun(fun(X788,bool),fun(X787,bool)),image(X788,X787),X790),X791))) )
& ( ti(fun(X787,bool),X789) = hAPP(fun(X788,bool),fun(X787,bool),hAPP(fun(X788,X787),fun(fun(X788,bool),fun(X787,bool)),image(X788,X787),X790),esk6_5(X787,X788,X789,X790,X791))
| ~ hBOOL(hAPP(fun(X787,bool),bool,hAPP(fun(X787,bool),fun(fun(X787,bool),bool),ord_less_eq(fun(X787,bool)),X789),hAPP(fun(X788,bool),fun(X787,bool),hAPP(fun(X788,X787),fun(fun(X788,bool),fun(X787,bool)),image(X788,X787),X790),X791))) )
& ( ~ hBOOL(hAPP(fun(X794,bool),bool,hAPP(fun(X794,bool),fun(fun(X794,bool),bool),ord_less_eq(fun(X794,bool)),X798),X797))
| ti(fun(X793,bool),X795) != hAPP(fun(X794,bool),fun(X793,bool),hAPP(fun(X794,X793),fun(fun(X794,bool),fun(X793,bool)),image(X794,X793),X796),X798)
| hBOOL(hAPP(fun(X793,bool),bool,hAPP(fun(X793,bool),fun(fun(X793,bool),bool),ord_less_eq(fun(X793,bool)),X795),hAPP(fun(X794,bool),fun(X793,bool),hAPP(fun(X794,X793),fun(fun(X794,bool),fun(X793,bool)),image(X794,X793),X796),X797))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_subset__image__iff])])])])])]) ).
fof(i_0_170,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)],[fact_85_subset__insert]) ).
fof(i_0_171,plain,
! [X804,X805,X806,X807,X808] :
( ( ti(X804,X806) = hAPP(X805,X804,X807,esk7_5(X804,X805,X806,X807,X808))
| ~ hBOOL(hAPP(fun(X804,bool),bool,hAPP(X804,fun(fun(X804,bool),bool),member(X804),X806),hAPP(fun(X805,bool),fun(X804,bool),hAPP(fun(X805,X804),fun(fun(X805,bool),fun(X804,bool)),image(X805,X804),X807),X808))) )
& ( hBOOL(hAPP(fun(X805,bool),bool,hAPP(X805,fun(fun(X805,bool),bool),member(X805),esk7_5(X804,X805,X806,X807,X808)),X808))
| ~ hBOOL(hAPP(fun(X804,bool),bool,hAPP(X804,fun(fun(X804,bool),bool),member(X804),X806),hAPP(fun(X805,bool),fun(X804,bool),hAPP(fun(X805,X804),fun(fun(X805,bool),fun(X804,bool)),image(X805,X804),X807),X808))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_161])])])]) ).
fof(i_0_172,plain,
! [X724,X725,X726,X727,X728,X730,X731,X732,X733,X734,X735] :
( ( hBOOL(hAPP(fun(X725,bool),bool,hAPP(X725,fun(fun(X725,bool),bool),member(X725),esk5_5(X724,X725,X726,X727,X728)),X728))
| ~ hBOOL(hAPP(fun(X724,bool),bool,hAPP(X724,fun(fun(X724,bool),bool),member(X724),X726),hAPP(fun(X725,bool),fun(X724,bool),hAPP(fun(X725,X724),fun(fun(X725,bool),fun(X724,bool)),image(X725,X724),X727),X728))) )
& ( ti(X724,X726) = hAPP(X725,X724,X727,esk5_5(X724,X725,X726,X727,X728))
| ~ hBOOL(hAPP(fun(X724,bool),bool,hAPP(X724,fun(fun(X724,bool),bool),member(X724),X726),hAPP(fun(X725,bool),fun(X724,bool),hAPP(fun(X725,X724),fun(fun(X725,bool),fun(X724,bool)),image(X725,X724),X727),X728))) )
& ( ~ hBOOL(hAPP(fun(X731,bool),bool,hAPP(X731,fun(fun(X731,bool),bool),member(X731),X735),X734))
| ti(X730,X732) != hAPP(X731,X730,X733,X735)
| hBOOL(hAPP(fun(X730,bool),bool,hAPP(X730,fun(fun(X730,bool),bool),member(X730),X732),hAPP(fun(X731,bool),fun(X730,bool),hAPP(fun(X731,X730),fun(fun(X731,bool),fun(X730,bool)),image(X731,X730),X733),X734))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_77_image__iff])])])])])]) ).
fof(i_0_173,plain,
! [X516,X517,X518] :
( ~ hBOOL(hAPP(fun(X516,bool),bool,finite_finite(X516),X518))
| ~ hBOOL(hAPP(fun(X516,bool),bool,hAPP(fun(X516,bool),fun(fun(X516,bool),bool),ord_less_eq(fun(X516,bool)),X517),X518))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X516,bool),nat,finite_card(X516),X518)),hAPP(fun(X516,bool),nat,finite_card(X516),X517)))
| ti(fun(X516,bool),X517) = ti(fun(X516,bool),X518) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_card__seteq])]) ).
fof(i_0_174,plain,
! [X665,X666,X667,X668] :
( ( ~ hBOOL(hAPP(fun(X665,bool),bool,hAPP(X665,fun(fun(X665,bool),bool),member(X665),X666),hAPP(fun(X665,bool),fun(X665,bool),hAPP(X665,fun(fun(X665,bool),fun(X665,bool)),insert(X665),X667),X668)))
| ti(X665,X666) = ti(X665,X667)
| hBOOL(hAPP(fun(X665,bool),bool,hAPP(X665,fun(fun(X665,bool),bool),member(X665),X666),X668)) )
& ( ti(X665,X666) != ti(X665,X667)
| hBOOL(hAPP(fun(X665,bool),bool,hAPP(X665,fun(fun(X665,bool),bool),member(X665),X666),hAPP(fun(X665,bool),fun(X665,bool),hAPP(X665,fun(fun(X665,bool),fun(X665,bool)),insert(X665),X667),X668))) )
& ( ~ hBOOL(hAPP(fun(X665,bool),bool,hAPP(X665,fun(fun(X665,bool),bool),member(X665),X666),X668))
| hBOOL(hAPP(fun(X665,bool),bool,hAPP(X665,fun(fun(X665,bool),bool),member(X665),X666),hAPP(fun(X665,bool),fun(X665,bool),hAPP(X665,fun(fun(X665,bool),fun(X665,bool)),insert(X665),X667),X668))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_60_insert__iff])])]) ).
fof(i_0_175,plain,
! [X645,X646,X647,X648] :
( ~ hBOOL(hAPP(fun(X645,bool),bool,hAPP(X645,fun(fun(X645,bool),bool),member(X645),X646),hAPP(fun(X645,bool),fun(X645,bool),hAPP(X645,fun(fun(X645,bool),fun(X645,bool)),insert(X645),X647),X648)))
| ti(X645,X646) = ti(X645,X647)
| hBOOL(hAPP(fun(X645,bool),bool,hAPP(X645,fun(fun(X645,bool),bool),member(X645),X646),X648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_insertE])]) ).
fof(i_0_176,plain,
! [X628,X629,X630,X631,X632,X633] :
( ti(X628,X631) != hAPP(X629,X628,X632,X633)
| ~ hBOOL(hAPP(fun(X629,bool),bool,hAPP(X629,fun(fun(X629,bool),bool),member(X629),X633),X630))
| hBOOL(hAPP(fun(X628,bool),bool,hAPP(X628,fun(fun(X628,bool),bool),member(X628),X631),hAPP(fun(X629,bool),fun(X628,bool),hAPP(fun(X629,X628),fun(fun(X629,bool),fun(X628,bool)),image(X629,X628),X632),X630))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_image__eqI])]) ).
fof(i_0_177,plain,
! [X741,X742,X743,X744,X745,X746] :
( ~ hBOOL(hAPP(fun(X742,bool),bool,hAPP(X742,fun(fun(X742,bool),bool),member(X742),X745),X746))
| ti(X741,X743) != hAPP(X742,X741,X744,X745)
| hBOOL(hAPP(fun(X741,bool),bool,hAPP(X741,fun(fun(X741,bool),bool),member(X741),X743),hAPP(fun(X742,bool),fun(X741,bool),hAPP(fun(X742,X741),fun(fun(X742,bool),fun(X741,bool)),image(X742,X741),X744),X746))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_79_rev__image__eqI])]) ).
fof(i_0_178,plain,
! [X669,X670,X671,X672] :
( ( ~ hBOOL(hAPP(X669,bool,hAPP(fun(X669,bool),fun(X669,bool),hAPP(X669,fun(fun(X669,bool),fun(X669,bool)),insert(X669),X670),X671),X672))
| ti(X669,X670) = ti(X669,X672)
| hBOOL(hAPP(X669,bool,X671,X672)) )
& ( ti(X669,X670) != ti(X669,X672)
| hBOOL(hAPP(X669,bool,hAPP(fun(X669,bool),fun(X669,bool),hAPP(X669,fun(fun(X669,bool),fun(X669,bool)),insert(X669),X670),X671),X672)) )
& ( ~ hBOOL(hAPP(X669,bool,X671,X672))
| hBOOL(hAPP(X669,bool,hAPP(fun(X669,bool),fun(X669,bool),hAPP(X669,fun(fun(X669,bool),fun(X669,bool)),insert(X669),X670),X671),X672)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_61_insert__code])])]) ).
fof(i_0_179,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)],[fact_35_not__less__eq__eq]) ).
fof(i_0_180,plain,
! [X673,X674,X675,X676] :
( ( hAPP(fun(X673,bool),fun(X673,bool),hAPP(X673,fun(fun(X673,bool),fun(X673,bool)),insert(X673),X675),X676) != hAPP(fun(X673,bool),fun(X673,bool),hAPP(X673,fun(fun(X673,bool),fun(X673,bool)),insert(X673),X675),X674)
| ti(fun(X673,bool),X676) = ti(fun(X673,bool),X674)
| hBOOL(hAPP(fun(X673,bool),bool,hAPP(X673,fun(fun(X673,bool),bool),member(X673),X675),X674))
| hBOOL(hAPP(fun(X673,bool),bool,hAPP(X673,fun(fun(X673,bool),bool),member(X673),X675),X676)) )
& ( ti(fun(X673,bool),X676) != ti(fun(X673,bool),X674)
| hAPP(fun(X673,bool),fun(X673,bool),hAPP(X673,fun(fun(X673,bool),fun(X673,bool)),insert(X673),X675),X676) = hAPP(fun(X673,bool),fun(X673,bool),hAPP(X673,fun(fun(X673,bool),fun(X673,bool)),insert(X673),X675),X674)
| hBOOL(hAPP(fun(X673,bool),bool,hAPP(X673,fun(fun(X673,bool),bool),member(X673),X675),X674))
| hBOOL(hAPP(fun(X673,bool),bool,hAPP(X673,fun(fun(X673,bool),bool),member(X673),X675),X676)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_162])])]) ).
fof(i_0_181,plain,
! [X686,X687,X688] :
( ( hBOOL(hAPP(fun(X686,bool),bool,hAPP(fun(X686,bool),fun(fun(X686,bool),bool),ord_less_eq(fun(X686,bool)),X687),X688))
| ti(fun(X686,bool),X687) != ti(fun(X686,bool),X688) )
& ( hBOOL(hAPP(fun(X686,bool),bool,hAPP(fun(X686,bool),fun(fun(X686,bool),bool),ord_less_eq(fun(X686,bool)),X688),X687))
| ti(fun(X686,bool),X687) != ti(fun(X686,bool),X688) )
& ( ~ hBOOL(hAPP(fun(X686,bool),bool,hAPP(fun(X686,bool),fun(fun(X686,bool),bool),ord_less_eq(fun(X686,bool)),X687),X688))
| ~ hBOOL(hAPP(fun(X686,bool),bool,hAPP(fun(X686,bool),fun(fun(X686,bool),bool),ord_less_eq(fun(X686,bool)),X688),X687))
| ti(fun(X686,bool),X687) = ti(fun(X686,bool),X688) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_set__eq__subset])])]) ).
fof(i_0_182,plain,
! [X634,X635,X636] :
( ~ hBOOL(hAPP(fun(X634,bool),bool,hAPP(fun(X634,bool),fun(fun(X634,bool),bool),ord_less_eq(fun(X634,bool)),X635),X636))
| ~ hBOOL(hAPP(fun(X634,bool),bool,hAPP(fun(X634,bool),fun(fun(X634,bool),bool),ord_less_eq(fun(X634,bool)),X636),X635))
| ti(fun(X634,bool),X635) = ti(fun(X634,bool),X636) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_equalityI])]) ).
fof(i_0_183,plain,
! [X641,X642,X643,X644] :
( ( ~ hBOOL(hAPP(fun(X641,bool),bool,hAPP(X641,fun(fun(X641,bool),bool),member(X641),X643),X644))
| hBOOL(hAPP(fun(X641,bool),bool,hAPP(X641,fun(fun(X641,bool),bool),member(X641),X643),hAPP(fun(X641,bool),fun(X641,bool),hAPP(X641,fun(fun(X641,bool),fun(X641,bool)),insert(X641),X642),X644))) )
& ( ti(X641,X643) != ti(X641,X642)
| hBOOL(hAPP(fun(X641,bool),bool,hAPP(X641,fun(fun(X641,bool),bool),member(X641),X643),hAPP(fun(X641,bool),fun(X641,bool),hAPP(X641,fun(fun(X641,bool),fun(X641,bool)),insert(X641),X642),X644))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_163])])]) ).
fof(i_0_184,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)],[fact_8_card__insert__if]) ).
fof(i_0_185,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)],[fact_9_card__insert__disjoint]) ).
fof(i_0_186,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)],[fact_31_le__SucE]) ).
fof(i_0_187,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)],[fact_36_Suc__n__not__le__n]) ).
fof(i_0_188,plain,
! [X681,X682,X683] :
( ~ hBOOL(hAPP(fun(X681,bool),bool,hAPP(X681,fun(fun(X681,bool),bool),member(X681),X682),X683))
| hAPP(fun(X681,bool),fun(X681,bool),hAPP(X681,fun(fun(X681,bool),fun(X681,bool)),insert(X681),X682),X683) = ti(fun(X681,bool),X683) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_64_insert__absorb])]) ).
fof(i_0_189,plain,
! [X711,X712,X713] :
( ( hBOOL(hAPP(fun(X711,bool),bool,hAPP(fun(X711,bool),fun(fun(X711,bool),bool),ord_less_eq(fun(X711,bool)),X712),X713))
| ti(fun(X711,bool),X712) != ti(fun(X711,bool),X713) )
& ( hBOOL(hAPP(fun(X711,bool),bool,hAPP(fun(X711,bool),fun(fun(X711,bool),bool),ord_less_eq(fun(X711,bool)),X713),X712))
| ti(fun(X711,bool),X712) != ti(fun(X711,bool),X713) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_164])])]) ).
fof(i_0_190,plain,
! [X689,X690,X691] :
( ti(fun(X689,bool),X690) != ti(fun(X689,bool),X691)
| hBOOL(hAPP(fun(X689,bool),bool,hAPP(fun(X689,bool),fun(fun(X689,bool),bool),ord_less_eq(fun(X689,bool)),X690),X691)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_equalityD1])]) ).
fof(i_0_191,plain,
! [X692,X693,X694] :
( ti(fun(X692,bool),X693) != ti(fun(X692,bool),X694)
| hBOOL(hAPP(fun(X692,bool),bool,hAPP(fun(X692,bool),fun(fun(X692,bool),bool),ord_less_eq(fun(X692,bool)),X694),X693)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_equalityD2])]) ).
fof(i_0_192,plain,
! [X714,X715,X716,X717] :
( hAPP(X714,X715,X716,esk4_4(X714,X715,X716,X717)) != hAPP(X714,X715,X717,esk4_4(X714,X715,X716,X717))
| ti(fun(X714,X715),X716) = ti(fun(X714,X715),X717) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_74_ext])])]) ).
fof(i_0_193,plain,
! [X877,X878,X879] :
( ~ hBOOL(hAPP(X877,bool,hAPP(X877,fun(X877,bool),fequal(X877),X878),X879))
| ti(X877,X878) = ti(X877,X879) ),
inference(variable_rename,[status(thm)],[i_0_165]) ).
fof(i_0_194,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54))
| ~ hBOOL(X53)
| hBOOL(X54) ),
inference(fof_simplification,[status(thm)],[help_fimplies_3_1_U]) ).
fof(i_0_195,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54))
| hBOOL(X53)
| hBOOL(X54) ),
inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).
fof(i_0_196,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X53) ),
inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).
fof(i_0_197,plain,
! [X53,X54] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54))
| hBOOL(X54) ),
inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).
fof(i_0_198,plain,
! [X880,X881,X882] :
( ti(X880,X881) != ti(X880,X882)
| hBOOL(hAPP(X880,bool,hAPP(X880,fun(X880,bool),fequal(X880),X881),X882)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_T]) ).
fof(i_0_199,plain,
! [X472,X473,X474] : ti(fun(fun(X472,fun(X473,X474)),fun(fun(X472,X473),fun(X472,X474))),combs(X472,X473,X474)) = combs(X472,X473,X474),
inference(variable_rename,[status(thm)],[tsy_c_COMBS_res]) ).
fof(i_0_200,plain,
! [X468,X469,X470] : ti(fun(fun(X468,fun(X469,X470)),fun(X469,fun(X468,X470))),combc(X468,X469,X470)) = combc(X468,X469,X470),
inference(variable_rename,[status(thm)],[tsy_c_COMBC_res]) ).
fof(i_0_201,plain,
! [X465,X466,X467] : ti(fun(fun(X465,X466),fun(fun(X467,X465),fun(X467,X466))),combb(X465,X466,X467)) = combb(X465,X466,X467),
inference(variable_rename,[status(thm)],[tsy_c_COMBB_res]) ).
fof(i_0_202,plain,
! [X54,X53] :
( ~ hBOOL(X53)
| ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X53),X54)) ),
inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).
fof(i_0_203,plain,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X53),X54)) ),
inference(fof_simplification,[status(thm)],[help_fimplies_2_1_U]) ).
fof(i_0_204,plain,
! [X54,X53] :
( ~ hBOOL(X53)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).
fof(i_0_205,plain,
! [X53,X54] :
( ~ hBOOL(X54)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X53),X54)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).
fof(i_0_206,plain,
! [X480,X481] : ti(fun(fun(X480,X481),fun(fun(X480,bool),fun(X481,bool))),image(X480,X481)) = image(X480,X481),
inference(variable_rename,[status(thm)],[tsy_c_Set_Oimage_res]) ).
fof(i_0_207,plain,
! [X756,X757] : hAPP(fun(X756,bool),fun(X756,bool),hAPP(fun(X756,X756),fun(fun(X756,bool),fun(X756,bool)),image(X756,X756),combi(X756)),X757) = ti(fun(X756,bool),X757),
inference(variable_rename,[status(thm)],[fact_82_image__ident]) ).
fof(i_0_208,plain,
! [X482] : ti(fun(X482,fun(fun(X482,bool),fun(X482,bool))),insert(X482)) = insert(X482),
inference(variable_rename,[status(thm)],[tsy_c_Set_Oinsert_res]) ).
fof(i_0_209,plain,
! [X484,X485,X486,X487] : hAPP(X484,X485,ti(fun(X484,X485),X486),X487) = hAPP(X484,X485,X486,X487),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).
fof(i_0_210,plain,
! [X841,X842] : ti(X841,ti(X841,X842)) = ti(X841,X842),
inference(variable_rename,[status(thm)],[help_ti_idem]) ).
fof(i_0_211,plain,
! [X488,X489,X490,X491] : hAPP(X488,X489,X490,ti(X488,X491)) = hAPP(X488,X489,X490,X491),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).
fof(i_0_212,plain,
! [X492,X493,X494,X495] : ti(X492,hAPP(X493,X492,X494,X495)) = hAPP(X493,X492,X494,X495),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
fof(i_0_213,plain,
! [X497] : ti(fun(X497,fun(fun(X497,bool),bool)),member(X497)) = member(X497),
inference(variable_rename,[status(thm)],[tsy_c_member_res]) ).
fof(i_0_214,hypothesis,
! [X496] :
( ( ~ hBOOL(ti(bool,X496))
| hBOOL(X496) )
& ( ~ hBOOL(X496)
| hBOOL(ti(bool,X496)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1])]) ).
fof(i_0_215,plain,
! [X53] :
( ~ hBOOL(hAPP(bool,bool,fNot,X53))
| ~ hBOOL(X53) ),
inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).
fof(i_0_216,plain,
! [X479] : ti(fun(fun(X479,bool),fun(X479,bool)),collect(X479)) = collect(X479),
inference(variable_rename,[status(thm)],[tsy_c_Set_OCollect_res]) ).
fof(i_0_217,plain,
! [X722,X723] : hAPP(fun(X722,bool),fun(X722,bool),collect(X722),X723) = ti(fun(X722,bool),X723),
inference(variable_rename,[status(thm)],[fact_76_Collect__def]) ).
fof(i_0_218,plain,
! [X478] :
( ~ preorder(X478)
| ti(fun(X478,fun(X478,bool)),ord_less_eq(X478)) = ord_less_eq(X478) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res])]) ).
fof(i_0_219,plain,
! [X483] : ti(fun(X483,fun(X483,bool)),fequal(X483)) = fequal(X483),
inference(variable_rename,[status(thm)],[tsy_c_fequal_res]) ).
fof(i_0_220,plain,
! [X475] : ti(fun(fun(X475,bool),nat),finite_card(X475)) = finite_card(X475),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).
fof(i_0_221,plain,
! [X476] : ti(fun(fun(X476,bool),bool),finite_finite(X476)) = finite_finite(X476),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).
fof(i_0_222,plain,
! [X471] : ti(fun(X471,X471),combi(X471)) = combi(X471),
inference(variable_rename,[status(thm)],[tsy_c_COMBI_res]) ).
fof(i_0_223,plain,
! [X477] : ti(X477,undefined(X477)) = undefined(X477),
inference(variable_rename,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).
fof(i_0_224,plain,
! [X623,X624,X625,X626] :
( ( hBOOL(hAPP(fun(X624,bool),bool,hAPP(X624,fun(fun(X624,bool),bool),member(X624),esk3_4(X623,X624,X625,X626)),X626))
| ~ hBOOL(hAPP(fun(X623,bool),bool,finite_finite(X623),hAPP(fun(X624,bool),fun(X623,bool),hAPP(fun(X624,X623),fun(fun(X624,bool),fun(X623,bool)),image(X624,X623),X625),X626)))
| hBOOL(hAPP(fun(X624,bool),bool,finite_finite(X624),X626)) )
& ( ~ hBOOL(hAPP(fun(X624,bool),bool,finite_finite(X624),hAPP(fun(X624,bool),fun(X624,bool),collect(X624),hAPP(fun(X624,bool),fun(X624,bool),hAPP(fun(X624,fun(bool,bool)),fun(fun(X624,bool),fun(X624,bool)),combs(X624,bool,bool),hAPP(fun(X624,bool),fun(X624,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X624,bool),fun(X624,fun(bool,bool))),combb(bool,fun(bool,bool),X624),fconj),hAPP(fun(X624,bool),fun(X624,bool),hAPP(fun(X624,fun(fun(X624,bool),bool)),fun(fun(X624,bool),fun(X624,bool)),combc(X624,fun(X624,bool),bool),member(X624)),X626))),hAPP(X623,fun(X624,bool),hAPP(fun(X624,fun(X623,bool)),fun(X623,fun(X624,bool)),combc(X624,X623,bool),hAPP(fun(X624,X623),fun(X624,fun(X623,bool)),hAPP(fun(X623,fun(X623,bool)),fun(fun(X624,X623),fun(X624,fun(X623,bool))),combb(X623,fun(X623,bool),X624),fequal(X623)),X625)),hAPP(X624,X623,X625,esk3_4(X623,X624,X625,X626)))))))
| ~ hBOOL(hAPP(fun(X623,bool),bool,finite_finite(X623),hAPP(fun(X624,bool),fun(X623,bool),hAPP(fun(X624,X623),fun(fun(X624,bool),fun(X623,bool)),image(X624,X623),X625),X626)))
| hBOOL(hAPP(fun(X624,bool),bool,finite_finite(X624),X626)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_166])])])]) ).
fof(i_0_225,plain,
! [X558,X559,X560] :
( ( hBOOL(hAPP(fun(X558,bool),bool,finite_finite(X558),hAPP(fun(X558,bool),fun(X558,bool),collect(X558),X559)))
| ~ hBOOL(hAPP(fun(X558,bool),bool,finite_finite(X558),hAPP(fun(X558,bool),fun(X558,bool),collect(X558),hAPP(fun(X558,bool),fun(X558,bool),hAPP(fun(X558,fun(bool,bool)),fun(fun(X558,bool),fun(X558,bool)),combs(X558,bool,bool),hAPP(fun(X558,bool),fun(X558,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X558,bool),fun(X558,fun(bool,bool))),combb(bool,fun(bool,bool),X558),fdisj),X559)),X560)))) )
& ( hBOOL(hAPP(fun(X558,bool),bool,finite_finite(X558),hAPP(fun(X558,bool),fun(X558,bool),collect(X558),X560)))
| ~ hBOOL(hAPP(fun(X558,bool),bool,finite_finite(X558),hAPP(fun(X558,bool),fun(X558,bool),collect(X558),hAPP(fun(X558,bool),fun(X558,bool),hAPP(fun(X558,fun(bool,bool)),fun(fun(X558,bool),fun(X558,bool)),combs(X558,bool,bool),hAPP(fun(X558,bool),fun(X558,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X558,bool),fun(X558,fun(bool,bool))),combb(bool,fun(bool,bool),X558),fdisj),X559)),X560)))) )
& ( ~ hBOOL(hAPP(fun(X558,bool),bool,finite_finite(X558),hAPP(fun(X558,bool),fun(X558,bool),collect(X558),X559)))
| ~ hBOOL(hAPP(fun(X558,bool),bool,finite_finite(X558),hAPP(fun(X558,bool),fun(X558,bool),collect(X558),X560)))
| hBOOL(hAPP(fun(X558,bool),bool,finite_finite(X558),hAPP(fun(X558,bool),fun(X558,bool),collect(X558),hAPP(fun(X558,bool),fun(X558,bool),hAPP(fun(X558,fun(bool,bool)),fun(fun(X558,bool),fun(X558,bool)),combs(X558,bool,bool),hAPP(fun(X558,bool),fun(X558,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X558,bool),fun(X558,fun(bool,bool))),combb(bool,fun(bool,bool),X558),fdisj),X559)),X560)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_26_finite__Collect__disjI])])]) ).
fof(i_0_226,plain,
! [X655,X656,X657] : hAPP(fun(X655,bool),fun(X655,bool),hAPP(X655,fun(fun(X655,bool),fun(X655,bool)),insert(X655),X656),hAPP(fun(X655,bool),fun(X655,bool),collect(X655),X657)) = hAPP(fun(X655,bool),fun(X655,bool),collect(X655),hAPP(fun(X655,bool),fun(X655,bool),hAPP(fun(X655,fun(bool,bool)),fun(fun(X655,bool),fun(X655,bool)),combs(X655,bool,bool),hAPP(fun(X655,bool),fun(X655,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X655,bool),fun(X655,fun(bool,bool))),combb(bool,fun(bool,bool),X655),fimplies),hAPP(fun(X655,bool),fun(X655,bool),hAPP(fun(bool,bool),fun(fun(X655,bool),fun(X655,bool)),combb(bool,bool,X655),fNot),hAPP(X655,fun(X655,bool),hAPP(fun(X655,fun(X655,bool)),fun(X655,fun(X655,bool)),combc(X655,X655,bool),fequal(X655)),X656)))),X657)),
inference(variable_rename,[status(thm)],[fact_57_insert__Collect]) ).
fof(i_0_227,plain,
! [X528,X529,X530] :
( ( ~ hBOOL(hAPP(fun(X528,bool),bool,finite_finite(X528),hAPP(fun(X528,bool),fun(X528,bool),collect(X528),X530)))
| hBOOL(hAPP(fun(X528,bool),bool,finite_finite(X528),hAPP(fun(X528,bool),fun(X528,bool),collect(X528),hAPP(fun(X528,bool),fun(X528,bool),hAPP(fun(X528,fun(bool,bool)),fun(fun(X528,bool),fun(X528,bool)),combs(X528,bool,bool),hAPP(fun(X528,bool),fun(X528,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X528,bool),fun(X528,fun(bool,bool))),combb(bool,fun(bool,bool),X528),fconj),X530)),X529)))) )
& ( ~ hBOOL(hAPP(fun(X528,bool),bool,finite_finite(X528),hAPP(fun(X528,bool),fun(X528,bool),collect(X528),X529)))
| hBOOL(hAPP(fun(X528,bool),bool,finite_finite(X528),hAPP(fun(X528,bool),fun(X528,bool),collect(X528),hAPP(fun(X528,bool),fun(X528,bool),hAPP(fun(X528,fun(bool,bool)),fun(fun(X528,bool),fun(X528,bool)),combs(X528,bool,bool),hAPP(fun(X528,bool),fun(X528,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X528,bool),fun(X528,fun(bool,bool))),combb(bool,fun(bool,bool),X528),fconj),X530)),X529)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_finite__Collect__conjI])])]) ).
fof(i_0_228,plain,
! [X821,X822,X823,X824,X825] :
( ( hBOOL(hAPP(fun(X822,bool),bool,hAPP(X822,fun(fun(X822,bool),bool),member(X822),esk11_5(X821,X822,X823,X824,X825)),X825))
| hBOOL(hAPP(fun(X821,bool),bool,hAPP(fun(X821,bool),fun(fun(X821,bool),bool),ord_less_eq(fun(X821,bool)),hAPP(fun(X822,bool),fun(X821,bool),hAPP(fun(X822,X821),fun(fun(X822,bool),fun(X821,bool)),image(X822,X821),X823),X825)),X824)) )
& ( ~ hBOOL(hAPP(fun(X821,bool),bool,hAPP(X821,fun(fun(X821,bool),bool),member(X821),hAPP(X822,X821,X823,esk11_5(X821,X822,X823,X824,X825))),X824))
| hBOOL(hAPP(fun(X821,bool),bool,hAPP(fun(X821,bool),fun(fun(X821,bool),bool),ord_less_eq(fun(X821,bool)),hAPP(fun(X822,bool),fun(X821,bool),hAPP(fun(X822,X821),fun(fun(X822,bool),fun(X821,bool)),image(X822,X821),X823),X825)),X824)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_image__subsetI])])])]) ).
fof(i_0_229,plain,
! [X747,X748,X749] : hAPP(fun(X747,bool),fun(X747,bool),hAPP(X747,fun(fun(X747,bool),fun(X747,bool)),insert(X747),X748),X749) = hAPP(fun(X747,bool),fun(X747,bool),collect(X747),hAPP(fun(X747,bool),fun(X747,bool),hAPP(fun(X747,fun(bool,bool)),fun(fun(X747,bool),fun(X747,bool)),combs(X747,bool,bool),hAPP(fun(X747,bool),fun(X747,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X747,bool),fun(X747,fun(bool,bool))),combb(bool,fun(bool,bool),X747),fdisj),hAPP(X747,fun(X747,bool),hAPP(fun(X747,fun(X747,bool)),fun(X747,fun(X747,bool)),combc(X747,X747,bool),fequal(X747)),X748))),hAPP(fun(X747,bool),fun(X747,bool),hAPP(fun(X747,fun(fun(X747,bool),bool)),fun(fun(X747,bool),fun(X747,bool)),combc(X747,fun(X747,bool),bool),member(X747)),X749))),
inference(variable_rename,[status(thm)],[fact_80_insert__compr__raw]) ).
fof(i_0_230,plain,
! [X652,X653,X654] : hAPP(fun(X652,bool),fun(X652,bool),hAPP(X652,fun(fun(X652,bool),fun(X652,bool)),insert(X652),X653),X654) = hAPP(fun(X652,bool),fun(X652,bool),collect(X652),hAPP(fun(X652,bool),fun(X652,bool),hAPP(fun(X652,fun(bool,bool)),fun(fun(X652,bool),fun(X652,bool)),combs(X652,bool,bool),hAPP(fun(X652,bool),fun(X652,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X652,bool),fun(X652,fun(bool,bool))),combb(bool,fun(bool,bool),X652),fdisj),hAPP(X652,fun(X652,bool),hAPP(fun(X652,fun(X652,bool)),fun(X652,fun(X652,bool)),combc(X652,X652,bool),fequal(X652)),X653))),hAPP(fun(X652,bool),fun(X652,bool),hAPP(fun(X652,fun(fun(X652,bool),bool)),fun(fun(X652,bool),fun(X652,bool)),combc(X652,fun(X652,bool),bool),member(X652)),X654))),
inference(variable_rename,[status(thm)],[fact_56_insert__compr]) ).
fof(i_0_231,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)],[conj_6])]) ).
fof(i_0_232,plain,
! [X618,X619,X620,X621] :
( ~ order(X618)
| ~ hBOOL(hAPP(X618,bool,hAPP(X618,fun(X618,bool),ord_less_eq(X618),hAPP(nat,X618,X621,esk2_4(X618,X619,X620,X621))),hAPP(nat,X618,X621,hAPP(nat,nat,suc,esk2_4(X618,X619,X620,X621)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X619),X620))
| hBOOL(hAPP(X618,bool,hAPP(X618,fun(X618,bool),ord_less_eq(X618),hAPP(nat,X618,X621,X619)),hAPP(nat,X618,X621,X620))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_lift__Suc__mono__le])])])]) ).
fof(i_0_233,plain,
! [X509,X510,X511,X512] :
( ~ hBOOL(hAPP(fun(X510,bool),bool,finite_finite(X510),X512))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X509,bool),nat,finite_card(X509),hAPP(fun(X510,bool),fun(X509,bool),hAPP(fun(X510,X509),fun(fun(X510,bool),fun(X509,bool)),image(X510,X509),X511),X512))),hAPP(fun(X510,bool),nat,finite_card(X510),X512))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_card__image__le])]) ).
fof(i_0_234,plain,
! [X588,X589,X590] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X590),X589)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X588),X589)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X590),X588))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X589),X588))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X589),X590)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X590),X588))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X590),X589)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X588),X589)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X589),X588))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X589),X590)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_le__diff__iff])])]) ).
fof(i_0_235,plain,
! [X500,X501] :
( ~ hBOOL(hAPP(fun(X500,bool),bool,finite_finite(X500),X501))
| hBOOL(hAPP(fun(fun(X500,bool),bool),bool,finite_finite(fun(X500,bool)),hAPP(fun(fun(X500,bool),bool),fun(fun(X500,bool),bool),collect(fun(X500,bool)),hAPP(fun(X500,bool),fun(fun(X500,bool),bool),hAPP(fun(fun(X500,bool),fun(fun(X500,bool),bool)),fun(fun(X500,bool),fun(fun(X500,bool),bool)),combc(fun(X500,bool),fun(X500,bool),bool),ord_less_eq(fun(X500,bool))),X501)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets])]) ).
fof(i_0_236,plain,
! [X799,X800,X801,X802,X803] :
( ~ hBOOL(hAPP(fun(X800,bool),bool,hAPP(fun(X800,bool),fun(fun(X800,bool),bool),ord_less_eq(fun(X800,bool)),X802),X803))
| hBOOL(hAPP(fun(X799,bool),bool,hAPP(fun(X799,bool),fun(fun(X799,bool),bool),ord_less_eq(fun(X799,bool)),hAPP(fun(X800,bool),fun(X799,bool),hAPP(fun(X800,X799),fun(fun(X800,bool),fun(X799,bool)),image(X800,X799),X801),X802)),hAPP(fun(X800,bool),fun(X799,bool),hAPP(fun(X800,X799),fun(fun(X800,bool),fun(X799,bool)),image(X800,X799),X801),X803))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_image__mono])]) ).
fof(i_0_237,plain,
! [X761,X762,X763,X764] :
( ( hBOOL(hAPP(fun(X761,bool),bool,hAPP(X761,fun(fun(X761,bool),bool),member(X761),X762),X764))
| ~ hBOOL(hAPP(fun(X761,bool),bool,hAPP(fun(X761,bool),fun(fun(X761,bool),bool),ord_less_eq(fun(X761,bool)),hAPP(fun(X761,bool),fun(X761,bool),hAPP(X761,fun(fun(X761,bool),fun(X761,bool)),insert(X761),X762),X763)),X764)) )
& ( hBOOL(hAPP(fun(X761,bool),bool,hAPP(fun(X761,bool),fun(fun(X761,bool),bool),ord_less_eq(fun(X761,bool)),X763),X764))
| ~ hBOOL(hAPP(fun(X761,bool),bool,hAPP(fun(X761,bool),fun(fun(X761,bool),bool),ord_less_eq(fun(X761,bool)),hAPP(fun(X761,bool),fun(X761,bool),hAPP(X761,fun(fun(X761,bool),fun(X761,bool)),insert(X761),X762),X763)),X764)) )
& ( ~ hBOOL(hAPP(fun(X761,bool),bool,hAPP(X761,fun(fun(X761,bool),bool),member(X761),X762),X764))
| ~ hBOOL(hAPP(fun(X761,bool),bool,hAPP(fun(X761,bool),fun(fun(X761,bool),bool),ord_less_eq(fun(X761,bool)),X763),X764))
| hBOOL(hAPP(fun(X761,bool),bool,hAPP(fun(X761,bool),fun(fun(X761,bool),bool),ord_less_eq(fun(X761,bool)),hAPP(fun(X761,bool),fun(X761,bool),hAPP(X761,fun(fun(X761,bool),fun(X761,bool)),insert(X761),X762),X763)),X764)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_84_insert__subset])])]) ).
fof(i_0_238,plain,
! [X773,X774,X775,X776] :
( ~ hBOOL(hAPP(fun(X773,bool),bool,hAPP(fun(X773,bool),fun(fun(X773,bool),bool),ord_less_eq(fun(X773,bool)),X775),X776))
| hBOOL(hAPP(fun(X773,bool),bool,hAPP(fun(X773,bool),fun(fun(X773,bool),bool),ord_less_eq(fun(X773,bool)),hAPP(fun(X773,bool),fun(X773,bool),hAPP(X773,fun(fun(X773,bool),fun(X773,bool)),insert(X773),X774),X775)),hAPP(fun(X773,bool),fun(X773,bool),hAPP(X773,fun(fun(X773,bool),fun(X773,bool)),insert(X773),X774),X776))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_87_insert__mono])]) ).
cnf(i_0_239,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,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(split_conjunct,[status(thm)],[i_0_167]) ).
cnf(i_0_240,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_168]) ).
cnf(i_0_241,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)],[i_0_169]) ).
fof(i_0_242,plain,
! [X519,X520,X521] :
( ~ hBOOL(hAPP(fun(X519,bool),bool,finite_finite(X519),X521))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X519,bool),nat,finite_card(X519),X521)),hAPP(fun(X519,bool),nat,finite_card(X519),hAPP(fun(X519,bool),fun(X519,bool),hAPP(X519,fun(fun(X519,bool),fun(X519,bool)),insert(X519),X520),X521)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7_card__insert__le])]) ).
fof(i_0_243,plain,
! [X765,X766,X767,X768] :
( ( ~ hBOOL(hAPP(fun(X765,bool),bool,hAPP(fun(X765,bool),fun(fun(X765,bool),bool),ord_less_eq(fun(X765,bool)),X768),hAPP(fun(X765,bool),fun(X765,bool),hAPP(X765,fun(fun(X765,bool),fun(X765,bool)),insert(X765),X767),X766)))
| hBOOL(hAPP(fun(X765,bool),bool,hAPP(fun(X765,bool),fun(fun(X765,bool),bool),ord_less_eq(fun(X765,bool)),X768),X766))
| hBOOL(hAPP(fun(X765,bool),bool,hAPP(X765,fun(fun(X765,bool),bool),member(X765),X767),X768)) )
& ( ~ hBOOL(hAPP(fun(X765,bool),bool,hAPP(fun(X765,bool),fun(fun(X765,bool),bool),ord_less_eq(fun(X765,bool)),X768),X766))
| hBOOL(hAPP(fun(X765,bool),bool,hAPP(fun(X765,bool),fun(fun(X765,bool),bool),ord_less_eq(fun(X765,bool)),X768),hAPP(fun(X765,bool),fun(X765,bool),hAPP(X765,fun(fun(X765,bool),fun(X765,bool)),insert(X765),X767),X766)))
| hBOOL(hAPP(fun(X765,bool),bool,hAPP(X765,fun(fun(X765,bool),bool),member(X765),X767),X768)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_170])])]) ).
fof(i_0_244,plain,
! [X599,X600,X601] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X600),X601))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X600),X599)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X601),X599))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_diff__le__mono])]) ).
fof(i_0_245,plain,
! [X602,X603,X604] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X603),X604))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X602),X604)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X602),X603))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_44_diff__le__mono2])]) ).
cnf(i_0_246,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)],[i_0_171]) ).
cnf(i_0_247,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)],[i_0_172]) ).
cnf(i_0_248,plain,
( ti(fun(X1,bool),X3) = 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)),X3),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),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_173]) ).
cnf(i_0_249,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,bool),fun(fun(X4,bool),bool),ord_less_eq(fun(X4,bool)),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
| ~ 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(X4,bool),X5) != hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_169]) ).
fof(i_0_250,plain,
! [X583,X584,X585] : 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,X583)),X584)),hAPP(nat,nat,suc,X585)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X583),X584)),X585),
inference(variable_rename,[status(thm)],[fact_37_Suc__diff__diff]) ).
fof(i_0_251,plain,
! [X607,X608,X609,X610,X611] :
( ~ hBOOL(hAPP(fun(X608,bool),bool,finite_finite(X608),X611))
| ~ hBOOL(hAPP(fun(X607,bool),bool,hAPP(fun(X607,bool),fun(fun(X607,bool),bool),ord_less_eq(fun(X607,bool)),X609),hAPP(fun(X608,bool),fun(X607,bool),hAPP(fun(X608,X607),fun(fun(X608,bool),fun(X607,bool)),image(X608,X607),X610),X611)))
| hBOOL(hAPP(fun(X607,bool),bool,finite_finite(X607),X609)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_finite__surj])]) ).
cnf(i_0_252,plain,
( ti(X1,X2) = ti(X1,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_174]) ).
cnf(i_0_253,plain,
( ti(X1,X2) = ti(X1,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_175]) ).
fof(i_0_254,plain,
! [X533] : 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)),X533)))),
inference(variable_rename,[status(thm)],[fact_12_finite__Collect__le__nat]) ).
fof(i_0_255,plain,
! [X736,X737,X738,X739,X740] :
( ~ hBOOL(hAPP(fun(X737,bool),bool,hAPP(X737,fun(fun(X737,bool),bool),member(X737),X739),X740))
| hBOOL(hAPP(fun(X736,bool),bool,hAPP(X736,fun(fun(X736,bool),bool),member(X736),hAPP(X737,X736,X738,X739)),hAPP(fun(X737,bool),fun(X736,bool),hAPP(fun(X737,X736),fun(fun(X737,bool),fun(X736,bool)),image(X737,X736),X738),X740))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_imageI])]) ).
fof(i_0_256,plain,
! [X591,X592,X593] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X592),X593))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X592),X591))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X593),X592)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X591),X592)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X593),X591) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_40_Nat_Odiff__diff__eq])]) ).
cnf(i_0_257,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),X6)))
| ti(X1,X2) != hAPP(X3,X1,X4,X5)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_176]) ).
cnf(i_0_258,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X4,X5) != hAPP(X1,X4,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_177]) ).
cnf(i_0_259,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(X4,X5) != hAPP(X1,X4,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_172]) ).
fof(i_0_260,plain,
! [X750,X751,X752,X753,X754,X755] : hAPP(fun(X750,bool),fun(X751,bool),hAPP(fun(X750,X751),fun(fun(X750,bool),fun(X751,bool)),image(X750,X751),X753),hAPP(fun(X752,bool),fun(X750,bool),hAPP(fun(X752,X750),fun(fun(X752,bool),fun(X750,bool)),image(X752,X750),X754),X755)) = hAPP(fun(X752,bool),fun(X751,bool),hAPP(fun(X752,X751),fun(fun(X752,bool),fun(X751,bool)),image(X752,X751),hAPP(fun(X752,X750),fun(X752,X751),hAPP(fun(X750,X751),fun(fun(X752,X750),fun(X752,X751)),combb(X750,X751,X752),X753),X754)),X755),
inference(variable_rename,[status(thm)],[fact_81_image__image]) ).
fof(i_0_261,plain,
! [X769,X770,X771,X772] :
( ~ hBOOL(hAPP(fun(X769,bool),bool,hAPP(fun(X769,bool),fun(fun(X769,bool),bool),ord_less_eq(fun(X769,bool)),X771),X772))
| hBOOL(hAPP(fun(X769,bool),bool,hAPP(fun(X769,bool),fun(fun(X769,bool),bool),ord_less_eq(fun(X769,bool)),X771),hAPP(fun(X769,bool),fun(X769,bool),hAPP(X769,fun(fun(X769,bool),fun(X769,bool)),insert(X769),X770),X772))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_subset__insertI2])]) ).
fof(i_0_262,plain,
! [X513,X514,X515] :
( ~ hBOOL(hAPP(fun(X513,bool),bool,finite_finite(X513),X515))
| ~ hBOOL(hAPP(fun(X513,bool),bool,hAPP(fun(X513,bool),fun(fun(X513,bool),bool),ord_less_eq(fun(X513,bool)),X514),X515))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X513,bool),nat,finite_card(X513),X514)),hAPP(fun(X513,bool),nat,finite_card(X513),X515))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_card__mono])]) ).
fof(i_0_263,plain,
! [X677,X678,X679,X680] :
( ~ hBOOL(hAPP(fun(X677,bool),bool,hAPP(X677,fun(fun(X677,bool),bool),member(X677),X679),X680))
| hBOOL(hAPP(fun(X677,bool),bool,hAPP(X677,fun(fun(X677,bool),bool),member(X677),X679),hAPP(fun(X677,bool),fun(X677,bool),hAPP(X677,fun(fun(X677,bool),fun(X677,bool)),insert(X677),X678),X680))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_insertI2])]) ).
fof(i_0_264,plain,
! [X707,X708,X709,X710] :
( ~ hBOOL(hAPP(fun(X707,bool),bool,hAPP(fun(X707,bool),fun(fun(X707,bool),bool),ord_less_eq(fun(X707,bool)),X709),X710))
| ~ hBOOL(hAPP(fun(X707,bool),bool,hAPP(fun(X707,bool),fun(fun(X707,bool),bool),ord_less_eq(fun(X707,bool)),X710),X708))
| hBOOL(hAPP(fun(X707,bool),bool,hAPP(fun(X707,bool),fun(fun(X707,bool),bool),ord_less_eq(fun(X707,bool)),X709),X708)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_subset__trans])]) ).
fof(i_0_265,plain,
! [X576,X577] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X576)),hAPP(nat,nat,suc,X577)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X576),X577)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X576),X577))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X576)),hAPP(nat,nat,suc,X577))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_Suc__le__mono])]) ).
cnf(i_0_266,plain,
( ti(X1,X2) = ti(X1,X4)
| 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(split_conjunct,[status(thm)],[i_0_178]) ).
fof(i_0_267,plain,
! [X782,X783,X784,X785,X786] :
( ~ hBOOL(hAPP(fun(X783,bool),bool,hAPP(X783,fun(fun(X783,bool),bool),member(X783),X785),X786))
| hAPP(fun(X782,bool),fun(X782,bool),hAPP(X782,fun(fun(X782,bool),fun(X782,bool)),insert(X782),hAPP(X783,X782,X784,X785)),hAPP(fun(X783,bool),fun(X782,bool),hAPP(fun(X783,X782),fun(fun(X783,bool),fun(X782,bool)),image(X783,X782),X784),X786)) = hAPP(fun(X783,bool),fun(X782,bool),hAPP(fun(X783,X782),fun(fun(X783,bool),fun(X782,bool)),image(X783,X782),X784),X786) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_89_insert__image])]) ).
fof(i_0_268,plain,
! [X699,X700,X701,X702] :
( ~ hBOOL(hAPP(fun(X699,bool),bool,hAPP(X699,fun(fun(X699,bool),bool),member(X699),X701),X702))
| ~ hBOOL(hAPP(fun(X699,bool),bool,hAPP(fun(X699,bool),fun(fun(X699,bool),bool),ord_less_eq(fun(X699,bool)),X702),X700))
| hBOOL(hAPP(fun(X699,bool),bool,hAPP(X699,fun(fun(X699,bool),bool),member(X699),X701),X700)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_set__rev__mp])]) ).
fof(i_0_269,plain,
! [X703,X704,X705,X706] :
( ~ hBOOL(hAPP(fun(X703,bool),bool,hAPP(fun(X703,bool),fun(fun(X703,bool),bool),ord_less_eq(fun(X703,bool)),X705),X706))
| ~ hBOOL(hAPP(fun(X703,bool),bool,hAPP(X703,fun(fun(X703,bool),bool),member(X703),X704),X705))
| hBOOL(hAPP(fun(X703,bool),bool,hAPP(X703,fun(fun(X703,bool),bool),member(X703),X704),X706)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_set__mp])]) ).
fof(i_0_270,plain,
! [X695,X696,X697,X698] :
( ~ hBOOL(hAPP(fun(X695,bool),bool,hAPP(fun(X695,bool),fun(fun(X695,bool),bool),ord_less_eq(fun(X695,bool)),X697),X698))
| ~ hBOOL(hAPP(fun(X695,bool),bool,hAPP(X695,fun(fun(X695,bool),bool),member(X695),X696),X697))
| hBOOL(hAPP(fun(X695,bool),bool,hAPP(X695,fun(fun(X695,bool),bool),member(X695),X696),X698)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_in__mono])]) ).
fof(i_0_271,plain,
! [X637,X638,X639,X640] :
( ~ hBOOL(hAPP(fun(X637,bool),bool,hAPP(fun(X637,bool),fun(fun(X637,bool),bool),ord_less_eq(fun(X637,bool)),X639),X640))
| ~ hBOOL(hAPP(fun(X637,bool),bool,hAPP(X637,fun(fun(X637,bool),bool),member(X637),X638),X639))
| hBOOL(hAPP(fun(X637,bool),bool,hAPP(X637,fun(fun(X637,bool),bool),member(X637),X638),X640)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_subsetD])]) ).
fof(i_0_272,plain,
! [X580,X581] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X580),X581))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X581)),X580)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X581)),X580))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X580),X581)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_179])]) ).
fof(i_0_273,plain,
! [X561,X562,X563] :
( ( ~ hBOOL(hAPP(fun(X561,bool),bool,finite_finite(X561),hAPP(fun(X561,bool),fun(X561,bool),hAPP(X561,fun(fun(X561,bool),fun(X561,bool)),insert(X561),X562),X563)))
| hBOOL(hAPP(fun(X561,bool),bool,finite_finite(X561),X563)) )
& ( ~ hBOOL(hAPP(fun(X561,bool),bool,finite_finite(X561),X563))
| hBOOL(hAPP(fun(X561,bool),bool,finite_finite(X561),hAPP(fun(X561,bool),fun(X561,bool),hAPP(X561,fun(fun(X561,bool),fun(X561,bool)),insert(X561),X562),X563))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_finite__insert])]) ).
fof(i_0_274,plain,
! [X605,X606] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X605),X606)),X605)),
inference(variable_rename,[status(thm)],[fact_45_diff__le__self]) ).
fof(i_0_275,plain,
! [X555,X556,X557] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X555),X556)),X557) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X555),X557)),X556),
inference(variable_rename,[status(thm)],[fact_25_diff__commute]) ).
cnf(i_0_276,plain,
( 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(split_conjunct,[status(thm)],[i_0_180]) ).
fof(i_0_277,plain,
! [X777,X778,X779,X780,X781] : hAPP(fun(X777,bool),fun(X778,bool),hAPP(fun(X777,X778),fun(fun(X777,bool),fun(X778,bool)),image(X777,X778),X779),hAPP(fun(X777,bool),fun(X777,bool),hAPP(X777,fun(fun(X777,bool),fun(X777,bool)),insert(X777),X780),X781)) = hAPP(fun(X778,bool),fun(X778,bool),hAPP(X778,fun(fun(X778,bool),fun(X778,bool)),insert(X778),hAPP(X777,X778,X779,X780)),hAPP(fun(X777,bool),fun(X778,bool),hAPP(fun(X777,X778),fun(fun(X777,bool),fun(X778,bool)),image(X777,X778),X779),X781)),
inference(variable_rename,[status(thm)],[fact_88_image__insert]) ).
fof(i_0_278,plain,
! [X594,X595,X596] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X596),X595) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X594),X595)
| X596 = X594
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X595),X594))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X595),X596)) )
& ( X596 != X594
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X596),X595) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X594),X595)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X595),X594))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X595),X596)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_eq__diff__iff])])]) ).
cnf(i_0_279,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)),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)) ),
inference(split_conjunct,[status(thm)],[i_0_181]) ).
cnf(i_0_280,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)),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)) ),
inference(split_conjunct,[status(thm)],[i_0_182]) ).
fof(i_0_281,plain,
! [X570,X571] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X570)),X571))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X570),X571)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_Suc__leD])]) ).
cnf(i_0_282,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[i_0_180]) ).
cnf(i_0_283,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)],[i_0_174]) ).
cnf(i_0_284,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)],[i_0_183]) ).
fof(i_0_285,plain,
! [X547,X548,X549] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X548),X549))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X549),X547))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X548),X547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_le__trans])]) ).
fof(i_0_286,plain,
! [X522,X523,X524] :
( ( ~ hBOOL(hAPP(fun(X522,bool),bool,hAPP(X522,fun(fun(X522,bool),bool),member(X522),X523),X524))
| hAPP(fun(X522,bool),nat,finite_card(X522),hAPP(fun(X522,bool),fun(X522,bool),hAPP(X522,fun(fun(X522,bool),fun(X522,bool)),insert(X522),X523),X524)) = hAPP(fun(X522,bool),nat,finite_card(X522),X524)
| ~ hBOOL(hAPP(fun(X522,bool),bool,finite_finite(X522),X524)) )
& ( hBOOL(hAPP(fun(X522,bool),bool,hAPP(X522,fun(fun(X522,bool),bool),member(X522),X523),X524))
| hAPP(fun(X522,bool),nat,finite_card(X522),hAPP(fun(X522,bool),fun(X522,bool),hAPP(X522,fun(fun(X522,bool),fun(X522,bool)),insert(X522),X523),X524)) = hAPP(nat,nat,suc,hAPP(fun(X522,bool),nat,finite_card(X522),X524))
| ~ hBOOL(hAPP(fun(X522,bool),bool,finite_finite(X522),X524)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_184])])]) ).
fof(i_0_287,plain,
! [X814,X815,X816] :
( ( hBOOL(hAPP(nat,bool,X815,hAPP(nat,nat,suc,esk9_3(X814,X815,X816))))
| hBOOL(hAPP(nat,bool,X815,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X816),X814)))
| ~ hBOOL(hAPP(nat,bool,X815,X816)) )
& ( ~ hBOOL(hAPP(nat,bool,X815,esk9_3(X814,X815,X816)))
| hBOOL(hAPP(nat,bool,X815,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X816),X814)))
| ~ hBOOL(hAPP(nat,bool,X815,X816)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_zero__induct__lemma])])])]) ).
fof(i_0_288,plain,
! [X758,X759,X760] : hBOOL(hAPP(fun(X758,bool),bool,hAPP(fun(X758,bool),fun(fun(X758,bool),bool),ord_less_eq(fun(X758,bool)),X759),hAPP(fun(X758,bool),fun(X758,bool),hAPP(X758,fun(fun(X758,bool),fun(X758,bool)),insert(X758),X760),X759))),
inference(variable_rename,[status(thm)],[fact_83_subset__insertI]) ).
fof(i_0_289,plain,
! [X661,X662,X663,X664] : hAPP(fun(X661,bool),fun(X661,bool),hAPP(X661,fun(fun(X661,bool),fun(X661,bool)),insert(X661),X662),hAPP(fun(X661,bool),fun(X661,bool),hAPP(X661,fun(fun(X661,bool),fun(X661,bool)),insert(X661),X663),X664)) = hAPP(fun(X661,bool),fun(X661,bool),hAPP(X661,fun(fun(X661,bool),fun(X661,bool)),insert(X661),X663),hAPP(fun(X661,bool),fun(X661,bool),hAPP(X661,fun(fun(X661,bool),fun(X661,bool)),insert(X661),X662),X664)),
inference(variable_rename,[status(thm)],[fact_59_insert__commute]) ).
fof(i_0_290,plain,
! [X531,X532] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X531),X532))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X532)),X531) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X532),X531)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_Suc__diff__le])]) ).
fof(i_0_291,plain,
! [X649,X650,X651] : hBOOL(hAPP(fun(X649,bool),bool,hAPP(X649,fun(fun(X649,bool),bool),member(X649),X650),hAPP(fun(X649,bool),fun(X649,bool),hAPP(X649,fun(fun(X649,bool),fun(X649,bool)),insert(X649),X650),X651))),
inference(variable_rename,[status(thm)],[fact_55_insertI1]) ).
fof(i_0_292,plain,
! [X534] : 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)),X534))) = hAPP(nat,nat,suc,X534),
inference(variable_rename,[status(thm)],[fact_13_card__Collect__le__nat]) ).
fof(i_0_293,plain,
! [X502,X503,X504,X505] :
( ~ hBOOL(hAPP(fun(X503,bool),bool,finite_finite(X503),X505))
| hBOOL(hAPP(fun(X502,bool),bool,finite_finite(X502),hAPP(fun(X503,bool),fun(X502,bool),hAPP(fun(X503,X502),fun(fun(X503,bool),fun(X502,bool)),image(X503,X502),X504),X505))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_finite__imageI])]) ).
fof(i_0_294,plain,
! [X525,X526,X527] :
( ~ hBOOL(hAPP(fun(X525,bool),bool,finite_finite(X525),X527))
| hBOOL(hAPP(fun(X525,bool),bool,hAPP(X525,fun(fun(X525,bool),bool),member(X525),X526),X527))
| hAPP(fun(X525,bool),nat,finite_card(X525),hAPP(fun(X525,bool),fun(X525,bool),hAPP(X525,fun(fun(X525,bool),fun(X525,bool)),insert(X525),X526),X527)) = hAPP(nat,nat,suc,hAPP(fun(X525,bool),nat,finite_card(X525),X527)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_185])]) ).
fof(i_0_295,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)],[conj_5]) ).
fof(i_0_296,plain,
! [X578,X579] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X578),hAPP(nat,nat,suc,X579)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X578),X579))
| X578 = hAPP(nat,nat,suc,X579) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X578),X579))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X578),hAPP(nat,nat,suc,X579))) )
& ( X578 != hAPP(nat,nat,suc,X579)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X578),hAPP(nat,nat,suc,X579))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_34_le__Suc__eq])])]) ).
fof(i_0_297,plain,
! [X572,X573] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X572),hAPP(nat,nat,suc,X573)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X572),X573))
| X572 = hAPP(nat,nat,suc,X573) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_186])]) ).
fof(i_0_298,plain,
! [X818,X819] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X818)),X819))
| X819 = hAPP(nat,nat,suc,esk10_2(X818,X819)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_95_Suc__le__D])])]) ).
fof(i_0_299,plain,
! [X810,X811,X812] :
( ( hBOOL(hAPP(fun(X810,bool),bool,hAPP(X810,fun(fun(X810,bool),bool),member(X810),esk8_3(X810,X811,X812)),X812))
| hBOOL(hAPP(fun(X810,bool),bool,hAPP(fun(X810,bool),fun(fun(X810,bool),bool),ord_less_eq(fun(X810,bool)),X812),X811)) )
& ( ~ hBOOL(hAPP(fun(X810,bool),bool,hAPP(X810,fun(fun(X810,bool),bool),member(X810),esk8_3(X810,X811,X812)),X811))
| hBOOL(hAPP(fun(X810,bool),bool,hAPP(fun(X810,bool),fun(fun(X810,bool),bool),ord_less_eq(fun(X810,bool)),X812),X811)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_subsetI])])])]) ).
fof(i_0_300,plain,
! [X506,X507,X508] :
( ~ hBOOL(hAPP(fun(X506,bool),bool,finite_finite(X506),X508))
| hBOOL(hAPP(fun(X506,bool),bool,finite_finite(X506),hAPP(fun(X506,bool),fun(X506,bool),hAPP(X506,fun(fun(X506,bool),fun(X506,bool)),insert(X506),X507),X508))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_finite_OinsertI])]) ).
fof(i_0_301,plain,
! [X582] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X582)),X582)),
inference(variable_rename,[status(thm)],[i_0_187]) ).
cnf(i_0_302,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_178]) ).
fof(i_0_303,plain,
! [X829,X831,X832,X833] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X829))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X831),X829))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X831),esk12_1(X829))) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk13_2(X832,X833)),X832))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X832)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk13_2(X832,X833)),X833))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X832)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_304,plain,
! [X498,X499] :
( ~ 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)),X498),X499))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X499),X498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J])]) ).
fof(i_0_305,plain,
! [X574,X575] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X574),X575))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X574),hAPP(nat,nat,suc,X575))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_32_le__SucI])]) ).
fof(i_0_306,plain,
! [X545,X546] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X545),X546))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X546),X545))
| X545 = X546 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_20_le__antisym])]) ).
fof(i_0_307,plain,
! [X597,X598] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X597),X598))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X598),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X598),X597)) = X597 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_42_diff__diff__cancel])]) ).
fof(i_0_308,plain,
! [X564,X565,X566] :
( ~ hBOOL(hAPP(fun(X564,bool),bool,hAPP(fun(X564,bool),fun(fun(X564,bool),bool),ord_less_eq(fun(X564,bool)),X565),X566))
| ~ hBOOL(hAPP(fun(X564,bool),bool,finite_finite(X564),X566))
| hBOOL(hAPP(fun(X564,bool),bool,finite_finite(X564),X565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_finite__subset])]) ).
fof(i_0_309,plain,
! [X567,X568,X569] :
( ~ hBOOL(hAPP(fun(X567,bool),bool,finite_finite(X567),X569))
| ~ hBOOL(hAPP(fun(X567,bool),bool,hAPP(fun(X567,bool),fun(fun(X567,bool),bool),ord_less_eq(fun(X567,bool)),X568),X569))
| hBOOL(hAPP(fun(X567,bool),bool,finite_finite(X567),X568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_rev__finite__subset])]) ).
fof(i_0_310,plain,
! [X859,X860,X861,X862,X863,X864] : hAPP(X859,X860,hAPP(fun(X859,X861),fun(X859,X860),hAPP(fun(X859,fun(X861,X860)),fun(fun(X859,X861),fun(X859,X860)),combs(X859,X861,X860),X862),X863),X864) = hAPP(X861,X860,hAPP(X859,fun(X861,X860),X862,X864),hAPP(X859,X861,X863,X864)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_U]) ).
cnf(i_0_311,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)],[i_0_188]) ).
fof(i_0_312,plain,
! [X658,X659,X660] : hAPP(fun(X658,bool),fun(X658,bool),hAPP(X658,fun(fun(X658,bool),fun(X658,bool)),insert(X658),X659),hAPP(fun(X658,bool),fun(X658,bool),hAPP(X658,fun(fun(X658,bool),fun(X658,bool)),insert(X658),X659),X660)) = hAPP(fun(X658,bool),fun(X658,bool),hAPP(X658,fun(fun(X658,bool),fun(X658,bool)),insert(X658),X659),X660),
inference(variable_rename,[status(thm)],[fact_58_insert__absorb2]) ).
fof(i_0_313,plain,
! [X845,X846,X847,X848,X849,X850] : hAPP(X845,X846,hAPP(fun(X845,X847),fun(X845,X846),hAPP(fun(X847,X846),fun(fun(X845,X847),fun(X845,X846)),combb(X847,X846,X845),X848),X849),X850) = hAPP(X847,X846,X848,hAPP(X845,X847,X849,X850)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_U]) ).
fof(i_0_314,plain,
! [X851,X852,X853,X854,X855,X856] : hAPP(X851,X852,hAPP(X853,fun(X851,X852),hAPP(fun(X851,fun(X853,X852)),fun(X853,fun(X851,X852)),combc(X851,X853,X852),X854),X855),X856) = hAPP(X853,X852,hAPP(X851,fun(X853,X852),X854,X856),X855),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_U]) ).
fof(i_0_315,plain,
! [X719,X720,X721] :
( ( ~ hBOOL(hAPP(fun(X719,bool),bool,hAPP(X719,fun(fun(X719,bool),bool),member(X719),X720),X721))
| hBOOL(hAPP(X719,bool,X721,X720)) )
& ( ~ hBOOL(hAPP(X719,bool,X721,X720))
| hBOOL(hAPP(fun(X719,bool),bool,hAPP(X719,fun(fun(X719,bool),bool),member(X719),X720),X721)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_mem__def])]) ).
cnf(i_0_316,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)],[i_0_189]) ).
cnf(i_0_317,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)],[i_0_189]) ).
cnf(i_0_318,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)],[i_0_190]) ).
cnf(i_0_319,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)],[i_0_181]) ).
cnf(i_0_320,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)],[i_0_181]) ).
cnf(i_0_321,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)],[i_0_191]) ).
fof(i_0_322,plain,
! [X552,X553] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X552),X553))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X553),X552)) ),
inference(variable_rename,[status(thm)],[fact_23_nat__le__linear]) ).
cnf(i_0_323,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)],[i_0_192]) ).
cnf(i_0_324,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)],[i_0_193]) ).
fof(i_0_325,plain,
! [X586,X587] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X586)),hAPP(nat,nat,suc,X587)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X586),X587),
inference(variable_rename,[status(thm)],[fact_38_diff__Suc__Suc]) ).
fof(i_0_326,plain,
! [X887,X888] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X887),X888))
| ~ hBOOL(X887)
| hBOOL(X888) ),
inference(variable_rename,[status(thm)],[i_0_194]) ).
fof(i_0_327,plain,
! [X875,X876] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X875),X876))
| hBOOL(X875)
| hBOOL(X876) ),
inference(variable_rename,[status(thm)],[i_0_195]) ).
fof(i_0_328,plain,
! [X867,X868] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X867),X868))
| hBOOL(X867) ),
inference(variable_rename,[status(thm)],[i_0_196]) ).
fof(i_0_329,plain,
! [X869,X870] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X869),X870))
| hBOOL(X870) ),
inference(variable_rename,[status(thm)],[i_0_197]) ).
cnf(i_0_330,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)],[i_0_198]) ).
cnf(i_0_331,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)],[i_0_199]) ).
fof(i_0_332,plain,
! [X684,X685] : hBOOL(hAPP(fun(X684,bool),bool,hAPP(fun(X684,bool),fun(fun(X684,bool),bool),ord_less_eq(fun(X684,bool)),X685),X685)),
inference(variable_rename,[status(thm)],[fact_65_subset__refl]) ).
cnf(i_0_333,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)],[i_0_200]) ).
cnf(i_0_334,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)],[i_0_201]) ).
fof(i_0_335,plain,
! [X827,X828] :
( ~ preorder(X827)
| hBOOL(hAPP(X827,bool,hAPP(X827,fun(X827,bool),ord_less_eq(X827),X828),X828)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_order__refl])])]) ).
fof(i_0_336,plain,
! [X550,X551] :
( X550 != X551
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X550),X551)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_eq__imp__le])]) ).
fof(i_0_337,plain,
! [X554] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X554),X554)),
inference(variable_rename,[status(thm)],[fact_24_le__refl]) ).
fof(i_0_338,plain,
! [X865,X866] :
( ~ hBOOL(X866)
| ~ hBOOL(X865)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X866),X865)) ),
inference(variable_rename,[status(thm)],[i_0_202]) ).
fof(i_0_339,plain,
! [X885,X886] :
( ~ hBOOL(X886)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X885),X886)) ),
inference(variable_rename,[status(thm)],[i_0_203]) ).
fof(i_0_340,plain,
! [X871,X872] :
( ~ hBOOL(X872)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X872),X871)) ),
inference(variable_rename,[status(thm)],[i_0_204]) ).
fof(i_0_341,plain,
! [X873,X874] :
( ~ hBOOL(X874)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X873),X874)) ),
inference(variable_rename,[status(thm)],[i_0_205]) ).
fof(i_0_342,plain,
! [X883,X884] :
( hBOOL(X884)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X884),X883)) ),
inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).
cnf(i_0_343,plain,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_206]) ).
cnf(i_0_344,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)],[i_0_207]) ).
cnf(i_0_345,plain,
ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
inference(split_conjunct,[status(thm)],[i_0_208]) ).
cnf(i_0_346,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_209]) ).
cnf(i_0_347,plain,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
inference(split_conjunct,[status(thm)],[tsy_v_P_res]) ).
cnf(i_0_348,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_210]) ).
cnf(i_0_349,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_211]) ).
cnf(i_0_350,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_212]) ).
cnf(i_0_351,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(split_conjunct,[status(thm)],[i_0_213]) ).
cnf(i_0_352,hypothesis,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_214]) ).
fof(i_0_353,plain,
! [X843] :
( ~ hBOOL(hAPP(bool,bool,fNot,X843))
| ~ hBOOL(X843) ),
inference(variable_rename,[status(thm)],[i_0_215]) ).
fof(i_0_354,plain,
! [X541,X542] :
( ( hAPP(nat,nat,suc,X541) != hAPP(nat,nat,suc,X542)
| X541 = X542 )
& ( X541 != X542
| hAPP(nat,nat,suc,X541) = hAPP(nat,nat,suc,X542) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_nat_Oinject])]) ).
fof(i_0_355,plain,
! [X539,X540] :
( hAPP(nat,nat,suc,X539) != hAPP(nat,nat,suc,X540)
| X539 = X540 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_Suc__inject])]) ).
cnf(i_0_356,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(split_conjunct,[status(thm)],[i_0_216]) ).
cnf(i_0_357,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[i_0_217]) ).
fof(i_0_358,plain,
! [X537,X538] :
( ~ finite_finite_1(X537)
| hBOOL(hAPP(fun(X537,bool),bool,finite_finite(X537),X538)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_finite])])]) ).
fof(i_0_359,plain,
! [X535,X536] :
( ~ finite_finite_1(X535)
| hBOOL(hAPP(fun(X535,bool),bool,finite_finite(X535),X536)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_finite__code])])]) ).
cnf(i_0_360,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_218]) ).
cnf(i_0_361,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(split_conjunct,[status(thm)],[i_0_219]) ).
cnf(i_0_362,plain,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
inference(split_conjunct,[status(thm)],[i_0_220]) ).
cnf(i_0_363,plain,
ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
inference(split_conjunct,[status(thm)],[i_0_221]) ).
cnf(i_0_364,hypothesis,
ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
inference(split_conjunct,[status(thm)],[tsy_c_Groups_Ominus__class_Ominus_res]) ).
cnf(i_0_365,hypothesis,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_214]) ).
cnf(i_0_366,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(split_conjunct,[status(thm)],[tsy_c_fimplies_res]) ).
cnf(i_0_367,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(split_conjunct,[status(thm)],[tsy_c_fdisj_res]) ).
cnf(i_0_368,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(split_conjunct,[status(thm)],[tsy_c_fconj_res]) ).
fof(i_0_369,plain,
! [X844] :
( hBOOL(X844)
| hBOOL(hAPP(bool,bool,fNot,X844)) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
fof(i_0_370,plain,
! [X543] : hAPP(nat,nat,suc,X543) != X543,
inference(variable_rename,[status(thm)],[fact_18_Suc__n__not__n]) ).
fof(i_0_371,plain,
! [X544] : X544 != hAPP(nat,nat,suc,X544),
inference(variable_rename,[status(thm)],[fact_19_n__not__Suc__n]) ).
cnf(i_0_372,plain,
ti(fun(X1,X1),combi(X1)) = combi(X1),
inference(split_conjunct,[status(thm)],[i_0_222]) ).
cnf(i_0_373,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
inference(split_conjunct,[status(thm)],[tsy_v_mgt__call_res]) ).
cnf(i_0_374,hypothesis,
ti(fun(pname,bool),u) = u,
inference(split_conjunct,[status(thm)],[tsy_v_U_res]) ).
cnf(i_0_375,hypothesis,
ti(fun(x_a,bool),g) = g,
inference(split_conjunct,[status(thm)],[tsy_v_G_res]) ).
cnf(i_0_376,hypothesis,
ti(fun(nat,nat),suc) = suc,
inference(split_conjunct,[status(thm)],[tsy_c_Nat_OSuc_res]) ).
cnf(i_0_377,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(split_conjunct,[status(thm)],[tsy_c_fNot_res]) ).
cnf(i_0_378,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[i_0_223]) ).
cnf(i_0_379,hypothesis,
ti(pname,pn) = pn,
inference(split_conjunct,[status(thm)],[tsy_v_pn_res]) ).
cnf(i_0_380,hypothesis,
ti(nat,na) = na,
inference(split_conjunct,[status(thm)],[tsy_v_na_res]) ).
fof(i_0_381,plain,
! [X837,X838] :
( ~ finite_finite_1(X838)
| ~ finite_finite_1(X837)
| finite_finite_1(fun(X837,X838)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite])]) ).
fof(i_0_382,plain,
! [X839,X840] :
( ~ order(X840)
| order(fun(X839,X840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oorder])]) ).
fof(i_0_383,plain,
! [X835,X836] :
( ~ preorder(X836)
| preorder(fun(X835,X836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Opreorder])]) ).
cnf(i_0_384,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),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)))))))
| ~ 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)],[i_0_224]),
[final] ).
cnf(i_0_385,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)],[i_0_225]),
[final] ).
cnf(i_0_386,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),X3)),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_225]),
[final] ).
cnf(i_0_387,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)],[i_0_226]),
[final] ).
cnf(i_0_388,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),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_225]),
[final] ).
cnf(i_0_389,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)],[i_0_227]),
[final] ).
cnf(i_0_390,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),X3)),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_227]),
[final] ).
cnf(i_0_391,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),X5)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk11_5(X1,X2,X3,X4,X5))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_228]),
[final] ).
cnf(i_0_392,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)],[i_0_229]),
[final] ).
cnf(i_0_393,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)],[i_0_230]),
[final] ).
cnf(i_0_394,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)],[i_0_231]),
[final] ).
cnf(i_0_395,plain,
( 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)
| ~ 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)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_232]),
[final] ).
cnf(i_0_396,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2))),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_233]),
[final] ).
cnf(i_0_397,plain,
( 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)))
| ~ 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)],[i_0_234]),
[final] ).
cnf(i_0_398,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),esk1_5(X1,X2,X3,X4,X5)),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_399,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk11_5(X2,X1,X3,X4,X5)),X5))
| 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),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_228]),
[final] ).
cnf(i_0_400,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),esk6_5(X2,X1,X3,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X3),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_401,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk7_5(X2,X1,X3,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_402,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk5_5(X2,X1,X3,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_172]),
[final] ).
cnf(i_0_403,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)],[i_0_235]),
[final] ).
cnf(i_0_404,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,bool),fun(fun(X4,bool),bool),ord_less_eq(fun(X4,bool)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),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)],[i_0_236]),
[final] ).
cnf(i_0_405,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)),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)],[i_0_237]),
[final] ).
cnf(i_0_406,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),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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),X3),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_407,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)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_237]),
[final] ).
cnf(i_0_408,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),X4),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),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(split_conjunct,[status(thm)],[i_0_238]),
[final] ).
cnf(i_0_409,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk1_5(X1,X2,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_410,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),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_237]),
[final] ).
cnf(i_0_411,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(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(rw,[status(thm)],[i_0_239,c_0_240]),
[final] ).
cnf(i_0_412,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(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(rw,[status(thm)],[i_0_241,c_0_240]),
[final] ).
cnf(i_0_413,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)],[i_0_242]),
[final] ).
cnf(i_0_414,plain,
( 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(X1,fun(fun(X1,bool),bool),member(X1),X3),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(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_243]),
[final] ).
cnf(i_0_415,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),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_244]),
[final] ).
cnf(i_0_416,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),X3),X2)),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)) ),
inference(split_conjunct,[status(thm)],[i_0_245]),
[final] ).
cnf(i_0_417,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)],[conj_2]),
[final] ).
cnf(i_0_418,plain,
( hAPP(X1,X1,combi(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(rw,[status(thm)],[i_0_246,c_0_240]),
[final] ).
cnf(i_0_419,plain,
( hAPP(X1,X1,combi(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(rw,[status(thm)],[i_0_247,c_0_240]),
[final] ).
cnf(i_0_420,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),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)),X3),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),X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_248,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_421,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk3_4(X2,X1,X3,X4)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ 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),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_422,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,bool),fun(fun(X4,bool),bool),ord_less_eq(fun(X4,bool)),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
| hAPP(fun(X4,bool),fun(X4,bool),combi(fun(X4,bool)),X5) != hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),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(rw,[status(thm)],[i_0_249,c_0_240]),
[final] ).
cnf(i_0_423,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,suc,X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_424,plain,
( hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X4))
| ~ 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)),X4),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_251]),
[final] ).
cnf(i_0_425,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_252,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_426,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_253,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_427,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)],[i_0_254]),
[final] ).
cnf(i_0_428,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),X4),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),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)],[i_0_243]),
[final] ).
cnf(i_0_429,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_255]),
[final] ).
cnf(i_0_430,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(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(split_conjunct,[status(thm)],[i_0_256]),
[final] ).
cnf(i_0_431,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)],[conj_3]),
[final] ).
cnf(i_0_432,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),X6)))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X3,X1,X4,X5)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X6)) ),
inference(rw,[status(thm)],[i_0_257,c_0_240]),
[final] ).
cnf(i_0_433,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
| hAPP(X4,X4,combi(X4),X5) != hAPP(X1,X4,X6,X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_258,c_0_240]),
[final] ).
cnf(i_0_434,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
| hAPP(X4,X4,combi(X4),X5) != hAPP(X1,X4,X6,X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_259,c_0_240]),
[final] ).
cnf(i_0_435,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)],[i_0_260]),
[final] ).
cnf(i_0_436,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),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(split_conjunct,[status(thm)],[i_0_261]),
[final] ).
cnf(i_0_437,plain,
( 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,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)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_262]),
[final] ).
cnf(i_0_438,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),X4),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_263]),
[final] ).
cnf(i_0_439,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),X4),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_174]),
[final] ).
cnf(i_0_440,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),X4),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_441,plain,
( 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),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(split_conjunct,[status(thm)],[i_0_264]),
[final] ).
cnf(i_0_442,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)],[i_0_265]),
[final] ).
cnf(i_0_443,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
| 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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_266,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_444,plain,
( hAPP(fun(X4,bool),fun(X4,bool),hAPP(X4,fun(fun(X4,bool),fun(X4,bool)),insert(X4),hAPP(X1,X4,X5,X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3)) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_267]),
[final] ).
cnf(i_0_445,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(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(split_conjunct,[status(thm)],[i_0_268]),
[final] ).
cnf(i_0_446,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),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(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_447,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),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(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_270]),
[final] ).
cnf(i_0_448,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),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(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_271]),
[final] ).
cnf(i_0_449,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)],[i_0_272]),
[final] ).
cnf(i_0_450,plain,
( 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(split_conjunct,[status(thm)],[i_0_273]),
[final] ).
cnf(i_0_451,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)],[i_0_274]),
[final] ).
cnf(i_0_452,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_275]),
[final] ).
cnf(i_0_453,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) = hAPP(fun(X1,bool),fun(X1,bool),combi(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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_276,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_454,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)],[i_0_277]),
[final] ).
cnf(i_0_455,plain,
( X1 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(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)],[i_0_278]),
[final] ).
cnf(i_0_456,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_279,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_457,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_280,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_458,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)],[i_0_281]),
[final] ).
cnf(i_0_459,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)],[i_0_265]),
[final] ).
cnf(i_0_460,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_282,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_461,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)))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_283,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_462,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)))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_284,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_463,plain,
( 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(split_conjunct,[status(thm)],[i_0_285]),
[final] ).
cnf(i_0_464,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(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)],[i_0_286]),
[final] ).
cnf(i_0_465,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)],[conj_1]),
[final] ).
cnf(i_0_466,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk9_3(X2,X1,X3))))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_287]),
[final] ).
cnf(i_0_467,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)],[i_0_288]),
[final] ).
cnf(i_0_468,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)],[i_0_289]),
[final] ).
cnf(i_0_469,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2)),X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_290]),
[final] ).
cnf(i_0_470,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)],[i_0_291]),
[final] ).
cnf(i_0_471,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)],[i_0_292]),
[final] ).
cnf(i_0_472,plain,
( 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(split_conjunct,[status(thm)],[i_0_293]),
[final] ).
cnf(i_0_473,plain,
( 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(split_conjunct,[status(thm)],[i_0_286]),
[final] ).
cnf(i_0_474,plain,
( 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(split_conjunct,[status(thm)],[i_0_294]),
[final] ).
cnf(i_0_475,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)],[i_0_295]),
[final] ).
cnf(i_0_476,plain,
( 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(split_conjunct,[status(thm)],[i_0_296]),
[final] ).
cnf(i_0_477,plain,
( 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(split_conjunct,[status(thm)],[i_0_297]),
[final] ).
cnf(i_0_478,plain,
( X2 = hAPP(nat,nat,suc,esk10_2(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)],[i_0_298]),
[final] ).
cnf(i_0_479,plain,
( 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(X1,fun(fun(X1,bool),bool),member(X1),esk8_3(X1,X2,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_299]),
[final] ).
cnf(i_0_480,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),X3),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_273]),
[final] ).
cnf(i_0_481,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),X3),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_300]),
[final] ).
cnf(i_0_482,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)],[i_0_301]),
[final] ).
cnf(i_0_483,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,X1,esk9_3(X2,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_287]),
[final] ).
cnf(i_0_484,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_302,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_485,plain,
( 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))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_178]),
[final] ).
cnf(i_0_486,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),esk12_1(X1)))
| ~ 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),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_303]),
[final] ).
cnf(i_0_487,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)],[i_0_272]),
[final] ).
cnf(i_0_488,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X2),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)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_304]),
[final] ).
cnf(i_0_489,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)],[i_0_296]),
[final] ).
cnf(i_0_490,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)],[i_0_305]),
[final] ).
cnf(i_0_491,plain,
( X1 = 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),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_306]),
[final] ).
cnf(i_0_492,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_307]),
[final] ).
cnf(i_0_493,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)],[i_0_308]),
[final] ).
cnf(i_0_494,plain,
( 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)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_309]),
[final] ).
cnf(i_0_495,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)],[i_0_310]),
[final] ).
cnf(i_0_496,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk8_3(X1,X2,X3)),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(split_conjunct,[status(thm)],[i_0_299]),
[final] ).
cnf(i_0_497,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),combi(fun(X1,bool)),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_311,c_0_240]),
[final] ).
cnf(i_0_498,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)],[i_0_312]),
[final] ).
cnf(i_0_499,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)],[i_0_313]),
[final] ).
cnf(i_0_500,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)],[i_0_314]),
[final] ).
cnf(i_0_501,plain,
( hBOOL(hAPP(X1,bool,X3,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_315]),
[final] ).
cnf(i_0_502,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_316,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_503,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_317,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_504,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_318,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_505,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_319,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_506,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_320,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_507,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_321,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_508,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)],[i_0_303]),
[final] ).
cnf(i_0_509,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)],[i_0_322]),
[final] ).
cnf(i_0_510,plain,
( hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3) = hAPP(fun(X1,X2),fun(X1,X2),combi(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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_323,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_511,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_324,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_512,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_325]),
[final] ).
cnf(i_0_513,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)],[i_0_296]),
[final] ).
cnf(i_0_514,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_315]),
[final] ).
cnf(i_0_515,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_326]),
[final] ).
cnf(i_0_516,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_327]),
[final] ).
cnf(i_0_517,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_328]),
[final] ).
cnf(i_0_518,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_329]),
[final] ).
cnf(i_0_519,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk13_2(X1,X2)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_303]),
[final] ).
cnf(i_0_520,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_330,c_0_240]),c_0_240]),
[final] ).
cnf(i_0_521,plain,
hAPP(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combi(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3)))),combs(X1,X2,X3)) = combs(X1,X2,X3),
inference(rw,[status(thm)],[i_0_331,c_0_240]),
[final] ).
cnf(i_0_522,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)],[i_0_332]),
[final] ).
cnf(i_0_523,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]),
[final] ).
cnf(i_0_524,plain,
hAPP(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combi(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)))),combc(X1,X2,X3)) = combc(X1,X2,X3),
inference(rw,[status(thm)],[i_0_333,c_0_240]),
[final] ).
cnf(i_0_525,plain,
hAPP(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combi(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)))),combb(X1,X2,X3)) = combb(X1,X2,X3),
inference(rw,[status(thm)],[i_0_334,c_0_240]),
[final] ).
cnf(i_0_526,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_335]),
[final] ).
cnf(i_0_527,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_528,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_337]),
[final] ).
cnf(i_0_529,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_338]),
[final] ).
cnf(i_0_530,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_339]),
[final] ).
cnf(i_0_531,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_340]),
[final] ).
cnf(i_0_532,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_341]),
[final] ).
cnf(i_0_533,plain,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_342]),
[final] ).
cnf(i_0_534,plain,
hAPP(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),combi(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)))),image(X1,X2)) = image(X1,X2),
inference(rw,[status(thm)],[i_0_343,c_0_240]),
[final] ).
cnf(i_0_535,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) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
inference(rw,[status(thm)],[i_0_344,c_0_240]),
[final] ).
cnf(i_0_536,plain,
hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),fun(X1,fun(fun(X1,bool),fun(X1,bool))),combi(fun(X1,fun(fun(X1,bool),fun(X1,bool)))),insert(X1)) = insert(X1),
inference(rw,[status(thm)],[i_0_345,c_0_240]),
[final] ).
cnf(i_0_537,plain,
hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3),X4) = hAPP(X1,X2,X3,X4),
inference(rw,[status(thm)],[i_0_346,c_0_240]),
[final] ).
cnf(i_0_538,plain,
hAPP(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),combi(fun(fun(x_a,bool),fun(fun(x_a,bool),bool))),p) = p,
inference(rw,[status(thm)],[i_0_347,c_0_240]),
[final] ).
cnf(i_0_539,plain,
hAPP(X1,X1,combi(X1),hAPP(X1,X1,combi(X1),X2)) = hAPP(X1,X1,combi(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_348,c_0_240]),c_0_240]),c_0_240]),
[final] ).
cnf(i_0_540,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rw,[status(thm)],[i_0_349,c_0_240]),
[final] ).
cnf(i_0_541,plain,
hAPP(X1,X1,combi(X1),hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(rw,[status(thm)],[i_0_350,c_0_240]),
[final] ).
cnf(i_0_542,plain,
hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(X1,fun(fun(X1,bool),bool)),combi(fun(X1,fun(fun(X1,bool),bool))),member(X1)) = member(X1),
inference(rw,[status(thm)],[i_0_351,c_0_240]),
[final] ).
cnf(i_0_543,hypothesis,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ),
inference(rw,[status(thm)],[i_0_352,c_0_240]),
[final] ).
cnf(i_0_544,plain,
( ~ hBOOL(hAPP(bool,bool,fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_353]),
[final] ).
cnf(i_0_545,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_354]),
[final] ).
cnf(i_0_546,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_547,plain,
hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X1,bool),fun(X1,bool)),combi(fun(fun(X1,bool),fun(X1,bool))),collect(X1)) = collect(X1),
inference(rw,[status(thm)],[i_0_356,c_0_240]),
[final] ).
cnf(i_0_548,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
inference(rw,[status(thm)],[i_0_357,c_0_240]),
[final] ).
cnf(i_0_549,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_358]),
[final] ).
cnf(i_0_550,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_359]),
[final] ).
cnf(i_0_551,plain,
( hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ preorder(X1) ),
inference(rw,[status(thm)],[i_0_360,c_0_240]),
[final] ).
cnf(i_0_552,plain,
hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),fequal(X1)) = fequal(X1),
inference(rw,[status(thm)],[i_0_361,c_0_240]),
[final] ).
cnf(i_0_553,plain,
hAPP(fun(fun(X1,bool),nat),fun(fun(X1,bool),nat),combi(fun(fun(X1,bool),nat)),finite_card(X1)) = finite_card(X1),
inference(rw,[status(thm)],[i_0_362,c_0_240]),
[final] ).
cnf(i_0_554,plain,
hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),combi(fun(fun(X1,bool),bool)),finite_finite(X1)) = finite_finite(X1),
inference(rw,[status(thm)],[i_0_363,c_0_240]),
[final] ).
cnf(i_0_555,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
inference(split_conjunct,[status(thm)],[conj_0]),
[final] ).
cnf(i_0_556,hypothesis,
hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combi(fun(nat,fun(nat,nat))),minus_minus(nat)) = minus_minus(nat),
inference(rw,[status(thm)],[i_0_364,c_0_240]),
[final] ).
cnf(i_0_557,hypothesis,
( hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[i_0_365,c_0_240]),
[final] ).
cnf(i_0_558,plain,
hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fimplies) = fimplies,
inference(rw,[status(thm)],[i_0_366,c_0_240]),
[final] ).
cnf(i_0_559,plain,
hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fdisj) = fdisj,
inference(rw,[status(thm)],[i_0_367,c_0_240]),
[final] ).
cnf(i_0_560,plain,
hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fconj) = fconj,
inference(rw,[status(thm)],[i_0_368,c_0_240]),
[final] ).
cnf(i_0_561,plain,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_369]),
[final] ).
cnf(i_0_562,plain,
hAPP(nat,nat,suc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_370]),
[final] ).
cnf(i_0_563,plain,
X1 != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_371]),
[final] ).
cnf(i_0_564,plain,
hAPP(fun(X1,X1),fun(X1,X1),combi(fun(X1,X1)),combi(X1)) = combi(X1),
inference(rw,[status(thm)],[i_0_372,c_0_240]),
[final] ).
cnf(i_0_565,hypothesis,
hAPP(fun(pname,x_a),fun(pname,x_a),combi(fun(pname,x_a)),mgt_call) = mgt_call,
inference(rw,[status(thm)],[i_0_373,c_0_240]),
[final] ).
cnf(i_0_566,hypothesis,
hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) = u,
inference(rw,[status(thm)],[i_0_374,c_0_240]),
[final] ).
cnf(i_0_567,hypothesis,
hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g) = g,
inference(rw,[status(thm)],[i_0_375,c_0_240]),
[final] ).
cnf(i_0_568,hypothesis,
hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc) = suc,
inference(rw,[status(thm)],[i_0_376,c_0_240]),
[final] ).
cnf(i_0_569,plain,
hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot) = fNot,
inference(rw,[status(thm)],[i_0_377,c_0_240]),
[final] ).
cnf(i_0_570,plain,
hAPP(X1,X1,combi(X1),undefined(X1)) = undefined(X1),
inference(rw,[status(thm)],[i_0_378,c_0_240]),
[final] ).
cnf(i_0_571,hypothesis,
hAPP(pname,pname,combi(pname),pn) = pn,
inference(rw,[status(thm)],[i_0_379,c_0_240]),
[final] ).
cnf(i_0_572,hypothesis,
hAPP(nat,nat,combi(nat),na) = na,
inference(rw,[status(thm)],[i_0_380,c_0_240]),
[final] ).
cnf(i_0_573,plain,
( finite_finite_1(fun(X2,X1))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_381]),
[final] ).
cnf(i_0_574,plain,
( order(fun(X2,X1))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_382]),
[final] ).
cnf(i_0_575,plain,
( preorder(fun(X2,X1))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_383]),
[final] ).
cnf(i_0_576,plain,
order(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]),
[final] ).
cnf(i_0_577,plain,
order(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]),
[final] ).
cnf(i_0_578,plain,
finite_finite_1(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]),
[final] ).
cnf(i_0_579,plain,
preorder(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]),
[final] ).
cnf(i_0_580,plain,
preorder(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]),
[final] ).
cnf(i_0_581,axiom,
X1 = X1 ).
cnf(i_0_582,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_583,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_584,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_585,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_586,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_587,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_588,axiom,
( X1 != X2
| image(X1,X3) = image(X2,X3) ) ).
cnf(i_0_589,axiom,
( X1 != X2
| image(X3,X1) = image(X3,X2) ) ).
cnf(i_0_590,axiom,
( X1 != X2
| insert(X1) = insert(X2) ) ).
cnf(i_0_591,axiom,
( X1 != X2
| ord_less_eq(X1) = ord_less_eq(X2) ) ).
cnf(i_0_592,axiom,
( X1 != X2
| finite_card(X1) = finite_card(X2) ) ).
cnf(i_0_593,axiom,
( X1 != X2
| minus_minus(X1) = minus_minus(X2) ) ).
cnf(i_0_594,axiom,
( X1 != X2
| combi(X1) = combi(X2) ) ).
cnf(i_0_595,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_596,axiom,
( X1 != X2
| finite_finite(X1) = finite_finite(X2) ) ).
cnf(i_0_597,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_598,axiom,
( X1 != X2
| combs(X1,X3,X4) = combs(X2,X3,X4) ) ).
cnf(i_0_599,axiom,
( X1 != X2
| combs(X3,X1,X4) = combs(X3,X2,X4) ) ).
cnf(i_0_600,axiom,
( X1 != X2
| combs(X3,X4,X1) = combs(X3,X4,X2) ) ).
cnf(i_0_601,axiom,
( X1 != X2
| combb(X1,X3,X4) = combb(X2,X3,X4) ) ).
cnf(i_0_602,axiom,
( X1 != X2
| combb(X3,X1,X4) = combb(X3,X2,X4) ) ).
cnf(i_0_603,axiom,
( X1 != X2
| combb(X3,X4,X1) = combb(X3,X4,X2) ) ).
cnf(i_0_604,axiom,
( X1 != X2
| combc(X1,X3,X4) = combc(X2,X3,X4) ) ).
cnf(i_0_605,axiom,
( X1 != X2
| combc(X3,X1,X4) = combc(X3,X2,X4) ) ).
cnf(i_0_606,axiom,
( X1 != X2
| combc(X3,X4,X1) = combc(X3,X4,X2) ) ).
cnf(i_0_607,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_608,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_609,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_610,axiom,
( X1 != X2
| ~ order(X1)
| order(X2) ) ).
cnf(i_0_611,axiom,
( X1 != X2
| ~ preorder(X1)
| preorder(X2) ) ).
cnf(i_0_612,axiom,
( X1 != X2
| ~ finite_finite_1(X1)
| finite_finite_1(X2) ) ).
cnf(i_0_581_001,axiom,
X1 = X1 ).
cnf(i_0_582_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_583_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_584_004,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_585_005,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_586_006,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_587_007,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_588_008,axiom,
( X1 != X2
| image(X1,X3) = image(X2,X3) ) ).
cnf(i_0_589_009,axiom,
( X1 != X2
| image(X3,X1) = image(X3,X2) ) ).
cnf(i_0_590_010,axiom,
( X1 != X2
| insert(X1) = insert(X2) ) ).
cnf(i_0_591_011,axiom,
( X1 != X2
| ord_less_eq(X1) = ord_less_eq(X2) ) ).
cnf(i_0_592_012,axiom,
( X1 != X2
| finite_card(X1) = finite_card(X2) ) ).
cnf(i_0_593_013,axiom,
( X1 != X2
| minus_minus(X1) = minus_minus(X2) ) ).
cnf(i_0_594_014,axiom,
( X1 != X2
| combi(X1) = combi(X2) ) ).
cnf(i_0_595_015,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_596_016,axiom,
( X1 != X2
| finite_finite(X1) = finite_finite(X2) ) ).
cnf(i_0_597_017,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_598_018,axiom,
( X1 != X2
| combs(X1,X3,X4) = combs(X2,X3,X4) ) ).
cnf(i_0_599_019,axiom,
( X1 != X2
| combs(X3,X1,X4) = combs(X3,X2,X4) ) ).
cnf(i_0_600_020,axiom,
( X1 != X2
| combs(X3,X4,X1) = combs(X3,X4,X2) ) ).
cnf(i_0_601_021,axiom,
( X1 != X2
| combb(X1,X3,X4) = combb(X2,X3,X4) ) ).
cnf(i_0_602_022,axiom,
( X1 != X2
| combb(X3,X1,X4) = combb(X3,X2,X4) ) ).
cnf(i_0_603_023,axiom,
( X1 != X2
| combb(X3,X4,X1) = combb(X3,X4,X2) ) ).
cnf(i_0_604_024,axiom,
( X1 != X2
| combc(X1,X3,X4) = combc(X2,X3,X4) ) ).
cnf(i_0_605_025,axiom,
( X1 != X2
| combc(X3,X1,X4) = combc(X3,X2,X4) ) ).
cnf(i_0_606_026,axiom,
( X1 != X2
| combc(X3,X4,X1) = combc(X3,X4,X2) ) ).
cnf(i_0_607_027,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_608_028,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_609_029,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_610_030,axiom,
( X1 != X2
| ~ order(X1)
| order(X2) ) ).
cnf(i_0_611_031,axiom,
( X1 != X2
| ~ preorder(X1)
| preorder(X2) ) ).
cnf(i_0_612_032,axiom,
( X1 != X2
| ~ finite_finite_1(X1)
| finite_finite_1(X2) ) ).
cnf(i_0_613,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X3))) ),
inference(equality_inference,[],[434]) ).
cnf(i_0_614,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(equality_inference,[],[453]) ).
cnf(i_0_615,plain,
( X1 = X1
| ~ 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),X1)) ),
inference(equality_inference,[],[455]) ).
cnf(i_0_616,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),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),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),X3)) ),
inference(equality_inference,[],[460]) ).
cnf(i_0_617,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(equality_inference,[],[462]) ).
cnf(i_0_618,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),X2)),
inference(equality_inference,[],[484]) ).
cnf(i_0_619,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(equality_inference,[],[506]) ).
cnf(i_0_620,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(equality_inference,[],[507]) ).
cnf(i_0_621,plain,
hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3) = hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3),
inference(equality_inference,[],[510]) ).
cnf(i_0_622,plain,
hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
inference(equality_inference,[],[520]) ).
cnf(i_0_623,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(equality_inference,[],[527]) ).
cnf(i_0_624,plain,
X1 = X1,
inference(equality_inference,[],[546]) ).
cnf(i_0_625,plain,
hBOOL(hAPP(pname,bool,u,pn)),
inference(scs_inference,[],[i_0_523,i_0_501]) ).
cnf(i_0_626,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(rename_variables,[],[i_0_501]) ).
cnf(i_0_627,plain,
hAPP(fun(x_a,bool),fun(x_a,bool),combi(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),combi(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)),
inference(scs_inference,[],[i_0_394,i_0_523,i_0_501,i_0_506]) ).
cnf(i_0_628,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(rename_variables,[],[i_0_506]) ).
cnf(i_0_629,plain,
hAPP(fun(x_a,bool),fun(x_a,bool),combi(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(x_a,bool),fun(x_a,bool),combi(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)),
inference(scs_inference,[],[i_0_394,i_0_523,i_0_501,i_0_506,i_0_507]) ).
cnf(i_0_630,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) ),
inference(rename_variables,[],[i_0_507]) ).
cnf(i_0_631,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(fun(pname,bool),fun(fun(pname,bool),bool),ord_less_eq(fun(pname,bool)),esk6_5(x_a,pname,g,mgt_call,u)),u)),
inference(scs_inference,[],[i_0_394,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400]) ).
cnf(i_0_632,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)))
| 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)) ),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_633,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1)),
inference(scs_inference,[],[i_0_394,i_0_528,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469]) ).
cnf(i_0_634,plain,
( ~ 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),hAPP(nat,nat,suc,X2)),X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) ),
inference(rename_variables,[],[i_0_469]) ).
cnf(i_0_635,plain,
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,esk10_2(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(scs_inference,[],[i_0_394,i_0_417,i_0_528,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478]) ).
cnf(i_0_636,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
| X2 = hAPP(nat,nat,suc,esk10_2(X1,X2)) ),
inference(rename_variables,[],[i_0_478]) ).
cnf(i_0_637,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1)) = X1,
inference(scs_inference,[],[i_0_394,i_0_417,i_0_528,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492]) ).
cnf(i_0_638,plain,
( ~ 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = X1 ),
inference(rename_variables,[],[i_0_492]) ).
cnf(i_0_639,plain,
hAPP(fun(pname,bool),fun(pname,bool),hAPP(pname,fun(fun(pname,bool),fun(pname,bool)),insert(pname),pn),u) = hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u),
inference(scs_inference,[],[i_0_394,i_0_417,i_0_528,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497]) ).
cnf(i_0_640,plain,
( ~ 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),combi(fun(X1,bool)),X3) ),
inference(rename_variables,[],[i_0_497]) ).
cnf(i_0_641,plain,
hAPP(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),esk4_4(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))) != hAPP(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),esk4_4(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(scs_inference,[],[i_0_394,i_0_417,i_0_528,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510]) ).
cnf(i_0_642,plain,
( hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3) = hAPP(fun(X1,X2),fun(X1,X2),combi(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(rename_variables,[],[i_0_510]) ).
cnf(i_0_643,plain,
~ hBOOL(hAPP(x_a,bool,g,hAPP(pname,x_a,mgt_call,pn))),
inference(scs_inference,[],[i_0_394,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514]) ).
cnf(i_0_644,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(rename_variables,[],[i_0_514]) ).
cnf(i_0_645,plain,
hAPP(nat,nat,combi(nat),X1) = X1,
inference(scs_inference,[],[i_0_394,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546]) ).
cnf(i_0_646,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rename_variables,[],[i_0_540]) ).
cnf(i_0_647,plain,
( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_546]) ).
cnf(i_0_648,plain,
combi(X1) = hAPP(fun(X1,X1),fun(X1,X1),combi(fun(X1,X1)),combi(X1)),
inference(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582]) ).
cnf(i_0_649,plain,
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(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586]) ).
cnf(i_0_650,plain,
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(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),
inference(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587]) ).
cnf(i_0_651,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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))),na)),
inference(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449]) ).
cnf(i_0_652,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(rename_variables,[],[i_0_449]) ).
cnf(i_0_653,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458]) ).
cnf(i_0_654,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),X1),X2)) ),
inference(rename_variables,[],[i_0_458]) ).
cnf(i_0_655,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,na))),hAPP(nat,nat,suc,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(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459]) ).
cnf(i_0_656,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(rename_variables,[],[i_0_459]) ).
cnf(i_0_657,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(nat,nat,suc,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(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459,i_0_490]) ).
cnf(i_0_658,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),X1),hAPP(nat,nat,suc,X2))) ),
inference(rename_variables,[],[i_0_490]) ).
cnf(i_0_659,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_482,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459,i_0_490,i_0_509]) ).
cnf(i_0_660,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(rename_variables,[],[i_0_509]) ).
cnf(i_0_661,plain,
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)) != na,
inference(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_482,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459,i_0_490,i_0_509,i_0_527]) ).
cnf(i_0_662,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_527]) ).
cnf(i_0_663,plain,
~ 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)),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(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_417,i_0_528,i_0_475,i_0_482,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459,i_0_490,i_0_509,i_0_527,i_0_410]) ).
cnf(i_0_664,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(rename_variables,[],[i_0_410]) ).
cnf(i_0_665,plain,
hAPP(fun(pname,bool),bool,finite_finite(pname),u) != 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(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_555,i_0_417,i_0_528,i_0_475,i_0_482,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459,i_0_490,i_0_509,i_0_527,i_0_410,i_0_609]) ).
cnf(i_0_666,plain,
hBOOL(hAPP(fun(x_a,bool),bool,finite_finite(x_a),g)),
inference(scs_inference,[],[i_0_394,i_0_564,i_0_540,i_0_555,i_0_417,i_0_528,i_0_475,i_0_482,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459,i_0_490,i_0_509,i_0_527,i_0_410,i_0_609,i_0_424]) ).
cnf(i_0_667,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)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X5)) ),
inference(rename_variables,[],[i_0_424]) ).
cnf(i_0_668,plain,
$false,
inference(scs_inference,[],[i_0_394,i_0_564,i_0_541,i_0_540,i_0_555,i_0_417,i_0_528,i_0_475,i_0_482,i_0_523,i_0_465,i_0_501,i_0_506,i_0_507,i_0_400,i_0_469,i_0_478,i_0_492,i_0_497,i_0_510,i_0_514,i_0_546,i_0_582,i_0_586,i_0_587,i_0_449,i_0_458,i_0_459,i_0_490,i_0_509,i_0_527,i_0_410,i_0_609,i_0_424,i_0_434]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+5 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n009.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 06:55:56 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.06/1.66 % Version : CSE_E---1.7
% 1.06/1.66 % Problem : theBenchmark.p
% 1.06/1.66 % SZS status Theorem for theBenchmark.p
% 1.06/1.66 % SZS output start CNFRefutation
% See solution above
% 1.21/1.88 % Total time : 1.325s
%------------------------------------------------------------------------------