%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW473+7 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 05:32:35 PM UTC 2026
% Result : Theorem 6.59s 5.91s
% Output : CNFRefutation 11.60s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1522)
% Comments :
%------------------------------------------------------------------------------
fof(fact_283_If__def,axiom,
! [X1,X14,X39,X16] :
( ( hBOOL(X16)
=> ti(X1,X14) = hAPP(fun(X1,bool),X1,the(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(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,X16)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14)))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X16))),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X39)))) )
& ( ~ hBOOL(X16)
=> ti(X1,X39) = hAPP(fun(X1,bool),X1,the(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(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,X16)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14)))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X16))),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X39)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_If__def) ).
fof(fact_219_finite__ne__induct,axiom,
! [X1,X16,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> ( ti(fun(X1,bool),X10) != bot_bot(fun(X1,bool))
=> ( ! [X33] : hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),bot_bot(fun(X1,bool)))))
=> ( ! [X33,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X57))
=> ( ti(fun(X1,bool),X57) != bot_bot(fun(X1,bool))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X57))
=> hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X57))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_finite__ne__induct) ).
fof(fact_111_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/sandbox2/benchmark/theBenchmark.p',fact_111_imageE) ).
fof(fact_281_flat__lub__def,axiom,
! [X1,X8,X34] :
( ( 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),bot_bot(fun(X1,bool)))))
=> hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X34),X8) = ti(X1,X34) )
& ( ~ 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),bot_bot(fun(X1,bool)))))
=> hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X34),X8) = hAPP(fun(X1,bool),X1,the(X1),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)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),bot_bot(fun(X1,bool)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_flat__lub__def) ).
fof(fact_212_folding__one_Oinsert,axiom,
! [X1,X14,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X12),X10))
=> ( 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))
=> ( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),hAPP(fun(X1,bool),X1,X10,X8)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_folding__one_Oinsert) ).
fof(fact_138_Diff__insert__absorb,axiom,
! [X1,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),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),bot_bot(fun(X1,bool)))) = ti(fun(X1,bool),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Diff__insert__absorb) ).
fof(fact_81_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/sandbox2/benchmark/theBenchmark.p',fact_81_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/sandbox2/benchmark/theBenchmark.p',fact_53_insertCI) ).
fof(fact_339_linorder__antisym__conv2,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ti(X1,X14) = ti(X1,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_linorder__antisym__conv2) ).
fof(fact_549_card__Suc__eq,axiom,
! [X1,X8,X19] :
( hAPP(fun(X1,bool),nat,finite_card(X1),X8) = hAPP(nat,nat,suc,X19)
<=> ? [X72,X61] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X72),X61)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X72),X61))
& hAPP(fun(X1,bool),nat,finite_card(X1),X61) = X19
& ( X19 = zero_zero(nat)
=> ti(fun(X1,bool),X61) = bot_bot(fun(X1,bool)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_card__Suc__eq) ).
fof(fact_308_linorder__antisym__conv3,axiom,
! [X1] :
( linorder(X1)
=> ! [X39,X14] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ti(X1,X14) = ti(X1,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_linorder__antisym__conv3) ).
fof(fact_334_linorder__antisym__conv1,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
<=> ti(X1,X14) = ti(X1,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_linorder__antisym__conv1) ).
fof(fact_188_nonempty__iff,axiom,
! [X1,X8] :
( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
<=> ? [X33,X61] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X61)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_nonempty__iff) ).
fof(fact_423_linorder__neqE__linordered__idom,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X21,X22] :
( ti(X3,X21) != ti(X3,X22)
=> ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_linorder__neqE__linordered__idom) ).
fof(fact_325_linorder__cases,axiom,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ( ti(X3,X21) != ti(X3,X22)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_linorder__cases) ).
fof(fact_309_linorder__neqE,axiom,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ti(X3,X21) != ti(X3,X22)
=> ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_linorder__neqE) ).
fof(fact_306_not__less__iff__gr__or__eq,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14))
| ti(X1,X14) = ti(X1,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_not__less__iff__gr__or__eq) ).
fof(fact_133_all__not__in__conv,axiom,
! [X1,X8] :
( ! [X33] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
<=> ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_all__not__in__conv) ).
fof(fact_125_equals0D,axiom,
! [X1,X11,X8] :
( ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_equals0D) ).
fof(fact_92_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/sandbox2/benchmark/theBenchmark.p',fact_92_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/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
fof(fact_556_card__eq__SucD,axiom,
! [X1,X8,X19] :
( hAPP(fun(X1,bool),nat,finite_card(X1),X8) = hAPP(nat,nat,suc,X19)
=> ? [X72,X61] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X72),X61)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X72),X61))
& hAPP(fun(X1,bool),nat,finite_card(X1),X61) = X19
& ( X19 = zero_zero(nat)
=> ti(fun(X1,bool),X61) = bot_bot(fun(X1,bool)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_card__eq__SucD) ).
fof(fact_533_card__eq__0__iff,axiom,
! [X1,X8] :
( hAPP(fun(X1,bool),nat,finite_card(X1),X8) = zero_zero(nat)
<=> ( ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_card__eq__0__iff) ).
fof(fact_898_fold__image__eq__general__inverses,axiom,
! [X2,X1,X48] :
( comm_monoid_mult(X48)
=> ! [X93,X44,X12,X9,X19,X112,X76] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X76))
=> ( ! [X62] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X62),X112))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X19,X62)),X76))
& hAPP(X1,X2,X9,hAPP(X2,X1,X19,X62)) = ti(X2,X62) ) )
=> ( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X76))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X9,X33)),X112))
& hAPP(X2,X1,X19,hAPP(X1,X2,X9,X33)) = ti(X1,X33)
& hAPP(X2,X48,X44,hAPP(X1,X2,X9,X33)) = hAPP(X1,X48,X12,X33) ) )
=> hAPP(fun(X1,bool),X48,hAPP(X48,fun(fun(X1,bool),X48),hAPP(fun(X1,X48),fun(X48,fun(fun(X1,bool),X48)),hAPP(fun(X48,fun(X48,X48)),fun(fun(X1,X48),fun(X48,fun(fun(X1,bool),X48))),finite_fold_image(X48,X1),times_times(X48)),X12),X93),X76) = hAPP(fun(X2,bool),X48,hAPP(X48,fun(fun(X2,bool),X48),hAPP(fun(X2,X48),fun(X48,fun(fun(X2,bool),X48)),hAPP(fun(X48,fun(X48,X48)),fun(fun(X2,X48),fun(X48,fun(fun(X2,bool),X48))),finite_fold_image(X48,X2),times_times(X48)),X44),X93),X112) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_fold__image__eq__general__inverses) ).
fof(help_COMBI_1_1_U,axiom,
! [X3,X122] : hAPP(X3,X3,combi(X3),X122) = ti(X3,X122),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
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/sandbox2/benchmark/theBenchmark.p',fact_49_pigeonhole__infinite) ).
fof(fact_543_card__less__Suc2,axiom,
! [X36,X74] :
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X74))
=> hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X74))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X36)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X74))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X36))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_card__less__Suc2) ).
fof(fact_214_folding__image__simple_Oneutral,axiom,
! [X2,X1,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite1357897459simple(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> ( ! [X33] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X33),X8))
=> hAPP(X2,X1,X44,X33) = ti(X1,X46) )
=> hAPP(fun(X2,bool),X1,X10,X8) = ti(X1,X46) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_folding__image__simple_Oneutral) ).
fof(fact_213_folding__one_Oclosed,axiom,
! [X1,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X12),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
=> ( ! [X33,X62] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X33),X62)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X62),bot_bot(fun(X1,bool))))))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(fun(X1,bool),X1,X10,X8)),X8)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_folding__one_Oclosed) ).
fof(fact_719_sum__squares__le__zero__iff,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X39),X39))),zero_zero(X1)))
<=> ( ti(X1,X14) = zero_zero(X1)
& ti(X1,X39) = zero_zero(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_sum__squares__le__zero__iff) ).
fof(fact_721_not__sum__squares__lt__zero,axiom,
! [X3] :
( linordered_ring(X3)
=> ! [X21,X22] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X22),X22))),zero_zero(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_not__sum__squares__lt__zero) ).
fof(fact_278_folding__one__idem_Ohom__commute,axiom,
! [X1,X52,X9,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X12),X10))
=> ( ! [X33,X62] : hAPP(X1,X1,X9,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X33),X62)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X1,X1,X9,X33)),hAPP(X1,X1,X9,X62))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X52))
=> ( ti(fun(X1,bool),X52) != bot_bot(fun(X1,bool))
=> hAPP(X1,X1,X9,hAPP(fun(X1,bool),X1,X10,X52)) = hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X9),X52)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_folding__one__idem_Ohom__commute) ).
fof(fact_424_psubset__insert__iff,axiom,
! [X1,X8,X14,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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(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(fun(X1,bool)),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(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(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_psubset__insert__iff) ).
fof(fact_144_subset__insert__iff,axiom,
! [X1,X8,X14,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),X14),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_subset__insert__iff) ).
fof(fact_445_image__cong,axiom,
! [X2,X1,X12,X44,X74,X52] :
( ti(fun(X1,bool),X74) = ti(fun(X1,bool),X52)
=> ( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X52))
=> hAPP(X1,X2,X12,X33) = hAPP(X1,X2,X44,X33) )
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X74) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X44),X52) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_image__cong) ).
fof(fact_210_folding__image__simple_Oinsert,axiom,
! [X2,X1,X14,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite1357897459simple(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X14),X8))
=> hAPP(fun(X2,bool),X1,X10,hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X2,X1,X44,X14)),hAPP(fun(X2,bool),X1,X10,X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_folding__image__simple_Oinsert) ).
fof(fact_142_folding__image__simple__idem_Oidem,axiom,
! [X2,X1,X14,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X12),X46),X44),X10))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),X14) = ti(X1,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_folding__image__simple__idem_Oidem) ).
fof(fact_206_folding__image__simple_Oempty,axiom,
! [X2,X1,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite1357897459simple(X1,X2),X12),X46),X44),X10))
=> hAPP(fun(X2,bool),X1,X10,bot_bot(fun(X2,bool))) = ti(X1,X46) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_folding__image__simple_Oempty) ).
fof(fact_722_sum__squares__gt__zero__iff,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X39),X39))))
<=> ( ti(X1,X14) != zero_zero(X1)
| ti(X1,X39) != zero_zero(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_sum__squares__gt__zero__iff) ).
fof(fact_164_Collect__conv__if,axiom,
! [X1,X16,X11] :
( ( hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11))),X16)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))) )
& ( ~ hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11))),X16)) = bot_bot(fun(X1,bool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Collect__conv__if) ).
fof(fact_691_eq__add__iff1,axiom,
! [X1] :
( ring(X1)
=> ! [X11,X93,X35,X34,X53] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X93)),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X93)),X53)
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34)),X93)),X35) = ti(X1,X53) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_eq__add__iff1) ).
fof(fact_690_eq__add__iff2,axiom,
! [X1] :
( ring(X1)
=> ! [X11,X93,X35,X34,X53] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X93)),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X93)),X53)
<=> ti(X1,X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X34),X11)),X93)),X53) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_eq__add__iff2) ).
fof(fact_735_fold__image__insert,axiom,
! [X1,X2] :
( ab_semigroup_mult(X2)
=> ! [X44,X46,X11,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),X11),X8))
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X44),X46),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(X1,X2,X44,X11)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X44),X46),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_fold__image__insert) ).
fof(fact_211_card__Diff__insert,axiom,
! [X1,X13,X11,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),X11),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13))),one_one(nat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_card__Diff__insert) ).
fof(fact_165_Collect__conv__if2,axiom,
! [X1,X16,X11] :
( ( hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),fequal(X1),X11))),X16)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))) )
& ( ~ hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),fequal(X1),X11))),X16)) = bot_bot(fun(X1,bool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Collect__conv__if2) ).
fof(fact_181_finite__subset__induct,axiom,
! [X1,X16,X8,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X10),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,bot_bot(fun(X1,bool))))
=> ( ! [X56,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X56),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X56),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X57))
=> hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X56),X57))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_finite__subset__induct) ).
fof(fact_648_crossproduct__eq,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X85,X39,X14,X46] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X85),X39)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X46)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X85),X46)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X39))
<=> ( ti(X1,X85) = ti(X1,X14)
| ti(X1,X39) = ti(X1,X46) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_crossproduct__eq) ).
fof(fact_645_crossproduct__noteq,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X35,X53,X11,X34] :
( ( ti(X1,X11) != ti(X1,X34)
& ti(X1,X35) != ti(X1,X53) )
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X53)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X53)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_crossproduct__noteq) ).
fof(fact_937_nat__number__of__add__left,axiom,
! [X115,X25,X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X115)))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),X25) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X115)))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),X115))),X25) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_937_nat__number__of__add__left) ).
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/sandbox2/benchmark/theBenchmark.p',fact_47_finite__subset__image) ).
fof(fact_651_le__number__of__eq__not__less,axiom,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X91,X85] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(int,X1,number_number_of(X1),X91)),hAPP(int,X1,number_number_of(X1),X85)))
<=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(int,X1,number_number_of(X1),X85)),hAPP(int,X1,number_number_of(X1),X91))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_le__number__of__eq__not__less) ).
fof(fact_109_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)))
<=> ? [X51] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X51),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),X51) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_subset__image__iff) ).
fof(fact_255_add__leE,axiom,
! [X18,X25,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X25)),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),X25),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add__leE) ).
fof(fact_104_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/sandbox2/benchmark/theBenchmark.p',fact_104_subset__insert) ).
fof(fact_198_folding__one_Oremove,axiom,
! [X1,X14,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X12),X10))
=> ( 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),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))) = bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),X1,X10,X8) = ti(X1,X14) )
& ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))) != bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),X1,X10,X8) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_folding__one_Oremove) ).
fof(fact_195_Diff__iff,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(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/sandbox2/benchmark/theBenchmark.p',fact_195_Diff__iff) ).
fof(fact_192_DiffD2,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_DiffD2) ).
fof(fact_197_folding__one_Oinsert__remove,axiom,
! [X1,X14,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X12),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))) = bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = ti(X1,X14) )
& ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))) != bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_folding__one_Oinsert__remove) ).
fof(fact_93_image__iff,axiom,
! [X1,X2,X46,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X46),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,X46) = hAPP(X2,X1,X12,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_image__iff) ).
fof(fact_670_not__square__less__zero,axiom,
! [X3] :
( linordered_ring(X3)
=> ! [X41] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X41)),zero_zero(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_not__square__less__zero) ).
fof(fact_203_card__Diff__singleton__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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),one_one(nat)) )
& ( ~ 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))) = hAPP(fun(X1,bool),nat,finite_card(X1),X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_card__Diff__singleton__if) ).
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/sandbox2/benchmark/theBenchmark.p',fact_6_card__seteq) ).
fof(fact_368_not__add__less1,axiom,
! [X26,X27] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X27)),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_not__add__less1) ).
fof(fact_369_not__add__less2,axiom,
! [X27,X26] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X26)),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_not__add__less2) ).
fof(fact_572_card__def,axiom,
! [X1,X8] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X8) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_card__def) ).
fof(fact_173_subset__singletonD,axiom,
! [X1,X8,X14] :
( 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),bot_bot(fun(X1,bool)))))
=> ( ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool))
| ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_subset__singletonD) ).
fof(fact_184_finite__induct,axiom,
! [X1,X16,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,bot_bot(fun(X1,bool))))
=> ( ! [X33,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X57))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X57))
=> hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X57))) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_finite__induct) ).
fof(fact_79_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/sandbox2/benchmark/theBenchmark.p',fact_79_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/sandbox2/benchmark/theBenchmark.p',fact_54_insertE) ).
fof(fact_217_folding__one__idem_Osubset__idem,axiom,
! [X1,X13,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X12),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ti(fun(X1,bool),X13) != bot_bot(fun(X1,bool))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(fun(X1,bool),X1,X10,X13)),hAPP(fun(X1,bool),X1,X10,X8)) = hAPP(fun(X1,bool),X1,X10,X8) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_folding__one__idem_Osubset__idem) ).
fof(fact_426_finite__conv__nat__seg__image,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
<=> ? [X32,X70] : ti(fun(X1,bool),X8) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X70),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(nat)),X32))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_finite__conv__nat__seg__image) ).
fof(fact_388_nat__seg__image__imp__finite,axiom,
! [X1,X8,X12,X20] :
( ti(fun(X1,bool),X8) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X12),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(nat)),X20)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_nat__seg__image__imp__finite) ).
fof(fact_191_DiffI,axiom,
! [X1,X13,X35,X8] :
( 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))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_DiffI) ).
fof(fact_153_doubleton__eq__iff,axiom,
! [X1,X11,X34,X35,X53] :
( 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),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),bot_bot(fun(X1,bool)))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X53),bot_bot(fun(X1,bool))))
<=> ( ( ti(X1,X11) = ti(X1,X35)
& ti(X1,X34) = ti(X1,X53) )
| ( ti(X1,X11) = ti(X1,X53)
& ti(X1,X34) = ti(X1,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_doubleton__eq__iff) ).
fof(fact_137_insert__Diff,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))))) = ti(fun(X1,bool),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_insert__Diff) ).
fof(fact_147_insert__Diff__if,axiom,
! [X1,X8,X14,X13] :
( ( 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13) )
& ( ~ 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13) = 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_insert__Diff__if) ).
fof(fact_148_double__diff,axiom,
! [X1,X45,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),X45))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X13),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X45),X8)) = ti(fun(X1,bool),X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_double__diff) ).
fof(fact_154_singleton__iff,axiom,
! [X1,X34,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool)))))
<=> ti(X1,X34) = ti(X1,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_singleton__iff) ).
fof(fact_152_singletonE,axiom,
! [X1,X34,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool)))))
=> ti(X1,X34) = ti(X1,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_singletonE) ).
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/sandbox2/benchmark/theBenchmark.p',fact_50_image__eqI) ).
fof(fact_95_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/sandbox2/benchmark/theBenchmark.p',fact_95_rev__image__eqI) ).
fof(fact_687_add__scale__eq__noteq,axiom,
! [X3] :
( semiri456707255roduct(X3)
=> ! [X40,X64,X41,X42,X92] :
( ti(X3,X92) != zero_zero(X3)
=> ( ( ti(X3,X41) = ti(X3,X42)
& ti(X3,X40) != ti(X3,X64) )
=> hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X92),X40)) != hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X92),X64)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_add__scale__eq__noteq) ).
fof(fact_573_fold__image__empty,axiom,
! [X2,X1,X12,X44,X46] : hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),X12),X44),X46),bot_bot(fun(X2,bool))) = ti(X1,X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_fold__image__empty) ).
fof(fact_688_sum__squares__eq__zero__iff,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X39] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X39),X39)) = zero_zero(X1)
<=> ( ti(X1,X14) = zero_zero(X1)
& ti(X1,X39) = zero_zero(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_sum__squares__eq__zero__iff) ).
fof(fact_218_folding__one__idem_Oinsert__idem,axiom,
! [X1,X14,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X12),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),hAPP(fun(X1,bool),X1,X10,X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_folding__one__idem_Oinsert__idem) ).
fof(fact_943_Suc__nat__number__of__add,axiom,
! [X17,X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X17) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X82))),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_Suc__nat__number__of__add) ).
fof(fact_936_eq__nat__number__of,axiom,
! [X91,X114] :
( hAPP(int,nat,number_number_of(nat),X91) = hAPP(int,nat,number_number_of(nat),X114)
<=> ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X91)))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X114)),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X91)))
=> ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X114)))
=> hAPP(int,int,number_number_of(int),X91) = zero_zero(int) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X114)))
=> X91 = X114 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_eq__nat__number__of) ).
fof(fact_540_nat__diff__split__asm,axiom,
! [X16,X11,X34] :
( hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X11),X34)))
<=> ~ ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X11),X34))
& ~ hBOOL(hAPP(nat,bool,X16,zero_zero(nat))) )
| ? [X79] :
( X11 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X79)
& ~ hBOOL(hAPP(nat,bool,X16,X79)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_nat__diff__split__asm) ).
fof(fact_80_insert__code,axiom,
! [X1,X39,X8,X14] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X39),X8),X14))
<=> ( ti(X1,X39) = ti(X1,X14)
| hBOOL(hAPP(X1,bool,X8,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_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/sandbox2/benchmark/theBenchmark.p',fact_35_not__less__eq__eq) ).
fof(tsy_c_Finite__Set_Ofolding__image__simple__idem_res,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple__idem_res) ).
fof(tsy_c_Finite__Set_Ofolding__image__simple_res,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite1357897459simple(X1,X2)) = finite1357897459simple(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple_res) ).
fof(fact_415_less__fun__def,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X12,X44] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X12),X44))
<=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X44))
& ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X44),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_less__fun__def) ).
fof(fact_85_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/sandbox2/benchmark/theBenchmark.p',fact_85_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/sandbox2/benchmark/theBenchmark.p',fact_51_equalityI) ).
fof(fact_947_nat__number__of__Bit1,axiom,
! [X86] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X86)))
=> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X86)) = zero_zero(nat) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X86)))
=> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X86)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X86)),hAPP(int,nat,number_number_of(nat),X86))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_nat__number__of__Bit1) ).
fof(fact_209_folding__one_Osingleton,axiom,
! [X1,X14,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X12),X10))
=> hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))) = ti(X1,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_folding__one_Osingleton) ).
fof(fact_495_add__nonneg__eq__0__iff,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X39,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X39))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X39) = zero_zero(X1)
<=> ( ti(X1,X14) = zero_zero(X1)
& ti(X1,X39) = zero_zero(X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_add__nonneg__eq__0__iff) ).
fof(fact_357_not__less__eq,axiom,
! [X28,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),hAPP(nat,nat,suc,X28))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_not__less__eq) ).
fof(fact_277_card_Oinsert,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,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_card_Oinsert) ).
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/sandbox2/benchmark/theBenchmark.p',fact_8_card__insert__if) ).
fof(fact_421_psubset__eq,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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),X13))
& ti(fun(X1,bool),X8) != ti(fun(X1,bool),X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_psubset__eq) ).
fof(fact_420_subset__iff__psubset__eq,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(fun(X1,bool)),X8),X13))
| ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_subset__iff__psubset__eq) ).
fof(fact_907_abs__le__zero__iff,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),X11)),zero_zero(X1)))
<=> ti(X1,X11) = zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_907_abs__le__zero__iff) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_31_le__SucE) ).
fof(fact_909_abs__not__less__zero,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,abs_abs(X3),X41)),zero_zero(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_abs__not__less__zero) ).
fof(fact_330_less__le__not__le,axiom,
! [X1] :
( preorder(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
& ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X39),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_less__le__not__le) ).
fof(fact_834_of__nat__less__0__iff,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X18] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X18)),zero_zero(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_of__nat__less__0__iff) ).
fof(fact_831_int__less__0__conv,axiom,
! [X25] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X25)),zero_zero(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_int__less__0__conv) ).
fof(fact_365_less__SucE,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),hAPP(nat,nat,suc,X17)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> X18 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_less__SucE) ).
fof(fact_361_less__antisym,axiom,
! [X17,X18] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X18))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,suc,X18)))
=> X18 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_less__antisym) ).
fof(fact_360_not__less__less__Suc__eq,axiom,
! [X20,X28] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),hAPP(nat,nat,suc,X28)))
<=> X20 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_not__less__less__Suc__eq) ).
fof(fact_68_xt1_I5_J,axiom,
! [X3] :
( order(X3)
=> ! [X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
=> ti(X3,X21) = ti(X3,X22) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_xt1_I5_J) ).
fof(fact_66_order__antisym,axiom,
! [X3] :
( order(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> ti(X3,X21) = ti(X3,X22) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_order__antisym) ).
fof(fact_61_order__antisym__conv,axiom,
! [X1] :
( order(X1)
=> ! [X39,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X39),X14))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
<=> ti(X1,X14) = ti(X1,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_order__antisym__conv) ).
fof(fact_59_order__eq__iff,axiom,
! [X1] :
( order(X1)
=> ! [X14,X39] :
( ti(X1,X14) = ti(X1,X39)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X39),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order__eq__iff) ).
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/sandbox2/benchmark/theBenchmark.p',fact_36_Suc__n__not__le__n) ).
fof(fact_821_pinf_I6_J,axiom,
! [X3] :
( linorder(X3)
=> ! [X68] :
? [X94] :
! [X33] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X94),X33))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X68)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_pinf_I6_J) ).
fof(fact_227_folding__one__idem_Oidem,axiom,
! [X1,X14,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X12),X10))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),X14) = ti(X1,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_folding__one__idem_Oidem) ).
fof(fact_820_minf_I8_J,axiom,
! [X3] :
( linorder(X3)
=> ! [X68] :
? [X94] :
! [X33] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X94))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X68),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_820_minf_I8_J) ).
fof(fact_548_ex__least__nat__less,axiom,
! [X20,X16] :
( ~ hBOOL(hAPP(nat,bool,X16,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X16,X20))
=> ? [X65] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),X20))
& ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X69),X65))
=> ~ hBOOL(hAPP(nat,bool,X16,X69)) )
& hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X65),one_one(nat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_ex__least__nat__less) ).
fof(fact_828_of__nat__number__of__lemma,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,X3,number_number_of(X3),X82) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = zero_zero(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_of__nat__number__of__lemma) ).
fof(fact_327_linorder__not__le,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_linorder__not__le) ).
fof(fact_337_leD,axiom,
! [X3] :
( linorder(X3)
=> ! [X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_leD) ).
fof(fact_326_linorder__not__less,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X39),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_linorder__not__less) ).
fof(fact_324_order__less__asym,axiom,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_order__less__asym) ).
fof(fact_316_order__less__asym_H,axiom,
! [X3] :
( preorder(X3)
=> ! [X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_order__less__asym_H) ).
fof(fact_312_order__less__imp__not__less,axiom,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_order__less__imp__not__less) ).
fof(fact_311_order__less__not__sym,axiom,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_order__less__not__sym) ).
fof(fact_317_xt1_I9_J,axiom,
! [X3] :
( order(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_xt1_I9_J) ).
fof(fact_63_xt1_I3_J,axiom,
! [X3] :
( order(X3)
=> ! [X40,X41,X42] :
( ti(X3,X41) = ti(X3,X42)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X41)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_xt1_I3_J) ).
fof(fact_65_xt1_I4_J,axiom,
! [X3] :
( order(X3)
=> ! [X40,X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X41))
=> ( ti(X3,X42) = ti(X3,X40)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X41)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_xt1_I4_J) ).
fof(fact_319_xt1_I1_J,axiom,
! [X3] :
( order(X3)
=> ! [X40,X41,X42] :
( ti(X3,X41) = ti(X3,X42)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X41)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_xt1_I1_J) ).
fof(fact_321_xt1_I2_J,axiom,
! [X3] :
( order(X3)
=> ! [X40,X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41))
=> ( ti(X3,X42) = ti(X3,X40)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X41)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_xt1_I2_J) ).
fof(fact_544_card__gt__0__iff,axiom,
! [X1,X8] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X8)))
<=> ( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_card__gt__0__iff) ).
fof(fact_342_xt1_I11_J,axiom,
! [X3] :
( order(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X41))
=> ( ti(X3,X41) != ti(X3,X42)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_xt1_I11_J) ).
fof(fact_341_order__le__neq__trans,axiom,
! [X3] :
( order(X3)
=> ! [X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( ti(X3,X41) != ti(X3,X42)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_order__le__neq__trans) ).
fof(fact_340_order__le__imp__less__or__eq,axiom,
! [X3] :
( order(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
| ti(X3,X21) = ti(X3,X22) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_order__le__imp__less__or__eq) ).
fof(fact_335_order__neq__le__trans,axiom,
! [X3] :
( order(X3)
=> ! [X41,X42] :
( ti(X3,X41) != ti(X3,X42)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_order__neq__le__trans) ).
fof(fact_331_order__le__less,axiom,
! [X1] :
( order(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
| ti(X1,X14) = ti(X1,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_order__le__less) ).
fof(fact_329_order__less__le,axiom,
! [X1] :
( order(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
& ti(X1,X14) != ti(X1,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_order__less__le) ).
fof(fact_336_xt1_I12_J,axiom,
! [X3] :
( order(X3)
=> ! [X41,X42] :
( ti(X3,X41) != ti(X3,X42)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X41))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_xt1_I12_J) ).
fof(fact_551_ex__least__nat__le,axiom,
! [X20,X16] :
( ~ hBOOL(hAPP(nat,bool,X16,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X16,X20))
=> ? [X65] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X20))
& ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X65))
=> ~ hBOOL(hAPP(nat,bool,X16,X69)) )
& hBOOL(hAPP(nat,bool,X16,X65)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_ex__least__nat__le) ).
fof(fact_910_zero__less__abs__iff,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,abs_abs(X1),X11)))
<=> ti(X1,X11) != zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_zero__less__abs__iff) ).
fof(fact_889_int__if__cong,axiom,
! [X14,X39,X16] :
( ( hBOOL(X16)
=> hAPP(nat,int,semiring_1_of_nat(int),X14) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X16),X14),X39)) )
& ( ~ hBOOL(X16)
=> hAPP(nat,int,semiring_1_of_nat(int),X39) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X16),X14),X39)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_889_int__if__cong) ).
fof(fact_706_Ints__double__eq__0__iff,axiom,
! [X1] :
( ring_char_0(X1)
=> ! [X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),ring_1_Ints(X1)))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11) = zero_zero(X1)
<=> ti(X1,X11) = zero_zero(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_Ints__double__eq__0__iff) ).
fof(tsy_c_Finite__Set_Ofold__image_res,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofold__image_res) ).
fof(fact_240_diff__add__cancel,axiom,
! [X3] :
( group_add(X3)
=> ! [X41,X42] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),X42)),X42) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_diff__add__cancel) ).
fof(fact_241_add__diff__cancel,axiom,
! [X3] :
( group_add(X3)
=> ! [X41,X42] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X42) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_add__diff__cancel) ).
fof(fact_83_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/sandbox2/benchmark/theBenchmark.p',fact_83_insert__absorb) ).
fof(fact_827_tsub__def,axiom,
! [X22,X21] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X21))
=> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X21),X22) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),X22) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X21))
=> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X21),X22) = zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_tsub__def) ).
fof(fact_964_mult__numeral__1,axiom,
! [X3] :
( number_ring(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(int,X3,number_number_of(X3),hAPP(int,int,bit1,pls))),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_mult__numeral__1) ).
fof(fact_151_singleton__inject,axiom,
! [X1,X11,X34] :
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),bot_bot(fun(X1,bool)))
=> ti(X1,X11) = ti(X1,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_singleton__inject) ).
fof(fact_405_add__diff__inverse,axiom,
! [X18,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_add__diff__inverse) ).
fof(fact_178_diff__eq__diff__eq,axiom,
! [X1] :
( ab_group_add(X1)
=> ! [X11,X34,X35,X53] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X35),X53)
=> ( ti(X1,X11) = ti(X1,X34)
<=> ti(X1,X35) = ti(X1,X53) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_diff__eq__diff__eq) ).
fof(fact_157_subset__empty,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),bot_bot(fun(X1,bool))))
<=> ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_subset__empty) ).
fof(fact_176_image__constant__conv,axiom,
! [X2,X1,X35,X8] :
( ( ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(X2,fun(X1,X2),combk(X2,X1),X35)),X8) = bot_bot(fun(X2,bool)) )
& ( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(X2,fun(X1,X2),combk(X2,X1),X35)),X8) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X35),bot_bot(fun(X2,bool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_image__constant__conv) ).
fof(fact_948_nat__1__add__number__of,axiom,
! [X82] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X82),pls))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X82)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X82),pls))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X82)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_nat__1__add__number__of) ).
fof(fact_307_linorder__less__linear,axiom,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
| ti(X3,X21) = ti(X3,X22)
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_linorder__less__linear) ).
fof(fact_305_linorder__neq__iff,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ti(X1,X14) != ti(X1,X39)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_linorder__neq__iff) ).
fof(fact_290_the1__equality,axiom,
! [X1,X11,X16] :
( ? [X33] :
( hBOOL(hAPP(X1,bool,X16,X33))
& ! [X62] :
( hBOOL(hAPP(X1,bool,X16,X62))
=> ti(X1,X62) = ti(X1,X33) ) )
=> ( hBOOL(hAPP(X1,bool,X16,X11))
=> hAPP(fun(X1,bool),X1,the(X1),X16) = ti(X1,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_the1__equality) ).
fof(fact_185_finite_Osimps,axiom,
! [X1,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X11))
<=> ( ti(fun(X1,bool),X11) = bot_bot(fun(X1,bool))
| ? [X59,X56] :
( ti(fun(X1,bool),X11) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X56),X59)
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X59)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_finite_Osimps) ).
fof(fact_416_not__psubset__empty,axiom,
! [X1,X8] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_not__psubset__empty) ).
fof(fact_132_ex__in__conv,axiom,
! [X1,X8] :
( ? [X33] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
<=> ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_ex__in__conv) ).
fof(fact_291_theI,axiom,
! [X1,X16,X11] :
( hBOOL(hAPP(X1,bool,X16,X11))
=> ( ! [X33] :
( hBOOL(hAPP(X1,bool,X16,X33))
=> ti(X1,X33) = ti(X1,X11) )
=> hBOOL(hAPP(X1,bool,X16,hAPP(fun(X1,bool),X1,the(X1),X16))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_theI) ).
fof(fact_289_theI_H,axiom,
! [X1,X16] :
( ? [X33] :
( hBOOL(hAPP(X1,bool,X16,X33))
& ! [X62] :
( hBOOL(hAPP(X1,bool,X16,X62))
=> ti(X1,X62) = ti(X1,X33) ) )
=> hBOOL(hAPP(X1,bool,X16,hAPP(fun(X1,bool),X1,the(X1),X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_theI_H) ).
fof(fact_314_order__less__imp__not__eq2,axiom,
! [X3] :
( order(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ti(X3,X22) != ti(X3,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_order__less__imp__not__eq2) ).
fof(fact_313_order__less__imp__not__eq,axiom,
! [X3] :
( order(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ti(X3,X21) != ti(X3,X22) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_order__less__imp__not__eq) ).
fof(fact_310_less__imp__neq,axiom,
! [X3] :
( order(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ti(X3,X21) != ti(X3,X22) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_less__imp__neq) ).
fof(fact_905_not__neg__eq__ge__0,axiom,
! [X14] :
( ~ hBOOL(hAPP(int,bool,nat_neg,X14))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_not__neg__eq__ge__0) ).
fof(fact_70_linorder__le__cases,axiom,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_linorder__le__cases) ).
fof(fact_332_leI,axiom,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_leI) ).
fof(fact_333_not__leE,axiom,
! [X3] :
( linorder(X3)
=> ! [X22,X21] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_not__leE) ).
fof(fact_86_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/sandbox2/benchmark/theBenchmark.p',fact_86_equalityD1) ).
fof(fact_87_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/sandbox2/benchmark/theBenchmark.p',fact_87_equalityD2) ).
fof(fact_299_linorder__neqE__nat,axiom,
! [X21,X22] :
( X21 != X22
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_linorder__neqE__nat) ).
fof(fact_899_of__nat__number__of__eq,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = zero_zero(X3) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,X3,number_number_of(X3),X82) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_of__nat__number__of__eq) ).
fof(fact_284_the__eq__trivial,axiom,
! [X1,X11] : hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11)) = ti(X1,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_the__eq__trivial) ).
fof(fact_906_abs__of__nonneg,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> hAPP(X3,X3,abs_abs(X3),X41) = ti(X3,X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_abs__of__nonneg) ).
fof(fact_911_abs__of__pos,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> hAPP(X3,X3,abs_abs(X3),X41) = ti(X3,X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_abs__of__pos) ).
fof(fact_938_int__nat__number__of,axiom,
! [X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X82)) = zero_zero(int) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,int,number_number_of(int),X82) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_938_int__nat__number__of) ).
fof(fact_946_Suc__nat__number__of,axiom,
! [X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X82)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X82)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_Suc__nat__number__of) ).
fof(fact_226_add__right__imp__eq,axiom,
! [X3] :
( cancel_semigroup_add(X3)
=> ! [X42,X41,X40] :
( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X41) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X41)
=> ti(X3,X42) = ti(X3,X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add__right__imp__eq) ).
fof(fact_223_add__right__cancel,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X34,X11,X35] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X34),X11) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X11)
<=> ti(X1,X34) = ti(X1,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_add__right__cancel) ).
fof(fact_225_add__imp__eq,axiom,
! [X3] :
( cancel146912293up_add(X3)
=> ! [X41,X42,X40] :
( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)
=> ti(X3,X42) = ti(X3,X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__imp__eq) ).
fof(fact_224_add__left__imp__eq,axiom,
! [X3] :
( cancel_semigroup_add(X3)
=> ! [X41,X42,X40] :
( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)
=> ti(X3,X42) = ti(X3,X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_add__left__imp__eq) ).
fof(fact_222_add__left__cancel,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X11,X34,X35] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X35)
<=> ti(X1,X34) = ti(X1,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add__left__cancel) ).
fof(fact_74_ext,axiom,
! [X1,X2,X12,X44] :
( ! [X33] : hAPP(X1,X2,X12,X33) = hAPP(X1,X2,X44,X33)
=> ti(fun(X1,X2),X12) = ti(fun(X1,X2),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
fof(fact_129_empty__iff,axiom,
! [X1,X35] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_empty__iff) ).
fof(fact_121_emptyE,axiom,
! [X1,X11] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_emptyE) ).
fof(fact_355_bot__less,axiom,
! [X1] :
( bot(X1)
=> ! [X11] :
( ti(X1,X11) != bot_bot(X1)
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),bot_bot(X1)),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_bot__less) ).
fof(fact_162_bot__unique,axiom,
! [X1] :
( bot(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),bot_bot(X1)))
<=> ti(X1,X11) = bot_bot(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_bot__unique) ).
fof(fact_161_le__bot,axiom,
! [X3] :
( bot(X3)
=> ! [X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),bot_bot(X3)))
=> ti(X3,X41) = bot_bot(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_le__bot) ).
fof(fact_187_the__elem__eq,axiom,
! [X1,X14] : hAPP(fun(X1,bool),X1,the_elem(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))) = ti(X1,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_the__elem__eq) ).
fof(fact_450_Plus__eq__empty__conv,axiom,
! [X2,X1,X8,X13] :
( hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13) = bot_bot(fun(sum_sum(X1,X2),bool))
<=> ( ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool))
& ti(fun(X2,bool),X13) = bot_bot(fun(X2,bool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_Plus__eq__empty__conv) ).
fof(fact_506_not__one__le__zero,axiom,
! [X3] :
( linordered_semidom(X3)
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),one_one(X3)),zero_zero(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_not__one__le__zero) ).
fof(fact_509_not__one__less__zero,axiom,
! [X3] :
( linordered_semidom(X3)
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),zero_zero(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_not__one__less__zero) ).
fof(fact_491_nat__case__0,axiom,
! [X1,X54,X55] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X54),X55),zero_zero(nat)) = ti(X1,X54),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_nat__case__0) ).
fof(fact_354_not__less__bot,axiom,
! [X3] :
( bot(X3)
=> ! [X41] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),bot_bot(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_not__less__bot) ).
fof(fact_963_mult__numeral__1__right,axiom,
! [X3] :
( number_ring(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),hAPP(int,X3,number_number_of(X3),hAPP(int,int,bit1,pls))) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_963_mult__numeral__1__right) ).
fof(fact_304_order__less__irrefl,axiom,
! [X3] :
( preorder(X3)
=> ! [X21] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_order__less__irrefl) ).
fof(fact_891_of__nat__aux_Osimps_I1_J,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X108,X36] : hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),X108),zero_zero(nat)),X36) = ti(X1,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_of__nat__aux_Osimps_I1_J) ).
fof(fact_484_not__less0,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_not__less0) ).
fof(fact_482_less__nat__zero__code,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_less__nat__zero__code) ).
fof(fact_454_less__zeroE,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_less__zeroE) ).
fof(fact_300_less__irrefl__nat,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_less__irrefl__nat) ).
fof(fact_297_less__not__refl,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_less__not__refl) ).
fof(help_fimplies_3_1_U,axiom,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X122),X123))
| ~ hBOOL(X122)
| hBOOL(X123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(help_fdisj_3_1_U,axiom,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X122),X123))
| hBOOL(X122)
| hBOOL(X123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X122),X123))
| hBOOL(X122) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X122),X123))
| hBOOL(X123) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
fof(help_If_1_1_T,axiom,
! [X3,X21,X22] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fTrue),X21),X22) = ti(X3,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
fof(help_If_2_1_T,axiom,
! [X3,X21,X22] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fFalse),X21),X22) = ti(X3,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
fof(tsy_c_Sum__Type_OPlus_res,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Sum__Type_OPlus_res) ).
fof(tsy_c_Finite__Set_Ofolding__one__idem_res,axiom,
! [X1] : ti(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),finite2073411215e_idem(X1)) = finite2073411215e_idem(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one__idem_res) ).
fof(tsy_c_Finite__Set_Ofolding__one_res,axiom,
! [X1] : ti(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),finite_folding_one(X1)) = finite_folding_one(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one_res) ).
fof(fact_933_not__neg__int,axiom,
! [X17] : ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_not__neg__int) ).
fof(fact_288_the__equality,axiom,
! [X1,X16,X11] :
( hBOOL(hAPP(X1,bool,X16,X11))
=> ( ! [X33] :
( hBOOL(hAPP(X1,bool,X16,X33))
=> ti(X1,X33) = ti(X1,X11) )
=> hAPP(fun(X1,bool),X1,the(X1),X16) = ti(X1,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_the__equality) ).
fof(fact_158_image__is__empty,axiom,
! [X2,X1,X12,X8] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8) = bot_bot(fun(X1,bool))
<=> ti(fun(X2,bool),X8) = bot_bot(fun(X2,bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_image__is__empty) ).
fof(fact_160_empty__is__image,axiom,
! [X1,X2,X12,X8] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)
<=> ti(fun(X2,bool),X8) = bot_bot(fun(X2,bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_empty__is__image) ).
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/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
fof(fact_972_add__numeral__0,axiom,
! [X3] :
( number_ring(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),pls)),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_add__numeral__0) ).
fof(fact_568_add__0__iff,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X34,X11] :
( ti(X1,X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X34),X11)
<=> ti(X1,X11) = zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_add__0__iff) ).
fof(fact_581_mult__eq__0__iff,axiom,
! [X1] :
( ring_n68954251visors(X1)
=> ! [X11,X34] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X34) = zero_zero(X1)
<=> ( ti(X1,X11) = zero_zero(X1)
| ti(X1,X34) = zero_zero(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_mult__eq__0__iff) ).
fof(fact_583_divisors__zero,axiom,
! [X3] :
( no_zero_divisors(X3)
=> ! [X41,X42] :
( hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42) = zero_zero(X3)
=> ( ti(X3,X41) = zero_zero(X3)
| ti(X3,X42) = zero_zero(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_divisors__zero) ).
fof(fact_582_no__zero__divisors,axiom,
! [X3] :
( no_zero_divisors(X3)
=> ! [X42,X41] :
( ti(X3,X41) != zero_zero(X3)
=> ( ti(X3,X42) != zero_zero(X3)
=> hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42) != zero_zero(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_no__zero__divisors) ).
fof(fact_470_right__minus__eq,axiom,
! [X1] :
( group_add(X1)
=> ! [X11,X34] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34) = zero_zero(X1)
<=> ti(X1,X11) = ti(X1,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_right__minus__eq) ).
fof(fact_471_eq__iff__diff__eq__0,axiom,
! [X1] :
( ab_group_add(X1)
=> ! [X11,X34] :
( ti(X1,X11) = ti(X1,X34)
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34) = zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_eq__iff__diff__eq__0) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
fof(fact_128_Diff__empty,axiom,
! [X1,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),bot_bot(fun(X1,bool))) = ti(fun(X1,bool),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Diff__empty) ).
fof(fact_973_add__numeral__0__right,axiom,
! [X3] :
( number_ring(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),hAPP(int,X3,number_number_of(X3),pls)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_add__numeral__0__right) ).
fof(help_fconj_1_1_U,axiom,
! [X123,X122] :
( ~ hBOOL(X122)
| ~ hBOOL(X123)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X122),X123)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fimplies_2_1_U,axiom,
! [X122,X123] :
( ~ hBOOL(X123)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X122),X123)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(help_fdisj_1_1_U,axiom,
! [X123,X122] :
( ~ hBOOL(X122)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X122),X123)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(help_fdisj_2_1_U,axiom,
! [X122,X123] :
( ~ hBOOL(X123)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X122),X123)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
fof(fact_555_double__eq__0__iff,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X11] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11) = zero_zero(X1)
<=> ti(X1,X11) = zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_double__eq__0__iff) ).
fof(fact_467_double__zero__sym,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X11] :
( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11)
<=> ti(X1,X11) = zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_double__zero__sym) ).
fof(fact_98_image__ident,axiom,
! [X1,X49] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X49) = ti(fun(X1,bool),X49),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_image__ident) ).
fof(tsy_c_Nat_Onat_Onat__case_res,axiom,
! [X1] : ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Onat_Onat__case_res) ).
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/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
fof(fact_126_Collect__empty__eq,axiom,
! [X1,X16] :
( hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = bot_bot(fun(X1,bool))
<=> ! [X33] : ~ hBOOL(hAPP(X1,bool,X16,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Collect__empty__eq) ).
fof(fact_130_empty__Collect__eq,axiom,
! [X1,X16] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)
<=> ! [X33] : ~ hBOOL(hAPP(X1,bool,X16,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_empty__Collect__eq) ).
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/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res,axiom,
! [X1] :
( semiring_1(X1)
=> ti(fun(fun(X1,X1),fun(nat,fun(X1,X1))),semiri532925092at_aux(X1)) = semiri532925092at_aux(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) ).
fof(help_COMBK_1_1_U,axiom,
! [X1,X3,X122,X123] : hAPP(X1,X3,hAPP(X3,fun(X1,X3),combk(X3,X1),X122),X123) = ti(X3,X122),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(fact_287_the__sym__eq__trivial,axiom,
! [X1,X14] : hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),X14)) = ti(X1,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_the__sym__eq__trivial) ).
fof(fact_594_mult__1,axiom,
! [X3] :
( comm_monoid_mult(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),one_one(X3)),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_mult__1) ).
fof(fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),one_one(X3)),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_595_mult__1__left,axiom,
! [X3] :
( monoid_mult(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),one_one(X3)),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_mult__1__left) ).
fof(fact_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_468_add__0,axiom,
! [X3] :
( comm_monoid_add(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_add__0) ).
fof(fact_469_add__0__left,axiom,
! [X3] :
( monoid_add(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_add__0__left) ).
fof(fact_592_mult_Ocomm__neutral,axiom,
! [X3] :
( comm_monoid_mult(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),one_one(X3)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_mult_Ocomm__neutral) ).
fof(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),one_one(X3)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_593_mult__1__right,axiom,
! [X3] :
( monoid_mult(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),one_one(X3)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_mult__1__right) ).
fof(fact_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),zero_zero(X3)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_465_add_Ocomm__neutral,axiom,
! [X3] :
( comm_monoid_add(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),zero_zero(X3)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_add_Ocomm__neutral) ).
fof(fact_466_add__0__right,axiom,
! [X3] :
( monoid_add(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),zero_zero(X3)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_add__0__right) ).
fof(fact_473_diff__0__right,axiom,
! [X3] :
( group_add(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),zero_zero(X3)) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_diff__0__right) ).
fof(fact_607_mult__idem,axiom,
! [X3] :
( ab_sem1668676832m_mult(X3)
=> ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),X21) = ti(X3,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_mult__idem) ).
fof(fact_606_times_Oidem,axiom,
! [X3] :
( ab_sem1668676832m_mult(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X41) = ti(X3,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_times_Oidem) ).
fof(help_ti_idem,axiom,
! [X120,X121] : ti(X120,ti(X120,X121)) = ti(X120,X121),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
fof(tsy_c_Finite__Set_Ocomp__fun__idem_res,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X2,X2)),bool),finite_comp_fun_idem(X1,X2)) = finite_comp_fun_idem(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocomp__fun__idem_res) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(tsy_c_If_res,axiom,
! [X3] : ti(fun(bool,fun(X3,fun(X3,X3))),if(X3)) = if(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_If_res) ).
fof(tsy_c_Partial__Function_Oflat__lub_res,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),X1)),partial_flat_lub(X1)) = partial_flat_lub(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Partial__Function_Oflat__lub_res) ).
fof(tsy_c_member_res,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).
fof(fact_517_card__infinite,axiom,
! [X1,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_card__infinite) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [X4] :
( hBOOL(ti(bool,X4))
<=> hBOOL(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(help_fNot_1_1_U,axiom,
! [X122] :
( ~ hBOOL(hAPP(bool,bool,fNot,X122))
| ~ hBOOL(X122) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
fof(fact_929_abs__eq__0,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X11] :
( hAPP(X1,X1,abs_abs(X1),X11) = zero_zero(X1)
<=> ti(X1,X11) = zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_929_abs__eq__0) ).
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/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
fof(tsy_c_COMBK_res,axiom,
! [X3,X1] : ti(fun(X3,fun(X1,X3)),combk(X3,X1)) = combk(X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
fof(tsy_c_Groups_Otimes__class_Otimes_4_res,axiom,
! [X3] :
( mult_zero(X3)
=> ti(fun(X3,fun(X3,X3)),times_times(X3)) = times_times(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).
fof(tsy_c_Groups_Otimes__class_Otimes_3_res,axiom,
! [X3] :
( no_zero_divisors(X3)
=> ti(fun(X3,fun(X3,X3)),times_times(X3)) = times_times(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_res) ).
fof(tsy_c_Groups_Otimes__class_Otimes_2_res,axiom,
! [X3] :
( semiring(X3)
=> ti(fun(X3,fun(X3,X3)),times_times(X3)) = times_times(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_res) ).
fof(tsy_c_Groups_Otimes__class_Otimes_1_res,axiom,
! [X3] :
( monoid_mult(X3)
=> ti(fun(X3,fun(X3,X3)),times_times(X3)) = times_times(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
fof(tsy_c_Groups_Otimes__class_Otimes_0_res,axiom,
! [X3] :
( ab_semigroup_mult(X3)
=> ti(fun(X3,fun(X3,X3)),times_times(X3)) = times_times(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
fof(tsy_c_Groups_Oplus__class_Oplus_2_res,axiom,
! [X3] :
( ab_semigroup_add(X3)
=> ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).
fof(tsy_c_Groups_Oplus__class_Oplus_1_res,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
fof(tsy_c_Groups_Oplus__class_Oplus_0_res,axiom,
! [X3] :
( monoid_add(X3)
=> ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
fof(tsy_c_Groups_Ominus__class_Ominus_res,axiom,
! [X2] :
( minus(X2)
=> ti(fun(X2,fun(X2,X2)),minus_minus(X2)) = minus_minus(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
! [X3] :
( ord(X3)
=> ti(fun(X3,fun(X3,bool)),ord_less_eq(X3)) = ord_less_eq(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(tsy_c_Orderings_Oord__class_Oless_res,axiom,
! [X3] :
( ord(X3)
=> ti(fun(X3,fun(X3,bool)),ord_less(X3)) = ord_less(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).
fof(tsy_c_Set_Othe__elem_res,axiom,
! [X1] : ti(fun(fun(X1,bool),X1),the_elem(X1)) = the_elem(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Othe__elem_res) ).
fof(tsy_c_HOL_OThe_res,axiom,
! [X1] : ti(fun(fun(X1,bool),X1),the(X1)) = the(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_OThe_res) ).
fof(tsy_c_fequal_res,axiom,
! [X3] : ti(fun(X3,fun(X3,bool)),fequal(X3)) = fequal(X3),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
fof(help_fFalse_1_1_T,axiom,
! [X122] :
( ti(bool,X122) = fTrue
| ti(bool,X122) = fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(help_If_3_1_T,axiom,
! [X122] :
( ti(bool,X122) = fTrue
| ti(bool,X122) = fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
fof(tsy_c_Groups_Oabs__class_Oabs_res,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ti(fun(X3,X3),abs_abs(X3)) = abs_abs(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oabs__class_Oabs_res) ).
fof(tsy_c_COMBI_res,axiom,
! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
fof(tsy_c_Int_Onumber__class_Onumber__of_res,axiom,
! [X1] :
( number(X1)
=> ti(fun(int,X1),number_number_of(X1)) = number_number_of(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
fof(tsy_c_Nat_Osemiring__1__class_Oof__nat_res,axiom,
! [X3] :
( semiring_1(X3)
=> ti(fun(nat,X3),semiring_1_of_nat(X3)) = semiring_1_of_nat(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).
fof(tsy_c_Int_Oring__1__class_OInts_res,axiom,
! [X1] :
( ring_1(X1)
=> ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Oring__1__class_OInts_res) ).
fof(tsy_c_Orderings_Obot__class_Obot_res,axiom,
! [X1] :
( bot(X1)
=> ti(X1,bot_bot(X1)) = bot_bot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
fof(tsy_c_Groups_Ozero__class_Ozero_res,axiom,
! [X1] :
( zero(X1)
=> ti(X1,zero_zero(X1)) = zero_zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).
fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
! [X1] :
( one(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
fof(tsy_c_HOL_Oundefined_res,axiom,
! [X3] : ti(X3,undefined(X3)) = undefined(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(fact_897_fold__image__related,axiom,
! [X2,X1] :
( comm_monoid_mult(X1)
=> ! [X9,X44,X76,X75,X93] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X75,X93),X93))
=> ( ! [X107,X109,X110,X111] :
( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X75,X107),X110))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X75,X109),X111)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X75,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X107),X109)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X110),X111))) )
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X76))
=> ( ! [X33] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X33),X76))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X75,hAPP(X2,X1,X9,X33)),hAPP(X2,X1,X44,X33))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X75,hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X93),X76)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X44),X93),X76))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_fold__image__related) ).
fof(fact_541_card__less__Suc,axiom,
! [X36,X74] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X74))
=> hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X74))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X36))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X74))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X36))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_card__less__Suc) ).
fof(fact_900_decr__lemma,axiom,
! [X21,X43,X64] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X64))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),X43))),one_one(int))),X64))),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_decr__lemma) ).
fof(fact_942_nat__intermed__int__val,axiom,
! [X19,X12,X20,X28] :
( ! [X69] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X69))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X20)) )
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X12,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X69),one_one(nat)))),hAPP(nat,int,X12,X69)))),one_one(int))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X12,X28)),X19))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),hAPP(nat,int,X12,X20)))
=> ? [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X69))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X69),X20))
& hAPP(nat,int,X12,X69) = X19 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_nat__intermed__int__val) ).
fof(fact_941_nat0__intermed__int__val,axiom,
! [X19,X12,X20] :
( ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X20))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X12,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X69),one_one(nat)))),hAPP(nat,int,X12,X69)))),one_one(int))) )
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X12,zero_zero(nat))),X19))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),hAPP(nat,int,X12,X20)))
=> ? [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X69),X20))
& hAPP(nat,int,X12,X69) = X19 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_nat0__intermed__int__val) ).
fof(fact_940_int__val__lemma,axiom,
! [X19,X12,X20] :
( ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X20))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X12,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X69),one_one(nat)))),hAPP(nat,int,X12,X69)))),one_one(int))) )
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X12,zero_zero(nat))),X19))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),hAPP(nat,int,X12,X20)))
=> ? [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X69),X20))
& hAPP(nat,int,X12,X69) = X19 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_940_int__val__lemma) ).
fof(fact_292_card__Diff2__less,axiom,
! [X1,X39,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))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X39),X8))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X39),bot_bot(fun(X1,bool)))))),hAPP(fun(X1,bool),nat,finite_card(X1),X8))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_card__Diff2__less) ).
fof(fact_939_incr__lemma,axiom,
! [X43,X21,X64] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X64))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X43),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X21),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),X43))),one_one(int))),X64)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_incr__lemma) ).
fof(fact_726_le__add__iff1,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X11,X93,X35,X34,X53] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X93)),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X93)),X53)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34)),X93)),X35)),X53)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_le__add__iff1) ).
fof(fact_728_less__add__iff1,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X11,X93,X35,X34,X53] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X93)),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X93)),X53)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34)),X93)),X35)),X53)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_less__add__iff1) ).
fof(fact_789_nat__le__add__iff1,axiom,
! [X60,X28,X20,X66,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X66),X36))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X36),X60)),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X66),X60)),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X36),X66)),X60)),X28)),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_nat__le__add__iff1) ).
fof(fact_795_nat__less__add__iff1,axiom,
! [X60,X28,X20,X66,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X66),X36))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X36),X60)),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X66),X60)),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X36),X66)),X60)),X28)),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_nat__less__add__iff1) ).
fof(fact_435_xt4,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X35,X12,X34,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X12,X34)),X11))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X35),X34))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X62),X33))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X12,X62)),hAPP(X2,X1,X12,X33))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X12,X35)),X11)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_xt4) ).
fof(fact_434_xt6,axiom,
! [X2,X1] :
( ( order(X1)
& ord(X2) )
=> ! [X35,X12,X34,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X12,X34)),X11))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X35),X34))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X62),X33))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X12,X62)),hAPP(X2,X1,X12,X33))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X12,X35)),X11)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_xt6) ).
fof(fact_442_order__le__less__subst2,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X12,X35,X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X34))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X34)),X35))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X33),X62))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X12,X62))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X11)),X35)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_order__le__less__subst2) ).
fof(fact_443_order__less__le__subst2,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X12,X35,X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X34)),X35))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X33),X62))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X12,X62))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X11)),X35)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_order__less__le__subst2) ).
fof(fact_441_xt7,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X35,X12,X34,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X11))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X35),hAPP(X1,X2,X12,X34)))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X62),X33))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X62)),hAPP(X1,X2,X12,X33))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X35),hAPP(X1,X2,X12,X11))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_xt7) ).
fof(fact_440_xt5,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X35,X12,X34,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X11))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X35),hAPP(X1,X2,X12,X34)))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X62),X33))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X62)),hAPP(X1,X2,X12,X33))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X35),hAPP(X1,X2,X12,X11))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_xt5) ).
fof(fact_437_order__less__le__subst1,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X35,X11,X12,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),hAPP(X2,X1,X12,X34)))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X34),X35))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X33),X62))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X12,X33)),hAPP(X2,X1,X12,X62))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),hAPP(X2,X1,X12,X35))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_order__less__le__subst1) ).
fof(fact_436_order__le__less__subst1,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X35,X11,X12,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),hAPP(X2,X1,X12,X34)))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X34),X35))
=> ( ! [X33,X62] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X33),X62))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X12,X33)),hAPP(X2,X1,X12,X62))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),hAPP(X2,X1,X12,X35))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_order__le__less__subst1) ).
fof(fact_725_le__add__iff2,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X11,X93,X35,X34,X53] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X93)),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X93)),X53)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X34),X11)),X93)),X53))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_725_le__add__iff2) ).
fof(fact_727_less__add__iff2,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X11,X93,X35,X34,X53] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X93)),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X93)),X53)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X34),X11)),X93)),X53))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_less__add__iff2) ).
fof(fact_792_nat__le__add__iff2,axiom,
! [X60,X28,X20,X36,X66] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X66))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X36),X60)),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X66),X60)),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X66),X36)),X60)),X20))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_nat__le__add__iff2) ).
fof(fact_742_nat__less__add__iff2,axiom,
! [X60,X28,X20,X36,X66] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X66))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X36),X60)),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X66),X60)),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X66),X36)),X60)),X20))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_nat__less__add__iff2) ).
fof(fact_542_card__less,axiom,
! [X36,X74] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X74))
=> hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X74))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X36))))) != zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_card__less) ).
fof(fact_902_abs__diff__triangle__ineq,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42,X40,X64] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X64)))),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),X40))),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X42),X64))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_902_abs__diff__triangle__ineq) ).
fof(fact_736_fold__image__distrib,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X44,X9,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X44)),X9)),one_one(X2)),X8) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X44),one_one(X2)),X8)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X9),one_one(X2)),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_fold__image__distrib) ).
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/sandbox2/benchmark/theBenchmark.p',fact_26_finite__Collect__disjI) ).
fof(fact_790_nat__diff__add__eq1,axiom,
! [X83,X18,X17,X27,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X26))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X26),X83)),X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X27),X83)),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X27)),X83)),X18)),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_790_nat__diff__add__eq1) ).
fof(fact_182_assms_I2_J,axiom,
! [X58,X7] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,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,X58)),X7)),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(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X58)))),bot_bot(fun(x_a,bool)))))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X7),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,X58)),bot_bot(fun(x_a,bool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_assms_I2_J) ).
fof(fact_804_unique__quotient__lemma,axiom,
! [X42,X103,X104,X101,X92] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X42),X103)),X104)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X42),X101)),X92)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X104))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X104),X42))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X92),X42))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X103),X101)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_unique__quotient__lemma) ).
fof(fact_797_unique__quotient__lemma__neg,axiom,
! [X42,X103,X104,X101,X92] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X42),X103)),X104)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X42),X101)),X92)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X92),zero_zero(int)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X42),X92))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X42),X104))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X101),X103)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_unique__quotient__lemma__neg) ).
fof(fact_390_finite__M__bounded__by__nat,axiom,
! [X16,X36] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X16)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X36))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_finite__M__bounded__by__nat) ).
fof(fact_172_image__diff__subset,axiom,
! [X1,X2,X12,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),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(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X8),X13)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_image__diff__subset) ).
fof(fact_73_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/sandbox2/benchmark/theBenchmark.p',fact_73_insert__Collect) ).
fof(fact_796_zdiv__mono2__neg__lemma,axiom,
! [X42,X101,X92,X102,X103,X104] :
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X42),X101)),X92) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X102),X103)),X104)
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X102),X103)),X104)),zero_zero(int)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X92),X42))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X104))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X102))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X102),X42))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X103),X101)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_zdiv__mono2__neg__lemma) ).
fof(fact_808_fold__image__cong,axiom,
! [X1,X2] :
( ab_semigroup_mult(X2)
=> ! [X46,X44,X9,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> hAPP(X1,X2,X44,X33) = hAPP(X1,X2,X9,X33) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X44),X46),X8) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X9),X46),X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_fold__image__cong) ).
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/sandbox2/benchmark/theBenchmark.p',fact_10_finite__Collect__conjI) ).
fof(fact_186_finite__less__ub,axiom,
! [X60,X12] :
( ! [X32] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),hAPP(nat,nat,X12,X32)))
=> 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),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X12)),X60)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_finite__less__ub) ).
fof(fact_196_set__diff__eq,axiom,
! [X1,X8,X13] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),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),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(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),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/sandbox2/benchmark/theBenchmark.p',fact_196_set__diff__eq) ).
fof(fact_293_card__Diff1__less,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))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))),hAPP(fun(X1,bool),nat,finite_card(X1),X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_card__Diff1__less) ).
fof(fact_200_folding__image__simple_Oremove,axiom,
! [X2,X1,X14,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite1357897459simple(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X14),X8))
=> hAPP(fun(X2,bool),X1,X10,X8) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X2,X1,X44,X14)),hAPP(fun(X2,bool),X1,X10,hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X8),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X14),bot_bot(fun(X2,bool)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_folding__image__simple_Oremove) ).
fof(fact_199_folding__image__simple_Oinsert__remove,axiom,
! [X2,X1,X14,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite1357897459simple(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> hAPP(fun(X2,bool),X1,X10,hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X2,X1,X44,X14)),hAPP(fun(X2,bool),X1,X10,hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X8),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X14),bot_bot(fun(X2,bool)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_folding__image__simple_Oinsert__remove) ).
fof(fact_793_nat__diff__add__eq2,axiom,
! [X83,X18,X17,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X26),X83)),X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X27),X83)),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X26)),X83)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_nat__diff__add__eq2) ).
fof(fact_170_card__Diff1__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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))),hAPP(fun(X1,bool),nat,finite_card(X1),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_card__Diff1__le) ).
fof(fact_575_Ints__odd__less__0,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X11)),X11)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),zero_zero(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_Ints__odd__less__0) ).
fof(fact_737_convex__bound__le,axiom,
! [X3] :
( linord1278240602ring_1(X3)
=> ! [X82,X83,X22,X21,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X83))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X82))
=> ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X83),X82) = one_one(X3)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X83),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X82),X22))),X41)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_convex__bound__le) ).
fof(fact_577_convex__bound__lt,axiom,
! [X3] :
( linord626643107strict(X3)
=> ! [X82,X83,X22,X21,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X83))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X82))
=> ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X83),X82) = one_one(X3)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X83),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X82),X22))),X41)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_convex__bound__lt) ).
fof(fact_803_q__neg__lemma,axiom,
! [X102,X103,X104] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X102),X103)),X104)),zero_zero(int)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X104))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X102))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X103),zero_zero(int))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_q__neg__lemma) ).
fof(fact_143_diff__single__insert,axiom,
! [X1,X8,X14,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))),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(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))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_diff__single__insert) ).
fof(fact_766_odd__less__0,axiom,
! [X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X46)),X46)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X46),zero_zero(int))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_odd__less__0) ).
fof(fact_282_comp__fun__idem__remove,axiom,
! [X1] : hBOOL(hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),bool,finite_comp_fun_idem(X1,fun(X1,bool)),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X1,bool),fun(X1,bool))),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),X1),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool))),combc(fun(X1,bool),fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)))),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X1,fun(X1,bool))),combc(X1,fun(X1,bool),fun(X1,bool)),insert(X1)),bot_bot(fun(X1,bool)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_comp__fun__idem__remove) ).
fof(fact_574_folding__image__simple_Oeq__fold__g,axiom,
! [X2,X1,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite1357897459simple(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> hAPP(fun(X2,bool),X1,X10,X8) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),X12),X44),X46),X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_folding__image__simple_Oeq__fold__g) ).
fof(fact_805_zdiv__mono2__lemma,axiom,
! [X42,X101,X92,X102,X103,X104] :
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X42),X101)),X92) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X102),X103)),X104)
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X102),X103)),X104)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X104),X102))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X92))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X102))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X102),X42))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X101),X103)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_zdiv__mono2__lemma) ).
fof(fact_119_folding__image__simple__idem_Osubset__idem,axiom,
! [X2,X1,X13,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X13),X8))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(fun(X2,bool),X1,X10,X13)),hAPP(fun(X2,bool),X1,X10,X8)) = hAPP(fun(X2,bool),X1,X10,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_folding__image__simple__idem_Osubset__idem) ).
fof(fact_177_folding__image__simple__idem_Oin__idem,axiom,
! [X2,X1,X14,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X14),X8))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X2,X1,X44,X14)),hAPP(fun(X2,bool),X1,X10,X8)) = hAPP(fun(X2,bool),X1,X10,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_folding__image__simple__idem_Oin__idem) ).
fof(fact_912_abs__triangle__ineq3,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42)))),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),X42)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_abs__triangle__ineq3) ).
fof(fact_120_folding__image__simple__idem_Oinsert__idem,axiom,
! [X2,X1,X14,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> hAPP(fun(X2,bool),X1,X10,hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X2,X1,X44,X14)),hAPP(fun(X2,bool),X1,X10,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_113_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/sandbox2/benchmark/theBenchmark.p',fact_113_image__subsetI) ).
fof(fact_96_insert__compr__raw,axiom,
! [X1,X33,X47] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X47) = 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)),X47))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insert__compr__raw) ).
fof(fact_72_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/sandbox2/benchmark/theBenchmark.p',fact_72_insert__compr) ).
fof(fact_815_transfer__nat__int__set__cong,axiom,
! [X105,X16] :
( ! [X33] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X33))
=> ( hBOOL(hAPP(int,bool,X16,X33))
<=> hBOOL(hAPP(int,bool,X105,X33)) ) )
=> hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X16)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X105)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_transfer__nat__int__set__cong) ).
fof(fact_704_Suc__mult__le__cancel1,axiom,
! [X19,X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X19)),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X19)),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_Suc__mult__le__cancel1) ).
fof(fact_701_Suc__mult__less__cancel1,axiom,
! [X19,X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X19)),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X19)),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_Suc__mult__less__cancel1) ).
fof(fact_452_pred__subset__eq,axiom,
! [X1,X75,X76] :
( 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(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X75)),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)),X76)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X75),X76)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_pred__subset__eq) ).
fof(fact_791_nat__eq__add__iff1,axiom,
! [X60,X28,X20,X66,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X66),X36))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X36),X60)),X28) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X66),X60)),X20)
<=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X36),X66)),X60)),X28) = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_nat__eq__add__iff1) ).
fof(fact_794_nat__eq__add__iff2,axiom,
! [X60,X28,X20,X36,X66] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X66))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X36),X60)),X28) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X66),X60)),X20)
<=> X28 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X66),X36)),X60)),X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_nat__eq__add__iff2) ).
fof(fact_915_abs__mult__less,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X42,X64,X41,X40] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,abs_abs(X3),X41)),X40))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,abs_abs(X3),X42)),X64))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42))),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_abs__mult__less) ).
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/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(fact_802_q__pos__lemma,axiom,
! [X102,X103,X104] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X102),X103)),X104)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X104),X102))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X102))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X103)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_q__pos__lemma) ).
fof(fact_180_diff__card__le__card__Diff,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),X13))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_diff__card__le__card__Diff) ).
fof(fact_409_mono__nat__linear__lb,axiom,
! [X28,X19,X12] :
( ! [X38,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X38),X32))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X12,X38)),hAPP(nat,nat,X12,X32))) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X12,X28)),X19)),hAPP(nat,nat,X12,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X19)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_mono__nat__linear__lb) ).
fof(fact_412_lift__Suc__mono__less__iff,axiom,
! [X1] :
( order(X1)
=> ! [X20,X28,X12] :
( ! [X32] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X12,X32)),hAPP(nat,X1,X12,hAPP(nat,nat,suc,X32))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X12,X20)),hAPP(nat,X1,X12,X28)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X28)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_lift__Suc__mono__less__iff) ).
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/sandbox2/benchmark/theBenchmark.p',fact_48_lift__Suc__mono__le) ).
fof(fact_413_lift__Suc__mono__less,axiom,
! [X1] :
( order(X1)
=> ! [X20,X31,X12] :
( ! [X32] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(nat),X20),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X12,X20)),hAPP(nat,X1,X12,X31))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_lift__Suc__mono__less) ).
fof(fact_826_plusinfinity,axiom,
! [X16,X105,X53] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X53))
=> ( ! [X33,X65] :
( hBOOL(hAPP(int,bool,X105,X33))
<=> hBOOL(hAPP(int,bool,X105,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X33),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X65),X53)))) )
=> ( ? [X94] :
! [X33] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X94),X33))
=> ( hBOOL(hAPP(int,bool,X16,X33))
<=> hBOOL(hAPP(int,bool,X105,X33)) ) )
=> ( ? [X107] : hBOOL(hAPP(int,bool,X105,X107))
=> ? [X107] : hBOOL(hAPP(int,bool,X16,X107)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_plusinfinity) ).
fof(fact_825_minusinfinity,axiom,
! [X16,X106,X53] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X53))
=> ( ! [X33,X65] :
( hBOOL(hAPP(int,bool,X106,X33))
<=> hBOOL(hAPP(int,bool,X106,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X33),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X65),X53)))) )
=> ( ? [X94] :
! [X33] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X33),X94))
=> ( hBOOL(hAPP(int,bool,X16,X33))
<=> hBOOL(hAPP(int,bool,X106,X33)) ) )
=> ( ? [X107] : hBOOL(hAPP(int,bool,X106,X107))
=> ? [X107] : hBOOL(hAPP(int,bool,X16,X107)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_minusinfinity) ).
fof(fact_591_combine__common__factor,axiom,
! [X3] :
( semiring(X3)
=> ! [X41,X84,X42,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X84)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X84)),X40)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X84)),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_combine__common__factor) ).
fof(fact_183_finite__empty__induct,axiom,
! [X1,X16,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X8))
=> ( ! [X56,X59] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X59))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X56),X59))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X59))
=> hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X59),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X56),bot_bot(fun(X1,bool)))))) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,bot_bot(fun(X1,bool)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_finite__empty__induct) ).
fof(fact_785_left__add__mult__distrib,axiom,
! [X26,X83,X27,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X26),X83)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X27),X83)),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X27)),X83)),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_785_left__add__mult__distrib) ).
fof(fact_876_zmult__zless__mono2__lemma,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X25))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X25)),X26)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X25)),X27))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_876_zmult__zless__mono2__lemma) ).
fof(fact_913_abs__triangle__ineq2,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42))),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),X42)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_abs__triangle__ineq2) ).
fof(fact_914_abs__triangle__ineq2__sym,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42))),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X42),X41)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_914_abs__triangle__ineq2__sym) ).
fof(fact_116_assms_I3_J,axiom,
! [X7,X35] :
( hBOOL(hAPP(com,bool,wt,X35))
=> ( ! [X33] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X33),u))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X7),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,X33)),bot_bot(fun(x_a,bool))))) )
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X7),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(com,x_a,mgt,X35)),bot_bot(fun(x_a,bool))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_assms_I3_J) ).
fof(fact_864_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
! [X16] : hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X16)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),X16),semiring_1_of_nat(int)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_864_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).
fof(fact_171_finite__Diff__insert,axiom,
! [X1,X8,X11,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))))
<=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_finite__Diff__insert) ).
fof(fact_916_abs__triangle__ineq,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42))),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_abs__triangle__ineq) ).
fof(fact_901_abs__triangle__ineq4,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),X42))),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_abs__triangle__ineq4) ).
fof(fact_885_transfer__nat__int__set__relations_I5_J,axiom,
! [X8,X13] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X8),X13))
<=> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X8)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_885_transfer__nat__int__set__relations_I5_J) ).
fof(fact_884_transfer__nat__int__set__relations_I4_J,axiom,
! [X8,X13] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),X8),X13))
<=> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X8)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_transfer__nat__int__set__relations_I4_J) ).
fof(fact_879_zdiff__int__split,axiom,
! [X16,X14,X39] :
( hBOOL(hAPP(int,bool,X16,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X14),X39))))
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X39),X14))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(nat,int,semiring_1_of_nat(int),X39)))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X39))
=> hBOOL(hAPP(int,bool,X16,zero_zero(int))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_zdiff__int__split) ).
fof(fact_720_sum__squares__ge__zero,axiom,
! [X3] :
( linordered_ring(X3)
=> ! [X21,X22] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X22),X22)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_sum__squares__ge__zero) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_39_le__diff__iff) ).
fof(fact_407_less__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(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(nat),X28),X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_less__diff__iff) ).
fof(fact_149_Diff__mono,axiom,
! [X1,X50,X13,X8,X45] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X45))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X50),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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X45),X50))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Diff__mono) ).
fof(fact_819_incr__mult__lemma,axiom,
! [X19,X16,X53] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X53))
=> ( ! [X33] :
( hBOOL(hAPP(int,bool,X16,X33))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X33),X53))) )
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X19))
=> ! [X33] :
( hBOOL(hAPP(int,bool,X16,X33))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X33),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X19),X53)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_819_incr__mult__lemma) ).
fof(fact_816_decr__mult__lemma,axiom,
! [X19,X16,X53] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X53))
=> ( ! [X33] :
( hBOOL(hAPP(int,bool,X16,X33))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X33),X53))) )
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X19))
=> ! [X33] :
( hBOOL(hAPP(int,bool,X16,X33))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X33),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X19),X53)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_decr__mult__lemma) ).
fof(fact_708_mult__right__le__imp__le,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X41,X40,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_mult__right__le__imp__le) ).
fof(fact_707_mult__left__le__imp__le,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_mult__left__le__imp__le) ).
fof(fact_718_mult__le__cancel__left__pos,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X11,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X11)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_mult__le__cancel__left__pos) ).
fof(fact_712_mult__right__less__imp__less,axiom,
! [X3] :
( linordered_semiring(X3)
=> ! [X41,X40,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_mult__right__less__imp__less) ).
fof(fact_711_mult__less__imp__less__right,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X41,X40,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_mult__less__imp__less__right) ).
fof(fact_710_mult__left__less__imp__less,axiom,
! [X3] :
( linordered_semiring(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_mult__left__less__imp__less) ).
fof(fact_709_mult__less__imp__less__left,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_mult__less__imp__less__left) ).
fof(fact_673_mult__less__cancel__left__pos,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X11,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X11)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_mult__less__cancel__left__pos) ).
fof(fact_717_mult__le__cancel__left__neg,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X11,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X11)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_mult__le__cancel__left__neg) ).
fof(fact_679_mult__less__cancel__left__neg,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X11,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X11)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_mult__less__cancel__left__neg) ).
fof(fact_656_mult__mono_H,axiom,
! [X3] :
( ordered_semiring(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X64))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_mult__mono_H) ).
fof(fact_655_mult__mono,axiom,
! [X3] :
( ordered_semiring(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X64))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_mult__mono) ).
fof(fact_714_mult__less__le__imp__less,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X64))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_mult__less__le__imp__less) ).
fof(fact_713_mult__le__less__imp__less,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X64))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_mult__le__less__imp__less) ).
fof(fact_715_mult__strict__mono_H,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X64))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_mult__strict__mono_H) ).
fof(fact_716_mult__strict__mono,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X64))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_mult__strict__mono) ).
fof(fact_734_mult__le__cancel2,axiom,
! [X28,X19,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X19)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X20),X19)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_mult__le__cancel2) ).
fof(fact_788_nat__mult__le__cancel1,axiom,
! [X28,X20,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_nat__mult__le__cancel1) ).
fof(fact_733_mult__le__cancel1,axiom,
! [X19,X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_mult__le__cancel1) ).
fof(fact_787_nat__mult__less__cancel1,axiom,
! [X28,X20,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_nat__mult__less__cancel1) ).
fof(fact_672_mult__less__cancel__left__disj,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X35,X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X11)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X35))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X11)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_mult__less__cancel__left__disj) ).
fof(fact_671_mult__less__cancel__right__disj,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X11,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X35))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X11)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_mult__less__cancel__right__disj) ).
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/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
fof(fact_263_le__add__diff,axiom,
! [X18,X25,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X18)),X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_le__add__diff) ).
fof(fact_266_le__diff__conv2,axiom,
! [X36,X19,X66] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X66))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X66),X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),X19)),X66)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_le__diff__conv2) ).
fof(fact_238_add__le__imp__le__right,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X41,X40,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X40)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_add__le__imp__le__right) ).
fof(fact_233_add__le__cancel__right,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X11,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X34),X35)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add__le__cancel__right) ).
fof(fact_239_add__le__imp__le__left,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X42)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_add__le__imp__le__left) ).
fof(fact_234_add__le__cancel__left,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X35,X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X11)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X34)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__le__cancel__left) ).
fof(fact_352_add__less__imp__less__right,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X41,X40,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X40)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_add__less__imp__less__right) ).
fof(fact_347_add__less__cancel__right,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X11,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X34),X35)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_add__less__cancel__right) ).
fof(fact_353_add__less__imp__less__left,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X42)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_add__less__imp__less__left) ).
fof(fact_348_add__less__cancel__left,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X35,X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X11)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X34)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_add__less__cancel__left) ).
fof(fact_110_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/sandbox2/benchmark/theBenchmark.p',fact_110_image__mono) ).
fof(fact_699_mult__less__cancel1,axiom,
! [X19,X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_mult__less__cancel1) ).
fof(fact_698_mult__less__cancel2,axiom,
! [X28,X19,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X19)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X20),X19)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_mult__less__cancel2) ).
fof(fact_248_nat__add__left__cancel__le,axiom,
! [X19,X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_nat__add__left__cancel__le) ).
fof(fact_370_nat__add__left__cancel__less,axiom,
! [X19,X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_nat__add__left__cancel__less) ).
fof(fact_215_card_Oremove,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),X8) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_card_Oremove) ).
fof(fact_114_le__funI,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X12,X44] :
( ! [X33] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X44,X33)))
=> hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X44)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_le__funI) ).
fof(fact_99_le__fun__def,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X12,X44] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X44))
<=> ! [X33] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X44,X33))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_le__fun__def) ).
fof(fact_103_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/sandbox2/benchmark/theBenchmark.p',fact_103_insert__subset) ).
fof(fact_168_card__Suc__Diff1,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(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))) = hAPP(fun(X1,bool),nat,finite_card(X1),X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_card__Suc__Diff1) ).
fof(fact_216_card_Oinsert__remove,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_card_Oinsert__remove) ).
fof(fact_106_insert__mono,axiom,
! [X1,X11,X45,X50] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X45),X50))
=> 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),X45)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X50))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_insert__mono) ).
fof(fact_140_Diff__insert2,axiom,
! [X1,X8,X11,X13] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),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),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))))),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Diff__insert2) ).
fof(fact_732_one__le__mult__iff,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X28))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_one__le__mult__iff) ).
fof(fact_731_one__less__mult,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X18))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_one__less__mult) ).
fof(fact_169_card__insert,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(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)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_card__insert) ).
fof(fact_262_le__diff__conv,axiom,
! [X66,X19,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X66),X19)),X36))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X66),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),X19))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_le__diff__conv) ).
fof(fact_404_less__diff__conv,axiom,
! [X36,X66,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X66),X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),X19)),X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_less__diff__conv) ).
fof(fact_740_field__le__mult__one__interval,axiom,
! [X3] :
( linord1117847801e_zero(X3)
=> ! [X21,X22] :
( ! [X94] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X94))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X94),one_one(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X94),X21)),X22)) ) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_field__le__mult__one__interval) ).
fof(fact_661_mult__right__mono,axiom,
! [X3] :
( ordered_semiring(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_mult__right__mono) ).
fof(fact_659_comm__mult__left__mono,axiom,
! [X3] :
( ordere1490568538miring(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_comm__mult__left__mono) ).
fof(fact_660_mult__left__mono,axiom,
! [X3] :
( ordered_semiring(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_mult__left__mono) ).
fof(fact_682_mult__strict__right__mono,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_mult__strict__right__mono) ).
fof(fact_684_comm__mult__strict__left__mono,axiom,
! [X3] :
( linord893533164strict(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_comm__mult__strict__left__mono) ).
fof(fact_683_mult__strict__left__mono,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_mult__strict__left__mono) ).
fof(fact_658_mult__right__mono__neg,axiom,
! [X3] :
( ordered_ring(X3)
=> ! [X40,X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_mult__right__mono__neg) ).
fof(fact_657_mult__left__mono__neg,axiom,
! [X3] :
( ordered_ring(X3)
=> ! [X40,X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_mult__left__mono__neg) ).
fof(fact_685_mult__strict__right__mono__neg,axiom,
! [X3] :
( linord581940658strict(X3)
=> ! [X40,X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_mult__strict__right__mono__neg) ).
fof(fact_686_mult__strict__left__mono__neg,axiom,
! [X3] :
( linord581940658strict(X3)
=> ! [X40,X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X40),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_mult__strict__left__mono__neg) ).
fof(fact_237_add__mono,axiom,
! [X3] :
( ordere779506340up_add(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X64))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add__mono) ).
fof(fact_391_add__less__le__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X40),X64))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_add__less__le__mono) ).
fof(fact_392_add__le__less__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X64))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_add__le__less__mono) ).
fof(fact_351_add__strict__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X40,X64,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X40),X64))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_add__strict__mono) ).
fof(fact_220_the__elem__def,axiom,
! [X1,X63] : hAPP(fun(X1,bool),X1,the_elem(X1),X63) = hAPP(fun(X1,bool),X1,the(X1),hAPP(fun(X1,fun(X1,bool)),fun(X1,bool),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,fun(X1,bool)),fun(X1,bool)),combb(fun(X1,bool),bool,X1),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),fequal(fun(X1,bool)),X63)),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X1,fun(X1,bool))),combc(X1,fun(X1,bool),fun(X1,bool)),insert(X1)),bot_bot(fun(X1,bool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_the__elem__def) ).
fof(fact_428_less__mono__imp__le__mono,axiom,
! [X36,X66,X12] :
( ! [X69,X71] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X71))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X12,X69)),hAPP(nat,nat,X12,X71))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X66))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X12,X36)),hAPP(nat,nat,X12,X66))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_less__mono__imp__le__mono) ).
fof(fact_667_mult__le__0__iff,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X34)),zero_zero(X1)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_mult__le__0__iff) ).
fof(fact_757_zmult__zless__mono2,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X26),X27))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X25))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X25),X26)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X25),X27))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_zmult__zless__mono2) ).
fof(fact_697_mult__less__mono1,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X26),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X27),X25))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_mult__less__mono1) ).
fof(fact_696_mult__less__mono2,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X26)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X27))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_mult__less__mono2) ).
fof(fact_779_zadd__zless__mono,axiom,
! [X99,X43,X100,X86] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X100),X86))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X99),X43))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X100),X99)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X86),X43))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_zadd__zless__mono) ).
fof(fact_599_mult__le__mono,axiom,
! [X25,X29,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),X25),X29))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X26),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X27),X29))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_mult__le__mono) ).
fof(fact_252_add__le__mono,axiom,
! [X25,X29,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),X25),X29))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X29))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__le__mono) ).
fof(fact_374_add__less__mono,axiom,
! [X25,X29,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X29))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X29))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_add__less__mono) ).
fof(fact_406_diff__less__mono,axiom,
! [X40,X41,X42] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X41),X42))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X40),X41))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X41),X40)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X42),X40))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_diff__less__mono) ).
fof(fact_386_diff__less__mono2,axiom,
! [X29,X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X29))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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/sandbox2/benchmark/theBenchmark.p',fact_386_diff__less__mono2) ).
fof(fact_730_n__less__n__mult__m,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X18))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X17),X18))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_n__less__n__mult__m) ).
fof(fact_729_n__less__m__mult__n,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X18))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_n__less__m__mult__n) ).
fof(fact_806_int__less__induct,axiom,
! [X16,X36,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X36),X19))
=> ( hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X19),one_one(int))))
=> ( ! [X69] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X69),X19))
=> ( hBOOL(hAPP(int,bool,X16,X69))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X69),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X16,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_int__less__induct) ).
fof(fact_809_int__gr__induct,axiom,
! [X16,X19,X36] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X19),X36))
=> ( hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X19),one_one(int))))
=> ( ! [X69] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X19),X69))
=> ( hBOOL(hAPP(int,bool,X16,X69))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X69),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X16,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_int__gr__induct) ).
fof(fact_724_mult__right__le__one__le,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),one_one(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),X22)),X21)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_mult__right__le__one__le) ).
fof(fact_723_mult__left__le__one__le,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),one_one(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X22),X21)),X21)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_mult__left__le__one__le) ).
fof(fact_824_int__induct,axiom,
! [X36,X16,X19] :
( hBOOL(hAPP(int,bool,X16,X19))
=> ( ! [X69] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),X69))
=> ( hBOOL(hAPP(int,bool,X16,X69))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X69),one_one(int)))) ) )
=> ( ! [X69] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X69),X19))
=> ( hBOOL(hAPP(int,bool,X16,X69))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X69),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X16,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_int__induct) ).
fof(fact_629_right__distrib__number__of,axiom,
! [X1] :
( ( number(X1)
& semiring(X1) )
=> ! [X82,X42,X40] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X82)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X42),X40)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X82)),X42)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X82)),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_right__distrib__number__of) ).
fof(fact_625_right__diff__distrib__number__of,axiom,
! [X1] :
( ( number(X1)
& ring(X1) )
=> ! [X82,X42,X40] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X82)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X42),X40)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X82)),X42)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X82)),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_right__diff__distrib__number__of) ).
fof(fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X87,X90,X88,X89] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X90)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),X89)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X90)),X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_888_transfer__nat__int__set__relations_I2_J,axiom,
! [X14,X8] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X14),X8))
<=> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_888_transfer__nat__int__set__relations_I2_J) ).
fof(fact_493_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),zero_zero(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_500_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),zero_zero(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_554_even__less__0__iff,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),zero_zero(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_even__less__0__iff) ).
fof(fact_504_le__iff__diff__le__0,axiom,
! [X1] :
( ordered_ab_group_add(X1)
=> ! [X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X34))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34)),zero_zero(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_le__iff__diff__le__0) ).
fof(fact_505_less__iff__diff__less__0,axiom,
! [X1] :
( ordered_ab_group_add(X1)
=> ! [X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34)),zero_zero(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_less__iff__diff__less__0) ).
fof(fact_536_diff__Suc__less,axiom,
! [X26,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),hAPP(nat,nat,suc,X26))),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_diff__Suc__less) ).
fof(fact_621_Ints__mult,axiom,
! [X1] :
( ring_1(X1)
=> ! [X34,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),ring_1_Ints(X1)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X34)),ring_1_Ints(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_Ints__mult) ).
fof(fact_626_Ints__add,axiom,
! [X1] :
( ring_1(X1)
=> ! [X34,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),ring_1_Ints(X1)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X34)),ring_1_Ints(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_Ints__add) ).
fof(fact_578_Ints__diff,axiom,
! [X1] :
( ring_1(X1)
=> ! [X34,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),ring_1_Ints(X1)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34)),ring_1_Ints(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_Ints__diff) ).
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/sandbox2/benchmark/theBenchmark.p',fact_7_card__insert__le) ).
fof(fact_425_card__psubset,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(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),X13)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_card__psubset) ).
fof(fact_118_less__eq__nat_Osimps_I2_J,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X28)),X20))
<=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28)),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_less__eq__nat_Osimps_I2_J) ).
fof(fact_781_add1__zle__eq,axiom,
! [X85,X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X85),one_one(int))),X46))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X85),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_add1__zle__eq) ).
fof(fact_764_less__bin__lemma,axiom,
! [X19,X95] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X19),X95))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X19),X95)),zero_zero(int))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_less__bin__lemma) ).
fof(fact_254_add__leD1,axiom,
! [X18,X25,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X25)),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_add__leD1) ).
fof(fact_253_add__leD2,axiom,
! [X18,X25,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X25)),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_add__leD2) ).
fof(fact_376_add__lessD1,axiom,
! [X26,X27,X25] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X27)),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_add__lessD1) ).
fof(fact_235_add__right__mono,axiom,
! [X3] :
( ordere779506340up_add(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X40))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__right__mono) ).
fof(fact_236_add__left__mono,axiom,
! [X3] :
( ordere779506340up_add(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X42))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add__left__mono) ).
fof(fact_349_add__strict__right__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X40))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_add__strict__right__mono) ).
fof(fact_350_add__strict__left__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X40,X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X41)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X42))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_add__strict__left__mono) ).
fof(fact_276_diff__Suc__diff__eq2,axiom,
! [X18,X25,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X25))),X18) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X27)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_diff__Suc__diff__eq2) ).
fof(fact_741_fold__image__1,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X12,X76] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X76))
=> ( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X76))
=> hAPP(X1,X2,X12,X33) = one_one(X2) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X12),one_one(X2)),X76) = one_one(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_fold__image__1) ).
fof(fact_620_mult__number__of__left,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86,X43] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(int,X3,number_number_of(X3),X86)),X43)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X82),X86))),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_mult__number__of__left) ).
fof(fact_630_add__number__of__left,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86,X43] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),X86)),X43)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),X86))),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_add__number__of__left) ).
fof(fact_652_add__number__of__diff1,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(int,X3,number_number_of(X3),X86)),X40)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),X86))),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_add__number__of__diff1) ).
fof(fact_767_zadd__left__mono,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X26),X27))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X25),X26)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X25),X27))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_zadd__left__mono) ).
fof(fact_778_zadd__strict__right__mono,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X26),X27))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X26),X25)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X27),X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_zadd__strict__right__mono) ).
fof(fact_601_mult__le__mono1,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X26),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X27),X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_mult__le__mono1) ).
fof(fact_600_mult__le__mono2,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X26)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X27))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_mult__le__mono2) ).
fof(fact_251_add__le__mono1,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_add__le__mono1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_44_diff__le__mono2) ).
fof(fact_373_add__less__mono1,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_add__less__mono1) ).
fof(fact_850_zadd__int__left,axiom,
! [X18,X17,X43] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X18)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X17)),X43)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17))),X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_zadd__int__left) ).
fof(fact_631_left__distrib__number__of,axiom,
! [X1] :
( ( number(X1)
& semiring(X1) )
=> ! [X41,X42,X82] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X41),X42)),hAPP(int,X1,number_number_of(X1),X82)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),hAPP(int,X1,number_number_of(X1),X82))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X42),hAPP(int,X1,number_number_of(X1),X82))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_left__distrib__number__of) ).
fof(fact_624_left__diff__distrib__number__of,axiom,
! [X1] :
( ( number(X1)
& ring(X1) )
=> ! [X41,X42,X82] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X41),X42)),hAPP(int,X1,number_number_of(X1),X82)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),hAPP(int,X1,number_number_of(X1),X82))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X42),hAPP(int,X1,number_number_of(X1),X82))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_left__diff__distrib__number__of) ).
fof(fact_663_mult__nonpos__nonneg,axiom,
! [X3] :
( ordere453448008miring(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_mult__nonpos__nonneg) ).
fof(fact_653_split__mult__neg__le,axiom,
! [X3] :
( ordere453448008miring(X3)
=> ! [X42,X41] :
( ( ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
& hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3))) )
| ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),zero_zero(X3)))
& hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42)) ) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)),zero_zero(X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_split__mult__neg__le) ).
fof(fact_665_mult__nonneg__nonpos,axiom,
! [X3] :
( ordere453448008miring(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_mult__nonneg__nonpos) ).
fof(fact_664_mult__nonneg__nonpos2,axiom,
! [X3] :
( ordere453448008miring(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X41)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_mult__nonneg__nonpos2) ).
fof(fact_680_mult__neg__pos,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_mult__neg__pos) ).
fof(fact_675_mult__pos__neg,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_mult__pos__neg) ).
fof(fact_676_mult__pos__neg2,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X41)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_mult__pos__neg2) ).
fof(fact_498_add__nonpos__nonpos,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_add__nonpos__nonpos) ).
fof(fact_529_add__neg__nonpos,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_add__neg__nonpos) ).
fof(fact_530_add__nonpos__neg,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_add__nonpos__neg) ).
fof(fact_502_add__neg__neg,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_add__neg__neg) ).
fof(fact_190_DiffE,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(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/sandbox2/benchmark/theBenchmark.p',fact_190_DiffE) ).
fof(fact_882_semiring__1__class_Oof__nat__code,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X20] : hAPP(nat,X1,semiring_1_of_nat(X1),X20) = hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),hAPP(X1,fun(X1,X1),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combc(X1,X1,X1),plus_plus(X1)),one_one(X1))),X20),zero_zero(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_882_semiring__1__class_Oof__nat__code) ).
fof(fact_519_diff__less,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X18))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_diff__less) ).
fof(fact_204_card__Diff__singleton,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),one_one(nat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_card__Diff__singleton) ).
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/sandbox2/benchmark/theBenchmark.p',fact_37_Suc__diff__diff) ).
fof(fact_193_DiffD1,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_DiffD1) ).
fof(fact_571_card_Oeq__fold__g,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_card_Oeq__fold__g) ).
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/sandbox2/benchmark/theBenchmark.p',fact_46_finite__surj) ).
fof(fact_678_zero__less__mult__pos2,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X41)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_zero__less__mult__pos2) ).
fof(fact_677_zero__less__mult__pos,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_zero__less__mult__pos) ).
fof(fact_150_Diff__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)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Diff__subset) ).
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/sandbox2/benchmark/theBenchmark.p',fact_12_finite__Collect__le__nat) ).
fof(fact_296_finite__Collect__less__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(nat)),X19)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_finite__Collect__less__nat) ).
fof(fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X87,X90,X88,X89] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X90)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),X89)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X88)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X90),X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X42,X40,X64] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X64)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X64)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X87,X90,X88,X89] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X90)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),X89)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X90),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),X89))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_141_Diff__insert,axiom,
! [X1,X8,X11,X13] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),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),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Diff__insert) ).
fof(fact_275_diff__Suc__diff__eq1,axiom,
! [X18,X25,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X25))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X25)),hAPP(nat,nat,suc,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_diff__Suc__diff__eq1) ).
fof(fact_94_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/sandbox2/benchmark/theBenchmark.p',fact_94_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/sandbox2/benchmark/theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).
fof(fact_602_le__cube,axiom,
! [X18] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X18)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_le__cube) ).
fof(fact_668_zero__le__mult__iff,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X11,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X34)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),zero_zero(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_zero__le__mult__iff) ).
fof(fact_807_int__le__induct,axiom,
! [X16,X36,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X36),X19))
=> ( hBOOL(hAPP(int,bool,X16,X19))
=> ( ! [X69] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X69),X19))
=> ( hBOOL(hAPP(int,bool,X16,X69))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X69),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X16,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_int__le__induct) ).
fof(fact_810_int__ge__induct,axiom,
! [X16,X19,X36] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),X36))
=> ( hBOOL(hAPP(int,bool,X16,X19))
=> ( ! [X69] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),X69))
=> ( hBOOL(hAPP(int,bool,X16,X69))
=> hBOOL(hAPP(int,bool,X16,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X69),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X16,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_int__ge__induct) ).
fof(fact_515_add__gr__0,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X28))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_add__gr__0) ).
fof(fact_449_finite__Plus__iff,axiom,
! [X1,X2,X8,X13] :
( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_finite__Plus__iff) ).
fof(fact_447_finite__PlusD_I1_J,axiom,
! [X1,X2,X8,X13] :
( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_finite__PlusD_I1_J) ).
fof(fact_446_finite__PlusD_I2_J,axiom,
! [X1,X2,X8,X13] :
( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_finite__PlusD_I2_J) ).
fof(fact_782_zless__imp__add1__zle,axiom,
! [X86,X43] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X86),X43))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X86),one_one(int))),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_zless__imp__add1__zle) ).
fof(fact_385_less__imp__diff__less,axiom,
! [X17,X27,X25] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X17)),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_less__imp__diff__less) ).
fof(fact_271_diff__add__assoc2,axiom,
! [X26,X25,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X26)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X25)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_diff__add__assoc2) ).
fof(fact_270_add__diff__assoc2,axiom,
! [X26,X25,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X25)),X26) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X26)),X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_add__diff__assoc2) ).
fof(fact_433_psubset__imp__ex__mem,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X13))
=> ? [X72] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X72),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X13),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_psubset__imp__ex__mem) ).
fof(fact_801_self__quotient__aux2,axiom,
! [X92,X101,X41] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X41))
=> ( X41 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X92),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X41),X101))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X92))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X101),one_one(int))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_self__quotient__aux2) ).
fof(fact_800_self__quotient__aux1,axiom,
! [X92,X101,X41] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X41))
=> ( X41 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X92),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X41),X101))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X92),X41))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X101)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_self__quotient__aux1) ).
fof(fact_654_split__mult__pos__le,axiom,
! [X3] :
( ordered_ring(X3)
=> ! [X42,X41] :
( ( ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
& hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42)) )
| ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),zero_zero(X3)))
& hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3))) ) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_split__mult__pos__le) ).
fof(fact_666_mult__nonneg__nonneg,axiom,
! [X3] :
( ordere453448008miring(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_mult__nonneg__nonneg) ).
fof(fact_494_add__nonneg__nonneg,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_add__nonneg__nonneg) ).
fof(fact_674_mult__pos__pos,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_mult__pos__pos) ).
fof(fact_525_add__pos__nonneg,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_add__pos__nonneg) ).
fof(fact_526_add__nonneg__pos,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_add__nonneg__pos) ).
fof(fact_501_add__pos__pos,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_add__pos__pos) ).
fof(fact_689_less__1__mult,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X17,X18] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X18))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X17))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X18),X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_less__1__mult) ).
fof(fact_662_mult__nonpos__nonpos,axiom,
! [X3] :
( ordered_ring(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_mult__nonpos__nonpos) ).
fof(fact_681_mult__neg__neg,axiom,
! [X3] :
( linord581940658strict(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),zero_zero(X3)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_mult__neg__neg) ).
fof(fact_496_add__increasing,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X40,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_add__increasing) ).
fof(fact_497_add__increasing2,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X41,X40] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X40))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X41))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_add__increasing2) ).
fof(fact_527_add__strict__increasing,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X40,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_add__strict__increasing) ).
fof(fact_528_add__strict__increasing2,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X42,X40,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_add__strict__increasing2) ).
fof(fact_503_pos__add__strict,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X42,X40,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X41))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X40))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_pos__add__strict) ).
fof(fact_570_field__le__epsilon,axiom,
! [X3] :
( linordered_field(X3)
=> ! [X21,X22] :
( ! [X81] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X81))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X81))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_field__le__epsilon) ).
fof(fact_97_image__image,axiom,
! [X2,X1,X48,X12,X44,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(X48,bool),fun(X2,bool),hAPP(fun(X48,X2),fun(fun(X48,bool),fun(X2,bool)),image(X48,X2),X44),X8)) = hAPP(fun(X48,bool),fun(X1,bool),hAPP(fun(X48,X1),fun(fun(X48,bool),fun(X1,bool)),image(X48,X1),hAPP(fun(X48,X2),fun(X48,X1),hAPP(fun(X2,X1),fun(fun(X48,X2),fun(X48,X1)),combb(X2,X1,X48),X12),X44)),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_image__image) ).
fof(fact_439_dense__le__bounded,axiom,
! [X3] :
( dense_linorder(X3)
=> ! [X43,X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ( ! [X73] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X73))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X73),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X73),X43)) ) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X43)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_dense__le__bounded) ).
fof(fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X18,X42] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X18)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X18)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_590_comm__semiring__class_Odistrib,axiom,
! [X3] :
( comm_semiring(X3)
=> ! [X41,X42,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X40) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_comm__semiring__class_Odistrib) ).
fof(fact_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X42,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X40) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X40)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_145_finite__Diff2,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)))
<=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_finite__Diff2) ).
fof(fact_811_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X22,X21] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X21))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X22))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X21),X22))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_813_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X22,X21] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X21))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X22))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X21),X22))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_700_nat__0__less__mult__iff,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X28))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_nat__0__less__mult__iff) ).
fof(fact_878_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X22,X21] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X21))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X22))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X21),X22))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_878_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_105_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/sandbox2/benchmark/theBenchmark.p',fact_105_subset__insertI2) ).
fof(fact_274_folding__one__idem_Oin__idem,axiom,
! [X1,X14,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X12),X10))
=> ( 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(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),hAPP(fun(X1,bool),X1,X10,X8)) = hAPP(fun(X1,bool),X1,X10,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_folding__one__idem_Oin__idem) ).
fof(fact_738_mult__eq__if,axiom,
! [X17,X18] :
( ( X18 = zero_zero(nat)
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17) = zero_zero(nat) )
& ( X18 != zero_zero(nat)
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),one_one(nat))),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_mult__eq__if) ).
fof(fact_756_zadd__zmult__distrib,axiom,
! [X96,X97,X86] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X96),X97)),X86) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X96),X86)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X97),X86)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_zadd__zmult__distrib) ).
fof(fact_752_zdiff__zmult__distrib,axiom,
! [X96,X97,X86] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X96),X97)),X86) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X96),X86)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X97),X86)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_zdiff__zmult__distrib) ).
fof(fact_597_add__mult__distrib,axiom,
! [X18,X17,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X17),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_add__mult__distrib) ).
fof(fact_604_diff__mult__distrib,axiom,
! [X18,X17,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X17),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_diff__mult__distrib) ).
fof(fact_146_insert__Diff1,axiom,
! [X1,X8,X14,X13] :
( 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_insert__Diff1) ).
fof(fact_739_Ints__odd__nonzero,axiom,
! [X1] :
( ring_char_0(X1)
=> ! [X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),ring_1_Ints(X1)))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X11)),X11) != zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_Ints__odd__nonzero) ).
fof(fact_919_abs__eq__mult,axiom,
! [X3] :
( ordered_ring_abs(X3)
=> ! [X42,X41] :
( ( ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X41))
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),zero_zero(X3))) )
& ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X42))
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),zero_zero(X3))) ) )
=> hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_919_abs__eq__mult) ).
fof(fact_956_Suc3__eq__add__3,axiom,
! [X17] : hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X17))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_Suc3__eq__add__3) ).
fof(fact_492_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_499_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X11),X11)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_179_card__Diff__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)),X13),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_card__Diff__subset) ).
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/sandbox2/benchmark/theBenchmark.p',fact_5_card__mono) ).
fof(fact_422_psubset__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(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_psubset__card__mono) ).
fof(fact_783_zless__add1__eq,axiom,
! [X85,X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X85),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X46),one_one(int))))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X85),X46))
| X85 = X46 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_zless__add1__eq) ).
fof(fact_518_zero__less__diff,axiom,
! [X20,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X28)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_zero__less__diff) ).
fof(fact_780_zle__add1__eq__le,axiom,
! [X85,X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X85),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X46),one_one(int))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X85),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_zle__add1__eq__le) ).
fof(fact_775_zle__diff1__eq,axiom,
! [X85,X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X85),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X46),one_one(int))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X85),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_zle__diff1__eq) ).
fof(fact_547_add__eq__if,axiom,
! [X17,X18] :
( ( X18 = zero_zero(nat)
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17) = X17 )
& ( X18 != zero_zero(nat)
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),one_one(nat))),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_add__eq__if) ).
fof(fact_82_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/sandbox2/benchmark/theBenchmark.p',fact_82_insertI2) ).
fof(fact_622_le__number__of,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(int,X1,number_number_of(X1),X14)),hAPP(int,X1,number_number_of(X1),X39)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14),X39)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_le__number__of) ).
fof(fact_614_less__number__of,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(int,X1,number_number_of(X1),X14)),hAPP(int,X1,number_number_of(X1),X39)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),X39)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_less__number__of) ).
fof(fact_843_of__nat__le__iff,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X20] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X28)),hAPP(nat,X1,semiring_1_of_nat(X1),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_of__nat__le__iff) ).
fof(fact_846_of__nat__less__imp__less,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X18,X17] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X18)),hAPP(nat,X3,semiring_1_of_nat(X3),X17)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_of__nat__less__imp__less) ).
fof(fact_844_of__nat__less__iff,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X20] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X28)),hAPP(nat,X1,semiring_1_of_nat(X1),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_of__nat__less__iff) ).
fof(fact_403_diff__less__Suc,axiom,
! [X18,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),hAPP(nat,nat,suc,X18))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_diff__less__Suc) ).
fof(fact_393_less__add__Suc1,axiom,
! [X26,X18] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X18)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_less__add__Suc1) ).
fof(fact_394_less__add__Suc2,axiom,
! [X26,X18] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X26)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_less__add__Suc2) ).
fof(fact_139_insert__Diff__single,axiom,
! [X1,X11,X8] : 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),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_insert__Diff__single) ).
fof(fact_91_subset__trans,axiom,
! [X1,X45,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),X45))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X45)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subset__trans) ).
fof(fact_418_psubset__subset__trans,axiom,
! [X1,X45,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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),X45))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X45)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_psubset__subset__trans) ).
fof(fact_417_subset__psubset__trans,axiom,
! [X1,X45,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(fun(X1,bool)),X13),X45))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X45)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_subset__psubset__trans) ).
fof(fact_432_psubset__trans,axiom,
! [X1,X45,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X13),X45))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X45)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_psubset__trans) ).
fof(fact_269_diff__add__assoc,axiom,
! [X26,X25,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X27)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_diff__add__assoc) ).
fof(fact_265_add__diff__assoc,axiom,
! [X26,X25,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X27)),X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_add__diff__assoc) ).
fof(fact_261_diff__diff__right,axiom,
! [X26,X25,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X27))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X25)),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_diff__diff__right) ).
fof(fact_751_less__eq__number__of__int__code,axiom,
! [X19,X95] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X19)),hAPP(int,int,number_number_of(int),X95)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),X95)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_less__eq__number__of__int__code) ).
fof(fact_745_less__number__of__int__code,axiom,
! [X19,X95] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),X19)),hAPP(int,int,number_number_of(int),X95)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X19),X95)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_less__number__of__int__code) ).
fof(fact_857_transfer__int__nat__relations_I3_J,axiom,
! [X14,X39] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(nat,int,semiring_1_of_nat(int),X39)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_857_transfer__int__nat__relations_I3_J) ).
fof(fact_848_zle__int,axiom,
! [X28,X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X28)),hAPP(nat,int,semiring_1_of_nat(int),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_zle__int) ).
fof(fact_856_transfer__int__nat__relations_I2_J,axiom,
! [X14,X39] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(nat,int,semiring_1_of_nat(int),X39)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_transfer__int__nat__relations_I2_J) ).
fof(fact_847_zless__int,axiom,
! [X28,X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X28)),hAPP(nat,int,semiring_1_of_nat(int),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_zless__int) ).
fof(fact_539_nat__diff__split,axiom,
! [X16,X11,X34] :
( hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X11),X34)))
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X11),X34))
=> hBOOL(hAPP(nat,bool,X16,zero_zero(nat))) )
& ! [X79] :
( X11 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X79)
=> hBOOL(hAPP(nat,bool,X16,X79)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_nat__diff__split) ).
fof(fact_988_less__eq__int__code_I16_J,axiom,
! [X116,X117] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X116)),hAPP(int,int,bit1,X117)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X116),X117)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_less__eq__int__code_I16_J) ).
fof(fact_987_rel__simps_I34_J,axiom,
! [X19,X95] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X19)),hAPP(int,int,bit1,X95)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X19),X95)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_987_rel__simps_I34_J) ).
fof(fact_992_less__int__code_I16_J,axiom,
! [X116,X117] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X116)),hAPP(int,int,bit1,X117)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X116),X117)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_less__int__code_I16_J) ).
fof(fact_991_rel__simps_I17_J,axiom,
! [X19,X95] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X19)),hAPP(int,int,bit1,X95)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X19),X95)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_rel__simps_I17_J) ).
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/sandbox2/benchmark/theBenchmark.p',fact_33_Suc__le__mono) ).
fof(fact_367_Suc__less__SucD,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X18)),hAPP(nat,nat,suc,X17)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_Suc__less__SucD) ).
fof(fact_359_Suc__less__eq,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X28)),hAPP(nat,nat,suc,X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_Suc__less__eq) ).
fof(fact_364_less__trans__Suc,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X26)),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_less__trans__Suc) ).
fof(fact_108_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/sandbox2/benchmark/theBenchmark.p',fact_108_insert__image) ).
fof(fact_861_transfer__nat__int__set__relations_I1_J,axiom,
! [X8] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X8))
<=> hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_transfer__nat__int__set__relations_I1_J) ).
fof(fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X18] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X18)),X18) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),one_one(X3))),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_576_expand__Suc,axiom,
! [X82] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),X82)))
=> hAPP(int,nat,number_number_of(nat),X82) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),X82)),one_one(nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_expand__Suc) ).
fof(fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X21,X22,X43] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X43)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),X22)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X87,X90,X88] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X90)),X88) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X88)),X90) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X42,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X40) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_448_finite__Plus,axiom,
! [X2,X1,X13,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13))
=> hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_finite__Plus) ).
fof(fact_89_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/sandbox2/benchmark/theBenchmark.p',fact_89_set__rev__mp) ).
fof(fact_90_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/sandbox2/benchmark/theBenchmark.p',fact_90_set__mp) ).
fof(fact_88_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/sandbox2/benchmark/theBenchmark.p',fact_88_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/sandbox2/benchmark/theBenchmark.p',fact_52_subsetD) ).
fof(fact_431_psubsetD,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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/sandbox2/benchmark/theBenchmark.p',fact_431_psubsetD) ).
fof(fact_101_le__funE,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X14,X12,X44] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X44))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X14)),hAPP(X1,X2,X44,X14))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_le__funE) ).
fof(fact_100_le__funD,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X14,X12,X44] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X44))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X14)),hAPP(X1,X2,X44,X14))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_le__funD) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_45_diff__le__self) ).
fof(fact_754_zadd__zmult__distrib2,axiom,
! [X86,X96,X97] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X86),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X96),X97)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X86),X96)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X86),X97)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_zadd__zmult__distrib2) ).
fof(fact_753_zdiff__zmult__distrib2,axiom,
! [X86,X96,X97] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X86),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X96),X97)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X86),X96)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X86),X97)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_zdiff__zmult__distrib2) ).
fof(fact_598_add__mult__distrib2,axiom,
! [X25,X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_add__mult__distrib2) ).
fof(fact_605_diff__mult__distrib2,axiom,
! [X25,X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X25),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_diff__mult__distrib2) ).
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/sandbox2/benchmark/theBenchmark.p',fact_25_diff__commute) ).
fof(fact_107_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/sandbox2/benchmark/theBenchmark.p',fact_107_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/sandbox2/benchmark/theBenchmark.p',fact_41_eq__diff__iff) ).
fof(fact_953_number__of__Bit1,axiom,
! [X3] :
( number_ring(X3)
=> ! [X86] : hAPP(int,X3,number_number_of(X3),hAPP(int,int,bit1,X86)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),hAPP(int,X3,number_number_of(X3),X86))),hAPP(int,X3,number_number_of(X3),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_number__of__Bit1) ).
fof(fact_451_card__Plus__conv__if,axiom,
! [X2,X1,X13,X8] :
( ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13)) )
=> hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X2,bool),nat,finite_card(X2),X13)) )
& ( ~ ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13)) )
=> hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13)) = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_card__Plus__conv__if) ).
fof(fact_444_card__Plus,axiom,
! [X2,X1,X13,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13))
=> hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X8),X13)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X2,bool),nat,finite_card(X2),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_card__Plus) ).
fof(fact_917_abs__le__D1,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,abs_abs(X3),X41)),X42))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_abs__le__D1) ).
fof(fact_924_abs__add__abs,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] : hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42))) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_abs__add__abs) ).
fof(fact_765_le__imp__0__less,axiom,
! [X43] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X43))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X43))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_le__imp__0__less) ).
fof(fact_280_termination__basic__simps_I3_J,axiom,
! [X43,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),X43))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_termination__basic__simps_I3_J) ).
fof(fact_249_trans__le__add1,axiom,
! [X18,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),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_trans__le__add1) ).
fof(fact_279_termination__basic__simps_I4_J,axiom,
! [X22,X21,X43] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),X43))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_termination__basic__simps_I4_J) ).
fof(fact_250_trans__le__add2,axiom,
! [X18,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),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X27))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_trans__le__add2) ).
fof(fact_377_termination__basic__simps_I1_J,axiom,
! [X43,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),X43))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_termination__basic__simps_I1_J) ).
fof(fact_371_trans__less__add1,axiom,
! [X18,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_trans__less__add1) ).
fof(fact_378_termination__basic__simps_I2_J,axiom,
! [X22,X21,X43] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),X43))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_termination__basic__simps_I2_J) ).
fof(fact_372_trans__less__add2,axiom,
! [X18,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X27))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_trans__less__add2) ).
fof(fact_430_Suc__lessE,axiom,
! [X26,X25] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X26)),X25))
=> ~ ! [X71] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X71))
=> X25 != hAPP(nat,nat,suc,X71) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_Suc__lessE) ).
fof(fact_845_less__imp__of__nat__less,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X18)),hAPP(nat,X3,semiring_1_of_nat(X3),X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_less__imp__of__nat__less) ).
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/sandbox2/benchmark/theBenchmark.p',fact_30_Suc__leD) ).
fof(fact_402_Suc__le__lessD,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(nat),X18),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Suc__le__lessD) ).
fof(fact_398_Suc__le__eq,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X28)),X20))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_Suc__le__eq) ).
fof(fact_396_less__eq__Suc__le,axiom,
! [X20,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X28))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X20)),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_less__eq__Suc__le) ).
fof(fact_366_Suc__lessD,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X18)),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_Suc__lessD) ).
fof(fact_993_rel__simps_I29_J,axiom,
! [X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X19)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X19),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_rel__simps_I29_J) ).
fof(fact_990_rel__simps_I12_J,axiom,
! [X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X19)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X19),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_rel__simps_I12_J) ).
fof(fact_194_Diff__idemp,axiom,
! [X1,X8,X13] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)),X13) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_Diff__idemp) ).
fof(fact_295_Suc__mono,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X18)),hAPP(nat,nat,suc,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Suc__mono) ).
fof(fact_950_neg__number__of__Bit1,axiom,
! [X85] :
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,X85))))
<=> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X85))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_neg__number__of__Bit1) ).
fof(fact_453_Collect__mono,axiom,
! [X1,X15,X16] :
( ! [X33] :
( hBOOL(hAPP(X1,bool,X16,X33))
=> hBOOL(hAPP(X1,bool,X15,X33)) )
=> 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),collect(X1),X16)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_Collect__mono) ).
fof(fact_117_diff__eq__diff__less__eq,axiom,
! [X1] :
( ordered_ab_group_add(X1)
=> ! [X11,X34,X35,X53] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X35),X53)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X34))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X53)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_diff__eq__diff__less__eq) ).
fof(fact_356_diff__eq__diff__less,axiom,
! [X1] :
( ordered_ab_group_add(X1)
=> ! [X11,X34,X35,X53] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X11),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X35),X53)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X34))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X53)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_diff__eq__diff__less) ).
fof(fact_67_order__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X43,X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X43))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X43)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_order__trans) ).
fof(fact_69_xt1_I6_J,axiom,
! [X3] :
( order(X3)
=> ! [X43,X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X43),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X43),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_xt1_I6_J) ).
fof(fact_343_order__less__le__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X43,X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X43))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X43)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_order__less__le__trans) ).
fof(fact_345_order__le__less__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X43,X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X43))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X43)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_order__le__less__trans) ).
fof(fact_322_order__less__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X43,X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X43))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X43)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_order__less__trans) ).
fof(fact_344_xt1_I7_J,axiom,
! [X3] :
( order(X3)
=> ! [X43,X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X43),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X43),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_xt1_I7_J) ).
fof(fact_346_xt1_I8_J,axiom,
! [X3] :
( order(X3)
=> ! [X43,X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X43),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X43),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_xt1_I8_J) ).
fof(fact_323_xt1_I10_J,axiom,
! [X3] :
( order(X3)
=> ! [X43,X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X43),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X43),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_xt1_I10_J) ).
fof(fact_874_of__nat__diff,axiom,
! [X3] :
( ring_1(X3)
=> ! [X17,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X18)),hAPP(nat,X3,semiring_1_of_nat(X3),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_of__nat__diff) ).
fof(fact_872_zdiff__int,axiom,
! [X17,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18))
=> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X18)),hAPP(nat,int,semiring_1_of_nat(int),X17)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_zdiff__int) ).
fof(fact_773_zle__trans,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X26),X27))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X27),X25))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X26),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_zle__trans) ).
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/sandbox2/benchmark/theBenchmark.p',fact_21_le__trans) ).
fof(fact_375_less__add__eq__less,axiom,
! [X18,X17,X25,X29] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X29))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X29) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X17)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_less__add__eq__less) ).
fof(fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X18,X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X18),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X18)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),one_one(X3))),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X87,X90,X88] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X90)),X88) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X90),X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_609_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X3] :
( ab_semigroup_mult(X3)
=> ! [X41,X42,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)),X40) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X42,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X40) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_221_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X3] :
( ab_semigroup_add(X3)
=> ! [X41,X42,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X42)),X40) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X42),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X87,X88,X89] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),X89)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X88)),X89) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X40,X64] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X64)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40)),X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_401_le__less__Suc__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(nat),X20),hAPP(nat,nat,suc,X28)))
<=> X20 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_le__less__Suc__eq) ).
fof(fact_267_le__add__diff__inverse2,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),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X17) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_le__add__diff__inverse2) ).
fof(fact_175_image__constant,axiom,
! [X2,X1,X35,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(X2,fun(X1,X2),combk(X2,X1),X35)),X8) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X35),bot_bot(fun(X2,bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_image__constant) ).
fof(fact_55_zero__induct__lemma,axiom,
! [X36,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),X36))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_zero__induct__lemma) ).
fof(fact_189_assms_I4_J,axiom,
! [X58] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X58),u))
=> hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X58)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_assms_I4_J) ).
fof(fact_259_diff__cancel,axiom,
! [X25,X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_diff__cancel) ).
fof(fact_260_diff__cancel2,axiom,
! [X18,X25,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_diff__cancel2) ).
fof(fact_750_zmult__assoc,axiom,
! [X96,X97,X98] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X96),X97)),X98) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X96),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X97),X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_zmult__assoc) ).
fof(fact_768_zadd__assoc,axiom,
! [X96,X97,X98] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X96),X97)),X98) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X96),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X97),X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_zadd__assoc) ).
fof(fact_744_nat__mult__assoc,axiom,
! [X18,X17,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X17),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_nat__mult__assoc) ).
fof(fact_230_nat__add__assoc,axiom,
! [X18,X17,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_nat__add__assoc) ).
fof(fact_258_diff__diff__left,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),X26),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_diff__diff__left) ).
fof(fact_920_abs__mult__pos,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
=> hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,abs_abs(X3),X22)),X21) = hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_abs__mult__pos) ).
fof(fact_102_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/sandbox2/benchmark/theBenchmark.p',fact_102_subset__insertI) ).
fof(fact_363_Suc__lessI,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> ( hAPP(nat,nat,suc,X18) != X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X18)),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_Suc__lessI) ).
fof(fact_78_insert__commute,axiom,
! [X1,X14,X39,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),X39),X8)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_insert__commute) ).
fof(fact_759_odd__nonzero,axiom,
! [X43] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X43)),X43) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_odd__nonzero) ).
fof(fact_122_finite__Diff,axiom,
! [X1,X13,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_finite__Diff) ).
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/sandbox2/benchmark/theBenchmark.p',fact_11_Suc__diff__le) ).
fof(fact_71_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/sandbox2/benchmark/theBenchmark.p',fact_71_insertI1) ).
fof(fact_400_Suc__leI,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X18)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_Suc__leI) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_2_finite__imageI) ).
fof(fact_892_of__nat__aux_Osimps_I2_J,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X108,X20,X36] : hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),X108),hAPP(nat,nat,suc,X20)),X36) = hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),X108),X20),hAPP(X1,X1,X108,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_of__nat__aux_Osimps_I2_J) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_34_le__Suc__eq) ).
fof(fact_56_Suc__le__D,axiom,
! [X17,X37] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X37))
=> ? [X38] : X37 = hAPP(nat,nat,suc,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Suc__le__D) ).
fof(fact_410_inc__induct,axiom,
! [X16,X36,X66] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X66))
=> ( hBOOL(hAPP(nat,bool,X16,X66))
=> ( ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X66))
=> ( hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,suc,X69)))
=> hBOOL(hAPP(nat,bool,X16,X69)) ) )
=> hBOOL(hAPP(nat,bool,X16,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_inc__induct) ).
fof(fact_877_of__nat__0__less__iff,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X20] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_of__nat__0__less__iff) ).
fof(fact_389_card__Collect__less__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(nat)),X20))) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_card__Collect__less__nat) ).
fof(fact_512_less__Suc__eq__0__disj,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),hAPP(nat,nat,suc,X20)))
<=> ( X28 = zero_zero(nat)
| ? [X71] :
( X28 = hAPP(nat,nat,suc,X71)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X71),X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_less__Suc__eq__0__disj) ).
fof(fact_112_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/sandbox2/benchmark/theBenchmark.p',fact_112_subsetI) ).
fof(fact_875_zero__less__int__conv,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_875_zero__less__int__conv) ).
fof(fact_903_zabs__less__one__iff,axiom,
! [X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),X46)),one_one(int)))
<=> X46 = zero_zero(int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_zabs__less__one__iff) ).
fof(fact_868_int__le__0__conv,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X20)),zero_zero(int)))
<=> X20 = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_int__le__0__conv) ).
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/sandbox2/benchmark/theBenchmark.p',fact_3_finite_OinsertI) ).
fof(fact_358_less__Suc__eq,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),hAPP(nat,nat,suc,X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
| X28 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_less__Suc__eq) ).
fof(fact_397_less__Suc__eq__le,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),hAPP(nat,nat,suc,X20)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_less__Suc__eq__le) ).
fof(fact_986_rel__simps_I22_J,axiom,
! [X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_986_rel__simps_I22_J) ).
fof(fact_994_rel__simps_I5_J,axiom,
! [X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_rel__simps_I5_J) ).
fof(fact_596_Suc__mult__cancel1,axiom,
! [X19,X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X19)),X28) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X19)),X20)
<=> X28 = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_Suc__mult__cancel1) ).
fof(fact_419_psubset__imp__subset,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_psubset__imp__subset) ).
fof(fact_867_transfer__int__nat__quantifiers_I1_J,axiom,
! [X16] :
( ! [X33] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X33))
=> hBOOL(hAPP(int,bool,X16,X33)) )
<=> ! [X33] : hBOOL(hAPP(int,bool,X16,hAPP(nat,int,semiring_1_of_nat(int),X33))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_transfer__int__nat__quantifiers_I1_J) ).
fof(fact_535_Suc__pred,axiom,
! [X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17))
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),hAPP(nat,nat,suc,zero_zero(nat)))) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_Suc__pred) ).
fof(fact_115_finite__nat__set__iff__bounded__le,axiom,
! [X52] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X52))
<=> ? [X38] :
! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X52))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_finite__nat__set__iff__bounded__le) ).
fof(fact_387_finite__nat__set__iff__bounded,axiom,
! [X52] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X52))
<=> ? [X38] :
! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X52))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_finite__nat__set__iff__bounded) ).
fof(fact_208_diff__Suc__eq__diff__pred,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),hAPP(nat,nat,suc,X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),one_one(nat))),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__Suc__eq__diff__pred) ).
fof(fact_870_zless__iff__Suc__zadd,axiom,
! [X85,X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X85),X46))
<=> ? [X32] : X46 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X85),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X32))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_zless__iff__Suc__zadd) ).
fof(fact_524_diff__Suc,axiom,
! [X28,X20] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),hAPP(nat,nat,suc,X20)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_diff__Suc) ).
fof(fact_966_add__special_I2_J,axiom,
! [X3] :
( number_ring(X3)
=> ! [X86] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),hAPP(int,X3,number_number_of(X3),X86)) = hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_966_add__special_I2_J) ).
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/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
fof(fact_315_order__less__imp__triv,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14))
=> hBOOL(X16) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_order__less__imp__triv) ).
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/sandbox2/benchmark/theBenchmark.p',fact_32_le__SucI) ).
fof(fact_399_le__imp__less__Suc,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(nat),X18),hAPP(nat,nat,suc,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_le__imp__less__Suc) ).
fof(fact_362_less__SucI,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),hAPP(nat,nat,suc,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_less__SucI) ).
fof(fact_202_minus__apply,axiom,
! [X2,X1] :
( minus(X1)
=> ! [X8,X13,X14] : hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),minus_minus(fun(X2,X1)),X8),X13),X14) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X2,X1,X8,X14)),hAPP(X2,X1,X13,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_minus__apply) ).
fof(fact_201_fun__diff__def,axiom,
! [X1,X2] :
( minus(X2)
=> ! [X8,X13,X33] : hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),minus_minus(fun(X1,X2)),X8),X13),X33) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),minus_minus(X2),hAPP(X1,X2,X8,X33)),hAPP(X1,X2,X13,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_fun__diff__def) ).
fof(fact_786_nat__mult__eq__cancel1,axiom,
! [X28,X20,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X28) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X20)
<=> X28 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_786_nat__mult__eq__cancel1) ).
fof(fact_531_zero__less__two,axiom,
! [X3] :
( linordered_semidom(X3)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),one_one(X3)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_zero__less__two) ).
fof(fact_774_zle__antisym,axiom,
! [X43,X86] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X43),X86))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X86),X43))
=> X43 = X86 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_zle__antisym) ).
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/sandbox2/benchmark/theBenchmark.p',fact_20_le__antisym) ).
fof(fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X18] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X18),X18) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),one_one(X3))),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_669_zero__le__square,axiom,
! [X3] :
( linordered_ring(X3)
=> ! [X41] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X41))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_zero__le__square) ).
fof(fact_414_less__add__one,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X41] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),one_one(X3)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_less__add__one) ).
fof(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X87,X88,X89] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),X89)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X88),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X87),X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X40,X64] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X64)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X64)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_264_le__add__diff__inverse,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),plus_plus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_le__add__diff__inverse) ).
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/sandbox2/benchmark/theBenchmark.p',fact_42_diff__diff__cancel) ).
fof(fact_438_dense__le,axiom,
! [X3] :
( dense_linorder(X3)
=> ! [X43,X22] :
( ! [X33] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X43)) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_dense__le) ).
fof(fact_534_card__ge__0__finite,axiom,
! [X1,X8] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X8)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_card__ge__0__finite) ).
fof(fact_866_transfer__int__nat__quantifiers_I2_J,axiom,
! [X16] :
( ? [X33] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X33))
& hBOOL(hAPP(int,bool,X16,X33)) )
<=> ? [X33] : hBOOL(hAPP(int,bool,X16,hAPP(nat,int,semiring_1_of_nat(int),X33))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_transfer__int__nat__quantifiers_I2_J) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
fof(fact_603_le__square,axiom,
! [X18] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X18))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_le__square) ).
fof(fact_246_le__add1,axiom,
! [X17,X18] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X18))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_le__add1) ).
fof(fact_245_le__add2,axiom,
! [X17,X18] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_le__add2) ).
fof(fact_303_nat__less__cases,axiom,
! [X16,X28,X20] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X16,X20),X28)) )
=> ( ( X28 = X20
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X16,X20),X28)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X28))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X16,X20),X28)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X16,X20),X28)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_nat__less__cases) ).
fof(fact_769_zadd__left__commute,axiom,
! [X21,X22,X43] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X21),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X22),X43)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X22),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X21),X43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_769_zadd__left__commute) ).
fof(fact_229_nat__add__left__commute,axiom,
! [X21,X22,X43] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),X43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_nat__add__left__commute) ).
fof(fact_965_add__special_I3_J,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),X82)),one_one(X3)) = hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),hAPP(int,int,bit1,pls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_965_add__special_I3_J) ).
fof(fact_538_predicate1D,axiom,
! [X1,X14,X16,X15] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X16),X15))
=> ( hBOOL(hAPP(X1,bool,X16,X14))
=> hBOOL(hAPP(X1,bool,X15,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_predicate1D) ).
fof(fact_537_rev__predicate1D,axiom,
! [X1,X15,X16,X14] :
( hBOOL(hAPP(X1,bool,X16,X14))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X16),X15))
=> hBOOL(hAPP(X1,bool,X15,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_rev__predicate1D) ).
fof(fact_268_le__imp__diff__is__add,axiom,
! [X19,X36,X66] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X66))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X66),X36) = X19
<=> X66 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_le__imp__diff__is__add) ).
fof(fact_395_less__iff__Suc__add,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
<=> ? [X65] : X20 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_less__iff__Suc__add) ).
fof(help_COMBS_1_1_U,axiom,
! [X3,X2,X1,X122,X123,X124] : 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),X122),X123),X124) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X122,X124),hAPP(X3,X1,X123,X124)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
fof(fact_429_lessE,axiom,
! [X26,X25] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X25))
=> ( X25 != hAPP(nat,nat,suc,X26)
=> ~ ! [X71] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X71))
=> X25 != hAPP(nat,nat,suc,X71) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_lessE) ).
fof(fact_411_less__imp__Suc__add,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> ? [X65] : X17 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_less__imp__Suc__add) ).
fof(fact_545_Suc__diff__1,axiom,
! [X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17))
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),one_one(nat))) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_Suc__diff__1) ).
fof(fact_546_Suc__pred_H,axiom,
! [X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17))
=> X17 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),one_one(nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_Suc__pred_H) ).
fof(fact_823_pinf_I8_J,axiom,
! [X3] :
( linorder(X3)
=> ! [X68] :
? [X94] :
! [X33] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X94),X33))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X68),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_pinf_I8_J) ).
fof(fact_285_comp__fun__idem_Ofun__left__idem,axiom,
! [X1,X2,X14,X46,X12] :
( hBOOL(hAPP(fun(X1,fun(X2,X2)),bool,finite_comp_fun_idem(X1,X2),X12))
=> hAPP(X2,X2,hAPP(X1,fun(X2,X2),X12,X14),hAPP(X2,X2,hAPP(X1,fun(X2,X2),X12,X14),X46)) = hAPP(X2,X2,hAPP(X1,fun(X2,X2),X12,X14),X46) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_comp__fun__idem_Ofun__left__idem) ).
fof(fact_822_minf_I6_J,axiom,
! [X3] :
( linorder(X3)
=> ! [X68] :
? [X94] :
! [X33] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X94))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X68)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_minf_I6_J) ).
fof(fact_921_abs__mult,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X41,X42] : hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_921_abs__mult) ).
fof(fact_968_Bit1__def,axiom,
! [X25] : hAPP(int,int,bit1,X25) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X25)),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_Bit1__def) ).
fof(fact_77_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/sandbox2/benchmark/theBenchmark.p',fact_77_insert__absorb2) ).
fof(fact_618_arith__simps_I32_J,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(int,X3,number_number_of(X3),X86)) = hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X82),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_arith__simps_I32_J) ).
fof(fact_628_add__number__of__eq,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(int,X3,number_number_of(X3),X86)) = hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_add__number__of__eq) ).
fof(fact_616_number__of__mult,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86] : hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X82),X86)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(int,X3,number_number_of(X3),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_number__of__mult) ).
fof(fact_627_number__of__add,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86] : hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),X86)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(int,X3,number_number_of(X3),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_number__of__add) ).
fof(fact_623_number__of__diff,axiom,
! [X3] :
( number_ring(X3)
=> ! [X82,X86] : hAPP(int,X3,number_number_of(X3),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X82),X86)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(int,X3,number_number_of(X3),X82)),hAPP(int,X3,number_number_of(X3),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_number__of__diff) ).
fof(fact_854_of__nat__mult,axiom,
! [X3] :
( semiring_1(X3)
=> ! [X18,X17] : hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X18)),hAPP(nat,X3,semiring_1_of_nat(X3),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_of__nat__mult) ).
fof(fact_842_of__nat__add,axiom,
! [X3] :
( semiring_1(X3)
=> ! [X18,X17] : hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X18)),hAPP(nat,X3,semiring_1_of_nat(X3),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_of__nat__add) ).
fof(fact_338_order__less__imp__le,axiom,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_order__less__imp__le) ).
fof(fact_703_mult__Suc,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X18)),X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_mult__Suc) ).
fof(fact_552_less__imp__add__positive,axiom,
! [X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X27))
=> ? [X65] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X65))
& hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X65) = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_less__imp__add__positive) ).
fof(fact_749_times__numeral__code_I5_J,axiom,
! [X82,X86] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),X82)),hAPP(int,int,number_number_of(int),X86)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X82),X86)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_times__numeral__code_I5_J) ).
fof(fact_855_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [X21,X22] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X21)),hAPP(nat,int,semiring_1_of_nat(int),X22)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X21),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_852_zmult__int,axiom,
! [X18,X17] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X18)),hAPP(nat,int,semiring_1_of_nat(int),X17)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_zmult__int) ).
fof(fact_755_plus__numeral__code_I9_J,axiom,
! [X82,X86] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),X82)),hAPP(int,int,number_number_of(int),X86)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),X86)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_plus__numeral__code_I9_J) ).
fof(fact_859_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [X21,X22] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X21)),hAPP(nat,int,semiring_1_of_nat(int),X22)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(fact_849_zadd__int,axiom,
! [X18,X17] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X18)),hAPP(nat,int,semiring_1_of_nat(int),X17)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_zadd__int) ).
fof(fact_853_int__mult,axiom,
! [X18,X17] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X18)),hAPP(nat,int,semiring_1_of_nat(int),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_int__mult) ).
fof(fact_881_zero__less__imp__eq__int,axiom,
! [X25] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X25))
=> ? [X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X32))
& X25 = hAPP(nat,int,semiring_1_of_nat(int),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_zero__less__imp__eq__int) ).
fof(fact_858_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [X21,X22] : hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X21)),hAPP(nat,int,semiring_1_of_nat(int),X22)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X21),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
fof(fact_763_int__one__le__iff__zero__less,axiom,
! [X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X46))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_int__one__le__iff__zero__less) ).
fof(fact_777_zless__le,axiom,
! [X46,X85] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X46),X85))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X46),X85))
& X46 != X85 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_777_zless__le) ).
fof(fact_382_le__neq__implies__less,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> ( X18 != X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_le__neq__implies__less) ).
fof(fact_380_le__eq__less__or__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(nat),X28),X20))
| X28 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_le__eq__less__or__eq) ).
fof(fact_379_nat__less__le,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
& X28 != X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_nat__less__le) ).
fof(fact_384_termination__basic__simps_I5_J,axiom,
! [X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_termination__basic__simps_I5_J) ).
fof(fact_383_less__or__eq__imp__le,axiom,
! [X18,X17] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
| X18 = X17 )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_less__or__eq__imp__le) ).
fof(fact_381_less__imp__le__nat,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_less__imp__le__nat) ).
fof(fact_880_tsub__eq,axiom,
! [X22,X21] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X21))
=> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X21),X22) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_880_tsub__eq) ).
fof(fact_511_less__Suc0,axiom,
! [X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),hAPP(nat,nat,suc,zero_zero(nat))))
<=> X20 = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_less__Suc0) ).
fof(fact_166_singleton__conv,axiom,
! [X1,X11] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),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(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_singleton__conv) ).
fof(fact_257_diff__add__inverse,axiom,
! [X17,X18] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X18)),X17) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_diff__add__inverse) ).
fof(fact_256_diff__add__inverse2,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)),X17) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_diff__add__inverse2) ).
fof(fact_615_Ints__number__of,axiom,
! [X1] :
( number_ring(X1)
=> ! [X85] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(int,X1,number_number_of(X1),X85)),ring_1_Ints(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_Ints__number__of) ).
fof(fact_840_Ints__of__nat,axiom,
! [X1] :
( ring_1(X1)
=> ! [X20] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X20)),ring_1_Ints(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_Ints__of__nat) ).
fof(fact_851_zle__iff__zadd,axiom,
! [X85,X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X85),X46))
<=> ? [X32] : X46 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X85),hAPP(nat,int,semiring_1_of_nat(int),X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_zle__iff__zadd) ).
fof(fact_560_nat__induct,axiom,
! [X20,X16] :
( hBOOL(hAPP(nat,bool,X16,zero_zero(nat)))
=> ( ! [X32] :
( hBOOL(hAPP(nat,bool,X16,X32))
=> hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,suc,X32))) )
=> hBOOL(hAPP(nat,bool,X16,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_nat__induct) ).
fof(fact_923_abs__minus__commute,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41,X42] : hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),X42)) = hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X42),X41)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_923_abs__minus__commute) ).
fof(fact_758_pos__zmult__eq__1__iff,axiom,
! [X20,X28] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X28))
=> ( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X28),X20) = one_one(int)
<=> ( X28 = one_one(int)
& X20 = one_one(int) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_pos__zmult__eq__1__iff) ).
fof(fact_532_bot__empty__eq,axiom,
! [X1,X33] :
( hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X33))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),bot_bot(fun(X1,bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_bot__empty__eq) ).
fof(help_COMBB_1_1_U,axiom,
! [X3,X2,X1,X122,X123,X124] : 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),X122),X123),X124) = hAPP(X1,X2,X122,hAPP(X3,X1,X123,X124)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
fof(help_COMBC_1_1_U,axiom,
! [X3,X2,X1,X122,X123,X124] : hAPP(X3,X2,hAPP(X1,fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2)),combc(X3,X1,X2),X122),X123),X124) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X122,X124),X123),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
fof(fact_702_mult__Suc__right,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),hAPP(nat,nat,suc,X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_mult__Suc__right) ).
fof(fact_243_add__Suc,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X18)),X17) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_add__Suc) ).
fof(fact_887_transfer__nat__int__set__relations_I3_J,axiom,
! [X8,X13] :
( X8 = X13
<=> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X8) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_transfer__nat__int__set__relations_I3_J) ).
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/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
fof(fact_247_le__iff__add,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
<=> ? [X65] : X20 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X65) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_le__iff__add) ).
fof(fact_522_diff__is__0__eq_H,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17) = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_diff__is__0__eq_H) ).
fof(fact_521_diff__is__0__eq,axiom,
! [X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X20) = zero_zero(nat)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_diff__is__0__eq) ).
fof(fact_608_mult__left__idem,axiom,
! [X3] :
( ab_sem1668676832m_mult(X3)
=> ! [X41,X42] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_mult__left__idem) ).
fof(fact_58_linorder__linear,axiom,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_linorder__linear) ).
fof(fact_328_linorder__le__less__linear,axiom,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_linorder__le__less__linear) ).
fof(fact_427_bounded__nat__set__is__finite,axiom,
! [X20,X52] :
( ! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X52))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X20)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_bounded__nat__set__is__finite) ).
fof(fact_922_abs__mult__self,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),hAPP(X3,X3,abs_abs(X3),X41)),hAPP(X3,X3,abs_abs(X3),X41)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_abs__mult__self) ).
fof(fact_776_zless__linear,axiom,
! [X21,X22] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X21),X22))
| X21 = X22
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X22),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_zless__linear) ).
fof(fact_298_nat__neq__iff,axiom,
! [X28,X20] :
( X28 != X20
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_nat__neq__iff) ).
fof(fact_772_zle__linear,axiom,
! [X43,X86] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X43),X86))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X86),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_zle__linear) ).
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/sandbox2/benchmark/theBenchmark.p',fact_23_nat__le__linear) ).
fof(fact_931_abs__zmult__eq__1,axiom,
! [X18,X17] :
( hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X18),X17)) = one_one(int)
=> hAPP(int,int,abs_abs(int),X18) = one_one(int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_931_abs__zmult__eq__1) ).
fof(fact_550_card_Oneutral,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ( ? [X33] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> one_one(nat) = zero_zero(nat) )
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_card_Oneutral) ).
fof(fact_242_add__Suc__right,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),hAPP(nat,nat,suc,X17)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_add__Suc__right) ).
fof(fact_174_nat__case__Suc,axiom,
! [X1,X54,X55,X23] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X54),X55),hAPP(nat,nat,suc,X23)) = hAPP(nat,X1,X55,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_nat__case__Suc) ).
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/sandbox2/benchmark/theBenchmark.p',fact_38_diff__Suc__Suc) ).
fof(fact_244_add__Suc__shift,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X18)),X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),hAPP(nat,nat,suc,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_add__Suc__shift) ).
fof(fact_904_neg__def,axiom,
! [X113] :
( hBOOL(hAPP(int,bool,nat_neg,X113))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X113),zero_zero(int))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_neg__def) ).
fof(fact_558_zero__induct,axiom,
! [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,zero_zero(nat))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_zero__induct) ).
fof(fact_895_zero__le__imp__eq__int,axiom,
! [X25] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X25))
=> ? [X32] : X25 = hAPP(nat,int,semiring_1_of_nat(int),X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_zero__le__imp__eq__int) ).
fof(fact_894_nonneg__eq__int,axiom,
! [X43] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X43))
=> ~ ! [X38] : X43 != hAPP(nat,int,semiring_1_of_nat(int),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_nonneg__eq__int) ).
fof(fact_893_nonneg__int__cases,axiom,
! [X25] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X25))
=> ~ ! [X32] : X25 != hAPP(nat,int,semiring_1_of_nat(int),X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_nonneg__int__cases) ).
fof(fact_553_gr0__implies__Suc,axiom,
! [X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17))
=> ? [X38] : X17 = hAPP(nat,nat,suc,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_gr0__implies__Suc) ).
fof(fact_510_gr0__conv__Suc,axiom,
! [X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20))
<=> ? [X38] : X20 = hAPP(nat,nat,suc,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_gr0__conv__Suc) ).
fof(fact_860_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
! [X8] : hAPP(fun(nat,bool),nat,finite_card(nat),X8) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_908_abs__ge__zero,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,abs_abs(X3),X41))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_abs__ge__zero) ).
fof(fact_833_zero__le__imp__of__nat,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X18] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(nat,X3,semiring_1_of_nat(X3),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_zero__le__imp__of__nat) ).
fof(fact_832_of__nat__0__le__iff,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X17] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(nat,X3,semiring_1_of_nat(X3),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_of__nat__0__le__iff) ).
fof(fact_918_abs__ge__self,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X41),hAPP(X3,X3,abs_abs(X3),X41))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_abs__ge__self) ).
fof(fact_935_neg__imp__number__of__eq__0,axiom,
! [X82] :
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(int,nat,number_number_of(nat),X82) = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_neg__imp__number__of__eq__0) ).
fof(fact_865_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
! [X43] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X43))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(fact_830_zero__zle__int,axiom,
! [X17] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_zero__zle__int) ).
fof(fact_456_zero__less__Suc,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_zero__less__Suc) ).
fof(fact_294_lessI,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,suc,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_lessI) ).
fof(fact_483_neq0__conv,axiom,
! [X20] :
( X20 != zero_zero(nat)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_neq0__conv) ).
fof(fact_457_le__0__eq,axiom,
! [X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),zero_zero(nat)))
<=> X20 = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_le__0__eq) ).
fof(fact_459_diffs0__imp__equal,axiom,
! [X18,X17] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17) = zero_zero(nat)
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X18) = zero_zero(nat)
=> X18 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_diffs0__imp__equal) ).
fof(fact_481_gr__implies__not0,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> X17 != zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_gr__implies__not0) ).
fof(fact_302_less__not__refl3,axiom,
! [X67,X68] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X67),X68))
=> X67 != X68 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_less__not__refl3) ).
fof(fact_301_less__not__refl2,axiom,
! [X17,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X18))
=> X18 != X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_less__not__refl2) ).
fof(fact_588_mult__cancel2,axiom,
! [X28,X19,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X19) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X20),X19)
<=> ( X28 = X20
| X19 = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_mult__cancel2) ).
fof(fact_784_nat__mult__eq__cancel__disj,axiom,
! [X19,X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X28) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X20)
<=> ( X19 = zero_zero(nat)
| X28 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_nat__mult__eq__cancel__disj) ).
fof(fact_587_mult__cancel1,axiom,
! [X19,X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X28) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X19),X20)
<=> ( X28 = X20
| X19 = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_mult__cancel1) ).
fof(fact_232_nat__add__right__cancel,axiom,
! [X28,X19,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X19) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X20),X19)
<=> X28 = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_nat__add__right__cancel) ).
fof(fact_231_nat__add__left__cancel,axiom,
! [X19,X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X28) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X20)
<=> X28 = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_nat__add__left__cancel) ).
fof(fact_989_rel__simps_I2_J,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_989_rel__simps_I2_J) ).
fof(fact_520_diff__add__0,axiom,
! [X17,X18] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X18)) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_diff__add__0) ).
fof(fact_124_empty__subsetI,axiom,
! [X1,X8] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),bot_bot(fun(X1,bool))),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_empty__subsetI) ).
fof(fact_951_not__neg__number__of__Pls,axiom,
~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_not__neg__number__of__Pls) ).
fof(fact_896_int__diff__cases,axiom,
! [X43] :
~ ! [X38,X32] : X43 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X38)),hAPP(nat,int,semiring_1_of_nat(int),X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_int__diff__cases) ).
fof(fact_514_add__is__1,axiom,
! [X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X20) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( ( X28 = hAPP(nat,nat,suc,zero_zero(nat))
& X20 = zero_zero(nat) )
| ( X28 = zero_zero(nat)
& X20 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_add__is__1) ).
fof(fact_513_one__is__add,axiom,
! [X28,X20] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X20)
<=> ( ( X28 = hAPP(nat,nat,suc,zero_zero(nat))
& X20 = zero_zero(nat) )
| ( X28 = zero_zero(nat)
& X20 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_one__is__add) ).
fof(fact_84_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/sandbox2/benchmark/theBenchmark.p',fact_84_subset__refl) ).
fof(fact_945_number__of__succ,axiom,
! [X3] :
( number_ring(X3)
=> ! [X25] : hAPP(int,X3,number_number_of(X3),hAPP(int,int,succ,X25)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),hAPP(int,X3,number_number_of(X3),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_number__of__succ) ).
fof(fact_873_of__nat__Suc,axiom,
! [X3] :
( semiring_1(X3)
=> ! [X18] : hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(nat,nat,suc,X18)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),hAPP(nat,X3,semiring_1_of_nat(X3),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_of__nat__Suc) ).
fof(fact_871_int__Suc,axiom,
! [X18] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X18)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_int__Suc) ).
fof(fact_167_singleton__conv2,axiom,
! [X1,X11] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X11)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_singleton__conv2) ).
fof(fact_632_Ints__0,axiom,
! [X1] :
( ring_1(X1)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_Ints__0) ).
fof(fact_633_Ints__1,axiom,
! [X1] :
( ring_1(X1)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_Ints__1) ).
fof(fact_695_mult__eq__1__iff,axiom,
! [X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X20) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( X28 = hAPP(nat,nat,suc,zero_zero(nat))
& X20 = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_mult__eq__1__iff) ).
fof(fact_207_diff__Suc__1,axiom,
! [X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X17)),one_one(nat)) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_diff__Suc__1) ).
fof(fact_155_insert__not__empty,axiom,
! [X1,X11,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8) != bot_bot(fun(X1,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_insert__not__empty) ).
fof(fact_156_empty__not__insert,axiom,
! [X1,X11,X8] : bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_empty__not__insert) ).
fof(fact_507_zero__le__one,axiom,
! [X3] :
( linordered_semidom(X3)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),one_one(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_zero__le__one) ).
fof(fact_508_zero__less__one,axiom,
! [X3] :
( linordered_semidom(X3)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),one_one(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_zero__less__one) ).
fof(fact_163_bot__least,axiom,
! [X3] :
( bot(X3)
=> ! [X41] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),bot_bot(X3)),X41)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_bot__least) ).
fof(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X42] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X42) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X42),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41,X40] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X41),X40) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X40),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_60_order__eq__refl,axiom,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( X21 = X22
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order__eq__refl) ).
fof(fact_57_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/sandbox2/benchmark/theBenchmark.p',fact_57_order__refl) ).
fof(fact_480_gr0I,axiom,
! [X17] :
( X17 != zero_zero(nat)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_gr0I) ).
fof(fact_458_less__eq__nat_Osimps_I1_J,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_less__eq__nat_Osimps_I1_J) ).
fof(fact_455_le0,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_le0) ).
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/sandbox2/benchmark/theBenchmark.p',fact_22_eq__imp__le) ).
fof(fact_771_zle__refl,axiom,
! [X86] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X86),X86)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_zle__refl) ).
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/sandbox2/benchmark/theBenchmark.p',fact_24_le__refl) ).
fof(fact_748_zmult__commute,axiom,
! [X43,X86] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X43),X86) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X86),X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_zmult__commute) ).
fof(fact_770_zadd__commute,axiom,
! [X43,X86] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X43),X86) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X86),X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_zadd__commute) ).
fof(fact_743_nat__mult__commute,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X17),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_nat__mult__commute) ).
fof(fact_228_nat__add__commute,axiom,
! [X18,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_nat__add__commute) ).
fof(help_fimplies_1_1_U,axiom,
! [X123,X122] :
( hBOOL(X122)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X122),X123)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(fact_131_empty__Diff,axiom,
! [X1,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),bot_bot(fun(X1,bool))),X8) = bot_bot(fun(X1,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_empty__Diff) ).
fof(fact_586_mult__is__0,axiom,
! [X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X20) = zero_zero(nat)
<=> ( X28 = zero_zero(nat)
| X20 = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_mult__is__0) ).
fof(fact_705_mult__eq__self__implies__10,axiom,
! [X18,X17] :
( X18 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),X17)
=> ( X17 = one_one(nat)
| X18 = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_mult__eq__self__implies__10) ).
fof(fact_477_add__is__0,axiom,
! [X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X20) = zero_zero(nat)
<=> ( X28 = zero_zero(nat)
& X20 = zero_zero(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_add__is__0) ).
fof(fact_610_nat__mult__eq__1__iff,axiom,
! [X28,X20] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X20) = one_one(nat)
<=> ( X28 = one_one(nat)
& X20 = one_one(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_nat__mult__eq__1__iff) ).
fof(fact_612_nat__1__eq__mult__iff,axiom,
! [X28,X20] :
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X28),X20)
<=> ( X28 = one_one(nat)
& X20 = one_one(nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_nat__1__eq__mult__iff) ).
fof(fact_476_add__eq__self__zero,axiom,
! [X18,X17] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X17) = X18
=> X17 = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_add__eq__self__zero) ).
fof(fact_159_image__empty,axiom,
! [X2,X1,X12] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),bot_bot(fun(X2,bool))) = bot_bot(fun(X1,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_image__empty) ).
fof(fact_127_Diff__cancel,axiom,
! [X1,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X8) = bot_bot(fun(X1,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Diff__cancel) ).
fof(fact_286_comp__fun__idem__insert,axiom,
! [X1] : hBOOL(hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),bool,finite_comp_fun_idem(X1,fun(X1,bool)),insert(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_comp__fun__idem__insert) ).
fof(fact_272_Suc__eq__plus1__left,axiom,
! [X17] : hAPP(nat,nat,suc,X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Suc__eq__plus1__left) ).
fof(fact_944_succ__def,axiom,
! [X25] : hAPP(int,int,succ,X25) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X25),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_succ__def) ).
fof(fact_273_Suc__eq__plus1,axiom,
! [X17] : hAPP(nat,nat,suc,X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),one_one(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Suc__eq__plus1) ).
fof(fact_408_less__eq__Suc__le__raw,axiom,
! [X33] : hAPP(nat,fun(nat,bool),ord_less(nat),X33) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_less__eq__Suc__le__raw) ).
fof(fact_925_abs__idempotent,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41] : hAPP(X3,X3,abs_abs(X3),hAPP(X3,X3,abs_abs(X3),X41)) = hAPP(X3,X3,abs_abs(X3),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_abs__idempotent) ).
fof(tsy_v_P_res,axiom,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_P_res) ).
fof(fact_932_abs__of__nat,axiom,
! [X3] :
( linordered_idom(X3)
=> ! [X17] : hAPP(X3,X3,abs_abs(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X17)) = hAPP(nat,X3,semiring_1_of_nat(X3),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_abs__of__nat) ).
fof(fact_829_number__of__int,axiom,
! [X3] :
( number_semiring(X3)
=> ! [X17] : hAPP(int,X3,number_number_of(X3),hAPP(nat,int,semiring_1_of_nat(int),X17)) = hAPP(nat,X3,semiring_1_of_nat(X3),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_number__of__int) ).
fof(fact_934_abs__int__eq,axiom,
! [X18] : hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),X18)) = hAPP(nat,int,semiring_1_of_nat(int),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_934_abs__int__eq) ).
fof(fact_135_empty__def,axiom,
! [X1] : bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_empty__def) ).
fof(fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),zero_zero(X3)),X41) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_579_mult__zero__left,axiom,
! [X3] :
( mult_zero(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),zero_zero(X3)),X41) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_mult__zero__left) ).
fof(fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X3] :
( comm_semiring_1(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),zero_zero(X3)) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_580_mult__zero__right,axiom,
! [X3] :
( mult_zero(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),zero_zero(X3)) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_mult__zero__right) ).
fof(fact_472_diff__self,axiom,
! [X3] :
( group_add(X3)
=> ! [X41] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X41),X41) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_diff__self) ).
fof(fact_619_eq__number__of,axiom,
! [X1] :
( ( number_ring(X1)
& ring_char_0(X1) )
=> ! [X14,X39] :
( hAPP(int,X1,number_number_of(X1),X14) = hAPP(int,X1,number_number_of(X1),X39)
<=> X14 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_eq__number__of) ).
fof(fact_841_of__nat__eq__iff,axiom,
! [X1] :
( semiring_char_0(X1)
=> ! [X28,X20] :
( hAPP(nat,X1,semiring_1_of_nat(X1),X28) = hAPP(nat,X1,semiring_1_of_nat(X1),X20)
<=> X28 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_841_of__nat__eq__iff) ).
fof(fact_584_mult__0,axiom,
! [X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X17) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_mult__0) ).
fof(fact_462_diff__0__eq__0,axiom,
! [X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X17) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_diff__0__eq__0) ).
fof(fact_746_zmult__1,axiom,
! [X43] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),X43) = X43,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_zmult__1) ).
fof(fact_761_zadd__0,axiom,
! [X43] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),X43) = X43,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_zadd__0) ).
fof(fact_613_nat__mult__1,axiom,
! [X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_nat__mult__1) ).
fof(fact_479_plus__nat_Oadd__0,axiom,
! [X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_plus__nat_Oadd__0) ).
fof(fact_585_mult__0__right,axiom,
! [X18] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X18),zero_zero(nat)) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_mult__0__right) ).
fof(fact_747_zmult__1__right,axiom,
! [X43] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X43),one_one(int)) = X43,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_zmult__1__right) ).
fof(fact_760_zadd__0__right,axiom,
! [X43] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X43),zero_zero(int)) = X43,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_zadd__0__right) ).
fof(fact_611_nat__mult__1__right,axiom,
! [X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X17),one_one(nat)) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_nat__mult__1__right) ).
fof(fact_478_Nat_Oadd__0__right,axiom,
! [X18] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),zero_zero(nat)) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_Nat_Oadd__0__right) ).
fof(fact_461_minus__nat_Odiff__0,axiom,
! [X18] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),zero_zero(nat)) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_minus__nat_Odiff__0) ).
fof(fact_460_diff__self__eq__0,axiom,
! [X18] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X18) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_diff__self__eq__0) ).
fof(fact_890_transfer__int__nat__relations_I1_J,axiom,
! [X14,X39] :
( hAPP(nat,int,semiring_1_of_nat(int),X14) = hAPP(nat,int,semiring_1_of_nat(int),X39)
<=> X14 = X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_890_transfer__int__nat__relations_I1_J) ).
fof(fact_883_int__int__eq,axiom,
! [X28,X20] :
( hAPP(nat,int,semiring_1_of_nat(int),X28) = hAPP(nat,int,semiring_1_of_nat(int),X20)
<=> X28 = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_883_int__int__eq) ).
fof(fact_982_add__Pls__right,axiom,
! [X25] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X25),pls) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_add__Pls__right) ).
fof(fact_980_diff__bin__simps_I1_J,axiom,
! [X25] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X25),pls) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_diff__bin__simps_I1_J) ).
fof(fact_981_add__Pls,axiom,
! [X25] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X25) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_add__Pls) ).
fof(fact_983_mult__Pls,axiom,
! [X86] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X86) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_mult__Pls) ).
fof(fact_928_not__neg__0,axiom,
~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_928_not__neg__0) ).
fof(fact_926_not__neg__1,axiom,
~ hBOOL(hAPP(int,bool,nat_neg,one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_not__neg__1) ).
fof(fact_977_rel__simps_I51_J,axiom,
! [X19,X95] :
( hAPP(int,int,bit1,X19) = hAPP(int,int,bit1,X95)
<=> X19 = X95 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_rel__simps_I51_J) ).
fof(fact_17_nat_Oinject,axiom,
! [X23,X24] :
( hAPP(nat,nat,suc,X23) = hAPP(nat,nat,suc,X24)
<=> X23 = X24 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_16_Suc__inject) ).
fof(fact_962_semiring__numeral__1__eq__1,axiom,
! [X3] :
( number_semiring(X3)
=> hAPP(int,X3,number_number_of(X3),hAPP(int,int,bit1,pls)) = one_one(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_962_semiring__numeral__1__eq__1) ).
fof(fact_961_numeral__1__eq__1,axiom,
! [X3] :
( number_ring(X3)
=> hAPP(int,X3,number_number_of(X3),hAPP(int,int,bit1,pls)) = one_one(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_numeral__1__eq__1) ).
fof(fact_957_semiring__norm_I110_J,axiom,
! [X3] :
( number_ring(X3)
=> one_one(X3) = hAPP(int,X3,number_number_of(X3),hAPP(int,int,bit1,pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_957_semiring__norm_I110_J) ).
fof(fact_589_comp__fun__idem,axiom,
! [X1] :
( ab_sem1668676832m_mult(X1)
=> hBOOL(hAPP(fun(X1,fun(X1,X1)),bool,finite_comp_fun_idem(X1,X1),times_times(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_comp__fun__idem) ).
fof(fact_123_finite_OemptyI,axiom,
! [X1] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_finite_OemptyI) ).
fof(fact_15_finite,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_14_finite__code) ).
fof(tsy_c_Nat__Transfer_Otsub_res,axiom,
ti(fun(int,fun(int,int)),nat_tsub) = nat_tsub,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat__Transfer_Otsub_res) ).
fof(tsy_c_fimplies_res,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
fof(tsy_c_fdisj_res,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
fof(tsy_c_fconj_res,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
fof(help_fNot_2_1_U,axiom,
! [X122] :
( hBOOL(X122)
| hBOOL(hAPP(bool,bool,fNot,X122)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(fact_839_int__eq__0__conv,axiom,
! [X20] :
( hAPP(nat,int,semiring_1_of_nat(int),X20) = zero_zero(int)
<=> X20 = zero_zero(nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_int__eq__0__conv) ).
fof(fact_488_Suc__not__Zero,axiom,
! [X18] : hAPP(nat,nat,suc,X18) != zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_Suc__not__Zero) ).
fof(fact_487_nat_Osimps_I3_J,axiom,
! [X77] : hAPP(nat,nat,suc,X77) != zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_nat_Osimps_I3_J) ).
fof(fact_485_Suc__neq__Zero,axiom,
! [X18] : hAPP(nat,nat,suc,X18) != zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_Suc__neq__Zero) ).
fof(fact_490_Zero__not__Suc,axiom,
! [X18] : zero_zero(nat) != hAPP(nat,nat,suc,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_Zero__not__Suc) ).
fof(fact_489_nat_Osimps_I2_J,axiom,
! [X78] : zero_zero(nat) != hAPP(nat,nat,suc,X78),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_nat_Osimps_I2_J) ).
fof(fact_486_Zero__neq__Suc,axiom,
! [X18] : zero_zero(nat) != hAPP(nat,nat,suc,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_Zero__neq__Suc) ).
fof(fact_18_Suc__n__not__n,axiom,
! [X17] : hAPP(nat,nat,suc,X17) != X17,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_19_n__not__Suc__n) ).
fof(fact_978_rel__simps_I46_J,axiom,
! [X25] : hAPP(int,int,bit1,X25) != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_rel__simps_I46_J) ).
fof(fact_979_rel__simps_I39_J,axiom,
! [X29] : pls != hAPP(int,int,bit1,X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_rel__simps_I39_J) ).
fof(tsy_c_Option_Othe_res,axiom,
ti(fun(option(com),com),the_1(com)) = the_1(com),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Option_Othe_res) ).
fof(tsy_c_Com_Obody_res,axiom,
ti(fun(pname,option(com)),body) = body,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Com_Obody_res) ).
fof(tsy_v_G_res,hypothesis,
ti(fun(x_a,bool),g) = g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_G_res) ).
fof(tsy_c_Int_Osucc_res,axiom,
ti(fun(int,int),succ) = succ,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Osucc_res) ).
fof(tsy_c_Int_OBit1_res,axiom,
ti(fun(int,int),bit1) = bit1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
fof(tsy_c_Nat__Numeral_Oneg_res,axiom,
ti(fun(int,bool),nat_neg) = nat_neg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat__Numeral_Oneg_res) ).
fof(tsy_c_Nat_OSuc_res,hypothesis,
ti(fun(nat,nat),suc) = suc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).
fof(tsy_c_fNot_res,axiom,
ti(fun(bool,bool),fNot) = fNot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
fof(tsy_v_mgt_res,axiom,
ti(fun(com,x_a),mgt) = mgt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_mgt_res) ).
fof(tsy_v_wt_res,axiom,
ti(fun(com,bool),wt) = wt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_wt_res) ).
fof(tsy_v_mgt__call_res,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_mgt__call_res) ).
fof(tsy_v_U_res,hypothesis,
ti(fun(pname,bool),u) = u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_U_res) ).
fof(fact_516_card_Oempty,axiom,
! [X1] : hAPP(fun(X1,bool),nat,finite_card(X1),bot_bot(fun(X1,bool))) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_card_Oempty) ).
fof(fact_136_bot__fun__def,axiom,
! [X1,X2] :
( bot(X2)
=> ! [X33] : hAPP(X1,X2,bot_bot(fun(X1,X2)),X33) = bot_bot(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_bot__fun__def) ).
fof(fact_134_bot__apply,axiom,
! [X2,X1] :
( bot(X1)
=> ! [X14] : hAPP(X2,X1,bot_bot(fun(X2,X1)),X14) = bot_bot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_bot__apply) ).
fof(fact_930_abs__zero,axiom,
! [X3] :
( ordere142940540dd_abs(X3)
=> hAPP(X3,X3,abs_abs(X3),zero_zero(X3)) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_930_abs__zero) ).
fof(fact_927_abs__one,axiom,
! [X3] :
( linordered_idom(X3)
=> hAPP(X3,X3,abs_abs(X3),one_one(X3)) = one_one(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_abs__one) ).
fof(fact_835_of__nat__0,axiom,
! [X3] :
( semiring_1(X3)
=> hAPP(nat,X3,semiring_1_of_nat(X3),zero_zero(nat)) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_of__nat__0) ).
fof(fact_836_of__nat__1,axiom,
! [X3] :
( semiring_1(X3)
=> hAPP(nat,X3,semiring_1_of_nat(X3),one_one(nat)) = one_one(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_of__nat__1) ).
fof(fact_969_semiring__numeral__0__eq__0,axiom,
! [X3] :
( number_semiring(X3)
=> hAPP(int,X3,number_number_of(X3),pls) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_semiring__numeral__0__eq__0) ).
fof(fact_970_number__of__Pls,axiom,
! [X3] :
( number_ring(X3)
=> hAPP(int,X3,number_number_of(X3),pls) = zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_number__of__Pls) ).
fof(fact_971_semiring__norm_I112_J,axiom,
! [X3] :
( number_ring(X3)
=> zero_zero(X3) = hAPP(int,X3,number_number_of(X3),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_971_semiring__norm_I112_J) ).
fof(fact_559_not0__implies__Suc,axiom,
! [X17] :
( X17 != zero_zero(nat)
=> ? [X38] : X17 = hAPP(nat,nat,suc,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_not0__implies__Suc) ).
fof(fact_557_nat_Oexhaust,axiom,
! [X22] :
( X22 != zero_zero(nat)
=> ~ ! [X80] : X22 != hAPP(nat,nat,suc,X80) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_nat_Oexhaust) ).
fof(fact_798_number__of__is__id,axiom,
! [X25] : hAPP(int,int,number_number_of(int),X25) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_number__of__is__id) ).
fof(tsy_c_Int_OPls_res,axiom,
ti(int,pls) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
fof(tsy_v_na_res,hypothesis,
ti(nat,na) = na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_na_res) ).
fof(tsy_c_fTrue_res,axiom,
ti(bool,fTrue) = fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
fof(tsy_c_fFalse_res,axiom,
ti(bool,fFalse) = fFalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(tsy_v_pn_res,hypothesis,
ti(pname,pn) = pn,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_pn_res) ).
fof(arity_sum___Finite__Set_Ofinite,axiom,
! [X118,X119] :
( ( finite_finite_1(X119)
& finite_finite_1(X118) )
=> finite_finite_1(sum_sum(X118,X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).
fof(arity_fun___Finite__Set_Ofinite,axiom,
! [X118,X119] :
( ( finite_finite_1(X119)
& finite_finite_1(X118) )
=> finite_finite_1(fun(X118,X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
fof(arity_fun___Orderings_Opreorder,axiom,
! [X118,X119] :
( preorder(X119)
=> preorder(fun(X118,X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
fof(arity_fun___Orderings_Oorder,axiom,
! [X118,X119] :
( order(X119)
=> order(fun(X118,X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
fof(arity_fun___Orderings_Oord,axiom,
! [X118,X119] :
( ord(X119)
=> ord(fun(X118,X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
fof(arity_fun___Orderings_Obot,axiom,
! [X118,X119] :
( bot(X119)
=> bot(fun(X118,X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
fof(arity_fun___Groups_Ominus,axiom,
! [X118,X119] :
( minus(X119)
=> minus(fun(X118,X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
fof(fact_464_zero__neq__one,axiom,
! [X3] :
( zero_neq_one(X3)
=> zero_zero(X3) != one_one(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_zero__neq__one) ).
fof(fact_463_one__neq__zero,axiom,
! [X3] :
( zero_neq_one(X3)
=> one_one(X3) != zero_zero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_one__neq__zero) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(fact_984_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
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/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_952_transfer__int__nat__numerals_I4_J,axiom,
hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_transfer__int__nat__numerals_I4_J) ).
fof(fact_955_numeral__3__eq__3,axiom,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_955_numeral__3__eq__3) ).
fof(conj_4,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(fact_812_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_814_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_762_int__0__less__1,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_int__0__less__1) ).
fof(fact_985_rel__simps_I19_J,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_rel__simps_I19_J) ).
fof(fact_886_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
bot_bot(fun(int,bool)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_886_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
fof(fact_954_numeral__1__eq__Suc__0,axiom,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_954_numeral__1__eq__Suc__0) ).
fof(fact_869_int__Suc0__eq__1,axiom,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat))) = one_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_int__Suc0__eq__1) ).
fof(fact_959_nat__numeral__1__eq__1,axiom,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_nat__numeral__1__eq__1) ).
fof(fact_960_one__is__num__one,axiom,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_one__is__num__one) ).
fof(fact_958_Numeral1__eq1__nat,axiom,
one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_Numeral1__eq1__nat) ).
fof(conj_0,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_949_succ__Pls,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_succ__Pls) ).
fof(fact_838_int__0,axiom,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_838_int__0) ).
fof(fact_837_int__1,axiom,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_int__1) ).
fof(fact_863_transfer__int__nat__numerals_I1_J,axiom,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_transfer__int__nat__numerals_I1_J) ).
fof(fact_862_transfer__int__nat__numerals_I2_J,axiom,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_transfer__int__nat__numerals_I2_J) ).
fof(fact_974_nat__number__of__Pls,axiom,
hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_nat__number__of__Pls) ).
fof(fact_967_zero__is__num__zero,axiom,
zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_zero__is__num__zero) ).
fof(fact_975_semiring__norm_I113_J,axiom,
zero_zero(nat) = hAPP(int,nat,number_number_of(nat),pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_semiring__norm_I113_J) ).
fof(fact_523_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_One__nat__def) ).
fof(fact_799_int__0__neq__1,axiom,
zero_zero(int) != one_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_int__0__neq__1) ).
fof(fact_475_bot__nat__def,axiom,
bot_bot(nat) = zero_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_bot__nat__def) ).
fof(arity_Int_Oint___Rings_Oordered__ring__abs,axiom,
ordered_ring_abs(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring__abs) ).
fof(arity_Int_Oint___Nat_Osemiring__char__0,axiom,
semiring_char_0(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
fof(arity_Nat_Onat___Nat_Osemiring__char__0,axiom,
semiring_char_0(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
fof(arity_Int_Oint___Int_Onumber__semiring,axiom,
number_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
fof(arity_Nat_Onat___Int_Onumber__semiring,axiom,
number_semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
fof(arity_Int_Oint___Rings_Olinordered__semiring__1,axiom,
linord1278240602ring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1) ).
fof(arity_Int_Oint___Rings_Olinordered__semiring,axiom,
linordered_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring) ).
fof(arity_Nat_Onat___Rings_Olinordered__semiring,axiom,
linordered_semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring) ).
fof(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict,axiom,
linord893533164strict(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict,axiom,
linord893533164strict(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int_Oint___Rings_Olinordered__semiring__strict,axiom,
linord20386208strict(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__strict) ).
fof(arity_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
linord20386208strict(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).
fof(arity_Int_Oint___Rings_Olinordered__ring,axiom,
linordered_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
fof(arity_Int_Oint___Rings_Olinordered__ring__strict,axiom,
linord581940658strict(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
fof(arity_Int_Oint___Rings_Oordered__comm__semiring,axiom,
ordere1490568538miring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__comm__semiring) ).
fof(arity_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
ordere1490568538miring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__comm__semiring) ).
fof(arity_Int_Oint___Rings_Oordered__semiring,axiom,
ordered_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__semiring) ).
fof(arity_Nat_Onat___Rings_Oordered__semiring,axiom,
ordered_semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__semiring) ).
fof(arity_Int_Oint___Rings_Oordered__ring,axiom,
ordered_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring) ).
fof(arity_Int_Oint___Rings_Oordered__cancel__semiring,axiom,
ordere453448008miring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__cancel__semiring) ).
fof(arity_Nat_Onat___Rings_Oordered__cancel__semiring,axiom,
ordere453448008miring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).
fof(arity_Int_Oint___Rings_Oring,axiom,
ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
fof(arity_Int_Oint___Int_Oring__char__0,axiom,
ring_char_0(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
fof(arity_Int_Oint___Int_Onumber__ring,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(arity_Int_Oint___Groups_Ocomm__monoid__mult,axiom,
comm_monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
fof(arity_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
comm_monoid_mult(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
fof(arity_Int_Oint___Rings_Ocomm__semiring,axiom,
comm_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
fof(arity_Nat_Onat___Rings_Ocomm__semiring,axiom,
comm_semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).
fof(arity_Int_Oint___Rings_Oring__no__zero__divisors,axiom,
ring_n68954251visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
fof(arity_Int_Oint___Rings_Olinordered__semiring__1__strict,axiom,
linord626643107strict(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc,axiom,
semiri456707255roduct(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
fof(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc,axiom,
semiri456707255roduct(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
fof(arity_Int_Oint___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
fof(arity_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
fof(arity_Int_Oint___Groups_Oordered__comm__monoid__add,axiom,
ordere216010020id_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
ordere216010020id_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
fof(arity_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
fof(arity_Int_Oint___Groups_Ocomm__monoid__add,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
fof(arity_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
fof(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(arity_Nat_Onat___Rings_Ozero__neq__one,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(arity_Int_Oint___Rings_Olinordered__semidom,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
fof(arity_Nat_Onat___Rings_Olinordered__semidom,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
fof(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add,axiom,
ordere223160158up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
ordere223160158up_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int_Oint___Groups_Ogroup__add,axiom,
group_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
fof(arity_Int_Oint___Groups_Oordered__ab__semigroup__add,axiom,
ordere779506340up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
ordere779506340up_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int_Oint___Groups_Oab__group__add,axiom,
ab_group_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
fof(arity_Int_Oint___Groups_Oordered__ab__group__add,axiom,
ordered_ab_group_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add) ).
fof(arity_Int_Oint___Orderings_Olinorder,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
fof(arity_Int_Oint___Orderings_Opreorder,axiom,
preorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
fof(arity_Nat_Onat___Orderings_Opreorder,axiom,
preorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
fof(arity_HOL_Obool___Orderings_Opreorder,axiom,
preorder(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
fof(arity_Int_Oint___Orderings_Oorder,axiom,
order(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
fof(arity_Nat_Onat___Orderings_Oorder,axiom,
order(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
fof(arity_HOL_Obool___Orderings_Oorder,axiom,
order(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
finite_finite_1(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(arity_Int_Oint___Orderings_Oord,axiom,
ord(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
fof(arity_Nat_Onat___Orderings_Oord,axiom,
ord(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
fof(arity_HOL_Obool___Orderings_Oord,axiom,
ord(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
fof(arity_Nat_Onat___Orderings_Obot,axiom,
bot(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
fof(arity_HOL_Obool___Orderings_Obot,axiom,
bot(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
fof(arity_Int_Oint___Rings_Osemiring__1,axiom,
semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
fof(arity_Nat_Onat___Rings_Osemiring__1,axiom,
semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
fof(arity_Int_Oint___Rings_Oring__1,axiom,
ring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
fof(arity_Int_Oint___Int_Onumber,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
fof(arity_Nat_Onat___Int_Onumber,axiom,
number(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
fof(arity_Int_Oint___Groups_Ozero,axiom,
zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
fof(arity_Nat_Onat___Groups_Ozero,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
fof(arity_Int_Oint___Rings_Omult__zero,axiom,
mult_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
fof(arity_Nat_Onat___Rings_Omult__zero,axiom,
mult_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
fof(arity_Int_Oint___Rings_Ono__zero__divisors,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
fof(arity_Nat_Onat___Rings_Ono__zero__divisors,axiom,
no_zero_divisors(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
fof(arity_Int_Oint___Rings_Osemiring,axiom,
semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
fof(arity_Nat_Onat___Rings_Osemiring,axiom,
semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
fof(arity_Int_Oint___Groups_Omonoid__mult,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
fof(arity_Nat_Onat___Groups_Omonoid__mult,axiom,
monoid_mult(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
fof(arity_Int_Oint___Groups_Oab__semigroup__mult,axiom,
ab_semigroup_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
fof(arity_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
ab_semigroup_mult(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
fof(arity_Int_Oint___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
fof(arity_Int_Oint___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
fof(arity_Int_Oint___Groups_Omonoid__add,axiom,
monoid_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
fof(arity_Nat_Onat___Groups_Omonoid__add,axiom,
monoid_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
fof(arity_Int_Oint___Groups_Oone,axiom,
one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
fof(arity_Nat_Onat___Groups_Oone,axiom,
one(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
fof(arity_Int_Oint___Groups_Ominus,axiom,
minus(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
fof(arity_Nat_Onat___Groups_Ominus,axiom,
minus(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ominus) ).
fof(arity_HOL_Obool___Groups_Ominus,axiom,
minus(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
fof(arity_Int_Oint___Groups_Oordered__ab__group__add__abs,axiom,
ordere142940540dd_abs(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add__abs) ).
fof(fact_976_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_Pls__def) ).
fof(i_0_1192,plain,
! [X1,X14,X39,X16] :
( ( hBOOL(X16)
=> ti(X1,X14) = hAPP(fun(X1,bool),X1,the(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(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,X16)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14)))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X16))),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X39)))) )
& ( ~ hBOOL(X16)
=> ti(X1,X39) = hAPP(fun(X1,bool),X1,the(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(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,X16)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14)))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X16))),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X39)))) ) ),
inference(fof_simplification,[status(thm)],[fact_283_If__def]) ).
fof(i_0_1193,plain,
! [X1,X16,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> ( ti(fun(X1,bool),X10) != bot_bot(fun(X1,bool))
=> ( ! [X33] : hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),bot_bot(fun(X1,bool)))))
=> ( ! [X33,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X57))
=> ( ti(fun(X1,bool),X57) != bot_bot(fun(X1,bool))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X57))
=> hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X57))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_219_finite__ne__induct]) ).
fof(i_0_1194,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_111_imageE]) ).
fof(i_0_1195,plain,
! [X1,X8,X34] :
( ( 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),bot_bot(fun(X1,bool)))))
=> hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X34),X8) = ti(X1,X34) )
& ( ~ 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),bot_bot(fun(X1,bool)))))
=> hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X34),X8) = hAPP(fun(X1,bool),X1,the(X1),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)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),bot_bot(fun(X1,bool)))))) ) ),
inference(fof_simplification,[status(thm)],[fact_281_flat__lub__def]) ).
fof(i_0_1196,plain,
! [X1,X14,X8,X12,X10] :
( hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X12),X10))
=> ( 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))
=> ( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
=> hAPP(fun(X1,bool),X1,X10,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X14),hAPP(fun(X1,bool),X1,X10,X8)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_212_folding__one_Oinsert]) ).
fof(i_0_1197,plain,
! [X1,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),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),bot_bot(fun(X1,bool)))) = ti(fun(X1,bool),X8) ),
inference(fof_simplification,[status(thm)],[fact_138_Diff__insert__absorb]) ).
fof(i_0_1198,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_81_insert__ident]) ).
fof(i_0_1199,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_1200,plain,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ti(X1,X14) = ti(X1,X39) ) ) ),
inference(fof_simplification,[status(thm)],[fact_339_linorder__antisym__conv2]) ).
fof(i_0_1201,plain,
! [X1,X8,X19] :
( hAPP(fun(X1,bool),nat,finite_card(X1),X8) = hAPP(nat,nat,suc,X19)
<=> ? [X72,X61] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X72),X61)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X72),X61))
& hAPP(fun(X1,bool),nat,finite_card(X1),X61) = X19
& ( X19 = zero_zero(nat)
=> ti(fun(X1,bool),X61) = bot_bot(fun(X1,bool)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_549_card__Suc__eq]) ).
fof(i_0_1202,plain,
! [X1] :
( linorder(X1)
=> ! [X39,X14] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ti(X1,X14) = ti(X1,X39) ) ) ),
inference(fof_simplification,[status(thm)],[fact_308_linorder__antisym__conv3]) ).
fof(i_0_1203,plain,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
<=> ti(X1,X14) = ti(X1,X39) ) ) ),
inference(fof_simplification,[status(thm)],[fact_334_linorder__antisym__conv1]) ).
fof(i_0_1204,plain,
! [X1,X8] :
( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
<=> ? [X33,X61] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X61)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X61)) ) ),
inference(fof_simplification,[status(thm)],[fact_188_nonempty__iff]) ).
fof(i_0_1205,plain,
! [X3] :
( linordered_idom(X3)
=> ! [X21,X22] :
( ti(X3,X21) != ti(X3,X22)
=> ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_423_linorder__neqE__linordered__idom]) ).
fof(i_0_1206,plain,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ( ti(X3,X21) != ti(X3,X22)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_325_linorder__cases]) ).
fof(i_0_1207,plain,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ti(X3,X21) != ti(X3,X22)
=> ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_309_linorder__neqE]) ).
fof(i_0_1208,plain,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14))
| ti(X1,X14) = ti(X1,X39) ) ) ),
inference(fof_simplification,[status(thm)],[fact_306_not__less__iff__gr__or__eq]) ).
fof(i_0_1209,plain,
! [X1,X8] :
( ! [X33] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
<=> ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool)) ),
inference(fof_simplification,[status(thm)],[fact_133_all__not__in__conv]) ).
fof(i_0_1210,plain,
! [X1,X11,X8] :
( ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ),
inference(fof_simplification,[status(thm)],[fact_125_equals0D]) ).
fof(i_0_1211,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_92_equalityE]) ).
fof(i_0_1212,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_1213,plain,
! [X1,X8,X19] :
( hAPP(fun(X1,bool),nat,finite_card(X1),X8) = hAPP(nat,nat,suc,X19)
=> ? [X72,X61] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X72),X61)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X72),X61))
& hAPP(fun(X1,bool),nat,finite_card(X1),X61) = X19
& ( X19 = zero_zero(nat)
=> ti(fun(X1,bool),X61) = bot_bot(fun(X1,bool)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_556_card__eq__SucD]) ).
fof(i_0_1214,plain,
! [X1,X8] :
( hAPP(fun(X1,bool),nat,finite_card(X1),X8) = zero_zero(nat)
<=> ( ti(fun(X1,bool),X8) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_533_card__eq__0__iff]) ).
fof(i_0_1215,plain,
! [X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133] :
( ( hBOOL(hAPP(fun(X6125,bool),bool,hAPP(X6125,fun(fun(X6125,bool),bool),member(X6125),esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133)),X6133))
| hAPP(fun(X6125,bool),X6126,hAPP(X6126,fun(fun(X6125,bool),X6126),hAPP(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126))),finite_fold_image(X6126,X6125),times_times(X6126)),X6129),X6127),X6133) = hAPP(fun(X6124,bool),X6126,hAPP(X6126,fun(fun(X6124,bool),X6126),hAPP(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126))),finite_fold_image(X6126,X6124),times_times(X6126)),X6128),X6127),X6132)
| hBOOL(hAPP(fun(X6124,bool),bool,hAPP(X6124,fun(fun(X6124,bool),bool),member(X6124),esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133)),X6132))
| ~ hBOOL(hAPP(fun(X6125,bool),bool,finite_finite(X6125),X6133))
| ~ comm_monoid_mult(X6126) )
& ( ~ hBOOL(hAPP(fun(X6124,bool),bool,hAPP(X6124,fun(fun(X6124,bool),bool),member(X6124),hAPP(X6125,X6124,X6130,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))),X6132))
| hAPP(X6124,X6125,X6131,hAPP(X6125,X6124,X6130,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))) != ti(X6125,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))
| hAPP(X6124,X6126,X6128,hAPP(X6125,X6124,X6130,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))) != hAPP(X6125,X6126,X6129,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))
| hAPP(fun(X6125,bool),X6126,hAPP(X6126,fun(fun(X6125,bool),X6126),hAPP(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126))),finite_fold_image(X6126,X6125),times_times(X6126)),X6129),X6127),X6133) = hAPP(fun(X6124,bool),X6126,hAPP(X6126,fun(fun(X6124,bool),X6126),hAPP(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126))),finite_fold_image(X6126,X6124),times_times(X6126)),X6128),X6127),X6132)
| hBOOL(hAPP(fun(X6124,bool),bool,hAPP(X6124,fun(fun(X6124,bool),bool),member(X6124),esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133)),X6132))
| ~ hBOOL(hAPP(fun(X6125,bool),bool,finite_finite(X6125),X6133))
| ~ comm_monoid_mult(X6126) )
& ( hBOOL(hAPP(fun(X6125,bool),bool,hAPP(X6125,fun(fun(X6125,bool),bool),member(X6125),esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133)),X6133))
| hAPP(fun(X6125,bool),X6126,hAPP(X6126,fun(fun(X6125,bool),X6126),hAPP(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126))),finite_fold_image(X6126,X6125),times_times(X6126)),X6129),X6127),X6133) = hAPP(fun(X6124,bool),X6126,hAPP(X6126,fun(fun(X6124,bool),X6126),hAPP(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126))),finite_fold_image(X6126,X6124),times_times(X6126)),X6128),X6127),X6132)
| ~ hBOOL(hAPP(fun(X6125,bool),bool,hAPP(X6125,fun(fun(X6125,bool),bool),member(X6125),hAPP(X6124,X6125,X6131,esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))),X6133))
| hAPP(X6125,X6124,X6130,hAPP(X6124,X6125,X6131,esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))) != ti(X6124,esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))
| ~ hBOOL(hAPP(fun(X6125,bool),bool,finite_finite(X6125),X6133))
| ~ comm_monoid_mult(X6126) )
& ( ~ hBOOL(hAPP(fun(X6124,bool),bool,hAPP(X6124,fun(fun(X6124,bool),bool),member(X6124),hAPP(X6125,X6124,X6130,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))),X6132))
| hAPP(X6124,X6125,X6131,hAPP(X6125,X6124,X6130,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))) != ti(X6125,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))
| hAPP(X6124,X6126,X6128,hAPP(X6125,X6124,X6130,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))) != hAPP(X6125,X6126,X6129,esk142_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))
| hAPP(fun(X6125,bool),X6126,hAPP(X6126,fun(fun(X6125,bool),X6126),hAPP(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6125,X6126),fun(X6126,fun(fun(X6125,bool),X6126))),finite_fold_image(X6126,X6125),times_times(X6126)),X6129),X6127),X6133) = hAPP(fun(X6124,bool),X6126,hAPP(X6126,fun(fun(X6124,bool),X6126),hAPP(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126)),hAPP(fun(X6126,fun(X6126,X6126)),fun(fun(X6124,X6126),fun(X6126,fun(fun(X6124,bool),X6126))),finite_fold_image(X6126,X6124),times_times(X6126)),X6128),X6127),X6132)
| ~ hBOOL(hAPP(fun(X6125,bool),bool,hAPP(X6125,fun(fun(X6125,bool),bool),member(X6125),hAPP(X6124,X6125,X6131,esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))),X6133))
| hAPP(X6125,X6124,X6130,hAPP(X6124,X6125,X6131,esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))) != ti(X6124,esk141_10(X6124,X6125,X6126,X6127,X6128,X6129,X6130,X6131,X6132,X6133))
| ~ hBOOL(hAPP(fun(X6125,bool),bool,finite_finite(X6125),X6133))
| ~ comm_monoid_mult(X6126) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_898_fold__image__eq__general__inverses])])])])]) ).
fof(i_0_1216,plain,
! [X6329,X6330] : hAPP(X6329,X6329,combi(X6329),X6330) = ti(X6329,X6330),
inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).
fof(i_0_1217,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_1218,plain,
! [X36,X74] :
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X74))
=> hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X74))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X36)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X74))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X36))))) ),
inference(fof_simplification,[status(thm)],[fact_543_card__less__Suc2]) ).
fof(i_0_1219,plain,
! [X4059,X4060,X4061,X4062,X4063,X4064,X4065] :
( ( hBOOL(hAPP(fun(X4059,bool),bool,hAPP(X4059,fun(fun(X4059,bool),bool),member(X4059),esk34_7(X4059,X4060,X4061,X4062,X4063,X4064,X4065)),X4061))
| hAPP(fun(X4059,bool),X4060,X4065,X4061) = ti(X4060,X4063)
| ~ hBOOL(hAPP(fun(X4059,bool),bool,finite_finite(X4059),X4061))
| ~ hBOOL(hAPP(fun(fun(X4059,bool),X4060),bool,hAPP(fun(X4059,X4060),fun(fun(fun(X4059,bool),X4060),bool),hAPP(X4060,fun(fun(X4059,X4060),fun(fun(fun(X4059,bool),X4060),bool)),hAPP(fun(X4060,fun(X4060,X4060)),fun(X4060,fun(fun(X4059,X4060),fun(fun(fun(X4059,bool),X4060),bool))),finite1357897459simple(X4060,X4059),X4062),X4063),X4064),X4065)) )
& ( hAPP(X4059,X4060,X4064,esk34_7(X4059,X4060,X4061,X4062,X4063,X4064,X4065)) != ti(X4060,X4063)
| hAPP(fun(X4059,bool),X4060,X4065,X4061) = ti(X4060,X4063)
| ~ hBOOL(hAPP(fun(X4059,bool),bool,finite_finite(X4059),X4061))
| ~ hBOOL(hAPP(fun(fun(X4059,bool),X4060),bool,hAPP(fun(X4059,X4060),fun(fun(fun(X4059,bool),X4060),bool),hAPP(X4060,fun(fun(X4059,X4060),fun(fun(fun(X4059,bool),X4060),bool)),hAPP(fun(X4060,fun(X4060,X4060)),fun(X4060,fun(fun(X4059,X4060),fun(fun(fun(X4059,bool),X4060),bool))),finite1357897459simple(X4060,X4059),X4062),X4063),X4064),X4065)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_214_folding__image__simple_Oneutral])])])]) ).
fof(i_0_1220,plain,
! [X4286,X4287,X4288,X4289] :
( ( ~ hBOOL(X4289)
| ti(X4286,X4287) = hAPP(fun(X4286,bool),X4286,the(X4286),hAPP(fun(X4286,bool),fun(X4286,bool),hAPP(fun(X4286,fun(bool,bool)),fun(fun(X4286,bool),fun(X4286,bool)),combs(X4286,bool,bool),hAPP(fun(X4286,bool),fun(X4286,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4286,bool),fun(X4286,fun(bool,bool))),combb(bool,fun(bool,bool),X4286),fconj),hAPP(fun(X4286,bool),fun(X4286,bool),hAPP(fun(bool,bool),fun(fun(X4286,bool),fun(X4286,bool)),combb(bool,bool,X4286),hAPP(bool,fun(bool,bool),fimplies,X4289)),hAPP(X4286,fun(X4286,bool),hAPP(fun(X4286,fun(X4286,bool)),fun(X4286,fun(X4286,bool)),combc(X4286,X4286,bool),fequal(X4286)),X4287)))),hAPP(fun(X4286,bool),fun(X4286,bool),hAPP(fun(bool,bool),fun(fun(X4286,bool),fun(X4286,bool)),combb(bool,bool,X4286),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X4289))),hAPP(X4286,fun(X4286,bool),hAPP(fun(X4286,fun(X4286,bool)),fun(X4286,fun(X4286,bool)),combc(X4286,X4286,bool),fequal(X4286)),X4288)))) )
& ( hBOOL(X4289)
| ti(X4286,X4288) = hAPP(fun(X4286,bool),X4286,the(X4286),hAPP(fun(X4286,bool),fun(X4286,bool),hAPP(fun(X4286,fun(bool,bool)),fun(fun(X4286,bool),fun(X4286,bool)),combs(X4286,bool,bool),hAPP(fun(X4286,bool),fun(X4286,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4286,bool),fun(X4286,fun(bool,bool))),combb(bool,fun(bool,bool),X4286),fconj),hAPP(fun(X4286,bool),fun(X4286,bool),hAPP(fun(bool,bool),fun(fun(X4286,bool),fun(X4286,bool)),combb(bool,bool,X4286),hAPP(bool,fun(bool,bool),fimplies,X4289)),hAPP(X4286,fun(X4286,bool),hAPP(fun(X4286,fun(X4286,bool)),fun(X4286,fun(X4286,bool)),combc(X4286,X4286,bool),fequal(X4286)),X4287)))),hAPP(fun(X4286,bool),fun(X4286,bool),hAPP(fun(bool,bool),fun(fun(X4286,bool),fun(X4286,bool)),combb(bool,bool,X4286),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X4289))),hAPP(X4286,fun(X4286,bool),hAPP(fun(X4286,fun(X4286,bool)),fun(X4286,fun(X4286,bool)),combc(X4286,X4286,bool),fequal(X4286)),X4288)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1192])]) ).
fof(i_0_1221,plain,
! [X4053,X4054,X4055,X4056] :
( ~ hBOOL(hAPP(fun(fun(X4053,bool),X4053),bool,hAPP(fun(X4053,fun(X4053,X4053)),fun(fun(fun(X4053,bool),X4053),bool),finite_folding_one(X4053),X4055),X4056))
| ~ hBOOL(hAPP(fun(X4053,bool),bool,finite_finite(X4053),X4054))
| ti(fun(X4053,bool),X4054) = bot_bot(fun(X4053,bool))
| ~ hBOOL(hAPP(fun(X4053,bool),bool,hAPP(X4053,fun(fun(X4053,bool),bool),member(X4053),hAPP(X4053,X4053,hAPP(X4053,fun(X4053,X4053),X4055,esk32_4(X4053,X4054,X4055,X4056)),esk33_4(X4053,X4054,X4055,X4056))),hAPP(fun(X4053,bool),fun(X4053,bool),hAPP(X4053,fun(fun(X4053,bool),fun(X4053,bool)),insert(X4053),esk32_4(X4053,X4054,X4055,X4056)),hAPP(fun(X4053,bool),fun(X4053,bool),hAPP(X4053,fun(fun(X4053,bool),fun(X4053,bool)),insert(X4053),esk33_4(X4053,X4054,X4055,X4056)),bot_bot(fun(X4053,bool))))))
| hBOOL(hAPP(fun(X4053,bool),bool,hAPP(X4053,fun(fun(X4053,bool),bool),member(X4053),hAPP(fun(X4053,bool),X4053,X4056,X4054)),X4054)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_213_folding__one_Oclosed])])]) ).
fof(i_0_1222,plain,
! [X5617,X5618,X5619] :
( ( ti(X5617,X5618) = zero_zero(X5617)
| ~ hBOOL(hAPP(X5617,bool,hAPP(X5617,fun(X5617,bool),ord_less_eq(X5617),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),plus_plus(X5617),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),times_times(X5617),X5618),X5618)),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),times_times(X5617),X5619),X5619))),zero_zero(X5617)))
| ~ linord581940658strict(X5617) )
& ( ti(X5617,X5619) = zero_zero(X5617)
| ~ hBOOL(hAPP(X5617,bool,hAPP(X5617,fun(X5617,bool),ord_less_eq(X5617),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),plus_plus(X5617),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),times_times(X5617),X5618),X5618)),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),times_times(X5617),X5619),X5619))),zero_zero(X5617)))
| ~ linord581940658strict(X5617) )
& ( ti(X5617,X5618) != zero_zero(X5617)
| ti(X5617,X5619) != zero_zero(X5617)
| hBOOL(hAPP(X5617,bool,hAPP(X5617,fun(X5617,bool),ord_less_eq(X5617),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),plus_plus(X5617),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),times_times(X5617),X5618),X5618)),hAPP(X5617,X5617,hAPP(X5617,fun(X5617,X5617),times_times(X5617),X5619),X5619))),zero_zero(X5617)))
| ~ linord581940658strict(X5617) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_719_sum__squares__le__zero__iff])])])]) ).
fof(i_0_1223,plain,
! [X3] :
( linordered_ring(X3)
=> ! [X21,X22] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X21),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X22),X22))),zero_zero(X3))) ),
inference(fof_simplification,[status(thm)],[fact_721_not__sum__squares__lt__zero]) ).
fof(i_0_1224,plain,
! [X4269,X4270,X4271,X4272,X4273] :
( ~ hBOOL(hAPP(fun(fun(X4269,bool),X4269),bool,hAPP(fun(X4269,fun(X4269,X4269)),fun(fun(fun(X4269,bool),X4269),bool),finite2073411215e_idem(X4269),X4272),X4273))
| hAPP(X4269,X4269,X4271,hAPP(X4269,X4269,hAPP(X4269,fun(X4269,X4269),X4272,esk39_5(X4269,X4270,X4271,X4272,X4273)),esk40_5(X4269,X4270,X4271,X4272,X4273))) != hAPP(X4269,X4269,hAPP(X4269,fun(X4269,X4269),X4272,hAPP(X4269,X4269,X4271,esk39_5(X4269,X4270,X4271,X4272,X4273))),hAPP(X4269,X4269,X4271,esk40_5(X4269,X4270,X4271,X4272,X4273)))
| ~ hBOOL(hAPP(fun(X4269,bool),bool,finite_finite(X4269),X4270))
| ti(fun(X4269,bool),X4270) = bot_bot(fun(X4269,bool))
| hAPP(X4269,X4269,X4271,hAPP(fun(X4269,bool),X4269,X4273,X4270)) = hAPP(fun(X4269,bool),X4269,X4273,hAPP(fun(X4269,bool),fun(X4269,bool),hAPP(fun(X4269,X4269),fun(fun(X4269,bool),fun(X4269,bool)),image(X4269,X4269),X4271),X4270)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_278_folding__one__idem_Ohom__commute])])]) ).
fof(i_0_1225,plain,
! [X1,X8,X14,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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(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(fun(X1,bool)),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(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(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_424_psubset__insert__iff]) ).
fof(i_0_1226,plain,
! [X1,X8,X14,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),X14),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_144_subset__insert__iff]) ).
fof(i_0_1227,plain,
! [X4824,X4825,X4826,X4827,X4828,X4829] :
( ( hBOOL(hAPP(fun(X4825,bool),bool,hAPP(X4825,fun(fun(X4825,bool),bool),member(X4825),esk80_6(X4824,X4825,X4826,X4827,X4828,X4829)),X4829))
| hAPP(fun(X4825,bool),fun(X4824,bool),hAPP(fun(X4825,X4824),fun(fun(X4825,bool),fun(X4824,bool)),image(X4825,X4824),X4826),X4828) = hAPP(fun(X4825,bool),fun(X4824,bool),hAPP(fun(X4825,X4824),fun(fun(X4825,bool),fun(X4824,bool)),image(X4825,X4824),X4827),X4829)
| ti(fun(X4825,bool),X4828) != ti(fun(X4825,bool),X4829) )
& ( hAPP(X4825,X4824,X4826,esk80_6(X4824,X4825,X4826,X4827,X4828,X4829)) != hAPP(X4825,X4824,X4827,esk80_6(X4824,X4825,X4826,X4827,X4828,X4829))
| hAPP(fun(X4825,bool),fun(X4824,bool),hAPP(fun(X4825,X4824),fun(fun(X4825,bool),fun(X4824,bool)),image(X4825,X4824),X4826),X4828) = hAPP(fun(X4825,bool),fun(X4824,bool),hAPP(fun(X4825,X4824),fun(fun(X4825,bool),fun(X4824,bool)),image(X4825,X4824),X4827),X4829)
| ti(fun(X4825,bool),X4828) != ti(fun(X4825,bool),X4829) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_445_image__cong])])])]) ).
fof(i_0_1228,plain,
! [X2,X1,X14,X8,X12,X46,X44,X10] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite1357897459simple(X1,X2),X12),X46),X44),X10))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X8))
=> ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X14),X8))
=> hAPP(fun(X2,bool),X1,X10,hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X14),X8)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X2,X1,X44,X14)),hAPP(fun(X2,bool),X1,X10,X8)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_210_folding__image__simple_Oinsert]) ).
fof(i_0_1229,plain,
! [X3773,X3774,X3775,X3776,X3777,X3778,X3779] :
( ~ hBOOL(hAPP(fun(fun(X3773,bool),X3774),bool,hAPP(fun(X3773,X3774),fun(fun(fun(X3773,bool),X3774),bool),hAPP(X3774,fun(fun(X3773,X3774),fun(fun(fun(X3773,bool),X3774),bool)),hAPP(fun(X3774,fun(X3774,X3774)),fun(X3774,fun(fun(X3773,X3774),fun(fun(fun(X3773,bool),X3774),bool))),finite908156982e_idem(X3774,X3773),X3776),X3777),X3778),X3779))
| hAPP(X3774,X3774,hAPP(X3774,fun(X3774,X3774),X3776,X3775),X3775) = ti(X3774,X3775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_142_folding__image__simple__idem_Oidem])]) ).
fof(i_0_1230,plain,
! [X4023,X4024,X4025,X4026,X4027,X4028] :
( ~ hBOOL(hAPP(fun(fun(X4023,bool),X4024),bool,hAPP(fun(X4023,X4024),fun(fun(fun(X4023,bool),X4024),bool),hAPP(X4024,fun(fun(X4023,X4024),fun(fun(fun(X4023,bool),X4024),bool)),hAPP(fun(X4024,fun(X4024,X4024)),fun(X4024,fun(fun(X4023,X4024),fun(fun(fun(X4023,bool),X4024),bool))),finite1357897459simple(X4024,X4023),X4025),X4026),X4027),X4028))
| hAPP(fun(X4023,bool),X4024,X4028,bot_bot(fun(X4023,bool))) = ti(X4024,X4026) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_206_folding__image__simple_Oempty])]) ).
fof(i_0_1231,plain,
! [X5626,X5627,X5628] :
( ( ~ hBOOL(hAPP(X5626,bool,hAPP(X5626,fun(X5626,bool),ord_less(X5626),zero_zero(X5626)),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),plus_plus(X5626),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),times_times(X5626),X5627),X5627)),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),times_times(X5626),X5628),X5628))))
| ti(X5626,X5627) != zero_zero(X5626)
| ti(X5626,X5628) != zero_zero(X5626)
| ~ linord581940658strict(X5626) )
& ( ti(X5626,X5627) = zero_zero(X5626)
| hBOOL(hAPP(X5626,bool,hAPP(X5626,fun(X5626,bool),ord_less(X5626),zero_zero(X5626)),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),plus_plus(X5626),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),times_times(X5626),X5627),X5627)),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),times_times(X5626),X5628),X5628))))
| ~ linord581940658strict(X5626) )
& ( ti(X5626,X5628) = zero_zero(X5626)
| hBOOL(hAPP(X5626,bool,hAPP(X5626,fun(X5626,bool),ord_less(X5626),zero_zero(X5626)),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),plus_plus(X5626),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),times_times(X5626),X5627),X5627)),hAPP(X5626,X5626,hAPP(X5626,fun(X5626,X5626),times_times(X5626),X5628),X5628))))
| ~ linord581940658strict(X5626) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_722_sum__squares__gt__zero__iff])])])]) ).
fof(i_0_1232,plain,
! [X1,X16,X11] :
( ( hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11))),X16)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))) )
& ( ~ hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11))),X16)) = bot_bot(fun(X1,bool)) ) ),
inference(fof_simplification,[status(thm)],[fact_164_Collect__conv__if]) ).
fof(i_0_1233,plain,
! [X5521,X5522,X5523,X5524,X5525,X5526] :
( ( hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),plus_plus(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),times_times(X5521),X5522),X5523)),X5524) != hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),plus_plus(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),times_times(X5521),X5525),X5523)),X5526)
| hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),plus_plus(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),times_times(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),minus_minus(X5521),X5522),X5525)),X5523)),X5524) = ti(X5521,X5526)
| ~ ring(X5521) )
& ( hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),plus_plus(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),times_times(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),minus_minus(X5521),X5522),X5525)),X5523)),X5524) != ti(X5521,X5526)
| hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),plus_plus(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),times_times(X5521),X5522),X5523)),X5524) = hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),plus_plus(X5521),hAPP(X5521,X5521,hAPP(X5521,fun(X5521,X5521),times_times(X5521),X5525),X5523)),X5526)
| ~ ring(X5521) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_691_eq__add__iff1])])])]) ).
fof(i_0_1234,plain,
! [X5515,X5516,X5517,X5518,X5519,X5520] :
( ( hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),plus_plus(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),times_times(X5515),X5516),X5517)),X5518) != hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),plus_plus(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),times_times(X5515),X5519),X5517)),X5520)
| ti(X5515,X5518) = hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),plus_plus(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),times_times(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),minus_minus(X5515),X5519),X5516)),X5517)),X5520)
| ~ ring(X5515) )
& ( ti(X5515,X5518) != hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),plus_plus(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),times_times(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),minus_minus(X5515),X5519),X5516)),X5517)),X5520)
| hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),plus_plus(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),times_times(X5515),X5516),X5517)),X5518) = hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),plus_plus(X5515),hAPP(X5515,X5515,hAPP(X5515,fun(X5515,X5515),times_times(X5515),X5519),X5517)),X5520)
| ~ ring(X5515) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_690_eq__add__iff2])])])]) ).
fof(i_0_1235,plain,
! [X1,X2] :
( ab_semigroup_mult(X2)
=> ! [X44,X46,X11,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),X11),X8))
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X44),X46),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(X1,X2,X44,X11)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X44),X46),X8)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_735_fold__image__insert]) ).
fof(i_0_1236,plain,
! [X1,X13,X11,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),X11),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13))),one_one(nat)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_211_card__Diff__insert]) ).
fof(i_0_1237,plain,
! [X1,X16,X11] :
( ( hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),fequal(X1),X11))),X16)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),bot_bot(fun(X1,bool))) )
& ( ~ hBOOL(hAPP(X1,bool,X16,X11))
=> 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(X1,fun(X1,bool),fequal(X1),X11))),X16)) = bot_bot(fun(X1,bool)) ) ),
inference(fof_simplification,[status(thm)],[fact_165_Collect__conv__if2]) ).
fof(i_0_1238,plain,
! [X1,X16,X8,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X10),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,bot_bot(fun(X1,bool))))
=> ( ! [X56,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X56),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X56),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X57))
=> hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X56),X57))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_181_finite__subset__induct]) ).
fof(i_0_1239,plain,
! [X4083,X4084,X4085] :
( ( hBOOL(hAPP(fun(X4083,bool),bool,finite_finite(X4083),esk37_3(X4083,X4084,X4085)))
| hBOOL(hAPP(fun(X4083,bool),bool,X4084,X4085))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,X4084,hAPP(fun(X4083,bool),fun(X4083,bool),hAPP(X4083,fun(fun(X4083,bool),fun(X4083,bool)),insert(X4083),esk35_3(X4083,X4084,X4085)),bot_bot(fun(X4083,bool)))))
| ti(fun(X4083,bool),X4085) = bot_bot(fun(X4083,bool))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,finite_finite(X4083),X4085)) )
& ( ti(fun(X4083,bool),esk37_3(X4083,X4084,X4085)) != bot_bot(fun(X4083,bool))
| hBOOL(hAPP(fun(X4083,bool),bool,X4084,X4085))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,X4084,hAPP(fun(X4083,bool),fun(X4083,bool),hAPP(X4083,fun(fun(X4083,bool),fun(X4083,bool)),insert(X4083),esk35_3(X4083,X4084,X4085)),bot_bot(fun(X4083,bool)))))
| ti(fun(X4083,bool),X4085) = bot_bot(fun(X4083,bool))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,finite_finite(X4083),X4085)) )
& ( ~ hBOOL(hAPP(fun(X4083,bool),bool,hAPP(X4083,fun(fun(X4083,bool),bool),member(X4083),esk36_3(X4083,X4084,X4085)),esk37_3(X4083,X4084,X4085)))
| hBOOL(hAPP(fun(X4083,bool),bool,X4084,X4085))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,X4084,hAPP(fun(X4083,bool),fun(X4083,bool),hAPP(X4083,fun(fun(X4083,bool),fun(X4083,bool)),insert(X4083),esk35_3(X4083,X4084,X4085)),bot_bot(fun(X4083,bool)))))
| ti(fun(X4083,bool),X4085) = bot_bot(fun(X4083,bool))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,finite_finite(X4083),X4085)) )
& ( hBOOL(hAPP(fun(X4083,bool),bool,X4084,esk37_3(X4083,X4084,X4085)))
| hBOOL(hAPP(fun(X4083,bool),bool,X4084,X4085))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,X4084,hAPP(fun(X4083,bool),fun(X4083,bool),hAPP(X4083,fun(fun(X4083,bool),fun(X4083,bool)),insert(X4083),esk35_3(X4083,X4084,X4085)),bot_bot(fun(X4083,bool)))))
| ti(fun(X4083,bool),X4085) = bot_bot(fun(X4083,bool))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,finite_finite(X4083),X4085)) )
& ( ~ hBOOL(hAPP(fun(X4083,bool),bool,X4084,hAPP(fun(X4083,bool),fun(X4083,bool),hAPP(X4083,fun(fun(X4083,bool),fun(X4083,bool)),insert(X4083),esk36_3(X4083,X4084,X4085)),esk37_3(X4083,X4084,X4085))))
| hBOOL(hAPP(fun(X4083,bool),bool,X4084,X4085))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,X4084,hAPP(fun(X4083,bool),fun(X4083,bool),hAPP(X4083,fun(fun(X4083,bool),fun(X4083,bool)),insert(X4083),esk35_3(X4083,X4084,X4085)),bot_bot(fun(X4083,bool)))))
| ti(fun(X4083,bool),X4085) = bot_bot(fun(X4083,bool))
| ~ hBOOL(hAPP(fun(X4083,bool),bool,finite_finite(X4083),X4085)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1193])])])]) ).
fof(i_0_1240,plain,
! [X5369,X5370,X5371,X5372,X5373] :
( ( hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),plus_plus(X5369),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5370),X5371)),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5372),X5373)) != hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),plus_plus(X5369),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5370),X5373)),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5372),X5371))
| ti(X5369,X5370) = ti(X5369,X5372)
| ti(X5369,X5371) = ti(X5369,X5373)
| ~ semiri456707255roduct(X5369) )
& ( ti(X5369,X5370) != ti(X5369,X5372)
| hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),plus_plus(X5369),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5370),X5371)),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5372),X5373)) = hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),plus_plus(X5369),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5370),X5373)),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5372),X5371))
| ~ semiri456707255roduct(X5369) )
& ( ti(X5369,X5371) != ti(X5369,X5373)
| hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),plus_plus(X5369),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5370),X5371)),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5372),X5373)) = hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),plus_plus(X5369),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5370),X5373)),hAPP(X5369,X5369,hAPP(X5369,fun(X5369,X5369),times_times(X5369),X5372),X5371))
| ~ semiri456707255roduct(X5369) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_648_crossproduct__eq])])])]) ).
fof(i_0_1241,plain,
! [X5356,X5357,X5358,X5359,X5360] :
( ( ti(X5356,X5359) = ti(X5356,X5360)
| ti(X5356,X5357) = ti(X5356,X5358)
| hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),plus_plus(X5356),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5359),X5357)),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5360),X5358)) != hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),plus_plus(X5356),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5359),X5358)),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5360),X5357))
| ~ semiri456707255roduct(X5356) )
& ( ti(X5356,X5359) != ti(X5356,X5360)
| hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),plus_plus(X5356),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5359),X5357)),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5360),X5358)) = hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),plus_plus(X5356),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5359),X5358)),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5360),X5357))
| ~ semiri456707255roduct(X5356) )
& ( ti(X5356,X5357) != ti(X5356,X5358)
| hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),plus_plus(X5356),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5359),X5357)),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5360),X5358)) = hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),plus_plus(X5356),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5359),X5358)),hAPP(X5356,X5356,hAPP(X5356,fun(X5356,X5356),times_times(X5356),X5360),X5357))
| ~ semiri456707255roduct(X5356) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_645_crossproduct__noteq])])])]) ).
fof(i_0_1242,plain,
! [X115,X25,X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X115)))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),X25) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X115)))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X115)),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X82),X115))),X25) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_937_nat__number__of__add__left]) ).
fof(i_0_1243,plain,
! [X3389,X3390,X3391,X3392,X3393] :
( ( hBOOL(hAPP(fun(X3389,bool),bool,hAPP(fun(X3389,bool),fun(fun(X3389,bool),bool),ord_less_eq(fun(X3389,bool)),esk1_5(X3389,X3390,X3391,X3392,X3393)),X3392))
| ~ hBOOL(hAPP(fun(X3390,bool),bool,hAPP(fun(X3390,bool),fun(fun(X3390,bool),bool),ord_less_eq(fun(X3390,bool)),X3393),hAPP(fun(X3389,bool),fun(X3390,bool),hAPP(fun(X3389,X3390),fun(fun(X3389,bool),fun(X3390,bool)),image(X3389,X3390),X3391),X3392)))
| ~ hBOOL(hAPP(fun(X3390,bool),bool,finite_finite(X3390),X3393)) )
& ( hBOOL(hAPP(fun(X3389,bool),bool,finite_finite(X3389),esk1_5(X3389,X3390,X3391,X3392,X3393)))
| ~ hBOOL(hAPP(fun(X3390,bool),bool,hAPP(fun(X3390,bool),fun(fun(X3390,bool),bool),ord_less_eq(fun(X3390,bool)),X3393),hAPP(fun(X3389,bool),fun(X3390,bool),hAPP(fun(X3389,X3390),fun(fun(X3389,bool),fun(X3390,bool)),image(X3389,X3390),X3391),X3392)))
| ~ hBOOL(hAPP(fun(X3390,bool),bool,finite_finite(X3390),X3393)) )
& ( ti(fun(X3390,bool),X3393) = hAPP(fun(X3389,bool),fun(X3390,bool),hAPP(fun(X3389,X3390),fun(fun(X3389,bool),fun(X3390,bool)),image(X3389,X3390),X3391),esk1_5(X3389,X3390,X3391,X3392,X3393))
| ~ hBOOL(hAPP(fun(X3390,bool),bool,hAPP(fun(X3390,bool),fun(fun(X3390,bool),bool),ord_less_eq(fun(X3390,bool)),X3393),hAPP(fun(X3389,bool),fun(X3390,bool),hAPP(fun(X3389,X3390),fun(fun(X3389,bool),fun(X3390,bool)),image(X3389,X3390),X3391),X3392)))
| ~ hBOOL(hAPP(fun(X3390,bool),bool,finite_finite(X3390),X3393)) ) ),
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_1244,plain,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X91,X85] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(int,X1,number_number_of(X1),X91)),hAPP(int,X1,number_number_of(X1),X85)))
<=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(int,X1,number_number_of(X1),X85)),hAPP(int,X1,number_number_of(X1),X91))) ) ),
inference(fof_simplification,[status(thm)],[fact_651_le__number__of__eq__not__less]) ).
fof(i_0_1245,plain,
! [X3636,X3637,X3638,X3639,X3640,X3642,X3643,X3644,X3645,X3646,X3647] :
( ( hBOOL(hAPP(fun(X3637,bool),bool,hAPP(fun(X3637,bool),fun(fun(X3637,bool),bool),ord_less_eq(fun(X3637,bool)),esk9_5(X3636,X3637,X3638,X3639,X3640)),X3640))
| ~ hBOOL(hAPP(fun(X3636,bool),bool,hAPP(fun(X3636,bool),fun(fun(X3636,bool),bool),ord_less_eq(fun(X3636,bool)),X3638),hAPP(fun(X3637,bool),fun(X3636,bool),hAPP(fun(X3637,X3636),fun(fun(X3637,bool),fun(X3636,bool)),image(X3637,X3636),X3639),X3640))) )
& ( ti(fun(X3636,bool),X3638) = hAPP(fun(X3637,bool),fun(X3636,bool),hAPP(fun(X3637,X3636),fun(fun(X3637,bool),fun(X3636,bool)),image(X3637,X3636),X3639),esk9_5(X3636,X3637,X3638,X3639,X3640))
| ~ hBOOL(hAPP(fun(X3636,bool),bool,hAPP(fun(X3636,bool),fun(fun(X3636,bool),bool),ord_less_eq(fun(X3636,bool)),X3638),hAPP(fun(X3637,bool),fun(X3636,bool),hAPP(fun(X3637,X3636),fun(fun(X3637,bool),fun(X3636,bool)),image(X3637,X3636),X3639),X3640))) )
& ( ~ hBOOL(hAPP(fun(X3643,bool),bool,hAPP(fun(X3643,bool),fun(fun(X3643,bool),bool),ord_less_eq(fun(X3643,bool)),X3647),X3646))
| ti(fun(X3642,bool),X3644) != hAPP(fun(X3643,bool),fun(X3642,bool),hAPP(fun(X3643,X3642),fun(fun(X3643,bool),fun(X3642,bool)),image(X3643,X3642),X3645),X3647)
| hBOOL(hAPP(fun(X3642,bool),bool,hAPP(fun(X3642,bool),fun(fun(X3642,bool),bool),ord_less_eq(fun(X3642,bool)),X3644),hAPP(fun(X3643,bool),fun(X3642,bool),hAPP(fun(X3643,X3642),fun(fun(X3643,bool),fun(X3642,bool)),image(X3643,X3642),X3645),X3646))) ) ),
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_109_subset__image__iff])])])])])]) ).
fof(i_0_1246,plain,
! [X18,X25,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X25)),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),X25),X17)) ) ),
inference(fof_simplification,[status(thm)],[fact_255_add__leE]) ).
fof(i_0_1247,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_104_subset__insert]) ).
fof(i_0_1248,plain,
! [X3984,X3985,X3986,X3987,X3988] :
( ( hAPP(fun(X3984,bool),fun(X3984,bool),hAPP(fun(X3984,bool),fun(fun(X3984,bool),fun(X3984,bool)),minus_minus(fun(X3984,bool)),X3986),hAPP(fun(X3984,bool),fun(X3984,bool),hAPP(X3984,fun(fun(X3984,bool),fun(X3984,bool)),insert(X3984),X3985),bot_bot(fun(X3984,bool)))) != bot_bot(fun(X3984,bool))
| hAPP(fun(X3984,bool),X3984,X3988,X3986) = ti(X3984,X3985)
| ~ hBOOL(hAPP(fun(X3984,bool),bool,hAPP(X3984,fun(fun(X3984,bool),bool),member(X3984),X3985),X3986))
| ~ hBOOL(hAPP(fun(X3984,bool),bool,finite_finite(X3984),X3986))
| ~ hBOOL(hAPP(fun(fun(X3984,bool),X3984),bool,hAPP(fun(X3984,fun(X3984,X3984)),fun(fun(fun(X3984,bool),X3984),bool),finite_folding_one(X3984),X3987),X3988)) )
& ( hAPP(fun(X3984,bool),fun(X3984,bool),hAPP(fun(X3984,bool),fun(fun(X3984,bool),fun(X3984,bool)),minus_minus(fun(X3984,bool)),X3986),hAPP(fun(X3984,bool),fun(X3984,bool),hAPP(X3984,fun(fun(X3984,bool),fun(X3984,bool)),insert(X3984),X3985),bot_bot(fun(X3984,bool)))) = bot_bot(fun(X3984,bool))
| hAPP(fun(X3984,bool),X3984,X3988,X3986) = hAPP(X3984,X3984,hAPP(X3984,fun(X3984,X3984),X3987,X3985),hAPP(fun(X3984,bool),X3984,X3988,hAPP(fun(X3984,bool),fun(X3984,bool),hAPP(fun(X3984,bool),fun(fun(X3984,bool),fun(X3984,bool)),minus_minus(fun(X3984,bool)),X3986),hAPP(fun(X3984,bool),fun(X3984,bool),hAPP(X3984,fun(fun(X3984,bool),fun(X3984,bool)),insert(X3984),X3985),bot_bot(fun(X3984,bool))))))
| ~ hBOOL(hAPP(fun(X3984,bool),bool,hAPP(X3984,fun(fun(X3984,bool),bool),member(X3984),X3985),X3986))
| ~ hBOOL(hAPP(fun(X3984,bool),bool,finite_finite(X3984),X3986))
| ~ hBOOL(hAPP(fun(fun(X3984,bool),X3984),bool,hAPP(fun(X3984,fun(X3984,X3984)),fun(fun(fun(X3984,bool),X3984),bool),finite_folding_one(X3984),X3987),X3988)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_198_folding__one_Oremove])])]) ).
fof(i_0_1249,plain,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(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)) ) ),
inference(fof_simplification,[status(thm)],[fact_195_Diff__iff]) ).
fof(i_0_1250,plain,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X13)) ),
inference(fof_simplification,[status(thm)],[fact_192_DiffD2]) ).
fof(i_0_1251,plain,
! [X3979,X3980,X3981,X3982,X3983] :
( ( hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(fun(X3979,bool),fun(fun(X3979,bool),fun(X3979,bool)),minus_minus(fun(X3979,bool)),X3981),hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(X3979,fun(fun(X3979,bool),fun(X3979,bool)),insert(X3979),X3980),bot_bot(fun(X3979,bool)))) != bot_bot(fun(X3979,bool))
| hAPP(fun(X3979,bool),X3979,X3983,hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(X3979,fun(fun(X3979,bool),fun(X3979,bool)),insert(X3979),X3980),X3981)) = ti(X3979,X3980)
| ~ hBOOL(hAPP(fun(X3979,bool),bool,finite_finite(X3979),X3981))
| ~ hBOOL(hAPP(fun(fun(X3979,bool),X3979),bool,hAPP(fun(X3979,fun(X3979,X3979)),fun(fun(fun(X3979,bool),X3979),bool),finite_folding_one(X3979),X3982),X3983)) )
& ( hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(fun(X3979,bool),fun(fun(X3979,bool),fun(X3979,bool)),minus_minus(fun(X3979,bool)),X3981),hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(X3979,fun(fun(X3979,bool),fun(X3979,bool)),insert(X3979),X3980),bot_bot(fun(X3979,bool)))) = bot_bot(fun(X3979,bool))
| hAPP(fun(X3979,bool),X3979,X3983,hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(X3979,fun(fun(X3979,bool),fun(X3979,bool)),insert(X3979),X3980),X3981)) = hAPP(X3979,X3979,hAPP(X3979,fun(X3979,X3979),X3982,X3980),hAPP(fun(X3979,bool),X3979,X3983,hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(fun(X3979,bool),fun(fun(X3979,bool),fun(X3979,bool)),minus_minus(fun(X3979,bool)),X3981),hAPP(fun(X3979,bool),fun(X3979,bool),hAPP(X3979,fun(fun(X3979,bool),fun(X3979,bool)),insert(X3979),X3980),bot_bot(fun(X3979,bool))))))
| ~ hBOOL(hAPP(fun(X3979,bool),bool,finite_finite(X3979),X3981))
| ~ hBOOL(hAPP(fun(fun(X3979,bool),X3979),bool,hAPP(fun(X3979,fun(X3979,X3979)),fun(fun(fun(X3979,bool),X3979),bool),finite_folding_one(X3979),X3982),X3983)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_197_folding__one_Oinsert__remove])])]) ).
fof(i_0_1252,plain,
! [X3653,X3654,X3655,X3656,X3657] :
( ( ti(X3653,X3655) = hAPP(X3654,X3653,X3656,esk10_5(X3653,X3654,X3655,X3656,X3657))
| ~ hBOOL(hAPP(fun(X3653,bool),bool,hAPP(X3653,fun(fun(X3653,bool),bool),member(X3653),X3655),hAPP(fun(X3654,bool),fun(X3653,bool),hAPP(fun(X3654,X3653),fun(fun(X3654,bool),fun(X3653,bool)),image(X3654,X3653),X3656),X3657))) )
& ( hBOOL(hAPP(fun(X3654,bool),bool,hAPP(X3654,fun(fun(X3654,bool),bool),member(X3654),esk10_5(X3653,X3654,X3655,X3656,X3657)),X3657))
| ~ hBOOL(hAPP(fun(X3653,bool),bool,hAPP(X3653,fun(fun(X3653,bool),bool),member(X3653),X3655),hAPP(fun(X3654,bool),fun(X3653,bool),hAPP(fun(X3654,X3653),fun(fun(X3654,bool),fun(X3653,bool)),image(X3654,X3653),X3656),X3657))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1194])])])]) ).
fof(i_0_1253,plain,
! [X3555,X3556,X3557,X3558,X3559,X3561,X3562,X3563,X3564,X3565,X3566] :
( ( hBOOL(hAPP(fun(X3556,bool),bool,hAPP(X3556,fun(fun(X3556,bool),bool),member(X3556),esk7_5(X3555,X3556,X3557,X3558,X3559)),X3559))
| ~ hBOOL(hAPP(fun(X3555,bool),bool,hAPP(X3555,fun(fun(X3555,bool),bool),member(X3555),X3557),hAPP(fun(X3556,bool),fun(X3555,bool),hAPP(fun(X3556,X3555),fun(fun(X3556,bool),fun(X3555,bool)),image(X3556,X3555),X3558),X3559))) )
& ( ti(X3555,X3557) = hAPP(X3556,X3555,X3558,esk7_5(X3555,X3556,X3557,X3558,X3559))
| ~ hBOOL(hAPP(fun(X3555,bool),bool,hAPP(X3555,fun(fun(X3555,bool),bool),member(X3555),X3557),hAPP(fun(X3556,bool),fun(X3555,bool),hAPP(fun(X3556,X3555),fun(fun(X3556,bool),fun(X3555,bool)),image(X3556,X3555),X3558),X3559))) )
& ( ~ hBOOL(hAPP(fun(X3562,bool),bool,hAPP(X3562,fun(fun(X3562,bool),bool),member(X3562),X3566),X3565))
| ti(X3561,X3563) != hAPP(X3562,X3561,X3564,X3566)
| hBOOL(hAPP(fun(X3561,bool),bool,hAPP(X3561,fun(fun(X3561,bool),bool),member(X3561),X3563),hAPP(fun(X3562,bool),fun(X3561,bool),hAPP(fun(X3562,X3561),fun(fun(X3562,bool),fun(X3561,bool)),image(X3562,X3561),X3564),X3565))) ) ),
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_93_image__iff])])])])])]) ).
fof(i_0_1254,plain,
! [X3] :
( linordered_ring(X3)
=> ! [X41] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),times_times(X3),X41),X41)),zero_zero(X3))) ),
inference(fof_simplification,[status(thm)],[fact_670_not__square__less__zero]) ).
fof(i_0_1255,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),one_one(nat)) )
& ( ~ 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),bot_bot(fun(X1,bool))))) = hAPP(fun(X1,bool),nat,finite_card(X1),X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_203_card__Diff__singleton__if]) ).
fof(i_0_1256,plain,
! [X3293,X3294,X3295] :
( ~ hBOOL(hAPP(fun(X3293,bool),bool,finite_finite(X3293),X3295))
| ~ hBOOL(hAPP(fun(X3293,bool),bool,hAPP(fun(X3293,bool),fun(fun(X3293,bool),bool),ord_less_eq(fun(X3293,bool)),X3294),X3295))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3293,bool),nat,finite_card(X3293),X3295)),hAPP(fun(X3293,bool),nat,finite_card(X3293),X3294)))
| ti(fun(X3293,bool),X3294) = ti(fun(X3293,bool),X3295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_card__seteq])]) ).
fof(i_0_1257,plain,
! [X26,X27] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X27)),X26)),
inference(fof_simplification,[status(thm)],[fact_368_not__add__less1]) ).
fof(i_0_1258,plain,
! [X27,X26] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X26)),X26)),
inference(fof_simplification,[status(thm)],[fact_369_not__add__less2]) ).
fof(i_0_1259,plain,
! [X1,X8] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X8) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = zero_zero(nat) ) ),
inference(fof_simplification,[status(thm)],[fact_572_card__def]) ).
fof(i_0_1260,plain,
! [X3878,X3879,X3880] :
( ~ hBOOL(hAPP(fun(X3878,bool),bool,hAPP(fun(X3878,bool),fun(fun(X3878,bool),bool),ord_less_eq(fun(X3878,bool)),X3879),hAPP(fun(X3878,bool),fun(X3878,bool),hAPP(X3878,fun(fun(X3878,bool),fun(X3878,bool)),insert(X3878),X3880),bot_bot(fun(X3878,bool)))))
| ti(fun(X3878,bool),X3879) = bot_bot(fun(X3878,bool))
| ti(fun(X3878,bool),X3879) = hAPP(fun(X3878,bool),fun(X3878,bool),hAPP(X3878,fun(fun(X3878,bool),fun(X3878,bool)),insert(X3878),X3880),bot_bot(fun(X3878,bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_173_subset__singletonD])]) ).
fof(i_0_1261,plain,
! [X1,X16,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,bot_bot(fun(X1,bool))))
=> ( ! [X33,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X57))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X57))
=> hBOOL(hAPP(fun(X1,bool),bool,X16,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X57))) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_184_finite__induct]) ).
fof(i_0_1262,plain,
! [X3506,X3507,X3508,X3509] :
( ( ~ hBOOL(hAPP(fun(X3506,bool),bool,hAPP(X3506,fun(fun(X3506,bool),bool),member(X3506),X3507),hAPP(fun(X3506,bool),fun(X3506,bool),hAPP(X3506,fun(fun(X3506,bool),fun(X3506,bool)),insert(X3506),X3508),X3509)))
| ti(X3506,X3507) = ti(X3506,X3508)
| hBOOL(hAPP(fun(X3506,bool),bool,hAPP(X3506,fun(fun(X3506,bool),bool),member(X3506),X3507),X3509)) )
& ( ti(X3506,X3507) != ti(X3506,X3508)
| hBOOL(hAPP(fun(X3506,bool),bool,hAPP(X3506,fun(fun(X3506,bool),bool),member(X3506),X3507),hAPP(fun(X3506,bool),fun(X3506,bool),hAPP(X3506,fun(fun(X3506,bool),fun(X3506,bool)),insert(X3506),X3508),X3509))) )
& ( ~ hBOOL(hAPP(fun(X3506,bool),bool,hAPP(X3506,fun(fun(X3506,bool),bool),member(X3506),X3507),X3509))
| hBOOL(hAPP(fun(X3506,bool),bool,hAPP(X3506,fun(fun(X3506,bool),bool),member(X3506),X3507),hAPP(fun(X3506,bool),fun(X3506,bool),hAPP(X3506,fun(fun(X3506,bool),fun(X3506,bool)),insert(X3506),X3508),X3509))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_79_insert__iff])])]) ).
fof(i_0_1263,plain,
! [X3422,X3423,X3424,X3425] :
( ~ hBOOL(hAPP(fun(X3422,bool),bool,hAPP(X3422,fun(fun(X3422,bool),bool),member(X3422),X3423),hAPP(fun(X3422,bool),fun(X3422,bool),hAPP(X3422,fun(fun(X3422,bool),fun(X3422,bool)),insert(X3422),X3424),X3425)))
| ti(X3422,X3423) = ti(X3422,X3424)
| hBOOL(hAPP(fun(X3422,bool),bool,hAPP(X3422,fun(fun(X3422,bool),bool),member(X3422),X3423),X3425)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_insertE])]) ).
fof(i_0_1264,plain,
! [X4073,X4074,X4075,X4076,X4077] :
( ~ hBOOL(hAPP(fun(fun(X4073,bool),X4073),bool,hAPP(fun(X4073,fun(X4073,X4073)),fun(fun(fun(X4073,bool),X4073),bool),finite2073411215e_idem(X4073),X4076),X4077))
| ~ hBOOL(hAPP(fun(X4073,bool),bool,finite_finite(X4073),X4075))
| ti(fun(X4073,bool),X4074) = bot_bot(fun(X4073,bool))
| ~ hBOOL(hAPP(fun(X4073,bool),bool,hAPP(fun(X4073,bool),fun(fun(X4073,bool),bool),ord_less_eq(fun(X4073,bool)),X4074),X4075))
| hAPP(X4073,X4073,hAPP(X4073,fun(X4073,X4073),X4076,hAPP(fun(X4073,bool),X4073,X4077,X4074)),hAPP(fun(X4073,bool),X4073,X4077,X4075)) = hAPP(fun(X4073,bool),X4073,X4077,X4075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_217_folding__one__idem_Osubset__idem])]) ).
fof(i_0_1265,plain,
! [X4713,X4714,X4717,X4718,X4719,X4720] :
( ( ~ hBOOL(hAPP(fun(X4713,bool),bool,finite_finite(X4713),X4714))
| ti(fun(X4713,bool),X4714) = hAPP(fun(nat,bool),fun(X4713,bool),hAPP(fun(nat,X4713),fun(fun(nat,bool),fun(X4713,bool)),image(nat,X4713),esk55_2(X4713,X4714)),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(nat)),esk54_2(X4713,X4714)))) )
& ( ti(fun(X4717,bool),X4718) != hAPP(fun(nat,bool),fun(X4717,bool),hAPP(fun(nat,X4717),fun(fun(nat,bool),fun(X4717,bool)),image(nat,X4717),X4720),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(nat)),X4719)))
| hBOOL(hAPP(fun(X4717,bool),bool,finite_finite(X4717),X4718)) ) ),
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_426_finite__conv__nat__seg__image])])])])]) ).
fof(i_0_1266,plain,
! [X4598,X4599,X4600,X4601] :
( ti(fun(X4598,bool),X4599) != hAPP(fun(nat,bool),fun(X4598,bool),hAPP(fun(nat,X4598),fun(fun(nat,bool),fun(X4598,bool)),image(nat,X4598),X4600),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(nat)),X4601)))
| hBOOL(hAPP(fun(X4598,bool),bool,finite_finite(X4598),X4599)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_388_nat__seg__image__imp__finite])]) ).
fof(i_0_1267,plain,
! [X4282,X4283,X4284] :
( ( ~ hBOOL(hAPP(fun(X4282,bool),bool,hAPP(fun(X4282,bool),fun(fun(X4282,bool),bool),ord_less_eq(fun(X4282,bool)),X4283),hAPP(fun(X4282,bool),fun(X4282,bool),hAPP(X4282,fun(fun(X4282,bool),fun(X4282,bool)),insert(X4282),X4284),bot_bot(fun(X4282,bool)))))
| hAPP(fun(X4282,bool),X4282,hAPP(X4282,fun(fun(X4282,bool),X4282),partial_flat_lub(X4282),X4284),X4283) = ti(X4282,X4284) )
& ( hBOOL(hAPP(fun(X4282,bool),bool,hAPP(fun(X4282,bool),fun(fun(X4282,bool),bool),ord_less_eq(fun(X4282,bool)),X4283),hAPP(fun(X4282,bool),fun(X4282,bool),hAPP(X4282,fun(fun(X4282,bool),fun(X4282,bool)),insert(X4282),X4284),bot_bot(fun(X4282,bool)))))
| hAPP(fun(X4282,bool),X4282,hAPP(X4282,fun(fun(X4282,bool),X4282),partial_flat_lub(X4282),X4284),X4283) = hAPP(fun(X4282,bool),X4282,the(X4282),hAPP(fun(X4282,bool),fun(X4282,bool),hAPP(fun(X4282,fun(fun(X4282,bool),bool)),fun(fun(X4282,bool),fun(X4282,bool)),combc(X4282,fun(X4282,bool),bool),member(X4282)),hAPP(fun(X4282,bool),fun(X4282,bool),hAPP(fun(X4282,bool),fun(fun(X4282,bool),fun(X4282,bool)),minus_minus(fun(X4282,bool)),X4283),hAPP(fun(X4282,bool),fun(X4282,bool),hAPP(X4282,fun(fun(X4282,bool),fun(X4282,bool)),insert(X4282),X4284),bot_bot(fun(X4282,bool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1195])]) ).
fof(i_0_1268,plain,
! [X1,X13,X35,X8] :
( 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))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13))) ) ),
inference(fof_simplification,[status(thm)],[fact_191_DiffI]) ).
fof(i_0_1269,plain,
! [X3817,X3818,X3819,X3820,X3821] :
( ( ti(X3817,X3818) = ti(X3817,X3821)
| ti(X3817,X3818) = ti(X3817,X3820)
| hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3818),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3819),bot_bot(fun(X3817,bool)))) != hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3820),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3821),bot_bot(fun(X3817,bool)))) )
& ( ti(X3817,X3819) = ti(X3817,X3820)
| ti(X3817,X3818) = ti(X3817,X3820)
| hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3818),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3819),bot_bot(fun(X3817,bool)))) != hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3820),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3821),bot_bot(fun(X3817,bool)))) )
& ( ti(X3817,X3818) = ti(X3817,X3821)
| ti(X3817,X3819) = ti(X3817,X3821)
| hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3818),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3819),bot_bot(fun(X3817,bool)))) != hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3820),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3821),bot_bot(fun(X3817,bool)))) )
& ( ti(X3817,X3819) = ti(X3817,X3820)
| ti(X3817,X3819) = ti(X3817,X3821)
| hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3818),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3819),bot_bot(fun(X3817,bool)))) != hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3820),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3821),bot_bot(fun(X3817,bool)))) )
& ( ti(X3817,X3818) != ti(X3817,X3820)
| ti(X3817,X3819) != ti(X3817,X3821)
| hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3818),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3819),bot_bot(fun(X3817,bool)))) = hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3820),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3821),bot_bot(fun(X3817,bool)))) )
& ( ti(X3817,X3818) != ti(X3817,X3821)
| ti(X3817,X3819) != ti(X3817,X3820)
| hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3818),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3819),bot_bot(fun(X3817,bool)))) = hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3820),hAPP(fun(X3817,bool),fun(X3817,bool),hAPP(X3817,fun(fun(X3817,bool),fun(X3817,bool)),insert(X3817),X3821),bot_bot(fun(X3817,bool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_153_doubleton__eq__iff])])]) ).
fof(i_0_1270,plain,
! [X3756,X3757,X3758] :
( ~ hBOOL(hAPP(fun(X3756,bool),bool,hAPP(X3756,fun(fun(X3756,bool),bool),member(X3756),X3757),X3758))
| hAPP(fun(X3756,bool),fun(X3756,bool),hAPP(X3756,fun(fun(X3756,bool),fun(X3756,bool)),insert(X3756),X3757),hAPP(fun(X3756,bool),fun(X3756,bool),hAPP(fun(X3756,bool),fun(fun(X3756,bool),fun(X3756,bool)),minus_minus(fun(X3756,bool)),X3758),hAPP(fun(X3756,bool),fun(X3756,bool),hAPP(X3756,fun(fun(X3756,bool),fun(X3756,bool)),insert(X3756),X3757),bot_bot(fun(X3756,bool))))) = ti(fun(X3756,bool),X3758) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_insert__Diff])]) ).
fof(i_0_1271,plain,
! [X4048,X4049,X4050,X4051,X4052] :
( ~ hBOOL(hAPP(fun(fun(X4048,bool),X4048),bool,hAPP(fun(X4048,fun(X4048,X4048)),fun(fun(fun(X4048,bool),X4048),bool),finite_folding_one(X4048),X4051),X4052))
| ~ hBOOL(hAPP(fun(X4048,bool),bool,finite_finite(X4048),X4050))
| hBOOL(hAPP(fun(X4048,bool),bool,hAPP(X4048,fun(fun(X4048,bool),bool),member(X4048),X4049),X4050))
| ti(fun(X4048,bool),X4050) = bot_bot(fun(X4048,bool))
| hAPP(fun(X4048,bool),X4048,X4052,hAPP(fun(X4048,bool),fun(X4048,bool),hAPP(X4048,fun(fun(X4048,bool),fun(X4048,bool)),insert(X4048),X4049),X4050)) = hAPP(X4048,X4048,hAPP(X4048,fun(X4048,X4048),X4051,X4049),hAPP(fun(X4048,bool),X4048,X4052,X4050)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1196])]) ).
fof(i_0_1272,plain,
! [X1,X8,X14,X13] :
( ( 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13) )
& ( ~ 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13) = 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X8),X13)) ) ),
inference(fof_simplification,[status(thm)],[fact_147_insert__Diff__if]) ).
fof(i_0_1273,plain,
! [X3799,X3800,X3801,X3802] :
( ~ hBOOL(hAPP(fun(X3799,bool),bool,hAPP(fun(X3799,bool),fun(fun(X3799,bool),bool),ord_less_eq(fun(X3799,bool)),X3801),X3802))
| ~ hBOOL(hAPP(fun(X3799,bool),bool,hAPP(fun(X3799,bool),fun(fun(X3799,bool),bool),ord_less_eq(fun(X3799,bool)),X3802),X3800))
| hAPP(fun(X3799,bool),fun(X3799,bool),hAPP(fun(X3799,bool),fun(fun(X3799,bool),fun(X3799,bool)),minus_minus(fun(X3799,bool)),X3802),hAPP(fun(X3799,bool),fun(X3799,bool),hAPP(fun(X3799,bool),fun(fun(X3799,bool),fun(X3799,bool)),minus_minus(fun(X3799,bool)),X3800),X3801)) = ti(fun(X3799,bool),X3801) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_148_double__diff])]) ).
fof(i_0_1274,plain,
! [X3822,X3823,X3824] :
( ( ~ hBOOL(hAPP(fun(X3822,bool),bool,hAPP(X3822,fun(fun(X3822,bool),bool),member(X3822),X3823),hAPP(fun(X3822,bool),fun(X3822,bool),hAPP(X3822,fun(fun(X3822,bool),fun(X3822,bool)),insert(X3822),X3824),bot_bot(fun(X3822,bool)))))
| ti(X3822,X3823) = ti(X3822,X3824) )
& ( ti(X3822,X3823) != ti(X3822,X3824)
| hBOOL(hAPP(fun(X3822,bool),bool,hAPP(X3822,fun(fun(X3822,bool),bool),member(X3822),X3823),hAPP(fun(X3822,bool),fun(X3822,bool),hAPP(X3822,fun(fun(X3822,bool),fun(X3822,bool)),insert(X3822),X3824),bot_bot(fun(X3822,bool))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_154_singleton__iff])]) ).
fof(i_0_1275,plain,
! [X3814,X3815,X3816] :
( ~ hBOOL(hAPP(fun(X3814,bool),bool,hAPP(X3814,fun(fun(X3814,bool),bool),member(X3814),X3815),hAPP(fun(X3814,bool),fun(X3814,bool),hAPP(X3814,fun(fun(X3814,bool),fun(X3814,bool)),insert(X3814),X3816),bot_bot(fun(X3814,bool)))))
| ti(X3814,X3815) = ti(X3814,X3816) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_singletonE])]) ).
fof(i_0_1276,plain,
! [X3405,X3406,X3407,X3408,X3409,X3410] :
( ti(X3405,X3408) != hAPP(X3406,X3405,X3409,X3410)
| ~ hBOOL(hAPP(fun(X3406,bool),bool,hAPP(X3406,fun(fun(X3406,bool),bool),member(X3406),X3410),X3407))
| hBOOL(hAPP(fun(X3405,bool),bool,hAPP(X3405,fun(fun(X3405,bool),bool),member(X3405),X3408),hAPP(fun(X3406,bool),fun(X3405,bool),hAPP(fun(X3406,X3405),fun(fun(X3406,bool),fun(X3405,bool)),image(X3406,X3405),X3409),X3407))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_image__eqI])]) ).
fof(i_0_1277,plain,
! [X3572,X3573,X3574,X3575,X3576,X3577] :
( ~ hBOOL(hAPP(fun(X3573,bool),bool,hAPP(X3573,fun(fun(X3573,bool),bool),member(X3573),X3576),X3577))
| ti(X3572,X3574) != hAPP(X3573,X3572,X3575,X3576)
| hBOOL(hAPP(fun(X3572,bool),bool,hAPP(X3572,fun(fun(X3572,bool),bool),member(X3572),X3574),hAPP(fun(X3573,bool),fun(X3572,bool),hAPP(fun(X3573,X3572),fun(fun(X3573,bool),fun(X3572,bool)),image(X3573,X3572),X3575),X3577))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_95_rev__image__eqI])]) ).
fof(i_0_1278,plain,
! [X3759,X3760,X3761] :
( hBOOL(hAPP(fun(X3759,bool),bool,hAPP(X3759,fun(fun(X3759,bool),bool),member(X3759),X3760),X3761))
| hAPP(fun(X3759,bool),fun(X3759,bool),hAPP(fun(X3759,bool),fun(fun(X3759,bool),fun(X3759,bool)),minus_minus(fun(X3759,bool)),hAPP(fun(X3759,bool),fun(X3759,bool),hAPP(X3759,fun(fun(X3759,bool),fun(X3759,bool)),insert(X3759),X3760),X3761)),hAPP(fun(X3759,bool),fun(X3759,bool),hAPP(X3759,fun(fun(X3759,bool),fun(X3759,bool)),insert(X3759),X3760),bot_bot(fun(X3759,bool)))) = ti(fun(X3759,bool),X3761) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1197])]) ).
fof(i_0_1279,plain,
! [X5503,X5504,X5505,X5506,X5507,X5508] :
( ~ semiri456707255roduct(X5503)
| ti(X5503,X5508) = zero_zero(X5503)
| ti(X5503,X5506) != ti(X5503,X5507)
| ti(X5503,X5504) = ti(X5503,X5505)
| hAPP(X5503,X5503,hAPP(X5503,fun(X5503,X5503),plus_plus(X5503),X5506),hAPP(X5503,X5503,hAPP(X5503,fun(X5503,X5503),times_times(X5503),X5508),X5504)) != hAPP(X5503,X5503,hAPP(X5503,fun(X5503,X5503),plus_plus(X5503),X5507),hAPP(X5503,X5503,hAPP(X5503,fun(X5503,X5503),times_times(X5503),X5508),X5505)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_687_add__scale__eq__noteq])])]) ).
fof(i_0_1280,plain,
! [X5144,X5145,X5146,X5147,X5148] : hAPP(fun(X5144,bool),X5145,hAPP(X5145,fun(fun(X5144,bool),X5145),hAPP(fun(X5144,X5145),fun(X5145,fun(fun(X5144,bool),X5145)),hAPP(fun(X5145,fun(X5145,X5145)),fun(fun(X5144,X5145),fun(X5145,fun(fun(X5144,bool),X5145))),finite_fold_image(X5145,X5144),X5146),X5147),X5148),bot_bot(fun(X5144,bool))) = ti(X5145,X5148),
inference(variable_rename,[status(thm)],[fact_573_fold__image__empty]) ).
fof(i_0_1281,plain,
! [X5509,X5510,X5511] :
( ( ti(X5509,X5510) = zero_zero(X5509)
| hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),plus_plus(X5509),hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),times_times(X5509),X5510),X5510)),hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),times_times(X5509),X5511),X5511)) != zero_zero(X5509)
| ~ linord581940658strict(X5509) )
& ( ti(X5509,X5511) = zero_zero(X5509)
| hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),plus_plus(X5509),hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),times_times(X5509),X5510),X5510)),hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),times_times(X5509),X5511),X5511)) != zero_zero(X5509)
| ~ linord581940658strict(X5509) )
& ( ti(X5509,X5510) != zero_zero(X5509)
| ti(X5509,X5511) != zero_zero(X5509)
| hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),plus_plus(X5509),hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),times_times(X5509),X5510),X5510)),hAPP(X5509,X5509,hAPP(X5509,fun(X5509,X5509),times_times(X5509),X5511),X5511)) = zero_zero(X5509)
| ~ linord581940658strict(X5509) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_688_sum__squares__eq__zero__iff])])])]) ).
fof(i_0_1282,plain,
! [X4078,X4079,X4080,X4081,X4082] :
( ~ hBOOL(hAPP(fun(fun(X4078,bool),X4078),bool,hAPP(fun(X4078,fun(X4078,X4078)),fun(fun(fun(X4078,bool),X4078),bool),finite2073411215e_idem(X4078),X4081),X4082))
| ~ hBOOL(hAPP(fun(X4078,bool),bool,finite_finite(X4078),X4080))
| ti(fun(X4078,bool),X4080) = bot_bot(fun(X4078,bool))
| hAPP(fun(X4078,bool),X4078,X4082,hAPP(fun(X4078,bool),fun(X4078,bool),hAPP(X4078,fun(fun(X4078,bool),fun(X4078,bool)),insert(X4078),X4079),X4080)) = hAPP(X4078,X4078,hAPP(X4078,fun(X4078,X4078),X4081,X4079),hAPP(fun(X4078,bool),X4078,X4082,X4080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_218_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_1283,plain,
! [X17,X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X17) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X82)),X17)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X82))),X17) ) ),
inference(fof_simplification,[status(thm)],[fact_943_Suc__nat__number__of__add]) ).
fof(i_0_1284,plain,
! [X91,X114] :
( hAPP(int,nat,number_number_of(nat),X91) = hAPP(int,nat,number_number_of(nat),X114)
<=> ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X91)))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X114)),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X91)))
=> ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X114)))
=> hAPP(int,int,number_number_of(int),X91) = zero_zero(int) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X114)))
=> X91 = X114 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_936_eq__nat__number__of]) ).
fof(i_0_1285,plain,
! [X16,X11,X34] :
( hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X11),X34)))
<=> ~ ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X11),X34))
& ~ hBOOL(hAPP(nat,bool,X16,zero_zero(nat))) )
| ? [X79] :
( X11 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X79)
& ~ hBOOL(hAPP(nat,bool,X16,X79)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_540_nat__diff__split__asm]) ).
fof(i_0_1286,plain,
! [X3510,X3511,X3512,X3513] :
( ( ~ hBOOL(hAPP(X3510,bool,hAPP(fun(X3510,bool),fun(X3510,bool),hAPP(X3510,fun(fun(X3510,bool),fun(X3510,bool)),insert(X3510),X3511),X3512),X3513))
| ti(X3510,X3511) = ti(X3510,X3513)
| hBOOL(hAPP(X3510,bool,X3512,X3513)) )
& ( ti(X3510,X3511) != ti(X3510,X3513)
| hBOOL(hAPP(X3510,bool,hAPP(fun(X3510,bool),fun(X3510,bool),hAPP(X3510,fun(fun(X3510,bool),fun(X3510,bool)),insert(X3510),X3511),X3512),X3513)) )
& ( ~ hBOOL(hAPP(X3510,bool,X3512,X3513))
| hBOOL(hAPP(X3510,bool,hAPP(fun(X3510,bool),fun(X3510,bool),hAPP(X3510,fun(fun(X3510,bool),fun(X3510,bool)),insert(X3510),X3511),X3512),X3513)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_80_insert__code])])]) ).
fof(i_0_1287,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_1288,plain,
! [X3225,X3226] : ti(fun(fun(X3225,fun(X3225,X3225)),fun(X3225,fun(fun(X3226,X3225),fun(fun(fun(X3226,bool),X3225),bool)))),finite908156982e_idem(X3225,X3226)) = finite908156982e_idem(X3225,X3226),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple__idem_res]) ).
fof(i_0_1289,plain,
! [X3223,X3224] : ti(fun(fun(X3223,fun(X3223,X3223)),fun(X3223,fun(fun(X3224,X3223),fun(fun(fun(X3224,bool),X3223),bool)))),finite1357897459simple(X3223,X3224)) = finite1357897459simple(X3223,X3224),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple_res]) ).
fof(i_0_1290,plain,
! [X1,X2] :
( ord(X2)
=> ! [X12,X44] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X12),X44))
<=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X44))
& ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X44),X12)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_415_less__fun__def]) ).
fof(i_0_1291,plain,
! [X3514,X3515,X3516,X3517] :
( ( hAPP(fun(X3514,bool),fun(X3514,bool),hAPP(X3514,fun(fun(X3514,bool),fun(X3514,bool)),insert(X3514),X3516),X3517) != hAPP(fun(X3514,bool),fun(X3514,bool),hAPP(X3514,fun(fun(X3514,bool),fun(X3514,bool)),insert(X3514),X3516),X3515)
| ti(fun(X3514,bool),X3517) = ti(fun(X3514,bool),X3515)
| hBOOL(hAPP(fun(X3514,bool),bool,hAPP(X3514,fun(fun(X3514,bool),bool),member(X3514),X3516),X3515))
| hBOOL(hAPP(fun(X3514,bool),bool,hAPP(X3514,fun(fun(X3514,bool),bool),member(X3514),X3516),X3517)) )
& ( ti(fun(X3514,bool),X3517) != ti(fun(X3514,bool),X3515)
| hAPP(fun(X3514,bool),fun(X3514,bool),hAPP(X3514,fun(fun(X3514,bool),fun(X3514,bool)),insert(X3514),X3516),X3517) = hAPP(fun(X3514,bool),fun(X3514,bool),hAPP(X3514,fun(fun(X3514,bool),fun(X3514,bool)),insert(X3514),X3516),X3515)
| hBOOL(hAPP(fun(X3514,bool),bool,hAPP(X3514,fun(fun(X3514,bool),bool),member(X3514),X3516),X3515))
| hBOOL(hAPP(fun(X3514,bool),bool,hAPP(X3514,fun(fun(X3514,bool),bool),member(X3514),X3516),X3517)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1198])])]) ).
fof(i_0_1292,plain,
! [X3527,X3528,X3529] :
( ( hBOOL(hAPP(fun(X3527,bool),bool,hAPP(fun(X3527,bool),fun(fun(X3527,bool),bool),ord_less_eq(fun(X3527,bool)),X3528),X3529))
| ti(fun(X3527,bool),X3528) != ti(fun(X3527,bool),X3529) )
& ( hBOOL(hAPP(fun(X3527,bool),bool,hAPP(fun(X3527,bool),fun(fun(X3527,bool),bool),ord_less_eq(fun(X3527,bool)),X3529),X3528))
| ti(fun(X3527,bool),X3528) != ti(fun(X3527,bool),X3529) )
& ( ~ hBOOL(hAPP(fun(X3527,bool),bool,hAPP(fun(X3527,bool),fun(fun(X3527,bool),bool),ord_less_eq(fun(X3527,bool)),X3528),X3529))
| ~ hBOOL(hAPP(fun(X3527,bool),bool,hAPP(fun(X3527,bool),fun(fun(X3527,bool),bool),ord_less_eq(fun(X3527,bool)),X3529),X3528))
| ti(fun(X3527,bool),X3528) = ti(fun(X3527,bool),X3529) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_set__eq__subset])])]) ).
fof(i_0_1293,plain,
! [X3411,X3412,X3413] :
( ~ hBOOL(hAPP(fun(X3411,bool),bool,hAPP(fun(X3411,bool),fun(fun(X3411,bool),bool),ord_less_eq(fun(X3411,bool)),X3412),X3413))
| ~ hBOOL(hAPP(fun(X3411,bool),bool,hAPP(fun(X3411,bool),fun(fun(X3411,bool),bool),ord_less_eq(fun(X3411,bool)),X3413),X3412))
| ti(fun(X3411,bool),X3412) = ti(fun(X3411,bool),X3413) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_equalityI])]) ).
fof(i_0_1294,plain,
! [X86] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X86)))
=> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X86)) = zero_zero(nat) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X86)))
=> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X86)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X86)),hAPP(int,nat,number_number_of(nat),X86))) ) ),
inference(fof_simplification,[status(thm)],[fact_947_nat__number__of__Bit1]) ).
fof(i_0_1295,plain,
! [X4032,X4033,X4034,X4035] :
( ~ hBOOL(hAPP(fun(fun(X4032,bool),X4032),bool,hAPP(fun(X4032,fun(X4032,X4032)),fun(fun(fun(X4032,bool),X4032),bool),finite_folding_one(X4032),X4034),X4035))
| hAPP(fun(X4032,bool),X4032,X4035,hAPP(fun(X4032,bool),fun(X4032,bool),hAPP(X4032,fun(fun(X4032,bool),fun(X4032,bool)),insert(X4032),X4033),bot_bot(fun(X4032,bool)))) = ti(X4032,X4033) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_209_folding__one_Osingleton])]) ).
fof(i_0_1296,plain,
! [X3418,X3419,X3420,X3421] :
( ( ~ hBOOL(hAPP(fun(X3418,bool),bool,hAPP(X3418,fun(fun(X3418,bool),bool),member(X3418),X3420),X3421))
| hBOOL(hAPP(fun(X3418,bool),bool,hAPP(X3418,fun(fun(X3418,bool),bool),member(X3418),X3420),hAPP(fun(X3418,bool),fun(X3418,bool),hAPP(X3418,fun(fun(X3418,bool),fun(X3418,bool)),insert(X3418),X3419),X3421))) )
& ( ti(X3418,X3420) != ti(X3418,X3419)
| hBOOL(hAPP(fun(X3418,bool),bool,hAPP(X3418,fun(fun(X3418,bool),bool),member(X3418),X3420),hAPP(fun(X3418,bool),fun(X3418,bool),hAPP(X3418,fun(fun(X3418,bool),fun(X3418,bool)),insert(X3418),X3419),X3421))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1199])])]) ).
fof(i_0_1297,plain,
! [X4924,X4925,X4926] :
( ( ti(X4924,X4926) = zero_zero(X4924)
| hAPP(X4924,X4924,hAPP(X4924,fun(X4924,X4924),plus_plus(X4924),X4926),X4925) != zero_zero(X4924)
| ~ hBOOL(hAPP(X4924,bool,hAPP(X4924,fun(X4924,bool),ord_less_eq(X4924),zero_zero(X4924)),X4925))
| ~ hBOOL(hAPP(X4924,bool,hAPP(X4924,fun(X4924,bool),ord_less_eq(X4924),zero_zero(X4924)),X4926))
| ~ ordere216010020id_add(X4924) )
& ( ti(X4924,X4925) = zero_zero(X4924)
| hAPP(X4924,X4924,hAPP(X4924,fun(X4924,X4924),plus_plus(X4924),X4926),X4925) != zero_zero(X4924)
| ~ hBOOL(hAPP(X4924,bool,hAPP(X4924,fun(X4924,bool),ord_less_eq(X4924),zero_zero(X4924)),X4925))
| ~ hBOOL(hAPP(X4924,bool,hAPP(X4924,fun(X4924,bool),ord_less_eq(X4924),zero_zero(X4924)),X4926))
| ~ ordere216010020id_add(X4924) )
& ( ti(X4924,X4926) != zero_zero(X4924)
| ti(X4924,X4925) != zero_zero(X4924)
| hAPP(X4924,X4924,hAPP(X4924,fun(X4924,X4924),plus_plus(X4924),X4926),X4925) = zero_zero(X4924)
| ~ hBOOL(hAPP(X4924,bool,hAPP(X4924,fun(X4924,bool),ord_less_eq(X4924),zero_zero(X4924)),X4925))
| ~ hBOOL(hAPP(X4924,bool,hAPP(X4924,fun(X4924,bool),ord_less_eq(X4924),zero_zero(X4924)),X4926))
| ~ ordere216010020id_add(X4924) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_495_add__nonneg__eq__0__iff])])])]) ).
fof(i_0_1298,plain,
! [X28,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),hAPP(nat,nat,suc,X28))) ),
inference(fof_simplification,[status(thm)],[fact_357_not__less__eq]) ).
fof(i_0_1299,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,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_277_card_Oinsert]) ).
fof(i_0_1300,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_1301,plain,
! [X4697,X4698,X4699] :
( ( hBOOL(hAPP(fun(X4697,bool),bool,hAPP(fun(X4697,bool),fun(fun(X4697,bool),bool),ord_less_eq(fun(X4697,bool)),X4698),X4699))
| ~ hBOOL(hAPP(fun(X4697,bool),bool,hAPP(fun(X4697,bool),fun(fun(X4697,bool),bool),ord_less(fun(X4697,bool)),X4698),X4699)) )
& ( ti(fun(X4697,bool),X4698) != ti(fun(X4697,bool),X4699)
| ~ hBOOL(hAPP(fun(X4697,bool),bool,hAPP(fun(X4697,bool),fun(fun(X4697,bool),bool),ord_less(fun(X4697,bool)),X4698),X4699)) )
& ( ~ hBOOL(hAPP(fun(X4697,bool),bool,hAPP(fun(X4697,bool),fun(fun(X4697,bool),bool),ord_less_eq(fun(X4697,bool)),X4698),X4699))
| ti(fun(X4697,bool),X4698) = ti(fun(X4697,bool),X4699)
| hBOOL(hAPP(fun(X4697,bool),bool,hAPP(fun(X4697,bool),fun(fun(X4697,bool),bool),ord_less(fun(X4697,bool)),X4698),X4699)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_421_psubset__eq])])]) ).
fof(i_0_1302,plain,
! [X4694,X4695,X4696] :
( ( ~ hBOOL(hAPP(fun(X4694,bool),bool,hAPP(fun(X4694,bool),fun(fun(X4694,bool),bool),ord_less_eq(fun(X4694,bool)),X4695),X4696))
| hBOOL(hAPP(fun(X4694,bool),bool,hAPP(fun(X4694,bool),fun(fun(X4694,bool),bool),ord_less(fun(X4694,bool)),X4695),X4696))
| ti(fun(X4694,bool),X4695) = ti(fun(X4694,bool),X4696) )
& ( ~ hBOOL(hAPP(fun(X4694,bool),bool,hAPP(fun(X4694,bool),fun(fun(X4694,bool),bool),ord_less(fun(X4694,bool)),X4695),X4696))
| hBOOL(hAPP(fun(X4694,bool),bool,hAPP(fun(X4694,bool),fun(fun(X4694,bool),bool),ord_less_eq(fun(X4694,bool)),X4695),X4696)) )
& ( ti(fun(X4694,bool),X4695) != ti(fun(X4694,bool),X4696)
| hBOOL(hAPP(fun(X4694,bool),bool,hAPP(fun(X4694,bool),fun(fun(X4694,bool),bool),ord_less_eq(fun(X4694,bool)),X4695),X4696)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_420_subset__iff__psubset__eq])])]) ).
fof(i_0_1303,plain,
! [X6154,X6155] :
( ( ~ hBOOL(hAPP(X6154,bool,hAPP(X6154,fun(X6154,bool),ord_less_eq(X6154),hAPP(X6154,X6154,abs_abs(X6154),X6155)),zero_zero(X6154)))
| ti(X6154,X6155) = zero_zero(X6154)
| ~ ordere142940540dd_abs(X6154) )
& ( ti(X6154,X6155) != zero_zero(X6154)
| hBOOL(hAPP(X6154,bool,hAPP(X6154,fun(X6154,bool),ord_less_eq(X6154),hAPP(X6154,X6154,abs_abs(X6154),X6155)),zero_zero(X6154)))
| ~ ordere142940540dd_abs(X6154) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_907_abs__le__zero__iff])])])]) ).
fof(i_0_1304,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_1305,plain,
! [X4452,X4453,X4454] :
( ( hBOOL(hAPP(X4452,bool,hAPP(X4452,fun(X4452,bool),ord_less(X4452),X4453),X4454))
| ti(X4452,X4453) = ti(X4452,X4454)
| ~ hBOOL(hAPP(X4452,bool,hAPP(X4452,fun(X4452,bool),ord_less_eq(X4452),X4453),X4454))
| ~ linorder(X4452) )
& ( ti(X4452,X4453) != ti(X4452,X4454)
| ~ hBOOL(hAPP(X4452,bool,hAPP(X4452,fun(X4452,bool),ord_less(X4452),X4453),X4454))
| ~ hBOOL(hAPP(X4452,bool,hAPP(X4452,fun(X4452,bool),ord_less_eq(X4452),X4453),X4454))
| ~ linorder(X4452) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1200])])])]) ).
fof(i_0_1306,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_1307,plain,
! [X3] :
( ordere142940540dd_abs(X3)
=> ! [X41] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,abs_abs(X3),X41)),zero_zero(X3))) ),
inference(fof_simplification,[status(thm)],[fact_909_abs__not__less__zero]) ).
fof(i_0_1308,plain,
! [X1] :
( preorder(X1)
=> ! [X14,X39] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
& ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X39),X14)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_330_less__le__not__le]) ).
fof(i_0_1309,plain,
! [X3] :
( linordered_semidom(X3)
=> ! [X18] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X18)),zero_zero(X3))) ),
inference(fof_simplification,[status(thm)],[fact_834_of__nat__less__0__iff]) ).
fof(i_0_1310,plain,
! [X25] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X25)),zero_zero(int))),
inference(fof_simplification,[status(thm)],[fact_831_int__less__0__conv]) ).
fof(i_0_1311,plain,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),hAPP(nat,nat,suc,X17)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> X18 = X17 ) ),
inference(fof_simplification,[status(thm)],[fact_365_less__SucE]) ).
fof(i_0_1312,plain,
! [X17,X18] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X18))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,suc,X18)))
=> X18 = X17 ) ),
inference(fof_simplification,[status(thm)],[fact_361_less__antisym]) ).
fof(i_0_1313,plain,
! [X20,X28] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),hAPP(nat,nat,suc,X28)))
<=> X20 = X28 ) ),
inference(fof_simplification,[status(thm)],[fact_360_not__less__less__Suc__eq]) ).
fof(i_0_1314,plain,
! [X3470,X3471,X3472] :
( ~ order(X3470)
| ~ hBOOL(hAPP(X3470,bool,hAPP(X3470,fun(X3470,bool),ord_less_eq(X3470),X3471),X3472))
| ~ hBOOL(hAPP(X3470,bool,hAPP(X3470,fun(X3470,bool),ord_less_eq(X3470),X3472),X3471))
| ti(X3470,X3472) = ti(X3470,X3471) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_xt1_I5_J])])]) ).
fof(i_0_1315,plain,
! [X3463,X3464,X3465] :
( ~ order(X3463)
| ~ hBOOL(hAPP(X3463,bool,hAPP(X3463,fun(X3463,bool),ord_less_eq(X3463),X3464),X3465))
| ~ hBOOL(hAPP(X3463,bool,hAPP(X3463,fun(X3463,bool),ord_less_eq(X3463),X3465),X3464))
| ti(X3463,X3464) = ti(X3463,X3465) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_order__antisym])])]) ).
fof(i_0_1316,plain,
! [X3444,X3445,X3446] :
( ( ~ hBOOL(hAPP(X3444,bool,hAPP(X3444,fun(X3444,bool),ord_less_eq(X3444),X3446),X3445))
| ti(X3444,X3446) = ti(X3444,X3445)
| ~ hBOOL(hAPP(X3444,bool,hAPP(X3444,fun(X3444,bool),ord_less_eq(X3444),X3445),X3446))
| ~ order(X3444) )
& ( ti(X3444,X3446) != ti(X3444,X3445)
| hBOOL(hAPP(X3444,bool,hAPP(X3444,fun(X3444,bool),ord_less_eq(X3444),X3446),X3445))
| ~ hBOOL(hAPP(X3444,bool,hAPP(X3444,fun(X3444,bool),ord_less_eq(X3444),X3445),X3446))
| ~ order(X3444) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_61_order__antisym__conv])])])]) ).
fof(i_0_1317,plain,
! [X3438,X3439,X3440] :
( ( hBOOL(hAPP(X3438,bool,hAPP(X3438,fun(X3438,bool),ord_less_eq(X3438),X3439),X3440))
| ti(X3438,X3439) != ti(X3438,X3440)
| ~ order(X3438) )
& ( hBOOL(hAPP(X3438,bool,hAPP(X3438,fun(X3438,bool),ord_less_eq(X3438),X3440),X3439))
| ti(X3438,X3439) != ti(X3438,X3440)
| ~ order(X3438) )
& ( ~ hBOOL(hAPP(X3438,bool,hAPP(X3438,fun(X3438,bool),ord_less_eq(X3438),X3439),X3440))
| ~ hBOOL(hAPP(X3438,bool,hAPP(X3438,fun(X3438,bool),ord_less_eq(X3438),X3440),X3439))
| ti(X3438,X3439) = ti(X3438,X3440)
| ~ order(X3438) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_59_order__eq__iff])])])]) ).
fof(i_0_1318,plain,
! [X5064,X5065,X5066,X5069,X5070,X5071,X5072,X5073] :
( ( ti(fun(X5064,bool),X5065) = hAPP(fun(X5064,bool),fun(X5064,bool),hAPP(X5064,fun(fun(X5064,bool),fun(X5064,bool)),insert(X5064),esk87_3(X5064,X5065,X5066)),esk88_3(X5064,X5065,X5066))
| hAPP(fun(X5064,bool),nat,finite_card(X5064),X5065) != hAPP(nat,nat,suc,X5066) )
& ( ~ hBOOL(hAPP(fun(X5064,bool),bool,hAPP(X5064,fun(fun(X5064,bool),bool),member(X5064),esk87_3(X5064,X5065,X5066)),esk88_3(X5064,X5065,X5066)))
| hAPP(fun(X5064,bool),nat,finite_card(X5064),X5065) != hAPP(nat,nat,suc,X5066) )
& ( hAPP(fun(X5064,bool),nat,finite_card(X5064),esk88_3(X5064,X5065,X5066)) = X5066
| hAPP(fun(X5064,bool),nat,finite_card(X5064),X5065) != hAPP(nat,nat,suc,X5066) )
& ( X5066 != zero_zero(nat)
| ti(fun(X5064,bool),esk88_3(X5064,X5065,X5066)) = bot_bot(fun(X5064,bool))
| hAPP(fun(X5064,bool),nat,finite_card(X5064),X5065) != hAPP(nat,nat,suc,X5066) )
& ( X5071 = zero_zero(nat)
| ti(fun(X5069,bool),X5070) != hAPP(fun(X5069,bool),fun(X5069,bool),hAPP(X5069,fun(fun(X5069,bool),fun(X5069,bool)),insert(X5069),X5072),X5073)
| hBOOL(hAPP(fun(X5069,bool),bool,hAPP(X5069,fun(fun(X5069,bool),bool),member(X5069),X5072),X5073))
| hAPP(fun(X5069,bool),nat,finite_card(X5069),X5073) != X5071
| hAPP(fun(X5069,bool),nat,finite_card(X5069),X5070) = hAPP(nat,nat,suc,X5071) )
& ( ti(fun(X5069,bool),X5073) != bot_bot(fun(X5069,bool))
| ti(fun(X5069,bool),X5070) != hAPP(fun(X5069,bool),fun(X5069,bool),hAPP(X5069,fun(fun(X5069,bool),fun(X5069,bool)),insert(X5069),X5072),X5073)
| hBOOL(hAPP(fun(X5069,bool),bool,hAPP(X5069,fun(fun(X5069,bool),bool),member(X5069),X5072),X5073))
| hAPP(fun(X5069,bool),nat,finite_card(X5069),X5073) != X5071
| hAPP(fun(X5069,bool),nat,finite_card(X5069),X5070) = hAPP(nat,nat,suc,X5071) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1201])])])])])]) ).
fof(i_0_1319,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_1320,plain,
! [X3] :
( linorder(X3)
=> ! [X68] :
? [X94] :
! [X33] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X94),X33))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X68)) ) ),
inference(fof_simplification,[status(thm)],[fact_821_pinf_I6_J]) ).
fof(i_0_1321,plain,
! [X4115,X4116,X4117,X4118] :
( ~ hBOOL(hAPP(fun(fun(X4115,bool),X4115),bool,hAPP(fun(X4115,fun(X4115,X4115)),fun(fun(fun(X4115,bool),X4115),bool),finite2073411215e_idem(X4115),X4117),X4118))
| hAPP(X4115,X4115,hAPP(X4115,fun(X4115,X4115),X4117,X4116),X4116) = ti(X4115,X4116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_227_folding__one__idem_Oidem])]) ).
fof(i_0_1322,plain,
! [X3] :
( linorder(X3)
=> ! [X68] :
? [X94] :
! [X33] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X94))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X68),X33)) ) ),
inference(fof_simplification,[status(thm)],[fact_820_minf_I8_J]) ).
fof(i_0_1323,plain,
! [X20,X16] :
( ~ hBOOL(hAPP(nat,bool,X16,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X16,X20))
=> ? [X65] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),X20))
& ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X69),X65))
=> ~ hBOOL(hAPP(nat,bool,X16,X69)) )
& hBOOL(hAPP(nat,bool,X16,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X65),one_one(nat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_548_ex__least__nat__less]) ).
fof(i_0_1324,plain,
! [X3] :
( number_ring(X3)
=> ! [X82] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,X3,number_number_of(X3),X82) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = zero_zero(X3) ) ) ),
inference(fof_simplification,[status(thm)],[fact_828_of__nat__number__of__lemma]) ).
fof(i_0_1325,plain,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X39))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X39),X14)) ) ),
inference(fof_simplification,[status(thm)],[fact_327_linorder__not__le]) ).
fof(i_0_1326,plain,
! [X3] :
( linorder(X3)
=> ! [X22,X21] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
inference(fof_simplification,[status(thm)],[fact_337_leD]) ).
fof(i_0_1327,plain,
! [X1] :
( linorder(X1)
=> ! [X14,X39] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X39))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X39),X14)) ) ),
inference(fof_simplification,[status(thm)],[fact_326_linorder__not__less]) ).
fof(i_0_1328,plain,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_324_order__less__asym]) ).
fof(i_0_1329,plain,
! [X3] :
( preorder(X3)
=> ! [X41,X42] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41)) ) ),
inference(fof_simplification,[status(thm)],[fact_316_order__less__asym_H]) ).
fof(i_0_1330,plain,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_312_order__less__imp__not__less]) ).
fof(i_0_1331,plain,
! [X3] :
( preorder(X3)
=> ! [X21,X22] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_311_order__less__not__sym]) ).
fof(i_0_1332,plain,
! [X3] :
( order(X3)
=> ! [X42,X41] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X41))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),X42)) ) ),
inference(fof_simplification,[status(thm)],[fact_317_xt1_I9_J]) ).
fof(i_0_1333,plain,
! [X3451,X3452,X3453,X3454] :
( ~ order(X3451)
| ti(X3451,X3453) != ti(X3451,X3454)
| ~ hBOOL(hAPP(X3451,bool,hAPP(X3451,fun(X3451,bool),ord_less_eq(X3451),X3452),X3454))
| hBOOL(hAPP(X3451,bool,hAPP(X3451,fun(X3451,bool),ord_less_eq(X3451),X3452),X3453)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_xt1_I3_J])])]) ).
fof(i_0_1334,plain,
! [X3459,X3460,X3461,X3462] :
( ~ order(X3459)
| ~ hBOOL(hAPP(X3459,bool,hAPP(X3459,fun(X3459,bool),ord_less_eq(X3459),X3461),X3462))
| ti(X3459,X3461) != ti(X3459,X3460)
| hBOOL(hAPP(X3459,bool,hAPP(X3459,fun(X3459,bool),ord_less_eq(X3459),X3460),X3462)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_xt1_I4_J])])]) ).
fof(i_0_1335,plain,
! [X4352,X4353,X4354] :
( ( hBOOL(hAPP(X4352,bool,hAPP(X4352,fun(X4352,bool),ord_less(X4352),X4354),X4353))
| ti(X4352,X4354) = ti(X4352,X4353)
| hBOOL(hAPP(X4352,bool,hAPP(X4352,fun(X4352,bool),ord_less(X4352),X4353),X4354))
| ~ linorder(X4352) )
& ( ti(X4352,X4354) != ti(X4352,X4353)
| ~ hBOOL(hAPP(X4352,bool,hAPP(X4352,fun(X4352,bool),ord_less(X4352),X4354),X4353))
| hBOOL(hAPP(X4352,bool,hAPP(X4352,fun(X4352,bool),ord_less(X4352),X4353),X4354))
| ~ linorder(X4352) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1202])])])]) ).
fof(i_0_1336,plain,
! [X4387,X4388,X4389,X4390] :
( ~ order(X4387)
| ti(X4387,X4389) != ti(X4387,X4390)
| ~ hBOOL(hAPP(X4387,bool,hAPP(X4387,fun(X4387,bool),ord_less(X4387),X4388),X4390))
| hBOOL(hAPP(X4387,bool,hAPP(X4387,fun(X4387,bool),ord_less(X4387),X4388),X4389)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_319_xt1_I1_J])])]) ).
fof(i_0_1337,plain,
! [X4395,X4396,X4397,X4398] :
( ~ order(X4395)
| ~ hBOOL(hAPP(X4395,bool,hAPP(X4395,fun(X4395,bool),ord_less(X4395),X4397),X4398))
| ti(X4395,X4397) != ti(X4395,X4396)
| hBOOL(hAPP(X4395,bool,hAPP(X4395,fun(X4395,bool),ord_less(X4395),X4396),X4398)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_321_xt1_I2_J])])]) ).
fof(i_0_1338,plain,
! [X5054,X5055] :
( ( ti(fun(X5054,bool),X5055) != bot_bot(fun(X5054,bool))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X5054,bool),nat,finite_card(X5054),X5055))) )
& ( hBOOL(hAPP(fun(X5054,bool),bool,finite_finite(X5054),X5055))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X5054,bool),nat,finite_card(X5054),X5055))) )
& ( ti(fun(X5054,bool),X5055) = bot_bot(fun(X5054,bool))
| ~ hBOOL(hAPP(fun(X5054,bool),bool,finite_finite(X5054),X5055))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X5054,bool),nat,finite_card(X5054),X5055))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_544_card__gt__0__iff])])]) ).
fof(i_0_1339,plain,
! [X4437,X4438,X4439] :
( ( ~ hBOOL(hAPP(X4437,bool,hAPP(X4437,fun(X4437,bool),ord_less_eq(X4437),X4438),X4439))
| ti(X4437,X4438) = ti(X4437,X4439)
| hBOOL(hAPP(X4437,bool,hAPP(X4437,fun(X4437,bool),ord_less(X4437),X4438),X4439))
| ~ linorder(X4437) )
& ( ti(X4437,X4438) != ti(X4437,X4439)
| hBOOL(hAPP(X4437,bool,hAPP(X4437,fun(X4437,bool),ord_less_eq(X4437),X4438),X4439))
| hBOOL(hAPP(X4437,bool,hAPP(X4437,fun(X4437,bool),ord_less(X4437),X4438),X4439))
| ~ linorder(X4437) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1203])])])]) ).
fof(i_0_1340,plain,
! [X4461,X4462,X4463] :
( ~ order(X4461)
| ~ hBOOL(hAPP(X4461,bool,hAPP(X4461,fun(X4461,bool),ord_less_eq(X4461),X4462),X4463))
| ti(X4461,X4463) = ti(X4461,X4462)
| hBOOL(hAPP(X4461,bool,hAPP(X4461,fun(X4461,bool),ord_less(X4461),X4462),X4463)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_342_xt1_I11_J])])]) ).
fof(i_0_1341,plain,
! [X4458,X4459,X4460] :
( ~ order(X4458)
| ~ hBOOL(hAPP(X4458,bool,hAPP(X4458,fun(X4458,bool),ord_less_eq(X4458),X4459),X4460))
| ti(X4458,X4459) = ti(X4458,X4460)
| hBOOL(hAPP(X4458,bool,hAPP(X4458,fun(X4458,bool),ord_less(X4458),X4459),X4460)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_341_order__le__neq__trans])])]) ).
fof(i_0_1342,plain,
! [X4455,X4456,X4457] :
( ~ order(X4455)
| ~ hBOOL(hAPP(X4455,bool,hAPP(X4455,fun(X4455,bool),ord_less_eq(X4455),X4456),X4457))
| hBOOL(hAPP(X4455,bool,hAPP(X4455,fun(X4455,bool),ord_less(X4455),X4456),X4457))
| ti(X4455,X4456) = ti(X4455,X4457) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_340_order__le__imp__less__or__eq])])]) ).
fof(i_0_1343,plain,
! [X4440,X4441,X4442] :
( ~ order(X4440)
| ti(X4440,X4441) = ti(X4440,X4442)
| ~ hBOOL(hAPP(X4440,bool,hAPP(X4440,fun(X4440,bool),ord_less_eq(X4440),X4441),X4442))
| hBOOL(hAPP(X4440,bool,hAPP(X4440,fun(X4440,bool),ord_less(X4440),X4441),X4442)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_335_order__neq__le__trans])])]) ).
fof(i_0_1344,plain,
! [X4428,X4429,X4430] :
( ( ~ hBOOL(hAPP(X4428,bool,hAPP(X4428,fun(X4428,bool),ord_less_eq(X4428),X4429),X4430))
| hBOOL(hAPP(X4428,bool,hAPP(X4428,fun(X4428,bool),ord_less(X4428),X4429),X4430))
| ti(X4428,X4429) = ti(X4428,X4430)
| ~ order(X4428) )
& ( ~ hBOOL(hAPP(X4428,bool,hAPP(X4428,fun(X4428,bool),ord_less(X4428),X4429),X4430))
| hBOOL(hAPP(X4428,bool,hAPP(X4428,fun(X4428,bool),ord_less_eq(X4428),X4429),X4430))
| ~ order(X4428) )
& ( ti(X4428,X4429) != ti(X4428,X4430)
| hBOOL(hAPP(X4428,bool,hAPP(X4428,fun(X4428,bool),ord_less_eq(X4428),X4429),X4430))
| ~ order(X4428) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_331_order__le__less])])])]) ).
fof(i_0_1345,plain,
! [X4422,X4423,X4424] :
( ( hBOOL(hAPP(X4422,bool,hAPP(X4422,fun(X4422,bool),ord_less_eq(X4422),X4423),X4424))
| ~ hBOOL(hAPP(X4422,bool,hAPP(X4422,fun(X4422,bool),ord_less(X4422),X4423),X4424))
| ~ order(X4422) )
& ( ti(X4422,X4423) != ti(X4422,X4424)
| ~ hBOOL(hAPP(X4422,bool,hAPP(X4422,fun(X4422,bool),ord_less(X4422),X4423),X4424))
| ~ order(X4422) )
& ( ~ hBOOL(hAPP(X4422,bool,hAPP(X4422,fun(X4422,bool),ord_less_eq(X4422),X4423),X4424))
| ti(X4422,X4423) = ti(X4422,X4424)
| hBOOL(hAPP(X4422,bool,hAPP(X4422,fun(X4422,bool),ord_less(X4422),X4423),X4424))
| ~ order(X4422) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_329_order__less__le])])])]) ).
fof(i_0_1346,plain,
! [X4443,X4444,X4445] :
( ~ order(X4443)
| ti(X4443,X4444) = ti(X4443,X4445)
| ~ hBOOL(hAPP(X4443,bool,hAPP(X4443,fun(X4443,bool),ord_less_eq(X4443),X4445),X4444))
| hBOOL(hAPP(X4443,bool,hAPP(X4443,fun(X4443,bool),ord_less(X4443),X4445),X4444)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_336_xt1_I12_J])])]) ).
fof(i_0_1347,plain,
! [X20,X16] :
( ~ hBOOL(hAPP(nat,bool,X16,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X16,X20))
=> ? [X65] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X20))
& ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X65))
=> ~ hBOOL(hAPP(nat,bool,X16,X69)) )
& hBOOL(hAPP(nat,bool,X16,X65)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_551_ex__least__nat__le]) ).
fof(i_0_1348,plain,
! [X3944,X3945,X3948,X3949,X3950,X3951] :
( ( ti(fun(X3944,bool),X3945) = hAPP(fun(X3944,bool),fun(X3944,bool),hAPP(X3944,fun(fun(X3944,bool),fun(X3944,bool)),insert(X3944),esk30_2(X3944,X3945)),esk31_2(X3944,X3945))
| ti(fun(X3944,bool),X3945) = bot_bot(fun(X3944,bool)) )
& ( ~ hBOOL(hAPP(fun(X3944,bool),bool,hAPP(X3944,fun(fun(X3944,bool),bool),member(X3944),esk30_2(X3944,X3945)),esk31_2(X3944,X3945)))
| ti(fun(X3944,bool),X3945) = bot_bot(fun(X3944,bool)) )
& ( ti(fun(X3948,bool),X3949) != hAPP(fun(X3948,bool),fun(X3948,bool),hAPP(X3948,fun(fun(X3948,bool),fun(X3948,bool)),insert(X3948),X3950),X3951)
| hBOOL(hAPP(fun(X3948,bool),bool,hAPP(X3948,fun(fun(X3948,bool),bool),member(X3948),X3950),X3951))
| ti(fun(X3948,bool),X3949) != bot_bot(fun(X3948,bool)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1204])])])])])]) ).
fof(i_0_1349,plain,
! [X6160,X6161] :
( ( ~ hBOOL(hAPP(X6160,bool,hAPP(X6160,fun(X6160,bool),ord_less(X6160),zero_zero(X6160)),hAPP(X6160,X6160,abs_abs(X6160),X6161)))
| ti(X6160,X6161) != zero_zero(X6160)
| ~ ordere142940540dd_abs(X6160) )
& ( ti(X6160,X6161) = zero_zero(X6160)
| hBOOL(hAPP(X6160,bool,hAPP(X6160,fun(X6160,bool),ord_less(X6160),zero_zero(X6160)),hAPP(X6160,X6160,abs_abs(X6160),X6161)))
| ~ ordere142940540dd_abs(X6160) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_910_zero__less__abs__iff])])])]) ).
fof(i_0_1350,plain,
! [X14,X39,X16] :
( ( hBOOL(X16)
=> hAPP(nat,int,semiring_1_of_nat(int),X14) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X16),X14),X39)) )
& ( ~ hBOOL(X16)
=> hAPP(nat,int,semiring_1_of_nat(int),X39) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X16),X14),X39)) ) ),
inference(fof_simplification,[status(thm)],[fact_889_int__if__cong]) ).
fof(i_0_1351,plain,
! [X5563,X5564] :
( ( hAPP(X5563,X5563,hAPP(X5563,fun(X5563,X5563),plus_plus(X5563),X5564),X5564) != zero_zero(X5563)
| ti(X5563,X5564) = zero_zero(X5563)
| ~ hBOOL(hAPP(fun(X5563,bool),bool,hAPP(X5563,fun(fun(X5563,bool),bool),member(X5563),X5564),ring_1_Ints(X5563)))
| ~ ring_char_0(X5563) )
& ( ti(X5563,X5564) != zero_zero(X5563)
| hAPP(X5563,X5563,hAPP(X5563,fun(X5563,X5563),plus_plus(X5563),X5564),X5564) = zero_zero(X5563)
| ~ hBOOL(hAPP(fun(X5563,bool),bool,hAPP(X5563,fun(fun(X5563,bool),bool),member(X5563),X5564),ring_1_Ints(X5563)))
| ~ ring_char_0(X5563) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_706_Ints__double__eq__0__iff])])])]) ).
fof(i_0_1352,plain,
! [X3221,X3222] : ti(fun(fun(X3221,fun(X3221,X3221)),fun(fun(X3222,X3221),fun(X3221,fun(fun(X3222,bool),X3221)))),finite_fold_image(X3221,X3222)) = finite_fold_image(X3221,X3222),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofold__image_res]) ).
fof(i_0_1353,plain,
! [X4162,X4163,X4164] :
( ~ group_add(X4162)
| hAPP(X4162,X4162,hAPP(X4162,fun(X4162,X4162),plus_plus(X4162),hAPP(X4162,X4162,hAPP(X4162,fun(X4162,X4162),minus_minus(X4162),X4163),X4164)),X4164) = ti(X4162,X4163) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_240_diff__add__cancel])])]) ).
fof(i_0_1354,plain,
! [X4165,X4166,X4167] :
( ~ group_add(X4165)
| hAPP(X4165,X4165,hAPP(X4165,fun(X4165,X4165),minus_minus(X4165),hAPP(X4165,X4165,hAPP(X4165,fun(X4165,X4165),plus_plus(X4165),X4166),X4167)),X4167) = ti(X4165,X4166) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_241_add__diff__cancel])])]) ).
fof(i_0_1355,plain,
! [X3522,X3523,X3524] :
( ~ hBOOL(hAPP(fun(X3522,bool),bool,hAPP(X3522,fun(fun(X3522,bool),bool),member(X3522),X3523),X3524))
| hAPP(fun(X3522,bool),fun(X3522,bool),hAPP(X3522,fun(fun(X3522,bool),fun(X3522,bool)),insert(X3522),X3523),X3524) = ti(fun(X3522,bool),X3524) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_83_insert__absorb])]) ).
fof(i_0_1356,plain,
! [X22,X21] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X21))
=> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X21),X22) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),X22) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X21))
=> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X21),X22) = zero_zero(int) ) ),
inference(fof_simplification,[status(thm)],[fact_827_tsub__def]) ).
fof(i_0_1357,plain,
! [X6258,X6259] :
( ~ number_ring(X6258)
| hAPP(X6258,X6258,hAPP(X6258,fun(X6258,X6258),times_times(X6258),hAPP(int,X6258,number_number_of(X6258),hAPP(int,int,bit1,pls))),X6259) = ti(X6258,X6259) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_964_mult__numeral__1])])]) ).
fof(i_0_1358,plain,
! [X3811,X3812,X3813] :
( hAPP(fun(X3811,bool),fun(X3811,bool),hAPP(X3811,fun(fun(X3811,bool),fun(X3811,bool)),insert(X3811),X3812),bot_bot(fun(X3811,bool))) != hAPP(fun(X3811,bool),fun(X3811,bool),hAPP(X3811,fun(fun(X3811,bool),fun(X3811,bool)),insert(X3811),X3813),bot_bot(fun(X3811,bool)))
| ti(X3811,X3812) = ti(X3811,X3813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_151_singleton__inject])]) ).
fof(i_0_1359,plain,
! [X18,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)) = X18 ),
inference(fof_simplification,[status(thm)],[fact_405_add__diff__inverse]) ).
fof(i_0_1360,plain,
! [X3902,X3903,X3904,X3905,X3906] :
( ( ti(X3902,X3903) != ti(X3902,X3904)
| ti(X3902,X3905) = ti(X3902,X3906)
| hAPP(X3902,X3902,hAPP(X3902,fun(X3902,X3902),minus_minus(X3902),X3903),X3904) != hAPP(X3902,X3902,hAPP(X3902,fun(X3902,X3902),minus_minus(X3902),X3905),X3906)
| ~ ab_group_add(X3902) )
& ( ti(X3902,X3905) != ti(X3902,X3906)
| ti(X3902,X3903) = ti(X3902,X3904)
| hAPP(X3902,X3902,hAPP(X3902,fun(X3902,X3902),minus_minus(X3902),X3903),X3904) != hAPP(X3902,X3902,hAPP(X3902,fun(X3902,X3902),minus_minus(X3902),X3905),X3906)
| ~ ab_group_add(X3902) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_178_diff__eq__diff__eq])])])]) ).
fof(i_0_1361,plain,
! [X3831,X3832] :
( ( ~ hBOOL(hAPP(fun(X3831,bool),bool,hAPP(fun(X3831,bool),fun(fun(X3831,bool),bool),ord_less_eq(fun(X3831,bool)),X3832),bot_bot(fun(X3831,bool))))
| ti(fun(X3831,bool),X3832) = bot_bot(fun(X3831,bool)) )
& ( ti(fun(X3831,bool),X3832) != bot_bot(fun(X3831,bool))
| hBOOL(hAPP(fun(X3831,bool),bool,hAPP(fun(X3831,bool),fun(fun(X3831,bool),bool),ord_less_eq(fun(X3831,bool)),X3832),bot_bot(fun(X3831,bool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_subset__empty])]) ).
fof(i_0_1362,plain,
! [X3890,X3891,X3892,X3893] :
( ( ti(fun(X3891,bool),X3893) != bot_bot(fun(X3891,bool))
| hAPP(fun(X3891,bool),fun(X3890,bool),hAPP(fun(X3891,X3890),fun(fun(X3891,bool),fun(X3890,bool)),image(X3891,X3890),hAPP(X3890,fun(X3891,X3890),combk(X3890,X3891),X3892)),X3893) = bot_bot(fun(X3890,bool)) )
& ( ti(fun(X3891,bool),X3893) = bot_bot(fun(X3891,bool))
| hAPP(fun(X3891,bool),fun(X3890,bool),hAPP(fun(X3891,X3890),fun(fun(X3891,bool),fun(X3890,bool)),image(X3891,X3890),hAPP(X3890,fun(X3891,X3890),combk(X3890,X3891),X3892)),X3893) = hAPP(fun(X3890,bool),fun(X3890,bool),hAPP(X3890,fun(fun(X3890,bool),fun(X3890,bool)),insert(X3890),X3892),bot_bot(fun(X3890,bool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_176_image__constant__conv])]) ).
fof(i_0_1363,plain,
! [X82] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X82),pls))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X82)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X82),pls))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X82)) ) ),
inference(fof_simplification,[status(thm)],[fact_948_nat__1__add__number__of]) ).
fof(i_0_1364,plain,
! [X4703,X4704,X4705] :
( ~ linordered_idom(X4703)
| ti(X4703,X4704) = ti(X4703,X4705)
| hBOOL(hAPP(X4703,bool,hAPP(X4703,fun(X4703,bool),ord_less(X4703),X4704),X4705))
| hBOOL(hAPP(X4703,bool,hAPP(X4703,fun(X4703,bool),ord_less(X4703),X4705),X4704)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1205])])]) ).
fof(i_0_1365,plain,
! [X4410,X4411,X4412] :
( ~ linorder(X4410)
| hBOOL(hAPP(X4410,bool,hAPP(X4410,fun(X4410,bool),ord_less(X4410),X4411),X4412))
| ti(X4410,X4411) = ti(X4410,X4412)
| hBOOL(hAPP(X4410,bool,hAPP(X4410,fun(X4410,bool),ord_less(X4410),X4412),X4411)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1206])])]) ).
fof(i_0_1366,plain,
! [X4355,X4356,X4357] :
( ~ linorder(X4355)
| ti(X4355,X4356) = ti(X4355,X4357)
| hBOOL(hAPP(X4355,bool,hAPP(X4355,fun(X4355,bool),ord_less(X4355),X4356),X4357))
| hBOOL(hAPP(X4355,bool,hAPP(X4355,fun(X4355,bool),ord_less(X4355),X4357),X4356)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1207])])]) ).
fof(i_0_1367,plain,
! [X4349,X4350,X4351] :
( ~ linorder(X4349)
| hBOOL(hAPP(X4349,bool,hAPP(X4349,fun(X4349,bool),ord_less(X4349),X4350),X4351))
| ti(X4349,X4350) = ti(X4349,X4351)
| hBOOL(hAPP(X4349,bool,hAPP(X4349,fun(X4349,bool),ord_less(X4349),X4351),X4350)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_307_linorder__less__linear])])]) ).
fof(i_0_1368,plain,
! [X4346,X4347,X4348] :
( ( hBOOL(hAPP(X4346,bool,hAPP(X4346,fun(X4346,bool),ord_less(X4346),X4347),X4348))
| hBOOL(hAPP(X4346,bool,hAPP(X4346,fun(X4346,bool),ord_less(X4346),X4348),X4347))
| ti(X4346,X4347) = ti(X4346,X4348)
| ~ linorder(X4346) )
& ( ~ hBOOL(hAPP(X4346,bool,hAPP(X4346,fun(X4346,bool),ord_less(X4346),X4348),X4347))
| ~ hBOOL(hAPP(X4346,bool,hAPP(X4346,fun(X4346,bool),ord_less(X4346),X4347),X4348))
| ~ linorder(X4346) )
& ( ti(X4346,X4347) != ti(X4346,X4348)
| ~ hBOOL(hAPP(X4346,bool,hAPP(X4346,fun(X4346,bool),ord_less(X4346),X4347),X4348))
| ~ linorder(X4346) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1208])])])]) ).
fof(i_0_1369,plain,
! [X4343,X4344,X4345] :
( ( ti(X4343,X4344) = ti(X4343,X4345)
| hBOOL(hAPP(X4343,bool,hAPP(X4343,fun(X4343,bool),ord_less(X4343),X4344),X4345))
| hBOOL(hAPP(X4343,bool,hAPP(X4343,fun(X4343,bool),ord_less(X4343),X4345),X4344))
| ~ linorder(X4343) )
& ( ~ hBOOL(hAPP(X4343,bool,hAPP(X4343,fun(X4343,bool),ord_less(X4343),X4344),X4345))
| ti(X4343,X4344) != ti(X4343,X4345)
| ~ linorder(X4343) )
& ( ~ hBOOL(hAPP(X4343,bool,hAPP(X4343,fun(X4343,bool),ord_less(X4343),X4345),X4344))
| ti(X4343,X4344) != ti(X4343,X4345)
| ~ linorder(X4343) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_305_linorder__neq__iff])])])]) ).
fof(i_0_1370,plain,
! [X4308,X4309,X4310,X4311] :
( ( hBOOL(hAPP(X4308,bool,X4310,esk43_4(X4308,X4309,X4310,X4311)))
| ~ hBOOL(hAPP(X4308,bool,X4310,X4311))
| ~ hBOOL(hAPP(X4308,bool,X4310,X4309))
| hAPP(fun(X4308,bool),X4308,the(X4308),X4310) = ti(X4308,X4309) )
& ( ti(X4308,esk43_4(X4308,X4309,X4310,X4311)) != ti(X4308,X4311)
| ~ hBOOL(hAPP(X4308,bool,X4310,X4311))
| ~ hBOOL(hAPP(X4308,bool,X4310,X4309))
| hAPP(fun(X4308,bool),X4308,the(X4308),X4310) = ti(X4308,X4309) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_290_the1__equality])])])])]) ).
fof(i_0_1371,plain,
! [X3931,X3932,X3935,X3936,X3937,X3938] :
( ( ti(fun(X3931,bool),X3932) = hAPP(fun(X3931,bool),fun(X3931,bool),hAPP(X3931,fun(fun(X3931,bool),fun(X3931,bool)),insert(X3931),esk28_2(X3931,X3932)),esk27_2(X3931,X3932))
| ti(fun(X3931,bool),X3932) = bot_bot(fun(X3931,bool))
| ~ hBOOL(hAPP(fun(X3931,bool),bool,finite_finite(X3931),X3932)) )
& ( hBOOL(hAPP(fun(X3931,bool),bool,finite_finite(X3931),esk27_2(X3931,X3932)))
| ti(fun(X3931,bool),X3932) = bot_bot(fun(X3931,bool))
| ~ hBOOL(hAPP(fun(X3931,bool),bool,finite_finite(X3931),X3932)) )
& ( ti(fun(X3935,bool),X3936) != bot_bot(fun(X3935,bool))
| hBOOL(hAPP(fun(X3935,bool),bool,finite_finite(X3935),X3936)) )
& ( ti(fun(X3935,bool),X3936) != hAPP(fun(X3935,bool),fun(X3935,bool),hAPP(X3935,fun(fun(X3935,bool),fun(X3935,bool)),insert(X3935),X3938),X3937)
| ~ hBOOL(hAPP(fun(X3935,bool),bool,finite_finite(X3935),X3937))
| hBOOL(hAPP(fun(X3935,bool),bool,finite_finite(X3935),X3936)) ) ),
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_185_finite_Osimps])])])])])]) ).
fof(i_0_1372,plain,
! [X1,X8] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),bot_bot(fun(X1,bool)))),
inference(fof_simplification,[status(thm)],[fact_416_not__psubset__empty]) ).
fof(i_0_1373,plain,
! [X3743,X3744,X3746,X3747,X3748] :
( ( hBOOL(hAPP(fun(X3743,bool),bool,hAPP(X3743,fun(fun(X3743,bool),bool),member(X3743),esk20_2(X3743,X3744)),X3744))
| ti(fun(X3743,bool),X3744) = bot_bot(fun(X3743,bool)) )
& ( ti(fun(X3746,bool),X3747) != bot_bot(fun(X3746,bool))
| ~ hBOOL(hAPP(fun(X3746,bool),bool,hAPP(X3746,fun(fun(X3746,bool),bool),member(X3746),X3748),X3747)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1209])])])])]) ).
fof(i_0_1374,plain,
! [X3714,X3715,X3716] :
( ti(fun(X3714,bool),X3716) != bot_bot(fun(X3714,bool))
| ~ hBOOL(hAPP(fun(X3714,bool),bool,hAPP(X3714,fun(fun(X3714,bool),bool),member(X3714),X3715),X3716)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1210])]) ).
fof(i_0_1375,plain,
! [X3737,X3738,X3739,X3740,X3741] :
( ( ~ hBOOL(hAPP(fun(X3737,bool),bool,hAPP(X3737,fun(fun(X3737,bool),bool),member(X3737),X3739),X3738))
| ti(fun(X3737,bool),X3738) != bot_bot(fun(X3737,bool)) )
& ( ti(fun(X3740,bool),X3741) = bot_bot(fun(X3740,bool))
| hBOOL(hAPP(fun(X3740,bool),bool,hAPP(X3740,fun(fun(X3740,bool),bool),member(X3740),esk19_2(X3740,X3741)),X3741)) ) ),
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_132_ex__in__conv])])])])]) ).
fof(i_0_1376,plain,
! [X4313,X4314,X4315] :
( ( hBOOL(hAPP(X4313,bool,X4314,esk44_3(X4313,X4314,X4315)))
| hBOOL(hAPP(X4313,bool,X4314,hAPP(fun(X4313,bool),X4313,the(X4313),X4314)))
| ~ hBOOL(hAPP(X4313,bool,X4314,X4315)) )
& ( ti(X4313,esk44_3(X4313,X4314,X4315)) != ti(X4313,X4315)
| hBOOL(hAPP(X4313,bool,X4314,hAPP(fun(X4313,bool),X4313,the(X4313),X4314)))
| ~ hBOOL(hAPP(X4313,bool,X4314,X4315)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_291_theI])])])]) ).
fof(i_0_1377,plain,
! [X4304,X4305,X4306] :
( ( hBOOL(hAPP(X4304,bool,X4305,esk42_3(X4304,X4305,X4306)))
| ~ hBOOL(hAPP(X4304,bool,X4305,X4306))
| hBOOL(hAPP(X4304,bool,X4305,hAPP(fun(X4304,bool),X4304,the(X4304),X4305))) )
& ( ti(X4304,esk42_3(X4304,X4305,X4306)) != ti(X4304,X4306)
| ~ hBOOL(hAPP(X4304,bool,X4305,X4306))
| hBOOL(hAPP(X4304,bool,X4305,hAPP(fun(X4304,bool),X4304,the(X4304),X4305))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_289_theI_H])])])])]) ).
fof(i_0_1378,plain,
! [X4370,X4371,X4372] :
( ~ order(X4370)
| ~ hBOOL(hAPP(X4370,bool,hAPP(X4370,fun(X4370,bool),ord_less(X4370),X4371),X4372))
| ti(X4370,X4372) != ti(X4370,X4371) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_314_order__less__imp__not__eq2])])]) ).
fof(i_0_1379,plain,
! [X4367,X4368,X4369] :
( ~ order(X4367)
| ~ hBOOL(hAPP(X4367,bool,hAPP(X4367,fun(X4367,bool),ord_less(X4367),X4368),X4369))
| ti(X4367,X4368) != ti(X4367,X4369) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_313_order__less__imp__not__eq])])]) ).
fof(i_0_1380,plain,
! [X4358,X4359,X4360] :
( ~ order(X4358)
| ~ hBOOL(hAPP(X4358,bool,hAPP(X4358,fun(X4358,bool),ord_less(X4358),X4359),X4360))
| ti(X4358,X4359) != ti(X4358,X4360) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_310_less__imp__neq])])]) ).
fof(i_0_1381,plain,
! [X14] :
( ~ hBOOL(hAPP(int,bool,nat_neg,X14))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X14)) ),
inference(fof_simplification,[status(thm)],[fact_905_not__neg__eq__ge__0]) ).
fof(i_0_1382,plain,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_70_linorder__le__cases]) ).
fof(i_0_1383,plain,
! [X3] :
( linorder(X3)
=> ! [X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_332_leI]) ).
fof(i_0_1384,plain,
! [X3] :
( linorder(X3)
=> ! [X22,X21] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
inference(fof_simplification,[status(thm)],[fact_333_not__leE]) ).
fof(i_0_1385,plain,
! [X3552,X3553,X3554] :
( ( hBOOL(hAPP(fun(X3552,bool),bool,hAPP(fun(X3552,bool),fun(fun(X3552,bool),bool),ord_less_eq(fun(X3552,bool)),X3553),X3554))
| ti(fun(X3552,bool),X3553) != ti(fun(X3552,bool),X3554) )
& ( hBOOL(hAPP(fun(X3552,bool),bool,hAPP(fun(X3552,bool),fun(fun(X3552,bool),bool),ord_less_eq(fun(X3552,bool)),X3554),X3553))
| ti(fun(X3552,bool),X3553) != ti(fun(X3552,bool),X3554) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1211])])]) ).
fof(i_0_1386,plain,
! [X3530,X3531,X3532] :
( ti(fun(X3530,bool),X3531) != ti(fun(X3530,bool),X3532)
| hBOOL(hAPP(fun(X3530,bool),bool,hAPP(fun(X3530,bool),fun(fun(X3530,bool),bool),ord_less_eq(fun(X3530,bool)),X3531),X3532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_equalityD1])]) ).
fof(i_0_1387,plain,
! [X3533,X3534,X3535] :
( ti(fun(X3533,bool),X3534) != ti(fun(X3533,bool),X3535)
| hBOOL(hAPP(fun(X3533,bool),bool,hAPP(fun(X3533,bool),fun(fun(X3533,bool),bool),ord_less_eq(fun(X3533,bool)),X3535),X3534)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_87_equalityD2])]) ).
fof(i_0_1388,plain,
! [X21,X22] :
( X21 != X22
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X22),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_299_linorder__neqE__nat]) ).
fof(i_0_1389,plain,
! [X3] :
( number_ring(X3)
=> ! [X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = zero_zero(X3) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,X3,semiring_1_of_nat(X3),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,X3,number_number_of(X3),X82) ) ) ),
inference(fof_simplification,[status(thm)],[fact_899_of__nat__number__of__eq]) ).
fof(i_0_1390,plain,
! [X4290,X4291] : hAPP(fun(X4290,bool),X4290,the(X4290),hAPP(X4290,fun(X4290,bool),hAPP(fun(X4290,fun(X4290,bool)),fun(X4290,fun(X4290,bool)),combc(X4290,X4290,bool),fequal(X4290)),X4291)) = ti(X4290,X4291),
inference(variable_rename,[status(thm)],[fact_284_the__eq__trivial]) ).
fof(i_0_1391,plain,
! [X6152,X6153] :
( ~ ordere142940540dd_abs(X6152)
| ~ hBOOL(hAPP(X6152,bool,hAPP(X6152,fun(X6152,bool),ord_less_eq(X6152),zero_zero(X6152)),X6153))
| hAPP(X6152,X6152,abs_abs(X6152),X6153) = ti(X6152,X6153) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_906_abs__of__nonneg])])]) ).
fof(i_0_1392,plain,
! [X6162,X6163] :
( ~ ordere142940540dd_abs(X6162)
| ~ hBOOL(hAPP(X6162,bool,hAPP(X6162,fun(X6162,bool),ord_less(X6162),zero_zero(X6162)),X6163))
| hAPP(X6162,X6162,abs_abs(X6162),X6163) = ti(X6162,X6163) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_911_abs__of__pos])])]) ).
fof(i_0_1393,plain,
! [X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X82)) = zero_zero(int) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,int,number_number_of(int),X82) ) ),
inference(fof_simplification,[status(thm)],[fact_938_int__nat__number__of]) ).
fof(i_0_1394,plain,
! [X82] :
( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X82)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X82)))
=> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X82)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X82)) ) ),
inference(fof_simplification,[status(thm)],[fact_946_Suc__nat__number__of]) ).
fof(i_0_1395,plain,
! [X4111,X4112,X4113,X4114] :
( ~ cancel_semigroup_add(X4111)
| hAPP(X4111,X4111,hAPP(X4111,fun(X4111,X4111),plus_plus(X4111),X4112),X4113) != hAPP(X4111,X4111,hAPP(X4111,fun(X4111,X4111),plus_plus(X4111),X4114),X4113)
| ti(X4111,X4112) = ti(X4111,X4114) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_226_add__right__imp__eq])])]) ).
fof(i_0_1396,plain,
! [X4099,X4100,X4101,X4102] :
( ( hAPP(X4099,X4099,hAPP(X4099,fun(X4099,X4099),plus_plus(X4099),X4100),X4101) != hAPP(X4099,X4099,hAPP(X4099,fun(X4099,X4099),plus_plus(X4099),X4102),X4101)
| ti(X4099,X4100) = ti(X4099,X4102)
| ~ cancel_semigroup_add(X4099) )
& ( ti(X4099,X4100) != ti(X4099,X4102)
| hAPP(X4099,X4099,hAPP(X4099,fun(X4099,X4099),plus_plus(X4099),X4100),X4101) = hAPP(X4099,X4099,hAPP(X4099,fun(X4099,X4099),plus_plus(X4099),X4102),X4101)
| ~ cancel_semigroup_add(X4099) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_223_add__right__cancel])])])]) ).
fof(i_0_1397,plain,
! [X4107,X4108,X4109,X4110] :
( ~ cancel146912293up_add(X4107)
| hAPP(X4107,X4107,hAPP(X4107,fun(X4107,X4107),plus_plus(X4107),X4108),X4109) != hAPP(X4107,X4107,hAPP(X4107,fun(X4107,X4107),plus_plus(X4107),X4108),X4110)
| ti(X4107,X4109) = ti(X4107,X4110) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_225_add__imp__eq])])]) ).
fof(i_0_1398,plain,
! [X4103,X4104,X4105,X4106] :
( ~ cancel_semigroup_add(X4103)
| hAPP(X4103,X4103,hAPP(X4103,fun(X4103,X4103),plus_plus(X4103),X4104),X4105) != hAPP(X4103,X4103,hAPP(X4103,fun(X4103,X4103),plus_plus(X4103),X4104),X4106)
| ti(X4103,X4105) = ti(X4103,X4106) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_224_add__left__imp__eq])])]) ).
fof(i_0_1399,plain,
! [X4095,X4096,X4097,X4098] :
( ( hAPP(X4095,X4095,hAPP(X4095,fun(X4095,X4095),plus_plus(X4095),X4096),X4097) != hAPP(X4095,X4095,hAPP(X4095,fun(X4095,X4095),plus_plus(X4095),X4096),X4098)
| ti(X4095,X4097) = ti(X4095,X4098)
| ~ cancel_semigroup_add(X4095) )
& ( ti(X4095,X4097) != ti(X4095,X4098)
| hAPP(X4095,X4095,hAPP(X4095,fun(X4095,X4095),plus_plus(X4095),X4096),X4097) = hAPP(X4095,X4095,hAPP(X4095,fun(X4095,X4095),plus_plus(X4095),X4096),X4098)
| ~ cancel_semigroup_add(X4095) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_222_add__left__cancel])])])]) ).
fof(i_0_1400,plain,
! [X3489,X3490,X3491,X3492] :
( hAPP(X3489,X3490,X3491,esk6_4(X3489,X3490,X3491,X3492)) != hAPP(X3489,X3490,X3492,esk6_4(X3489,X3490,X3491,X3492))
| ti(fun(X3489,X3490),X3491) = ti(fun(X3489,X3490),X3492) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_74_ext])])]) ).
fof(i_0_1401,plain,
! [X1,X35] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),bot_bot(fun(X1,bool)))),
inference(fof_simplification,[status(thm)],[fact_129_empty__iff]) ).
fof(i_0_1402,plain,
! [X1,X11] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),bot_bot(fun(X1,bool)))),
inference(fof_simplification,[status(thm)],[fact_121_emptyE]) ).
fof(i_0_1403,plain,
! [X6354,X6355,X6356] :
( ~ hBOOL(hAPP(X6354,bool,hAPP(X6354,fun(X6354,bool),fequal(X6354),X6355),X6356))
| ti(X6354,X6355) = ti(X6354,X6356) ),
inference(variable_rename,[status(thm)],[i_0_1212]) ).
fof(i_0_1404,plain,
! [X4511,X4512] :
( ( ti(X4511,X4512) = bot_bot(X4511)
| hBOOL(hAPP(X4511,bool,hAPP(X4511,fun(X4511,bool),ord_less(X4511),bot_bot(X4511)),X4512))
| ~ bot(X4511) )
& ( ~ hBOOL(hAPP(X4511,bool,hAPP(X4511,fun(X4511,bool),ord_less(X4511),bot_bot(X4511)),X4512))
| ti(X4511,X4512) != bot_bot(X4511)
| ~ bot(X4511) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_355_bot__less])])])]) ).
fof(i_0_1405,plain,
! [X3846,X3847] :
( ( ~ hBOOL(hAPP(X3846,bool,hAPP(X3846,fun(X3846,bool),ord_less_eq(X3846),X3847),bot_bot(X3846)))
| ti(X3846,X3847) = bot_bot(X3846)
| ~ bot(X3846) )
& ( ti(X3846,X3847) != bot_bot(X3846)
| hBOOL(hAPP(X3846,bool,hAPP(X3846,fun(X3846,bool),ord_less_eq(X3846),X3847),bot_bot(X3846)))
| ~ bot(X3846) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_162_bot__unique])])])]) ).
fof(i_0_1406,plain,
! [X3844,X3845] :
( ~ bot(X3844)
| ~ hBOOL(hAPP(X3844,bool,hAPP(X3844,fun(X3844,bool),ord_less_eq(X3844),X3845),bot_bot(X3844)))
| ti(X3844,X3845) = bot_bot(X3844) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_161_le__bot])])]) ).
fof(i_0_1407,plain,
! [X3942,X3943] : hAPP(fun(X3942,bool),X3942,the_elem(X3942),hAPP(fun(X3942,bool),fun(X3942,bool),hAPP(X3942,fun(fun(X3942,bool),fun(X3942,bool)),insert(X3942),X3943),bot_bot(fun(X3942,bool)))) = ti(X3942,X3943),
inference(variable_rename,[status(thm)],[fact_187_the__elem__eq]) ).
fof(i_0_1408,plain,
! [X4847,X4848,X4849,X4850] :
( ( ti(fun(X4848,bool),X4849) = bot_bot(fun(X4848,bool))
| hAPP(fun(X4847,bool),fun(sum_sum(X4848,X4847),bool),hAPP(fun(X4848,bool),fun(fun(X4847,bool),fun(sum_sum(X4848,X4847),bool)),sum_Plus(X4848,X4847),X4849),X4850) != bot_bot(fun(sum_sum(X4848,X4847),bool)) )
& ( ti(fun(X4847,bool),X4850) = bot_bot(fun(X4847,bool))
| hAPP(fun(X4847,bool),fun(sum_sum(X4848,X4847),bool),hAPP(fun(X4848,bool),fun(fun(X4847,bool),fun(sum_sum(X4848,X4847),bool)),sum_Plus(X4848,X4847),X4849),X4850) != bot_bot(fun(sum_sum(X4848,X4847),bool)) )
& ( ti(fun(X4848,bool),X4849) != bot_bot(fun(X4848,bool))
| ti(fun(X4847,bool),X4850) != bot_bot(fun(X4847,bool))
| hAPP(fun(X4847,bool),fun(sum_sum(X4848,X4847),bool),hAPP(fun(X4848,bool),fun(fun(X4847,bool),fun(sum_sum(X4848,X4847),bool)),sum_Plus(X4848,X4847),X4849),X4850) = bot_bot(fun(sum_sum(X4848,X4847),bool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_450_Plus__eq__empty__conv])])]) ).
fof(i_0_1409,plain,
! [X3] :
( linordered_semidom(X3)
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),one_one(X3)),zero_zero(X3))) ),
inference(fof_simplification,[status(thm)],[fact_506_not__one__le__zero]) ).
fof(i_0_1410,plain,
! [X3] :
( linordered_semidom(X3)
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),zero_zero(X3))) ),
inference(fof_simplification,[status(thm)],[fact_509_not__one__less__zero]) ).
fof(i_0_1411,plain,
! [X4914,X4915,X4916] : hAPP(nat,X4914,hAPP(fun(nat,X4914),fun(nat,X4914),hAPP(X4914,fun(fun(nat,X4914),fun(nat,X4914)),nat_case(X4914),X4915),X4916),zero_zero(nat)) = ti(X4914,X4915),
inference(variable_rename,[status(thm)],[fact_491_nat__case__0]) ).
fof(i_0_1412,plain,
! [X3] :
( bot(X3)
=> ! [X41] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X41),bot_bot(X3))) ),
inference(fof_simplification,[status(thm)],[fact_354_not__less__bot]) ).
fof(i_0_1413,plain,
! [X6256,X6257] :
( ~ number_ring(X6256)
| hAPP(X6256,X6256,hAPP(X6256,fun(X6256,X6256),times_times(X6256),X6257),hAPP(int,X6256,number_number_of(X6256),hAPP(int,int,bit1,pls))) = ti(X6256,X6257) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_963_mult__numeral__1__right])])]) ).
fof(i_0_1414,plain,
! [X3] :
( preorder(X3)
=> ! [X21] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X21)) ),
inference(fof_simplification,[status(thm)],[fact_304_order__less__irrefl]) ).
fof(i_0_1415,plain,
! [X5090,X5091,X5092] :
( ( ti(fun(X5090,bool),X5091) = hAPP(fun(X5090,bool),fun(X5090,bool),hAPP(X5090,fun(fun(X5090,bool),fun(X5090,bool)),insert(X5090),esk93_3(X5090,X5091,X5092)),esk94_3(X5090,X5091,X5092))
| hAPP(fun(X5090,bool),nat,finite_card(X5090),X5091) != hAPP(nat,nat,suc,X5092) )
& ( ~ hBOOL(hAPP(fun(X5090,bool),bool,hAPP(X5090,fun(fun(X5090,bool),bool),member(X5090),esk93_3(X5090,X5091,X5092)),esk94_3(X5090,X5091,X5092)))
| hAPP(fun(X5090,bool),nat,finite_card(X5090),X5091) != hAPP(nat,nat,suc,X5092) )
& ( hAPP(fun(X5090,bool),nat,finite_card(X5090),esk94_3(X5090,X5091,X5092)) = X5092
| hAPP(fun(X5090,bool),nat,finite_card(X5090),X5091) != hAPP(nat,nat,suc,X5092) )
& ( X5092 != zero_zero(nat)
| ti(fun(X5090,bool),esk94_3(X5090,X5091,X5092)) = bot_bot(fun(X5090,bool))
| hAPP(fun(X5090,bool),nat,finite_card(X5090),X5091) != hAPP(nat,nat,suc,X5092) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1213])])])]) ).
fof(i_0_1416,plain,
! [X6096,X6097,X6098] :
( ~ semiring_1(X6096)
| hAPP(X6096,X6096,hAPP(nat,fun(X6096,X6096),hAPP(fun(X6096,X6096),fun(nat,fun(X6096,X6096)),semiri532925092at_aux(X6096),X6097),zero_zero(nat)),X6098) = ti(X6096,X6098) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_891_of__nat__aux_Osimps_I1_J])])]) ).
fof(i_0_1417,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[fact_484_not__less0]) ).
fof(i_0_1418,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[fact_482_less__nat__zero__code]) ).
fof(i_0_1419,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[fact_454_less__zeroE]) ).
fof(i_0_1420,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_300_less__irrefl__nat]) ).
fof(i_0_1421,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_297_less__not__refl]) ).
fof(i_0_1422,plain,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X122),X123))
| ~ hBOOL(X122)
| hBOOL(X123) ),
inference(fof_simplification,[status(thm)],[help_fimplies_3_1_U]) ).
fof(i_0_1423,plain,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X122),X123))
| hBOOL(X122)
| hBOOL(X123) ),
inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).
fof(i_0_1424,plain,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X122),X123))
| hBOOL(X122) ),
inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).
fof(i_0_1425,plain,
! [X122,X123] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X122),X123))
| hBOOL(X123) ),
inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).
fof(i_0_1426,plain,
! [X6357,X6358,X6359] :
( ti(X6357,X6358) != ti(X6357,X6359)
| hBOOL(hAPP(X6357,bool,hAPP(X6357,fun(X6357,bool),fequal(X6357),X6358),X6359)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_T]) ).
fof(i_0_1427,plain,
! [X6308,X6309,X6310] : hAPP(X6308,X6308,hAPP(X6308,fun(X6308,X6308),hAPP(bool,fun(X6308,fun(X6308,X6308)),if(X6308),fTrue),X6309),X6310) = ti(X6308,X6309),
inference(variable_rename,[status(thm)],[help_If_1_1_T]) ).
fof(i_0_1428,plain,
! [X6311,X6312,X6313] : hAPP(X6311,X6311,hAPP(X6311,fun(X6311,X6311),hAPP(bool,fun(X6311,fun(X6311,X6311)),if(X6311),fFalse),X6312),X6313) = ti(X6311,X6313),
inference(variable_rename,[status(thm)],[help_If_2_1_T]) ).
fof(i_0_1429,plain,
! [X3258,X3259] : ti(fun(fun(X3258,bool),fun(fun(X3259,bool),fun(sum_sum(X3258,X3259),bool))),sum_Plus(X3258,X3259)) = sum_Plus(X3258,X3259),
inference(variable_rename,[status(thm)],[tsy_c_Sum__Type_OPlus_res]) ).
fof(i_0_1430,plain,
! [X3228] : ti(fun(fun(X3228,fun(X3228,X3228)),fun(fun(fun(X3228,bool),X3228),bool)),finite2073411215e_idem(X3228)) = finite2073411215e_idem(X3228),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__one__idem_res]) ).
fof(i_0_1431,plain,
! [X3227] : ti(fun(fun(X3227,fun(X3227,X3227)),fun(fun(fun(X3227,bool),X3227),bool)),finite_folding_one(X3227)) = finite_folding_one(X3227),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__one_res]) ).
fof(i_0_1432,plain,
! [X17] : ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),X17))),
inference(fof_simplification,[status(thm)],[fact_933_not__neg__int]) ).
fof(i_0_1433,plain,
! [X4300,X4301,X4302] :
( ( hBOOL(hAPP(X4300,bool,X4301,esk41_3(X4300,X4301,X4302)))
| hAPP(fun(X4300,bool),X4300,the(X4300),X4301) = ti(X4300,X4302)
| ~ hBOOL(hAPP(X4300,bool,X4301,X4302)) )
& ( ti(X4300,esk41_3(X4300,X4301,X4302)) != ti(X4300,X4302)
| hAPP(fun(X4300,bool),X4300,the(X4300),X4301) = ti(X4300,X4302)
| ~ hBOOL(hAPP(X4300,bool,X4301,X4302)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_288_the__equality])])])]) ).
fof(i_0_1434,plain,
! [X3833,X3834,X3835,X3836] :
( ( hAPP(fun(X3833,bool),fun(X3834,bool),hAPP(fun(X3833,X3834),fun(fun(X3833,bool),fun(X3834,bool)),image(X3833,X3834),X3835),X3836) != bot_bot(fun(X3834,bool))
| ti(fun(X3833,bool),X3836) = bot_bot(fun(X3833,bool)) )
& ( ti(fun(X3833,bool),X3836) != bot_bot(fun(X3833,bool))
| hAPP(fun(X3833,bool),fun(X3834,bool),hAPP(fun(X3833,X3834),fun(fun(X3833,bool),fun(X3834,bool)),image(X3833,X3834),X3835),X3836) = bot_bot(fun(X3834,bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_158_image__is__empty])]) ).
fof(i_0_1435,plain,
! [X3840,X3841,X3842,X3843] :
( ( bot_bot(fun(X3840,bool)) != hAPP(fun(X3841,bool),fun(X3840,bool),hAPP(fun(X3841,X3840),fun(fun(X3841,bool),fun(X3840,bool)),image(X3841,X3840),X3842),X3843)
| ti(fun(X3841,bool),X3843) = bot_bot(fun(X3841,bool)) )
& ( ti(fun(X3841,bool),X3843) != bot_bot(fun(X3841,bool))
| bot_bot(fun(X3840,bool)) = hAPP(fun(X3841,bool),fun(X3840,bool),hAPP(fun(X3841,X3840),fun(fun(X3841,bool),fun(X3840,bool)),image(X3841,X3840),X3842),X3843) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_160_empty__is__image])]) ).
fof(i_0_1436,plain,
! [X3214,X3215,X3216] : ti(fun(fun(X3214,fun(X3215,X3216)),fun(fun(X3214,X3215),fun(X3214,X3216))),combs(X3214,X3215,X3216)) = combs(X3214,X3215,X3216),
inference(variable_rename,[status(thm)],[tsy_c_COMBS_res]) ).
fof(i_0_1437,plain,
! [X6268,X6269] :
( ~ number_ring(X6268)
| hAPP(X6268,X6268,hAPP(X6268,fun(X6268,X6268),plus_plus(X6268),hAPP(int,X6268,number_number_of(X6268),pls)),X6269) = ti(X6268,X6269) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_972_add__numeral__0])])]) ).
fof(i_0_1438,plain,
! [X5131,X5132,X5133] :
( ( ti(X5131,X5132) != hAPP(X5131,X5131,hAPP(X5131,fun(X5131,X5131),plus_plus(X5131),X5132),X5133)
| ti(X5131,X5133) = zero_zero(X5131)
| ~ semiri456707255roduct(X5131) )
& ( ti(X5131,X5133) != zero_zero(X5131)
| ti(X5131,X5132) = hAPP(X5131,X5131,hAPP(X5131,fun(X5131,X5131),plus_plus(X5131),X5132),X5133)
| ~ semiri456707255roduct(X5131) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_568_add__0__iff])])])]) ).
fof(i_0_1439,plain,
! [X5172,X5173,X5174] :
( ( hAPP(X5172,X5172,hAPP(X5172,fun(X5172,X5172),times_times(X5172),X5173),X5174) != zero_zero(X5172)
| ti(X5172,X5173) = zero_zero(X5172)
| ti(X5172,X5174) = zero_zero(X5172)
| ~ ring_n68954251visors(X5172) )
& ( ti(X5172,X5173) != zero_zero(X5172)
| hAPP(X5172,X5172,hAPP(X5172,fun(X5172,X5172),times_times(X5172),X5173),X5174) = zero_zero(X5172)
| ~ ring_n68954251visors(X5172) )
& ( ti(X5172,X5174) != zero_zero(X5172)
| hAPP(X5172,X5172,hAPP(X5172,fun(X5172,X5172),times_times(X5172),X5173),X5174) = zero_zero(X5172)
| ~ ring_n68954251visors(X5172) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_581_mult__eq__0__iff])])])]) ).
fof(i_0_1440,plain,
! [X5178,X5179,X5180] :
( ~ no_zero_divisors(X5178)
| hAPP(X5178,X5178,hAPP(X5178,fun(X5178,X5178),times_times(X5178),X5179),X5180) != zero_zero(X5178)
| ti(X5178,X5179) = zero_zero(X5178)
| ti(X5178,X5180) = zero_zero(X5178) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_583_divisors__zero])])]) ).
fof(i_0_1441,plain,
! [X5175,X5176,X5177] :
( ~ no_zero_divisors(X5175)
| ti(X5175,X5177) = zero_zero(X5175)
| ti(X5175,X5176) = zero_zero(X5175)
| hAPP(X5175,X5175,hAPP(X5175,fun(X5175,X5175),times_times(X5175),X5177),X5176) != zero_zero(X5175) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_582_no__zero__divisors])])]) ).
fof(i_0_1442,plain,
! [X4884,X4885,X4886] :
( ( hAPP(X4884,X4884,hAPP(X4884,fun(X4884,X4884),minus_minus(X4884),X4885),X4886) != zero_zero(X4884)
| ti(X4884,X4885) = ti(X4884,X4886)
| ~ group_add(X4884) )
& ( ti(X4884,X4885) != ti(X4884,X4886)
| hAPP(X4884,X4884,hAPP(X4884,fun(X4884,X4884),minus_minus(X4884),X4885),X4886) = zero_zero(X4884)
| ~ group_add(X4884) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_470_right__minus__eq])])])]) ).
fof(i_0_1443,plain,
! [X4887,X4888,X4889] :
( ( ti(X4887,X4888) != ti(X4887,X4889)
| hAPP(X4887,X4887,hAPP(X4887,fun(X4887,X4887),minus_minus(X4887),X4888),X4889) = zero_zero(X4887)
| ~ ab_group_add(X4887) )
& ( hAPP(X4887,X4887,hAPP(X4887,fun(X4887,X4887),minus_minus(X4887),X4888),X4889) != zero_zero(X4887)
| ti(X4887,X4888) = ti(X4887,X4889)
| ~ ab_group_add(X4887) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_471_eq__iff__diff__eq__0])])])]) ).
fof(i_0_1444,plain,
! [X3208,X3209,X3210] : ti(fun(fun(X3208,fun(X3209,X3210)),fun(X3209,fun(X3208,X3210))),combc(X3208,X3209,X3210)) = combc(X3208,X3209,X3210),
inference(variable_rename,[status(thm)],[tsy_c_COMBC_res]) ).
fof(i_0_1445,plain,
! [X3205,X3206,X3207] : ti(fun(fun(X3205,X3206),fun(fun(X3207,X3205),fun(X3207,X3206))),combb(X3205,X3206,X3207)) = combb(X3205,X3206,X3207),
inference(variable_rename,[status(thm)],[tsy_c_COMBB_res]) ).
fof(i_0_1446,plain,
! [X5017,X5018] :
( ( hAPP(fun(X5017,bool),nat,finite_card(X5017),X5018) != zero_zero(nat)
| ti(fun(X5017,bool),X5018) = bot_bot(fun(X5017,bool))
| ~ hBOOL(hAPP(fun(X5017,bool),bool,finite_finite(X5017),X5018)) )
& ( ti(fun(X5017,bool),X5018) != bot_bot(fun(X5017,bool))
| hAPP(fun(X5017,bool),nat,finite_card(X5017),X5018) = zero_zero(nat) )
& ( hBOOL(hAPP(fun(X5017,bool),bool,finite_finite(X5017),X5018))
| hAPP(fun(X5017,bool),nat,finite_card(X5017),X5018) = zero_zero(nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1214])])]) ).
fof(i_0_1447,plain,
! [X3725,X3726] : hAPP(fun(X3725,bool),fun(X3725,bool),hAPP(fun(X3725,bool),fun(fun(X3725,bool),fun(X3725,bool)),minus_minus(fun(X3725,bool)),X3726),bot_bot(fun(X3725,bool))) = ti(fun(X3725,bool),X3726),
inference(variable_rename,[status(thm)],[fact_128_Diff__empty]) ).
fof(i_0_1448,plain,
! [X6270,X6271] :
( ~ number_ring(X6270)
| hAPP(X6270,X6270,hAPP(X6270,fun(X6270,X6270),plus_plus(X6270),X6271),hAPP(int,X6270,number_number_of(X6270),pls)) = ti(X6270,X6271) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_973_add__numeral__0__right])])]) ).
fof(i_0_1449,plain,
! [X123,X122] :
( ~ hBOOL(X122)
| ~ hBOOL(X123)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X122),X123)) ),
inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).
fof(i_0_1450,plain,
! [X122,X123] :
( ~ hBOOL(X123)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X122),X123)) ),
inference(fof_simplification,[status(thm)],[help_fimplies_2_1_U]) ).
fof(i_0_1451,plain,
! [X123,X122] :
( ~ hBOOL(X122)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X122),X123)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).
fof(i_0_1452,plain,
! [X122,X123] :
( ~ hBOOL(X123)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X122),X123)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).
fof(i_0_1453,plain,
! [X3254,X3255] : ti(fun(fun(X3254,X3255),fun(fun(X3254,bool),fun(X3255,bool))),image(X3254,X3255)) = image(X3254,X3255),
inference(variable_rename,[status(thm)],[tsy_c_Set_Oimage_res]) ).
fof(i_0_1454,plain,
! [X5088,X5089] :
( ( hAPP(X5088,X5088,hAPP(X5088,fun(X5088,X5088),plus_plus(X5088),X5089),X5089) != zero_zero(X5088)
| ti(X5088,X5089) = zero_zero(X5088)
| ~ linord219039673up_add(X5088) )
& ( ti(X5088,X5089) != zero_zero(X5088)
| hAPP(X5088,X5088,hAPP(X5088,fun(X5088,X5088),plus_plus(X5088),X5089),X5089) = zero_zero(X5088)
| ~ linord219039673up_add(X5088) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_555_double__eq__0__iff])])])]) ).
fof(i_0_1455,plain,
! [X4878,X4879] :
( ( zero_zero(X4878) != hAPP(X4878,X4878,hAPP(X4878,fun(X4878,X4878),plus_plus(X4878),X4879),X4879)
| ti(X4878,X4879) = zero_zero(X4878)
| ~ linord219039673up_add(X4878) )
& ( ti(X4878,X4879) != zero_zero(X4878)
| zero_zero(X4878) = hAPP(X4878,X4878,hAPP(X4878,fun(X4878,X4878),plus_plus(X4878),X4879),X4879)
| ~ linord219039673up_add(X4878) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_467_double__zero__sym])])])]) ).
fof(i_0_1456,plain,
! [X3587,X3588] : hAPP(fun(X3587,bool),fun(X3587,bool),hAPP(fun(X3587,X3587),fun(fun(X3587,bool),fun(X3587,bool)),image(X3587,X3587),combi(X3587)),X3588) = ti(fun(X3587,bool),X3588),
inference(variable_rename,[status(thm)],[fact_98_image__ident]) ).
fof(i_0_1457,plain,
! [X3246] : ti(fun(X3246,fun(fun(nat,X3246),fun(nat,X3246))),nat_case(X3246)) = nat_case(X3246),
inference(variable_rename,[status(thm)],[tsy_c_Nat_Onat_Onat__case_res]) ).
fof(i_0_1458,plain,
! [X3256] : ti(fun(X3256,fun(fun(X3256,bool),fun(X3256,bool))),insert(X3256)) = insert(X3256),
inference(variable_rename,[status(thm)],[tsy_c_Set_Oinsert_res]) ).
fof(i_0_1459,plain,
! [X1,X16] :
( hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = bot_bot(fun(X1,bool))
<=> ! [X33] : ~ hBOOL(hAPP(X1,bool,X16,X33)) ),
inference(fof_simplification,[status(thm)],[fact_126_Collect__empty__eq]) ).
fof(i_0_1460,plain,
! [X1,X16] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)
<=> ! [X33] : ~ hBOOL(hAPP(X1,bool,X16,X33)) ),
inference(fof_simplification,[status(thm)],[fact_130_empty__Collect__eq]) ).
fof(i_0_1461,plain,
! [X3261,X3262,X3263,X3264] : hAPP(X3261,X3262,ti(fun(X3261,X3262),X3263),X3264) = hAPP(X3261,X3262,X3263,X3264),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).
fof(i_0_1462,plain,
! [X3248] :
( ~ semiring_1(X3248)
| ti(fun(fun(X3248,X3248),fun(nat,fun(X3248,X3248))),semiri532925092at_aux(X3248)) = semiri532925092at_aux(X3248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res])]) ).
fof(i_0_1463,plain,
! [X6331,X6332,X6333,X6334] : hAPP(X6331,X6332,hAPP(X6332,fun(X6331,X6332),combk(X6332,X6331),X6333),X6334) = ti(X6332,X6333),
inference(variable_rename,[status(thm)],[help_COMBK_1_1_U]) ).
fof(i_0_1464,plain,
! [X4298,X4299] : hAPP(fun(X4298,bool),X4298,the(X4298),hAPP(X4298,fun(X4298,bool),fequal(X4298),X4299)) = ti(X4298,X4299),
inference(variable_rename,[status(thm)],[fact_287_the__sym__eq__trivial]) ).
fof(i_0_1465,plain,
! [X5205,X5206] :
( ~ comm_monoid_mult(X5205)
| hAPP(X5205,X5205,hAPP(X5205,fun(X5205,X5205),times_times(X5205),one_one(X5205)),X5206) = ti(X5205,X5206) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_594_mult__1])])]) ).
fof(i_0_1466,plain,
! [X5314,X5315] :
( ~ comm_semiring_1(X5314)
| hAPP(X5314,X5314,hAPP(X5314,fun(X5314,X5314),times_times(X5314),one_one(X5314)),X5315) = ti(X5314,X5315) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])])]) ).
fof(i_0_1467,plain,
! [X5207,X5208] :
( ~ monoid_mult(X5207)
| hAPP(X5207,X5207,hAPP(X5207,fun(X5207,X5207),times_times(X5207),one_one(X5207)),X5208) = ti(X5207,X5208) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_595_mult__1__left])])]) ).
fof(i_0_1468,plain,
! [X5105,X5106] :
( ~ comm_semiring_1(X5105)
| hAPP(X5105,X5105,hAPP(X5105,fun(X5105,X5105),plus_plus(X5105),zero_zero(X5105)),X5106) = ti(X5105,X5106) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).
fof(i_0_1469,plain,
! [X4880,X4881] :
( ~ comm_monoid_add(X4880)
| hAPP(X4880,X4880,hAPP(X4880,fun(X4880,X4880),plus_plus(X4880),zero_zero(X4880)),X4881) = ti(X4880,X4881) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_468_add__0])])]) ).
fof(i_0_1470,plain,
! [X4882,X4883] :
( ~ monoid_add(X4882)
| hAPP(X4882,X4882,hAPP(X4882,fun(X4882,X4882),plus_plus(X4882),zero_zero(X4882)),X4883) = ti(X4882,X4883) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_469_add__0__left])])]) ).
fof(i_0_1471,plain,
! [X5201,X5202] :
( ~ comm_monoid_mult(X5201)
| hAPP(X5201,X5201,hAPP(X5201,fun(X5201,X5201),times_times(X5201),X5202),one_one(X5201)) = ti(X5201,X5202) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_592_mult_Ocomm__neutral])])]) ).
fof(i_0_1472,plain,
! [X5316,X5317] :
( ~ comm_semiring_1(X5316)
| hAPP(X5316,X5316,hAPP(X5316,fun(X5316,X5316),times_times(X5316),X5317),one_one(X5316)) = ti(X5316,X5317) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])]) ).
fof(i_0_1473,plain,
! [X5203,X5204] :
( ~ monoid_mult(X5203)
| hAPP(X5203,X5203,hAPP(X5203,fun(X5203,X5203),times_times(X5203),X5204),one_one(X5203)) = ti(X5203,X5204) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_593_mult__1__right])])]) ).
fof(i_0_1474,plain,
! [X5134,X5135] :
( ~ comm_semiring_1(X5134)
| hAPP(X5134,X5134,hAPP(X5134,fun(X5134,X5134),plus_plus(X5134),X5135),zero_zero(X5134)) = ti(X5134,X5135) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])]) ).
fof(i_0_1475,plain,
! [X4874,X4875] :
( ~ comm_monoid_add(X4874)
| hAPP(X4874,X4874,hAPP(X4874,fun(X4874,X4874),plus_plus(X4874),X4875),zero_zero(X4874)) = ti(X4874,X4875) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_465_add_Ocomm__neutral])])]) ).
fof(i_0_1476,plain,
! [X4876,X4877] :
( ~ monoid_add(X4876)
| hAPP(X4876,X4876,hAPP(X4876,fun(X4876,X4876),plus_plus(X4876),X4877),zero_zero(X4876)) = ti(X4876,X4877) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_466_add__0__right])])]) ).
fof(i_0_1477,plain,
! [X4892,X4893] :
( ~ group_add(X4892)
| hAPP(X4892,X4892,hAPP(X4892,fun(X4892,X4892),minus_minus(X4892),X4893),zero_zero(X4892)) = ti(X4892,X4893) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_473_diff__0__right])])]) ).
fof(i_0_1478,plain,
! [X5238,X5239] :
( ~ ab_sem1668676832m_mult(X5238)
| hAPP(X5238,X5238,hAPP(X5238,fun(X5238,X5238),times_times(X5238),X5239),X5239) = ti(X5238,X5239) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_607_mult__idem])])]) ).
fof(i_0_1479,plain,
! [X5236,X5237] :
( ~ ab_sem1668676832m_mult(X5236)
| hAPP(X5236,X5236,hAPP(X5236,fun(X5236,X5236),times_times(X5236),X5237),X5237) = ti(X5236,X5237) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_606_times_Oidem])])]) ).
fof(i_0_1480,plain,
! [X6306,X6307] : ti(X6306,ti(X6306,X6307)) = ti(X6306,X6307),
inference(variable_rename,[status(thm)],[help_ti_idem]) ).
fof(i_0_1481,plain,
! [X3218,X3219] : ti(fun(fun(X3218,fun(X3219,X3219)),bool),finite_comp_fun_idem(X3218,X3219)) = finite_comp_fun_idem(X3218,X3219),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ocomp__fun__idem_res]) ).
fof(i_0_1482,plain,
! [X3265,X3266,X3267,X3268] : hAPP(X3265,X3266,X3267,ti(X3265,X3268)) = hAPP(X3265,X3266,X3267,X3268),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).
fof(i_0_1483,plain,
! [X3269,X3270,X3271,X3272] : ti(X3269,hAPP(X3270,X3269,X3271,X3272)) = hAPP(X3270,X3269,X3271,X3272),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
fof(i_0_1484,plain,
! [X3243] : ti(fun(bool,fun(X3243,fun(X3243,X3243))),if(X3243)) = if(X3243),
inference(variable_rename,[status(thm)],[tsy_c_If_res]) ).
fof(i_0_1485,plain,
! [X3252] : ti(fun(X3252,fun(fun(X3252,bool),X3252)),partial_flat_lub(X3252)) = partial_flat_lub(X3252),
inference(variable_rename,[status(thm)],[tsy_c_Partial__Function_Oflat__lub_res]) ).
fof(i_0_1486,plain,
! [X3274] : ti(fun(X3274,fun(fun(X3274,bool),bool)),member(X3274)) = member(X3274),
inference(variable_rename,[status(thm)],[tsy_c_member_res]) ).
fof(i_0_1487,plain,
! [X1,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X8) = zero_zero(nat) ),
inference(fof_simplification,[status(thm)],[fact_517_card__infinite]) ).
fof(i_0_1488,hypothesis,
! [X3273] :
( ( ~ hBOOL(ti(bool,X3273))
| hBOOL(X3273) )
& ( ~ hBOOL(X3273)
| hBOOL(ti(bool,X3273)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1])]) ).
fof(i_0_1489,plain,
! [X122] :
( ~ hBOOL(hAPP(bool,bool,fNot,X122))
| ~ hBOOL(X122) ),
inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).
fof(i_0_1490,plain,
! [X3253] : ti(fun(fun(X3253,bool),fun(X3253,bool)),collect(X3253)) = collect(X3253),
inference(variable_rename,[status(thm)],[tsy_c_Set_OCollect_res]) ).
fof(i_0_1491,plain,
! [X6206,X6207] :
( ( hAPP(X6206,X6206,abs_abs(X6206),X6207) != zero_zero(X6206)
| ti(X6206,X6207) = zero_zero(X6206)
| ~ ordere142940540dd_abs(X6206) )
& ( ti(X6206,X6207) != zero_zero(X6206)
| hAPP(X6206,X6206,abs_abs(X6206),X6207) = zero_zero(X6206)
| ~ ordere142940540dd_abs(X6206) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_929_abs__eq__0])])])]) ).
fof(i_0_1492,plain,
! [X3497,X3498] : hAPP(fun(X3497,bool),fun(X3497,bool),collect(X3497),X3498) = ti(fun(X3497,bool),X3498),
inference(variable_rename,[status(thm)],[fact_76_Collect__def]) ).
fof(i_0_1493,plain,
! [X3212,X3213] : ti(fun(X3212,fun(X3213,X3212)),combk(X3212,X3213)) = combk(X3212,X3213),
inference(variable_rename,[status(thm)],[tsy_c_COMBK_res]) ).
fof(i_0_1494,plain,
! [X3239] :
( ~ mult_zero(X3239)
| ti(fun(X3239,fun(X3239,X3239)),times_times(X3239)) = times_times(X3239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_4_res])]) ).
fof(i_0_1495,plain,
! [X3238] :
( ~ no_zero_divisors(X3238)
| ti(fun(X3238,fun(X3238,X3238)),times_times(X3238)) = times_times(X3238) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_3_res])]) ).
fof(i_0_1496,plain,
! [X3237] :
( ~ semiring(X3237)
| ti(fun(X3237,fun(X3237,X3237)),times_times(X3237)) = times_times(X3237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_2_res])]) ).
fof(i_0_1497,plain,
! [X3236] :
( ~ monoid_mult(X3236)
| ti(fun(X3236,fun(X3236,X3236)),times_times(X3236)) = times_times(X3236) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_1_res])]) ).
fof(i_0_1498,plain,
! [X3235] :
( ~ ab_semigroup_mult(X3235)
| ti(fun(X3235,fun(X3235,X3235)),times_times(X3235)) = times_times(X3235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_0_res])]) ).
fof(i_0_1499,plain,
! [X3234] :
( ~ ab_semigroup_add(X3234)
| ti(fun(X3234,fun(X3234,X3234)),plus_plus(X3234)) = plus_plus(X3234) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_2_res])]) ).
fof(i_0_1500,plain,
! [X3233] :
( ~ cancel_semigroup_add(X3233)
| ti(fun(X3233,fun(X3233,X3233)),plus_plus(X3233)) = plus_plus(X3233) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_1_res])]) ).
fof(i_0_1501,plain,
! [X3232] :
( ~ monoid_add(X3232)
| ti(fun(X3232,fun(X3232,X3232)),plus_plus(X3232)) = plus_plus(X3232) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_0_res])]) ).
fof(i_0_1502,plain,
! [X3230] :
( ~ minus(X3230)
| ti(fun(X3230,fun(X3230,X3230)),minus_minus(X3230)) = minus_minus(X3230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ominus__class_Ominus_res])]) ).
fof(i_0_1503,plain,
! [X3251] :
( ~ ord(X3251)
| ti(fun(X3251,fun(X3251,bool)),ord_less_eq(X3251)) = ord_less_eq(X3251) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res])]) ).
fof(i_0_1504,plain,
! [X3250] :
( ~ ord(X3250)
| ti(fun(X3250,fun(X3250,bool)),ord_less(X3250)) = ord_less(X3250) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_res])]) ).
fof(i_0_1505,plain,
! [X3257] : ti(fun(fun(X3257,bool),X3257),the_elem(X3257)) = the_elem(X3257),
inference(variable_rename,[status(thm)],[tsy_c_Set_Othe__elem_res]) ).
fof(i_0_1506,plain,
! [X3241] : ti(fun(fun(X3241,bool),X3241),the(X3241)) = the(X3241),
inference(variable_rename,[status(thm)],[tsy_c_HOL_OThe_res]) ).
fof(i_0_1507,plain,
! [X3260] : ti(fun(X3260,fun(X3260,bool)),fequal(X3260)) = fequal(X3260),
inference(variable_rename,[status(thm)],[tsy_c_fequal_res]) ).
fof(i_0_1508,plain,
! [X3217] : ti(fun(fun(X3217,bool),nat),finite_card(X3217)) = finite_card(X3217),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).
fof(i_0_1509,plain,
! [X3220] : ti(fun(fun(X3220,bool),bool),finite_finite(X3220)) = finite_finite(X3220),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).
fof(i_0_1510,plain,
! [X6353] :
( ti(bool,X6353) = fTrue
| ti(bool,X6353) = fFalse ),
inference(variable_rename,[status(thm)],[help_fFalse_1_1_T]) ).
fof(i_0_1511,plain,
! [X6314] :
( ti(bool,X6314) = fTrue
| ti(bool,X6314) = fFalse ),
inference(variable_rename,[status(thm)],[help_If_3_1_T]) ).
fof(i_0_1512,plain,
! [X3229] :
( ~ ordere142940540dd_abs(X3229)
| ti(fun(X3229,X3229),abs_abs(X3229)) = abs_abs(X3229) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oabs__class_Oabs_res])]) ).
fof(i_0_1513,plain,
! [X3211] : ti(fun(X3211,X3211),combi(X3211)) = combi(X3211),
inference(variable_rename,[status(thm)],[tsy_c_COMBI_res]) ).
fof(i_0_1514,plain,
! [X3244] :
( ~ number(X3244)
| ti(fun(int,X3244),number_number_of(X3244)) = number_number_of(X3244) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Int_Onumber__class_Onumber__of_res])]) ).
fof(i_0_1515,plain,
! [X3247] :
( ~ semiring_1(X3247)
| ti(fun(nat,X3247),semiring_1_of_nat(X3247)) = semiring_1_of_nat(X3247) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Nat_Osemiring__1__class_Oof__nat_res])]) ).
fof(i_0_1516,plain,
! [X3245] :
( ~ ring_1(X3245)
| ti(fun(X3245,bool),ring_1_Ints(X3245)) = ring_1_Ints(X3245) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Int_Oring__1__class_OInts_res])]) ).
fof(i_0_1517,plain,
! [X3249] :
( ~ bot(X3249)
| ti(X3249,bot_bot(X3249)) = bot_bot(X3249) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Obot__class_Obot_res])]) ).
fof(i_0_1518,plain,
! [X3240] :
( ~ zero(X3240)
| ti(X3240,zero_zero(X3240)) = zero_zero(X3240) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ozero__class_Ozero_res])]) ).
fof(i_0_1519,plain,
! [X3231] :
( ~ one(X3231)
| ti(X3231,one_one(X3231)) = one_one(X3231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_res])]) ).
fof(i_0_1520,plain,
! [X3242] : ti(X3242,undefined(X3242)) = undefined(X3242),
inference(variable_rename,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).
cnf(i_0_1521,plain,
( hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10) = hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9))
| hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != ti(X2,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X8,esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X10))
| hAPP(X2,X1,X3,hAPP(X1,X2,X8,esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != ti(X1,esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X10))
| ~ comm_monoid_mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1215]) ).
cnf(i_0_1522,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1216]) ).
cnf(i_0_1523,plain,
( hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10) = hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10)),X9))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9))
| hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != ti(X2,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X10))
| ~ comm_monoid_mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1215]) ).
cnf(i_0_1524,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk142_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X10))
| hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X6),X4),X10) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X5),X4),X9)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X8,esk141_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))),X10))
| hAPP(X1,X2,X7,hAPP(X2,X1,X8,esk141_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))) != ti(X2,esk141_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
| ~ comm_monoid_mult(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1215]) ).
fof(i_0_1525,plain,
! [X6112,X6113,X6114,X6115,X6116,X6117,X6118] :
( ( hBOOL(hAPP(fun(X6112,bool),bool,hAPP(X6112,fun(fun(X6112,bool),bool),member(X6112),esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),X6116))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6114),X6118),X6116)),hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6115),X6118),X6116)))
| ~ hBOOL(hAPP(fun(X6112,bool),bool,finite_finite(X6112),X6116))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,esk136_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk138_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,X6118),X6118))
| ~ comm_monoid_mult(X6113) )
& ( ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(X6112,X6113,X6114,esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))),hAPP(X6112,X6113,X6115,esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6114),X6118),X6116)),hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6115),X6118),X6116)))
| ~ hBOOL(hAPP(fun(X6112,bool),bool,finite_finite(X6112),X6116))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,esk136_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk138_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,X6118),X6118))
| ~ comm_monoid_mult(X6113) )
& ( hBOOL(hAPP(fun(X6112,bool),bool,hAPP(X6112,fun(fun(X6112,bool),bool),member(X6112),esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),X6116))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6114),X6118),X6116)),hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6115),X6118),X6116)))
| ~ hBOOL(hAPP(fun(X6112,bool),bool,finite_finite(X6112),X6116))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,esk137_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk139_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,X6118),X6118))
| ~ comm_monoid_mult(X6113) )
& ( ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(X6112,X6113,X6114,esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))),hAPP(X6112,X6113,X6115,esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6114),X6118),X6116)),hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6115),X6118),X6116)))
| ~ hBOOL(hAPP(fun(X6112,bool),bool,finite_finite(X6112),X6116))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,esk137_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk139_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,X6118),X6118))
| ~ comm_monoid_mult(X6113) )
& ( hBOOL(hAPP(fun(X6112,bool),bool,hAPP(X6112,fun(fun(X6112,bool),bool),member(X6112),esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),X6116))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6114),X6118),X6116)),hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6115),X6118),X6116)))
| ~ hBOOL(hAPP(fun(X6112,bool),bool,finite_finite(X6112),X6116))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(X6113,X6113,hAPP(X6113,fun(X6113,X6113),times_times(X6113),esk136_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk137_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))),hAPP(X6113,X6113,hAPP(X6113,fun(X6113,X6113),times_times(X6113),esk138_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk139_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,X6118),X6118))
| ~ comm_monoid_mult(X6113) )
& ( ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(X6112,X6113,X6114,esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))),hAPP(X6112,X6113,X6115,esk140_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))))
| hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6114),X6118),X6116)),hAPP(fun(X6112,bool),X6113,hAPP(X6113,fun(fun(X6112,bool),X6113),hAPP(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113)),hAPP(fun(X6113,fun(X6113,X6113)),fun(fun(X6112,X6113),fun(X6113,fun(fun(X6112,bool),X6113))),finite_fold_image(X6113,X6112),times_times(X6113)),X6115),X6118),X6116)))
| ~ hBOOL(hAPP(fun(X6112,bool),bool,finite_finite(X6112),X6116))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,hAPP(X6113,X6113,hAPP(X6113,fun(X6113,X6113),times_times(X6113),esk136_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk137_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))),hAPP(X6113,X6113,hAPP(X6113,fun(X6113,X6113),times_times(X6113),esk138_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118)),esk139_7(X6112,X6113,X6114,X6115,X6116,X6117,X6118))))
| ~ hBOOL(hAPP(X6113,bool,hAPP(X6113,fun(X6113,bool),X6117,X6118),X6118))
| ~ comm_monoid_mult(X6113) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_897_fold__image__related])])])])]) ).
fof(i_0_1526,plain,
! [X5048,X5049] :
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X5049))
| hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X5049))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X5048))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X5049))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X5048))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_541_card__less__Suc])]) ).
fof(i_0_1527,plain,
! [X6138,X6139,X6140] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X6140))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X6138),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X6138),X6139))),one_one(int))),X6140))),X6139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_900_decr__lemma])]) ).
fof(i_0_1528,plain,
! [X3400,X3401,X3402,X3403] :
( ( hBOOL(hAPP(fun(X3401,bool),bool,hAPP(X3401,fun(fun(X3401,bool),bool),member(X3401),esk3_4(X3400,X3401,X3402,X3403)),X3403))
| ~ hBOOL(hAPP(fun(X3400,bool),bool,finite_finite(X3400),hAPP(fun(X3401,bool),fun(X3400,bool),hAPP(fun(X3401,X3400),fun(fun(X3401,bool),fun(X3400,bool)),image(X3401,X3400),X3402),X3403)))
| hBOOL(hAPP(fun(X3401,bool),bool,finite_finite(X3401),X3403)) )
& ( ~ hBOOL(hAPP(fun(X3401,bool),bool,finite_finite(X3401),hAPP(fun(X3401,bool),fun(X3401,bool),collect(X3401),hAPP(fun(X3401,bool),fun(X3401,bool),hAPP(fun(X3401,fun(bool,bool)),fun(fun(X3401,bool),fun(X3401,bool)),combs(X3401,bool,bool),hAPP(fun(X3401,bool),fun(X3401,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3401,bool),fun(X3401,fun(bool,bool))),combb(bool,fun(bool,bool),X3401),fconj),hAPP(fun(X3401,bool),fun(X3401,bool),hAPP(fun(X3401,fun(fun(X3401,bool),bool)),fun(fun(X3401,bool),fun(X3401,bool)),combc(X3401,fun(X3401,bool),bool),member(X3401)),X3403))),hAPP(X3400,fun(X3401,bool),hAPP(fun(X3401,fun(X3400,bool)),fun(X3400,fun(X3401,bool)),combc(X3401,X3400,bool),hAPP(fun(X3401,X3400),fun(X3401,fun(X3400,bool)),hAPP(fun(X3400,fun(X3400,bool)),fun(fun(X3401,X3400),fun(X3401,fun(X3400,bool))),combb(X3400,fun(X3400,bool),X3401),fequal(X3400)),X3402)),hAPP(X3401,X3400,X3402,esk3_4(X3400,X3401,X3402,X3403)))))))
| ~ hBOOL(hAPP(fun(X3400,bool),bool,finite_finite(X3400),hAPP(fun(X3401,bool),fun(X3400,bool),hAPP(fun(X3401,X3400),fun(fun(X3401,bool),fun(X3400,bool)),image(X3401,X3400),X3402),X3403)))
| hBOOL(hAPP(fun(X3401,bool),bool,finite_finite(X3401),X3403)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1217])])])]) ).
fof(i_0_1529,plain,
! [X5052,X5053] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X5053))
| hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X5053))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X5052)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X5053))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X5052))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1218])]) ).
fof(i_0_1530,plain,
! [X6235,X6236,X6237,X6238] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6238),esk148_4(X6235,X6236,X6237,X6238)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6238),esk147_4(X6235,X6236,X6237,X6238))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk148_4(X6235,X6236,X6237,X6238)),X6237))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6238),esk147_4(X6235,X6236,X6237,X6238))) )
& ( hAPP(nat,int,X6236,esk148_4(X6235,X6236,X6237,X6238)) = X6235
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6238),esk147_4(X6235,X6236,X6237,X6238))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6238),esk148_4(X6235,X6236,X6237,X6238)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk147_4(X6235,X6236,X6237,X6238)),X6237)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk148_4(X6235,X6236,X6237,X6238)),X6237))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk147_4(X6235,X6236,X6237,X6238)),X6237)) )
& ( hAPP(nat,int,X6236,esk148_4(X6235,X6236,X6237,X6238)) = X6235
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk147_4(X6235,X6236,X6237,X6238)),X6237)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6238),esk148_4(X6235,X6236,X6237,X6238)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X6236,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk147_4(X6235,X6236,X6237,X6238)),one_one(nat)))),hAPP(nat,int,X6236,esk147_4(X6235,X6236,X6237,X6238))))),one_one(int))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk148_4(X6235,X6236,X6237,X6238)),X6237))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X6236,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk147_4(X6235,X6236,X6237,X6238)),one_one(nat)))),hAPP(nat,int,X6236,esk147_4(X6235,X6236,X6237,X6238))))),one_one(int))) )
& ( hAPP(nat,int,X6236,esk148_4(X6235,X6236,X6237,X6238)) = X6235
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6235),hAPP(nat,int,X6236,X6237)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6236,X6238)),X6235))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6238),X6237))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X6236,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk147_4(X6235,X6236,X6237,X6238)),one_one(nat)))),hAPP(nat,int,X6236,esk147_4(X6235,X6236,X6237,X6238))))),one_one(int))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_942_nat__intermed__int__val])])])]) ).
cnf(i_0_1531,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk34_7(X1,X2,X3,X4,X5,X6,X7)),X3))
| hAPP(fun(X1,bool),X2,X7,X3) = ti(X2,X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X4),X5),X6),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1219]) ).
fof(i_0_1532,plain,
! [X6230,X6231,X6232] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk146_3(X6230,X6231,X6232)),X6232))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6230),hAPP(nat,int,X6231,X6232)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6231,zero_zero(nat))),X6230))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk145_3(X6230,X6231,X6232)),X6232)) )
& ( hAPP(nat,int,X6231,esk146_3(X6230,X6231,X6232)) = X6230
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6230),hAPP(nat,int,X6231,X6232)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6231,zero_zero(nat))),X6230))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk145_3(X6230,X6231,X6232)),X6232)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk146_3(X6230,X6231,X6232)),X6232))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6230),hAPP(nat,int,X6231,X6232)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6231,zero_zero(nat))),X6230))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X6231,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk145_3(X6230,X6231,X6232)),one_one(nat)))),hAPP(nat,int,X6231,esk145_3(X6230,X6231,X6232))))),one_one(int))) )
& ( hAPP(nat,int,X6231,esk146_3(X6230,X6231,X6232)) = X6230
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6230),hAPP(nat,int,X6231,X6232)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6231,zero_zero(nat))),X6230))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X6231,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk145_3(X6230,X6231,X6232)),one_one(nat)))),hAPP(nat,int,X6231,esk145_3(X6230,X6231,X6232))))),one_one(int))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_941_nat0__intermed__int__val])])])]) ).
fof(i_0_1533,plain,
! [X6225,X6226,X6227] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk144_3(X6225,X6226,X6227)),X6227))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6225),hAPP(nat,int,X6226,X6227)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6226,zero_zero(nat))),X6225))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk143_3(X6225,X6226,X6227)),X6227)) )
& ( hAPP(nat,int,X6226,esk144_3(X6225,X6226,X6227)) = X6225
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6225),hAPP(nat,int,X6226,X6227)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6226,zero_zero(nat))),X6225))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk143_3(X6225,X6226,X6227)),X6227)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk144_3(X6225,X6226,X6227)),X6227))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6225),hAPP(nat,int,X6226,X6227)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6226,zero_zero(nat))),X6225))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X6226,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk143_3(X6225,X6226,X6227)),one_one(nat)))),hAPP(nat,int,X6226,esk143_3(X6225,X6226,X6227))))),one_one(int))) )
& ( hAPP(nat,int,X6226,esk144_3(X6225,X6226,X6227)) = X6225
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6225),hAPP(nat,int,X6226,X6227)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X6226,zero_zero(nat))),X6225))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X6226,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk143_3(X6225,X6226,X6227)),one_one(nat)))),hAPP(nat,int,X6226,esk143_3(X6225,X6226,X6227))))),one_one(int))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_940_int__val__lemma])])])]) ).
fof(i_0_1534,plain,
! [X4317,X4318,X4319,X4320] :
( ~ hBOOL(hAPP(fun(X4317,bool),bool,finite_finite(X4317),X4320))
| ~ hBOOL(hAPP(fun(X4317,bool),bool,hAPP(X4317,fun(fun(X4317,bool),bool),member(X4317),X4319),X4320))
| ~ hBOOL(hAPP(fun(X4317,bool),bool,hAPP(X4317,fun(fun(X4317,bool),bool),member(X4317),X4318),X4320))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X4317,bool),nat,finite_card(X4317),hAPP(fun(X4317,bool),fun(X4317,bool),hAPP(fun(X4317,bool),fun(fun(X4317,bool),fun(X4317,bool)),minus_minus(fun(X4317,bool)),hAPP(fun(X4317,bool),fun(X4317,bool),hAPP(fun(X4317,bool),fun(fun(X4317,bool),fun(X4317,bool)),minus_minus(fun(X4317,bool)),X4320),hAPP(fun(X4317,bool),fun(X4317,bool),hAPP(X4317,fun(fun(X4317,bool),fun(X4317,bool)),insert(X4317),X4319),bot_bot(fun(X4317,bool))))),hAPP(fun(X4317,bool),fun(X4317,bool),hAPP(X4317,fun(fun(X4317,bool),fun(X4317,bool)),insert(X4317),X4318),bot_bot(fun(X4317,bool)))))),hAPP(fun(X4317,bool),nat,finite_card(X4317),X4320))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_292_card__Diff2__less])]) ).
fof(i_0_1535,plain,
! [X6222,X6223,X6224] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X6224))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6222),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6223),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X6223),X6222))),one_one(int))),X6224)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_939_incr__lemma])]) ).
fof(i_0_1536,plain,
! [X5641,X5642,X5643,X5644,X5645,X5646] :
( ( ~ hBOOL(hAPP(X5641,bool,hAPP(X5641,fun(X5641,bool),ord_less_eq(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),plus_plus(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),times_times(X5641),X5642),X5643)),X5644)),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),plus_plus(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),times_times(X5641),X5645),X5643)),X5646)))
| hBOOL(hAPP(X5641,bool,hAPP(X5641,fun(X5641,bool),ord_less_eq(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),plus_plus(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),times_times(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),minus_minus(X5641),X5642),X5645)),X5643)),X5644)),X5646))
| ~ ordered_ring(X5641) )
& ( ~ hBOOL(hAPP(X5641,bool,hAPP(X5641,fun(X5641,bool),ord_less_eq(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),plus_plus(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),times_times(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),minus_minus(X5641),X5642),X5645)),X5643)),X5644)),X5646))
| hBOOL(hAPP(X5641,bool,hAPP(X5641,fun(X5641,bool),ord_less_eq(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),plus_plus(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),times_times(X5641),X5642),X5643)),X5644)),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),plus_plus(X5641),hAPP(X5641,X5641,hAPP(X5641,fun(X5641,X5641),times_times(X5641),X5645),X5643)),X5646)))
| ~ ordered_ring(X5641) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_726_le__add__iff1])])])]) ).
fof(i_0_1537,plain,
! [X5653,X5654,X5655,X5656,X5657,X5658] :
( ( ~ hBOOL(hAPP(X5653,bool,hAPP(X5653,fun(X5653,bool),ord_less(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),plus_plus(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),times_times(X5653),X5654),X5655)),X5656)),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),plus_plus(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),times_times(X5653),X5657),X5655)),X5658)))
| hBOOL(hAPP(X5653,bool,hAPP(X5653,fun(X5653,bool),ord_less(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),plus_plus(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),times_times(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),minus_minus(X5653),X5654),X5657)),X5655)),X5656)),X5658))
| ~ ordered_ring(X5653) )
& ( ~ hBOOL(hAPP(X5653,bool,hAPP(X5653,fun(X5653,bool),ord_less(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),plus_plus(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),times_times(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),minus_minus(X5653),X5654),X5657)),X5655)),X5656)),X5658))
| hBOOL(hAPP(X5653,bool,hAPP(X5653,fun(X5653,bool),ord_less(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),plus_plus(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),times_times(X5653),X5654),X5655)),X5656)),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),plus_plus(X5653),hAPP(X5653,X5653,hAPP(X5653,fun(X5653,X5653),times_times(X5653),X5657),X5655)),X5658)))
| ~ ordered_ring(X5653) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_728_less__add__iff1])])])]) ).
fof(i_0_1538,plain,
! [X5809,X5810,X5811,X5812,X5813] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5813),X5809)),X5810)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5812),X5809)),X5811)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5813),X5812)),X5809)),X5810)),X5811))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5812),X5813)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5813),X5812)),X5809)),X5810)),X5811))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5813),X5809)),X5810)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5812),X5809)),X5811)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5812),X5813)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_789_nat__le__add__iff1])])]) ).
fof(i_0_1539,plain,
! [X5839,X5840,X5841,X5842,X5843] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5843),X5839)),X5840)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5842),X5839)),X5841)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5843),X5842)),X5839)),X5840)),X5841))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5842),X5843)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5843),X5842)),X5839)),X5840)),X5841))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5843),X5839)),X5840)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5842),X5839)),X5841)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5842),X5843)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_795_nat__less__add__iff1])])]) ).
fof(i_0_1540,plain,
! [X4755,X4756,X4757,X4758,X4759,X4760] :
( ( hBOOL(hAPP(X4755,bool,hAPP(X4755,fun(X4755,bool),ord_less_eq(X4755),esk65_6(X4755,X4756,X4757,X4758,X4759,X4760)),esk64_6(X4755,X4756,X4757,X4758,X4759,X4760)))
| hBOOL(hAPP(X4756,bool,hAPP(X4756,fun(X4756,bool),ord_less(X4756),hAPP(X4755,X4756,X4758,X4757)),X4760))
| ~ hBOOL(hAPP(X4755,bool,hAPP(X4755,fun(X4755,bool),ord_less_eq(X4755),X4757),X4759))
| ~ hBOOL(hAPP(X4756,bool,hAPP(X4756,fun(X4756,bool),ord_less(X4756),hAPP(X4755,X4756,X4758,X4759)),X4760))
| ~ order(X4756)
| ~ order(X4755) )
& ( ~ hBOOL(hAPP(X4756,bool,hAPP(X4756,fun(X4756,bool),ord_less_eq(X4756),hAPP(X4755,X4756,X4758,esk65_6(X4755,X4756,X4757,X4758,X4759,X4760))),hAPP(X4755,X4756,X4758,esk64_6(X4755,X4756,X4757,X4758,X4759,X4760))))
| hBOOL(hAPP(X4756,bool,hAPP(X4756,fun(X4756,bool),ord_less(X4756),hAPP(X4755,X4756,X4758,X4757)),X4760))
| ~ hBOOL(hAPP(X4755,bool,hAPP(X4755,fun(X4755,bool),ord_less_eq(X4755),X4757),X4759))
| ~ hBOOL(hAPP(X4756,bool,hAPP(X4756,fun(X4756,bool),ord_less(X4756),hAPP(X4755,X4756,X4758,X4759)),X4760))
| ~ order(X4756)
| ~ order(X4755) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_435_xt4])])])])]) ).
fof(i_0_1541,plain,
! [X4747,X4748,X4749,X4750,X4751,X4752] :
( ( hBOOL(hAPP(X4747,bool,hAPP(X4747,fun(X4747,bool),ord_less(X4747),esk63_6(X4747,X4748,X4749,X4750,X4751,X4752)),esk62_6(X4747,X4748,X4749,X4750,X4751,X4752)))
| hBOOL(hAPP(X4748,bool,hAPP(X4748,fun(X4748,bool),ord_less(X4748),hAPP(X4747,X4748,X4750,X4749)),X4752))
| ~ hBOOL(hAPP(X4747,bool,hAPP(X4747,fun(X4747,bool),ord_less(X4747),X4749),X4751))
| ~ hBOOL(hAPP(X4748,bool,hAPP(X4748,fun(X4748,bool),ord_less_eq(X4748),hAPP(X4747,X4748,X4750,X4751)),X4752))
| ~ order(X4748)
| ~ ord(X4747) )
& ( ~ hBOOL(hAPP(X4748,bool,hAPP(X4748,fun(X4748,bool),ord_less(X4748),hAPP(X4747,X4748,X4750,esk63_6(X4747,X4748,X4749,X4750,X4751,X4752))),hAPP(X4747,X4748,X4750,esk62_6(X4747,X4748,X4749,X4750,X4751,X4752))))
| hBOOL(hAPP(X4748,bool,hAPP(X4748,fun(X4748,bool),ord_less(X4748),hAPP(X4747,X4748,X4750,X4749)),X4752))
| ~ hBOOL(hAPP(X4747,bool,hAPP(X4747,fun(X4747,bool),ord_less(X4747),X4749),X4751))
| ~ hBOOL(hAPP(X4748,bool,hAPP(X4748,fun(X4748,bool),ord_less_eq(X4748),hAPP(X4747,X4748,X4750,X4751)),X4752))
| ~ order(X4748)
| ~ ord(X4747) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_434_xt6])])])])]) ).
fof(i_0_1542,plain,
! [X4804,X4805,X4806,X4807,X4808,X4809] :
( ( hBOOL(hAPP(X4804,bool,hAPP(X4804,fun(X4804,bool),ord_less_eq(X4804),esk76_6(X4804,X4805,X4806,X4807,X4808,X4809)),esk77_6(X4804,X4805,X4806,X4807,X4808,X4809)))
| hBOOL(hAPP(X4805,bool,hAPP(X4805,fun(X4805,bool),ord_less(X4805),hAPP(X4804,X4805,X4806,X4808)),X4807))
| ~ hBOOL(hAPP(X4805,bool,hAPP(X4805,fun(X4805,bool),ord_less(X4805),hAPP(X4804,X4805,X4806,X4809)),X4807))
| ~ hBOOL(hAPP(X4804,bool,hAPP(X4804,fun(X4804,bool),ord_less_eq(X4804),X4808),X4809))
| ~ order(X4805)
| ~ order(X4804) )
& ( ~ hBOOL(hAPP(X4805,bool,hAPP(X4805,fun(X4805,bool),ord_less_eq(X4805),hAPP(X4804,X4805,X4806,esk76_6(X4804,X4805,X4806,X4807,X4808,X4809))),hAPP(X4804,X4805,X4806,esk77_6(X4804,X4805,X4806,X4807,X4808,X4809))))
| hBOOL(hAPP(X4805,bool,hAPP(X4805,fun(X4805,bool),ord_less(X4805),hAPP(X4804,X4805,X4806,X4808)),X4807))
| ~ hBOOL(hAPP(X4805,bool,hAPP(X4805,fun(X4805,bool),ord_less(X4805),hAPP(X4804,X4805,X4806,X4809)),X4807))
| ~ hBOOL(hAPP(X4804,bool,hAPP(X4804,fun(X4804,bool),ord_less_eq(X4804),X4808),X4809))
| ~ order(X4805)
| ~ order(X4804) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_442_order__le__less__subst2])])])])]) ).
fof(i_0_1543,plain,
! [X4812,X4813,X4814,X4815,X4816,X4817] :
( ( hBOOL(hAPP(X4812,bool,hAPP(X4812,fun(X4812,bool),ord_less(X4812),esk78_6(X4812,X4813,X4814,X4815,X4816,X4817)),esk79_6(X4812,X4813,X4814,X4815,X4816,X4817)))
| hBOOL(hAPP(X4813,bool,hAPP(X4813,fun(X4813,bool),ord_less(X4813),hAPP(X4812,X4813,X4814,X4816)),X4815))
| ~ hBOOL(hAPP(X4813,bool,hAPP(X4813,fun(X4813,bool),ord_less_eq(X4813),hAPP(X4812,X4813,X4814,X4817)),X4815))
| ~ hBOOL(hAPP(X4812,bool,hAPP(X4812,fun(X4812,bool),ord_less(X4812),X4816),X4817))
| ~ order(X4813)
| ~ order(X4812) )
& ( ~ hBOOL(hAPP(X4813,bool,hAPP(X4813,fun(X4813,bool),ord_less(X4813),hAPP(X4812,X4813,X4814,esk78_6(X4812,X4813,X4814,X4815,X4816,X4817))),hAPP(X4812,X4813,X4814,esk79_6(X4812,X4813,X4814,X4815,X4816,X4817))))
| hBOOL(hAPP(X4813,bool,hAPP(X4813,fun(X4813,bool),ord_less(X4813),hAPP(X4812,X4813,X4814,X4816)),X4815))
| ~ hBOOL(hAPP(X4813,bool,hAPP(X4813,fun(X4813,bool),ord_less_eq(X4813),hAPP(X4812,X4813,X4814,X4817)),X4815))
| ~ hBOOL(hAPP(X4812,bool,hAPP(X4812,fun(X4812,bool),ord_less(X4812),X4816),X4817))
| ~ order(X4813)
| ~ order(X4812) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_443_order__less__le__subst2])])])])]) ).
fof(i_0_1544,plain,
! [X4796,X4797,X4798,X4799,X4800,X4801] :
( ( hBOOL(hAPP(X4797,bool,hAPP(X4797,fun(X4797,bool),ord_less_eq(X4797),esk75_6(X4796,X4797,X4798,X4799,X4800,X4801)),esk74_6(X4796,X4797,X4798,X4799,X4800,X4801)))
| hBOOL(hAPP(X4796,bool,hAPP(X4796,fun(X4796,bool),ord_less(X4796),X4798),hAPP(X4797,X4796,X4799,X4801)))
| ~ hBOOL(hAPP(X4796,bool,hAPP(X4796,fun(X4796,bool),ord_less(X4796),X4798),hAPP(X4797,X4796,X4799,X4800)))
| ~ hBOOL(hAPP(X4797,bool,hAPP(X4797,fun(X4797,bool),ord_less_eq(X4797),X4800),X4801))
| ~ order(X4797)
| ~ order(X4796) )
& ( ~ hBOOL(hAPP(X4796,bool,hAPP(X4796,fun(X4796,bool),ord_less_eq(X4796),hAPP(X4797,X4796,X4799,esk75_6(X4796,X4797,X4798,X4799,X4800,X4801))),hAPP(X4797,X4796,X4799,esk74_6(X4796,X4797,X4798,X4799,X4800,X4801))))
| hBOOL(hAPP(X4796,bool,hAPP(X4796,fun(X4796,bool),ord_less(X4796),X4798),hAPP(X4797,X4796,X4799,X4801)))
| ~ hBOOL(hAPP(X4796,bool,hAPP(X4796,fun(X4796,bool),ord_less(X4796),X4798),hAPP(X4797,X4796,X4799,X4800)))
| ~ hBOOL(hAPP(X4797,bool,hAPP(X4797,fun(X4797,bool),ord_less_eq(X4797),X4800),X4801))
| ~ order(X4797)
| ~ order(X4796) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_441_xt7])])])])]) ).
fof(i_0_1545,plain,
! [X4788,X4789,X4790,X4791,X4792,X4793] :
( ( hBOOL(hAPP(X4789,bool,hAPP(X4789,fun(X4789,bool),ord_less(X4789),esk73_6(X4788,X4789,X4790,X4791,X4792,X4793)),esk72_6(X4788,X4789,X4790,X4791,X4792,X4793)))
| hBOOL(hAPP(X4788,bool,hAPP(X4788,fun(X4788,bool),ord_less(X4788),X4790),hAPP(X4789,X4788,X4791,X4793)))
| ~ hBOOL(hAPP(X4788,bool,hAPP(X4788,fun(X4788,bool),ord_less_eq(X4788),X4790),hAPP(X4789,X4788,X4791,X4792)))
| ~ hBOOL(hAPP(X4789,bool,hAPP(X4789,fun(X4789,bool),ord_less(X4789),X4792),X4793))
| ~ order(X4789)
| ~ order(X4788) )
& ( ~ hBOOL(hAPP(X4788,bool,hAPP(X4788,fun(X4788,bool),ord_less(X4788),hAPP(X4789,X4788,X4791,esk73_6(X4788,X4789,X4790,X4791,X4792,X4793))),hAPP(X4789,X4788,X4791,esk72_6(X4788,X4789,X4790,X4791,X4792,X4793))))
| hBOOL(hAPP(X4788,bool,hAPP(X4788,fun(X4788,bool),ord_less(X4788),X4790),hAPP(X4789,X4788,X4791,X4793)))
| ~ hBOOL(hAPP(X4788,bool,hAPP(X4788,fun(X4788,bool),ord_less_eq(X4788),X4790),hAPP(X4789,X4788,X4791,X4792)))
| ~ hBOOL(hAPP(X4789,bool,hAPP(X4789,fun(X4789,bool),ord_less(X4789),X4792),X4793))
| ~ order(X4789)
| ~ order(X4788) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_440_xt5])])])])]) ).
fof(i_0_1546,plain,
! [X4771,X4772,X4773,X4774,X4775,X4776] :
( ( hBOOL(hAPP(X4772,bool,hAPP(X4772,fun(X4772,bool),ord_less_eq(X4772),esk68_6(X4771,X4772,X4773,X4774,X4775,X4776)),esk69_6(X4771,X4772,X4773,X4774,X4775,X4776)))
| hBOOL(hAPP(X4771,bool,hAPP(X4771,fun(X4771,bool),ord_less(X4771),X4774),hAPP(X4772,X4771,X4775,X4773)))
| ~ hBOOL(hAPP(X4772,bool,hAPP(X4772,fun(X4772,bool),ord_less_eq(X4772),X4776),X4773))
| ~ hBOOL(hAPP(X4771,bool,hAPP(X4771,fun(X4771,bool),ord_less(X4771),X4774),hAPP(X4772,X4771,X4775,X4776)))
| ~ order(X4772)
| ~ order(X4771) )
& ( ~ hBOOL(hAPP(X4771,bool,hAPP(X4771,fun(X4771,bool),ord_less_eq(X4771),hAPP(X4772,X4771,X4775,esk68_6(X4771,X4772,X4773,X4774,X4775,X4776))),hAPP(X4772,X4771,X4775,esk69_6(X4771,X4772,X4773,X4774,X4775,X4776))))
| hBOOL(hAPP(X4771,bool,hAPP(X4771,fun(X4771,bool),ord_less(X4771),X4774),hAPP(X4772,X4771,X4775,X4773)))
| ~ hBOOL(hAPP(X4772,bool,hAPP(X4772,fun(X4772,bool),ord_less_eq(X4772),X4776),X4773))
| ~ hBOOL(hAPP(X4771,bool,hAPP(X4771,fun(X4771,bool),ord_less(X4771),X4774),hAPP(X4772,X4771,X4775,X4776)))
| ~ order(X4772)
| ~ order(X4771) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_437_order__less__le__subst1])])])])]) ).
fof(i_0_1547,plain,
! [X4763,X4764,X4765,X4766,X4767,X4768] :
( ( hBOOL(hAPP(X4764,bool,hAPP(X4764,fun(X4764,bool),ord_less(X4764),esk66_6(X4763,X4764,X4765,X4766,X4767,X4768)),esk67_6(X4763,X4764,X4765,X4766,X4767,X4768)))
| hBOOL(hAPP(X4763,bool,hAPP(X4763,fun(X4763,bool),ord_less(X4763),X4766),hAPP(X4764,X4763,X4767,X4765)))
| ~ hBOOL(hAPP(X4764,bool,hAPP(X4764,fun(X4764,bool),ord_less(X4764),X4768),X4765))
| ~ hBOOL(hAPP(X4763,bool,hAPP(X4763,fun(X4763,bool),ord_less_eq(X4763),X4766),hAPP(X4764,X4763,X4767,X4768)))
| ~ order(X4764)
| ~ order(X4763) )
& ( ~ hBOOL(hAPP(X4763,bool,hAPP(X4763,fun(X4763,bool),ord_less(X4763),hAPP(X4764,X4763,X4767,esk66_6(X4763,X4764,X4765,X4766,X4767,X4768))),hAPP(X4764,X4763,X4767,esk67_6(X4763,X4764,X4765,X4766,X4767,X4768))))
| hBOOL(hAPP(X4763,bool,hAPP(X4763,fun(X4763,bool),ord_less(X4763),X4766),hAPP(X4764,X4763,X4767,X4765)))
| ~ hBOOL(hAPP(X4764,bool,hAPP(X4764,fun(X4764,bool),ord_less(X4764),X4768),X4765))
| ~ hBOOL(hAPP(X4763,bool,hAPP(X4763,fun(X4763,bool),ord_less_eq(X4763),X4766),hAPP(X4764,X4763,X4767,X4768)))
| ~ order(X4764)
| ~ order(X4763) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_436_order__le__less__subst1])])])])]) ).
fof(i_0_1548,plain,
! [X5635,X5636,X5637,X5638,X5639,X5640] :
( ( ~ hBOOL(hAPP(X5635,bool,hAPP(X5635,fun(X5635,bool),ord_less_eq(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),plus_plus(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),times_times(X5635),X5636),X5637)),X5638)),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),plus_plus(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),times_times(X5635),X5639),X5637)),X5640)))
| hBOOL(hAPP(X5635,bool,hAPP(X5635,fun(X5635,bool),ord_less_eq(X5635),X5638),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),plus_plus(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),times_times(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),minus_minus(X5635),X5639),X5636)),X5637)),X5640)))
| ~ ordered_ring(X5635) )
& ( ~ hBOOL(hAPP(X5635,bool,hAPP(X5635,fun(X5635,bool),ord_less_eq(X5635),X5638),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),plus_plus(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),times_times(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),minus_minus(X5635),X5639),X5636)),X5637)),X5640)))
| hBOOL(hAPP(X5635,bool,hAPP(X5635,fun(X5635,bool),ord_less_eq(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),plus_plus(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),times_times(X5635),X5636),X5637)),X5638)),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),plus_plus(X5635),hAPP(X5635,X5635,hAPP(X5635,fun(X5635,X5635),times_times(X5635),X5639),X5637)),X5640)))
| ~ ordered_ring(X5635) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_725_le__add__iff2])])])]) ).
fof(i_0_1549,plain,
! [X5647,X5648,X5649,X5650,X5651,X5652] :
( ( ~ hBOOL(hAPP(X5647,bool,hAPP(X5647,fun(X5647,bool),ord_less(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),plus_plus(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),times_times(X5647),X5648),X5649)),X5650)),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),plus_plus(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),times_times(X5647),X5651),X5649)),X5652)))
| hBOOL(hAPP(X5647,bool,hAPP(X5647,fun(X5647,bool),ord_less(X5647),X5650),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),plus_plus(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),times_times(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),minus_minus(X5647),X5651),X5648)),X5649)),X5652)))
| ~ ordered_ring(X5647) )
& ( ~ hBOOL(hAPP(X5647,bool,hAPP(X5647,fun(X5647,bool),ord_less(X5647),X5650),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),plus_plus(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),times_times(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),minus_minus(X5647),X5651),X5648)),X5649)),X5652)))
| hBOOL(hAPP(X5647,bool,hAPP(X5647,fun(X5647,bool),ord_less(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),plus_plus(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),times_times(X5647),X5648),X5649)),X5650)),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),plus_plus(X5647),hAPP(X5647,X5647,hAPP(X5647,fun(X5647,X5647),times_times(X5647),X5651),X5649)),X5652)))
| ~ ordered_ring(X5647) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_727_less__add__iff2])])])]) ).
fof(i_0_1550,plain,
! [X5824,X5825,X5826,X5827,X5828] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5827),X5824)),X5825)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5828),X5824)),X5826)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5825),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5828),X5827)),X5824)),X5826)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5827),X5828)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5825),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5828),X5827)),X5824)),X5826)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5827),X5824)),X5825)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5828),X5824)),X5826)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5827),X5828)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_792_nat__le__add__iff2])])]) ).
fof(i_0_1551,plain,
! [X5703,X5704,X5705,X5706,X5707] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5706),X5703)),X5704)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5707),X5703)),X5705)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5704),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5707),X5706)),X5703)),X5705)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5706),X5707)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5704),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5707),X5706)),X5703)),X5705)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5706),X5703)),X5704)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5707),X5703)),X5705)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5706),X5707)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_742_nat__less__add__iff2])])]) ).
fof(i_0_1552,plain,
! [X5050,X5051] :
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X5051))
| hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X5051))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X5050))))) != zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_542_card__less])]) ).
fof(i_0_1553,plain,
! [X6144,X6145,X6146,X6147,X6148] :
( ~ ordere142940540dd_abs(X6144)
| hBOOL(hAPP(X6144,bool,hAPP(X6144,fun(X6144,bool),ord_less_eq(X6144),hAPP(X6144,X6144,abs_abs(X6144),hAPP(X6144,X6144,hAPP(X6144,fun(X6144,X6144),minus_minus(X6144),hAPP(X6144,X6144,hAPP(X6144,fun(X6144,X6144),plus_plus(X6144),X6145),X6146)),hAPP(X6144,X6144,hAPP(X6144,fun(X6144,X6144),plus_plus(X6144),X6147),X6148)))),hAPP(X6144,X6144,hAPP(X6144,fun(X6144,X6144),plus_plus(X6144),hAPP(X6144,X6144,abs_abs(X6144),hAPP(X6144,X6144,hAPP(X6144,fun(X6144,X6144),minus_minus(X6144),X6145),X6147))),hAPP(X6144,X6144,abs_abs(X6144),hAPP(X6144,X6144,hAPP(X6144,fun(X6144,X6144),minus_minus(X6144),X6146),X6148))))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_902_abs__diff__triangle__ineq])])]) ).
cnf(i_0_1554,plain,
( hAPP(fun(X1,bool),X2,X7,X4) = ti(X2,X6)
| hAPP(X1,X2,X3,esk34_7(X1,X2,X4,X5,X6,X3,X7)) != ti(X2,X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X5),X6),X3),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1219]) ).
fof(i_0_1555,plain,
! [X5679,X5680,X5681,X5682,X5683] :
( ~ comm_monoid_mult(X5680)
| ~ hBOOL(hAPP(fun(X5679,bool),bool,finite_finite(X5679),X5683))
| hAPP(fun(X5679,bool),X5680,hAPP(X5680,fun(fun(X5679,bool),X5680),hAPP(fun(X5679,X5680),fun(X5680,fun(fun(X5679,bool),X5680)),hAPP(fun(X5680,fun(X5680,X5680)),fun(fun(X5679,X5680),fun(X5680,fun(fun(X5679,bool),X5680))),finite_fold_image(X5680,X5679),times_times(X5680)),hAPP(fun(X5679,X5680),fun(X5679,X5680),hAPP(fun(X5679,fun(X5680,X5680)),fun(fun(X5679,X5680),fun(X5679,X5680)),combs(X5679,X5680,X5680),hAPP(fun(X5679,X5680),fun(X5679,fun(X5680,X5680)),hAPP(fun(X5680,fun(X5680,X5680)),fun(fun(X5679,X5680),fun(X5679,fun(X5680,X5680))),combb(X5680,fun(X5680,X5680),X5679),times_times(X5680)),X5681)),X5682)),one_one(X5680)),X5683) = hAPP(X5680,X5680,hAPP(X5680,fun(X5680,X5680),times_times(X5680),hAPP(fun(X5679,bool),X5680,hAPP(X5680,fun(fun(X5679,bool),X5680),hAPP(fun(X5679,X5680),fun(X5680,fun(fun(X5679,bool),X5680)),hAPP(fun(X5680,fun(X5680,X5680)),fun(fun(X5679,X5680),fun(X5680,fun(fun(X5679,bool),X5680))),finite_fold_image(X5680,X5679),times_times(X5680)),X5681),one_one(X5680)),X5683)),hAPP(fun(X5679,bool),X5680,hAPP(X5680,fun(fun(X5679,bool),X5680),hAPP(fun(X5679,X5680),fun(X5680,fun(fun(X5679,bool),X5680)),hAPP(fun(X5680,fun(X5680,X5680)),fun(fun(X5679,X5680),fun(X5680,fun(fun(X5679,bool),X5680))),finite_fold_image(X5680,X5679),times_times(X5680)),X5682),one_one(X5680)),X5683)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_736_fold__image__distrib])])]) ).
cnf(i_0_1556,plain,
( ti(X2,X3) = hAPP(fun(X2,bool),X2,the(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X3)))),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X1))),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1220]) ).
cnf(i_0_1557,plain,
( hBOOL(X1)
| ti(X2,X3) = hAPP(fun(X2,bool),X2,the(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4)))),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X1))),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1220]) ).
fof(i_0_1558,plain,
! [X3335,X3336,X3337] :
( ( hBOOL(hAPP(fun(X3335,bool),bool,finite_finite(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),collect(X3335),X3336)))
| ~ hBOOL(hAPP(fun(X3335,bool),bool,finite_finite(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),collect(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),hAPP(fun(X3335,fun(bool,bool)),fun(fun(X3335,bool),fun(X3335,bool)),combs(X3335,bool,bool),hAPP(fun(X3335,bool),fun(X3335,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3335,bool),fun(X3335,fun(bool,bool))),combb(bool,fun(bool,bool),X3335),fdisj),X3336)),X3337)))) )
& ( hBOOL(hAPP(fun(X3335,bool),bool,finite_finite(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),collect(X3335),X3337)))
| ~ hBOOL(hAPP(fun(X3335,bool),bool,finite_finite(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),collect(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),hAPP(fun(X3335,fun(bool,bool)),fun(fun(X3335,bool),fun(X3335,bool)),combs(X3335,bool,bool),hAPP(fun(X3335,bool),fun(X3335,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3335,bool),fun(X3335,fun(bool,bool))),combb(bool,fun(bool,bool),X3335),fdisj),X3336)),X3337)))) )
& ( ~ hBOOL(hAPP(fun(X3335,bool),bool,finite_finite(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),collect(X3335),X3336)))
| ~ hBOOL(hAPP(fun(X3335,bool),bool,finite_finite(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),collect(X3335),X3337)))
| hBOOL(hAPP(fun(X3335,bool),bool,finite_finite(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),collect(X3335),hAPP(fun(X3335,bool),fun(X3335,bool),hAPP(fun(X3335,fun(bool,bool)),fun(fun(X3335,bool),fun(X3335,bool)),combs(X3335,bool,bool),hAPP(fun(X3335,bool),fun(X3335,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3335,bool),fun(X3335,fun(bool,bool))),combb(bool,fun(bool,bool),X3335),fdisj),X3336)),X3337)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_26_finite__Collect__disjI])])]) ).
fof(i_0_1559,plain,
! [X5814,X5815,X5816,X5817,X5818] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5817),X5818))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5818),X5814)),X5815)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5817),X5814)),X5816)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5818),X5817)),X5814)),X5815)),X5816) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_790_nat__diff__add__eq1])]) ).
fof(i_0_1560,plain,
! [X3919,X3920] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,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,X3919)),X3920)),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(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X3919)))),bot_bot(fun(x_a,bool)))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X3920),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,X3919)),bot_bot(fun(x_a,bool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_182_assms_I2_J])]) ).
fof(i_0_1561,plain,
! [X5868,X5869,X5870,X5871,X5872] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5868),X5869)),X5870)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5868),X5871)),X5872)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5870))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5870),X5868))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5872),X5868))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5869),X5871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_804_unique__quotient__lemma])]) ).
fof(i_0_1562,plain,
! [X5850,X5851,X5852,X5853,X5854] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5850),X5851)),X5852)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5850),X5853)),X5854)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5854),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5850),X5854))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5850),X5852))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5853),X5851)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_797_unique__quotient__lemma__neg])]) ).
fof(i_0_1563,plain,
! [X4603,X4604] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X4603)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X4604))))),
inference(variable_rename,[status(thm)],[fact_390_finite__M__bounded__by__nat]) ).
cnf(i_0_1564,plain,
( ti(fun(X1,bool),X4) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(fun(X1,bool),X1,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,esk32_4(X1,X4,X2,X3)),esk33_4(X1,X4,X2,X3))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk32_4(X1,X4,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk33_4(X1,X4,X2,X3)),bot_bot(fun(X1,bool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_1221]) ).
fof(i_0_1565,plain,
! [X3873,X3874,X3875,X3876,X3877] : hBOOL(hAPP(fun(X3873,bool),bool,hAPP(fun(X3873,bool),fun(fun(X3873,bool),bool),ord_less_eq(fun(X3873,bool)),hAPP(fun(X3873,bool),fun(X3873,bool),hAPP(fun(X3873,bool),fun(fun(X3873,bool),fun(X3873,bool)),minus_minus(fun(X3873,bool)),hAPP(fun(X3874,bool),fun(X3873,bool),hAPP(fun(X3874,X3873),fun(fun(X3874,bool),fun(X3873,bool)),image(X3874,X3873),X3875),X3876)),hAPP(fun(X3874,bool),fun(X3873,bool),hAPP(fun(X3874,X3873),fun(fun(X3874,bool),fun(X3873,bool)),image(X3874,X3873),X3875),X3877))),hAPP(fun(X3874,bool),fun(X3873,bool),hAPP(fun(X3874,X3873),fun(fun(X3874,bool),fun(X3873,bool)),image(X3874,X3873),X3875),hAPP(fun(X3874,bool),fun(X3874,bool),hAPP(fun(X3874,bool),fun(fun(X3874,bool),fun(X3874,bool)),minus_minus(fun(X3874,bool)),X3876),X3877)))),
inference(variable_rename,[status(thm)],[fact_172_image__diff__subset]) ).
fof(i_0_1566,plain,
! [X3486,X3487,X3488] : hAPP(fun(X3486,bool),fun(X3486,bool),hAPP(X3486,fun(fun(X3486,bool),fun(X3486,bool)),insert(X3486),X3487),hAPP(fun(X3486,bool),fun(X3486,bool),collect(X3486),X3488)) = hAPP(fun(X3486,bool),fun(X3486,bool),collect(X3486),hAPP(fun(X3486,bool),fun(X3486,bool),hAPP(fun(X3486,fun(bool,bool)),fun(fun(X3486,bool),fun(X3486,bool)),combs(X3486,bool,bool),hAPP(fun(X3486,bool),fun(X3486,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3486,bool),fun(X3486,fun(bool,bool))),combb(bool,fun(bool,bool),X3486),fimplies),hAPP(fun(X3486,bool),fun(X3486,bool),hAPP(fun(bool,bool),fun(fun(X3486,bool),fun(X3486,bool)),combb(bool,bool,X3486),fNot),hAPP(X3486,fun(X3486,bool),hAPP(fun(X3486,fun(X3486,bool)),fun(X3486,fun(X3486,bool)),combc(X3486,X3486,bool),fequal(X3486)),X3487)))),X3488)),
inference(variable_rename,[status(thm)],[fact_73_insert__Collect]) ).
fof(i_0_1567,plain,
! [X5844,X5845,X5846,X5847,X5848,X5849] :
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5844),X5845)),X5846) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5847),X5848)),X5849)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5847),X5848)),X5849)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5846),X5844))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5849))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5847))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5847),X5844))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5848),X5845)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_796_zdiv__mono2__neg__lemma])]) ).
cnf(i_0_1568,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1222]) ).
cnf(i_0_1569,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1222]) ).
fof(i_0_1570,plain,
! [X5623,X5624,X5625] :
( ~ linordered_ring(X5623)
| ~ hBOOL(hAPP(X5623,bool,hAPP(X5623,fun(X5623,bool),ord_less(X5623),hAPP(X5623,X5623,hAPP(X5623,fun(X5623,X5623),plus_plus(X5623),hAPP(X5623,X5623,hAPP(X5623,fun(X5623,X5623),times_times(X5623),X5624),X5624)),hAPP(X5623,X5623,hAPP(X5623,fun(X5623,X5623),times_times(X5623),X5625),X5625))),zero_zero(X5623))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1223])])]) ).
fof(i_0_1571,plain,
! [X5887,X5888,X5889,X5890,X5891,X5892] :
( ( hBOOL(hAPP(fun(X5887,bool),bool,hAPP(X5887,fun(fun(X5887,bool),bool),member(X5887),esk104_6(X5887,X5888,X5889,X5890,X5891,X5892)),X5892))
| hAPP(fun(X5887,bool),X5888,hAPP(X5888,fun(fun(X5887,bool),X5888),hAPP(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888)),hAPP(fun(X5888,fun(X5888,X5888)),fun(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888))),finite_fold_image(X5888,X5887),times_times(X5888)),X5890),X5889),X5892) = hAPP(fun(X5887,bool),X5888,hAPP(X5888,fun(fun(X5887,bool),X5888),hAPP(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888)),hAPP(fun(X5888,fun(X5888,X5888)),fun(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888))),finite_fold_image(X5888,X5887),times_times(X5888)),X5891),X5889),X5892)
| ~ hBOOL(hAPP(fun(X5887,bool),bool,finite_finite(X5887),X5892))
| ~ ab_semigroup_mult(X5888) )
& ( hAPP(X5887,X5888,X5890,esk104_6(X5887,X5888,X5889,X5890,X5891,X5892)) != hAPP(X5887,X5888,X5891,esk104_6(X5887,X5888,X5889,X5890,X5891,X5892))
| hAPP(fun(X5887,bool),X5888,hAPP(X5888,fun(fun(X5887,bool),X5888),hAPP(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888)),hAPP(fun(X5888,fun(X5888,X5888)),fun(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888))),finite_fold_image(X5888,X5887),times_times(X5888)),X5890),X5889),X5892) = hAPP(fun(X5887,bool),X5888,hAPP(X5888,fun(fun(X5887,bool),X5888),hAPP(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888)),hAPP(fun(X5888,fun(X5888,X5888)),fun(fun(X5887,X5888),fun(X5888,fun(fun(X5887,bool),X5888))),finite_fold_image(X5888,X5887),times_times(X5888)),X5891),X5889),X5892)
| ~ hBOOL(hAPP(fun(X5887,bool),bool,finite_finite(X5887),X5892))
| ~ ab_semigroup_mult(X5888) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_808_fold__image__cong])])])])]) ).
fof(i_0_1572,plain,
! [X3305,X3306,X3307] :
( ( ~ hBOOL(hAPP(fun(X3305,bool),bool,finite_finite(X3305),hAPP(fun(X3305,bool),fun(X3305,bool),collect(X3305),X3307)))
| hBOOL(hAPP(fun(X3305,bool),bool,finite_finite(X3305),hAPP(fun(X3305,bool),fun(X3305,bool),collect(X3305),hAPP(fun(X3305,bool),fun(X3305,bool),hAPP(fun(X3305,fun(bool,bool)),fun(fun(X3305,bool),fun(X3305,bool)),combs(X3305,bool,bool),hAPP(fun(X3305,bool),fun(X3305,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3305,bool),fun(X3305,fun(bool,bool))),combb(bool,fun(bool,bool),X3305),fconj),X3307)),X3306)))) )
& ( ~ hBOOL(hAPP(fun(X3305,bool),bool,finite_finite(X3305),hAPP(fun(X3305,bool),fun(X3305,bool),collect(X3305),X3306)))
| hBOOL(hAPP(fun(X3305,bool),bool,finite_finite(X3305),hAPP(fun(X3305,bool),fun(X3305,bool),collect(X3305),hAPP(fun(X3305,bool),fun(X3305,bool),hAPP(fun(X3305,fun(bool,bool)),fun(fun(X3305,bool),fun(X3305,bool)),combs(X3305,bool,bool),hAPP(fun(X3305,bool),fun(X3305,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3305,bool),fun(X3305,fun(bool,bool))),combb(bool,fun(bool,bool),X3305),fconj),X3307)),X3306)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_finite__Collect__conjI])])]) ).
fof(i_0_1573,plain,
! [X3939,X3940] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk29_2(X3939,X3940)),hAPP(nat,nat,X3940,esk29_2(X3939,X3940))))
| 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),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X3940)),X3939)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_finite__less__ub])])]) ).
fof(i_0_1574,plain,
! [X3976,X3977,X3978] : hAPP(fun(X3976,bool),fun(X3976,bool),hAPP(fun(X3976,bool),fun(fun(X3976,bool),fun(X3976,bool)),minus_minus(fun(X3976,bool)),X3977),X3978) = hAPP(fun(X3976,bool),fun(X3976,bool),collect(X3976),hAPP(fun(X3976,bool),fun(X3976,bool),hAPP(fun(X3976,fun(bool,bool)),fun(fun(X3976,bool),fun(X3976,bool)),combs(X3976,bool,bool),hAPP(fun(X3976,bool),fun(X3976,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3976,bool),fun(X3976,fun(bool,bool))),combb(bool,fun(bool,bool),X3976),fconj),hAPP(fun(X3976,bool),fun(X3976,bool),hAPP(fun(X3976,fun(fun(X3976,bool),bool)),fun(fun(X3976,bool),fun(X3976,bool)),combc(X3976,fun(X3976,bool),bool),member(X3976)),X3977))),hAPP(fun(X3976,bool),fun(X3976,bool),hAPP(fun(bool,bool),fun(fun(X3976,bool),fun(X3976,bool)),combb(bool,bool,X3976),fNot),hAPP(fun(X3976,bool),fun(X3976,bool),hAPP(fun(X3976,fun(fun(X3976,bool),bool)),fun(fun(X3976,bool),fun(X3976,bool)),combc(X3976,fun(X3976,bool),bool),member(X3976)),X3978)))),
inference(variable_rename,[status(thm)],[fact_196_set__diff__eq]) ).
fof(i_0_1575,plain,
! [X4321,X4322,X4323] :
( ~ hBOOL(hAPP(fun(X4321,bool),bool,finite_finite(X4321),X4323))
| ~ hBOOL(hAPP(fun(X4321,bool),bool,hAPP(X4321,fun(fun(X4321,bool),bool),member(X4321),X4322),X4323))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X4321,bool),nat,finite_card(X4321),hAPP(fun(X4321,bool),fun(X4321,bool),hAPP(fun(X4321,bool),fun(fun(X4321,bool),fun(X4321,bool)),minus_minus(fun(X4321,bool)),X4323),hAPP(fun(X4321,bool),fun(X4321,bool),hAPP(X4321,fun(fun(X4321,bool),fun(X4321,bool)),insert(X4321),X4322),bot_bot(fun(X4321,bool)))))),hAPP(fun(X4321,bool),nat,finite_card(X4321),X4323))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_293_card__Diff1__less])]) ).
fof(i_0_1576,plain,
! [X3997,X3998,X3999,X4000,X4001,X4002,X4003,X4004] :
( ~ hBOOL(hAPP(fun(fun(X3997,bool),X3998),bool,hAPP(fun(X3997,X3998),fun(fun(fun(X3997,bool),X3998),bool),hAPP(X3998,fun(fun(X3997,X3998),fun(fun(fun(X3997,bool),X3998),bool)),hAPP(fun(X3998,fun(X3998,X3998)),fun(X3998,fun(fun(X3997,X3998),fun(fun(fun(X3997,bool),X3998),bool))),finite1357897459simple(X3998,X3997),X4001),X4002),X4003),X4004))
| ~ hBOOL(hAPP(fun(X3997,bool),bool,finite_finite(X3997),X4000))
| ~ hBOOL(hAPP(fun(X3997,bool),bool,hAPP(X3997,fun(fun(X3997,bool),bool),member(X3997),X3999),X4000))
| hAPP(fun(X3997,bool),X3998,X4004,X4000) = hAPP(X3998,X3998,hAPP(X3998,fun(X3998,X3998),X4001,hAPP(X3997,X3998,X4003,X3999)),hAPP(fun(X3997,bool),X3998,X4004,hAPP(fun(X3997,bool),fun(X3997,bool),hAPP(fun(X3997,bool),fun(fun(X3997,bool),fun(X3997,bool)),minus_minus(fun(X3997,bool)),X4000),hAPP(fun(X3997,bool),fun(X3997,bool),hAPP(X3997,fun(fun(X3997,bool),fun(X3997,bool)),insert(X3997),X3999),bot_bot(fun(X3997,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_200_folding__image__simple_Oremove])]) ).
fof(i_0_1577,plain,
! [X3989,X3990,X3991,X3992,X3993,X3994,X3995,X3996] :
( ~ hBOOL(hAPP(fun(fun(X3989,bool),X3990),bool,hAPP(fun(X3989,X3990),fun(fun(fun(X3989,bool),X3990),bool),hAPP(X3990,fun(fun(X3989,X3990),fun(fun(fun(X3989,bool),X3990),bool)),hAPP(fun(X3990,fun(X3990,X3990)),fun(X3990,fun(fun(X3989,X3990),fun(fun(fun(X3989,bool),X3990),bool))),finite1357897459simple(X3990,X3989),X3993),X3994),X3995),X3996))
| ~ hBOOL(hAPP(fun(X3989,bool),bool,finite_finite(X3989),X3992))
| hAPP(fun(X3989,bool),X3990,X3996,hAPP(fun(X3989,bool),fun(X3989,bool),hAPP(X3989,fun(fun(X3989,bool),fun(X3989,bool)),insert(X3989),X3991),X3992)) = hAPP(X3990,X3990,hAPP(X3990,fun(X3990,X3990),X3993,hAPP(X3989,X3990,X3995,X3991)),hAPP(fun(X3989,bool),X3990,X3996,hAPP(fun(X3989,bool),fun(X3989,bool),hAPP(fun(X3989,bool),fun(fun(X3989,bool),fun(X3989,bool)),minus_minus(fun(X3989,bool)),X3992),hAPP(fun(X3989,bool),fun(X3989,bool),hAPP(X3989,fun(fun(X3989,bool),fun(X3989,bool)),insert(X3989),X3991),bot_bot(fun(X3989,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_199_folding__image__simple_Oinsert__remove])]) ).
cnf(i_0_1578,plain,
( ti(fun(X1,bool),X5) = bot_bot(fun(X1,bool))
| hAPP(X1,X1,X4,hAPP(fun(X1,bool),X1,X3,X5)) = hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3))
| hAPP(X1,X1,X4,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,esk39_5(X1,X5,X4,X2,X3)),esk40_5(X1,X5,X4,X2,X3))) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X1,X1,X4,esk39_5(X1,X5,X4,X2,X3))),hAPP(X1,X1,X4,esk40_5(X1,X5,X4,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1224]) ).
fof(i_0_1579,plain,
! [X5829,X5830,X5831,X5832,X5833] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5832),X5833))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5832),X5829)),X5830)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5833),X5829)),X5831)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5830),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5833),X5832)),X5829)),X5831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_793_nat__diff__add__eq2])]) ).
fof(i_0_1580,plain,
! [X3866,X3867,X3868] :
( ~ hBOOL(hAPP(fun(X3866,bool),bool,finite_finite(X3866),X3868))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3866,bool),nat,finite_card(X3866),hAPP(fun(X3866,bool),fun(X3866,bool),hAPP(fun(X3866,bool),fun(fun(X3866,bool),fun(X3866,bool)),minus_minus(fun(X3866,bool)),X3868),hAPP(fun(X3866,bool),fun(X3866,bool),hAPP(X3866,fun(fun(X3866,bool),fun(X3866,bool)),insert(X3866),X3867),bot_bot(fun(X3866,bool)))))),hAPP(fun(X3866,bool),nat,finite_card(X3866),X3868))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_170_card__Diff1__le])]) ).
fof(i_0_1581,plain,
! [X5156,X5157] :
( ( ~ hBOOL(hAPP(X5156,bool,hAPP(X5156,fun(X5156,bool),ord_less(X5156),hAPP(X5156,X5156,hAPP(X5156,fun(X5156,X5156),plus_plus(X5156),hAPP(X5156,X5156,hAPP(X5156,fun(X5156,X5156),plus_plus(X5156),one_one(X5156)),X5157)),X5157)),zero_zero(X5156)))
| hBOOL(hAPP(X5156,bool,hAPP(X5156,fun(X5156,bool),ord_less(X5156),X5157),zero_zero(X5156)))
| ~ hBOOL(hAPP(fun(X5156,bool),bool,hAPP(X5156,fun(fun(X5156,bool),bool),member(X5156),X5157),ring_1_Ints(X5156)))
| ~ linordered_idom(X5156) )
& ( ~ hBOOL(hAPP(X5156,bool,hAPP(X5156,fun(X5156,bool),ord_less(X5156),X5157),zero_zero(X5156)))
| hBOOL(hAPP(X5156,bool,hAPP(X5156,fun(X5156,bool),ord_less(X5156),hAPP(X5156,X5156,hAPP(X5156,fun(X5156,X5156),plus_plus(X5156),hAPP(X5156,X5156,hAPP(X5156,fun(X5156,X5156),plus_plus(X5156),one_one(X5156)),X5157)),X5157)),zero_zero(X5156)))
| ~ hBOOL(hAPP(fun(X5156,bool),bool,hAPP(X5156,fun(fun(X5156,bool),bool),member(X5156),X5157),ring_1_Ints(X5156)))
| ~ linordered_idom(X5156) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_575_Ints__odd__less__0])])])]) ).
fof(i_0_1582,plain,
! [X4706,X4707,X4708,X4709] :
( ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(fun(X4706,bool),fun(fun(X4706,bool),fun(X4706,bool)),minus_minus(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),bot_bot(fun(X4706,bool))))),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less_eq(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less_eq(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(fun(X4706,bool),fun(fun(X4706,bool),fun(X4706,bool)),minus_minus(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),bot_bot(fun(X4706,bool))))),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less_eq(fun(X4706,bool)),X4707),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(fun(X4706,bool),fun(fun(X4706,bool),fun(X4706,bool)),minus_minus(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),bot_bot(fun(X4706,bool))))),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less_eq(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(X4706,fun(fun(X4706,bool),bool),member(X4706),X4708),X4707))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(fun(X4706,bool),fun(fun(X4706,bool),fun(X4706,bool)),minus_minus(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),bot_bot(fun(X4706,bool))))),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) )
& ( ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less_eq(fun(X4706,bool)),X4707),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(fun(X4706,bool),fun(fun(X4706,bool),fun(X4706,bool)),minus_minus(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),bot_bot(fun(X4706,bool))))),X4709))
| ~ hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),X4709))
| hBOOL(hAPP(fun(X4706,bool),bool,hAPP(fun(X4706,bool),fun(fun(X4706,bool),bool),ord_less(fun(X4706,bool)),X4707),hAPP(fun(X4706,bool),fun(X4706,bool),hAPP(X4706,fun(fun(X4706,bool),fun(X4706,bool)),insert(X4706),X4708),X4709))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1225])])]) ).
fof(i_0_1583,plain,
! [X5684,X5685,X5686,X5687,X5688,X5689] :
( ~ linord1278240602ring_1(X5684)
| ~ hBOOL(hAPP(X5684,bool,hAPP(X5684,fun(X5684,bool),ord_less_eq(X5684),X5688),X5689))
| ~ hBOOL(hAPP(X5684,bool,hAPP(X5684,fun(X5684,bool),ord_less_eq(X5684),X5687),X5689))
| ~ hBOOL(hAPP(X5684,bool,hAPP(X5684,fun(X5684,bool),ord_less_eq(X5684),zero_zero(X5684)),X5686))
| ~ hBOOL(hAPP(X5684,bool,hAPP(X5684,fun(X5684,bool),ord_less_eq(X5684),zero_zero(X5684)),X5685))
| hAPP(X5684,X5684,hAPP(X5684,fun(X5684,X5684),plus_plus(X5684),X5686),X5685) != one_one(X5684)
| hBOOL(hAPP(X5684,bool,hAPP(X5684,fun(X5684,bool),ord_less_eq(X5684),hAPP(X5684,X5684,hAPP(X5684,fun(X5684,X5684),plus_plus(X5684),hAPP(X5684,X5684,hAPP(X5684,fun(X5684,X5684),times_times(X5684),X5686),X5688)),hAPP(X5684,X5684,hAPP(X5684,fun(X5684,X5684),times_times(X5684),X5685),X5687))),X5689)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_737_convex__bound__le])])]) ).
fof(i_0_1584,plain,
! [X5159,X5160,X5161,X5162,X5163,X5164] :
( ~ linord626643107strict(X5159)
| ~ hBOOL(hAPP(X5159,bool,hAPP(X5159,fun(X5159,bool),ord_less(X5159),X5163),X5164))
| ~ hBOOL(hAPP(X5159,bool,hAPP(X5159,fun(X5159,bool),ord_less(X5159),X5162),X5164))
| ~ hBOOL(hAPP(X5159,bool,hAPP(X5159,fun(X5159,bool),ord_less_eq(X5159),zero_zero(X5159)),X5161))
| ~ hBOOL(hAPP(X5159,bool,hAPP(X5159,fun(X5159,bool),ord_less_eq(X5159),zero_zero(X5159)),X5160))
| hAPP(X5159,X5159,hAPP(X5159,fun(X5159,X5159),plus_plus(X5159),X5161),X5160) != one_one(X5159)
| hBOOL(hAPP(X5159,bool,hAPP(X5159,fun(X5159,bool),ord_less(X5159),hAPP(X5159,X5159,hAPP(X5159,fun(X5159,X5159),plus_plus(X5159),hAPP(X5159,X5159,hAPP(X5159,fun(X5159,X5159),times_times(X5159),X5161),X5163)),hAPP(X5159,X5159,hAPP(X5159,fun(X5159,X5159),times_times(X5159),X5160),X5162))),X5164)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_577_convex__bound__lt])])]) ).
fof(i_0_1585,plain,
! [X5865,X5866,X5867] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5865),X5866)),X5867)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5867))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5865))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5866),zero_zero(int))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_803_q__neg__lemma])]) ).
fof(i_0_1586,plain,
! [X3784,X3785,X3786,X3787] :
( ( ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(X3784,fun(fun(X3784,bool),bool),member(X3784),X3786),X3785))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(fun(X3784,bool),fun(fun(X3784,bool),fun(X3784,bool)),minus_minus(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),bot_bot(fun(X3784,bool))))),X3787))
| ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),X3787))) )
& ( hBOOL(hAPP(fun(X3784,bool),bool,hAPP(X3784,fun(fun(X3784,bool),bool),member(X3784),X3786),X3785))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),X3787))
| ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),X3787))) )
& ( ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(X3784,fun(fun(X3784,bool),bool),member(X3784),X3786),X3785))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(X3784,fun(fun(X3784,bool),bool),member(X3784),X3786),X3785))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),X3787))) )
& ( ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),X3787))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(X3784,fun(fun(X3784,bool),bool),member(X3784),X3786),X3785))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),X3787))) )
& ( ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(X3784,fun(fun(X3784,bool),bool),member(X3784),X3786),X3785))
| ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(fun(X3784,bool),fun(fun(X3784,bool),fun(X3784,bool)),minus_minus(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),bot_bot(fun(X3784,bool))))),X3787))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),X3787))) )
& ( ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),X3787))
| ~ hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(fun(X3784,bool),fun(fun(X3784,bool),fun(X3784,bool)),minus_minus(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),bot_bot(fun(X3784,bool))))),X3787))
| hBOOL(hAPP(fun(X3784,bool),bool,hAPP(fun(X3784,bool),fun(fun(X3784,bool),bool),ord_less_eq(fun(X3784,bool)),X3785),hAPP(fun(X3784,bool),fun(X3784,bool),hAPP(X3784,fun(fun(X3784,bool),fun(X3784,bool)),insert(X3784),X3786),X3787))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1226])])]) ).
fof(i_0_1587,plain,
! [X3780,X3781,X3782,X3783] :
( ~ hBOOL(hAPP(fun(X3780,bool),bool,hAPP(fun(X3780,bool),fun(fun(X3780,bool),bool),ord_less_eq(fun(X3780,bool)),hAPP(fun(X3780,bool),fun(X3780,bool),hAPP(fun(X3780,bool),fun(fun(X3780,bool),fun(X3780,bool)),minus_minus(fun(X3780,bool)),X3781),hAPP(fun(X3780,bool),fun(X3780,bool),hAPP(X3780,fun(fun(X3780,bool),fun(X3780,bool)),insert(X3780),X3782),bot_bot(fun(X3780,bool))))),X3783))
| ~ hBOOL(hAPP(fun(X3780,bool),bool,hAPP(X3780,fun(fun(X3780,bool),bool),member(X3780),X3782),X3781))
| hBOOL(hAPP(fun(X3780,bool),bool,hAPP(fun(X3780,bool),fun(fun(X3780,bool),bool),ord_less_eq(fun(X3780,bool)),X3781),hAPP(fun(X3780,bool),fun(X3780,bool),hAPP(X3780,fun(fun(X3780,bool),fun(X3780,bool)),insert(X3780),X3782),X3783))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_143_diff__single__insert])]) ).
fof(i_0_1588,plain,
! [X5752] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X5752)),X5752)),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5752),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5752),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X5752)),X5752)),zero_zero(int))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_766_odd__less__0])]) ).
fof(i_0_1589,plain,
! [X4285] : hBOOL(hAPP(fun(X4285,fun(fun(X4285,bool),fun(X4285,bool))),bool,finite_comp_fun_idem(X4285,fun(X4285,bool)),hAPP(fun(X4285,fun(X4285,bool)),fun(X4285,fun(fun(X4285,bool),fun(X4285,bool))),hAPP(fun(fun(X4285,bool),fun(fun(X4285,bool),fun(X4285,bool))),fun(fun(X4285,fun(X4285,bool)),fun(X4285,fun(fun(X4285,bool),fun(X4285,bool)))),combb(fun(X4285,bool),fun(fun(X4285,bool),fun(X4285,bool)),X4285),hAPP(fun(fun(X4285,bool),fun(fun(X4285,bool),fun(X4285,bool))),fun(fun(X4285,bool),fun(fun(X4285,bool),fun(X4285,bool))),combc(fun(X4285,bool),fun(X4285,bool),fun(X4285,bool)),minus_minus(fun(X4285,bool)))),hAPP(fun(X4285,bool),fun(X4285,fun(X4285,bool)),hAPP(fun(X4285,fun(fun(X4285,bool),fun(X4285,bool))),fun(fun(X4285,bool),fun(X4285,fun(X4285,bool))),combc(X4285,fun(X4285,bool),fun(X4285,bool)),insert(X4285)),bot_bot(fun(X4285,bool)))))),
inference(variable_rename,[status(thm)],[fact_282_comp__fun__idem__remove]) ).
cnf(i_0_1590,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk80_6(X2,X1,X3,X4,X5,X6)),X6))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X6)
| ti(fun(X1,bool),X5) != ti(fun(X1,bool),X6) ),
inference(split_conjunct,[status(thm)],[i_0_1227]) ).
fof(i_0_1591,plain,
! [X5149,X5150,X5151,X5152,X5153,X5154,X5155] :
( ~ hBOOL(hAPP(fun(fun(X5149,bool),X5150),bool,hAPP(fun(X5149,X5150),fun(fun(fun(X5149,bool),X5150),bool),hAPP(X5150,fun(fun(X5149,X5150),fun(fun(fun(X5149,bool),X5150),bool)),hAPP(fun(X5150,fun(X5150,X5150)),fun(X5150,fun(fun(X5149,X5150),fun(fun(fun(X5149,bool),X5150),bool))),finite1357897459simple(X5150,X5149),X5152),X5153),X5154),X5155))
| ~ hBOOL(hAPP(fun(X5149,bool),bool,finite_finite(X5149),X5151))
| hAPP(fun(X5149,bool),X5150,X5155,X5151) = hAPP(fun(X5149,bool),X5150,hAPP(X5150,fun(fun(X5149,bool),X5150),hAPP(fun(X5149,X5150),fun(X5150,fun(fun(X5149,bool),X5150)),hAPP(fun(X5150,fun(X5150,X5150)),fun(fun(X5149,X5150),fun(X5150,fun(fun(X5149,bool),X5150))),finite_fold_image(X5150,X5149),X5152),X5154),X5153),X5151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_574_folding__image__simple_Oeq__fold__g])]) ).
fof(i_0_1592,plain,
! [X5873,X5874,X5875,X5876,X5877,X5878] :
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5873),X5874)),X5875) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5876),X5877)),X5878)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5876),X5877)),X5878)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5878),X5876))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5875))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5876))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5876),X5873))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5874),X5877)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_805_zdiv__mono2__lemma])]) ).
fof(i_0_1593,plain,
! [X4036,X4037,X4038,X4039,X4040,X4041,X4042,X4043] :
( ~ hBOOL(hAPP(fun(fun(X4036,bool),X4037),bool,hAPP(fun(X4036,X4037),fun(fun(fun(X4036,bool),X4037),bool),hAPP(X4037,fun(fun(X4036,X4037),fun(fun(fun(X4036,bool),X4037),bool)),hAPP(fun(X4037,fun(X4037,X4037)),fun(X4037,fun(fun(X4036,X4037),fun(fun(fun(X4036,bool),X4037),bool))),finite1357897459simple(X4037,X4036),X4040),X4041),X4042),X4043))
| ~ hBOOL(hAPP(fun(X4036,bool),bool,finite_finite(X4036),X4039))
| hBOOL(hAPP(fun(X4036,bool),bool,hAPP(X4036,fun(fun(X4036,bool),bool),member(X4036),X4038),X4039))
| hAPP(fun(X4036,bool),X4037,X4043,hAPP(fun(X4036,bool),fun(X4036,bool),hAPP(X4036,fun(fun(X4036,bool),fun(X4036,bool)),insert(X4036),X4038),X4039)) = hAPP(X4037,X4037,hAPP(X4037,fun(X4037,X4037),X4040,hAPP(X4036,X4037,X4042,X4038)),hAPP(fun(X4036,bool),X4037,X4043,X4039)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1228])]) ).
fof(i_0_1594,plain,
! [X3690,X3691,X3692,X3693,X3694,X3695,X3696,X3697] :
( ~ hBOOL(hAPP(fun(fun(X3690,bool),X3691),bool,hAPP(fun(X3690,X3691),fun(fun(fun(X3690,bool),X3691),bool),hAPP(X3691,fun(fun(X3690,X3691),fun(fun(fun(X3690,bool),X3691),bool)),hAPP(fun(X3691,fun(X3691,X3691)),fun(X3691,fun(fun(X3690,X3691),fun(fun(fun(X3690,bool),X3691),bool))),finite908156982e_idem(X3691,X3690),X3694),X3695),X3696),X3697))
| ~ hBOOL(hAPP(fun(X3690,bool),bool,finite_finite(X3690),X3693))
| ~ hBOOL(hAPP(fun(X3690,bool),bool,hAPP(fun(X3690,bool),fun(fun(X3690,bool),bool),ord_less_eq(fun(X3690,bool)),X3692),X3693))
| hAPP(X3691,X3691,hAPP(X3691,fun(X3691,X3691),X3694,hAPP(fun(X3690,bool),X3691,X3697,X3692)),hAPP(fun(X3690,bool),X3691,X3697,X3693)) = hAPP(fun(X3690,bool),X3691,X3697,X3693) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_119_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_1595,plain,
! [X3894,X3895,X3896,X3897,X3898,X3899,X3900,X3901] :
( ~ hBOOL(hAPP(fun(fun(X3894,bool),X3895),bool,hAPP(fun(X3894,X3895),fun(fun(fun(X3894,bool),X3895),bool),hAPP(X3895,fun(fun(X3894,X3895),fun(fun(fun(X3894,bool),X3895),bool)),hAPP(fun(X3895,fun(X3895,X3895)),fun(X3895,fun(fun(X3894,X3895),fun(fun(fun(X3894,bool),X3895),bool))),finite908156982e_idem(X3895,X3894),X3898),X3899),X3900),X3901))
| ~ hBOOL(hAPP(fun(X3894,bool),bool,finite_finite(X3894),X3897))
| ~ hBOOL(hAPP(fun(X3894,bool),bool,hAPP(X3894,fun(fun(X3894,bool),bool),member(X3894),X3896),X3897))
| hAPP(X3895,X3895,hAPP(X3895,fun(X3895,X3895),X3898,hAPP(X3894,X3895,X3900,X3896)),hAPP(fun(X3894,bool),X3895,X3901,X3897)) = hAPP(fun(X3894,bool),X3895,X3901,X3897) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_177_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_1596,plain,
! [X6164,X6165,X6166] :
( ~ ordere142940540dd_abs(X6164)
| hBOOL(hAPP(X6164,bool,hAPP(X6164,fun(X6164,bool),ord_less_eq(X6164),hAPP(X6164,X6164,abs_abs(X6164),hAPP(X6164,X6164,hAPP(X6164,fun(X6164,X6164),minus_minus(X6164),hAPP(X6164,X6164,abs_abs(X6164),X6165)),hAPP(X6164,X6164,abs_abs(X6164),X6166)))),hAPP(X6164,X6164,abs_abs(X6164),hAPP(X6164,X6164,hAPP(X6164,fun(X6164,X6164),minus_minus(X6164),X6165),X6166)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_912_abs__triangle__ineq3])])]) ).
fof(i_0_1597,plain,
! [X3698,X3699,X3700,X3701,X3702,X3703,X3704,X3705] :
( ~ hBOOL(hAPP(fun(fun(X3698,bool),X3699),bool,hAPP(fun(X3698,X3699),fun(fun(fun(X3698,bool),X3699),bool),hAPP(X3699,fun(fun(X3698,X3699),fun(fun(fun(X3698,bool),X3699),bool)),hAPP(fun(X3699,fun(X3699,X3699)),fun(X3699,fun(fun(X3698,X3699),fun(fun(fun(X3698,bool),X3699),bool))),finite908156982e_idem(X3699,X3698),X3702),X3703),X3704),X3705))
| ~ hBOOL(hAPP(fun(X3698,bool),bool,finite_finite(X3698),X3701))
| hAPP(fun(X3698,bool),X3699,X3705,hAPP(fun(X3698,bool),fun(X3698,bool),hAPP(X3698,fun(fun(X3698,bool),fun(X3698,bool)),insert(X3698),X3700),X3701)) = hAPP(X3699,X3699,hAPP(X3699,fun(X3699,X3699),X3702,hAPP(X3698,X3699,X3704,X3700)),hAPP(fun(X3698,bool),X3699,X3705,X3701)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_120_folding__image__simple__idem_Oinsert__idem])]) ).
cnf(i_0_1598,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1222]) ).
fof(i_0_1599,plain,
! [X3663,X3664,X3665,X3666,X3667] :
( ( hBOOL(hAPP(fun(X3664,bool),bool,hAPP(X3664,fun(fun(X3664,bool),bool),member(X3664),esk12_5(X3663,X3664,X3665,X3666,X3667)),X3667))
| hBOOL(hAPP(fun(X3663,bool),bool,hAPP(fun(X3663,bool),fun(fun(X3663,bool),bool),ord_less_eq(fun(X3663,bool)),hAPP(fun(X3664,bool),fun(X3663,bool),hAPP(fun(X3664,X3663),fun(fun(X3664,bool),fun(X3663,bool)),image(X3664,X3663),X3665),X3667)),X3666)) )
& ( ~ hBOOL(hAPP(fun(X3663,bool),bool,hAPP(X3663,fun(fun(X3663,bool),bool),member(X3663),hAPP(X3664,X3663,X3665,esk12_5(X3663,X3664,X3665,X3666,X3667))),X3666))
| hBOOL(hAPP(fun(X3663,bool),bool,hAPP(fun(X3663,bool),fun(fun(X3663,bool),bool),ord_less_eq(fun(X3663,bool)),hAPP(fun(X3664,bool),fun(X3663,bool),hAPP(fun(X3664,X3663),fun(fun(X3664,bool),fun(X3663,bool)),image(X3664,X3663),X3665),X3667)),X3666)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_113_image__subsetI])])])]) ).
fof(i_0_1600,plain,
! [X3578,X3579,X3580] : hAPP(fun(X3578,bool),fun(X3578,bool),hAPP(X3578,fun(fun(X3578,bool),fun(X3578,bool)),insert(X3578),X3579),X3580) = hAPP(fun(X3578,bool),fun(X3578,bool),collect(X3578),hAPP(fun(X3578,bool),fun(X3578,bool),hAPP(fun(X3578,fun(bool,bool)),fun(fun(X3578,bool),fun(X3578,bool)),combs(X3578,bool,bool),hAPP(fun(X3578,bool),fun(X3578,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3578,bool),fun(X3578,fun(bool,bool))),combb(bool,fun(bool,bool),X3578),fdisj),hAPP(X3578,fun(X3578,bool),hAPP(fun(X3578,fun(X3578,bool)),fun(X3578,fun(X3578,bool)),combc(X3578,X3578,bool),fequal(X3578)),X3579))),hAPP(fun(X3578,bool),fun(X3578,bool),hAPP(fun(X3578,fun(fun(X3578,bool),bool)),fun(fun(X3578,bool),fun(X3578,bool)),combc(X3578,fun(X3578,bool),bool),member(X3578)),X3580))),
inference(variable_rename,[status(thm)],[fact_96_insert__compr__raw]) ).
fof(i_0_1601,plain,
! [X3483,X3484,X3485] : hAPP(fun(X3483,bool),fun(X3483,bool),hAPP(X3483,fun(fun(X3483,bool),fun(X3483,bool)),insert(X3483),X3484),X3485) = hAPP(fun(X3483,bool),fun(X3483,bool),collect(X3483),hAPP(fun(X3483,bool),fun(X3483,bool),hAPP(fun(X3483,fun(bool,bool)),fun(fun(X3483,bool),fun(X3483,bool)),combs(X3483,bool,bool),hAPP(fun(X3483,bool),fun(X3483,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3483,bool),fun(X3483,fun(bool,bool))),combb(bool,fun(bool,bool),X3483),fdisj),hAPP(X3483,fun(X3483,bool),hAPP(fun(X3483,fun(X3483,bool)),fun(X3483,fun(X3483,bool)),combc(X3483,X3483,bool),fequal(X3483)),X3484))),hAPP(fun(X3483,bool),fun(X3483,bool),hAPP(fun(X3483,fun(fun(X3483,bool),bool)),fun(fun(X3483,bool),fun(X3483,bool)),combc(X3483,fun(X3483,bool),bool),member(X3483)),X3485))),
inference(variable_rename,[status(thm)],[fact_72_insert__compr]) ).
cnf(i_0_1602,plain,
( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,X7),X7) = ti(X2,X7)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_1229]) ).
cnf(i_0_1603,plain,
( hAPP(fun(X1,bool),X2,X6,bot_bot(fun(X1,bool))) = ti(X2,X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_1230]) ).
fof(i_0_1604,plain,
! [X5906,X5907] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk107_2(X5906,X5907)))
| hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X5907)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X5906)) )
& ( ~ hBOOL(hAPP(int,bool,X5907,esk107_2(X5906,X5907)))
| ~ hBOOL(hAPP(int,bool,X5906,esk107_2(X5906,X5907)))
| hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X5907)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X5906)) )
& ( hBOOL(hAPP(int,bool,X5907,esk107_2(X5906,X5907)))
| hBOOL(hAPP(int,bool,X5906,esk107_2(X5906,X5907)))
| hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X5907)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X5906)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_815_transfer__nat__int__set__cong])])])]) ).
cnf(i_0_1605,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X6)
| hAPP(X1,X2,X3,esk80_6(X2,X1,X3,X4,X5,X6)) != hAPP(X1,X2,X4,esk80_6(X2,X1,X3,X4,X5,X6))
| ti(fun(X1,bool),X5) != ti(fun(X1,bool),X6) ),
inference(split_conjunct,[status(thm)],[i_0_1227]) ).
cnf(i_0_1606,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1231]) ).
fof(i_0_1607,plain,
! [X3850,X3851,X3852] :
( ( ~ hBOOL(hAPP(X3850,bool,X3851,X3852))
| hAPP(fun(X3850,bool),fun(X3850,bool),collect(X3850),hAPP(fun(X3850,bool),fun(X3850,bool),hAPP(fun(X3850,fun(bool,bool)),fun(fun(X3850,bool),fun(X3850,bool)),combs(X3850,bool,bool),hAPP(fun(X3850,bool),fun(X3850,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3850,bool),fun(X3850,fun(bool,bool))),combb(bool,fun(bool,bool),X3850),fconj),hAPP(X3850,fun(X3850,bool),hAPP(fun(X3850,fun(X3850,bool)),fun(X3850,fun(X3850,bool)),combc(X3850,X3850,bool),fequal(X3850)),X3852))),X3851)) = hAPP(fun(X3850,bool),fun(X3850,bool),hAPP(X3850,fun(fun(X3850,bool),fun(X3850,bool)),insert(X3850),X3852),bot_bot(fun(X3850,bool))) )
& ( hBOOL(hAPP(X3850,bool,X3851,X3852))
| hAPP(fun(X3850,bool),fun(X3850,bool),collect(X3850),hAPP(fun(X3850,bool),fun(X3850,bool),hAPP(fun(X3850,fun(bool,bool)),fun(fun(X3850,bool),fun(X3850,bool)),combs(X3850,bool,bool),hAPP(fun(X3850,bool),fun(X3850,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3850,bool),fun(X3850,fun(bool,bool))),combb(bool,fun(bool,bool),X3850),fconj),hAPP(X3850,fun(X3850,bool),hAPP(fun(X3850,fun(X3850,bool)),fun(X3850,fun(X3850,bool)),combc(X3850,X3850,bool),fequal(X3850)),X3852))),X3851)) = bot_bot(fun(X3850,bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1232])]) ).
fof(i_0_1608,plain,
! [X5558,X5559,X5560] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5558)),X5559)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5558)),X5560)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5559),X5560)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5559),X5560))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5558)),X5559)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5558)),X5560))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_704_Suc__mult__le__cancel1])]) ).
fof(i_0_1609,plain,
! [X5551,X5552,X5553] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5551)),X5552)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5551)),X5553)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5552),X5553)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5552),X5553))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5551)),X5552)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5551)),X5553))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_701_Suc__mult__less__cancel1])]) ).
fof(i_0_1610,plain,
! [X4855,X4856,X4857] :
( ( ~ hBOOL(hAPP(fun(X4855,bool),bool,hAPP(fun(X4855,bool),fun(fun(X4855,bool),bool),ord_less_eq(fun(X4855,bool)),hAPP(fun(X4855,bool),fun(X4855,bool),hAPP(fun(X4855,fun(fun(X4855,bool),bool)),fun(fun(X4855,bool),fun(X4855,bool)),combc(X4855,fun(X4855,bool),bool),member(X4855)),X4856)),hAPP(fun(X4855,bool),fun(X4855,bool),hAPP(fun(X4855,fun(fun(X4855,bool),bool)),fun(fun(X4855,bool),fun(X4855,bool)),combc(X4855,fun(X4855,bool),bool),member(X4855)),X4857)))
| hBOOL(hAPP(fun(X4855,bool),bool,hAPP(fun(X4855,bool),fun(fun(X4855,bool),bool),ord_less_eq(fun(X4855,bool)),X4856),X4857)) )
& ( ~ hBOOL(hAPP(fun(X4855,bool),bool,hAPP(fun(X4855,bool),fun(fun(X4855,bool),bool),ord_less_eq(fun(X4855,bool)),X4856),X4857))
| hBOOL(hAPP(fun(X4855,bool),bool,hAPP(fun(X4855,bool),fun(fun(X4855,bool),bool),ord_less_eq(fun(X4855,bool)),hAPP(fun(X4855,bool),fun(X4855,bool),hAPP(fun(X4855,fun(fun(X4855,bool),bool)),fun(fun(X4855,bool),fun(X4855,bool)),combc(X4855,fun(X4855,bool),bool),member(X4855)),X4856)),hAPP(fun(X4855,bool),fun(X4855,bool),hAPP(fun(X4855,fun(fun(X4855,bool),bool)),fun(fun(X4855,bool),fun(X4855,bool)),combc(X4855,fun(X4855,bool),bool),member(X4855)),X4857))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_452_pred__subset__eq])]) ).
fof(i_0_1611,plain,
! [X5819,X5820,X5821,X5822,X5823] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5823),X5819)),X5820) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5822),X5819)),X5821)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5823),X5822)),X5819)),X5820) = X5821
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5822),X5823)) )
& ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5823),X5822)),X5819)),X5820) != X5821
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5823),X5819)),X5820) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5822),X5819)),X5821)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5822),X5823)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_791_nat__eq__add__iff1])])]) ).
fof(i_0_1612,plain,
! [X5834,X5835,X5836,X5837,X5838] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5837),X5834)),X5835) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5838),X5834)),X5836)
| X5835 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5838),X5837)),X5834)),X5836)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5837),X5838)) )
& ( X5835 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5838),X5837)),X5834)),X5836)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5837),X5834)),X5835) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5838),X5834)),X5836)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5837),X5838)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_794_nat__eq__add__iff2])])]) ).
cnf(i_0_1613,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),X6)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),X4)),X5) != ti(X1,X6)
| ~ ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1233]) ).
cnf(i_0_1614,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)),X6)
| ti(X1,X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X4)),X5)),X6)
| ~ ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1234]) ).
fof(i_0_1615,plain,
! [X6173,X6174,X6175,X6176,X6177] :
( ~ linordered_idom(X6173)
| ~ hBOOL(hAPP(X6173,bool,hAPP(X6173,fun(X6173,bool),ord_less(X6173),hAPP(X6173,X6173,abs_abs(X6173),X6176)),X6177))
| ~ hBOOL(hAPP(X6173,bool,hAPP(X6173,fun(X6173,bool),ord_less(X6173),hAPP(X6173,X6173,abs_abs(X6173),X6174)),X6175))
| hBOOL(hAPP(X6173,bool,hAPP(X6173,fun(X6173,bool),ord_less(X6173),hAPP(X6173,X6173,hAPP(X6173,fun(X6173,X6173),times_times(X6173),hAPP(X6173,X6173,abs_abs(X6173),X6176)),hAPP(X6173,X6173,abs_abs(X6173),X6174))),hAPP(X6173,X6173,hAPP(X6173,fun(X6173,X6173),times_times(X6173),X6177),X6175))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_915_abs__mult__less])])]) ).
fof(i_0_1616,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_1617,plain,
! [X5862,X5863,X5864] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5862),X5863)),X5864)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5864),X5862))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5862))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_802_q__pos__lemma])]) ).
fof(i_0_1618,plain,
! [X5673,X5674,X5675,X5676,X5677,X5678] :
( ~ ab_semigroup_mult(X5674)
| ~ hBOOL(hAPP(fun(X5673,bool),bool,finite_finite(X5673),X5678))
| hBOOL(hAPP(fun(X5673,bool),bool,hAPP(X5673,fun(fun(X5673,bool),bool),member(X5673),X5677),X5678))
| hAPP(fun(X5673,bool),X5674,hAPP(X5674,fun(fun(X5673,bool),X5674),hAPP(fun(X5673,X5674),fun(X5674,fun(fun(X5673,bool),X5674)),hAPP(fun(X5674,fun(X5674,X5674)),fun(fun(X5673,X5674),fun(X5674,fun(fun(X5673,bool),X5674))),finite_fold_image(X5674,X5673),times_times(X5674)),X5675),X5676),hAPP(fun(X5673,bool),fun(X5673,bool),hAPP(X5673,fun(fun(X5673,bool),fun(X5673,bool)),insert(X5673),X5677),X5678)) = hAPP(X5674,X5674,hAPP(X5674,fun(X5674,X5674),times_times(X5674),hAPP(X5673,X5674,X5675,X5677)),hAPP(fun(X5673,bool),X5674,hAPP(X5674,fun(fun(X5673,bool),X5674),hAPP(fun(X5673,X5674),fun(X5674,fun(fun(X5673,bool),X5674)),hAPP(fun(X5674,fun(X5674,X5674)),fun(fun(X5673,X5674),fun(X5674,fun(fun(X5673,bool),X5674))),finite_fold_image(X5674,X5673),times_times(X5674)),X5675),X5676),X5678)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1235])])]) ).
fof(i_0_1619,plain,
! [X3910,X3911,X3912] :
( ~ hBOOL(hAPP(fun(X3910,bool),bool,finite_finite(X3910),X3912))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X3910,bool),nat,finite_card(X3910),X3911)),hAPP(fun(X3910,bool),nat,finite_card(X3910),X3912))),hAPP(fun(X3910,bool),nat,finite_card(X3910),hAPP(fun(X3910,bool),fun(X3910,bool),hAPP(fun(X3910,bool),fun(fun(X3910,bool),fun(X3910,bool)),minus_minus(fun(X3910,bool)),X3911),X3912)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_diff__card__le__card__Diff])]) ).
fof(i_0_1620,plain,
! [X4653,X4654,X4655] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk48_3(X4653,X4654,X4655)),esk49_3(X4653,X4654,X4655)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X4655,X4653)),X4654)),hAPP(nat,nat,X4655,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4653),X4654)))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X4655,esk48_3(X4653,X4654,X4655))),hAPP(nat,nat,X4655,esk49_3(X4653,X4654,X4655))))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X4655,X4653)),X4654)),hAPP(nat,nat,X4655,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4653),X4654)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_409_mono__nat__linear__lb])])])]) ).
fof(i_0_1621,plain,
! [X4665,X4666,X4667,X4668] :
( ( ~ hBOOL(hAPP(X4665,bool,hAPP(X4665,fun(X4665,bool),ord_less(X4665),hAPP(nat,X4665,X4668,X4666)),hAPP(nat,X4665,X4668,X4667)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4666),X4667))
| ~ hBOOL(hAPP(X4665,bool,hAPP(X4665,fun(X4665,bool),ord_less(X4665),hAPP(nat,X4665,X4668,esk52_4(X4665,X4666,X4667,X4668))),hAPP(nat,X4665,X4668,hAPP(nat,nat,suc,esk52_4(X4665,X4666,X4667,X4668)))))
| ~ order(X4665) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4666),X4667))
| hBOOL(hAPP(X4665,bool,hAPP(X4665,fun(X4665,bool),ord_less(X4665),hAPP(nat,X4665,X4668,X4666)),hAPP(nat,X4665,X4668,X4667)))
| ~ hBOOL(hAPP(X4665,bool,hAPP(X4665,fun(X4665,bool),ord_less(X4665),hAPP(nat,X4665,X4668,esk52_4(X4665,X4666,X4667,X4668))),hAPP(nat,X4665,X4668,hAPP(nat,nat,suc,esk52_4(X4665,X4666,X4667,X4668)))))
| ~ order(X4665) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_412_lift__Suc__mono__less__iff])])])])]) ).
cnf(i_0_1622,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X5)),X3)),X4) = ti(X1,X6)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)
| ~ ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1233]) ).
cnf(i_0_1623,plain,
( ti(X1,X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X5),X2)),X3)),X6)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)
| ~ ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1234]) ).
fof(i_0_1624,plain,
! [X3395,X3396,X3397,X3398] :
( ~ order(X3395)
| ~ hBOOL(hAPP(X3395,bool,hAPP(X3395,fun(X3395,bool),ord_less_eq(X3395),hAPP(nat,X3395,X3398,esk2_4(X3395,X3396,X3397,X3398))),hAPP(nat,X3395,X3398,hAPP(nat,nat,suc,esk2_4(X3395,X3396,X3397,X3398)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3396),X3397))
| hBOOL(hAPP(X3395,bool,hAPP(X3395,fun(X3395,bool),ord_less_eq(X3395),hAPP(nat,X3395,X3398,X3396)),hAPP(nat,X3395,X3398,X3397))) ),
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_1625,plain,
! [X4670,X4671,X4672,X4673] :
( ~ order(X4670)
| ~ hBOOL(hAPP(X4670,bool,hAPP(X4670,fun(X4670,bool),ord_less(X4670),hAPP(nat,X4670,X4673,esk53_4(X4670,X4671,X4672,X4673))),hAPP(nat,X4670,X4673,hAPP(nat,nat,suc,esk53_4(X4670,X4671,X4672,X4673)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4671),X4672))
| hBOOL(hAPP(X4670,bool,hAPP(X4670,fun(X4670,bool),ord_less(X4670),hAPP(nat,X4670,X4673,X4671)),hAPP(nat,X4670,X4673,X4672))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_413_lift__Suc__mono__less])])])]) ).
fof(i_0_1626,plain,
! [X5955,X5956,X5957,X5960,X5962] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5960),esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,X5962))
| hBOOL(hAPP(int,bool,X5955,esk123_3(X5955,X5956,X5957)))
| ~ hBOOL(hAPP(int,bool,X5956,esk120_3(X5955,X5956,X5957)))
| ~ hBOOL(hAPP(int,bool,X5956,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X5955,X5956,X5957)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X5955,X5956,X5957)),X5957))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5957)) )
& ( ~ hBOOL(hAPP(int,bool,X5955,esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,X5962))
| hBOOL(hAPP(int,bool,X5955,esk123_3(X5955,X5956,X5957)))
| ~ hBOOL(hAPP(int,bool,X5956,esk120_3(X5955,X5956,X5957)))
| ~ hBOOL(hAPP(int,bool,X5956,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X5955,X5956,X5957)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X5955,X5956,X5957)),X5957))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5957)) )
& ( hBOOL(hAPP(int,bool,X5955,esk122_4(X5955,X5956,X5957,X5960)))
| hBOOL(hAPP(int,bool,X5956,esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,X5962))
| hBOOL(hAPP(int,bool,X5955,esk123_3(X5955,X5956,X5957)))
| ~ hBOOL(hAPP(int,bool,X5956,esk120_3(X5955,X5956,X5957)))
| ~ hBOOL(hAPP(int,bool,X5956,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X5955,X5956,X5957)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X5955,X5956,X5957)),X5957))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5957)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5960),esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,X5962))
| hBOOL(hAPP(int,bool,X5955,esk123_3(X5955,X5956,X5957)))
| hBOOL(hAPP(int,bool,X5956,esk120_3(X5955,X5956,X5957)))
| hBOOL(hAPP(int,bool,X5956,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X5955,X5956,X5957)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X5955,X5956,X5957)),X5957))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5957)) )
& ( ~ hBOOL(hAPP(int,bool,X5955,esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,X5962))
| hBOOL(hAPP(int,bool,X5955,esk123_3(X5955,X5956,X5957)))
| hBOOL(hAPP(int,bool,X5956,esk120_3(X5955,X5956,X5957)))
| hBOOL(hAPP(int,bool,X5956,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X5955,X5956,X5957)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X5955,X5956,X5957)),X5957))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5957)) )
& ( hBOOL(hAPP(int,bool,X5955,esk122_4(X5955,X5956,X5957,X5960)))
| hBOOL(hAPP(int,bool,X5956,esk122_4(X5955,X5956,X5957,X5960)))
| ~ hBOOL(hAPP(int,bool,X5956,X5962))
| hBOOL(hAPP(int,bool,X5955,esk123_3(X5955,X5956,X5957)))
| hBOOL(hAPP(int,bool,X5956,esk120_3(X5955,X5956,X5957)))
| hBOOL(hAPP(int,bool,X5956,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X5955,X5956,X5957)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X5955,X5956,X5957)),X5957))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5957)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_826_plusinfinity])])])])]) ).
fof(i_0_1627,plain,
! [X5946,X5947,X5948,X5951,X5953] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),esk118_4(X5946,X5947,X5948,X5951)),X5951))
| ~ hBOOL(hAPP(int,bool,X5947,X5953))
| hBOOL(hAPP(int,bool,X5946,esk119_3(X5946,X5947,X5948)))
| ~ hBOOL(hAPP(int,bool,X5947,esk116_3(X5946,X5947,X5948)))
| ~ hBOOL(hAPP(int,bool,X5947,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X5946,X5947,X5948)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X5946,X5947,X5948)),X5948))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5948)) )
& ( ~ hBOOL(hAPP(int,bool,X5946,esk118_4(X5946,X5947,X5948,X5951)))
| ~ hBOOL(hAPP(int,bool,X5947,esk118_4(X5946,X5947,X5948,X5951)))
| ~ hBOOL(hAPP(int,bool,X5947,X5953))
| hBOOL(hAPP(int,bool,X5946,esk119_3(X5946,X5947,X5948)))
| ~ hBOOL(hAPP(int,bool,X5947,esk116_3(X5946,X5947,X5948)))
| ~ hBOOL(hAPP(int,bool,X5947,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X5946,X5947,X5948)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X5946,X5947,X5948)),X5948))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5948)) )
& ( hBOOL(hAPP(int,bool,X5946,esk118_4(X5946,X5947,X5948,X5951)))
| hBOOL(hAPP(int,bool,X5947,esk118_4(X5946,X5947,X5948,X5951)))
| ~ hBOOL(hAPP(int,bool,X5947,X5953))
| hBOOL(hAPP(int,bool,X5946,esk119_3(X5946,X5947,X5948)))
| ~ hBOOL(hAPP(int,bool,X5947,esk116_3(X5946,X5947,X5948)))
| ~ hBOOL(hAPP(int,bool,X5947,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X5946,X5947,X5948)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X5946,X5947,X5948)),X5948))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5948)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),esk118_4(X5946,X5947,X5948,X5951)),X5951))
| ~ hBOOL(hAPP(int,bool,X5947,X5953))
| hBOOL(hAPP(int,bool,X5946,esk119_3(X5946,X5947,X5948)))
| hBOOL(hAPP(int,bool,X5947,esk116_3(X5946,X5947,X5948)))
| hBOOL(hAPP(int,bool,X5947,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X5946,X5947,X5948)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X5946,X5947,X5948)),X5948))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5948)) )
& ( ~ hBOOL(hAPP(int,bool,X5946,esk118_4(X5946,X5947,X5948,X5951)))
| ~ hBOOL(hAPP(int,bool,X5947,esk118_4(X5946,X5947,X5948,X5951)))
| ~ hBOOL(hAPP(int,bool,X5947,X5953))
| hBOOL(hAPP(int,bool,X5946,esk119_3(X5946,X5947,X5948)))
| hBOOL(hAPP(int,bool,X5947,esk116_3(X5946,X5947,X5948)))
| hBOOL(hAPP(int,bool,X5947,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X5946,X5947,X5948)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X5946,X5947,X5948)),X5948))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5948)) )
& ( hBOOL(hAPP(int,bool,X5946,esk118_4(X5946,X5947,X5948,X5951)))
| hBOOL(hAPP(int,bool,X5947,esk118_4(X5946,X5947,X5948,X5951)))
| ~ hBOOL(hAPP(int,bool,X5947,X5953))
| hBOOL(hAPP(int,bool,X5946,esk119_3(X5946,X5947,X5948)))
| hBOOL(hAPP(int,bool,X5947,esk116_3(X5946,X5947,X5948)))
| hBOOL(hAPP(int,bool,X5947,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X5946,X5947,X5948)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X5946,X5947,X5948)),X5948))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5948)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_825_minusinfinity])])])])]) ).
fof(i_0_1628,plain,
! [X5196,X5197,X5198,X5199,X5200] :
( ~ semiring(X5196)
| hAPP(X5196,X5196,hAPP(X5196,fun(X5196,X5196),plus_plus(X5196),hAPP(X5196,X5196,hAPP(X5196,fun(X5196,X5196),times_times(X5196),X5197),X5198)),hAPP(X5196,X5196,hAPP(X5196,fun(X5196,X5196),plus_plus(X5196),hAPP(X5196,X5196,hAPP(X5196,fun(X5196,X5196),times_times(X5196),X5199),X5198)),X5200)) = hAPP(X5196,X5196,hAPP(X5196,fun(X5196,X5196),plus_plus(X5196),hAPP(X5196,X5196,hAPP(X5196,fun(X5196,X5196),times_times(X5196),hAPP(X5196,X5196,hAPP(X5196,fun(X5196,X5196),plus_plus(X5196),X5197),X5199)),X5198)),X5200) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_591_combine__common__factor])])]) ).
fof(i_0_1629,plain,
! [X3921,X3922,X3923] :
( ( hBOOL(hAPP(fun(X3921,bool),bool,finite_finite(X3921),esk24_3(X3921,X3922,X3923)))
| hBOOL(hAPP(fun(X3921,bool),bool,X3922,bot_bot(fun(X3921,bool))))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,X3922,X3923))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,finite_finite(X3921),X3923)) )
& ( hBOOL(hAPP(fun(X3921,bool),bool,hAPP(X3921,fun(fun(X3921,bool),bool),member(X3921),esk23_3(X3921,X3922,X3923)),esk24_3(X3921,X3922,X3923)))
| hBOOL(hAPP(fun(X3921,bool),bool,X3922,bot_bot(fun(X3921,bool))))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,X3922,X3923))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,finite_finite(X3921),X3923)) )
& ( hBOOL(hAPP(fun(X3921,bool),bool,X3922,esk24_3(X3921,X3922,X3923)))
| hBOOL(hAPP(fun(X3921,bool),bool,X3922,bot_bot(fun(X3921,bool))))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,X3922,X3923))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,finite_finite(X3921),X3923)) )
& ( ~ hBOOL(hAPP(fun(X3921,bool),bool,X3922,hAPP(fun(X3921,bool),fun(X3921,bool),hAPP(fun(X3921,bool),fun(fun(X3921,bool),fun(X3921,bool)),minus_minus(fun(X3921,bool)),esk24_3(X3921,X3922,X3923)),hAPP(fun(X3921,bool),fun(X3921,bool),hAPP(X3921,fun(fun(X3921,bool),fun(X3921,bool)),insert(X3921),esk23_3(X3921,X3922,X3923)),bot_bot(fun(X3921,bool))))))
| hBOOL(hAPP(fun(X3921,bool),bool,X3922,bot_bot(fun(X3921,bool))))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,X3922,X3923))
| ~ hBOOL(hAPP(fun(X3921,bool),bool,finite_finite(X3921),X3923)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_183_finite__empty__induct])])])]) ).
fof(i_0_1630,plain,
! [X5796,X5797,X5798,X5799] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5796),X5797)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5798),X5797)),X5799)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5796),X5798)),X5797)),X5799),
inference(variable_rename,[status(thm)],[fact_785_left__add__mult__distrib]) ).
fof(i_0_1631,plain,
! [X6065,X6066,X6067] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6066),X6067))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6065))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X6065)),X6066)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X6065)),X6067))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_876_zmult__zless__mono2__lemma])]) ).
fof(i_0_1632,plain,
! [X6167,X6168,X6169] :
( ~ ordere142940540dd_abs(X6167)
| hBOOL(hAPP(X6167,bool,hAPP(X6167,fun(X6167,bool),ord_less_eq(X6167),hAPP(X6167,X6167,hAPP(X6167,fun(X6167,X6167),minus_minus(X6167),hAPP(X6167,X6167,abs_abs(X6167),X6168)),hAPP(X6167,X6167,abs_abs(X6167),X6169))),hAPP(X6167,X6167,abs_abs(X6167),hAPP(X6167,X6167,hAPP(X6167,fun(X6167,X6167),minus_minus(X6167),X6168),X6169)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_913_abs__triangle__ineq2])])]) ).
fof(i_0_1633,plain,
! [X6170,X6171,X6172] :
( ~ ordere142940540dd_abs(X6170)
| hBOOL(hAPP(X6170,bool,hAPP(X6170,fun(X6170,bool),ord_less_eq(X6170),hAPP(X6170,X6170,hAPP(X6170,fun(X6170,X6170),minus_minus(X6170),hAPP(X6170,X6170,abs_abs(X6170),X6171)),hAPP(X6170,X6170,abs_abs(X6170),X6172))),hAPP(X6170,X6170,abs_abs(X6170),hAPP(X6170,X6170,hAPP(X6170,fun(X6170,X6170),minus_minus(X6170),X6172),X6171)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_914_abs__triangle__ineq2__sym])])]) ).
fof(i_0_1634,plain,
! [X3680,X3681] :
( ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),esk16_2(X3680,X3681)),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X3680),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(com,x_a,mgt,X3681)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X3681)) )
& ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X3680),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,esk16_2(X3680,X3681))),bot_bot(fun(x_a,bool)))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X3680),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(com,x_a,mgt,X3681)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X3681)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_116_assms_I3_J])])])]) ).
fof(i_0_1635,plain,
! [X6035] : hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X6035)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),X6035),semiring_1_of_nat(int)))),
inference(variable_rename,[status(thm)],[fact_864_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).
fof(i_0_1636,plain,
! [X3869,X3870,X3871,X3872] :
( ( ~ hBOOL(hAPP(fun(X3869,bool),bool,finite_finite(X3869),hAPP(fun(X3869,bool),fun(X3869,bool),hAPP(fun(X3869,bool),fun(fun(X3869,bool),fun(X3869,bool)),minus_minus(fun(X3869,bool)),X3870),hAPP(fun(X3869,bool),fun(X3869,bool),hAPP(X3869,fun(fun(X3869,bool),fun(X3869,bool)),insert(X3869),X3871),X3872))))
| hBOOL(hAPP(fun(X3869,bool),bool,finite_finite(X3869),hAPP(fun(X3869,bool),fun(X3869,bool),hAPP(fun(X3869,bool),fun(fun(X3869,bool),fun(X3869,bool)),minus_minus(fun(X3869,bool)),X3870),X3872))) )
& ( ~ hBOOL(hAPP(fun(X3869,bool),bool,finite_finite(X3869),hAPP(fun(X3869,bool),fun(X3869,bool),hAPP(fun(X3869,bool),fun(fun(X3869,bool),fun(X3869,bool)),minus_minus(fun(X3869,bool)),X3870),X3872)))
| hBOOL(hAPP(fun(X3869,bool),bool,finite_finite(X3869),hAPP(fun(X3869,bool),fun(X3869,bool),hAPP(fun(X3869,bool),fun(fun(X3869,bool),fun(X3869,bool)),minus_minus(fun(X3869,bool)),X3870),hAPP(fun(X3869,bool),fun(X3869,bool),hAPP(X3869,fun(fun(X3869,bool),fun(X3869,bool)),insert(X3869),X3871),X3872)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_171_finite__Diff__insert])]) ).
fof(i_0_1637,plain,
! [X6178,X6179,X6180] :
( ~ ordere142940540dd_abs(X6178)
| hBOOL(hAPP(X6178,bool,hAPP(X6178,fun(X6178,bool),ord_less_eq(X6178),hAPP(X6178,X6178,abs_abs(X6178),hAPP(X6178,X6178,hAPP(X6178,fun(X6178,X6178),plus_plus(X6178),X6179),X6180))),hAPP(X6178,X6178,hAPP(X6178,fun(X6178,X6178),plus_plus(X6178),hAPP(X6178,X6178,abs_abs(X6178),X6179)),hAPP(X6178,X6178,abs_abs(X6178),X6180)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_916_abs__triangle__ineq])])]) ).
fof(i_0_1638,plain,
! [X6141,X6142,X6143] :
( ~ ordere142940540dd_abs(X6141)
| hBOOL(hAPP(X6141,bool,hAPP(X6141,fun(X6141,bool),ord_less_eq(X6141),hAPP(X6141,X6141,abs_abs(X6141),hAPP(X6141,X6141,hAPP(X6141,fun(X6141,X6141),minus_minus(X6141),X6142),X6143))),hAPP(X6141,X6141,hAPP(X6141,fun(X6141,X6141),plus_plus(X6141),hAPP(X6141,X6141,abs_abs(X6141),X6142)),hAPP(X6141,X6141,abs_abs(X6141),X6143)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_901_abs__triangle__ineq4])])]) ).
fof(i_0_1639,plain,
! [X6085,X6086] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X6085),X6086))
| hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6085)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6086))) )
& ( ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6085)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6086)))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X6085),X6086)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_885_transfer__nat__int__set__relations_I5_J])]) ).
fof(i_0_1640,plain,
! [X6083,X6084] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),X6083),X6084))
| hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6083)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6084))) )
& ( ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6083)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6084)))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),X6083),X6084)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_884_transfer__nat__int__set__relations_I4_J])]) ).
cnf(i_0_1641,plain,
( ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1231]) ).
cnf(i_0_1642,plain,
( ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1231]) ).
fof(i_0_1643,plain,
! [X6072,X6073,X6074] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6074),X6073))
| hBOOL(hAPP(int,bool,X6072,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X6073)),hAPP(nat,int,semiring_1_of_nat(int),X6074))))
| ~ hBOOL(hAPP(int,bool,X6072,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6073),X6074)))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6073),X6074))
| hBOOL(hAPP(int,bool,X6072,zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,X6072,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6073),X6074)))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6073),X6074))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6074),X6073))
| hBOOL(hAPP(int,bool,X6072,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6073),X6074)))) )
& ( ~ hBOOL(hAPP(int,bool,X6072,zero_zero(int)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6074),X6073))
| hBOOL(hAPP(int,bool,X6072,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6073),X6074)))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6073),X6074))
| ~ hBOOL(hAPP(int,bool,X6072,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X6073)),hAPP(nat,int,semiring_1_of_nat(int),X6074))))
| hBOOL(hAPP(int,bool,X6072,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6073),X6074)))) )
& ( ~ hBOOL(hAPP(int,bool,X6072,zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,X6072,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X6073)),hAPP(nat,int,semiring_1_of_nat(int),X6074))))
| hBOOL(hAPP(int,bool,X6072,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6073),X6074)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_879_zdiff__int__split])])]) ).
fof(i_0_1644,plain,
! [X5620,X5621,X5622] :
( ~ linordered_ring(X5620)
| hBOOL(hAPP(X5620,bool,hAPP(X5620,fun(X5620,bool),ord_less_eq(X5620),zero_zero(X5620)),hAPP(X5620,X5620,hAPP(X5620,fun(X5620,X5620),plus_plus(X5620),hAPP(X5620,X5620,hAPP(X5620,fun(X5620,X5620),times_times(X5620),X5621),X5621)),hAPP(X5620,X5620,hAPP(X5620,fun(X5620,X5620),times_times(X5620),X5622),X5622)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_720_sum__squares__ge__zero])])]) ).
fof(i_0_1645,plain,
! [X3286,X3287,X3288,X3289] :
( ~ hBOOL(hAPP(fun(X3287,bool),bool,finite_finite(X3287),X3289))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3286,bool),nat,finite_card(X3286),hAPP(fun(X3287,bool),fun(X3286,bool),hAPP(fun(X3287,X3286),fun(fun(X3287,bool),fun(X3286,bool)),image(X3287,X3286),X3288),X3289))),hAPP(fun(X3287,bool),nat,finite_card(X3287),X3289))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_card__image__le])]) ).
fof(i_0_1646,plain,
! [X3365,X3366,X3367] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3367),X3366)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3365),X3366)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3367),X3365))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3366),X3365))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3366),X3367)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3367),X3365))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3367),X3366)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3365),X3366)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3366),X3365))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3366),X3367)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_le__diff__iff])])]) ).
fof(i_0_1647,plain,
! [X4649,X4650,X4651] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4651),X4650)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4649),X4650)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4651),X4649))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4650),X4649))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4650),X4651)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4651),X4649))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4651),X4650)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4649),X4650)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4650),X4649))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4650),X4651)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_407_less__diff__iff])])]) ).
fof(i_0_1648,plain,
! [X4044,X4045,X4046,X4047] :
( ~ hBOOL(hAPP(fun(X4044,bool),bool,finite_finite(X4044),X4047))
| ~ hBOOL(hAPP(fun(X4044,bool),bool,hAPP(X4044,fun(fun(X4044,bool),bool),member(X4044),X4046),X4047))
| hBOOL(hAPP(fun(X4044,bool),bool,hAPP(X4044,fun(fun(X4044,bool),bool),member(X4044),X4046),X4045))
| hAPP(fun(X4044,bool),nat,finite_card(X4044),hAPP(fun(X4044,bool),fun(X4044,bool),hAPP(fun(X4044,bool),fun(fun(X4044,bool),fun(X4044,bool)),minus_minus(fun(X4044,bool)),X4047),hAPP(fun(X4044,bool),fun(X4044,bool),hAPP(X4044,fun(fun(X4044,bool),fun(X4044,bool)),insert(X4044),X4046),X4045))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X4044,bool),nat,finite_card(X4044),hAPP(fun(X4044,bool),fun(X4044,bool),hAPP(fun(X4044,bool),fun(fun(X4044,bool),fun(X4044,bool)),minus_minus(fun(X4044,bool)),X4047),X4045))),one_one(nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1236])]) ).
fof(i_0_1649,plain,
! [X3803,X3804,X3805,X3806,X3807] :
( ~ hBOOL(hAPP(fun(X3803,bool),bool,hAPP(fun(X3803,bool),fun(fun(X3803,bool),bool),ord_less_eq(fun(X3803,bool)),X3806),X3807))
| ~ hBOOL(hAPP(fun(X3803,bool),bool,hAPP(fun(X3803,bool),fun(fun(X3803,bool),bool),ord_less_eq(fun(X3803,bool)),X3804),X3805))
| hBOOL(hAPP(fun(X3803,bool),bool,hAPP(fun(X3803,bool),fun(fun(X3803,bool),bool),ord_less_eq(fun(X3803,bool)),hAPP(fun(X3803,bool),fun(X3803,bool),hAPP(fun(X3803,bool),fun(fun(X3803,bool),fun(X3803,bool)),minus_minus(fun(X3803,bool)),X3806),X3805)),hAPP(fun(X3803,bool),fun(X3803,bool),hAPP(fun(X3803,bool),fun(fun(X3803,bool),fun(X3803,bool)),minus_minus(fun(X3803,bool)),X3807),X3804))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_Diff__mono])]) ).
fof(i_0_1650,plain,
! [X5920,X5921,X5922,X5924] :
( ( hBOOL(hAPP(int,bool,X5921,esk109_3(X5920,X5921,X5922)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5920))
| ~ hBOOL(hAPP(int,bool,X5921,X5924))
| hBOOL(hAPP(int,bool,X5921,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5924),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5920),X5922))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5922)) )
& ( ~ hBOOL(hAPP(int,bool,X5921,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk109_3(X5920,X5921,X5922)),X5922)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5920))
| ~ hBOOL(hAPP(int,bool,X5921,X5924))
| hBOOL(hAPP(int,bool,X5921,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5924),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5920),X5922))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5922)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_819_incr__mult__lemma])])])])]) ).
fof(i_0_1651,plain,
! [X5909,X5910,X5911,X5913] :
( ( hBOOL(hAPP(int,bool,X5910,esk108_3(X5909,X5910,X5911)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5909))
| ~ hBOOL(hAPP(int,bool,X5910,X5913))
| hBOOL(hAPP(int,bool,X5910,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5913),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5909),X5911))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5911)) )
& ( ~ hBOOL(hAPP(int,bool,X5910,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk108_3(X5909,X5910,X5911)),X5911)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5909))
| ~ hBOOL(hAPP(int,bool,X5910,X5913))
| hBOOL(hAPP(int,bool,X5910,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5913),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5909),X5911))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5911)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_816_decr__mult__lemma])])])])]) ).
fof(i_0_1652,plain,
! [X3853,X3854,X3855] :
( ( ~ hBOOL(hAPP(X3853,bool,X3854,X3855))
| hAPP(fun(X3853,bool),fun(X3853,bool),collect(X3853),hAPP(fun(X3853,bool),fun(X3853,bool),hAPP(fun(X3853,fun(bool,bool)),fun(fun(X3853,bool),fun(X3853,bool)),combs(X3853,bool,bool),hAPP(fun(X3853,bool),fun(X3853,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3853,bool),fun(X3853,fun(bool,bool))),combb(bool,fun(bool,bool),X3853),fconj),hAPP(X3853,fun(X3853,bool),fequal(X3853),X3855))),X3854)) = hAPP(fun(X3853,bool),fun(X3853,bool),hAPP(X3853,fun(fun(X3853,bool),fun(X3853,bool)),insert(X3853),X3855),bot_bot(fun(X3853,bool))) )
& ( hBOOL(hAPP(X3853,bool,X3854,X3855))
| hAPP(fun(X3853,bool),fun(X3853,bool),collect(X3853),hAPP(fun(X3853,bool),fun(X3853,bool),hAPP(fun(X3853,fun(bool,bool)),fun(fun(X3853,bool),fun(X3853,bool)),combs(X3853,bool,bool),hAPP(fun(X3853,bool),fun(X3853,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3853,bool),fun(X3853,fun(bool,bool))),combb(bool,fun(bool,bool),X3853),fconj),hAPP(X3853,fun(X3853,bool),fequal(X3853),X3855))),X3854)) = bot_bot(fun(X3853,bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1237])]) ).
fof(i_0_1653,plain,
! [X3913,X3914,X3915,X3916] :
( ( hBOOL(hAPP(fun(X3913,bool),bool,finite_finite(X3913),esk22_4(X3913,X3914,X3915,X3916)))
| hBOOL(hAPP(fun(X3913,bool),bool,X3914,X3916))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,X3914,bot_bot(fun(X3913,bool))))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,hAPP(fun(X3913,bool),fun(fun(X3913,bool),bool),ord_less_eq(fun(X3913,bool)),X3916),X3915))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,finite_finite(X3913),X3916)) )
& ( hBOOL(hAPP(fun(X3913,bool),bool,hAPP(X3913,fun(fun(X3913,bool),bool),member(X3913),esk21_4(X3913,X3914,X3915,X3916)),X3915))
| hBOOL(hAPP(fun(X3913,bool),bool,X3914,X3916))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,X3914,bot_bot(fun(X3913,bool))))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,hAPP(fun(X3913,bool),fun(fun(X3913,bool),bool),ord_less_eq(fun(X3913,bool)),X3916),X3915))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,finite_finite(X3913),X3916)) )
& ( ~ hBOOL(hAPP(fun(X3913,bool),bool,hAPP(X3913,fun(fun(X3913,bool),bool),member(X3913),esk21_4(X3913,X3914,X3915,X3916)),esk22_4(X3913,X3914,X3915,X3916)))
| hBOOL(hAPP(fun(X3913,bool),bool,X3914,X3916))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,X3914,bot_bot(fun(X3913,bool))))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,hAPP(fun(X3913,bool),fun(fun(X3913,bool),bool),ord_less_eq(fun(X3913,bool)),X3916),X3915))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,finite_finite(X3913),X3916)) )
& ( hBOOL(hAPP(fun(X3913,bool),bool,X3914,esk22_4(X3913,X3914,X3915,X3916)))
| hBOOL(hAPP(fun(X3913,bool),bool,X3914,X3916))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,X3914,bot_bot(fun(X3913,bool))))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,hAPP(fun(X3913,bool),fun(fun(X3913,bool),bool),ord_less_eq(fun(X3913,bool)),X3916),X3915))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,finite_finite(X3913),X3916)) )
& ( ~ hBOOL(hAPP(fun(X3913,bool),bool,X3914,hAPP(fun(X3913,bool),fun(X3913,bool),hAPP(X3913,fun(fun(X3913,bool),fun(X3913,bool)),insert(X3913),esk21_4(X3913,X3914,X3915,X3916)),esk22_4(X3913,X3914,X3915,X3916))))
| hBOOL(hAPP(fun(X3913,bool),bool,X3914,X3916))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,X3914,bot_bot(fun(X3913,bool))))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,hAPP(fun(X3913,bool),fun(fun(X3913,bool),bool),ord_less_eq(fun(X3913,bool)),X3916),X3915))
| ~ hBOOL(hAPP(fun(X3913,bool),bool,finite_finite(X3913),X3916)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1238])])])]) ).
fof(i_0_1654,plain,
! [X5569,X5570,X5571,X5572] :
( ~ linord20386208strict(X5569)
| ~ hBOOL(hAPP(X5569,bool,hAPP(X5569,fun(X5569,bool),ord_less_eq(X5569),hAPP(X5569,X5569,hAPP(X5569,fun(X5569,X5569),times_times(X5569),X5570),X5571)),hAPP(X5569,X5569,hAPP(X5569,fun(X5569,X5569),times_times(X5569),X5572),X5571)))
| ~ hBOOL(hAPP(X5569,bool,hAPP(X5569,fun(X5569,bool),ord_less(X5569),zero_zero(X5569)),X5571))
| hBOOL(hAPP(X5569,bool,hAPP(X5569,fun(X5569,bool),ord_less_eq(X5569),X5570),X5572)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_708_mult__right__le__imp__le])])]) ).
fof(i_0_1655,plain,
! [X5565,X5566,X5567,X5568] :
( ~ linord20386208strict(X5565)
| ~ hBOOL(hAPP(X5565,bool,hAPP(X5565,fun(X5565,bool),ord_less_eq(X5565),hAPP(X5565,X5565,hAPP(X5565,fun(X5565,X5565),times_times(X5565),X5566),X5567)),hAPP(X5565,X5565,hAPP(X5565,fun(X5565,X5565),times_times(X5565),X5566),X5568)))
| ~ hBOOL(hAPP(X5565,bool,hAPP(X5565,fun(X5565,bool),ord_less(X5565),zero_zero(X5565)),X5566))
| hBOOL(hAPP(X5565,bool,hAPP(X5565,fun(X5565,bool),ord_less_eq(X5565),X5567),X5568)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_707_mult__left__le__imp__le])])]) ).
fof(i_0_1656,plain,
! [X5613,X5614,X5615,X5616] :
( ( ~ hBOOL(hAPP(X5613,bool,hAPP(X5613,fun(X5613,bool),ord_less_eq(X5613),hAPP(X5613,X5613,hAPP(X5613,fun(X5613,X5613),times_times(X5613),X5616),X5614)),hAPP(X5613,X5613,hAPP(X5613,fun(X5613,X5613),times_times(X5613),X5616),X5615)))
| hBOOL(hAPP(X5613,bool,hAPP(X5613,fun(X5613,bool),ord_less_eq(X5613),X5614),X5615))
| ~ hBOOL(hAPP(X5613,bool,hAPP(X5613,fun(X5613,bool),ord_less(X5613),zero_zero(X5613)),X5616))
| ~ linord581940658strict(X5613) )
& ( ~ hBOOL(hAPP(X5613,bool,hAPP(X5613,fun(X5613,bool),ord_less_eq(X5613),X5614),X5615))
| hBOOL(hAPP(X5613,bool,hAPP(X5613,fun(X5613,bool),ord_less_eq(X5613),hAPP(X5613,X5613,hAPP(X5613,fun(X5613,X5613),times_times(X5613),X5616),X5614)),hAPP(X5613,X5613,hAPP(X5613,fun(X5613,X5613),times_times(X5613),X5616),X5615)))
| ~ hBOOL(hAPP(X5613,bool,hAPP(X5613,fun(X5613,bool),ord_less(X5613),zero_zero(X5613)),X5616))
| ~ linord581940658strict(X5613) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_718_mult__le__cancel__left__pos])])])]) ).
fof(i_0_1657,plain,
! [X5585,X5586,X5587,X5588] :
( ~ linordered_semiring(X5585)
| ~ hBOOL(hAPP(X5585,bool,hAPP(X5585,fun(X5585,bool),ord_less(X5585),hAPP(X5585,X5585,hAPP(X5585,fun(X5585,X5585),times_times(X5585),X5586),X5587)),hAPP(X5585,X5585,hAPP(X5585,fun(X5585,X5585),times_times(X5585),X5588),X5587)))
| ~ hBOOL(hAPP(X5585,bool,hAPP(X5585,fun(X5585,bool),ord_less_eq(X5585),zero_zero(X5585)),X5587))
| hBOOL(hAPP(X5585,bool,hAPP(X5585,fun(X5585,bool),ord_less(X5585),X5586),X5588)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_712_mult__right__less__imp__less])])]) ).
fof(i_0_1658,plain,
! [X5581,X5582,X5583,X5584] :
( ~ linord20386208strict(X5581)
| ~ hBOOL(hAPP(X5581,bool,hAPP(X5581,fun(X5581,bool),ord_less(X5581),hAPP(X5581,X5581,hAPP(X5581,fun(X5581,X5581),times_times(X5581),X5582),X5583)),hAPP(X5581,X5581,hAPP(X5581,fun(X5581,X5581),times_times(X5581),X5584),X5583)))
| ~ hBOOL(hAPP(X5581,bool,hAPP(X5581,fun(X5581,bool),ord_less_eq(X5581),zero_zero(X5581)),X5583))
| hBOOL(hAPP(X5581,bool,hAPP(X5581,fun(X5581,bool),ord_less(X5581),X5582),X5584)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_711_mult__less__imp__less__right])])]) ).
fof(i_0_1659,plain,
! [X5577,X5578,X5579,X5580] :
( ~ linordered_semiring(X5577)
| ~ hBOOL(hAPP(X5577,bool,hAPP(X5577,fun(X5577,bool),ord_less(X5577),hAPP(X5577,X5577,hAPP(X5577,fun(X5577,X5577),times_times(X5577),X5578),X5579)),hAPP(X5577,X5577,hAPP(X5577,fun(X5577,X5577),times_times(X5577),X5578),X5580)))
| ~ hBOOL(hAPP(X5577,bool,hAPP(X5577,fun(X5577,bool),ord_less_eq(X5577),zero_zero(X5577)),X5578))
| hBOOL(hAPP(X5577,bool,hAPP(X5577,fun(X5577,bool),ord_less(X5577),X5579),X5580)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_710_mult__left__less__imp__less])])]) ).
fof(i_0_1660,plain,
! [X5573,X5574,X5575,X5576] :
( ~ linord20386208strict(X5573)
| ~ hBOOL(hAPP(X5573,bool,hAPP(X5573,fun(X5573,bool),ord_less(X5573),hAPP(X5573,X5573,hAPP(X5573,fun(X5573,X5573),times_times(X5573),X5574),X5575)),hAPP(X5573,X5573,hAPP(X5573,fun(X5573,X5573),times_times(X5573),X5574),X5576)))
| ~ hBOOL(hAPP(X5573,bool,hAPP(X5573,fun(X5573,bool),ord_less_eq(X5573),zero_zero(X5573)),X5574))
| hBOOL(hAPP(X5573,bool,hAPP(X5573,fun(X5573,bool),ord_less(X5573),X5575),X5576)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_709_mult__less__imp__less__left])])]) ).
fof(i_0_1661,plain,
! [X5454,X5455,X5456,X5457] :
( ( ~ hBOOL(hAPP(X5454,bool,hAPP(X5454,fun(X5454,bool),ord_less(X5454),hAPP(X5454,X5454,hAPP(X5454,fun(X5454,X5454),times_times(X5454),X5457),X5455)),hAPP(X5454,X5454,hAPP(X5454,fun(X5454,X5454),times_times(X5454),X5457),X5456)))
| hBOOL(hAPP(X5454,bool,hAPP(X5454,fun(X5454,bool),ord_less(X5454),X5455),X5456))
| ~ hBOOL(hAPP(X5454,bool,hAPP(X5454,fun(X5454,bool),ord_less(X5454),zero_zero(X5454)),X5457))
| ~ linord581940658strict(X5454) )
& ( ~ hBOOL(hAPP(X5454,bool,hAPP(X5454,fun(X5454,bool),ord_less(X5454),X5455),X5456))
| hBOOL(hAPP(X5454,bool,hAPP(X5454,fun(X5454,bool),ord_less(X5454),hAPP(X5454,X5454,hAPP(X5454,fun(X5454,X5454),times_times(X5454),X5457),X5455)),hAPP(X5454,X5454,hAPP(X5454,fun(X5454,X5454),times_times(X5454),X5457),X5456)))
| ~ hBOOL(hAPP(X5454,bool,hAPP(X5454,fun(X5454,bool),ord_less(X5454),zero_zero(X5454)),X5457))
| ~ linord581940658strict(X5454) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_673_mult__less__cancel__left__pos])])])]) ).
fof(i_0_1662,plain,
! [X5609,X5610,X5611,X5612] :
( ( ~ hBOOL(hAPP(X5609,bool,hAPP(X5609,fun(X5609,bool),ord_less_eq(X5609),hAPP(X5609,X5609,hAPP(X5609,fun(X5609,X5609),times_times(X5609),X5612),X5610)),hAPP(X5609,X5609,hAPP(X5609,fun(X5609,X5609),times_times(X5609),X5612),X5611)))
| hBOOL(hAPP(X5609,bool,hAPP(X5609,fun(X5609,bool),ord_less_eq(X5609),X5611),X5610))
| ~ hBOOL(hAPP(X5609,bool,hAPP(X5609,fun(X5609,bool),ord_less(X5609),X5612),zero_zero(X5609)))
| ~ linord581940658strict(X5609) )
& ( ~ hBOOL(hAPP(X5609,bool,hAPP(X5609,fun(X5609,bool),ord_less_eq(X5609),X5611),X5610))
| hBOOL(hAPP(X5609,bool,hAPP(X5609,fun(X5609,bool),ord_less_eq(X5609),hAPP(X5609,X5609,hAPP(X5609,fun(X5609,X5609),times_times(X5609),X5612),X5610)),hAPP(X5609,X5609,hAPP(X5609,fun(X5609,X5609),times_times(X5609),X5612),X5611)))
| ~ hBOOL(hAPP(X5609,bool,hAPP(X5609,fun(X5609,bool),ord_less(X5609),X5612),zero_zero(X5609)))
| ~ linord581940658strict(X5609) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_717_mult__le__cancel__left__neg])])])]) ).
fof(i_0_1663,plain,
! [X5473,X5474,X5475,X5476] :
( ( ~ hBOOL(hAPP(X5473,bool,hAPP(X5473,fun(X5473,bool),ord_less(X5473),hAPP(X5473,X5473,hAPP(X5473,fun(X5473,X5473),times_times(X5473),X5476),X5474)),hAPP(X5473,X5473,hAPP(X5473,fun(X5473,X5473),times_times(X5473),X5476),X5475)))
| hBOOL(hAPP(X5473,bool,hAPP(X5473,fun(X5473,bool),ord_less(X5473),X5475),X5474))
| ~ hBOOL(hAPP(X5473,bool,hAPP(X5473,fun(X5473,bool),ord_less(X5473),X5476),zero_zero(X5473)))
| ~ linord581940658strict(X5473) )
& ( ~ hBOOL(hAPP(X5473,bool,hAPP(X5473,fun(X5473,bool),ord_less(X5473),X5475),X5474))
| hBOOL(hAPP(X5473,bool,hAPP(X5473,fun(X5473,bool),ord_less(X5473),hAPP(X5473,X5473,hAPP(X5473,fun(X5473,X5473),times_times(X5473),X5476),X5474)),hAPP(X5473,X5473,hAPP(X5473,fun(X5473,X5473),times_times(X5473),X5476),X5475)))
| ~ hBOOL(hAPP(X5473,bool,hAPP(X5473,fun(X5473,bool),ord_less(X5473),X5476),zero_zero(X5473)))
| ~ linord581940658strict(X5473) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_679_mult__less__cancel__left__neg])])])]) ).
fof(i_0_1664,plain,
! [X5396,X5397,X5398,X5399,X5400] :
( ~ ordered_semiring(X5396)
| ~ hBOOL(hAPP(X5396,bool,hAPP(X5396,fun(X5396,bool),ord_less_eq(X5396),X5399),X5400))
| ~ hBOOL(hAPP(X5396,bool,hAPP(X5396,fun(X5396,bool),ord_less_eq(X5396),X5397),X5398))
| ~ hBOOL(hAPP(X5396,bool,hAPP(X5396,fun(X5396,bool),ord_less_eq(X5396),zero_zero(X5396)),X5399))
| ~ hBOOL(hAPP(X5396,bool,hAPP(X5396,fun(X5396,bool),ord_less_eq(X5396),zero_zero(X5396)),X5397))
| hBOOL(hAPP(X5396,bool,hAPP(X5396,fun(X5396,bool),ord_less_eq(X5396),hAPP(X5396,X5396,hAPP(X5396,fun(X5396,X5396),times_times(X5396),X5399),X5397)),hAPP(X5396,X5396,hAPP(X5396,fun(X5396,X5396),times_times(X5396),X5400),X5398))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_656_mult__mono_H])])]) ).
fof(i_0_1665,plain,
! [X5391,X5392,X5393,X5394,X5395] :
( ~ ordered_semiring(X5391)
| ~ hBOOL(hAPP(X5391,bool,hAPP(X5391,fun(X5391,bool),ord_less_eq(X5391),X5394),X5395))
| ~ hBOOL(hAPP(X5391,bool,hAPP(X5391,fun(X5391,bool),ord_less_eq(X5391),X5392),X5393))
| ~ hBOOL(hAPP(X5391,bool,hAPP(X5391,fun(X5391,bool),ord_less_eq(X5391),zero_zero(X5391)),X5395))
| ~ hBOOL(hAPP(X5391,bool,hAPP(X5391,fun(X5391,bool),ord_less_eq(X5391),zero_zero(X5391)),X5392))
| hBOOL(hAPP(X5391,bool,hAPP(X5391,fun(X5391,bool),ord_less_eq(X5391),hAPP(X5391,X5391,hAPP(X5391,fun(X5391,X5391),times_times(X5391),X5394),X5392)),hAPP(X5391,X5391,hAPP(X5391,fun(X5391,X5391),times_times(X5391),X5395),X5393))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_655_mult__mono])])]) ).
fof(i_0_1666,plain,
! [X5594,X5595,X5596,X5597,X5598] :
( ~ linord20386208strict(X5594)
| ~ hBOOL(hAPP(X5594,bool,hAPP(X5594,fun(X5594,bool),ord_less(X5594),X5597),X5598))
| ~ hBOOL(hAPP(X5594,bool,hAPP(X5594,fun(X5594,bool),ord_less_eq(X5594),X5595),X5596))
| ~ hBOOL(hAPP(X5594,bool,hAPP(X5594,fun(X5594,bool),ord_less_eq(X5594),zero_zero(X5594)),X5597))
| ~ hBOOL(hAPP(X5594,bool,hAPP(X5594,fun(X5594,bool),ord_less(X5594),zero_zero(X5594)),X5595))
| hBOOL(hAPP(X5594,bool,hAPP(X5594,fun(X5594,bool),ord_less(X5594),hAPP(X5594,X5594,hAPP(X5594,fun(X5594,X5594),times_times(X5594),X5597),X5595)),hAPP(X5594,X5594,hAPP(X5594,fun(X5594,X5594),times_times(X5594),X5598),X5596))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_714_mult__less__le__imp__less])])]) ).
fof(i_0_1667,plain,
! [X5589,X5590,X5591,X5592,X5593] :
( ~ linord20386208strict(X5589)
| ~ hBOOL(hAPP(X5589,bool,hAPP(X5589,fun(X5589,bool),ord_less_eq(X5589),X5592),X5593))
| ~ hBOOL(hAPP(X5589,bool,hAPP(X5589,fun(X5589,bool),ord_less(X5589),X5590),X5591))
| ~ hBOOL(hAPP(X5589,bool,hAPP(X5589,fun(X5589,bool),ord_less(X5589),zero_zero(X5589)),X5592))
| ~ hBOOL(hAPP(X5589,bool,hAPP(X5589,fun(X5589,bool),ord_less_eq(X5589),zero_zero(X5589)),X5590))
| hBOOL(hAPP(X5589,bool,hAPP(X5589,fun(X5589,bool),ord_less(X5589),hAPP(X5589,X5589,hAPP(X5589,fun(X5589,X5589),times_times(X5589),X5592),X5590)),hAPP(X5589,X5589,hAPP(X5589,fun(X5589,X5589),times_times(X5589),X5593),X5591))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_713_mult__le__less__imp__less])])]) ).
fof(i_0_1668,plain,
! [X5599,X5600,X5601,X5602,X5603] :
( ~ linord20386208strict(X5599)
| ~ hBOOL(hAPP(X5599,bool,hAPP(X5599,fun(X5599,bool),ord_less(X5599),X5602),X5603))
| ~ hBOOL(hAPP(X5599,bool,hAPP(X5599,fun(X5599,bool),ord_less(X5599),X5600),X5601))
| ~ hBOOL(hAPP(X5599,bool,hAPP(X5599,fun(X5599,bool),ord_less_eq(X5599),zero_zero(X5599)),X5602))
| ~ hBOOL(hAPP(X5599,bool,hAPP(X5599,fun(X5599,bool),ord_less_eq(X5599),zero_zero(X5599)),X5600))
| hBOOL(hAPP(X5599,bool,hAPP(X5599,fun(X5599,bool),ord_less(X5599),hAPP(X5599,X5599,hAPP(X5599,fun(X5599,X5599),times_times(X5599),X5602),X5600)),hAPP(X5599,X5599,hAPP(X5599,fun(X5599,X5599),times_times(X5599),X5603),X5601))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_715_mult__strict__mono_H])])]) ).
fof(i_0_1669,plain,
! [X5604,X5605,X5606,X5607,X5608] :
( ~ linord20386208strict(X5604)
| ~ hBOOL(hAPP(X5604,bool,hAPP(X5604,fun(X5604,bool),ord_less(X5604),X5607),X5608))
| ~ hBOOL(hAPP(X5604,bool,hAPP(X5604,fun(X5604,bool),ord_less(X5604),X5605),X5606))
| ~ hBOOL(hAPP(X5604,bool,hAPP(X5604,fun(X5604,bool),ord_less(X5604),zero_zero(X5604)),X5608))
| ~ hBOOL(hAPP(X5604,bool,hAPP(X5604,fun(X5604,bool),ord_less_eq(X5604),zero_zero(X5604)),X5605))
| hBOOL(hAPP(X5604,bool,hAPP(X5604,fun(X5604,bool),ord_less(X5604),hAPP(X5604,X5604,hAPP(X5604,fun(X5604,X5604),times_times(X5604),X5607),X5605)),hAPP(X5604,X5604,hAPP(X5604,fun(X5604,X5604),times_times(X5604),X5608),X5606))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_716_mult__strict__mono])])]) ).
fof(i_0_1670,plain,
! [X5670,X5671,X5672] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5670),X5671)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5672),X5671)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5671))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5670),X5672)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5671))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5670),X5671)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5672),X5671))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5670),X5672))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5670),X5671)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5672),X5671))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_734_mult__le__cancel2])])]) ).
fof(i_0_1671,plain,
! [X5806,X5807,X5808] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5808),X5806)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5808),X5807)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5806),X5807))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5808)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5806),X5807))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5808),X5806)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5808),X5807)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5808)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_788_nat__mult__le__cancel1])])]) ).
fof(i_0_1672,plain,
! [X5667,X5668,X5669] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5667),X5668)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5667),X5669)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5667))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5668),X5669)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5667))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5667),X5668)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5667),X5669))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5668),X5669))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5667),X5668)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5667),X5669))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_733_mult__le__cancel1])])]) ).
fof(i_0_1673,plain,
! [X5803,X5804,X5805] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5805),X5803)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5805),X5804)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5803),X5804))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5805)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5803),X5804))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5805),X5803)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5805),X5804)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5805)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_787_nat__mult__less__cancel1])])]) ).
fof(i_0_1674,plain,
! [X5450,X5451,X5452,X5453] :
( ( hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5451),zero_zero(X5450)))
| hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),zero_zero(X5450)),X5451))
| ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5452)),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5453)))
| ~ linord581940658strict(X5450) )
& ( hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5453),X5452))
| hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),zero_zero(X5450)),X5451))
| ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5452)),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5453)))
| ~ linord581940658strict(X5450) )
& ( hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5451),zero_zero(X5450)))
| hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5452),X5453))
| ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5452)),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5453)))
| ~ linord581940658strict(X5450) )
& ( hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5453),X5452))
| hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5452),X5453))
| ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5452)),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5453)))
| ~ linord581940658strict(X5450) )
& ( ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),zero_zero(X5450)),X5451))
| ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5452),X5453))
| hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5452)),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5453)))
| ~ linord581940658strict(X5450) )
& ( ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5451),zero_zero(X5450)))
| ~ hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),X5453),X5452))
| hBOOL(hAPP(X5450,bool,hAPP(X5450,fun(X5450,bool),ord_less(X5450),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5452)),hAPP(X5450,X5450,hAPP(X5450,fun(X5450,X5450),times_times(X5450),X5451),X5453)))
| ~ linord581940658strict(X5450) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_672_mult__less__cancel__left__disj])])])]) ).
fof(i_0_1675,plain,
! [X5446,X5447,X5448,X5449] :
( ( hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5448),zero_zero(X5446)))
| hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),zero_zero(X5446)),X5448))
| ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5447),X5448)),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5449),X5448)))
| ~ linord581940658strict(X5446) )
& ( hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5449),X5447))
| hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),zero_zero(X5446)),X5448))
| ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5447),X5448)),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5449),X5448)))
| ~ linord581940658strict(X5446) )
& ( hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5448),zero_zero(X5446)))
| hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5447),X5449))
| ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5447),X5448)),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5449),X5448)))
| ~ linord581940658strict(X5446) )
& ( hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5449),X5447))
| hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5447),X5449))
| ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5447),X5448)),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5449),X5448)))
| ~ linord581940658strict(X5446) )
& ( ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),zero_zero(X5446)),X5448))
| ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5447),X5449))
| hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5447),X5448)),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5449),X5448)))
| ~ linord581940658strict(X5446) )
& ( ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5448),zero_zero(X5446)))
| ~ hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),X5449),X5447))
| hBOOL(hAPP(X5446,bool,hAPP(X5446,fun(X5446,bool),ord_less(X5446),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5447),X5448)),hAPP(X5446,X5446,hAPP(X5446,fun(X5446,X5446),times_times(X5446),X5449),X5448)))
| ~ linord581940658strict(X5446) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_671_mult__less__cancel__right__disj])])])]) ).
fof(i_0_1676,plain,
! [X3277,X3278] :
( ~ hBOOL(hAPP(fun(X3277,bool),bool,finite_finite(X3277),X3278))
| hBOOL(hAPP(fun(fun(X3277,bool),bool),bool,finite_finite(fun(X3277,bool)),hAPP(fun(fun(X3277,bool),bool),fun(fun(X3277,bool),bool),collect(fun(X3277,bool)),hAPP(fun(X3277,bool),fun(fun(X3277,bool),bool),hAPP(fun(fun(X3277,bool),fun(fun(X3277,bool),bool)),fun(fun(X3277,bool),fun(fun(X3277,bool),bool)),combc(fun(X3277,bool),fun(X3277,bool),bool),ord_less_eq(fun(X3277,bool))),X3278)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets])]) ).
cnf(i_0_1677,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ti(fun(X1,bool),X3) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk36_3(X1,X2,X3)),esk37_3(X1,X2,X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1239]) ).
fof(i_0_1678,plain,
! [X4228,X4229,X4230] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4229),X4230))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4228),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4230),X4228)),X4229))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_263_le__add__diff])]) ).
fof(i_0_1679,plain,
! [X4236,X4237,X4238] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4236),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4238),X4237)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4236),X4237)),X4238))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4237),X4238)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4236),X4237)),X4238))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4236),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4238),X4237)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4237),X4238)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_266_le__diff__conv2])])]) ).
fof(i_0_1680,plain,
! [X4154,X4155,X4156,X4157] :
( ~ ordere236663937imp_le(X4154)
| ~ hBOOL(hAPP(X4154,bool,hAPP(X4154,fun(X4154,bool),ord_less_eq(X4154),hAPP(X4154,X4154,hAPP(X4154,fun(X4154,X4154),plus_plus(X4154),X4155),X4156)),hAPP(X4154,X4154,hAPP(X4154,fun(X4154,X4154),plus_plus(X4154),X4157),X4156)))
| hBOOL(hAPP(X4154,bool,hAPP(X4154,fun(X4154,bool),ord_less_eq(X4154),X4155),X4157)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_238_add__le__imp__le__right])])]) ).
fof(i_0_1681,plain,
! [X4133,X4134,X4135,X4136] :
( ( ~ hBOOL(hAPP(X4133,bool,hAPP(X4133,fun(X4133,bool),ord_less_eq(X4133),hAPP(X4133,X4133,hAPP(X4133,fun(X4133,X4133),plus_plus(X4133),X4134),X4135)),hAPP(X4133,X4133,hAPP(X4133,fun(X4133,X4133),plus_plus(X4133),X4136),X4135)))
| hBOOL(hAPP(X4133,bool,hAPP(X4133,fun(X4133,bool),ord_less_eq(X4133),X4134),X4136))
| ~ ordere236663937imp_le(X4133) )
& ( ~ hBOOL(hAPP(X4133,bool,hAPP(X4133,fun(X4133,bool),ord_less_eq(X4133),X4134),X4136))
| hBOOL(hAPP(X4133,bool,hAPP(X4133,fun(X4133,bool),ord_less_eq(X4133),hAPP(X4133,X4133,hAPP(X4133,fun(X4133,X4133),plus_plus(X4133),X4134),X4135)),hAPP(X4133,X4133,hAPP(X4133,fun(X4133,X4133),plus_plus(X4133),X4136),X4135)))
| ~ ordere236663937imp_le(X4133) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_233_add__le__cancel__right])])])]) ).
fof(i_0_1682,plain,
! [X4158,X4159,X4160,X4161] :
( ~ ordere236663937imp_le(X4158)
| ~ hBOOL(hAPP(X4158,bool,hAPP(X4158,fun(X4158,bool),ord_less_eq(X4158),hAPP(X4158,X4158,hAPP(X4158,fun(X4158,X4158),plus_plus(X4158),X4159),X4160)),hAPP(X4158,X4158,hAPP(X4158,fun(X4158,X4158),plus_plus(X4158),X4159),X4161)))
| hBOOL(hAPP(X4158,bool,hAPP(X4158,fun(X4158,bool),ord_less_eq(X4158),X4160),X4161)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_239_add__le__imp__le__left])])]) ).
fof(i_0_1683,plain,
! [X4137,X4138,X4139,X4140] :
( ( ~ hBOOL(hAPP(X4137,bool,hAPP(X4137,fun(X4137,bool),ord_less_eq(X4137),hAPP(X4137,X4137,hAPP(X4137,fun(X4137,X4137),plus_plus(X4137),X4138),X4139)),hAPP(X4137,X4137,hAPP(X4137,fun(X4137,X4137),plus_plus(X4137),X4138),X4140)))
| hBOOL(hAPP(X4137,bool,hAPP(X4137,fun(X4137,bool),ord_less_eq(X4137),X4139),X4140))
| ~ ordere236663937imp_le(X4137) )
& ( ~ hBOOL(hAPP(X4137,bool,hAPP(X4137,fun(X4137,bool),ord_less_eq(X4137),X4139),X4140))
| hBOOL(hAPP(X4137,bool,hAPP(X4137,fun(X4137,bool),ord_less_eq(X4137),hAPP(X4137,X4137,hAPP(X4137,fun(X4137,X4137),plus_plus(X4137),X4138),X4139)),hAPP(X4137,X4137,hAPP(X4137,fun(X4137,X4137),plus_plus(X4137),X4138),X4140)))
| ~ ordere236663937imp_le(X4137) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_234_add__le__cancel__left])])])]) ).
fof(i_0_1684,plain,
! [X4501,X4502,X4503,X4504] :
( ~ ordere236663937imp_le(X4501)
| ~ hBOOL(hAPP(X4501,bool,hAPP(X4501,fun(X4501,bool),ord_less(X4501),hAPP(X4501,X4501,hAPP(X4501,fun(X4501,X4501),plus_plus(X4501),X4502),X4503)),hAPP(X4501,X4501,hAPP(X4501,fun(X4501,X4501),plus_plus(X4501),X4504),X4503)))
| hBOOL(hAPP(X4501,bool,hAPP(X4501,fun(X4501,bool),ord_less(X4501),X4502),X4504)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_352_add__less__imp__less__right])])]) ).
fof(i_0_1685,plain,
! [X4480,X4481,X4482,X4483] :
( ( ~ hBOOL(hAPP(X4480,bool,hAPP(X4480,fun(X4480,bool),ord_less(X4480),hAPP(X4480,X4480,hAPP(X4480,fun(X4480,X4480),plus_plus(X4480),X4481),X4482)),hAPP(X4480,X4480,hAPP(X4480,fun(X4480,X4480),plus_plus(X4480),X4483),X4482)))
| hBOOL(hAPP(X4480,bool,hAPP(X4480,fun(X4480,bool),ord_less(X4480),X4481),X4483))
| ~ ordere236663937imp_le(X4480) )
& ( ~ hBOOL(hAPP(X4480,bool,hAPP(X4480,fun(X4480,bool),ord_less(X4480),X4481),X4483))
| hBOOL(hAPP(X4480,bool,hAPP(X4480,fun(X4480,bool),ord_less(X4480),hAPP(X4480,X4480,hAPP(X4480,fun(X4480,X4480),plus_plus(X4480),X4481),X4482)),hAPP(X4480,X4480,hAPP(X4480,fun(X4480,X4480),plus_plus(X4480),X4483),X4482)))
| ~ ordere236663937imp_le(X4480) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_347_add__less__cancel__right])])])]) ).
fof(i_0_1686,plain,
! [X4505,X4506,X4507,X4508] :
( ~ ordere236663937imp_le(X4505)
| ~ hBOOL(hAPP(X4505,bool,hAPP(X4505,fun(X4505,bool),ord_less(X4505),hAPP(X4505,X4505,hAPP(X4505,fun(X4505,X4505),plus_plus(X4505),X4506),X4507)),hAPP(X4505,X4505,hAPP(X4505,fun(X4505,X4505),plus_plus(X4505),X4506),X4508)))
| hBOOL(hAPP(X4505,bool,hAPP(X4505,fun(X4505,bool),ord_less(X4505),X4507),X4508)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_353_add__less__imp__less__left])])]) ).
fof(i_0_1687,plain,
! [X4484,X4485,X4486,X4487] :
( ( ~ hBOOL(hAPP(X4484,bool,hAPP(X4484,fun(X4484,bool),ord_less(X4484),hAPP(X4484,X4484,hAPP(X4484,fun(X4484,X4484),plus_plus(X4484),X4485),X4486)),hAPP(X4484,X4484,hAPP(X4484,fun(X4484,X4484),plus_plus(X4484),X4485),X4487)))
| hBOOL(hAPP(X4484,bool,hAPP(X4484,fun(X4484,bool),ord_less(X4484),X4486),X4487))
| ~ ordere236663937imp_le(X4484) )
& ( ~ hBOOL(hAPP(X4484,bool,hAPP(X4484,fun(X4484,bool),ord_less(X4484),X4486),X4487))
| hBOOL(hAPP(X4484,bool,hAPP(X4484,fun(X4484,bool),ord_less(X4484),hAPP(X4484,X4484,hAPP(X4484,fun(X4484,X4484),plus_plus(X4484),X4485),X4486)),hAPP(X4484,X4484,hAPP(X4484,fun(X4484,X4484),plus_plus(X4484),X4485),X4487)))
| ~ ordere236663937imp_le(X4484) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_348_add__less__cancel__left])])])]) ).
fof(i_0_1688,plain,
! [X3648,X3649,X3650,X3651,X3652] :
( ~ hBOOL(hAPP(fun(X3649,bool),bool,hAPP(fun(X3649,bool),fun(fun(X3649,bool),bool),ord_less_eq(fun(X3649,bool)),X3651),X3652))
| hBOOL(hAPP(fun(X3648,bool),bool,hAPP(fun(X3648,bool),fun(fun(X3648,bool),bool),ord_less_eq(fun(X3648,bool)),hAPP(fun(X3649,bool),fun(X3648,bool),hAPP(fun(X3649,X3648),fun(fun(X3649,bool),fun(X3648,bool)),image(X3649,X3648),X3650),X3651)),hAPP(fun(X3649,bool),fun(X3648,bool),hAPP(fun(X3649,X3648),fun(fun(X3649,bool),fun(X3648,bool)),image(X3649,X3648),X3650),X3652))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_110_image__mono])]) ).
fof(i_0_1689,plain,
! [X5546,X5547,X5548] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5546))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5546),X5547)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5546),X5548))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5547),X5548))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5546),X5547)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5546),X5548))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5546))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5547),X5548))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5546),X5547)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5546),X5548))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_699_mult__less__cancel1])])]) ).
fof(i_0_1690,plain,
! [X5543,X5544,X5545] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5544))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5543),X5544)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5545),X5544))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5543),X5545))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5543),X5544)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5545),X5544))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5544))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5543),X5545))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5543),X5544)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5545),X5544))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_698_mult__less__cancel2])])]) ).
fof(i_0_1691,plain,
! [X4184,X4185,X4186] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4184),X4185)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4184),X4186)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4185),X4186)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4185),X4186))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4184),X4185)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4184),X4186))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_248_nat__add__left__cancel__le])]) ).
fof(i_0_1692,plain,
! [X4545,X4546,X4547] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4545),X4546)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4545),X4547)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4546),X4547)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4546),X4547))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4545),X4546)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4545),X4547))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_370_nat__add__left__cancel__less])]) ).
cnf(i_0_1693,plain,
( ti(X1,X2) = ti(X1,X4)
| ti(X1,X3) = ti(X1,X5)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1240]) ).
cnf(i_0_1694,plain,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X4) = ti(X1,X5)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1241]) ).
fof(i_0_1695,plain,
! [X4067,X4068,X4069] :
( ~ hBOOL(hAPP(fun(X4067,bool),bool,finite_finite(X4067),X4069))
| ~ hBOOL(hAPP(fun(X4067,bool),bool,hAPP(X4067,fun(fun(X4067,bool),bool),member(X4067),X4068),X4069))
| hAPP(fun(X4067,bool),nat,finite_card(X4067),X4069) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X4067,bool),nat,finite_card(X4067),hAPP(fun(X4067,bool),fun(X4067,bool),hAPP(fun(X4067,bool),fun(fun(X4067,bool),fun(X4067,bool)),minus_minus(fun(X4067,bool)),X4069),hAPP(fun(X4067,bool),fun(X4067,bool),hAPP(X4067,fun(fun(X4067,bool),fun(X4067,bool)),insert(X4067),X4068),bot_bot(fun(X4067,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_215_card_Oremove])]) ).
fof(i_0_1696,plain,
! [X3669,X3670,X3671,X3672] :
( ~ ord(X3670)
| ~ hBOOL(hAPP(X3670,bool,hAPP(X3670,fun(X3670,bool),ord_less_eq(X3670),hAPP(X3669,X3670,X3671,esk13_4(X3669,X3670,X3671,X3672))),hAPP(X3669,X3670,X3672,esk13_4(X3669,X3670,X3671,X3672))))
| hBOOL(hAPP(fun(X3669,X3670),bool,hAPP(fun(X3669,X3670),fun(fun(X3669,X3670),bool),ord_less_eq(fun(X3669,X3670)),X3671),X3672)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_le__funI])])])]) ).
fof(i_0_1697,plain,
! [X3589,X3590,X3591,X3592,X3593,X3594,X3595] :
( ( ~ hBOOL(hAPP(fun(X3589,X3590),bool,hAPP(fun(X3589,X3590),fun(fun(X3589,X3590),bool),ord_less_eq(fun(X3589,X3590)),X3591),X3592))
| hBOOL(hAPP(X3590,bool,hAPP(X3590,fun(X3590,bool),ord_less_eq(X3590),hAPP(X3589,X3590,X3591,X3593)),hAPP(X3589,X3590,X3592,X3593)))
| ~ ord(X3590) )
& ( ~ hBOOL(hAPP(X3590,bool,hAPP(X3590,fun(X3590,bool),ord_less_eq(X3590),hAPP(X3589,X3590,X3594,esk8_4(X3589,X3590,X3594,X3595))),hAPP(X3589,X3590,X3595,esk8_4(X3589,X3590,X3594,X3595))))
| hBOOL(hAPP(fun(X3589,X3590),bool,hAPP(fun(X3589,X3590),fun(fun(X3589,X3590),bool),ord_less_eq(fun(X3589,X3590)),X3594),X3595))
| ~ ord(X3590) ) ),
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_99_le__fun__def])])])])])]) ).
fof(i_0_1698,plain,
! [X3610,X3611,X3612,X3613] :
( ( hBOOL(hAPP(fun(X3610,bool),bool,hAPP(X3610,fun(fun(X3610,bool),bool),member(X3610),X3611),X3613))
| ~ hBOOL(hAPP(fun(X3610,bool),bool,hAPP(fun(X3610,bool),fun(fun(X3610,bool),bool),ord_less_eq(fun(X3610,bool)),hAPP(fun(X3610,bool),fun(X3610,bool),hAPP(X3610,fun(fun(X3610,bool),fun(X3610,bool)),insert(X3610),X3611),X3612)),X3613)) )
& ( hBOOL(hAPP(fun(X3610,bool),bool,hAPP(fun(X3610,bool),fun(fun(X3610,bool),bool),ord_less_eq(fun(X3610,bool)),X3612),X3613))
| ~ hBOOL(hAPP(fun(X3610,bool),bool,hAPP(fun(X3610,bool),fun(fun(X3610,bool),bool),ord_less_eq(fun(X3610,bool)),hAPP(fun(X3610,bool),fun(X3610,bool),hAPP(X3610,fun(fun(X3610,bool),fun(X3610,bool)),insert(X3610),X3611),X3612)),X3613)) )
& ( ~ hBOOL(hAPP(fun(X3610,bool),bool,hAPP(X3610,fun(fun(X3610,bool),bool),member(X3610),X3611),X3613))
| ~ hBOOL(hAPP(fun(X3610,bool),bool,hAPP(fun(X3610,bool),fun(fun(X3610,bool),bool),ord_less_eq(fun(X3610,bool)),X3612),X3613))
| hBOOL(hAPP(fun(X3610,bool),bool,hAPP(fun(X3610,bool),fun(fun(X3610,bool),bool),ord_less_eq(fun(X3610,bool)),hAPP(fun(X3610,bool),fun(X3610,bool),hAPP(X3610,fun(fun(X3610,bool),fun(X3610,bool)),insert(X3610),X3611),X3612)),X3613)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_103_insert__subset])])]) ).
fof(i_0_1699,plain,
! [X3860,X3861,X3862] :
( ~ hBOOL(hAPP(fun(X3860,bool),bool,finite_finite(X3860),X3862))
| ~ hBOOL(hAPP(fun(X3860,bool),bool,hAPP(X3860,fun(fun(X3860,bool),bool),member(X3860),X3861),X3862))
| hAPP(nat,nat,suc,hAPP(fun(X3860,bool),nat,finite_card(X3860),hAPP(fun(X3860,bool),fun(X3860,bool),hAPP(fun(X3860,bool),fun(fun(X3860,bool),fun(X3860,bool)),minus_minus(fun(X3860,bool)),X3862),hAPP(fun(X3860,bool),fun(X3860,bool),hAPP(X3860,fun(fun(X3860,bool),fun(X3860,bool)),insert(X3860),X3861),bot_bot(fun(X3860,bool)))))) = hAPP(fun(X3860,bool),nat,finite_card(X3860),X3862) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_card__Suc__Diff1])]) ).
fof(i_0_1700,plain,
! [X4070,X4071,X4072] :
( ~ hBOOL(hAPP(fun(X4070,bool),bool,finite_finite(X4070),X4072))
| hAPP(fun(X4070,bool),nat,finite_card(X4070),hAPP(fun(X4070,bool),fun(X4070,bool),hAPP(X4070,fun(fun(X4070,bool),fun(X4070,bool)),insert(X4070),X4071),X4072)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X4070,bool),nat,finite_card(X4070),hAPP(fun(X4070,bool),fun(X4070,bool),hAPP(fun(X4070,bool),fun(fun(X4070,bool),fun(X4070,bool)),minus_minus(fun(X4070,bool)),X4072),hAPP(fun(X4070,bool),fun(X4070,bool),hAPP(X4070,fun(fun(X4070,bool),fun(X4070,bool)),insert(X4070),X4071),bot_bot(fun(X4070,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_216_card_Oinsert__remove])]) ).
fof(i_0_1701,plain,
! [X3622,X3623,X3624,X3625] :
( ~ hBOOL(hAPP(fun(X3622,bool),bool,hAPP(fun(X3622,bool),fun(fun(X3622,bool),bool),ord_less_eq(fun(X3622,bool)),X3624),X3625))
| hBOOL(hAPP(fun(X3622,bool),bool,hAPP(fun(X3622,bool),fun(fun(X3622,bool),bool),ord_less_eq(fun(X3622,bool)),hAPP(fun(X3622,bool),fun(X3622,bool),hAPP(X3622,fun(fun(X3622,bool),fun(X3622,bool)),insert(X3622),X3623),X3624)),hAPP(fun(X3622,bool),fun(X3622,bool),hAPP(X3622,fun(fun(X3622,bool),fun(X3622,bool)),insert(X3622),X3623),X3625))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_106_insert__mono])]) ).
fof(i_0_1702,plain,
! [X3765,X3766,X3767,X3768] : hAPP(fun(X3765,bool),fun(X3765,bool),hAPP(fun(X3765,bool),fun(fun(X3765,bool),fun(X3765,bool)),minus_minus(fun(X3765,bool)),X3766),hAPP(fun(X3765,bool),fun(X3765,bool),hAPP(X3765,fun(fun(X3765,bool),fun(X3765,bool)),insert(X3765),X3767),X3768)) = hAPP(fun(X3765,bool),fun(X3765,bool),hAPP(fun(X3765,bool),fun(fun(X3765,bool),fun(X3765,bool)),minus_minus(fun(X3765,bool)),hAPP(fun(X3765,bool),fun(X3765,bool),hAPP(fun(X3765,bool),fun(fun(X3765,bool),fun(X3765,bool)),minus_minus(fun(X3765,bool)),X3766),hAPP(fun(X3765,bool),fun(X3765,bool),hAPP(X3765,fun(fun(X3765,bool),fun(X3765,bool)),insert(X3765),X3767),bot_bot(fun(X3765,bool))))),X3768),
inference(variable_rename,[status(thm)],[fact_140_Diff__insert2]) ).
fof(i_0_1703,plain,
! [X5665,X5666] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5665))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5665),X5666))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5666))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5665),X5666))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5665))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5666))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5665),X5666))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_732_one__le__mult__iff])])]) ).
fof(i_0_1704,plain,
! [X5663,X5664] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5664))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5663))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5663),X5664))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_731_one__less__mult])]) ).
fof(i_0_1705,plain,
! [X3863,X3864,X3865] :
( ~ hBOOL(hAPP(fun(X3863,bool),bool,finite_finite(X3863),X3865))
| hAPP(fun(X3863,bool),nat,finite_card(X3863),hAPP(fun(X3863,bool),fun(X3863,bool),hAPP(X3863,fun(fun(X3863,bool),fun(X3863,bool)),insert(X3863),X3864),X3865)) = hAPP(nat,nat,suc,hAPP(fun(X3863,bool),nat,finite_card(X3863),hAPP(fun(X3863,bool),fun(X3863,bool),hAPP(fun(X3863,bool),fun(fun(X3863,bool),fun(X3863,bool)),minus_minus(fun(X3863,bool)),X3865),hAPP(fun(X3863,bool),fun(X3863,bool),hAPP(X3863,fun(fun(X3863,bool),fun(X3863,bool)),insert(X3863),X3864),bot_bot(fun(X3863,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_169_card__insert])]) ).
fof(i_0_1706,plain,
! [X4225,X4226,X4227] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4225),X4226)),X4227))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4225),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4227),X4226))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4225),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4227),X4226)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4225),X4226)),X4227)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_le__diff__conv])]) ).
fof(i_0_1707,plain,
! [X4641,X4642,X4643] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4641),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4642),X4643)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4641),X4643)),X4642)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4641),X4643)),X4642))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4641),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4642),X4643))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_404_less__diff__conv])]) ).
fof(i_0_1708,plain,
! [X5694,X5695,X5696] :
( ( hBOOL(hAPP(X5694,bool,hAPP(X5694,fun(X5694,bool),ord_less(X5694),zero_zero(X5694)),esk100_3(X5694,X5695,X5696)))
| hBOOL(hAPP(X5694,bool,hAPP(X5694,fun(X5694,bool),ord_less_eq(X5694),X5695),X5696))
| ~ linord1117847801e_zero(X5694) )
& ( hBOOL(hAPP(X5694,bool,hAPP(X5694,fun(X5694,bool),ord_less(X5694),esk100_3(X5694,X5695,X5696)),one_one(X5694)))
| hBOOL(hAPP(X5694,bool,hAPP(X5694,fun(X5694,bool),ord_less_eq(X5694),X5695),X5696))
| ~ linord1117847801e_zero(X5694) )
& ( ~ hBOOL(hAPP(X5694,bool,hAPP(X5694,fun(X5694,bool),ord_less_eq(X5694),hAPP(X5694,X5694,hAPP(X5694,fun(X5694,X5694),times_times(X5694),esk100_3(X5694,X5695,X5696)),X5695)),X5696))
| hBOOL(hAPP(X5694,bool,hAPP(X5694,fun(X5694,bool),ord_less_eq(X5694),X5695),X5696))
| ~ linord1117847801e_zero(X5694) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_740_field__le__mult__one__interval])])])])]) ).
fof(i_0_1709,plain,
! [X5417,X5418,X5419,X5420] :
( ~ ordered_semiring(X5417)
| ~ hBOOL(hAPP(X5417,bool,hAPP(X5417,fun(X5417,bool),ord_less_eq(X5417),X5419),X5420))
| ~ hBOOL(hAPP(X5417,bool,hAPP(X5417,fun(X5417,bool),ord_less_eq(X5417),zero_zero(X5417)),X5418))
| hBOOL(hAPP(X5417,bool,hAPP(X5417,fun(X5417,bool),ord_less_eq(X5417),hAPP(X5417,X5417,hAPP(X5417,fun(X5417,X5417),times_times(X5417),X5419),X5418)),hAPP(X5417,X5417,hAPP(X5417,fun(X5417,X5417),times_times(X5417),X5420),X5418))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_661_mult__right__mono])])]) ).
fof(i_0_1710,plain,
! [X5409,X5410,X5411,X5412] :
( ~ ordere1490568538miring(X5409)
| ~ hBOOL(hAPP(X5409,bool,hAPP(X5409,fun(X5409,bool),ord_less_eq(X5409),X5411),X5412))
| ~ hBOOL(hAPP(X5409,bool,hAPP(X5409,fun(X5409,bool),ord_less_eq(X5409),zero_zero(X5409)),X5410))
| hBOOL(hAPP(X5409,bool,hAPP(X5409,fun(X5409,bool),ord_less_eq(X5409),hAPP(X5409,X5409,hAPP(X5409,fun(X5409,X5409),times_times(X5409),X5410),X5411)),hAPP(X5409,X5409,hAPP(X5409,fun(X5409,X5409),times_times(X5409),X5410),X5412))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_659_comm__mult__left__mono])])]) ).
fof(i_0_1711,plain,
! [X5413,X5414,X5415,X5416] :
( ~ ordered_semiring(X5413)
| ~ hBOOL(hAPP(X5413,bool,hAPP(X5413,fun(X5413,bool),ord_less_eq(X5413),X5415),X5416))
| ~ hBOOL(hAPP(X5413,bool,hAPP(X5413,fun(X5413,bool),ord_less_eq(X5413),zero_zero(X5413)),X5414))
| hBOOL(hAPP(X5413,bool,hAPP(X5413,fun(X5413,bool),ord_less_eq(X5413),hAPP(X5413,X5413,hAPP(X5413,fun(X5413,X5413),times_times(X5413),X5414),X5415)),hAPP(X5413,X5413,hAPP(X5413,fun(X5413,X5413),times_times(X5413),X5414),X5416))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_660_mult__left__mono])])]) ).
fof(i_0_1712,plain,
! [X5483,X5484,X5485,X5486] :
( ~ linord20386208strict(X5483)
| ~ hBOOL(hAPP(X5483,bool,hAPP(X5483,fun(X5483,bool),ord_less(X5483),X5485),X5486))
| ~ hBOOL(hAPP(X5483,bool,hAPP(X5483,fun(X5483,bool),ord_less(X5483),zero_zero(X5483)),X5484))
| hBOOL(hAPP(X5483,bool,hAPP(X5483,fun(X5483,bool),ord_less(X5483),hAPP(X5483,X5483,hAPP(X5483,fun(X5483,X5483),times_times(X5483),X5485),X5484)),hAPP(X5483,X5483,hAPP(X5483,fun(X5483,X5483),times_times(X5483),X5486),X5484))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_682_mult__strict__right__mono])])]) ).
fof(i_0_1713,plain,
! [X5491,X5492,X5493,X5494] :
( ~ linord893533164strict(X5491)
| ~ hBOOL(hAPP(X5491,bool,hAPP(X5491,fun(X5491,bool),ord_less(X5491),X5493),X5494))
| ~ hBOOL(hAPP(X5491,bool,hAPP(X5491,fun(X5491,bool),ord_less(X5491),zero_zero(X5491)),X5492))
| hBOOL(hAPP(X5491,bool,hAPP(X5491,fun(X5491,bool),ord_less(X5491),hAPP(X5491,X5491,hAPP(X5491,fun(X5491,X5491),times_times(X5491),X5492),X5493)),hAPP(X5491,X5491,hAPP(X5491,fun(X5491,X5491),times_times(X5491),X5492),X5494))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_684_comm__mult__strict__left__mono])])]) ).
fof(i_0_1714,plain,
! [X5487,X5488,X5489,X5490] :
( ~ linord20386208strict(X5487)
| ~ hBOOL(hAPP(X5487,bool,hAPP(X5487,fun(X5487,bool),ord_less(X5487),X5489),X5490))
| ~ hBOOL(hAPP(X5487,bool,hAPP(X5487,fun(X5487,bool),ord_less(X5487),zero_zero(X5487)),X5488))
| hBOOL(hAPP(X5487,bool,hAPP(X5487,fun(X5487,bool),ord_less(X5487),hAPP(X5487,X5487,hAPP(X5487,fun(X5487,X5487),times_times(X5487),X5488),X5489)),hAPP(X5487,X5487,hAPP(X5487,fun(X5487,X5487),times_times(X5487),X5488),X5490))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_683_mult__strict__left__mono])])]) ).
fof(i_0_1715,plain,
! [X5405,X5406,X5407,X5408] :
( ~ ordered_ring(X5405)
| ~ hBOOL(hAPP(X5405,bool,hAPP(X5405,fun(X5405,bool),ord_less_eq(X5405),X5407),X5408))
| ~ hBOOL(hAPP(X5405,bool,hAPP(X5405,fun(X5405,bool),ord_less_eq(X5405),X5406),zero_zero(X5405)))
| hBOOL(hAPP(X5405,bool,hAPP(X5405,fun(X5405,bool),ord_less_eq(X5405),hAPP(X5405,X5405,hAPP(X5405,fun(X5405,X5405),times_times(X5405),X5408),X5406)),hAPP(X5405,X5405,hAPP(X5405,fun(X5405,X5405),times_times(X5405),X5407),X5406))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_658_mult__right__mono__neg])])]) ).
fof(i_0_1716,plain,
! [X5401,X5402,X5403,X5404] :
( ~ ordered_ring(X5401)
| ~ hBOOL(hAPP(X5401,bool,hAPP(X5401,fun(X5401,bool),ord_less_eq(X5401),X5403),X5404))
| ~ hBOOL(hAPP(X5401,bool,hAPP(X5401,fun(X5401,bool),ord_less_eq(X5401),X5402),zero_zero(X5401)))
| hBOOL(hAPP(X5401,bool,hAPP(X5401,fun(X5401,bool),ord_less_eq(X5401),hAPP(X5401,X5401,hAPP(X5401,fun(X5401,X5401),times_times(X5401),X5402),X5404)),hAPP(X5401,X5401,hAPP(X5401,fun(X5401,X5401),times_times(X5401),X5402),X5403))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_657_mult__left__mono__neg])])]) ).
fof(i_0_1717,plain,
! [X5495,X5496,X5497,X5498] :
( ~ linord581940658strict(X5495)
| ~ hBOOL(hAPP(X5495,bool,hAPP(X5495,fun(X5495,bool),ord_less(X5495),X5497),X5498))
| ~ hBOOL(hAPP(X5495,bool,hAPP(X5495,fun(X5495,bool),ord_less(X5495),X5496),zero_zero(X5495)))
| hBOOL(hAPP(X5495,bool,hAPP(X5495,fun(X5495,bool),ord_less(X5495),hAPP(X5495,X5495,hAPP(X5495,fun(X5495,X5495),times_times(X5495),X5498),X5496)),hAPP(X5495,X5495,hAPP(X5495,fun(X5495,X5495),times_times(X5495),X5497),X5496))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_685_mult__strict__right__mono__neg])])]) ).
fof(i_0_1718,plain,
! [X5499,X5500,X5501,X5502] :
( ~ linord581940658strict(X5499)
| ~ hBOOL(hAPP(X5499,bool,hAPP(X5499,fun(X5499,bool),ord_less(X5499),X5501),X5502))
| ~ hBOOL(hAPP(X5499,bool,hAPP(X5499,fun(X5499,bool),ord_less(X5499),X5500),zero_zero(X5499)))
| hBOOL(hAPP(X5499,bool,hAPP(X5499,fun(X5499,bool),ord_less(X5499),hAPP(X5499,X5499,hAPP(X5499,fun(X5499,X5499),times_times(X5499),X5500),X5502)),hAPP(X5499,X5499,hAPP(X5499,fun(X5499,X5499),times_times(X5499),X5500),X5501))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_686_mult__strict__left__mono__neg])])]) ).
fof(i_0_1719,plain,
! [X4149,X4150,X4151,X4152,X4153] :
( ~ ordere779506340up_add(X4149)
| ~ hBOOL(hAPP(X4149,bool,hAPP(X4149,fun(X4149,bool),ord_less_eq(X4149),X4152),X4153))
| ~ hBOOL(hAPP(X4149,bool,hAPP(X4149,fun(X4149,bool),ord_less_eq(X4149),X4150),X4151))
| hBOOL(hAPP(X4149,bool,hAPP(X4149,fun(X4149,bool),ord_less_eq(X4149),hAPP(X4149,X4149,hAPP(X4149,fun(X4149,X4149),plus_plus(X4149),X4152),X4150)),hAPP(X4149,X4149,hAPP(X4149,fun(X4149,X4149),plus_plus(X4149),X4153),X4151))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_237_add__mono])])]) ).
fof(i_0_1720,plain,
! [X4605,X4606,X4607,X4608,X4609] :
( ~ ordere223160158up_add(X4605)
| ~ hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less(X4605),X4608),X4609))
| ~ hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less_eq(X4605),X4606),X4607))
| hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less(X4605),hAPP(X4605,X4605,hAPP(X4605,fun(X4605,X4605),plus_plus(X4605),X4608),X4606)),hAPP(X4605,X4605,hAPP(X4605,fun(X4605,X4605),plus_plus(X4605),X4609),X4607))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_391_add__less__le__mono])])]) ).
fof(i_0_1721,plain,
! [X4610,X4611,X4612,X4613,X4614] :
( ~ ordere223160158up_add(X4610)
| ~ hBOOL(hAPP(X4610,bool,hAPP(X4610,fun(X4610,bool),ord_less_eq(X4610),X4613),X4614))
| ~ hBOOL(hAPP(X4610,bool,hAPP(X4610,fun(X4610,bool),ord_less(X4610),X4611),X4612))
| hBOOL(hAPP(X4610,bool,hAPP(X4610,fun(X4610,bool),ord_less(X4610),hAPP(X4610,X4610,hAPP(X4610,fun(X4610,X4610),plus_plus(X4610),X4613),X4611)),hAPP(X4610,X4610,hAPP(X4610,fun(X4610,X4610),plus_plus(X4610),X4614),X4612))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_392_add__le__less__mono])])]) ).
fof(i_0_1722,plain,
! [X4496,X4497,X4498,X4499,X4500] :
( ~ ordere223160158up_add(X4496)
| ~ hBOOL(hAPP(X4496,bool,hAPP(X4496,fun(X4496,bool),ord_less(X4496),X4499),X4500))
| ~ hBOOL(hAPP(X4496,bool,hAPP(X4496,fun(X4496,bool),ord_less(X4496),X4497),X4498))
| hBOOL(hAPP(X4496,bool,hAPP(X4496,fun(X4496,bool),ord_less(X4496),hAPP(X4496,X4496,hAPP(X4496,fun(X4496,X4496),plus_plus(X4496),X4499),X4497)),hAPP(X4496,X4496,hAPP(X4496,fun(X4496,X4496),plus_plus(X4496),X4500),X4498))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_351_add__strict__mono])])]) ).
fof(i_0_1723,plain,
! [X6218,X6219,X6220] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6220)))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6220)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6218)),X6219)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6218)),X6219) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6218)))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6220)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6218)),X6219)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6220)),X6219)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6220))) )
& ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6218)))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6220)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6218)),X6219)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6220),X6218))),X6219)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6220))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1242])])]) ).
fof(i_0_1724,plain,
! [X4089,X4090] : hAPP(fun(X4089,bool),X4089,the_elem(X4089),X4090) = hAPP(fun(X4089,bool),X4089,the(X4089),hAPP(fun(X4089,fun(X4089,bool)),fun(X4089,bool),hAPP(fun(fun(X4089,bool),bool),fun(fun(X4089,fun(X4089,bool)),fun(X4089,bool)),combb(fun(X4089,bool),bool,X4089),hAPP(fun(X4089,bool),fun(fun(X4089,bool),bool),fequal(fun(X4089,bool)),X4090)),hAPP(fun(X4089,bool),fun(X4089,fun(X4089,bool)),hAPP(fun(X4089,fun(fun(X4089,bool),fun(X4089,bool))),fun(fun(X4089,bool),fun(X4089,fun(X4089,bool))),combc(X4089,fun(X4089,bool),fun(X4089,bool)),insert(X4089)),bot_bot(fun(X4089,bool))))),
inference(variable_rename,[status(thm)],[fact_220_the__elem__def]) ).
fof(i_0_1725,plain,
! [X4724,X4725,X4726] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk57_3(X4724,X4725,X4726)),esk58_3(X4724,X4725,X4726)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4724),X4725))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X4726,X4724)),hAPP(nat,nat,X4726,X4725))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X4726,esk57_3(X4724,X4725,X4726))),hAPP(nat,nat,X4726,esk58_3(X4724,X4725,X4726))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4724),X4725))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X4726,X4724)),hAPP(nat,nat,X4726,X4725))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_428_less__mono__imp__le__mono])])])]) ).
fof(i_0_1726,plain,
! [X5436,X5437,X5438] :
( ( hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),X5437),zero_zero(X5436)))
| hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),zero_zero(X5436)),X5437))
| ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),hAPP(X5436,X5436,hAPP(X5436,fun(X5436,X5436),times_times(X5436),X5437),X5438)),zero_zero(X5436)))
| ~ linord581940658strict(X5436) )
& ( hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),zero_zero(X5436)),X5438))
| hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),zero_zero(X5436)),X5437))
| ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),hAPP(X5436,X5436,hAPP(X5436,fun(X5436,X5436),times_times(X5436),X5437),X5438)),zero_zero(X5436)))
| ~ linord581940658strict(X5436) )
& ( hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),X5437),zero_zero(X5436)))
| hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),X5438),zero_zero(X5436)))
| ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),hAPP(X5436,X5436,hAPP(X5436,fun(X5436,X5436),times_times(X5436),X5437),X5438)),zero_zero(X5436)))
| ~ linord581940658strict(X5436) )
& ( hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),zero_zero(X5436)),X5438))
| hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),X5438),zero_zero(X5436)))
| ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),hAPP(X5436,X5436,hAPP(X5436,fun(X5436,X5436),times_times(X5436),X5437),X5438)),zero_zero(X5436)))
| ~ linord581940658strict(X5436) )
& ( ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),zero_zero(X5436)),X5437))
| ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),X5438),zero_zero(X5436)))
| hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),hAPP(X5436,X5436,hAPP(X5436,fun(X5436,X5436),times_times(X5436),X5437),X5438)),zero_zero(X5436)))
| ~ linord581940658strict(X5436) )
& ( ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),X5437),zero_zero(X5436)))
| ~ hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),zero_zero(X5436)),X5438))
| hBOOL(hAPP(X5436,bool,hAPP(X5436,fun(X5436,bool),ord_less_eq(X5436),hAPP(X5436,X5436,hAPP(X5436,fun(X5436,X5436),times_times(X5436),X5437),X5438)),zero_zero(X5436)))
| ~ linord581940658strict(X5436) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_667_mult__le__0__iff])])])]) ).
fof(i_0_1727,plain,
! [X5740,X5741,X5742] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5741),X5742))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5740))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5740),X5741)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5740),X5742))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_757_zmult__zless__mono2])]) ).
fof(i_0_1728,plain,
! [X5540,X5541,X5542] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5541),X5542))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5540))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5541),X5540)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5542),X5540))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_697_mult__less__mono1])]) ).
fof(i_0_1729,plain,
! [X5537,X5538,X5539] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5538),X5539))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5537))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5537),X5538)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5537),X5539))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_696_mult__less__mono2])]) ).
fof(i_0_1730,plain,
! [X5781,X5782,X5783,X5784] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5783),X5784))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5781),X5782))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5783),X5781)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5784),X5782))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_779_zadd__zless__mono])]) ).
fof(i_0_1731,plain,
! [X5218,X5219,X5220,X5221] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5220),X5221))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5218),X5219))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5220),X5218)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5221),X5219))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_599_mult__le__mono])]) ).
fof(i_0_1732,plain,
! [X4196,X4197,X4198,X4199] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4198),X4199))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4196),X4197))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4198),X4196)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4199),X4197))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_add__le__mono])]) ).
fof(i_0_1733,plain,
! [X4557,X4558,X4559,X4560] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4559),X4560))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4557),X4558))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4559),X4557)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4560),X4558))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_374_add__less__mono])]) ).
fof(i_0_1734,plain,
! [X4646,X4647,X4648] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4647),X4648))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4646),X4647))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4647),X4646)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4648),X4646))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_406_diff__less__mono])]) ).
fof(i_0_1735,plain,
! [X4589,X4590,X4591] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4590),X4591))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4590),X4589))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4589),X4591)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4589),X4590))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_386_diff__less__mono2])]) ).
fof(i_0_1736,plain,
! [X5661,X5662] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5662))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5661))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5662),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5662),X5661))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_730_n__less__n__mult__m])]) ).
fof(i_0_1737,plain,
! [X5659,X5660] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5660))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X5659))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5660),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5659),X5660))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_729_n__less__m__mult__n])]) ).
fof(i_0_1738,plain,
! [X5879,X5880,X5881] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),esk102_3(X5879,X5880,X5881)),X5881))
| hBOOL(hAPP(int,bool,X5879,X5880))
| ~ hBOOL(hAPP(int,bool,X5879,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5881),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5880),X5881)) )
& ( hBOOL(hAPP(int,bool,X5879,esk102_3(X5879,X5880,X5881)))
| hBOOL(hAPP(int,bool,X5879,X5880))
| ~ hBOOL(hAPP(int,bool,X5879,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5881),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5880),X5881)) )
& ( ~ hBOOL(hAPP(int,bool,X5879,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk102_3(X5879,X5880,X5881)),one_one(int))))
| hBOOL(hAPP(int,bool,X5879,X5880))
| ~ hBOOL(hAPP(int,bool,X5879,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5881),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5880),X5881)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_806_int__less__induct])])])]) ).
fof(i_0_1739,plain,
! [X5894,X5895,X5896] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5895),esk105_3(X5894,X5895,X5896)))
| hBOOL(hAPP(int,bool,X5894,X5896))
| ~ hBOOL(hAPP(int,bool,X5894,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5895),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5895),X5896)) )
& ( hBOOL(hAPP(int,bool,X5894,esk105_3(X5894,X5895,X5896)))
| hBOOL(hAPP(int,bool,X5894,X5896))
| ~ hBOOL(hAPP(int,bool,X5894,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5895),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5895),X5896)) )
& ( ~ hBOOL(hAPP(int,bool,X5894,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk105_3(X5894,X5895,X5896)),one_one(int))))
| hBOOL(hAPP(int,bool,X5894,X5896))
| ~ hBOOL(hAPP(int,bool,X5894,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5895),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5895),X5896)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_809_int__gr__induct])])])]) ).
fof(i_0_1740,plain,
! [X5632,X5633,X5634] :
( ~ linordered_idom(X5632)
| ~ hBOOL(hAPP(X5632,bool,hAPP(X5632,fun(X5632,bool),ord_less_eq(X5632),zero_zero(X5632)),X5634))
| ~ hBOOL(hAPP(X5632,bool,hAPP(X5632,fun(X5632,bool),ord_less_eq(X5632),zero_zero(X5632)),X5633))
| ~ hBOOL(hAPP(X5632,bool,hAPP(X5632,fun(X5632,bool),ord_less_eq(X5632),X5633),one_one(X5632)))
| hBOOL(hAPP(X5632,bool,hAPP(X5632,fun(X5632,bool),ord_less_eq(X5632),hAPP(X5632,X5632,hAPP(X5632,fun(X5632,X5632),times_times(X5632),X5634),X5633)),X5634)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_724_mult__right__le__one__le])])]) ).
fof(i_0_1741,plain,
! [X5629,X5630,X5631] :
( ~ linordered_idom(X5629)
| ~ hBOOL(hAPP(X5629,bool,hAPP(X5629,fun(X5629,bool),ord_less_eq(X5629),zero_zero(X5629)),X5631))
| ~ hBOOL(hAPP(X5629,bool,hAPP(X5629,fun(X5629,bool),ord_less_eq(X5629),zero_zero(X5629)),X5630))
| ~ hBOOL(hAPP(X5629,bool,hAPP(X5629,fun(X5629,bool),ord_less_eq(X5629),X5630),one_one(X5629)))
| hBOOL(hAPP(X5629,bool,hAPP(X5629,fun(X5629,bool),ord_less_eq(X5629),hAPP(X5629,X5629,hAPP(X5629,fun(X5629,X5629),times_times(X5629),X5630),X5631)),X5631)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_723_mult__left__le__one__le])])]) ).
fof(i_0_1742,plain,
! [X5941,X5942,X5943] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk115_3(X5941,X5942,X5943)),X5943))
| hBOOL(hAPP(int,bool,X5942,X5941))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5943),esk114_3(X5941,X5942,X5943)))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( hBOOL(hAPP(int,bool,X5942,esk115_3(X5941,X5942,X5943)))
| hBOOL(hAPP(int,bool,X5942,X5941))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5943),esk114_3(X5941,X5942,X5943)))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( ~ hBOOL(hAPP(int,bool,X5942,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk115_3(X5941,X5942,X5943)),one_one(int))))
| hBOOL(hAPP(int,bool,X5942,X5941))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5943),esk114_3(X5941,X5942,X5943)))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk115_3(X5941,X5942,X5943)),X5943))
| hBOOL(hAPP(int,bool,X5942,X5941))
| hBOOL(hAPP(int,bool,X5942,esk114_3(X5941,X5942,X5943)))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( hBOOL(hAPP(int,bool,X5942,esk115_3(X5941,X5942,X5943)))
| hBOOL(hAPP(int,bool,X5942,X5941))
| hBOOL(hAPP(int,bool,X5942,esk114_3(X5941,X5942,X5943)))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( ~ hBOOL(hAPP(int,bool,X5942,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk115_3(X5941,X5942,X5943)),one_one(int))))
| hBOOL(hAPP(int,bool,X5942,X5941))
| hBOOL(hAPP(int,bool,X5942,esk114_3(X5941,X5942,X5943)))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk115_3(X5941,X5942,X5943)),X5943))
| hBOOL(hAPP(int,bool,X5942,X5941))
| ~ hBOOL(hAPP(int,bool,X5942,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk114_3(X5941,X5942,X5943)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( hBOOL(hAPP(int,bool,X5942,esk115_3(X5941,X5942,X5943)))
| hBOOL(hAPP(int,bool,X5942,X5941))
| ~ hBOOL(hAPP(int,bool,X5942,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk114_3(X5941,X5942,X5943)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) )
& ( ~ hBOOL(hAPP(int,bool,X5942,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk115_3(X5941,X5942,X5943)),one_one(int))))
| hBOOL(hAPP(int,bool,X5942,X5941))
| ~ hBOOL(hAPP(int,bool,X5942,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk114_3(X5941,X5942,X5943)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X5942,X5943)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_824_int__induct])])])]) ).
cnf(i_0_1743,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_1243]) ).
fof(i_0_1744,plain,
! [X5300,X5301,X5302,X5303] :
( ~ number(X5300)
| ~ semiring(X5300)
| hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),times_times(X5300),hAPP(int,X5300,number_number_of(X5300),X5301)),hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),plus_plus(X5300),X5302),X5303)) = hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),plus_plus(X5300),hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),times_times(X5300),hAPP(int,X5300,number_number_of(X5300),X5301)),X5302)),hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),times_times(X5300),hAPP(int,X5300,number_number_of(X5300),X5301)),X5303)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_629_right__distrib__number__of])])]) ).
fof(i_0_1745,plain,
! [X5287,X5288,X5289,X5290] :
( ~ number(X5287)
| ~ ring(X5287)
| hAPP(X5287,X5287,hAPP(X5287,fun(X5287,X5287),times_times(X5287),hAPP(int,X5287,number_number_of(X5287),X5288)),hAPP(X5287,X5287,hAPP(X5287,fun(X5287,X5287),minus_minus(X5287),X5289),X5290)) = hAPP(X5287,X5287,hAPP(X5287,fun(X5287,X5287),minus_minus(X5287),hAPP(X5287,X5287,hAPP(X5287,fun(X5287,X5287),times_times(X5287),hAPP(int,X5287,number_number_of(X5287),X5288)),X5289)),hAPP(X5287,X5287,hAPP(X5287,fun(X5287,X5287),times_times(X5287),hAPP(int,X5287,number_number_of(X5287),X5288)),X5290)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_625_right__diff__distrib__number__of])])]) ).
cnf(i_0_1746,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ti(fun(X1,bool),X3) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk36_3(X1,X2,X3)),esk37_3(X1,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1239]) ).
fof(i_0_1747,plain,
! [X5378,X5379,X5380] :
( ( ~ hBOOL(hAPP(X5378,bool,hAPP(X5378,fun(X5378,bool),ord_less_eq(X5378),hAPP(int,X5378,number_number_of(X5378),X5379)),hAPP(int,X5378,number_number_of(X5378),X5380)))
| ~ hBOOL(hAPP(X5378,bool,hAPP(X5378,fun(X5378,bool),ord_less(X5378),hAPP(int,X5378,number_number_of(X5378),X5380)),hAPP(int,X5378,number_number_of(X5378),X5379)))
| ~ number(X5378)
| ~ linorder(X5378) )
& ( hBOOL(hAPP(X5378,bool,hAPP(X5378,fun(X5378,bool),ord_less(X5378),hAPP(int,X5378,number_number_of(X5378),X5380)),hAPP(int,X5378,number_number_of(X5378),X5379)))
| hBOOL(hAPP(X5378,bool,hAPP(X5378,fun(X5378,bool),ord_less_eq(X5378),hAPP(int,X5378,number_number_of(X5378),X5379)),hAPP(int,X5378,number_number_of(X5378),X5380)))
| ~ number(X5378)
| ~ linorder(X5378) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1244])])])]) ).
fof(i_0_1748,plain,
! [X5342,X5343,X5344,X5345,X5346] :
( ~ comm_semiring_1(X5342)
| hAPP(X5342,X5342,hAPP(X5342,fun(X5342,X5342),times_times(X5342),hAPP(X5342,X5342,hAPP(X5342,fun(X5342,X5342),times_times(X5342),X5343),X5344)),hAPP(X5342,X5342,hAPP(X5342,fun(X5342,X5342),times_times(X5342),X5345),X5346)) = hAPP(X5342,X5342,hAPP(X5342,fun(X5342,X5342),times_times(X5342),X5345),hAPP(X5342,X5342,hAPP(X5342,fun(X5342,X5342),times_times(X5342),hAPP(X5342,X5342,hAPP(X5342,fun(X5342,X5342),times_times(X5342),X5343),X5344)),X5346)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])])]) ).
fof(i_0_1749,plain,
! [X6089,X6090] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X6089),X6090))
| hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X6089)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6090))) )
& ( ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X6089)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6090)))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X6089),X6090)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_888_transfer__nat__int__set__relations_I2_J])]) ).
fof(i_0_1750,plain,
! [X4919,X4920] :
( ( ~ hBOOL(hAPP(X4919,bool,hAPP(X4919,fun(X4919,bool),ord_less_eq(X4919),hAPP(X4919,X4919,hAPP(X4919,fun(X4919,X4919),plus_plus(X4919),X4920),X4920)),zero_zero(X4919)))
| hBOOL(hAPP(X4919,bool,hAPP(X4919,fun(X4919,bool),ord_less_eq(X4919),X4920),zero_zero(X4919)))
| ~ linord219039673up_add(X4919) )
& ( ~ hBOOL(hAPP(X4919,bool,hAPP(X4919,fun(X4919,bool),ord_less_eq(X4919),X4920),zero_zero(X4919)))
| hBOOL(hAPP(X4919,bool,hAPP(X4919,fun(X4919,bool),ord_less_eq(X4919),hAPP(X4919,X4919,hAPP(X4919,fun(X4919,X4919),plus_plus(X4919),X4920),X4920)),zero_zero(X4919)))
| ~ linord219039673up_add(X4919) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_493_double__add__le__zero__iff__single__add__le__zero])])])]) ).
fof(i_0_1751,plain,
! [X4940,X4941] :
( ( ~ hBOOL(hAPP(X4940,bool,hAPP(X4940,fun(X4940,bool),ord_less(X4940),hAPP(X4940,X4940,hAPP(X4940,fun(X4940,X4940),plus_plus(X4940),X4941),X4941)),zero_zero(X4940)))
| hBOOL(hAPP(X4940,bool,hAPP(X4940,fun(X4940,bool),ord_less(X4940),X4941),zero_zero(X4940)))
| ~ linord219039673up_add(X4940) )
& ( ~ hBOOL(hAPP(X4940,bool,hAPP(X4940,fun(X4940,bool),ord_less(X4940),X4941),zero_zero(X4940)))
| hBOOL(hAPP(X4940,bool,hAPP(X4940,fun(X4940,bool),ord_less(X4940),hAPP(X4940,X4940,hAPP(X4940,fun(X4940,X4940),plus_plus(X4940),X4941),X4941)),zero_zero(X4940)))
| ~ linord219039673up_add(X4940) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_500_double__add__less__zero__iff__single__add__less__zero])])])]) ).
fof(i_0_1752,plain,
! [X5086,X5087] :
( ( ~ hBOOL(hAPP(X5086,bool,hAPP(X5086,fun(X5086,bool),ord_less(X5086),hAPP(X5086,X5086,hAPP(X5086,fun(X5086,X5086),plus_plus(X5086),X5087),X5087)),zero_zero(X5086)))
| hBOOL(hAPP(X5086,bool,hAPP(X5086,fun(X5086,bool),ord_less(X5086),X5087),zero_zero(X5086)))
| ~ linordered_idom(X5086) )
& ( ~ hBOOL(hAPP(X5086,bool,hAPP(X5086,fun(X5086,bool),ord_less(X5086),X5087),zero_zero(X5086)))
| hBOOL(hAPP(X5086,bool,hAPP(X5086,fun(X5086,bool),ord_less(X5086),hAPP(X5086,X5086,hAPP(X5086,fun(X5086,X5086),plus_plus(X5086),X5087),X5087)),zero_zero(X5086)))
| ~ linordered_idom(X5086) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_554_even__less__0__iff])])])]) ).
cnf(i_0_1753,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),esk9_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_1245]) ).
fof(i_0_1754,plain,
! [X4952,X4953,X4954] :
( ( ~ hBOOL(hAPP(X4952,bool,hAPP(X4952,fun(X4952,bool),ord_less_eq(X4952),X4953),X4954))
| hBOOL(hAPP(X4952,bool,hAPP(X4952,fun(X4952,bool),ord_less_eq(X4952),hAPP(X4952,X4952,hAPP(X4952,fun(X4952,X4952),minus_minus(X4952),X4953),X4954)),zero_zero(X4952)))
| ~ ordered_ab_group_add(X4952) )
& ( ~ hBOOL(hAPP(X4952,bool,hAPP(X4952,fun(X4952,bool),ord_less_eq(X4952),hAPP(X4952,X4952,hAPP(X4952,fun(X4952,X4952),minus_minus(X4952),X4953),X4954)),zero_zero(X4952)))
| hBOOL(hAPP(X4952,bool,hAPP(X4952,fun(X4952,bool),ord_less_eq(X4952),X4953),X4954))
| ~ ordered_ab_group_add(X4952) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_504_le__iff__diff__le__0])])])]) ).
fof(i_0_1755,plain,
! [X4955,X4956,X4957] :
( ( ~ hBOOL(hAPP(X4955,bool,hAPP(X4955,fun(X4955,bool),ord_less(X4955),X4956),X4957))
| hBOOL(hAPP(X4955,bool,hAPP(X4955,fun(X4955,bool),ord_less(X4955),hAPP(X4955,X4955,hAPP(X4955,fun(X4955,X4955),minus_minus(X4955),X4956),X4957)),zero_zero(X4955)))
| ~ ordered_ab_group_add(X4955) )
& ( ~ hBOOL(hAPP(X4955,bool,hAPP(X4955,fun(X4955,bool),ord_less(X4955),hAPP(X4955,X4955,hAPP(X4955,fun(X4955,X4955),minus_minus(X4955),X4956),X4957)),zero_zero(X4955)))
| hBOOL(hAPP(X4955,bool,hAPP(X4955,fun(X4955,bool),ord_less(X4955),X4956),X4957))
| ~ ordered_ab_group_add(X4955) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_505_less__iff__diff__less__0])])])]) ).
fof(i_0_1756,plain,
! [X5022,X5023] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5023))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5023),hAPP(nat,nat,suc,X5022))),X5023)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_536_diff__Suc__less])]) ).
fof(i_0_1757,plain,
! [X5274,X5275,X5276] :
( ~ ring_1(X5274)
| ~ hBOOL(hAPP(fun(X5274,bool),bool,hAPP(X5274,fun(fun(X5274,bool),bool),member(X5274),X5276),ring_1_Ints(X5274)))
| ~ hBOOL(hAPP(fun(X5274,bool),bool,hAPP(X5274,fun(fun(X5274,bool),bool),member(X5274),X5275),ring_1_Ints(X5274)))
| hBOOL(hAPP(fun(X5274,bool),bool,hAPP(X5274,fun(fun(X5274,bool),bool),member(X5274),hAPP(X5274,X5274,hAPP(X5274,fun(X5274,X5274),times_times(X5274),X5276),X5275)),ring_1_Ints(X5274))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_621_Ints__mult])])]) ).
fof(i_0_1758,plain,
! [X5291,X5292,X5293] :
( ~ ring_1(X5291)
| ~ hBOOL(hAPP(fun(X5291,bool),bool,hAPP(X5291,fun(fun(X5291,bool),bool),member(X5291),X5293),ring_1_Ints(X5291)))
| ~ hBOOL(hAPP(fun(X5291,bool),bool,hAPP(X5291,fun(fun(X5291,bool),bool),member(X5291),X5292),ring_1_Ints(X5291)))
| hBOOL(hAPP(fun(X5291,bool),bool,hAPP(X5291,fun(fun(X5291,bool),bool),member(X5291),hAPP(X5291,X5291,hAPP(X5291,fun(X5291,X5291),plus_plus(X5291),X5293),X5292)),ring_1_Ints(X5291))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_626_Ints__add])])]) ).
fof(i_0_1759,plain,
! [X5165,X5166,X5167] :
( ~ ring_1(X5165)
| ~ hBOOL(hAPP(fun(X5165,bool),bool,hAPP(X5165,fun(fun(X5165,bool),bool),member(X5165),X5167),ring_1_Ints(X5165)))
| ~ hBOOL(hAPP(fun(X5165,bool),bool,hAPP(X5165,fun(fun(X5165,bool),bool),member(X5165),X5166),ring_1_Ints(X5165)))
| hBOOL(hAPP(fun(X5165,bool),bool,hAPP(X5165,fun(fun(X5165,bool),bool),member(X5165),hAPP(X5165,X5165,hAPP(X5165,fun(X5165,X5165),minus_minus(X5165),X5167),X5166)),ring_1_Ints(X5165))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_578_Ints__diff])])]) ).
fof(i_0_1760,plain,
! [X3296,X3297,X3298] :
( ~ hBOOL(hAPP(fun(X3296,bool),bool,finite_finite(X3296),X3298))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3296,bool),nat,finite_card(X3296),X3298)),hAPP(fun(X3296,bool),nat,finite_card(X3296),hAPP(fun(X3296,bool),fun(X3296,bool),hAPP(X3296,fun(fun(X3296,bool),fun(X3296,bool)),insert(X3296),X3297),X3298)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7_card__insert__le])]) ).
fof(i_0_1761,plain,
! [X4710,X4711,X4712] :
( ~ hBOOL(hAPP(fun(X4710,bool),bool,finite_finite(X4710),X4712))
| ~ hBOOL(hAPP(fun(X4710,bool),bool,hAPP(fun(X4710,bool),fun(fun(X4710,bool),bool),ord_less_eq(fun(X4710,bool)),X4711),X4712))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X4710,bool),nat,finite_card(X4710),X4711)),hAPP(fun(X4710,bool),nat,finite_card(X4710),X4712)))
| hBOOL(hAPP(fun(X4710,bool),bool,hAPP(fun(X4710,bool),fun(fun(X4710,bool),bool),ord_less(fun(X4710,bool)),X4711),X4712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_425_card__psubset])]) ).
fof(i_0_1762,plain,
! [X3688,X3689] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3688)),X3689))
| hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3688)),X3689)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3688)),X3689))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3688)),X3689)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_118_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_1763,plain,
! [X5787,X5788] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5787),one_one(int))),X5788))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5787),X5788)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5787),X5788))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5787),one_one(int))),X5788)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_781_add1__zle__eq])]) ).
fof(i_0_1764,plain,
! [X5749,X5750] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5749),X5750))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5749),X5750)),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5749),X5750)),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5749),X5750)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_764_less__bin__lemma])]) ).
fof(i_0_1765,plain,
! [X4206,X4207,X4208] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4206),X4208))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4206),X4207)),X4208)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4207),X4208))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4206),X4207)),X4208)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1246])])]) ).
fof(i_0_1766,plain,
! [X4203,X4204,X4205] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4203),X4204)),X4205))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4203),X4205)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_254_add__leD1])]) ).
fof(i_0_1767,plain,
! [X4200,X4201,X4202] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4200),X4201)),X4202))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4201),X4202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_253_add__leD2])]) ).
fof(i_0_1768,plain,
! [X4565,X4566,X4567] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4565),X4566)),X4567))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4565),X4567)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_376_add__lessD1])]) ).
fof(i_0_1769,plain,
! [X4141,X4142,X4143,X4144] :
( ~ ordere779506340up_add(X4141)
| ~ hBOOL(hAPP(X4141,bool,hAPP(X4141,fun(X4141,bool),ord_less_eq(X4141),X4143),X4144))
| hBOOL(hAPP(X4141,bool,hAPP(X4141,fun(X4141,bool),ord_less_eq(X4141),hAPP(X4141,X4141,hAPP(X4141,fun(X4141,X4141),plus_plus(X4141),X4143),X4142)),hAPP(X4141,X4141,hAPP(X4141,fun(X4141,X4141),plus_plus(X4141),X4144),X4142))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_235_add__right__mono])])]) ).
fof(i_0_1770,plain,
! [X4145,X4146,X4147,X4148] :
( ~ ordere779506340up_add(X4145)
| ~ hBOOL(hAPP(X4145,bool,hAPP(X4145,fun(X4145,bool),ord_less_eq(X4145),X4147),X4148))
| hBOOL(hAPP(X4145,bool,hAPP(X4145,fun(X4145,bool),ord_less_eq(X4145),hAPP(X4145,X4145,hAPP(X4145,fun(X4145,X4145),plus_plus(X4145),X4146),X4147)),hAPP(X4145,X4145,hAPP(X4145,fun(X4145,X4145),plus_plus(X4145),X4146),X4148))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_236_add__left__mono])])]) ).
fof(i_0_1771,plain,
! [X4488,X4489,X4490,X4491] :
( ~ ordere223160158up_add(X4488)
| ~ hBOOL(hAPP(X4488,bool,hAPP(X4488,fun(X4488,bool),ord_less(X4488),X4490),X4491))
| hBOOL(hAPP(X4488,bool,hAPP(X4488,fun(X4488,bool),ord_less(X4488),hAPP(X4488,X4488,hAPP(X4488,fun(X4488,X4488),plus_plus(X4488),X4490),X4489)),hAPP(X4488,X4488,hAPP(X4488,fun(X4488,X4488),plus_plus(X4488),X4491),X4489))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_349_add__strict__right__mono])])]) ).
fof(i_0_1772,plain,
! [X4492,X4493,X4494,X4495] :
( ~ ordere223160158up_add(X4492)
| ~ hBOOL(hAPP(X4492,bool,hAPP(X4492,fun(X4492,bool),ord_less(X4492),X4494),X4495))
| hBOOL(hAPP(X4492,bool,hAPP(X4492,fun(X4492,bool),ord_less(X4492),hAPP(X4492,X4492,hAPP(X4492,fun(X4492,X4492),plus_plus(X4492),X4493),X4494)),hAPP(X4492,X4492,hAPP(X4492,fun(X4492,X4492),plus_plus(X4492),X4493),X4495))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_350_add__strict__left__mono])])]) ).
fof(i_0_1773,plain,
! [X4263,X4264,X4265] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4264),X4265))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4265),X4264))),X4263) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X4265)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4264),X4263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_276_diff__Suc__diff__eq2])]) ).
fof(i_0_1774,plain,
! [X3614,X3615,X3616,X3617] :
( ( ~ hBOOL(hAPP(fun(X3614,bool),bool,hAPP(fun(X3614,bool),fun(fun(X3614,bool),bool),ord_less_eq(fun(X3614,bool)),X3617),hAPP(fun(X3614,bool),fun(X3614,bool),hAPP(X3614,fun(fun(X3614,bool),fun(X3614,bool)),insert(X3614),X3616),X3615)))
| hBOOL(hAPP(fun(X3614,bool),bool,hAPP(fun(X3614,bool),fun(fun(X3614,bool),bool),ord_less_eq(fun(X3614,bool)),X3617),X3615))
| hBOOL(hAPP(fun(X3614,bool),bool,hAPP(X3614,fun(fun(X3614,bool),bool),member(X3614),X3616),X3617)) )
& ( ~ hBOOL(hAPP(fun(X3614,bool),bool,hAPP(fun(X3614,bool),fun(fun(X3614,bool),bool),ord_less_eq(fun(X3614,bool)),X3617),X3615))
| hBOOL(hAPP(fun(X3614,bool),bool,hAPP(fun(X3614,bool),fun(fun(X3614,bool),bool),ord_less_eq(fun(X3614,bool)),X3617),hAPP(fun(X3614,bool),fun(X3614,bool),hAPP(X3614,fun(fun(X3614,bool),fun(X3614,bool)),insert(X3614),X3616),X3615)))
| hBOOL(hAPP(fun(X3614,bool),bool,hAPP(X3614,fun(fun(X3614,bool),bool),member(X3614),X3616),X3617)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1247])])]) ).
cnf(i_0_1775,plain,
( hAPP(fun(X1,bool),X1,X4,X2) = ti(X1,X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1248]) ).
fof(i_0_1776,plain,
! [X5698,X5699,X5700,X5701] :
( ( hBOOL(hAPP(fun(X5698,bool),bool,hAPP(X5698,fun(fun(X5698,bool),bool),member(X5698),esk101_4(X5698,X5699,X5700,X5701)),X5701))
| hAPP(fun(X5698,bool),X5699,hAPP(X5699,fun(fun(X5698,bool),X5699),hAPP(fun(X5698,X5699),fun(X5699,fun(fun(X5698,bool),X5699)),hAPP(fun(X5699,fun(X5699,X5699)),fun(fun(X5698,X5699),fun(X5699,fun(fun(X5698,bool),X5699))),finite_fold_image(X5699,X5698),times_times(X5699)),X5700),one_one(X5699)),X5701) = one_one(X5699)
| ~ hBOOL(hAPP(fun(X5698,bool),bool,finite_finite(X5698),X5701))
| ~ comm_monoid_mult(X5699) )
& ( hAPP(X5698,X5699,X5700,esk101_4(X5698,X5699,X5700,X5701)) != one_one(X5699)
| hAPP(fun(X5698,bool),X5699,hAPP(X5699,fun(fun(X5698,bool),X5699),hAPP(fun(X5698,X5699),fun(X5699,fun(fun(X5698,bool),X5699)),hAPP(fun(X5699,fun(X5699,X5699)),fun(fun(X5698,X5699),fun(X5699,fun(fun(X5698,bool),X5699))),finite_fold_image(X5699,X5698),times_times(X5699)),X5700),one_one(X5699)),X5701) = one_one(X5699)
| ~ hBOOL(hAPP(fun(X5698,bool),bool,finite_finite(X5698),X5701))
| ~ comm_monoid_mult(X5699) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_741_fold__image__1])])])])]) ).
fof(i_0_1777,plain,
! [X5270,X5271,X5272,X5273] :
( ~ number_ring(X5270)
| hAPP(X5270,X5270,hAPP(X5270,fun(X5270,X5270),times_times(X5270),hAPP(int,X5270,number_number_of(X5270),X5271)),hAPP(X5270,X5270,hAPP(X5270,fun(X5270,X5270),times_times(X5270),hAPP(int,X5270,number_number_of(X5270),X5272)),X5273)) = hAPP(X5270,X5270,hAPP(X5270,fun(X5270,X5270),times_times(X5270),hAPP(int,X5270,number_number_of(X5270),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5271),X5272))),X5273) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_620_mult__number__of__left])])]) ).
fof(i_0_1778,plain,
! [X5304,X5305,X5306,X5307] :
( ~ number_ring(X5304)
| hAPP(X5304,X5304,hAPP(X5304,fun(X5304,X5304),plus_plus(X5304),hAPP(int,X5304,number_number_of(X5304),X5305)),hAPP(X5304,X5304,hAPP(X5304,fun(X5304,X5304),plus_plus(X5304),hAPP(int,X5304,number_number_of(X5304),X5306)),X5307)) = hAPP(X5304,X5304,hAPP(X5304,fun(X5304,X5304),plus_plus(X5304),hAPP(int,X5304,number_number_of(X5304),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5305),X5306))),X5307) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_630_add__number__of__left])])]) ).
fof(i_0_1779,plain,
! [X5381,X5382,X5383,X5384] :
( ~ number_ring(X5381)
| hAPP(X5381,X5381,hAPP(X5381,fun(X5381,X5381),plus_plus(X5381),hAPP(int,X5381,number_number_of(X5381),X5382)),hAPP(X5381,X5381,hAPP(X5381,fun(X5381,X5381),minus_minus(X5381),hAPP(int,X5381,number_number_of(X5381),X5383)),X5384)) = hAPP(X5381,X5381,hAPP(X5381,fun(X5381,X5381),minus_minus(X5381),hAPP(int,X5381,number_number_of(X5381),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5382),X5383))),X5384) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_652_add__number__of__diff1])])]) ).
fof(i_0_1780,plain,
! [X5753,X5754,X5755] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5754),X5755))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5753),X5754)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5753),X5755))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_767_zadd__left__mono])]) ).
fof(i_0_1781,plain,
! [X5778,X5779,X5780] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5779),X5780))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5779),X5778)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5780),X5778))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_778_zadd__strict__right__mono])]) ).
fof(i_0_1782,plain,
! [X5225,X5226,X5227] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5226),X5227))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5226),X5225)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5227),X5225))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_601_mult__le__mono1])]) ).
fof(i_0_1783,plain,
! [X5222,X5223,X5224] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5223),X5224))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5222),X5223)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5222),X5224))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_600_mult__le__mono2])]) ).
fof(i_0_1784,plain,
! [X4193,X4194,X4195] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4194),X4195))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4194),X4193)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4195),X4193))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_251_add__le__mono1])]) ).
fof(i_0_1785,plain,
! [X3376,X3377,X3378] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3377),X3378))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3377),X3376)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3378),X3376))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_diff__le__mono])]) ).
fof(i_0_1786,plain,
! [X3379,X3380,X3381] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3380),X3381))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3379),X3381)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3379),X3380))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_44_diff__le__mono2])]) ).
fof(i_0_1787,plain,
! [X4554,X4555,X4556] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4555),X4556))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4555),X4554)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4556),X4554))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_373_add__less__mono1])]) ).
fof(i_0_1788,plain,
! [X6007,X6008,X6009] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X6007)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X6008)),X6009)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6007),X6008))),X6009),
inference(variable_rename,[status(thm)],[fact_850_zadd__int__left]) ).
fof(i_0_1789,plain,
! [X5308,X5309,X5310,X5311] :
( ~ number(X5308)
| ~ semiring(X5308)
| hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),times_times(X5308),hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),X5309),X5310)),hAPP(int,X5308,number_number_of(X5308),X5311)) = hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),times_times(X5308),X5309),hAPP(int,X5308,number_number_of(X5308),X5311))),hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),times_times(X5308),X5310),hAPP(int,X5308,number_number_of(X5308),X5311))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_631_left__distrib__number__of])])]) ).
fof(i_0_1790,plain,
! [X5283,X5284,X5285,X5286] :
( ~ number(X5283)
| ~ ring(X5283)
| hAPP(X5283,X5283,hAPP(X5283,fun(X5283,X5283),times_times(X5283),hAPP(X5283,X5283,hAPP(X5283,fun(X5283,X5283),minus_minus(X5283),X5284),X5285)),hAPP(int,X5283,number_number_of(X5283),X5286)) = hAPP(X5283,X5283,hAPP(X5283,fun(X5283,X5283),minus_minus(X5283),hAPP(X5283,X5283,hAPP(X5283,fun(X5283,X5283),times_times(X5283),X5284),hAPP(int,X5283,number_number_of(X5283),X5286))),hAPP(X5283,X5283,hAPP(X5283,fun(X5283,X5283),times_times(X5283),X5285),hAPP(int,X5283,number_number_of(X5283),X5286))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_624_left__diff__distrib__number__of])])]) ).
fof(i_0_1791,plain,
! [X5424,X5425,X5426] :
( ~ ordere453448008miring(X5424)
| ~ hBOOL(hAPP(X5424,bool,hAPP(X5424,fun(X5424,bool),ord_less_eq(X5424),X5426),zero_zero(X5424)))
| ~ hBOOL(hAPP(X5424,bool,hAPP(X5424,fun(X5424,bool),ord_less_eq(X5424),zero_zero(X5424)),X5425))
| hBOOL(hAPP(X5424,bool,hAPP(X5424,fun(X5424,bool),ord_less_eq(X5424),hAPP(X5424,X5424,hAPP(X5424,fun(X5424,X5424),times_times(X5424),X5426),X5425)),zero_zero(X5424))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_663_mult__nonpos__nonneg])])]) ).
fof(i_0_1792,plain,
! [X5385,X5386,X5387] :
( ( ~ hBOOL(hAPP(X5385,bool,hAPP(X5385,fun(X5385,bool),ord_less_eq(X5385),zero_zero(X5385)),X5387))
| ~ hBOOL(hAPP(X5385,bool,hAPP(X5385,fun(X5385,bool),ord_less_eq(X5385),X5386),zero_zero(X5385)))
| hBOOL(hAPP(X5385,bool,hAPP(X5385,fun(X5385,bool),ord_less_eq(X5385),hAPP(X5385,X5385,hAPP(X5385,fun(X5385,X5385),times_times(X5385),X5387),X5386)),zero_zero(X5385)))
| ~ ordere453448008miring(X5385) )
& ( ~ hBOOL(hAPP(X5385,bool,hAPP(X5385,fun(X5385,bool),ord_less_eq(X5385),X5387),zero_zero(X5385)))
| ~ hBOOL(hAPP(X5385,bool,hAPP(X5385,fun(X5385,bool),ord_less_eq(X5385),zero_zero(X5385)),X5386))
| hBOOL(hAPP(X5385,bool,hAPP(X5385,fun(X5385,bool),ord_less_eq(X5385),hAPP(X5385,X5385,hAPP(X5385,fun(X5385,X5385),times_times(X5385),X5387),X5386)),zero_zero(X5385)))
| ~ ordere453448008miring(X5385) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_653_split__mult__neg__le])])])]) ).
fof(i_0_1793,plain,
! [X5430,X5431,X5432] :
( ~ ordere453448008miring(X5430)
| ~ hBOOL(hAPP(X5430,bool,hAPP(X5430,fun(X5430,bool),ord_less_eq(X5430),zero_zero(X5430)),X5432))
| ~ hBOOL(hAPP(X5430,bool,hAPP(X5430,fun(X5430,bool),ord_less_eq(X5430),X5431),zero_zero(X5430)))
| hBOOL(hAPP(X5430,bool,hAPP(X5430,fun(X5430,bool),ord_less_eq(X5430),hAPP(X5430,X5430,hAPP(X5430,fun(X5430,X5430),times_times(X5430),X5432),X5431)),zero_zero(X5430))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_665_mult__nonneg__nonpos])])]) ).
fof(i_0_1794,plain,
! [X5427,X5428,X5429] :
( ~ ordere453448008miring(X5427)
| ~ hBOOL(hAPP(X5427,bool,hAPP(X5427,fun(X5427,bool),ord_less_eq(X5427),zero_zero(X5427)),X5429))
| ~ hBOOL(hAPP(X5427,bool,hAPP(X5427,fun(X5427,bool),ord_less_eq(X5427),X5428),zero_zero(X5427)))
| hBOOL(hAPP(X5427,bool,hAPP(X5427,fun(X5427,bool),ord_less_eq(X5427),hAPP(X5427,X5427,hAPP(X5427,fun(X5427,X5427),times_times(X5427),X5428),X5429)),zero_zero(X5427))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_664_mult__nonneg__nonpos2])])]) ).
fof(i_0_1795,plain,
! [X5477,X5478,X5479] :
( ~ linord20386208strict(X5477)
| ~ hBOOL(hAPP(X5477,bool,hAPP(X5477,fun(X5477,bool),ord_less(X5477),X5479),zero_zero(X5477)))
| ~ hBOOL(hAPP(X5477,bool,hAPP(X5477,fun(X5477,bool),ord_less(X5477),zero_zero(X5477)),X5478))
| hBOOL(hAPP(X5477,bool,hAPP(X5477,fun(X5477,bool),ord_less(X5477),hAPP(X5477,X5477,hAPP(X5477,fun(X5477,X5477),times_times(X5477),X5479),X5478)),zero_zero(X5477))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_680_mult__neg__pos])])]) ).
fof(i_0_1796,plain,
! [X5461,X5462,X5463] :
( ~ linord20386208strict(X5461)
| ~ hBOOL(hAPP(X5461,bool,hAPP(X5461,fun(X5461,bool),ord_less(X5461),zero_zero(X5461)),X5463))
| ~ hBOOL(hAPP(X5461,bool,hAPP(X5461,fun(X5461,bool),ord_less(X5461),X5462),zero_zero(X5461)))
| hBOOL(hAPP(X5461,bool,hAPP(X5461,fun(X5461,bool),ord_less(X5461),hAPP(X5461,X5461,hAPP(X5461,fun(X5461,X5461),times_times(X5461),X5463),X5462)),zero_zero(X5461))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_675_mult__pos__neg])])]) ).
fof(i_0_1797,plain,
! [X5464,X5465,X5466] :
( ~ linord20386208strict(X5464)
| ~ hBOOL(hAPP(X5464,bool,hAPP(X5464,fun(X5464,bool),ord_less(X5464),zero_zero(X5464)),X5466))
| ~ hBOOL(hAPP(X5464,bool,hAPP(X5464,fun(X5464,bool),ord_less(X5464),X5465),zero_zero(X5464)))
| hBOOL(hAPP(X5464,bool,hAPP(X5464,fun(X5464,bool),ord_less(X5464),hAPP(X5464,X5464,hAPP(X5464,fun(X5464,X5464),times_times(X5464),X5465),X5466)),zero_zero(X5464))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_676_mult__pos__neg2])])]) ).
fof(i_0_1798,plain,
! [X4935,X4936,X4937] :
( ~ ordere216010020id_add(X4935)
| ~ hBOOL(hAPP(X4935,bool,hAPP(X4935,fun(X4935,bool),ord_less_eq(X4935),X4937),zero_zero(X4935)))
| ~ hBOOL(hAPP(X4935,bool,hAPP(X4935,fun(X4935,bool),ord_less_eq(X4935),X4936),zero_zero(X4935)))
| hBOOL(hAPP(X4935,bool,hAPP(X4935,fun(X4935,bool),ord_less_eq(X4935),hAPP(X4935,X4935,hAPP(X4935,fun(X4935,X4935),plus_plus(X4935),X4937),X4936)),zero_zero(X4935))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_498_add__nonpos__nonpos])])]) ).
fof(i_0_1799,plain,
! [X5008,X5009,X5010] :
( ~ ordere216010020id_add(X5008)
| ~ hBOOL(hAPP(X5008,bool,hAPP(X5008,fun(X5008,bool),ord_less(X5008),X5010),zero_zero(X5008)))
| ~ hBOOL(hAPP(X5008,bool,hAPP(X5008,fun(X5008,bool),ord_less_eq(X5008),X5009),zero_zero(X5008)))
| hBOOL(hAPP(X5008,bool,hAPP(X5008,fun(X5008,bool),ord_less(X5008),hAPP(X5008,X5008,hAPP(X5008,fun(X5008,X5008),plus_plus(X5008),X5010),X5009)),zero_zero(X5008))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_529_add__neg__nonpos])])]) ).
fof(i_0_1800,plain,
! [X5011,X5012,X5013] :
( ~ ordere216010020id_add(X5011)
| ~ hBOOL(hAPP(X5011,bool,hAPP(X5011,fun(X5011,bool),ord_less_eq(X5011),X5013),zero_zero(X5011)))
| ~ hBOOL(hAPP(X5011,bool,hAPP(X5011,fun(X5011,bool),ord_less(X5011),X5012),zero_zero(X5011)))
| hBOOL(hAPP(X5011,bool,hAPP(X5011,fun(X5011,bool),ord_less(X5011),hAPP(X5011,X5011,hAPP(X5011,fun(X5011,X5011),plus_plus(X5011),X5013),X5012)),zero_zero(X5011))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_530_add__nonpos__neg])])]) ).
fof(i_0_1801,plain,
! [X4945,X4946,X4947] :
( ~ ordere216010020id_add(X4945)
| ~ hBOOL(hAPP(X4945,bool,hAPP(X4945,fun(X4945,bool),ord_less(X4945),X4947),zero_zero(X4945)))
| ~ hBOOL(hAPP(X4945,bool,hAPP(X4945,fun(X4945,bool),ord_less(X4945),X4946),zero_zero(X4945)))
| hBOOL(hAPP(X4945,bool,hAPP(X4945,fun(X4945,bool),ord_less(X4945),hAPP(X4945,X4945,hAPP(X4945,fun(X4945,X4945),plus_plus(X4945),X4947),X4946)),zero_zero(X4945))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_502_add__neg__neg])])]) ).
fof(i_0_1802,plain,
! [X3972,X3973,X3974,X3975] :
( ( hBOOL(hAPP(fun(X3972,bool),bool,hAPP(X3972,fun(fun(X3972,bool),bool),member(X3972),X3973),X3974))
| ~ hBOOL(hAPP(fun(X3972,bool),bool,hAPP(X3972,fun(fun(X3972,bool),bool),member(X3972),X3973),hAPP(fun(X3972,bool),fun(X3972,bool),hAPP(fun(X3972,bool),fun(fun(X3972,bool),fun(X3972,bool)),minus_minus(fun(X3972,bool)),X3974),X3975))) )
& ( ~ hBOOL(hAPP(fun(X3972,bool),bool,hAPP(X3972,fun(fun(X3972,bool),bool),member(X3972),X3973),X3975))
| ~ hBOOL(hAPP(fun(X3972,bool),bool,hAPP(X3972,fun(fun(X3972,bool),bool),member(X3972),X3973),hAPP(fun(X3972,bool),fun(X3972,bool),hAPP(fun(X3972,bool),fun(fun(X3972,bool),fun(X3972,bool)),minus_minus(fun(X3972,bool)),X3974),X3975))) )
& ( ~ hBOOL(hAPP(fun(X3972,bool),bool,hAPP(X3972,fun(fun(X3972,bool),bool),member(X3972),X3973),X3974))
| hBOOL(hAPP(fun(X3972,bool),bool,hAPP(X3972,fun(fun(X3972,bool),bool),member(X3972),X3973),X3975))
| hBOOL(hAPP(fun(X3972,bool),bool,hAPP(X3972,fun(fun(X3972,bool),bool),member(X3972),X3973),hAPP(fun(X3972,bool),fun(X3972,bool),hAPP(fun(X3972,bool),fun(fun(X3972,bool),fun(X3972,bool)),minus_minus(fun(X3972,bool)),X3974),X3975))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1249])])]) ).
fof(i_0_1803,plain,
! [X3953,X3954,X3955,X3956] :
( ( hBOOL(hAPP(fun(X3953,bool),bool,hAPP(X3953,fun(fun(X3953,bool),bool),member(X3953),X3954),X3955))
| ~ hBOOL(hAPP(fun(X3953,bool),bool,hAPP(X3953,fun(fun(X3953,bool),bool),member(X3953),X3954),hAPP(fun(X3953,bool),fun(X3953,bool),hAPP(fun(X3953,bool),fun(fun(X3953,bool),fun(X3953,bool)),minus_minus(fun(X3953,bool)),X3955),X3956))) )
& ( ~ hBOOL(hAPP(fun(X3953,bool),bool,hAPP(X3953,fun(fun(X3953,bool),bool),member(X3953),X3954),X3956))
| ~ hBOOL(hAPP(fun(X3953,bool),bool,hAPP(X3953,fun(fun(X3953,bool),bool),member(X3953),X3954),hAPP(fun(X3953,bool),fun(X3953,bool),hAPP(fun(X3953,bool),fun(fun(X3953,bool),fun(X3953,bool)),minus_minus(fun(X3953,bool)),X3955),X3956))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_190_DiffE])])]) ).
fof(i_0_1804,plain,
! [X3961,X3962,X3963,X3964] :
( ~ hBOOL(hAPP(fun(X3961,bool),bool,hAPP(X3961,fun(fun(X3961,bool),bool),member(X3961),X3962),hAPP(fun(X3961,bool),fun(X3961,bool),hAPP(fun(X3961,bool),fun(fun(X3961,bool),fun(X3961,bool)),minus_minus(fun(X3961,bool)),X3963),X3964)))
| ~ hBOOL(hAPP(fun(X3961,bool),bool,hAPP(X3961,fun(fun(X3961,bool),bool),member(X3961),X3962),X3964)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1250])]) ).
fof(i_0_1805,plain,
! [X6079,X6080] :
( ~ semiring_1(X6079)
| hAPP(nat,X6079,semiring_1_of_nat(X6079),X6080) = hAPP(X6079,X6079,hAPP(nat,fun(X6079,X6079),hAPP(fun(X6079,X6079),fun(nat,fun(X6079,X6079)),semiri532925092at_aux(X6079),hAPP(X6079,fun(X6079,X6079),hAPP(fun(X6079,fun(X6079,X6079)),fun(X6079,fun(X6079,X6079)),combc(X6079,X6079,X6079),plus_plus(X6079)),one_one(X6079))),X6080),zero_zero(X6079)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_882_semiring__1__class_Oof__nat__code])])]) ).
cnf(i_0_1806,plain,
( hAPP(fun(X1,bool),X1,X4,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = ti(X1,X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1251]) ).
cnf(i_0_1807,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk10_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_1252]) ).
cnf(i_0_1808,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_1253]) ).
fof(i_0_1809,plain,
! [X4984,X4985] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4985))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4984))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4984),X4985)),X4984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_519_diff__less])]) ).
fof(i_0_1810,plain,
! [X5444,X5445] :
( ~ linordered_ring(X5444)
| ~ hBOOL(hAPP(X5444,bool,hAPP(X5444,fun(X5444,bool),ord_less(X5444),hAPP(X5444,X5444,hAPP(X5444,fun(X5444,X5444),times_times(X5444),X5445),X5445)),zero_zero(X5444))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1254])])]) ).
fof(i_0_1811,plain,
! [X4018,X4019,X4020] :
( ~ hBOOL(hAPP(fun(X4018,bool),bool,finite_finite(X4018),X4020))
| ~ hBOOL(hAPP(fun(X4018,bool),bool,hAPP(X4018,fun(fun(X4018,bool),bool),member(X4018),X4019),X4020))
| hAPP(fun(X4018,bool),nat,finite_card(X4018),hAPP(fun(X4018,bool),fun(X4018,bool),hAPP(fun(X4018,bool),fun(fun(X4018,bool),fun(X4018,bool)),minus_minus(fun(X4018,bool)),X4020),hAPP(fun(X4018,bool),fun(X4018,bool),hAPP(X4018,fun(fun(X4018,bool),fun(X4018,bool)),insert(X4018),X4019),bot_bot(fun(X4018,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X4018,bool),nat,finite_card(X4018),X4020)),one_one(nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_204_card__Diff__singleton])]) ).
fof(i_0_1812,plain,
! [X4015,X4016,X4017] :
( ( ~ hBOOL(hAPP(fun(X4015,bool),bool,hAPP(X4015,fun(fun(X4015,bool),bool),member(X4015),X4016),X4017))
| hAPP(fun(X4015,bool),nat,finite_card(X4015),hAPP(fun(X4015,bool),fun(X4015,bool),hAPP(fun(X4015,bool),fun(fun(X4015,bool),fun(X4015,bool)),minus_minus(fun(X4015,bool)),X4017),hAPP(fun(X4015,bool),fun(X4015,bool),hAPP(X4015,fun(fun(X4015,bool),fun(X4015,bool)),insert(X4015),X4016),bot_bot(fun(X4015,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X4015,bool),nat,finite_card(X4015),X4017)),one_one(nat))
| ~ hBOOL(hAPP(fun(X4015,bool),bool,finite_finite(X4015),X4017)) )
& ( hBOOL(hAPP(fun(X4015,bool),bool,hAPP(X4015,fun(fun(X4015,bool),bool),member(X4015),X4016),X4017))
| hAPP(fun(X4015,bool),nat,finite_card(X4015),hAPP(fun(X4015,bool),fun(X4015,bool),hAPP(fun(X4015,bool),fun(fun(X4015,bool),fun(X4015,bool)),minus_minus(fun(X4015,bool)),X4017),hAPP(fun(X4015,bool),fun(X4015,bool),hAPP(X4015,fun(fun(X4015,bool),fun(X4015,bool)),insert(X4015),X4016),bot_bot(fun(X4015,bool))))) = hAPP(fun(X4015,bool),nat,finite_card(X4015),X4017)
| ~ hBOOL(hAPP(fun(X4015,bool),bool,finite_finite(X4015),X4017)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1255])])]) ).
cnf(i_0_1813,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_1256]) ).
fof(i_0_1814,plain,
! [X4541,X4542] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4541),X4542)),X4541)),
inference(variable_rename,[status(thm)],[i_0_1257]) ).
fof(i_0_1815,plain,
! [X4543,X4544] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4543),X4544)),X4544)),
inference(variable_rename,[status(thm)],[i_0_1258]) ).
cnf(i_0_1816,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_1245]) ).
fof(i_0_1817,plain,
! [X3360,X3361,X3362] : 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,X3360)),X3361)),hAPP(nat,nat,suc,X3362)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3360),X3361)),X3362),
inference(variable_rename,[status(thm)],[fact_37_Suc__diff__diff]) ).
cnf(i_0_1818,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ti(X1,X2) != ti(X1,X3)
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1240]) ).
cnf(i_0_1819,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ti(X1,X2) != ti(X1,X3)
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1241]) ).
cnf(i_0_1820,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
| ti(X1,X2) != ti(X1,X3)
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1240]) ).
cnf(i_0_1821,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
| ti(X1,X2) != ti(X1,X3)
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1241]) ).
fof(i_0_1822,plain,
! [X3965,X3966,X3967,X3968] :
( ~ hBOOL(hAPP(fun(X3965,bool),bool,hAPP(X3965,fun(fun(X3965,bool),bool),member(X3965),X3966),hAPP(fun(X3965,bool),fun(X3965,bool),hAPP(fun(X3965,bool),fun(fun(X3965,bool),fun(X3965,bool)),minus_minus(fun(X3965,bool)),X3967),X3968)))
| hBOOL(hAPP(fun(X3965,bool),bool,hAPP(X3965,fun(fun(X3965,bool),bool),member(X3965),X3966),X3967)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_193_DiffD1])]) ).
fof(i_0_1823,plain,
! [X5142,X5143] :
( ( ~ hBOOL(hAPP(fun(X5142,bool),bool,finite_finite(X5142),X5143))
| hAPP(fun(X5142,bool),nat,finite_card(X5142),X5143) = hAPP(fun(X5142,bool),nat,hAPP(nat,fun(fun(X5142,bool),nat),hAPP(fun(X5142,nat),fun(nat,fun(fun(X5142,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X5142,nat),fun(nat,fun(fun(X5142,bool),nat))),finite_fold_image(nat,X5142),plus_plus(nat)),hAPP(nat,fun(X5142,nat),combk(nat,X5142),one_one(nat))),zero_zero(nat)),X5143) )
& ( hBOOL(hAPP(fun(X5142,bool),bool,finite_finite(X5142),X5143))
| hAPP(fun(X5142,bool),nat,finite_card(X5142),X5143) = zero_zero(nat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1259])]) ).
fof(i_0_1824,plain,
! [X5140,X5141] :
( ~ hBOOL(hAPP(fun(X5140,bool),bool,finite_finite(X5140),X5141))
| hAPP(fun(X5140,bool),nat,finite_card(X5140),X5141) = hAPP(fun(X5140,bool),nat,hAPP(nat,fun(fun(X5140,bool),nat),hAPP(fun(X5140,nat),fun(nat,fun(fun(X5140,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X5140,nat),fun(nat,fun(fun(X5140,bool),nat))),finite_fold_image(nat,X5140),plus_plus(nat)),hAPP(nat,fun(X5140,nat),combk(nat,X5140),one_one(nat))),zero_zero(nat)),X5141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_571_card_Oeq__fold__g])]) ).
cnf(i_0_1825,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| ti(fun(X1,bool),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))
| ~ 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),bot_bot(fun(X1,bool))))) ),
inference(split_conjunct,[status(thm)],[i_0_1260]) ).
fof(i_0_1826,plain,
! [X3384,X3385,X3386,X3387,X3388] :
( ~ hBOOL(hAPP(fun(X3385,bool),bool,finite_finite(X3385),X3388))
| ~ hBOOL(hAPP(fun(X3384,bool),bool,hAPP(fun(X3384,bool),fun(fun(X3384,bool),bool),ord_less_eq(fun(X3384,bool)),X3386),hAPP(fun(X3385,bool),fun(X3384,bool),hAPP(fun(X3385,X3384),fun(fun(X3385,bool),fun(X3384,bool)),image(X3385,X3384),X3387),X3388)))
| hBOOL(hAPP(fun(X3384,bool),bool,finite_finite(X3384),X3386)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_finite__surj])]) ).
fof(i_0_1827,plain,
! [X3926,X3927,X3928] :
( ( hBOOL(hAPP(fun(X3926,bool),bool,finite_finite(X3926),esk26_3(X3926,X3927,X3928)))
| hBOOL(hAPP(fun(X3926,bool),bool,X3927,X3928))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,X3927,bot_bot(fun(X3926,bool))))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,finite_finite(X3926),X3928)) )
& ( ~ hBOOL(hAPP(fun(X3926,bool),bool,hAPP(X3926,fun(fun(X3926,bool),bool),member(X3926),esk25_3(X3926,X3927,X3928)),esk26_3(X3926,X3927,X3928)))
| hBOOL(hAPP(fun(X3926,bool),bool,X3927,X3928))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,X3927,bot_bot(fun(X3926,bool))))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,finite_finite(X3926),X3928)) )
& ( hBOOL(hAPP(fun(X3926,bool),bool,X3927,esk26_3(X3926,X3927,X3928)))
| hBOOL(hAPP(fun(X3926,bool),bool,X3927,X3928))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,X3927,bot_bot(fun(X3926,bool))))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,finite_finite(X3926),X3928)) )
& ( ~ hBOOL(hAPP(fun(X3926,bool),bool,X3927,hAPP(fun(X3926,bool),fun(X3926,bool),hAPP(X3926,fun(fun(X3926,bool),fun(X3926,bool)),insert(X3926),esk25_3(X3926,X3927,X3928)),esk26_3(X3926,X3927,X3928))))
| hBOOL(hAPP(fun(X3926,bool),bool,X3927,X3928))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,X3927,bot_bot(fun(X3926,bool))))
| ~ hBOOL(hAPP(fun(X3926,bool),bool,finite_finite(X3926),X3928)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1261])])])]) ).
fof(i_0_1828,plain,
! [X5470,X5471,X5472] :
( ~ linord20386208strict(X5470)
| ~ hBOOL(hAPP(X5470,bool,hAPP(X5470,fun(X5470,bool),ord_less(X5470),zero_zero(X5470)),hAPP(X5470,X5470,hAPP(X5470,fun(X5470,X5470),times_times(X5470),X5471),X5472)))
| ~ hBOOL(hAPP(X5470,bool,hAPP(X5470,fun(X5470,bool),ord_less(X5470),zero_zero(X5470)),X5472))
| hBOOL(hAPP(X5470,bool,hAPP(X5470,fun(X5470,bool),ord_less(X5470),zero_zero(X5470)),X5471)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_678_zero__less__mult__pos2])])]) ).
fof(i_0_1829,plain,
! [X5467,X5468,X5469] :
( ~ linord20386208strict(X5467)
| ~ hBOOL(hAPP(X5467,bool,hAPP(X5467,fun(X5467,bool),ord_less(X5467),zero_zero(X5467)),hAPP(X5467,X5467,hAPP(X5467,fun(X5467,X5467),times_times(X5467),X5468),X5469)))
| ~ hBOOL(hAPP(X5467,bool,hAPP(X5467,fun(X5467,bool),ord_less(X5467),zero_zero(X5467)),X5468))
| hBOOL(hAPP(X5467,bool,hAPP(X5467,fun(X5467,bool),ord_less(X5467),zero_zero(X5467)),X5469)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_677_zero__less__mult__pos])])]) ).
cnf(i_0_1830,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_1262]) ).
cnf(i_0_1831,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_1263]) ).
cnf(i_0_1832,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk37_3(X1,X2,X3)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ti(fun(X1,bool),X3) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1239]) ).
cnf(i_0_1833,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk37_3(X1,X2,X3)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ti(fun(X1,bool),X3) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1239]) ).
cnf(i_0_1834,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ti(fun(X1,bool),X3) = bot_bot(fun(X1,bool))
| ti(fun(X1,bool),esk37_3(X1,X2,X3)) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1239]) ).
fof(i_0_1835,plain,
! [X3808,X3809,X3810] : hBOOL(hAPP(fun(X3808,bool),bool,hAPP(fun(X3808,bool),fun(fun(X3808,bool),bool),ord_less_eq(fun(X3808,bool)),hAPP(fun(X3808,bool),fun(X3808,bool),hAPP(fun(X3808,bool),fun(fun(X3808,bool),fun(X3808,bool)),minus_minus(fun(X3808,bool)),X3809),X3810)),X3809)),
inference(variable_rename,[status(thm)],[fact_150_Diff__subset]) ).
fof(i_0_1836,plain,
! [X3310] : 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)),X3310)))),
inference(variable_rename,[status(thm)],[fact_12_finite__Collect__le__nat]) ).
fof(i_0_1837,plain,
! [X4327] : 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(nat)),X4327)))),
inference(variable_rename,[status(thm)],[fact_296_finite__Collect__less__nat]) ).
cnf(i_0_1838,plain,
( ti(fun(X1,bool),X5) = bot_bot(fun(X1,bool))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X1,bool),X1,X3,X5)),hAPP(fun(X1,bool),X1,X3,X4)) = hAPP(fun(X1,bool),X1,X3,X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1264]) ).
cnf(i_0_1839,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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(nat)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1265]) ).
cnf(i_0_1840,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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(nat)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1266]) ).
cnf(i_0_1841,plain,
( hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X3),X2) = ti(X1,X3)
| ~ 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),bot_bot(fun(X1,bool))))) ),
inference(split_conjunct,[status(thm)],[i_0_1267]) ).
fof(i_0_1842,plain,
! [X5347,X5348,X5349,X5350,X5351] :
( ~ comm_semiring_1(X5347)
| hAPP(X5347,X5347,hAPP(X5347,fun(X5347,X5347),times_times(X5347),hAPP(X5347,X5347,hAPP(X5347,fun(X5347,X5347),times_times(X5347),X5348),X5349)),hAPP(X5347,X5347,hAPP(X5347,fun(X5347,X5347),times_times(X5347),X5350),X5351)) = hAPP(X5347,X5347,hAPP(X5347,fun(X5347,X5347),times_times(X5347),hAPP(X5347,X5347,hAPP(X5347,fun(X5347,X5347),times_times(X5347),X5348),X5350)),hAPP(X5347,X5347,hAPP(X5347,fun(X5347,X5347),times_times(X5347),X5349),X5351)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])])]) ).
fof(i_0_1843,plain,
! [X5107,X5108,X5109,X5110,X5111] :
( ~ comm_semiring_1(X5107)
| hAPP(X5107,X5107,hAPP(X5107,fun(X5107,X5107),plus_plus(X5107),hAPP(X5107,X5107,hAPP(X5107,fun(X5107,X5107),plus_plus(X5107),X5108),X5109)),hAPP(X5107,X5107,hAPP(X5107,fun(X5107,X5107),plus_plus(X5107),X5110),X5111)) = hAPP(X5107,X5107,hAPP(X5107,fun(X5107,X5107),plus_plus(X5107),hAPP(X5107,X5107,hAPP(X5107,fun(X5107,X5107),plus_plus(X5107),X5108),X5110)),hAPP(X5107,X5107,hAPP(X5107,fun(X5107,X5107),plus_plus(X5107),X5109),X5111)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])])]) ).
fof(i_0_1844,plain,
! [X5337,X5338,X5339,X5340,X5341] :
( ~ comm_semiring_1(X5337)
| hAPP(X5337,X5337,hAPP(X5337,fun(X5337,X5337),times_times(X5337),hAPP(X5337,X5337,hAPP(X5337,fun(X5337,X5337),times_times(X5337),X5338),X5339)),hAPP(X5337,X5337,hAPP(X5337,fun(X5337,X5337),times_times(X5337),X5340),X5341)) = hAPP(X5337,X5337,hAPP(X5337,fun(X5337,X5337),times_times(X5337),X5338),hAPP(X5337,X5337,hAPP(X5337,fun(X5337,X5337),times_times(X5337),X5339),hAPP(X5337,X5337,hAPP(X5337,fun(X5337,X5337),times_times(X5337),X5340),X5341))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])])]) ).
fof(i_0_1845,plain,
! [X3769,X3770,X3771,X3772] : hAPP(fun(X3769,bool),fun(X3769,bool),hAPP(fun(X3769,bool),fun(fun(X3769,bool),fun(X3769,bool)),minus_minus(fun(X3769,bool)),X3770),hAPP(fun(X3769,bool),fun(X3769,bool),hAPP(X3769,fun(fun(X3769,bool),fun(X3769,bool)),insert(X3769),X3771),X3772)) = hAPP(fun(X3769,bool),fun(X3769,bool),hAPP(fun(X3769,bool),fun(fun(X3769,bool),fun(X3769,bool)),minus_minus(fun(X3769,bool)),hAPP(fun(X3769,bool),fun(X3769,bool),hAPP(fun(X3769,bool),fun(fun(X3769,bool),fun(X3769,bool)),minus_minus(fun(X3769,bool)),X3770),X3772)),hAPP(fun(X3769,bool),fun(X3769,bool),hAPP(X3769,fun(fun(X3769,bool),fun(X3769,bool)),insert(X3769),X3771),bot_bot(fun(X3769,bool)))),
inference(variable_rename,[status(thm)],[fact_141_Diff__insert]) ).
fof(i_0_1846,plain,
! [X4260,X4261,X4262] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4261),X4262))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4260),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4262),X4261))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4260),X4261)),hAPP(nat,nat,suc,X4262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_275_diff__Suc__diff__eq1])]) ).
fof(i_0_1847,plain,
! [X3957,X3958,X3959,X3960] :
( ~ hBOOL(hAPP(fun(X3957,bool),bool,hAPP(X3957,fun(fun(X3957,bool),bool),member(X3957),X3959),X3960))
| hBOOL(hAPP(fun(X3957,bool),bool,hAPP(X3957,fun(fun(X3957,bool),bool),member(X3957),X3959),X3958))
| hBOOL(hAPP(fun(X3957,bool),bool,hAPP(X3957,fun(fun(X3957,bool),bool),member(X3957),X3959),hAPP(fun(X3957,bool),fun(X3957,bool),hAPP(fun(X3957,bool),fun(fun(X3957,bool),fun(X3957,bool)),minus_minus(fun(X3957,bool)),X3960),X3958))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1268])]) ).
fof(i_0_1848,plain,
! [X3567,X3568,X3569,X3570,X3571] :
( ~ hBOOL(hAPP(fun(X3568,bool),bool,hAPP(X3568,fun(fun(X3568,bool),bool),member(X3568),X3570),X3571))
| hBOOL(hAPP(fun(X3567,bool),bool,hAPP(X3567,fun(fun(X3567,bool),bool),member(X3567),hAPP(X3568,X3567,X3569,X3570)),hAPP(fun(X3568,bool),fun(X3567,bool),hAPP(fun(X3568,X3567),fun(fun(X3568,bool),fun(X3567,bool)),image(X3568,X3567),X3569),X3571))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_imageI])]) ).
fof(i_0_1849,plain,
! [X3368,X3369,X3370] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3369),X3370))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3369),X3368))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3370),X3369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3368),X3369)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3370),X3368) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_40_Nat_Odiff__diff__eq])]) ).
cnf(i_0_1850,plain,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X2) = ti(X1,X4)
| 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),X5),bot_bot(fun(X1,bool)))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
cnf(i_0_1851,plain,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X2) = ti(X1,X4)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) != 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),X4),bot_bot(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
cnf(i_0_1852,plain,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X4) = ti(X1,X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool)))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
cnf(i_0_1853,plain,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X4) = ti(X1,X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) != 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),X5),bot_bot(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
cnf(i_0_1854,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))) = 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_1270]) ).
fof(i_0_1855,plain,
! [X5228] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5228),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5228),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5228),X5228)))),
inference(variable_rename,[status(thm)],[fact_602_le__cube]) ).
cnf(i_0_1856,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
| ti(fun(X1,bool),X4) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X5),hAPP(fun(X1,bool),X1,X3,X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1271]) ).
fof(i_0_1857,plain,
! [X5439,X5440,X5441] :
( ( hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),X5440),zero_zero(X5439)))
| hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),X5440))
| ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),hAPP(X5439,X5439,hAPP(X5439,fun(X5439,X5439),times_times(X5439),X5440),X5441)))
| ~ linord581940658strict(X5439) )
& ( hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),X5441),zero_zero(X5439)))
| hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),X5440))
| ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),hAPP(X5439,X5439,hAPP(X5439,fun(X5439,X5439),times_times(X5439),X5440),X5441)))
| ~ linord581940658strict(X5439) )
& ( hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),X5440),zero_zero(X5439)))
| hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),X5441))
| ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),hAPP(X5439,X5439,hAPP(X5439,fun(X5439,X5439),times_times(X5439),X5440),X5441)))
| ~ linord581940658strict(X5439) )
& ( hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),X5441),zero_zero(X5439)))
| hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),X5441))
| ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),hAPP(X5439,X5439,hAPP(X5439,fun(X5439,X5439),times_times(X5439),X5440),X5441)))
| ~ linord581940658strict(X5439) )
& ( ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),X5440))
| ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),X5441))
| hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),hAPP(X5439,X5439,hAPP(X5439,fun(X5439,X5439),times_times(X5439),X5440),X5441)))
| ~ linord581940658strict(X5439) )
& ( ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),X5440),zero_zero(X5439)))
| ~ hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),X5441),zero_zero(X5439)))
| hBOOL(hAPP(X5439,bool,hAPP(X5439,fun(X5439,bool),ord_less_eq(X5439),zero_zero(X5439)),hAPP(X5439,X5439,hAPP(X5439,fun(X5439,X5439),times_times(X5439),X5440),X5441)))
| ~ linord581940658strict(X5439) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_668_zero__le__mult__iff])])])]) ).
fof(i_0_1858,plain,
! [X5883,X5884,X5885] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk103_3(X5883,X5884,X5885)),X5885))
| hBOOL(hAPP(int,bool,X5883,X5884))
| ~ hBOOL(hAPP(int,bool,X5883,X5885))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5884),X5885)) )
& ( hBOOL(hAPP(int,bool,X5883,esk103_3(X5883,X5884,X5885)))
| hBOOL(hAPP(int,bool,X5883,X5884))
| ~ hBOOL(hAPP(int,bool,X5883,X5885))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5884),X5885)) )
& ( ~ hBOOL(hAPP(int,bool,X5883,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk103_3(X5883,X5884,X5885)),one_one(int))))
| hBOOL(hAPP(int,bool,X5883,X5884))
| ~ hBOOL(hAPP(int,bool,X5883,X5885))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5884),X5885)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_807_int__le__induct])])])]) ).
fof(i_0_1859,plain,
! [X5898,X5899,X5900] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5899),esk106_3(X5898,X5899,X5900)))
| hBOOL(hAPP(int,bool,X5898,X5900))
| ~ hBOOL(hAPP(int,bool,X5898,X5899))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5899),X5900)) )
& ( hBOOL(hAPP(int,bool,X5898,esk106_3(X5898,X5899,X5900)))
| hBOOL(hAPP(int,bool,X5898,X5900))
| ~ hBOOL(hAPP(int,bool,X5898,X5899))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5899),X5900)) )
& ( ~ hBOOL(hAPP(int,bool,X5898,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk106_3(X5898,X5899,X5900)),one_one(int))))
| hBOOL(hAPP(int,bool,X5898,X5900))
| ~ hBOOL(hAPP(int,bool,X5898,X5899))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5899),X5900)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_810_int__ge__induct])])])]) ).
fof(i_0_1860,plain,
! [X4977,X4978] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4977),X4978)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4977))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4978)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4977))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4977),X4978))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4978))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4977),X4978))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_515_add__gr__0])])]) ).
fof(i_0_1861,plain,
! [X3795,X3796,X3797,X3798] :
( ( ~ hBOOL(hAPP(fun(X3795,bool),bool,hAPP(X3795,fun(fun(X3795,bool),bool),member(X3795),X3797),X3798))
| hAPP(fun(X3795,bool),fun(X3795,bool),hAPP(fun(X3795,bool),fun(fun(X3795,bool),fun(X3795,bool)),minus_minus(fun(X3795,bool)),hAPP(fun(X3795,bool),fun(X3795,bool),hAPP(X3795,fun(fun(X3795,bool),fun(X3795,bool)),insert(X3795),X3797),X3796)),X3798) = hAPP(fun(X3795,bool),fun(X3795,bool),hAPP(fun(X3795,bool),fun(fun(X3795,bool),fun(X3795,bool)),minus_minus(fun(X3795,bool)),X3796),X3798) )
& ( hBOOL(hAPP(fun(X3795,bool),bool,hAPP(X3795,fun(fun(X3795,bool),bool),member(X3795),X3797),X3798))
| hAPP(fun(X3795,bool),fun(X3795,bool),hAPP(fun(X3795,bool),fun(fun(X3795,bool),fun(X3795,bool)),minus_minus(fun(X3795,bool)),hAPP(fun(X3795,bool),fun(X3795,bool),hAPP(X3795,fun(fun(X3795,bool),fun(X3795,bool)),insert(X3795),X3797),X3796)),X3798) = hAPP(fun(X3795,bool),fun(X3795,bool),hAPP(X3795,fun(fun(X3795,bool),fun(X3795,bool)),insert(X3795),X3797),hAPP(fun(X3795,bool),fun(X3795,bool),hAPP(fun(X3795,bool),fun(fun(X3795,bool),fun(X3795,bool)),minus_minus(fun(X3795,bool)),X3796),X3798)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1272])]) ).
cnf(i_0_1862,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X4),X2)) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),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_1273]) ).
fof(i_0_1863,plain,
! [X4843,X4844,X4845,X4846] :
( ( hBOOL(hAPP(fun(X4843,bool),bool,finite_finite(X4843),X4845))
| ~ hBOOL(hAPP(fun(sum_sum(X4843,X4844),bool),bool,finite_finite(sum_sum(X4843,X4844)),hAPP(fun(X4844,bool),fun(sum_sum(X4843,X4844),bool),hAPP(fun(X4843,bool),fun(fun(X4844,bool),fun(sum_sum(X4843,X4844),bool)),sum_Plus(X4843,X4844),X4845),X4846))) )
& ( hBOOL(hAPP(fun(X4844,bool),bool,finite_finite(X4844),X4846))
| ~ hBOOL(hAPP(fun(sum_sum(X4843,X4844),bool),bool,finite_finite(sum_sum(X4843,X4844)),hAPP(fun(X4844,bool),fun(sum_sum(X4843,X4844),bool),hAPP(fun(X4843,bool),fun(fun(X4844,bool),fun(sum_sum(X4843,X4844),bool)),sum_Plus(X4843,X4844),X4845),X4846))) )
& ( ~ hBOOL(hAPP(fun(X4843,bool),bool,finite_finite(X4843),X4845))
| ~ hBOOL(hAPP(fun(X4844,bool),bool,finite_finite(X4844),X4846))
| hBOOL(hAPP(fun(sum_sum(X4843,X4844),bool),bool,finite_finite(sum_sum(X4843,X4844)),hAPP(fun(X4844,bool),fun(sum_sum(X4843,X4844),bool),hAPP(fun(X4843,bool),fun(fun(X4844,bool),fun(sum_sum(X4843,X4844),bool)),sum_Plus(X4843,X4844),X4845),X4846))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_449_finite__Plus__iff])])]) ).
fof(i_0_1864,plain,
! [X4835,X4836,X4837,X4838] :
( ~ hBOOL(hAPP(fun(sum_sum(X4835,X4836),bool),bool,finite_finite(sum_sum(X4835,X4836)),hAPP(fun(X4836,bool),fun(sum_sum(X4835,X4836),bool),hAPP(fun(X4835,bool),fun(fun(X4836,bool),fun(sum_sum(X4835,X4836),bool)),sum_Plus(X4835,X4836),X4837),X4838)))
| hBOOL(hAPP(fun(X4835,bool),bool,finite_finite(X4835),X4837)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_finite__PlusD_I1_J])]) ).
fof(i_0_1865,plain,
! [X4831,X4832,X4833,X4834] :
( ~ hBOOL(hAPP(fun(sum_sum(X4831,X4832),bool),bool,finite_finite(sum_sum(X4831,X4832)),hAPP(fun(X4832,bool),fun(sum_sum(X4831,X4832),bool),hAPP(fun(X4831,bool),fun(fun(X4832,bool),fun(sum_sum(X4831,X4832),bool)),sum_Plus(X4831,X4832),X4833),X4834)))
| hBOOL(hAPP(fun(X4832,bool),bool,finite_finite(X4832),X4834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_446_finite__PlusD_I2_J])]) ).
fof(i_0_1866,plain,
! [X5789,X5790] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5789),X5790))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5789),one_one(int))),X5790)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_782_zless__imp__add1__zle])]) ).
fof(i_0_1867,plain,
! [X4586,X4587,X4588] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4587),X4588))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4587),X4586)),X4588)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_385_less__imp__diff__less])]) ).
fof(i_0_1868,plain,
! [X4250,X4251,X4252] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4251),X4252))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4252),X4250)),X4251) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4252),X4251)),X4250) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_271_diff__add__assoc2])]) ).
fof(i_0_1869,plain,
! [X4247,X4248,X4249] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4248),X4249))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4249),X4248)),X4247) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4249),X4247)),X4248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_270_add__diff__assoc2])]) ).
fof(i_0_1870,plain,
! [X4743,X4744,X4745] :
( ~ hBOOL(hAPP(fun(X4743,bool),bool,hAPP(fun(X4743,bool),fun(fun(X4743,bool),bool),ord_less(fun(X4743,bool)),X4744),X4745))
| hBOOL(hAPP(fun(X4743,bool),bool,hAPP(X4743,fun(fun(X4743,bool),bool),member(X4743),esk61_3(X4743,X4744,X4745)),hAPP(fun(X4743,bool),fun(X4743,bool),hAPP(fun(X4743,bool),fun(fun(X4743,bool),fun(X4743,bool)),minus_minus(fun(X4743,bool)),X4745),X4744))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_psubset__imp__ex__mem])])]) ).
fof(i_0_1871,plain,
! [X5859,X5860,X5861] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5861))
| X5861 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5859),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5861),X5860))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5859))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5860),one_one(int))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_801_self__quotient__aux2])]) ).
cnf(i_0_1872,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
cnf(i_0_1873,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))) ),
inference(split_conjunct,[status(thm)],[i_0_1275]) ).
fof(i_0_1874,plain,
! [X5856,X5857,X5858] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5858))
| X5858 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5856),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5858),X5857))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5856),X5858))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X5857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_800_self__quotient__aux1])]) ).
cnf(i_0_1875,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_1276]) ).
cnf(i_0_1876,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_1277]) ).
cnf(i_0_1877,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_1253]) ).
fof(i_0_1878,plain,
! [X5388,X5389,X5390] :
( ( ~ hBOOL(hAPP(X5388,bool,hAPP(X5388,fun(X5388,bool),ord_less_eq(X5388),zero_zero(X5388)),X5390))
| ~ hBOOL(hAPP(X5388,bool,hAPP(X5388,fun(X5388,bool),ord_less_eq(X5388),zero_zero(X5388)),X5389))
| hBOOL(hAPP(X5388,bool,hAPP(X5388,fun(X5388,bool),ord_less_eq(X5388),zero_zero(X5388)),hAPP(X5388,X5388,hAPP(X5388,fun(X5388,X5388),times_times(X5388),X5390),X5389)))
| ~ ordered_ring(X5388) )
& ( ~ hBOOL(hAPP(X5388,bool,hAPP(X5388,fun(X5388,bool),ord_less_eq(X5388),X5390),zero_zero(X5388)))
| ~ hBOOL(hAPP(X5388,bool,hAPP(X5388,fun(X5388,bool),ord_less_eq(X5388),X5389),zero_zero(X5388)))
| hBOOL(hAPP(X5388,bool,hAPP(X5388,fun(X5388,bool),ord_less_eq(X5388),zero_zero(X5388)),hAPP(X5388,X5388,hAPP(X5388,fun(X5388,X5388),times_times(X5388),X5390),X5389)))
| ~ ordered_ring(X5388) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_654_split__mult__pos__le])])])]) ).
fof(i_0_1879,plain,
! [X5433,X5434,X5435] :
( ~ ordere453448008miring(X5433)
| ~ hBOOL(hAPP(X5433,bool,hAPP(X5433,fun(X5433,bool),ord_less_eq(X5433),zero_zero(X5433)),X5435))
| ~ hBOOL(hAPP(X5433,bool,hAPP(X5433,fun(X5433,bool),ord_less_eq(X5433),zero_zero(X5433)),X5434))
| hBOOL(hAPP(X5433,bool,hAPP(X5433,fun(X5433,bool),ord_less_eq(X5433),zero_zero(X5433)),hAPP(X5433,X5433,hAPP(X5433,fun(X5433,X5433),times_times(X5433),X5435),X5434))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_666_mult__nonneg__nonneg])])]) ).
fof(i_0_1880,plain,
! [X4921,X4922,X4923] :
( ~ ordere216010020id_add(X4921)
| ~ hBOOL(hAPP(X4921,bool,hAPP(X4921,fun(X4921,bool),ord_less_eq(X4921),zero_zero(X4921)),X4923))
| ~ hBOOL(hAPP(X4921,bool,hAPP(X4921,fun(X4921,bool),ord_less_eq(X4921),zero_zero(X4921)),X4922))
| hBOOL(hAPP(X4921,bool,hAPP(X4921,fun(X4921,bool),ord_less_eq(X4921),zero_zero(X4921)),hAPP(X4921,X4921,hAPP(X4921,fun(X4921,X4921),plus_plus(X4921),X4923),X4922))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_494_add__nonneg__nonneg])])]) ).
fof(i_0_1881,plain,
! [X5458,X5459,X5460] :
( ~ linord20386208strict(X5458)
| ~ hBOOL(hAPP(X5458,bool,hAPP(X5458,fun(X5458,bool),ord_less(X5458),zero_zero(X5458)),X5460))
| ~ hBOOL(hAPP(X5458,bool,hAPP(X5458,fun(X5458,bool),ord_less(X5458),zero_zero(X5458)),X5459))
| hBOOL(hAPP(X5458,bool,hAPP(X5458,fun(X5458,bool),ord_less(X5458),zero_zero(X5458)),hAPP(X5458,X5458,hAPP(X5458,fun(X5458,X5458),times_times(X5458),X5460),X5459))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_674_mult__pos__pos])])]) ).
fof(i_0_1882,plain,
! [X4994,X4995,X4996] :
( ~ ordere216010020id_add(X4994)
| ~ hBOOL(hAPP(X4994,bool,hAPP(X4994,fun(X4994,bool),ord_less(X4994),zero_zero(X4994)),X4996))
| ~ hBOOL(hAPP(X4994,bool,hAPP(X4994,fun(X4994,bool),ord_less_eq(X4994),zero_zero(X4994)),X4995))
| hBOOL(hAPP(X4994,bool,hAPP(X4994,fun(X4994,bool),ord_less(X4994),zero_zero(X4994)),hAPP(X4994,X4994,hAPP(X4994,fun(X4994,X4994),plus_plus(X4994),X4996),X4995))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_525_add__pos__nonneg])])]) ).
fof(i_0_1883,plain,
! [X4997,X4998,X4999] :
( ~ ordere216010020id_add(X4997)
| ~ hBOOL(hAPP(X4997,bool,hAPP(X4997,fun(X4997,bool),ord_less_eq(X4997),zero_zero(X4997)),X4999))
| ~ hBOOL(hAPP(X4997,bool,hAPP(X4997,fun(X4997,bool),ord_less(X4997),zero_zero(X4997)),X4998))
| hBOOL(hAPP(X4997,bool,hAPP(X4997,fun(X4997,bool),ord_less(X4997),zero_zero(X4997)),hAPP(X4997,X4997,hAPP(X4997,fun(X4997,X4997),plus_plus(X4997),X4999),X4998))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_526_add__nonneg__pos])])]) ).
fof(i_0_1884,plain,
! [X4942,X4943,X4944] :
( ~ ordere216010020id_add(X4942)
| ~ hBOOL(hAPP(X4942,bool,hAPP(X4942,fun(X4942,bool),ord_less(X4942),zero_zero(X4942)),X4944))
| ~ hBOOL(hAPP(X4942,bool,hAPP(X4942,fun(X4942,bool),ord_less(X4942),zero_zero(X4942)),X4943))
| hBOOL(hAPP(X4942,bool,hAPP(X4942,fun(X4942,bool),ord_less(X4942),zero_zero(X4942)),hAPP(X4942,X4942,hAPP(X4942,fun(X4942,X4942),plus_plus(X4942),X4944),X4943))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_501_add__pos__pos])])]) ).
fof(i_0_1885,plain,
! [X5512,X5513,X5514] :
( ~ linordered_semidom(X5512)
| ~ hBOOL(hAPP(X5512,bool,hAPP(X5512,fun(X5512,bool),ord_less(X5512),one_one(X5512)),X5514))
| ~ hBOOL(hAPP(X5512,bool,hAPP(X5512,fun(X5512,bool),ord_less(X5512),one_one(X5512)),X5513))
| hBOOL(hAPP(X5512,bool,hAPP(X5512,fun(X5512,bool),ord_less(X5512),one_one(X5512)),hAPP(X5512,X5512,hAPP(X5512,fun(X5512,X5512),times_times(X5512),X5514),X5513))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_689_less__1__mult])])]) ).
fof(i_0_1886,plain,
! [X5421,X5422,X5423] :
( ~ ordered_ring(X5421)
| ~ hBOOL(hAPP(X5421,bool,hAPP(X5421,fun(X5421,bool),ord_less_eq(X5421),X5423),zero_zero(X5421)))
| ~ hBOOL(hAPP(X5421,bool,hAPP(X5421,fun(X5421,bool),ord_less_eq(X5421),X5422),zero_zero(X5421)))
| hBOOL(hAPP(X5421,bool,hAPP(X5421,fun(X5421,bool),ord_less_eq(X5421),zero_zero(X5421)),hAPP(X5421,X5421,hAPP(X5421,fun(X5421,X5421),times_times(X5421),X5423),X5422))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_662_mult__nonpos__nonpos])])]) ).
fof(i_0_1887,plain,
! [X5480,X5481,X5482] :
( ~ linord581940658strict(X5480)
| ~ hBOOL(hAPP(X5480,bool,hAPP(X5480,fun(X5480,bool),ord_less(X5480),X5482),zero_zero(X5480)))
| ~ hBOOL(hAPP(X5480,bool,hAPP(X5480,fun(X5480,bool),ord_less(X5480),X5481),zero_zero(X5480)))
| hBOOL(hAPP(X5480,bool,hAPP(X5480,fun(X5480,bool),ord_less(X5480),zero_zero(X5480)),hAPP(X5480,X5480,hAPP(X5480,fun(X5480,X5480),times_times(X5480),X5482),X5481))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_681_mult__neg__neg])])]) ).
fof(i_0_1888,plain,
! [X4927,X4928,X4929,X4930] :
( ~ ordere216010020id_add(X4927)
| ~ hBOOL(hAPP(X4927,bool,hAPP(X4927,fun(X4927,bool),ord_less_eq(X4927),zero_zero(X4927)),X4930))
| ~ hBOOL(hAPP(X4927,bool,hAPP(X4927,fun(X4927,bool),ord_less_eq(X4927),X4928),X4929))
| hBOOL(hAPP(X4927,bool,hAPP(X4927,fun(X4927,bool),ord_less_eq(X4927),X4928),hAPP(X4927,X4927,hAPP(X4927,fun(X4927,X4927),plus_plus(X4927),X4930),X4929))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_496_add__increasing])])]) ).
fof(i_0_1889,plain,
! [X4931,X4932,X4933,X4934] :
( ~ ordere216010020id_add(X4931)
| ~ hBOOL(hAPP(X4931,bool,hAPP(X4931,fun(X4931,bool),ord_less_eq(X4931),zero_zero(X4931)),X4934))
| ~ hBOOL(hAPP(X4931,bool,hAPP(X4931,fun(X4931,bool),ord_less_eq(X4931),X4932),X4933))
| hBOOL(hAPP(X4931,bool,hAPP(X4931,fun(X4931,bool),ord_less_eq(X4931),X4932),hAPP(X4931,X4931,hAPP(X4931,fun(X4931,X4931),plus_plus(X4931),X4933),X4934))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_497_add__increasing2])])]) ).
fof(i_0_1890,plain,
! [X5000,X5001,X5002,X5003] :
( ~ ordere216010020id_add(X5000)
| ~ hBOOL(hAPP(X5000,bool,hAPP(X5000,fun(X5000,bool),ord_less(X5000),zero_zero(X5000)),X5003))
| ~ hBOOL(hAPP(X5000,bool,hAPP(X5000,fun(X5000,bool),ord_less_eq(X5000),X5001),X5002))
| hBOOL(hAPP(X5000,bool,hAPP(X5000,fun(X5000,bool),ord_less(X5000),X5001),hAPP(X5000,X5000,hAPP(X5000,fun(X5000,X5000),plus_plus(X5000),X5003),X5002))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_527_add__strict__increasing])])]) ).
fof(i_0_1891,plain,
! [X5004,X5005,X5006,X5007] :
( ~ ordere216010020id_add(X5004)
| ~ hBOOL(hAPP(X5004,bool,hAPP(X5004,fun(X5004,bool),ord_less_eq(X5004),zero_zero(X5004)),X5007))
| ~ hBOOL(hAPP(X5004,bool,hAPP(X5004,fun(X5004,bool),ord_less(X5004),X5005),X5006))
| hBOOL(hAPP(X5004,bool,hAPP(X5004,fun(X5004,bool),ord_less(X5004),X5005),hAPP(X5004,X5004,hAPP(X5004,fun(X5004,X5004),plus_plus(X5004),X5007),X5006))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_528_add__strict__increasing2])])]) ).
fof(i_0_1892,plain,
! [X4948,X4949,X4950,X4951] :
( ~ linordered_semidom(X4948)
| ~ hBOOL(hAPP(X4948,bool,hAPP(X4948,fun(X4948,bool),ord_less(X4948),zero_zero(X4948)),X4951))
| ~ hBOOL(hAPP(X4948,bool,hAPP(X4948,fun(X4948,bool),ord_less(X4948),X4949),X4950))
| hBOOL(hAPP(X4948,bool,hAPP(X4948,fun(X4948,bool),ord_less(X4948),X4949),hAPP(X4948,X4948,hAPP(X4948,fun(X4948,X4948),plus_plus(X4948),X4951),X4950))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_503_pos__add__strict])])]) ).
fof(i_0_1893,plain,
! [X5136,X5137,X5138] :
( ( hBOOL(hAPP(X5136,bool,hAPP(X5136,fun(X5136,bool),ord_less(X5136),zero_zero(X5136)),esk99_3(X5136,X5137,X5138)))
| hBOOL(hAPP(X5136,bool,hAPP(X5136,fun(X5136,bool),ord_less_eq(X5136),X5137),X5138))
| ~ linordered_field(X5136) )
& ( ~ hBOOL(hAPP(X5136,bool,hAPP(X5136,fun(X5136,bool),ord_less_eq(X5136),X5137),hAPP(X5136,X5136,hAPP(X5136,fun(X5136,X5136),plus_plus(X5136),X5138),esk99_3(X5136,X5137,X5138))))
| hBOOL(hAPP(X5136,bool,hAPP(X5136,fun(X5136,bool),ord_less_eq(X5136),X5137),X5138))
| ~ linordered_field(X5136) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_570_field__le__epsilon])])])])]) ).
fof(i_0_1894,plain,
! [X3581,X3582,X3583,X3584,X3585,X3586] : hAPP(fun(X3581,bool),fun(X3582,bool),hAPP(fun(X3581,X3582),fun(fun(X3581,bool),fun(X3582,bool)),image(X3581,X3582),X3584),hAPP(fun(X3583,bool),fun(X3581,bool),hAPP(fun(X3583,X3581),fun(fun(X3583,bool),fun(X3581,bool)),image(X3583,X3581),X3585),X3586)) = hAPP(fun(X3583,bool),fun(X3582,bool),hAPP(fun(X3583,X3582),fun(fun(X3583,bool),fun(X3582,bool)),image(X3583,X3582),hAPP(fun(X3583,X3581),fun(X3583,X3582),hAPP(fun(X3581,X3582),fun(fun(X3583,X3581),fun(X3583,X3582)),combb(X3581,X3582,X3583),X3584),X3585)),X3586),
inference(variable_rename,[status(thm)],[fact_97_image__image]) ).
fof(i_0_1895,plain,
! [X4783,X4784,X4785,X4786] :
( ( hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less(X4783),X4785),esk71_4(X4783,X4784,X4785,X4786)))
| hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less_eq(X4783),X4786),X4784))
| ~ hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less(X4783),X4785),X4786))
| ~ dense_linorder(X4783) )
& ( hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less(X4783),esk71_4(X4783,X4784,X4785,X4786)),X4786))
| hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less_eq(X4783),X4786),X4784))
| ~ hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less(X4783),X4785),X4786))
| ~ dense_linorder(X4783) )
& ( ~ hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less_eq(X4783),esk71_4(X4783,X4784,X4785,X4786)),X4784))
| hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less_eq(X4783),X4786),X4784))
| ~ hBOOL(hAPP(X4783,bool,hAPP(X4783,fun(X4783,bool),ord_less(X4783),X4785),X4786))
| ~ dense_linorder(X4783) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_439_dense__le__bounded])])])])]) ).
fof(i_0_1896,plain,
! [X5365,X5366,X5367,X5368] :
( ~ comm_semiring_1(X5365)
| hAPP(X5365,X5365,hAPP(X5365,fun(X5365,X5365),plus_plus(X5365),hAPP(X5365,X5365,hAPP(X5365,fun(X5365,X5365),times_times(X5365),X5366),X5367)),hAPP(X5365,X5365,hAPP(X5365,fun(X5365,X5365),times_times(X5365),X5368),X5367)) = hAPP(X5365,X5365,hAPP(X5365,fun(X5365,X5365),times_times(X5365),hAPP(X5365,X5365,hAPP(X5365,fun(X5365,X5365),plus_plus(X5365),X5366),X5368)),X5367) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])])]) ).
fof(i_0_1897,plain,
! [X5192,X5193,X5194,X5195] :
( ~ comm_semiring(X5192)
| hAPP(X5192,X5192,hAPP(X5192,fun(X5192,X5192),times_times(X5192),hAPP(X5192,X5192,hAPP(X5192,fun(X5192,X5192),plus_plus(X5192),X5193),X5194)),X5195) = hAPP(X5192,X5192,hAPP(X5192,fun(X5192,X5192),plus_plus(X5192),hAPP(X5192,X5192,hAPP(X5192,fun(X5192,X5192),times_times(X5192),X5193),X5195)),hAPP(X5192,X5192,hAPP(X5192,fun(X5192,X5192),times_times(X5192),X5194),X5195)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_590_comm__semiring__class_Odistrib])])]) ).
fof(i_0_1898,plain,
! [X5361,X5362,X5363,X5364] :
( ~ comm_semiring_1(X5361)
| hAPP(X5361,X5361,hAPP(X5361,fun(X5361,X5361),times_times(X5361),hAPP(X5361,X5361,hAPP(X5361,fun(X5361,X5361),plus_plus(X5361),X5362),X5363)),X5364) = hAPP(X5361,X5361,hAPP(X5361,fun(X5361,X5361),plus_plus(X5361),hAPP(X5361,X5361,hAPP(X5361,fun(X5361,X5361),times_times(X5361),X5362),X5364)),hAPP(X5361,X5361,hAPP(X5361,fun(X5361,X5361),times_times(X5361),X5363),X5364)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])])]) ).
fof(i_0_1899,plain,
! [X3788,X3789,X3790] :
( ( ~ hBOOL(hAPP(fun(X3788,bool),bool,finite_finite(X3788),hAPP(fun(X3788,bool),fun(X3788,bool),hAPP(fun(X3788,bool),fun(fun(X3788,bool),fun(X3788,bool)),minus_minus(fun(X3788,bool)),X3789),X3790)))
| hBOOL(hAPP(fun(X3788,bool),bool,finite_finite(X3788),X3789))
| ~ hBOOL(hAPP(fun(X3788,bool),bool,finite_finite(X3788),X3790)) )
& ( ~ hBOOL(hAPP(fun(X3788,bool),bool,finite_finite(X3788),X3789))
| hBOOL(hAPP(fun(X3788,bool),bool,finite_finite(X3788),hAPP(fun(X3788,bool),fun(X3788,bool),hAPP(fun(X3788,bool),fun(fun(X3788,bool),fun(X3788,bool)),minus_minus(fun(X3788,bool)),X3789),X3790)))
| ~ hBOOL(hAPP(fun(X3788,bool),bool,finite_finite(X3788),X3790)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_finite__Diff2])])]) ).
fof(i_0_1900,plain,
! [X5902,X5903] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5903))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5902))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5903),X5902))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_811_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_1901,plain,
! [X5904,X5905] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5905))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5904))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5905),X5904))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_813_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_1902,plain,
! [X5549,X5550] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5549))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5549),X5550))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5550))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5549),X5550))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5549))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5550))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5549),X5550))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_700_nat__0__less__mult__iff])])]) ).
cnf(i_0_1903,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) = ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1278]) ).
fof(i_0_1904,plain,
! [X6070,X6071] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6071))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6070))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X6071),X6070))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_878_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_1905,plain,
! [X3618,X3619,X3620,X3621] :
( ~ hBOOL(hAPP(fun(X3618,bool),bool,hAPP(fun(X3618,bool),fun(fun(X3618,bool),bool),ord_less_eq(fun(X3618,bool)),X3620),X3621))
| hBOOL(hAPP(fun(X3618,bool),bool,hAPP(fun(X3618,bool),fun(fun(X3618,bool),bool),ord_less_eq(fun(X3618,bool)),X3620),hAPP(fun(X3618,bool),fun(X3618,bool),hAPP(X3618,fun(fun(X3618,bool),fun(X3618,bool)),insert(X3618),X3619),X3621))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_105_subset__insertI2])]) ).
fof(i_0_1906,plain,
! [X4255,X4256,X4257,X4258,X4259] :
( ~ hBOOL(hAPP(fun(fun(X4255,bool),X4255),bool,hAPP(fun(X4255,fun(X4255,X4255)),fun(fun(fun(X4255,bool),X4255),bool),finite2073411215e_idem(X4255),X4258),X4259))
| ~ hBOOL(hAPP(fun(X4255,bool),bool,finite_finite(X4255),X4257))
| ~ hBOOL(hAPP(fun(X4255,bool),bool,hAPP(X4255,fun(fun(X4255,bool),bool),member(X4255),X4256),X4257))
| hAPP(X4255,X4255,hAPP(X4255,fun(X4255,X4255),X4258,X4256),hAPP(fun(X4255,bool),X4255,X4259,X4257)) = hAPP(fun(X4255,bool),X4255,X4259,X4257) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_274_folding__one__idem_Oin__idem])]) ).
fof(i_0_1907,plain,
! [X5690,X5691] :
( ( X5691 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5691),X5690) = zero_zero(nat) )
& ( X5691 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5691),X5690) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5690),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5691),one_one(nat))),X5690)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_738_mult__eq__if])]) ).
fof(i_0_1908,plain,
! [X5737,X5738,X5739] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5737),X5738)),X5739) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5737),X5739)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5738),X5739)),
inference(variable_rename,[status(thm)],[fact_756_zadd__zmult__distrib]) ).
fof(i_0_1909,plain,
! [X5726,X5727,X5728] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5726),X5727)),X5728) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5726),X5728)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5727),X5728)),
inference(variable_rename,[status(thm)],[fact_752_zdiff__zmult__distrib]) ).
fof(i_0_1910,plain,
! [X5212,X5213,X5214] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5212),X5213)),X5214) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5212),X5214)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5213),X5214)),
inference(variable_rename,[status(thm)],[fact_597_add__mult__distrib]) ).
fof(i_0_1911,plain,
! [X5230,X5231,X5232] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5230),X5231)),X5232) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5230),X5232)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5231),X5232)),
inference(variable_rename,[status(thm)],[fact_604_diff__mult__distrib]) ).
fof(i_0_1912,plain,
! [X3791,X3792,X3793,X3794] :
( ~ hBOOL(hAPP(fun(X3791,bool),bool,hAPP(X3791,fun(fun(X3791,bool),bool),member(X3791),X3793),X3794))
| hAPP(fun(X3791,bool),fun(X3791,bool),hAPP(fun(X3791,bool),fun(fun(X3791,bool),fun(X3791,bool)),minus_minus(fun(X3791,bool)),hAPP(fun(X3791,bool),fun(X3791,bool),hAPP(X3791,fun(fun(X3791,bool),fun(X3791,bool)),insert(X3791),X3793),X3792)),X3794) = hAPP(fun(X3791,bool),fun(X3791,bool),hAPP(fun(X3791,bool),fun(fun(X3791,bool),fun(X3791,bool)),minus_minus(fun(X3791,bool)),X3792),X3794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_insert__Diff1])]) ).
fof(i_0_1913,plain,
! [X5692,X5693] :
( ~ ring_char_0(X5692)
| ~ hBOOL(hAPP(fun(X5692,bool),bool,hAPP(X5692,fun(fun(X5692,bool),bool),member(X5692),X5693),ring_1_Ints(X5692)))
| hAPP(X5692,X5692,hAPP(X5692,fun(X5692,X5692),plus_plus(X5692),hAPP(X5692,X5692,hAPP(X5692,fun(X5692,X5692),plus_plus(X5692),one_one(X5692)),X5693)),X5693) != zero_zero(X5692) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_739_Ints__odd__nonzero])])]) ).
fof(i_0_1914,plain,
! [X6186,X6187,X6188] :
( ( ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),zero_zero(X6186)),X6187))
| ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),zero_zero(X6186)),X6188))
| hAPP(X6186,X6186,abs_abs(X6186),hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),X6188),X6187)) = hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),hAPP(X6186,X6186,abs_abs(X6186),X6188)),hAPP(X6186,X6186,abs_abs(X6186),X6187))
| ~ ordered_ring_abs(X6186) )
& ( ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),X6187),zero_zero(X6186)))
| ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),zero_zero(X6186)),X6188))
| hAPP(X6186,X6186,abs_abs(X6186),hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),X6188),X6187)) = hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),hAPP(X6186,X6186,abs_abs(X6186),X6188)),hAPP(X6186,X6186,abs_abs(X6186),X6187))
| ~ ordered_ring_abs(X6186) )
& ( ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),zero_zero(X6186)),X6187))
| ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),X6188),zero_zero(X6186)))
| hAPP(X6186,X6186,abs_abs(X6186),hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),X6188),X6187)) = hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),hAPP(X6186,X6186,abs_abs(X6186),X6188)),hAPP(X6186,X6186,abs_abs(X6186),X6187))
| ~ ordered_ring_abs(X6186) )
& ( ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),X6187),zero_zero(X6186)))
| ~ hBOOL(hAPP(X6186,bool,hAPP(X6186,fun(X6186,bool),ord_less_eq(X6186),X6188),zero_zero(X6186)))
| hAPP(X6186,X6186,abs_abs(X6186),hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),X6188),X6187)) = hAPP(X6186,X6186,hAPP(X6186,fun(X6186,X6186),times_times(X6186),hAPP(X6186,X6186,abs_abs(X6186),X6188)),hAPP(X6186,X6186,abs_abs(X6186),X6187))
| ~ ordered_ring_abs(X6186) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_919_abs__eq__mult])])])]) ).
fof(i_0_1915,plain,
! [X6252] : hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X6252))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),X6252),
inference(variable_rename,[status(thm)],[fact_956_Suc3__eq__add__3]) ).
fof(i_0_1916,plain,
! [X4917,X4918] :
( ( ~ hBOOL(hAPP(X4917,bool,hAPP(X4917,fun(X4917,bool),ord_less_eq(X4917),zero_zero(X4917)),hAPP(X4917,X4917,hAPP(X4917,fun(X4917,X4917),plus_plus(X4917),X4918),X4918)))
| hBOOL(hAPP(X4917,bool,hAPP(X4917,fun(X4917,bool),ord_less_eq(X4917),zero_zero(X4917)),X4918))
| ~ linord219039673up_add(X4917) )
& ( ~ hBOOL(hAPP(X4917,bool,hAPP(X4917,fun(X4917,bool),ord_less_eq(X4917),zero_zero(X4917)),X4918))
| hBOOL(hAPP(X4917,bool,hAPP(X4917,fun(X4917,bool),ord_less_eq(X4917),zero_zero(X4917)),hAPP(X4917,X4917,hAPP(X4917,fun(X4917,X4917),plus_plus(X4917),X4918),X4918)))
| ~ linord219039673up_add(X4917) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_492_zero__le__double__add__iff__zero__le__single__add])])])]) ).
fof(i_0_1917,plain,
! [X4938,X4939] :
( ( ~ hBOOL(hAPP(X4938,bool,hAPP(X4938,fun(X4938,bool),ord_less(X4938),zero_zero(X4938)),hAPP(X4938,X4938,hAPP(X4938,fun(X4938,X4938),plus_plus(X4938),X4939),X4939)))
| hBOOL(hAPP(X4938,bool,hAPP(X4938,fun(X4938,bool),ord_less(X4938),zero_zero(X4938)),X4939))
| ~ linord219039673up_add(X4938) )
& ( ~ hBOOL(hAPP(X4938,bool,hAPP(X4938,fun(X4938,bool),ord_less(X4938),zero_zero(X4938)),X4939))
| hBOOL(hAPP(X4938,bool,hAPP(X4938,fun(X4938,bool),ord_less(X4938),zero_zero(X4938)),hAPP(X4938,X4938,hAPP(X4938,fun(X4938,X4938),plus_plus(X4938),X4939),X4939)))
| ~ linord219039673up_add(X4938) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_499_zero__less__double__add__iff__zero__less__single__add])])])]) ).
fof(i_0_1918,plain,
! [X3907,X3908,X3909] :
( ~ hBOOL(hAPP(fun(X3907,bool),bool,finite_finite(X3907),X3909))
| ~ hBOOL(hAPP(fun(X3907,bool),bool,hAPP(fun(X3907,bool),fun(fun(X3907,bool),bool),ord_less_eq(fun(X3907,bool)),X3909),X3908))
| hAPP(fun(X3907,bool),nat,finite_card(X3907),hAPP(fun(X3907,bool),fun(X3907,bool),hAPP(fun(X3907,bool),fun(fun(X3907,bool),fun(X3907,bool)),minus_minus(fun(X3907,bool)),X3908),X3909)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X3907,bool),nat,finite_card(X3907),X3908)),hAPP(fun(X3907,bool),nat,finite_card(X3907),X3909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_179_card__Diff__subset])]) ).
cnf(i_0_1919,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X5) = ti(X1,X6)
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != ti(X1,X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_1279]) ).
cnf(i_0_1920,plain,
hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X3),X4),X5),bot_bot(fun(X1,bool))) = ti(X2,X5),
inference(split_conjunct,[status(thm)],[i_0_1280]) ).
cnf(i_0_1921,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1281]) ).
cnf(i_0_1922,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1281]) ).
cnf(i_0_1923,plain,
( ti(fun(X1,bool),X4) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X5),hAPP(fun(X1,bool),X1,X3,X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1282]) ).
fof(i_0_1924,plain,
! [X3290,X3291,X3292] :
( ~ hBOOL(hAPP(fun(X3290,bool),bool,finite_finite(X3290),X3292))
| ~ hBOOL(hAPP(fun(X3290,bool),bool,hAPP(fun(X3290,bool),fun(fun(X3290,bool),bool),ord_less_eq(fun(X3290,bool)),X3291),X3292))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3290,bool),nat,finite_card(X3290),X3291)),hAPP(fun(X3290,bool),nat,finite_card(X3290),X3292))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_card__mono])]) ).
fof(i_0_1925,plain,
! [X4700,X4701,X4702] :
( ~ hBOOL(hAPP(fun(X4700,bool),bool,finite_finite(X4700),X4702))
| ~ hBOOL(hAPP(fun(X4700,bool),bool,hAPP(fun(X4700,bool),fun(fun(X4700,bool),bool),ord_less(fun(X4700,bool)),X4701),X4702))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X4700,bool),nat,finite_card(X4700),X4701)),hAPP(fun(X4700,bool),nat,finite_card(X4700),X4702))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_422_psubset__card__mono])]) ).
fof(i_0_1926,plain,
! [X6241,X6242] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6242)))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6242)),X6241)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X6241) )
& ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6242)))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6242)),X6241)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X6242))),X6241) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1283])]) ).
fof(i_0_1927,plain,
! [X5791,X5792] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5791),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5792),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5791),X5792))
| X5791 = X5792 )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5791),X5792))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5791),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5792),one_one(int)))) )
& ( X5791 != X5792
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5791),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5792),one_one(int)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_783_zless__add1__eq])])]) ).
fof(i_0_1928,plain,
! [X4982,X4983] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4982),X4983)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4983),X4982)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4983),X4982))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4982),X4983))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_518_zero__less__diff])]) ).
fof(i_0_1929,plain,
! [X5785,X5786] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5785),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5786),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5785),X5786)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5785),X5786))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5785),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5786),one_one(int)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_780_zle__add1__eq__le])]) ).
fof(i_0_1930,plain,
! [X5772,X5773] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5772),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5773),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5772),X5773)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5772),X5773))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5772),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5773),one_one(int)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_775_zle__diff1__eq])]) ).
fof(i_0_1931,plain,
! [X5058,X5059] :
( ( X5059 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5059),X5058) = X5058 )
& ( X5059 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5059),X5058) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5059),one_one(nat))),X5058)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_547_add__eq__if])]) ).
fof(i_0_1932,plain,
! [X3518,X3519,X3520,X3521] :
( ~ hBOOL(hAPP(fun(X3518,bool),bool,hAPP(X3518,fun(fun(X3518,bool),bool),member(X3518),X3520),X3521))
| hBOOL(hAPP(fun(X3518,bool),bool,hAPP(X3518,fun(fun(X3518,bool),bool),member(X3518),X3520),hAPP(fun(X3518,bool),fun(X3518,bool),hAPP(X3518,fun(fun(X3518,bool),fun(X3518,bool)),insert(X3518),X3519),X3521))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_82_insertI2])]) ).
fof(i_0_1933,plain,
! [X5277,X5278,X5279] :
( ( ~ hBOOL(hAPP(X5277,bool,hAPP(X5277,fun(X5277,bool),ord_less_eq(X5277),hAPP(int,X5277,number_number_of(X5277),X5278)),hAPP(int,X5277,number_number_of(X5277),X5279)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5278),X5279))
| ~ number_ring(X5277)
| ~ linordered_idom(X5277) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5278),X5279))
| hBOOL(hAPP(X5277,bool,hAPP(X5277,fun(X5277,bool),ord_less_eq(X5277),hAPP(int,X5277,number_number_of(X5277),X5278)),hAPP(int,X5277,number_number_of(X5277),X5279)))
| ~ number_ring(X5277)
| ~ linordered_idom(X5277) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_622_le__number__of])])])]) ).
fof(i_0_1934,plain,
! [X5253,X5254,X5255] :
( ( ~ hBOOL(hAPP(X5253,bool,hAPP(X5253,fun(X5253,bool),ord_less(X5253),hAPP(int,X5253,number_number_of(X5253),X5254)),hAPP(int,X5253,number_number_of(X5253),X5255)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5254),X5255))
| ~ number_ring(X5253)
| ~ linordered_idom(X5253) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5254),X5255))
| hBOOL(hAPP(X5253,bool,hAPP(X5253,fun(X5253,bool),ord_less(X5253),hAPP(int,X5253,number_number_of(X5253),X5254)),hAPP(int,X5253,number_number_of(X5253),X5255)))
| ~ number_ring(X5253)
| ~ linordered_idom(X5253) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_614_less__number__of])])])]) ).
fof(i_0_1935,plain,
! [X5989,X5990,X5991] :
( ( ~ hBOOL(hAPP(X5989,bool,hAPP(X5989,fun(X5989,bool),ord_less_eq(X5989),hAPP(nat,X5989,semiring_1_of_nat(X5989),X5990)),hAPP(nat,X5989,semiring_1_of_nat(X5989),X5991)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5990),X5991))
| ~ linordered_semidom(X5989) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5990),X5991))
| hBOOL(hAPP(X5989,bool,hAPP(X5989,fun(X5989,bool),ord_less_eq(X5989),hAPP(nat,X5989,semiring_1_of_nat(X5989),X5990)),hAPP(nat,X5989,semiring_1_of_nat(X5989),X5991)))
| ~ linordered_semidom(X5989) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_843_of__nat__le__iff])])])]) ).
fof(i_0_1936,plain,
! [X5998,X5999,X6000] :
( ~ linordered_semidom(X5998)
| ~ hBOOL(hAPP(X5998,bool,hAPP(X5998,fun(X5998,bool),ord_less(X5998),hAPP(nat,X5998,semiring_1_of_nat(X5998),X5999)),hAPP(nat,X5998,semiring_1_of_nat(X5998),X6000)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5999),X6000)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_846_of__nat__less__imp__less])])]) ).
fof(i_0_1937,plain,
! [X5992,X5993,X5994] :
( ( ~ hBOOL(hAPP(X5992,bool,hAPP(X5992,fun(X5992,bool),ord_less(X5992),hAPP(nat,X5992,semiring_1_of_nat(X5992),X5993)),hAPP(nat,X5992,semiring_1_of_nat(X5992),X5994)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5993),X5994))
| ~ linordered_semidom(X5992) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5993),X5994))
| hBOOL(hAPP(X5992,bool,hAPP(X5992,fun(X5992,bool),ord_less(X5992),hAPP(nat,X5992,semiring_1_of_nat(X5992),X5993)),hAPP(nat,X5992,semiring_1_of_nat(X5992),X5994)))
| ~ linordered_semidom(X5992) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_844_of__nat__less__iff])])])]) ).
fof(i_0_1938,plain,
! [X6216,X6217] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X6217)),zero_zero(int)))
| hAPP(int,nat,number_number_of(nat),X6216) != hAPP(int,nat,number_number_of(nat),X6217) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| hAPP(int,int,number_number_of(int),X6216) = zero_zero(int)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hAPP(int,nat,number_number_of(nat),X6216) != hAPP(int,nat,number_number_of(nat),X6217) )
& ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| X6216 = X6217
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hAPP(int,nat,number_number_of(nat),X6216) != hAPP(int,nat,number_number_of(nat),X6217) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( X6216 != X6217
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| hAPP(int,int,number_number_of(int),X6216) != zero_zero(int)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( X6216 != X6217
| hAPP(int,int,number_number_of(int),X6216) != zero_zero(int)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6216)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X6217)),zero_zero(int)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X6217)),zero_zero(int)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( X6216 != X6217
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X6217)),zero_zero(int)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6217)))
| hAPP(int,int,number_number_of(int),X6216) != zero_zero(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X6217)),zero_zero(int)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) )
& ( X6216 != X6217
| hAPP(int,int,number_number_of(int),X6216) != zero_zero(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X6217)),zero_zero(int)))
| hAPP(int,nat,number_number_of(nat),X6216) = hAPP(int,nat,number_number_of(nat),X6217) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1284])])]) ).
fof(i_0_1939,plain,
! [X4639,X4640] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4639),X4640)),hAPP(nat,nat,suc,X4639))),
inference(variable_rename,[status(thm)],[fact_403_diff__less__Suc]) ).
fof(i_0_1940,plain,
! [X4615,X4616] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4615),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4615),X4616)))),
inference(variable_rename,[status(thm)],[fact_393_less__add__Suc1]) ).
fof(i_0_1941,plain,
! [X4617,X4618] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4617),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4618),X4617)))),
inference(variable_rename,[status(thm)],[fact_394_less__add__Suc2]) ).
fof(i_0_1942,plain,
! [X3762,X3763,X3764] : hAPP(fun(X3762,bool),fun(X3762,bool),hAPP(X3762,fun(fun(X3762,bool),fun(X3762,bool)),insert(X3762),X3763),hAPP(fun(X3762,bool),fun(X3762,bool),hAPP(fun(X3762,bool),fun(fun(X3762,bool),fun(X3762,bool)),minus_minus(fun(X3762,bool)),X3764),hAPP(fun(X3762,bool),fun(X3762,bool),hAPP(X3762,fun(fun(X3762,bool),fun(X3762,bool)),insert(X3762),X3763),bot_bot(fun(X3762,bool))))) = hAPP(fun(X3762,bool),fun(X3762,bool),hAPP(X3762,fun(fun(X3762,bool),fun(X3762,bool)),insert(X3762),X3763),X3764),
inference(variable_rename,[status(thm)],[fact_139_insert__Diff__single]) ).
fof(i_0_1943,plain,
! [X3548,X3549,X3550,X3551] :
( ~ hBOOL(hAPP(fun(X3548,bool),bool,hAPP(fun(X3548,bool),fun(fun(X3548,bool),bool),ord_less_eq(fun(X3548,bool)),X3550),X3551))
| ~ hBOOL(hAPP(fun(X3548,bool),bool,hAPP(fun(X3548,bool),fun(fun(X3548,bool),bool),ord_less_eq(fun(X3548,bool)),X3551),X3549))
| hBOOL(hAPP(fun(X3548,bool),bool,hAPP(fun(X3548,bool),fun(fun(X3548,bool),bool),ord_less_eq(fun(X3548,bool)),X3550),X3549)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_subset__trans])]) ).
fof(i_0_1944,plain,
! [X4687,X4688,X4689,X4690] :
( ~ hBOOL(hAPP(fun(X4687,bool),bool,hAPP(fun(X4687,bool),fun(fun(X4687,bool),bool),ord_less(fun(X4687,bool)),X4689),X4690))
| ~ hBOOL(hAPP(fun(X4687,bool),bool,hAPP(fun(X4687,bool),fun(fun(X4687,bool),bool),ord_less_eq(fun(X4687,bool)),X4690),X4688))
| hBOOL(hAPP(fun(X4687,bool),bool,hAPP(fun(X4687,bool),fun(fun(X4687,bool),bool),ord_less(fun(X4687,bool)),X4689),X4688)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_418_psubset__subset__trans])]) ).
fof(i_0_1945,plain,
! [X4683,X4684,X4685,X4686] :
( ~ hBOOL(hAPP(fun(X4683,bool),bool,hAPP(fun(X4683,bool),fun(fun(X4683,bool),bool),ord_less_eq(fun(X4683,bool)),X4685),X4686))
| ~ hBOOL(hAPP(fun(X4683,bool),bool,hAPP(fun(X4683,bool),fun(fun(X4683,bool),bool),ord_less(fun(X4683,bool)),X4686),X4684))
| hBOOL(hAPP(fun(X4683,bool),bool,hAPP(fun(X4683,bool),fun(fun(X4683,bool),bool),ord_less(fun(X4683,bool)),X4685),X4684)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_417_subset__psubset__trans])]) ).
fof(i_0_1946,plain,
! [X4739,X4740,X4741,X4742] :
( ~ hBOOL(hAPP(fun(X4739,bool),bool,hAPP(fun(X4739,bool),fun(fun(X4739,bool),bool),ord_less(fun(X4739,bool)),X4741),X4742))
| ~ hBOOL(hAPP(fun(X4739,bool),bool,hAPP(fun(X4739,bool),fun(fun(X4739,bool),bool),ord_less(fun(X4739,bool)),X4742),X4740))
| hBOOL(hAPP(fun(X4739,bool),bool,hAPP(fun(X4739,bool),fun(fun(X4739,bool),bool),ord_less(fun(X4739,bool)),X4741),X4740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_432_psubset__trans])]) ).
fof(i_0_1947,plain,
! [X4244,X4245,X4246] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4245),X4246))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4244),X4246)),X4245) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4244),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4246),X4245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_269_diff__add__assoc])]) ).
fof(i_0_1948,plain,
! [X4233,X4234,X4235] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4234),X4235))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4233),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4235),X4234)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4233),X4235)),X4234) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_265_add__diff__assoc])]) ).
fof(i_0_1949,plain,
! [X4222,X4223,X4224] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4223),X4224))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4222),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4224),X4223)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4222),X4223)),X4224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_diff__diff__right])]) ).
fof(i_0_1950,plain,
! [X5724,X5725] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X5724)),hAPP(int,int,number_number_of(int),X5725)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5724),X5725)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5724),X5725))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X5724)),hAPP(int,int,number_number_of(int),X5725))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_751_less__eq__number__of__int__code])]) ).
fof(i_0_1951,plain,
! [X5713,X5714] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),X5713)),hAPP(int,int,number_number_of(int),X5714)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5713),X5714)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5713),X5714))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),X5713)),hAPP(int,int,number_number_of(int),X5714))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_745_less__number__of__int__code])]) ).
fof(i_0_1952,plain,
! [X6027,X6028] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X6027)),hAPP(nat,int,semiring_1_of_nat(int),X6028)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6027),X6028)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6027),X6028))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X6027)),hAPP(nat,int,semiring_1_of_nat(int),X6028))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_857_transfer__int__nat__relations_I3_J])]) ).
fof(i_0_1953,plain,
! [X6003,X6004] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X6003)),hAPP(nat,int,semiring_1_of_nat(int),X6004)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6003),X6004)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6003),X6004))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X6003)),hAPP(nat,int,semiring_1_of_nat(int),X6004))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_848_zle__int])]) ).
fof(i_0_1954,plain,
! [X6025,X6026] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X6025)),hAPP(nat,int,semiring_1_of_nat(int),X6026)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6025),X6026)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6025),X6026))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X6025)),hAPP(nat,int,semiring_1_of_nat(int),X6026))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_856_transfer__int__nat__relations_I2_J])]) ).
fof(i_0_1955,plain,
! [X6001,X6002] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X6001)),hAPP(nat,int,semiring_1_of_nat(int),X6002)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6001),X6002)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6001),X6002))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X6001)),hAPP(nat,int,semiring_1_of_nat(int),X6002))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_847_zless__int])]) ).
fof(i_0_1956,plain,
! [X5040,X5041,X5042,X5043,X5044,X5045,X5046] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5041),X5042))
| hBOOL(hAPP(nat,bool,X5040,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X5040,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5041),X5042))) )
& ( X5041 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5042),X5043)
| hBOOL(hAPP(nat,bool,X5040,X5043))
| ~ hBOOL(hAPP(nat,bool,X5040,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5041),X5042))) )
& ( X5045 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5046),esk85_3(X5044,X5045,X5046))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5045),X5046))
| hBOOL(hAPP(nat,bool,X5044,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5045),X5046))) )
& ( ~ hBOOL(hAPP(nat,bool,X5044,esk85_3(X5044,X5045,X5046)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5045),X5046))
| hBOOL(hAPP(nat,bool,X5044,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5045),X5046))) )
& ( X5045 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5046),esk85_3(X5044,X5045,X5046))
| ~ hBOOL(hAPP(nat,bool,X5044,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X5044,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5045),X5046))) )
& ( ~ hBOOL(hAPP(nat,bool,X5044,esk85_3(X5044,X5045,X5046)))
| ~ hBOOL(hAPP(nat,bool,X5044,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X5044,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5045),X5046))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1285])])])])])]) ).
fof(i_0_1957,plain,
! [X5032,X5033,X5034,X5035,X5036,X5037,X5038] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5033),X5034))
| hBOOL(hAPP(nat,bool,X5032,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X5032,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5033),X5034))) )
& ( X5033 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5034),X5035)
| hBOOL(hAPP(nat,bool,X5032,X5035))
| ~ hBOOL(hAPP(nat,bool,X5032,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5033),X5034))) )
& ( X5037 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5038),esk84_3(X5036,X5037,X5038))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5037),X5038))
| hBOOL(hAPP(nat,bool,X5036,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5037),X5038))) )
& ( ~ hBOOL(hAPP(nat,bool,X5036,esk84_3(X5036,X5037,X5038)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5037),X5038))
| hBOOL(hAPP(nat,bool,X5036,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5037),X5038))) )
& ( X5037 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5038),esk84_3(X5036,X5037,X5038))
| ~ hBOOL(hAPP(nat,bool,X5036,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X5036,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5037),X5038))) )
& ( ~ hBOOL(hAPP(nat,bool,X5036,esk84_3(X5036,X5037,X5038)))
| ~ hBOOL(hAPP(nat,bool,X5036,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X5036,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5037),X5038))) ) ),
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_539_nat__diff__split])])])])])]) ).
fof(i_0_1958,plain,
! [X6283,X6284] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X6283)),hAPP(int,int,bit1,X6284)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6283),X6284)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6283),X6284))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X6283)),hAPP(int,int,bit1,X6284))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_988_less__eq__int__code_I16_J])]) ).
fof(i_0_1959,plain,
! [X6281,X6282] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X6281)),hAPP(int,int,bit1,X6282)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6281),X6282)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6281),X6282))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X6281)),hAPP(int,int,bit1,X6282))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_987_rel__simps_I34_J])]) ).
fof(i_0_1960,plain,
! [X6288,X6289] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X6288)),hAPP(int,int,bit1,X6289)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6288),X6289)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6288),X6289))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X6288)),hAPP(int,int,bit1,X6289))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_992_less__int__code_I16_J])]) ).
fof(i_0_1961,plain,
! [X6286,X6287] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X6286)),hAPP(int,int,bit1,X6287)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6286),X6287)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6286),X6287))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X6286)),hAPP(int,int,bit1,X6287))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_991_rel__simps_I17_J])]) ).
fof(i_0_1962,plain,
! [X3353,X3354] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3353)),hAPP(nat,nat,suc,X3354)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3353),X3354)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3353),X3354))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3353)),hAPP(nat,nat,suc,X3354))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_Suc__le__mono])]) ).
fof(i_0_1963,plain,
! [X4539,X4540] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4539)),hAPP(nat,nat,suc,X4540)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4539),X4540)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_367_Suc__less__SucD])]) ).
fof(i_0_1964,plain,
! [X4522,X4523] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4522)),hAPP(nat,nat,suc,X4523)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4522),X4523)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4522),X4523))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4522)),hAPP(nat,nat,suc,X4523))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_359_Suc__less__eq])]) ).
fof(i_0_1965,plain,
! [X4532,X4533,X4534] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4533),X4534))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4534),X4532))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4533)),X4532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_364_less__trans__Suc])]) ).
cnf(i_0_1966,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_1286]) ).
fof(i_0_1967,plain,
! [X3631,X3632,X3633,X3634,X3635] :
( ~ hBOOL(hAPP(fun(X3632,bool),bool,hAPP(X3632,fun(fun(X3632,bool),bool),member(X3632),X3634),X3635))
| hAPP(fun(X3631,bool),fun(X3631,bool),hAPP(X3631,fun(fun(X3631,bool),fun(X3631,bool)),insert(X3631),hAPP(X3632,X3631,X3633,X3634)),hAPP(fun(X3632,bool),fun(X3631,bool),hAPP(fun(X3632,X3631),fun(fun(X3632,bool),fun(X3631,bool)),image(X3632,X3631),X3633),X3635)) = hAPP(fun(X3632,bool),fun(X3631,bool),hAPP(fun(X3632,X3631),fun(fun(X3632,bool),fun(X3631,bool)),image(X3632,X3631),X3633),X3635) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_108_insert__image])]) ).
fof(i_0_1968,plain,
! [X6034] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X6034))
| hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6034))) )
& ( ~ hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6034)))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X6034)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_861_transfer__nat__int__set__relations_I1_J])]) ).
fof(i_0_1969,plain,
! [X5527,X5528,X5529] :
( ~ comm_semiring_1(X5527)
| hAPP(X5527,X5527,hAPP(X5527,fun(X5527,X5527),plus_plus(X5527),hAPP(X5527,X5527,hAPP(X5527,fun(X5527,X5527),times_times(X5527),X5528),X5529)),X5529) = hAPP(X5527,X5527,hAPP(X5527,fun(X5527,X5527),times_times(X5527),hAPP(X5527,X5527,hAPP(X5527,fun(X5527,X5527),plus_plus(X5527),X5528),one_one(X5527))),X5529) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])])]) ).
fof(i_0_1970,plain,
! [X5158] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),X5158)))
| hAPP(int,nat,number_number_of(nat),X5158) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),X5158)),one_one(nat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_576_expand__Suc])]) ).
fof(i_0_1971,plain,
! [X5352,X5353,X5354,X5355] :
( ~ comm_semiring_1(X5352)
| hAPP(X5352,X5352,hAPP(X5352,fun(X5352,X5352),times_times(X5352),X5353),hAPP(X5352,X5352,hAPP(X5352,fun(X5352,X5352),plus_plus(X5352),X5354),X5355)) = hAPP(X5352,X5352,hAPP(X5352,fun(X5352,X5352),plus_plus(X5352),hAPP(X5352,X5352,hAPP(X5352,fun(X5352,X5352),times_times(X5352),X5353),X5354)),hAPP(X5352,X5352,hAPP(X5352,fun(X5352,X5352),times_times(X5352),X5353),X5355)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])])]) ).
fof(i_0_1972,plain,
! [X5333,X5334,X5335,X5336] :
( ~ comm_semiring_1(X5333)
| hAPP(X5333,X5333,hAPP(X5333,fun(X5333,X5333),times_times(X5333),hAPP(X5333,X5333,hAPP(X5333,fun(X5333,X5333),times_times(X5333),X5334),X5335)),X5336) = hAPP(X5333,X5333,hAPP(X5333,fun(X5333,X5333),times_times(X5333),hAPP(X5333,X5333,hAPP(X5333,fun(X5333,X5333),times_times(X5333),X5334),X5336)),X5335) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])])]) ).
fof(i_0_1973,plain,
! [X5112,X5113,X5114,X5115] :
( ~ comm_semiring_1(X5112)
| hAPP(X5112,X5112,hAPP(X5112,fun(X5112,X5112),plus_plus(X5112),hAPP(X5112,X5112,hAPP(X5112,fun(X5112,X5112),plus_plus(X5112),X5113),X5114)),X5115) = hAPP(X5112,X5112,hAPP(X5112,fun(X5112,X5112),plus_plus(X5112),hAPP(X5112,X5112,hAPP(X5112,fun(X5112,X5112),plus_plus(X5112),X5113),X5115)),X5114) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])]) ).
fof(i_0_1974,plain,
! [X4839,X4840,X4841,X4842] :
( ~ hBOOL(hAPP(fun(X4840,bool),bool,finite_finite(X4840),X4842))
| ~ hBOOL(hAPP(fun(X4839,bool),bool,finite_finite(X4839),X4841))
| hBOOL(hAPP(fun(sum_sum(X4840,X4839),bool),bool,finite_finite(sum_sum(X4840,X4839)),hAPP(fun(X4839,bool),fun(sum_sum(X4840,X4839),bool),hAPP(fun(X4840,bool),fun(fun(X4839,bool),fun(sum_sum(X4840,X4839),bool)),sum_Plus(X4840,X4839),X4842),X4841))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_448_finite__Plus])]) ).
cnf(i_0_1975,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),X4),bot_bot(fun(X1,bool)))) = 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),X5),bot_bot(fun(X1,bool))))
| ti(X1,X2) != ti(X1,X3)
| ti(X1,X4) != ti(X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
cnf(i_0_1976,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),X4),bot_bot(fun(X1,bool)))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))
| ti(X1,X2) != ti(X1,X3)
| ti(X1,X4) != ti(X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
fof(i_0_1977,plain,
! [X3540,X3541,X3542,X3543] :
( ~ hBOOL(hAPP(fun(X3540,bool),bool,hAPP(X3540,fun(fun(X3540,bool),bool),member(X3540),X3542),X3543))
| ~ hBOOL(hAPP(fun(X3540,bool),bool,hAPP(fun(X3540,bool),fun(fun(X3540,bool),bool),ord_less_eq(fun(X3540,bool)),X3543),X3541))
| hBOOL(hAPP(fun(X3540,bool),bool,hAPP(X3540,fun(fun(X3540,bool),bool),member(X3540),X3542),X3541)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_89_set__rev__mp])]) ).
fof(i_0_1978,plain,
! [X3544,X3545,X3546,X3547] :
( ~ hBOOL(hAPP(fun(X3544,bool),bool,hAPP(fun(X3544,bool),fun(fun(X3544,bool),bool),ord_less_eq(fun(X3544,bool)),X3546),X3547))
| ~ hBOOL(hAPP(fun(X3544,bool),bool,hAPP(X3544,fun(fun(X3544,bool),bool),member(X3544),X3545),X3546))
| hBOOL(hAPP(fun(X3544,bool),bool,hAPP(X3544,fun(fun(X3544,bool),bool),member(X3544),X3545),X3547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_set__mp])]) ).
fof(i_0_1979,plain,
! [X3536,X3537,X3538,X3539] :
( ~ hBOOL(hAPP(fun(X3536,bool),bool,hAPP(fun(X3536,bool),fun(fun(X3536,bool),bool),ord_less_eq(fun(X3536,bool)),X3538),X3539))
| ~ hBOOL(hAPP(fun(X3536,bool),bool,hAPP(X3536,fun(fun(X3536,bool),bool),member(X3536),X3537),X3538))
| hBOOL(hAPP(fun(X3536,bool),bool,hAPP(X3536,fun(fun(X3536,bool),bool),member(X3536),X3537),X3539)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_88_in__mono])]) ).
fof(i_0_1980,plain,
! [X3414,X3415,X3416,X3417] :
( ~ hBOOL(hAPP(fun(X3414,bool),bool,hAPP(fun(X3414,bool),fun(fun(X3414,bool),bool),ord_less_eq(fun(X3414,bool)),X3416),X3417))
| ~ hBOOL(hAPP(fun(X3414,bool),bool,hAPP(X3414,fun(fun(X3414,bool),bool),member(X3414),X3415),X3416))
| hBOOL(hAPP(fun(X3414,bool),bool,hAPP(X3414,fun(fun(X3414,bool),bool),member(X3414),X3415),X3417)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_subsetD])]) ).
fof(i_0_1981,plain,
! [X4735,X4736,X4737,X4738] :
( ~ hBOOL(hAPP(fun(X4735,bool),bool,hAPP(fun(X4735,bool),fun(fun(X4735,bool),bool),ord_less(fun(X4735,bool)),X4737),X4738))
| ~ hBOOL(hAPP(fun(X4735,bool),bool,hAPP(X4735,fun(fun(X4735,bool),bool),member(X4735),X4736),X4737))
| hBOOL(hAPP(fun(X4735,bool),bool,hAPP(X4735,fun(fun(X4735,bool),bool),member(X4735),X4736),X4738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_431_psubsetD])]) ).
fof(i_0_1982,plain,
! [X3602,X3603,X3604,X3605,X3606] :
( ~ ord(X3603)
| ~ hBOOL(hAPP(fun(X3602,X3603),bool,hAPP(fun(X3602,X3603),fun(fun(X3602,X3603),bool),ord_less_eq(fun(X3602,X3603)),X3605),X3606))
| hBOOL(hAPP(X3603,bool,hAPP(X3603,fun(X3603,bool),ord_less_eq(X3603),hAPP(X3602,X3603,X3605,X3604)),hAPP(X3602,X3603,X3606,X3604))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_101_le__funE])])]) ).
fof(i_0_1983,plain,
! [X3597,X3598,X3599,X3600,X3601] :
( ~ ord(X3598)
| ~ hBOOL(hAPP(fun(X3597,X3598),bool,hAPP(fun(X3597,X3598),fun(fun(X3597,X3598),bool),ord_less_eq(fun(X3597,X3598)),X3600),X3601))
| hBOOL(hAPP(X3598,bool,hAPP(X3598,fun(X3598,bool),ord_less_eq(X3598),hAPP(X3597,X3598,X3600,X3599)),hAPP(X3597,X3598,X3601,X3599))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_100_le__funD])])]) ).
fof(i_0_1984,plain,
! [X3357,X3358] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3357),X3358))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3358)),X3357)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3358)),X3357))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3357),X3358)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1287])]) ).
fof(i_0_1985,plain,
! [X3338,X3339,X3340] :
( ( ~ hBOOL(hAPP(fun(X3338,bool),bool,finite_finite(X3338),hAPP(fun(X3338,bool),fun(X3338,bool),hAPP(X3338,fun(fun(X3338,bool),fun(X3338,bool)),insert(X3338),X3339),X3340)))
| hBOOL(hAPP(fun(X3338,bool),bool,finite_finite(X3338),X3340)) )
& ( ~ hBOOL(hAPP(fun(X3338,bool),bool,finite_finite(X3338),X3340))
| hBOOL(hAPP(fun(X3338,bool),bool,finite_finite(X3338),hAPP(fun(X3338,bool),fun(X3338,bool),hAPP(X3338,fun(fun(X3338,bool),fun(X3338,bool)),insert(X3338),X3339),X3340))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_finite__insert])]) ).
cnf(i_0_1986,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk55_2(X1,X2)),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(nat)),esk54_2(X1,X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1265]) ).
cnf(i_0_1987,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1288]) ).
cnf(i_0_1988,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite1357897459simple(X1,X2)) = finite1357897459simple(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1289]) ).
fof(i_0_1989,plain,
! [X3382,X3383] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3382),X3383)),X3382)),
inference(variable_rename,[status(thm)],[fact_45_diff__le__self]) ).
fof(i_0_1990,plain,
! [X5732,X5733,X5734] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5732),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5733),X5734)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5732),X5733)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5732),X5734)),
inference(variable_rename,[status(thm)],[fact_754_zadd__zmult__distrib2]) ).
fof(i_0_1991,plain,
! [X5729,X5730,X5731] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5729),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5730),X5731)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5729),X5730)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5729),X5731)),
inference(variable_rename,[status(thm)],[fact_753_zdiff__zmult__distrib2]) ).
fof(i_0_1992,plain,
! [X5215,X5216,X5217] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5215),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5216),X5217)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5215),X5216)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5215),X5217)),
inference(variable_rename,[status(thm)],[fact_598_add__mult__distrib2]) ).
fof(i_0_1993,plain,
! [X5233,X5234,X5235] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5233),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5234),X5235)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5233),X5234)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5233),X5235)),
inference(variable_rename,[status(thm)],[fact_605_diff__mult__distrib2]) ).
fof(i_0_1994,plain,
! [X3332,X3333,X3334] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3332),X3333)),X3334) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3332),X3334)),X3333),
inference(variable_rename,[status(thm)],[fact_25_diff__commute]) ).
fof(i_0_1995,plain,
! [X4677,X4678,X4679,X4680] :
( ( hBOOL(hAPP(fun(X4677,X4678),bool,hAPP(fun(X4677,X4678),fun(fun(X4677,X4678),bool),ord_less_eq(fun(X4677,X4678)),X4679),X4680))
| ~ hBOOL(hAPP(fun(X4677,X4678),bool,hAPP(fun(X4677,X4678),fun(fun(X4677,X4678),bool),ord_less(fun(X4677,X4678)),X4679),X4680))
| ~ ord(X4678) )
& ( ~ hBOOL(hAPP(fun(X4677,X4678),bool,hAPP(fun(X4677,X4678),fun(fun(X4677,X4678),bool),ord_less_eq(fun(X4677,X4678)),X4680),X4679))
| ~ hBOOL(hAPP(fun(X4677,X4678),bool,hAPP(fun(X4677,X4678),fun(fun(X4677,X4678),bool),ord_less(fun(X4677,X4678)),X4679),X4680))
| ~ ord(X4678) )
& ( ~ hBOOL(hAPP(fun(X4677,X4678),bool,hAPP(fun(X4677,X4678),fun(fun(X4677,X4678),bool),ord_less_eq(fun(X4677,X4678)),X4679),X4680))
| hBOOL(hAPP(fun(X4677,X4678),bool,hAPP(fun(X4677,X4678),fun(fun(X4677,X4678),bool),ord_less_eq(fun(X4677,X4678)),X4680),X4679))
| hBOOL(hAPP(fun(X4677,X4678),bool,hAPP(fun(X4677,X4678),fun(fun(X4677,X4678),bool),ord_less(fun(X4677,X4678)),X4679),X4680))
| ~ ord(X4678) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1290])])])]) ).
cnf(i_0_1996,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_1291]) ).
fof(i_0_1997,plain,
! [X3626,X3627,X3628,X3629,X3630] : hAPP(fun(X3626,bool),fun(X3627,bool),hAPP(fun(X3626,X3627),fun(fun(X3626,bool),fun(X3627,bool)),image(X3626,X3627),X3628),hAPP(fun(X3626,bool),fun(X3626,bool),hAPP(X3626,fun(fun(X3626,bool),fun(X3626,bool)),insert(X3626),X3629),X3630)) = hAPP(fun(X3627,bool),fun(X3627,bool),hAPP(X3627,fun(fun(X3627,bool),fun(X3627,bool)),insert(X3627),hAPP(X3626,X3627,X3628,X3629)),hAPP(fun(X3626,bool),fun(X3627,bool),hAPP(fun(X3626,X3627),fun(fun(X3626,bool),fun(X3627,bool)),image(X3626,X3627),X3628),X3630)),
inference(variable_rename,[status(thm)],[fact_107_image__insert]) ).
fof(i_0_1998,plain,
! [X3371,X3372,X3373] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3373),X3372) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3371),X3372)
| X3373 = X3371
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3372),X3371))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3372),X3373)) )
& ( X3373 != X3371
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3373),X3372) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3371),X3372)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3372),X3371))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3372),X3373)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_eq__diff__iff])])]) ).
fof(i_0_1999,plain,
! [X6250,X6251] :
( ~ number_ring(X6250)
| hAPP(int,X6250,number_number_of(X6250),hAPP(int,int,bit1,X6251)) = hAPP(X6250,X6250,hAPP(X6250,fun(X6250,X6250),plus_plus(X6250),hAPP(X6250,X6250,hAPP(X6250,fun(X6250,X6250),plus_plus(X6250),one_one(X6250)),hAPP(int,X6250,number_number_of(X6250),X6251))),hAPP(int,X6250,number_number_of(X6250),X6251)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_953_number__of__Bit1])])]) ).
fof(i_0_2000,plain,
! [X4851,X4852,X4853,X4854] :
( ( ~ hBOOL(hAPP(fun(X4852,bool),bool,finite_finite(X4852),X4854))
| ~ hBOOL(hAPP(fun(X4851,bool),bool,finite_finite(X4851),X4853))
| hAPP(fun(sum_sum(X4852,X4851),bool),nat,finite_card(sum_sum(X4852,X4851)),hAPP(fun(X4851,bool),fun(sum_sum(X4852,X4851),bool),hAPP(fun(X4852,bool),fun(fun(X4851,bool),fun(sum_sum(X4852,X4851),bool)),sum_Plus(X4852,X4851),X4854),X4853)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X4852,bool),nat,finite_card(X4852),X4854)),hAPP(fun(X4851,bool),nat,finite_card(X4851),X4853)) )
& ( hBOOL(hAPP(fun(X4852,bool),bool,finite_finite(X4852),X4854))
| hAPP(fun(sum_sum(X4852,X4851),bool),nat,finite_card(sum_sum(X4852,X4851)),hAPP(fun(X4851,bool),fun(sum_sum(X4852,X4851),bool),hAPP(fun(X4852,bool),fun(fun(X4851,bool),fun(sum_sum(X4852,X4851),bool)),sum_Plus(X4852,X4851),X4854),X4853)) = zero_zero(nat) )
& ( hBOOL(hAPP(fun(X4851,bool),bool,finite_finite(X4851),X4853))
| hAPP(fun(sum_sum(X4852,X4851),bool),nat,finite_card(sum_sum(X4852,X4851)),hAPP(fun(X4851,bool),fun(sum_sum(X4852,X4851),bool),hAPP(fun(X4852,bool),fun(fun(X4851,bool),fun(sum_sum(X4852,X4851),bool)),sum_Plus(X4852,X4851),X4854),X4853)) = zero_zero(nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_451_card__Plus__conv__if])])]) ).
fof(i_0_2001,plain,
! [X4820,X4821,X4822,X4823] :
( ~ hBOOL(hAPP(fun(X4821,bool),bool,finite_finite(X4821),X4823))
| ~ hBOOL(hAPP(fun(X4820,bool),bool,finite_finite(X4820),X4822))
| hAPP(fun(sum_sum(X4821,X4820),bool),nat,finite_card(sum_sum(X4821,X4820)),hAPP(fun(X4820,bool),fun(sum_sum(X4821,X4820),bool),hAPP(fun(X4821,bool),fun(fun(X4820,bool),fun(sum_sum(X4821,X4820),bool)),sum_Plus(X4821,X4820),X4823),X4822)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X4821,bool),nat,finite_card(X4821),X4823)),hAPP(fun(X4820,bool),nat,finite_card(X4820),X4822)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_444_card__Plus])]) ).
cnf(i_0_2002,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_1292]) ).
cnf(i_0_2003,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_1293]) ).
fof(i_0_2004,plain,
! [X6181,X6182,X6183] :
( ~ ordere142940540dd_abs(X6181)
| ~ hBOOL(hAPP(X6181,bool,hAPP(X6181,fun(X6181,bool),ord_less_eq(X6181),hAPP(X6181,X6181,abs_abs(X6181),X6182)),X6183))
| hBOOL(hAPP(X6181,bool,hAPP(X6181,fun(X6181,bool),ord_less_eq(X6181),X6182),X6183)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_917_abs__le__D1])])]) ).
fof(i_0_2005,plain,
! [X6200,X6201,X6202] :
( ~ ordere142940540dd_abs(X6200)
| hAPP(X6200,X6200,abs_abs(X6200),hAPP(X6200,X6200,hAPP(X6200,fun(X6200,X6200),plus_plus(X6200),hAPP(X6200,X6200,abs_abs(X6200),X6201)),hAPP(X6200,X6200,abs_abs(X6200),X6202))) = hAPP(X6200,X6200,hAPP(X6200,fun(X6200,X6200),plus_plus(X6200),hAPP(X6200,X6200,abs_abs(X6200),X6201)),hAPP(X6200,X6200,abs_abs(X6200),X6202)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_924_abs__add__abs])])]) ).
fof(i_0_2006,plain,
! [X5751] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5751))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X5751))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_765_le__imp__0__less])]) ).
fof(i_0_2007,plain,
! [X4279,X4280,X4281] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4280),X4281))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4280),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4281),X4279))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_280_termination__basic__simps_I3_J])]) ).
fof(i_0_2008,plain,
! [X4187,X4188,X4189] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4188),X4189))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4188),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4189),X4187))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_249_trans__le__add1])]) ).
fof(i_0_2009,plain,
! [X4276,X4277,X4278] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4277),X4278))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4277),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4276),X4278))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_termination__basic__simps_I4_J])]) ).
fof(i_0_2010,plain,
! [X4190,X4191,X4192] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4191),X4192))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4191),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4190),X4192))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_250_trans__le__add2])]) ).
fof(i_0_2011,plain,
! [X4568,X4569,X4570] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4569),X4570))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4569),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4570),X4568))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_377_termination__basic__simps_I1_J])]) ).
fof(i_0_2012,plain,
! [X4548,X4549,X4550] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4549),X4550))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4549),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4550),X4548))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_371_trans__less__add1])]) ).
fof(i_0_2013,plain,
! [X4571,X4572,X4573] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4572),X4573))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4572),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4571),X4573))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_378_termination__basic__simps_I2_J])]) ).
fof(i_0_2014,plain,
! [X4551,X4552,X4553] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4552),X4553))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4552),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4551),X4553))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_372_trans__less__add2])]) ).
fof(i_0_2015,plain,
! [X4732,X4733] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4732),esk60_2(X4732,X4733)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4732)),X4733)) )
& ( X4733 = hAPP(nat,nat,suc,esk60_2(X4732,X4733))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4732)),X4733)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_430_Suc__lessE])])])]) ).
fof(i_0_2016,plain,
! [X5995,X5996,X5997] :
( ~ linordered_semidom(X5995)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5996),X5997))
| hBOOL(hAPP(X5995,bool,hAPP(X5995,fun(X5995,bool),ord_less(X5995),hAPP(nat,X5995,semiring_1_of_nat(X5995),X5996)),hAPP(nat,X5995,semiring_1_of_nat(X5995),X5997))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_845_less__imp__of__nat__less])])]) ).
fof(i_0_2017,plain,
! [X3347,X3348] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3347)),X3348))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3347),X3348)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_Suc__leD])]) ).
fof(i_0_2018,plain,
! [X4637,X4638] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X4637)),X4638))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4637),X4638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_402_Suc__le__lessD])]) ).
fof(i_0_2019,plain,
! [X4629,X4630] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X4629)),X4630))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4629),X4630)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4629),X4630))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X4629)),X4630)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_398_Suc__le__eq])]) ).
fof(i_0_2020,plain,
! [X4625,X4626] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4625),X4626))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X4625)),X4626)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X4625)),X4626))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4625),X4626)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_396_less__eq__Suc__le])]) ).
fof(i_0_2021,plain,
! [X4537,X4538] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4537)),X4538))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4537),X4538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_366_Suc__lessD])]) ).
fof(i_0_2022,plain,
! [X6290] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X6290)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6290),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6290),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X6290)),pls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_993_rel__simps_I29_J])]) ).
fof(i_0_2023,plain,
! [X6285] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X6285)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6285),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6285),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X6285)),pls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_990_rel__simps_I12_J])]) ).
fof(i_0_2024,plain,
! [X3969,X3970,X3971] : hAPP(fun(X3969,bool),fun(X3969,bool),hAPP(fun(X3969,bool),fun(fun(X3969,bool),fun(X3969,bool)),minus_minus(fun(X3969,bool)),hAPP(fun(X3969,bool),fun(X3969,bool),hAPP(fun(X3969,bool),fun(fun(X3969,bool),fun(X3969,bool)),minus_minus(fun(X3969,bool)),X3970),X3971)),X3971) = hAPP(fun(X3969,bool),fun(X3969,bool),hAPP(fun(X3969,bool),fun(fun(X3969,bool),fun(X3969,bool)),minus_minus(fun(X3969,bool)),X3970),X3971),
inference(variable_rename,[status(thm)],[fact_194_Diff__idemp]) ).
fof(i_0_2025,plain,
! [X6247] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6247)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X6247)) = zero_zero(nat) )
& ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6247)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X6247)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X6247)),hAPP(int,nat,number_number_of(nat),X6247))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1294])]) ).
cnf(i_0_2026,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),bot_bot(fun(X1,bool)))))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
fof(i_0_2027,plain,
! [X4325,X4326] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4325),X4326))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4325)),hAPP(nat,nat,suc,X4326))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_295_Suc__mono])]) ).
fof(i_0_2028,plain,
! [X6249] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,X6249))))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6249))) )
& ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6249)))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,X6249)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_950_neg__number__of__Bit1])]) ).
cnf(i_0_2029,plain,
( hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool)))) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1295]) ).
cnf(i_0_2030,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_1291]) ).
fof(i_0_2031,plain,
! [X4858,X4859,X4860] :
( ( hBOOL(hAPP(X4858,bool,X4860,esk81_3(X4858,X4859,X4860)))
| hBOOL(hAPP(fun(X4858,bool),bool,hAPP(fun(X4858,bool),fun(fun(X4858,bool),bool),ord_less_eq(fun(X4858,bool)),hAPP(fun(X4858,bool),fun(X4858,bool),collect(X4858),X4860)),hAPP(fun(X4858,bool),fun(X4858,bool),collect(X4858),X4859))) )
& ( ~ hBOOL(hAPP(X4858,bool,X4859,esk81_3(X4858,X4859,X4860)))
| hBOOL(hAPP(fun(X4858,bool),bool,hAPP(fun(X4858,bool),fun(fun(X4858,bool),bool),ord_less_eq(fun(X4858,bool)),hAPP(fun(X4858,bool),fun(X4858,bool),collect(X4858),X4860)),hAPP(fun(X4858,bool),fun(X4858,bool),collect(X4858),X4859))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_453_Collect__mono])])])]) ).
cnf(i_0_2032,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_1262]) ).
cnf(i_0_2033,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_1296]) ).
cnf(i_0_2034,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1297]) ).
fof(i_0_2035,plain,
! [X3683,X3684,X3685,X3686,X3687] :
( ( ~ hBOOL(hAPP(X3683,bool,hAPP(X3683,fun(X3683,bool),ord_less_eq(X3683),X3684),X3685))
| hBOOL(hAPP(X3683,bool,hAPP(X3683,fun(X3683,bool),ord_less_eq(X3683),X3686),X3687))
| hAPP(X3683,X3683,hAPP(X3683,fun(X3683,X3683),minus_minus(X3683),X3684),X3685) != hAPP(X3683,X3683,hAPP(X3683,fun(X3683,X3683),minus_minus(X3683),X3686),X3687)
| ~ ordered_ab_group_add(X3683) )
& ( ~ hBOOL(hAPP(X3683,bool,hAPP(X3683,fun(X3683,bool),ord_less_eq(X3683),X3686),X3687))
| hBOOL(hAPP(X3683,bool,hAPP(X3683,fun(X3683,bool),ord_less_eq(X3683),X3684),X3685))
| hAPP(X3683,X3683,hAPP(X3683,fun(X3683,X3683),minus_minus(X3683),X3684),X3685) != hAPP(X3683,X3683,hAPP(X3683,fun(X3683,X3683),minus_minus(X3683),X3686),X3687)
| ~ ordered_ab_group_add(X3683) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_117_diff__eq__diff__less__eq])])])]) ).
fof(i_0_2036,plain,
! [X4513,X4514,X4515,X4516,X4517] :
( ( ~ hBOOL(hAPP(X4513,bool,hAPP(X4513,fun(X4513,bool),ord_less(X4513),X4514),X4515))
| hBOOL(hAPP(X4513,bool,hAPP(X4513,fun(X4513,bool),ord_less(X4513),X4516),X4517))
| hAPP(X4513,X4513,hAPP(X4513,fun(X4513,X4513),minus_minus(X4513),X4514),X4515) != hAPP(X4513,X4513,hAPP(X4513,fun(X4513,X4513),minus_minus(X4513),X4516),X4517)
| ~ ordered_ab_group_add(X4513) )
& ( ~ hBOOL(hAPP(X4513,bool,hAPP(X4513,fun(X4513,bool),ord_less(X4513),X4516),X4517))
| hBOOL(hAPP(X4513,bool,hAPP(X4513,fun(X4513,bool),ord_less(X4513),X4514),X4515))
| hAPP(X4513,X4513,hAPP(X4513,fun(X4513,X4513),minus_minus(X4513),X4514),X4515) != hAPP(X4513,X4513,hAPP(X4513,fun(X4513,X4513),minus_minus(X4513),X4516),X4517)
| ~ ordered_ab_group_add(X4513) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_356_diff__eq__diff__less])])])]) ).
cnf(i_0_2037,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1297]) ).
cnf(i_0_2038,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1297]) ).
fof(i_0_2039,plain,
! [X3466,X3467,X3468,X3469] :
( ~ preorder(X3466)
| ~ hBOOL(hAPP(X3466,bool,hAPP(X3466,fun(X3466,bool),ord_less_eq(X3466),X3468),X3469))
| ~ hBOOL(hAPP(X3466,bool,hAPP(X3466,fun(X3466,bool),ord_less_eq(X3466),X3469),X3467))
| hBOOL(hAPP(X3466,bool,hAPP(X3466,fun(X3466,bool),ord_less_eq(X3466),X3468),X3467)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_order__trans])])]) ).
fof(i_0_2040,plain,
! [X3473,X3474,X3475,X3476] :
( ~ order(X3473)
| ~ hBOOL(hAPP(X3473,bool,hAPP(X3473,fun(X3473,bool),ord_less_eq(X3473),X3475),X3476))
| ~ hBOOL(hAPP(X3473,bool,hAPP(X3473,fun(X3473,bool),ord_less_eq(X3473),X3474),X3475))
| hBOOL(hAPP(X3473,bool,hAPP(X3473,fun(X3473,bool),ord_less_eq(X3473),X3474),X3476)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_xt1_I6_J])])]) ).
fof(i_0_2041,plain,
! [X4464,X4465,X4466,X4467] :
( ~ preorder(X4464)
| ~ hBOOL(hAPP(X4464,bool,hAPP(X4464,fun(X4464,bool),ord_less(X4464),X4466),X4467))
| ~ hBOOL(hAPP(X4464,bool,hAPP(X4464,fun(X4464,bool),ord_less_eq(X4464),X4467),X4465))
| hBOOL(hAPP(X4464,bool,hAPP(X4464,fun(X4464,bool),ord_less(X4464),X4466),X4465)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_343_order__less__le__trans])])]) ).
fof(i_0_2042,plain,
! [X4472,X4473,X4474,X4475] :
( ~ preorder(X4472)
| ~ hBOOL(hAPP(X4472,bool,hAPP(X4472,fun(X4472,bool),ord_less_eq(X4472),X4474),X4475))
| ~ hBOOL(hAPP(X4472,bool,hAPP(X4472,fun(X4472,bool),ord_less(X4472),X4475),X4473))
| hBOOL(hAPP(X4472,bool,hAPP(X4472,fun(X4472,bool),ord_less(X4472),X4474),X4473)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_345_order__le__less__trans])])]) ).
fof(i_0_2043,plain,
! [X4399,X4400,X4401,X4402] :
( ~ preorder(X4399)
| ~ hBOOL(hAPP(X4399,bool,hAPP(X4399,fun(X4399,bool),ord_less(X4399),X4401),X4402))
| ~ hBOOL(hAPP(X4399,bool,hAPP(X4399,fun(X4399,bool),ord_less(X4399),X4402),X4400))
| hBOOL(hAPP(X4399,bool,hAPP(X4399,fun(X4399,bool),ord_less(X4399),X4401),X4400)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_322_order__less__trans])])]) ).
fof(i_0_2044,plain,
! [X4468,X4469,X4470,X4471] :
( ~ order(X4468)
| ~ hBOOL(hAPP(X4468,bool,hAPP(X4468,fun(X4468,bool),ord_less(X4468),X4470),X4471))
| ~ hBOOL(hAPP(X4468,bool,hAPP(X4468,fun(X4468,bool),ord_less_eq(X4468),X4469),X4470))
| hBOOL(hAPP(X4468,bool,hAPP(X4468,fun(X4468,bool),ord_less(X4468),X4469),X4471)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_344_xt1_I7_J])])]) ).
fof(i_0_2045,plain,
! [X4476,X4477,X4478,X4479] :
( ~ order(X4476)
| ~ hBOOL(hAPP(X4476,bool,hAPP(X4476,fun(X4476,bool),ord_less_eq(X4476),X4478),X4479))
| ~ hBOOL(hAPP(X4476,bool,hAPP(X4476,fun(X4476,bool),ord_less(X4476),X4477),X4478))
| hBOOL(hAPP(X4476,bool,hAPP(X4476,fun(X4476,bool),ord_less(X4476),X4477),X4479)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_346_xt1_I8_J])])]) ).
fof(i_0_2046,plain,
! [X4403,X4404,X4405,X4406] :
( ~ order(X4403)
| ~ hBOOL(hAPP(X4403,bool,hAPP(X4403,fun(X4403,bool),ord_less(X4403),X4405),X4406))
| ~ hBOOL(hAPP(X4403,bool,hAPP(X4403,fun(X4403,bool),ord_less(X4403),X4404),X4405))
| hBOOL(hAPP(X4403,bool,hAPP(X4403,fun(X4403,bool),ord_less(X4403),X4404),X4406)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_323_xt1_I10_J])])]) ).
fof(i_0_2047,plain,
! [X6061,X6062,X6063] :
( ~ ring_1(X6061)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6062),X6063))
| hAPP(nat,X6061,semiring_1_of_nat(X6061),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6063),X6062)) = hAPP(X6061,X6061,hAPP(X6061,fun(X6061,X6061),minus_minus(X6061),hAPP(nat,X6061,semiring_1_of_nat(X6061),X6063)),hAPP(nat,X6061,semiring_1_of_nat(X6061),X6062)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_874_of__nat__diff])])]) ).
fof(i_0_2048,plain,
! [X6057,X6058] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6057),X6058))
| hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X6058)),hAPP(nat,int,semiring_1_of_nat(int),X6057)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6058),X6057)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_872_zdiff__int])]) ).
fof(i_0_2049,plain,
! [X5767,X5768,X5769] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5768),X5769))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5769),X5767))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5768),X5767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_773_zle__trans])]) ).
fof(i_0_2050,plain,
! [X3324,X3325,X3326] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3325),X3326))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3326),X3324))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3325),X3324)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_le__trans])]) ).
fof(i_0_2051,plain,
! [X4561,X4562,X4563,X4564] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4563),X4564))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4561),X4564) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4563),X4562)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4561),X4562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_375_less__add__eq__less])]) ).
fof(i_0_2052,plain,
! [X5530,X5531,X5532] :
( ~ comm_semiring_1(X5530)
| hAPP(X5530,X5530,hAPP(X5530,fun(X5530,X5530),plus_plus(X5530),X5531),hAPP(X5530,X5530,hAPP(X5530,fun(X5530,X5530),times_times(X5530),X5532),X5531)) = hAPP(X5530,X5530,hAPP(X5530,fun(X5530,X5530),times_times(X5530),hAPP(X5530,X5530,hAPP(X5530,fun(X5530,X5530),plus_plus(X5530),X5532),one_one(X5530))),X5531) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])])]) ).
cnf(i_0_2053,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1281]) ).
fof(i_0_2054,plain,
! [X5329,X5330,X5331,X5332] :
( ~ comm_semiring_1(X5329)
| hAPP(X5329,X5329,hAPP(X5329,fun(X5329,X5329),times_times(X5329),hAPP(X5329,X5329,hAPP(X5329,fun(X5329,X5329),times_times(X5329),X5330),X5331)),X5332) = hAPP(X5329,X5329,hAPP(X5329,fun(X5329,X5329),times_times(X5329),X5330),hAPP(X5329,X5329,hAPP(X5329,fun(X5329,X5329),times_times(X5329),X5331),X5332)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])])]) ).
fof(i_0_2055,plain,
! [X5243,X5244,X5245,X5246] :
( ~ ab_semigroup_mult(X5243)
| hAPP(X5243,X5243,hAPP(X5243,fun(X5243,X5243),times_times(X5243),hAPP(X5243,X5243,hAPP(X5243,fun(X5243,X5243),times_times(X5243),X5244),X5245)),X5246) = hAPP(X5243,X5243,hAPP(X5243,fun(X5243,X5243),times_times(X5243),X5244),hAPP(X5243,X5243,hAPP(X5243,fun(X5243,X5243),times_times(X5243),X5245),X5246)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_609_ab__semigroup__mult__class_Omult__ac_I1_J])])]) ).
fof(i_0_2056,plain,
! [X5116,X5117,X5118,X5119] :
( ~ comm_semiring_1(X5116)
| hAPP(X5116,X5116,hAPP(X5116,fun(X5116,X5116),plus_plus(X5116),hAPP(X5116,X5116,hAPP(X5116,fun(X5116,X5116),plus_plus(X5116),X5117),X5118)),X5119) = hAPP(X5116,X5116,hAPP(X5116,fun(X5116,X5116),plus_plus(X5116),X5117),hAPP(X5116,X5116,hAPP(X5116,fun(X5116,X5116),plus_plus(X5116),X5118),X5119)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])]) ).
fof(i_0_2057,plain,
! [X4091,X4092,X4093,X4094] :
( ~ ab_semigroup_add(X4091)
| hAPP(X4091,X4091,hAPP(X4091,fun(X4091,X4091),plus_plus(X4091),hAPP(X4091,X4091,hAPP(X4091,fun(X4091,X4091),plus_plus(X4091),X4092),X4093)),X4094) = hAPP(X4091,X4091,hAPP(X4091,fun(X4091,X4091),plus_plus(X4091),X4092),hAPP(X4091,X4091,hAPP(X4091,fun(X4091,X4091),plus_plus(X4091),X4093),X4094)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_221_ab__semigroup__add__class_Oadd__ac_I1_J])])]) ).
fof(i_0_2058,plain,
! [X5325,X5326,X5327,X5328] :
( ~ comm_semiring_1(X5325)
| hAPP(X5325,X5325,hAPP(X5325,fun(X5325,X5325),times_times(X5325),X5326),hAPP(X5325,X5325,hAPP(X5325,fun(X5325,X5325),times_times(X5325),X5327),X5328)) = hAPP(X5325,X5325,hAPP(X5325,fun(X5325,X5325),times_times(X5325),hAPP(X5325,X5325,hAPP(X5325,fun(X5325,X5325),times_times(X5325),X5326),X5327)),X5328) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])])]) ).
fof(i_0_2059,plain,
! [X5120,X5121,X5122,X5123] :
( ~ comm_semiring_1(X5120)
| hAPP(X5120,X5120,hAPP(X5120,fun(X5120,X5120),plus_plus(X5120),X5121),hAPP(X5120,X5120,hAPP(X5120,fun(X5120,X5120),plus_plus(X5120),X5122),X5123)) = hAPP(X5120,X5120,hAPP(X5120,fun(X5120,X5120),plus_plus(X5120),hAPP(X5120,X5120,hAPP(X5120,fun(X5120,X5120),plus_plus(X5120),X5121),X5122)),X5123) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])])]) ).
fof(i_0_2060,plain,
! [X4635,X4636] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4636),hAPP(nat,nat,suc,X4635)))
| X4636 = X4635
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4635),X4636)) )
& ( X4636 != X4635
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4636),hAPP(nat,nat,suc,X4635)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4635),X4636)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_401_le__less__Suc__eq])])]) ).
fof(i_0_2061,plain,
! [X4518,X4519] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4518),X4519))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4519),hAPP(nat,nat,suc,X4518))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4519),hAPP(nat,nat,suc,X4518)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4518),X4519)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1298])]) ).
fof(i_0_2062,plain,
! [X4266,X4267,X4268] :
( ~ hBOOL(hAPP(fun(X4266,bool),bool,finite_finite(X4266),X4268))
| hBOOL(hAPP(fun(X4266,bool),bool,hAPP(X4266,fun(fun(X4266,bool),bool),member(X4266),X4267),X4268))
| hAPP(fun(X4266,bool),nat,finite_card(X4266),hAPP(fun(X4266,bool),fun(X4266,bool),hAPP(X4266,fun(fun(X4266,bool),fun(X4266,bool)),insert(X4266),X4267),X4268)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X4266,bool),nat,finite_card(X4266),X4268)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1299])]) ).
fof(i_0_2063,plain,
! [X4239,X4240] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4239),X4240))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4240),X4239)),X4239) = X4240 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_267_le__add__diff__inverse2])]) ).
fof(i_0_2064,plain,
! [X3299,X3300,X3301] :
( ( ~ hBOOL(hAPP(fun(X3299,bool),bool,hAPP(X3299,fun(fun(X3299,bool),bool),member(X3299),X3300),X3301))
| hAPP(fun(X3299,bool),nat,finite_card(X3299),hAPP(fun(X3299,bool),fun(X3299,bool),hAPP(X3299,fun(fun(X3299,bool),fun(X3299,bool)),insert(X3299),X3300),X3301)) = hAPP(fun(X3299,bool),nat,finite_card(X3299),X3301)
| ~ hBOOL(hAPP(fun(X3299,bool),bool,finite_finite(X3299),X3301)) )
& ( hBOOL(hAPP(fun(X3299,bool),bool,hAPP(X3299,fun(fun(X3299,bool),bool),member(X3299),X3300),X3301))
| hAPP(fun(X3299,bool),nat,finite_card(X3299),hAPP(fun(X3299,bool),fun(X3299,bool),hAPP(X3299,fun(fun(X3299,bool),fun(X3299,bool)),insert(X3299),X3300),X3301)) = hAPP(nat,nat,suc,hAPP(fun(X3299,bool),nat,finite_card(X3299),X3301))
| ~ hBOOL(hAPP(fun(X3299,bool),bool,finite_finite(X3299),X3301)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1300])])]) ).
fof(i_0_2065,plain,
! [X3885,X3886,X3887,X3888,X3889] :
( ~ hBOOL(hAPP(fun(X3886,bool),bool,hAPP(X3886,fun(fun(X3886,bool),bool),member(X3886),X3888),X3889))
| hAPP(fun(X3886,bool),fun(X3885,bool),hAPP(fun(X3886,X3885),fun(fun(X3886,bool),fun(X3885,bool)),image(X3886,X3885),hAPP(X3885,fun(X3886,X3885),combk(X3885,X3886),X3887)),X3889) = hAPP(fun(X3885,bool),fun(X3885,bool),hAPP(X3885,fun(fun(X3885,bool),fun(X3885,bool)),insert(X3885),X3887),bot_bot(fun(X3885,bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_175_image__constant])]) ).
fof(i_0_2066,plain,
! [X3426,X3427,X3428] :
( ( hBOOL(hAPP(nat,bool,X3427,hAPP(nat,nat,suc,esk4_3(X3426,X3427,X3428))))
| hBOOL(hAPP(nat,bool,X3427,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3428),X3426)))
| ~ hBOOL(hAPP(nat,bool,X3427,X3428)) )
& ( ~ hBOOL(hAPP(nat,bool,X3427,esk4_3(X3426,X3427,X3428)))
| hBOOL(hAPP(nat,bool,X3427,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3428),X3426)))
| ~ hBOOL(hAPP(nat,bool,X3427,X3428)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_55_zero__induct__lemma])])])]) ).
fof(i_0_2067,plain,
! [X3952] :
( ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X3952),u))
| hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X3952)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_189_assms_I4_J])]) ).
fof(i_0_2068,plain,
! [X4216,X4217,X4218] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4216),X4217)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4216),X4218)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4217),X4218),
inference(variable_rename,[status(thm)],[fact_259_diff__cancel]) ).
fof(i_0_2069,plain,
! [X4219,X4220,X4221] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4219),X4220)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4221),X4220)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4219),X4221),
inference(variable_rename,[status(thm)],[fact_260_diff__cancel2]) ).
fof(i_0_2070,plain,
! [X5721,X5722,X5723] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5721),X5722)),X5723) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5721),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5722),X5723)),
inference(variable_rename,[status(thm)],[fact_750_zmult__assoc]) ).
fof(i_0_2071,plain,
! [X5756,X5757,X5758] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5756),X5757)),X5758) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5756),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5757),X5758)),
inference(variable_rename,[status(thm)],[fact_768_zadd__assoc]) ).
fof(i_0_2072,plain,
! [X5710,X5711,X5712] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5710),X5711)),X5712) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5710),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5711),X5712)),
inference(variable_rename,[status(thm)],[fact_744_nat__mult__assoc]) ).
fof(i_0_2073,plain,
! [X4124,X4125,X4126] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4124),X4125)),X4126) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4124),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4125),X4126)),
inference(variable_rename,[status(thm)],[fact_230_nat__add__assoc]) ).
fof(i_0_2074,plain,
! [X4213,X4214,X4215] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4213),X4214)),X4215) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4213),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4214),X4215)),
inference(variable_rename,[status(thm)],[fact_258_diff__diff__left]) ).
fof(i_0_2075,plain,
! [X6189,X6190,X6191] :
( ~ linordered_idom(X6189)
| ~ hBOOL(hAPP(X6189,bool,hAPP(X6189,fun(X6189,bool),ord_less_eq(X6189),zero_zero(X6189)),X6191))
| hAPP(X6189,X6189,hAPP(X6189,fun(X6189,X6189),times_times(X6189),hAPP(X6189,X6189,abs_abs(X6189),X6190)),X6191) = hAPP(X6189,X6189,abs_abs(X6189),hAPP(X6189,X6189,hAPP(X6189,fun(X6189,X6189),times_times(X6189),X6190),X6191)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_920_abs__mult__pos])])]) ).
fof(i_0_2076,plain,
! [X3607,X3608,X3609] : hBOOL(hAPP(fun(X3607,bool),bool,hAPP(fun(X3607,bool),fun(fun(X3607,bool),bool),ord_less_eq(fun(X3607,bool)),X3608),hAPP(fun(X3607,bool),fun(X3607,bool),hAPP(X3607,fun(fun(X3607,bool),fun(X3607,bool)),insert(X3607),X3609),X3608))),
inference(variable_rename,[status(thm)],[fact_102_subset__insertI]) ).
fof(i_0_2077,plain,
! [X4530,X4531] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4530),X4531))
| hAPP(nat,nat,suc,X4530) = X4531
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4530)),X4531)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_363_Suc__lessI])]) ).
fof(i_0_2078,plain,
! [X3502,X3503,X3504,X3505] : hAPP(fun(X3502,bool),fun(X3502,bool),hAPP(X3502,fun(fun(X3502,bool),fun(X3502,bool)),insert(X3502),X3503),hAPP(fun(X3502,bool),fun(X3502,bool),hAPP(X3502,fun(fun(X3502,bool),fun(X3502,bool)),insert(X3502),X3504),X3505)) = hAPP(fun(X3502,bool),fun(X3502,bool),hAPP(X3502,fun(fun(X3502,bool),fun(X3502,bool)),insert(X3502),X3504),hAPP(fun(X3502,bool),fun(X3502,bool),hAPP(X3502,fun(fun(X3502,bool),fun(X3502,bool)),insert(X3502),X3503),X3505)),
inference(variable_rename,[status(thm)],[fact_78_insert__commute]) ).
fof(i_0_2079,plain,
! [X5745] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X5745)),X5745) != zero_zero(int),
inference(variable_rename,[status(thm)],[fact_759_odd__nonzero]) ).
fof(i_0_2080,plain,
! [X3708,X3709,X3710] :
( ~ hBOOL(hAPP(fun(X3708,bool),bool,finite_finite(X3708),X3710))
| hBOOL(hAPP(fun(X3708,bool),bool,finite_finite(X3708),hAPP(fun(X3708,bool),fun(X3708,bool),hAPP(fun(X3708,bool),fun(fun(X3708,bool),fun(X3708,bool)),minus_minus(fun(X3708,bool)),X3710),X3709))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_122_finite__Diff])]) ).
cnf(i_0_2081,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(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1301]) ).
cnf(i_0_2082,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
| ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1302]) ).
fof(i_0_2083,plain,
! [X3308,X3309] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3308),X3309))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X3309)),X3308) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3309),X3308)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_Suc__diff__le])]) ).
cnf(i_0_2084,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),X2)),zero_zero(X1)))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1303]) ).
fof(i_0_2085,plain,
! [X3480,X3481,X3482] : hBOOL(hAPP(fun(X3480,bool),bool,hAPP(X3480,fun(fun(X3480,bool),bool),member(X3480),X3481),hAPP(fun(X3480,bool),fun(X3480,bool),hAPP(X3480,fun(fun(X3480,bool),fun(X3480,bool)),insert(X3480),X3481),X3482))),
inference(variable_rename,[status(thm)],[fact_71_insertI1]) ).
fof(i_0_2086,plain,
! [X4633,X4634] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4633),X4634))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X4633)),X4634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_400_Suc__leI])]) ).
fof(i_0_2087,plain,
! [X3311] : 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)),X3311))) = hAPP(nat,nat,suc,X3311),
inference(variable_rename,[status(thm)],[fact_13_card__Collect__le__nat]) ).
fof(i_0_2088,plain,
! [X3279,X3280,X3281,X3282] :
( ~ hBOOL(hAPP(fun(X3280,bool),bool,finite_finite(X3280),X3282))
| hBOOL(hAPP(fun(X3279,bool),bool,finite_finite(X3279),hAPP(fun(X3280,bool),fun(X3279,bool),hAPP(fun(X3280,X3279),fun(fun(X3280,bool),fun(X3279,bool)),image(X3280,X3279),X3281),X3282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_finite__imageI])]) ).
fof(i_0_2089,plain,
! [X6099,X6100,X6101,X6102] :
( ~ semiring_1(X6099)
| hAPP(X6099,X6099,hAPP(nat,fun(X6099,X6099),hAPP(fun(X6099,X6099),fun(nat,fun(X6099,X6099)),semiri532925092at_aux(X6099),X6100),hAPP(nat,nat,suc,X6101)),X6102) = hAPP(X6099,X6099,hAPP(nat,fun(X6099,X6099),hAPP(fun(X6099,X6099),fun(nat,fun(X6099,X6099)),semiri532925092at_aux(X6099),X6100),X6101),hAPP(X6099,X6099,X6100,X6102)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_892_of__nat__aux_Osimps_I2_J])])]) ).
fof(i_0_2090,plain,
! [X3302,X3303,X3304] :
( ~ hBOOL(hAPP(fun(X3302,bool),bool,finite_finite(X3302),X3304))
| hBOOL(hAPP(fun(X3302,bool),bool,hAPP(X3302,fun(fun(X3302,bool),bool),member(X3302),X3303),X3304))
| hAPP(fun(X3302,bool),nat,finite_card(X3302),hAPP(fun(X3302,bool),fun(X3302,bool),hAPP(X3302,fun(fun(X3302,bool),fun(X3302,bool)),insert(X3302),X3303),X3304)) = hAPP(nat,nat,suc,hAPP(fun(X3302,bool),nat,finite_card(X3302),X3304)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1304])]) ).
cnf(i_0_2091,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1305]) ).
fof(i_0_2092,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_2093,plain,
! [X3355,X3356] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3355),hAPP(nat,nat,suc,X3356)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3355),X3356))
| X3355 = hAPP(nat,nat,suc,X3356) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3355),X3356))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3355),hAPP(nat,nat,suc,X3356))) )
& ( X3355 != hAPP(nat,nat,suc,X3356)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3355),hAPP(nat,nat,suc,X3356))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_34_le__Suc__eq])])]) ).
fof(i_0_2094,plain,
! [X3349,X3350] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3349),hAPP(nat,nat,suc,X3350)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3349),X3350))
| X3349 = hAPP(nat,nat,suc,X3350) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1306])]) ).
fof(i_0_2095,plain,
! [X3430,X3431] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3430)),X3431))
| X3431 = hAPP(nat,nat,suc,esk5_2(X3430,X3431)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_Suc__le__D])])]) ).
fof(i_0_2096,plain,
! [X6158,X6159] :
( ~ ordere142940540dd_abs(X6158)
| ~ hBOOL(hAPP(X6158,bool,hAPP(X6158,fun(X6158,bool),ord_less(X6158),hAPP(X6158,X6158,abs_abs(X6158),X6159)),zero_zero(X6158))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1307])])]) ).
fof(i_0_2097,plain,
! [X4658,X4659,X4660] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk50_3(X4658,X4659,X4660)),X4660))
| hBOOL(hAPP(nat,bool,X4658,X4659))
| ~ hBOOL(hAPP(nat,bool,X4658,X4660))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4659),X4660)) )
& ( hBOOL(hAPP(nat,bool,X4658,hAPP(nat,nat,suc,esk50_3(X4658,X4659,X4660))))
| hBOOL(hAPP(nat,bool,X4658,X4659))
| ~ hBOOL(hAPP(nat,bool,X4658,X4660))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4659),X4660)) )
& ( ~ hBOOL(hAPP(nat,bool,X4658,esk50_3(X4658,X4659,X4660)))
| hBOOL(hAPP(nat,bool,X4658,X4659))
| ~ hBOOL(hAPP(nat,bool,X4658,X4660))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4659),X4660)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_410_inc__induct])])])]) ).
fof(i_0_2098,plain,
! [X4425,X4426,X4427] :
( ( hBOOL(hAPP(X4425,bool,hAPP(X4425,fun(X4425,bool),ord_less_eq(X4425),X4426),X4427))
| ~ hBOOL(hAPP(X4425,bool,hAPP(X4425,fun(X4425,bool),ord_less(X4425),X4426),X4427))
| ~ preorder(X4425) )
& ( ~ hBOOL(hAPP(X4425,bool,hAPP(X4425,fun(X4425,bool),ord_less_eq(X4425),X4427),X4426))
| ~ hBOOL(hAPP(X4425,bool,hAPP(X4425,fun(X4425,bool),ord_less(X4425),X4426),X4427))
| ~ preorder(X4425) )
& ( ~ hBOOL(hAPP(X4425,bool,hAPP(X4425,fun(X4425,bool),ord_less_eq(X4425),X4426),X4427))
| hBOOL(hAPP(X4425,bool,hAPP(X4425,fun(X4425,bool),ord_less_eq(X4425),X4427),X4426))
| hBOOL(hAPP(X4425,bool,hAPP(X4425,fun(X4425,bool),ord_less(X4425),X4426),X4427))
| ~ preorder(X4425) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1308])])])]) ).
fof(i_0_2099,plain,
! [X6068,X6069] :
( ( ~ hBOOL(hAPP(X6068,bool,hAPP(X6068,fun(X6068,bool),ord_less(X6068),zero_zero(X6068)),hAPP(nat,X6068,semiring_1_of_nat(X6068),X6069)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6069))
| ~ linordered_semidom(X6068) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6069))
| hBOOL(hAPP(X6068,bool,hAPP(X6068,fun(X6068,bool),ord_less(X6068),zero_zero(X6068)),hAPP(nat,X6068,semiring_1_of_nat(X6068),X6069)))
| ~ linordered_semidom(X6068) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_877_of__nat__0__less__iff])])])]) ).
fof(i_0_2100,plain,
! [X5976,X5977] :
( ~ linordered_semidom(X5976)
| ~ hBOOL(hAPP(X5976,bool,hAPP(X5976,fun(X5976,bool),ord_less(X5976),hAPP(nat,X5976,semiring_1_of_nat(X5976),X5977)),zero_zero(X5976))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1309])])]) ).
fof(i_0_2101,plain,
! [X4602] : 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(nat)),X4602))) = X4602,
inference(variable_rename,[status(thm)],[fact_389_card__Collect__less__nat]) ).
fof(i_0_2102,plain,
! [X4967,X4968,X4970,X4971,X4972] :
( ( X4967 = hAPP(nat,nat,suc,esk83_2(X4967,X4968))
| X4967 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4967),hAPP(nat,nat,suc,X4968))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk83_2(X4967,X4968)),X4968))
| X4967 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4967),hAPP(nat,nat,suc,X4968))) )
& ( X4970 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4970),hAPP(nat,nat,suc,X4971))) )
& ( X4970 != hAPP(nat,nat,suc,X4972)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4972),X4971))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4970),hAPP(nat,nat,suc,X4971))) ) ),
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_512_less__Suc__eq__0__disj])])])])])]) ).
fof(i_0_2103,plain,
! [X3659,X3660,X3661] :
( ( hBOOL(hAPP(fun(X3659,bool),bool,hAPP(X3659,fun(fun(X3659,bool),bool),member(X3659),esk11_3(X3659,X3660,X3661)),X3661))
| hBOOL(hAPP(fun(X3659,bool),bool,hAPP(fun(X3659,bool),fun(fun(X3659,bool),bool),ord_less_eq(fun(X3659,bool)),X3661),X3660)) )
& ( ~ hBOOL(hAPP(fun(X3659,bool),bool,hAPP(X3659,fun(fun(X3659,bool),bool),member(X3659),esk11_3(X3659,X3660,X3661)),X3660))
| hBOOL(hAPP(fun(X3659,bool),bool,hAPP(fun(X3659,bool),fun(fun(X3659,bool),bool),ord_less_eq(fun(X3659,bool)),X3661),X3660)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_112_subsetI])])])]) ).
fof(i_0_2104,plain,
! [X6064] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X6064)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6064)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6064))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X6064))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_875_zero__less__int__conv])]) ).
fof(i_0_2105,plain,
! [X6149] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),X6149)),one_one(int)))
| X6149 = zero_zero(int) )
& ( X6149 != zero_zero(int)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),X6149)),one_one(int))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_903_zabs__less__one__iff])]) ).
fof(i_0_2106,plain,
! [X6049] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X6049)),zero_zero(int)))
| X6049 = zero_zero(nat) )
& ( X6049 != zero_zero(nat)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X6049)),zero_zero(int))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_868_int__le__0__conv])]) ).
fof(i_0_2107,plain,
! [X5971] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X5971)),zero_zero(int))),
inference(variable_rename,[status(thm)],[i_0_1310]) ).
fof(i_0_2108,plain,
! [X3283,X3284,X3285] :
( ~ hBOOL(hAPP(fun(X3283,bool),bool,finite_finite(X3283),X3285))
| hBOOL(hAPP(fun(X3283,bool),bool,finite_finite(X3283),hAPP(fun(X3283,bool),fun(X3283,bool),hAPP(X3283,fun(fun(X3283,bool),fun(X3283,bool)),insert(X3283),X3284),X3285))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_finite_OinsertI])]) ).
fof(i_0_2109,plain,
! [X4535,X4536] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4535),hAPP(nat,nat,suc,X4536)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4535),X4536))
| X4535 = X4536 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1311])]) ).
fof(i_0_2110,plain,
! [X4526,X4527] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4526),X4527))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4526),hAPP(nat,nat,suc,X4527)))
| X4527 = X4526 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1312])]) ).
fof(i_0_2111,plain,
! [X4524,X4525] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4524),hAPP(nat,nat,suc,X4525)))
| X4524 = X4525
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4524),X4525)) )
& ( X4524 != X4525
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4524),hAPP(nat,nat,suc,X4525)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4524),X4525)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1313])])]) ).
fof(i_0_2112,plain,
! [X4520,X4521] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4520),hAPP(nat,nat,suc,X4521)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4520),X4521))
| X4520 = X4521 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4520),X4521))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4520),hAPP(nat,nat,suc,X4521))) )
& ( X4520 != X4521
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4520),hAPP(nat,nat,suc,X4521))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_358_less__Suc__eq])])]) ).
fof(i_0_2113,plain,
! [X4627,X4628] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4627),hAPP(nat,nat,suc,X4628)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4627),X4628)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4627),X4628))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4627),hAPP(nat,nat,suc,X4628))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_397_less__Suc__eq__le])]) ).
cnf(i_0_2114,plain,
( ti(X1,X3) = ti(X1,X2)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1314]) ).
cnf(i_0_2115,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1315]) ).
cnf(i_0_2116,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1316]) ).
cnf(i_0_2117,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1317]) ).
cnf(i_0_2118,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),X3) = hAPP(nat,nat,suc,X5)
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool))
| ti(fun(X1,bool),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2)
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_1318]) ).
fof(i_0_2119,plain,
! [X6280] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X6280)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X6280)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X6280))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X6280))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_986_rel__simps_I22_J])]) ).
fof(i_0_2120,plain,
! [X6291] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X6291)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X6291)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X6291))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X6291))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_994_rel__simps_I5_J])]) ).
fof(i_0_2121,plain,
! [X3359] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3359)),X3359)),
inference(variable_rename,[status(thm)],[i_0_1319]) ).
fof(i_0_2122,plain,
! [X5209,X5210,X5211] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5209)),X5210) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5209)),X5211)
| X5210 = X5211 )
& ( X5210 != X5211
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5209)),X5210) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5209)),X5211) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_596_Suc__mult__cancel1])]) ).
cnf(i_0_2123,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_1286]) ).
fof(i_0_2124,plain,
! [X4691,X4692,X4693] :
( ~ hBOOL(hAPP(fun(X4691,bool),bool,hAPP(fun(X4691,bool),fun(fun(X4691,bool),bool),ord_less(fun(X4691,bool)),X4692),X4693))
| hBOOL(hAPP(fun(X4691,bool),bool,hAPP(fun(X4691,bool),fun(fun(X4691,bool),bool),ord_less_eq(fun(X4691,bool)),X4692),X4693)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_419_psubset__imp__subset])]) ).
fof(i_0_2125,plain,
! [X6043,X6045,X6046,X6048] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk127_1(X6043)))
| hBOOL(hAPP(int,bool,X6043,hAPP(nat,int,semiring_1_of_nat(int),X6045))) )
& ( ~ hBOOL(hAPP(int,bool,X6043,esk127_1(X6043)))
| hBOOL(hAPP(int,bool,X6043,hAPP(nat,int,semiring_1_of_nat(int),X6045))) )
& ( ~ hBOOL(hAPP(int,bool,X6046,hAPP(nat,int,semiring_1_of_nat(int),esk128_1(X6046))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6048))
| hBOOL(hAPP(int,bool,X6046,X6048)) ) ),
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_867_transfer__int__nat__quantifiers_I1_J])])])])])]) ).
fof(i_0_2126,plain,
! [X5021] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5021))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5021),hAPP(nat,nat,suc,zero_zero(nat)))) = X5021 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_535_Suc__pred])]) ).
fof(i_0_2127,plain,
! [X3674,X3676,X3677,X3678] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3674))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3676),X3674))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3676),esk14_1(X3674))) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk15_2(X3677,X3678)),X3677))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3677)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk15_2(X3677,X3678)),X3678))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3677)) ) ),
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_115_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_2128,plain,
! [X4592,X4594,X4595,X4596] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X4592))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4594),X4592))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4594),esk45_1(X4592))) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk46_2(X4595,X4596)),X4595))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X4595)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk46_2(X4595,X4596)),X4596))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X4595)) ) ),
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_387_finite__nat__set__iff__bounded])])])])])]) ).
fof(i_0_2129,plain,
! [X5929,X5930,X5932] :
( ~ linorder(X5929)
| ~ hBOOL(hAPP(X5929,bool,hAPP(X5929,fun(X5929,bool),ord_less(X5929),esk111_2(X5929,X5930)),X5932))
| ~ hBOOL(hAPP(X5929,bool,hAPP(X5929,fun(X5929,bool),ord_less_eq(X5929),X5932),X5930)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1320])])])]) ).
fof(i_0_2130,plain,
! [X4030,X4031] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4030),hAPP(nat,nat,suc,X4031)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4030),one_one(nat))),X4031),
inference(variable_rename,[status(thm)],[fact_208_diff__Suc__eq__diff__pred]) ).
cnf(i_0_2131,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X4),X4) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1321]) ).
fof(i_0_2132,plain,
! [X5925,X5926,X5928] :
( ~ linorder(X5925)
| ~ hBOOL(hAPP(X5925,bool,hAPP(X5925,fun(X5925,bool),ord_less(X5925),X5928),esk110_2(X5925,X5926)))
| ~ hBOOL(hAPP(X5925,bool,hAPP(X5925,fun(X5925,bool),ord_less_eq(X5925),X5926),X5928)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1322])])])]) ).
fof(i_0_2133,plain,
! [X5060,X5061,X5063] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk86_2(X5060,X5061)),X5060))
| ~ hBOOL(hAPP(nat,bool,X5061,X5060))
| hBOOL(hAPP(nat,bool,X5061,zero_zero(nat))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5063),esk86_2(X5060,X5061)))
| ~ hBOOL(hAPP(nat,bool,X5061,X5063))
| ~ hBOOL(hAPP(nat,bool,X5061,X5060))
| hBOOL(hAPP(nat,bool,X5061,zero_zero(nat))) )
& ( hBOOL(hAPP(nat,bool,X5061,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk86_2(X5060,X5061)),one_one(nat))))
| ~ hBOOL(hAPP(nat,bool,X5061,X5060))
| hBOOL(hAPP(nat,bool,X5061,zero_zero(nat))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1323])])])])]) ).
fof(i_0_2134,plain,
! [X6050,X6051,X6053,X6054,X6055] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6050),X6051))
| X6051 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6050),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,esk129_2(X6050,X6051)))) )
& ( X6054 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6053),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X6055)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6053),X6054)) ) ),
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_870_zless__iff__Suc__zadd])])])])]) ).
fof(i_0_2135,plain,
! [X4992,X4993] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4992),hAPP(nat,nat,suc,X4993)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4992),X4993)),
inference(variable_rename,[status(thm)],[fact_524_diff__Suc]) ).
fof(i_0_2136,plain,
! [X6262,X6263] :
( ~ number_ring(X6262)
| hAPP(X6262,X6262,hAPP(X6262,fun(X6262,X6262),plus_plus(X6262),one_one(X6262)),hAPP(int,X6262,number_number_of(X6262),X6263)) = hAPP(int,X6262,number_number_of(X6262),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),X6263)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_966_add__special_I2_J])])]) ).
fof(i_0_2137,plain,
! [X3275,X3276] :
( ~ 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)),X3275),X3276))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X3276),X3275)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J])]) ).
fof(i_0_2138,plain,
! [X4373,X4374,X4375,X4376] :
( ~ preorder(X4373)
| ~ hBOOL(hAPP(X4373,bool,hAPP(X4373,fun(X4373,bool),ord_less(X4373),X4375),X4376))
| ~ hBOOL(hAPP(X4373,bool,hAPP(X4373,fun(X4373,bool),ord_less(X4373),X4376),X4375))
| hBOOL(X4374) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_315_order__less__imp__triv])])]) ).
fof(i_0_2139,plain,
! [X5966,X5967] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X5967)))
| hAPP(nat,X5966,semiring_1_of_nat(X5966),hAPP(int,nat,number_number_of(nat),X5967)) = hAPP(int,X5966,number_number_of(X5966),X5967)
| ~ number_ring(X5966) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X5967)))
| hAPP(nat,X5966,semiring_1_of_nat(X5966),hAPP(int,nat,number_number_of(nat),X5967)) = zero_zero(X5966)
| ~ number_ring(X5966) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1324])])])]) ).
fof(i_0_2140,plain,
! [X4416,X4417,X4418] :
( ( hBOOL(hAPP(X4416,bool,hAPP(X4416,fun(X4416,bool),ord_less_eq(X4416),X4417),X4418))
| hBOOL(hAPP(X4416,bool,hAPP(X4416,fun(X4416,bool),ord_less(X4416),X4418),X4417))
| ~ linorder(X4416) )
& ( ~ hBOOL(hAPP(X4416,bool,hAPP(X4416,fun(X4416,bool),ord_less(X4416),X4418),X4417))
| ~ hBOOL(hAPP(X4416,bool,hAPP(X4416,fun(X4416,bool),ord_less_eq(X4416),X4417),X4418))
| ~ linorder(X4416) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1325])])])]) ).
fof(i_0_2141,plain,
! [X4446,X4447,X4448] :
( ~ linorder(X4446)
| ~ hBOOL(hAPP(X4446,bool,hAPP(X4446,fun(X4446,bool),ord_less_eq(X4446),X4447),X4448))
| ~ hBOOL(hAPP(X4446,bool,hAPP(X4446,fun(X4446,bool),ord_less(X4446),X4448),X4447)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1326])])]) ).
fof(i_0_2142,plain,
! [X4413,X4414,X4415] :
( ( hBOOL(hAPP(X4413,bool,hAPP(X4413,fun(X4413,bool),ord_less(X4413),X4414),X4415))
| hBOOL(hAPP(X4413,bool,hAPP(X4413,fun(X4413,bool),ord_less_eq(X4413),X4415),X4414))
| ~ linorder(X4413) )
& ( ~ hBOOL(hAPP(X4413,bool,hAPP(X4413,fun(X4413,bool),ord_less_eq(X4413),X4415),X4414))
| ~ hBOOL(hAPP(X4413,bool,hAPP(X4413,fun(X4413,bool),ord_less(X4413),X4414),X4415))
| ~ linorder(X4413) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1327])])])]) ).
fof(i_0_2143,plain,
! [X4407,X4408,X4409] :
( ~ preorder(X4407)
| ~ hBOOL(hAPP(X4407,bool,hAPP(X4407,fun(X4407,bool),ord_less(X4407),X4408),X4409))
| ~ hBOOL(hAPP(X4407,bool,hAPP(X4407,fun(X4407,bool),ord_less(X4407),X4409),X4408)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1328])])]) ).
fof(i_0_2144,plain,
! [X4377,X4378,X4379] :
( ~ preorder(X4377)
| ~ hBOOL(hAPP(X4377,bool,hAPP(X4377,fun(X4377,bool),ord_less(X4377),X4378),X4379))
| ~ hBOOL(hAPP(X4377,bool,hAPP(X4377,fun(X4377,bool),ord_less(X4377),X4379),X4378)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1329])])]) ).
fof(i_0_2145,plain,
! [X4364,X4365,X4366] :
( ~ preorder(X4364)
| ~ hBOOL(hAPP(X4364,bool,hAPP(X4364,fun(X4364,bool),ord_less(X4364),X4365),X4366))
| ~ hBOOL(hAPP(X4364,bool,hAPP(X4364,fun(X4364,bool),ord_less(X4364),X4366),X4365)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1330])])]) ).
fof(i_0_2146,plain,
! [X4361,X4362,X4363] :
( ~ preorder(X4361)
| ~ hBOOL(hAPP(X4361,bool,hAPP(X4361,fun(X4361,bool),ord_less(X4361),X4362),X4363))
| ~ hBOOL(hAPP(X4361,bool,hAPP(X4361,fun(X4361,bool),ord_less(X4361),X4363),X4362)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1331])])]) ).
fof(i_0_2147,plain,
! [X4380,X4381,X4382] :
( ~ order(X4380)
| ~ hBOOL(hAPP(X4380,bool,hAPP(X4380,fun(X4380,bool),ord_less(X4380),X4381),X4382))
| ~ hBOOL(hAPP(X4380,bool,hAPP(X4380,fun(X4380,bool),ord_less(X4380),X4382),X4381)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1332])])]) ).
fof(i_0_2148,plain,
! [X3351,X3352] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3351),X3352))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3351),hAPP(nat,nat,suc,X3352))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_32_le__SucI])]) ).
fof(i_0_2149,plain,
! [X4631,X4632] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4631),X4632))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4631),hAPP(nat,nat,suc,X4632))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_399_le__imp__less__Suc])]) ).
fof(i_0_2150,plain,
! [X4528,X4529] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4528),X4529))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4528),hAPP(nat,nat,suc,X4529))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_362_less__SucI])]) ).
fof(i_0_2151,plain,
! [X4010,X4011,X4012,X4013,X4014] :
( ~ minus(X4011)
| hAPP(X4010,X4011,hAPP(fun(X4010,X4011),fun(X4010,X4011),hAPP(fun(X4010,X4011),fun(fun(X4010,X4011),fun(X4010,X4011)),minus_minus(fun(X4010,X4011)),X4012),X4013),X4014) = hAPP(X4011,X4011,hAPP(X4011,fun(X4011,X4011),minus_minus(X4011),hAPP(X4010,X4011,X4012,X4014)),hAPP(X4010,X4011,X4013,X4014)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_202_minus__apply])])]) ).
fof(i_0_2152,plain,
! [X4005,X4006,X4007,X4008,X4009] :
( ~ minus(X4006)
| hAPP(X4005,X4006,hAPP(fun(X4005,X4006),fun(X4005,X4006),hAPP(fun(X4005,X4006),fun(fun(X4005,X4006),fun(X4005,X4006)),minus_minus(fun(X4005,X4006)),X4007),X4008),X4009) = hAPP(X4006,X4006,hAPP(X4006,fun(X4006,X4006),minus_minus(X4006),hAPP(X4005,X4006,X4007,X4009)),hAPP(X4005,X4006,X4008,X4009)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_201_fun__diff__def])])]) ).
cnf(i_0_2153,plain,
( X1 = zero_zero(nat)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5))
| hAPP(fun(X2,bool),nat,finite_card(X2),X3) = hAPP(nat,nat,suc,X1)
| ti(fun(X2,bool),X3) != hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X4),X5)
| hAPP(fun(X2,bool),nat,finite_card(X2),X5) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1318]) ).
fof(i_0_2154,plain,
! [X5800,X5801,X5802] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5802),X5800) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5802),X5801)
| X5800 = X5801
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5802)) )
& ( X5800 != X5801
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5802),X5800) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5802),X5801)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5802)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_786_nat__mult__eq__cancel1])])]) ).
fof(i_0_2155,plain,
! [X5014] :
( ~ linordered_semidom(X5014)
| hBOOL(hAPP(X5014,bool,hAPP(X5014,fun(X5014,bool),ord_less(X5014),zero_zero(X5014)),hAPP(X5014,X5014,hAPP(X5014,fun(X5014,X5014),plus_plus(X5014),one_one(X5014)),one_one(X5014)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_531_zero__less__two])]) ).
fof(i_0_2156,plain,
! [X5770,X5771] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5770),X5771))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5771),X5770))
| X5770 = X5771 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_774_zle__antisym])]) ).
fof(i_0_2157,plain,
! [X3322,X3323] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3322),X3323))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3323),X3322))
| X3322 = X3323 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_20_le__antisym])]) ).
cnf(i_0_2158,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1316]) ).
cnf(i_0_2159,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1333]) ).
cnf(i_0_2160,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) != ti(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1334]) ).
cnf(i_0_2161,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1335]) ).
cnf(i_0_2162,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1336]) ).
cnf(i_0_2163,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1337]) ).
fof(i_0_2164,plain,
! [X5533,X5534] :
( ~ comm_semiring_1(X5533)
| hAPP(X5533,X5533,hAPP(X5533,fun(X5533,X5533),plus_plus(X5533),X5534),X5534) = hAPP(X5533,X5533,hAPP(X5533,fun(X5533,X5533),times_times(X5533),hAPP(X5533,X5533,hAPP(X5533,fun(X5533,X5533),plus_plus(X5533),one_one(X5533)),one_one(X5533))),X5534) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])])]) ).
fof(i_0_2165,plain,
! [X5442,X5443] :
( ~ linordered_ring(X5442)
| hBOOL(hAPP(X5442,bool,hAPP(X5442,fun(X5442,bool),ord_less_eq(X5442),zero_zero(X5442)),hAPP(X5442,X5442,hAPP(X5442,fun(X5442,X5442),times_times(X5442),X5443),X5443))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_669_zero__le__square])])]) ).
fof(i_0_2166,plain,
! [X4675,X4676] :
( ~ linordered_semidom(X4675)
| hBOOL(hAPP(X4675,bool,hAPP(X4675,fun(X4675,bool),ord_less(X4675),X4676),hAPP(X4675,X4675,hAPP(X4675,fun(X4675,X4675),plus_plus(X4675),X4676),one_one(X4675)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_414_less__add__one])])]) ).
fof(i_0_2167,plain,
! [X5321,X5322,X5323,X5324] :
( ~ comm_semiring_1(X5321)
| hAPP(X5321,X5321,hAPP(X5321,fun(X5321,X5321),times_times(X5321),X5322),hAPP(X5321,X5321,hAPP(X5321,fun(X5321,X5321),times_times(X5321),X5323),X5324)) = hAPP(X5321,X5321,hAPP(X5321,fun(X5321,X5321),times_times(X5321),X5323),hAPP(X5321,X5321,hAPP(X5321,fun(X5321,X5321),times_times(X5321),X5322),X5324)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])])]) ).
fof(i_0_2168,plain,
! [X5124,X5125,X5126,X5127] :
( ~ comm_semiring_1(X5124)
| hAPP(X5124,X5124,hAPP(X5124,fun(X5124,X5124),plus_plus(X5124),X5125),hAPP(X5124,X5124,hAPP(X5124,fun(X5124,X5124),plus_plus(X5124),X5126),X5127)) = hAPP(X5124,X5124,hAPP(X5124,fun(X5124,X5124),plus_plus(X5124),X5126),hAPP(X5124,X5124,hAPP(X5124,fun(X5124,X5124),plus_plus(X5124),X5125),X5127)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])])]) ).
fof(i_0_2169,plain,
! [X4231,X4232] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4231),X4232))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4231),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4232),X4231)) = X4232 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_le__add__diff__inverse])]) ).
fof(i_0_2170,plain,
! [X3374,X3375] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3374),X3375))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3375),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3375),X3374)) = X3374 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_42_diff__diff__cancel])]) ).
fof(i_0_2171,plain,
! [X4779,X4780,X4781] :
( ( hBOOL(hAPP(X4779,bool,hAPP(X4779,fun(X4779,bool),ord_less(X4779),esk70_3(X4779,X4780,X4781)),X4781))
| hBOOL(hAPP(X4779,bool,hAPP(X4779,fun(X4779,bool),ord_less_eq(X4779),X4781),X4780))
| ~ dense_linorder(X4779) )
& ( ~ hBOOL(hAPP(X4779,bool,hAPP(X4779,fun(X4779,bool),ord_less_eq(X4779),esk70_3(X4779,X4780,X4781)),X4780))
| hBOOL(hAPP(X4779,bool,hAPP(X4779,fun(X4779,bool),ord_less_eq(X4779),X4781),X4780))
| ~ dense_linorder(X4779) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_438_dense__le])])])])]) ).
cnf(i_0_2172,plain,
( ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1338]) ).
fof(i_0_2173,plain,
! [X5019,X5020] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X5019,bool),nat,finite_card(X5019),X5020)))
| hBOOL(hAPP(fun(X5019,bool),bool,finite_finite(X5019),X5020)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_534_card__ge__0__finite])]) ).
fof(i_0_2174,plain,
! [X6037,X6038,X6040,X6041] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6038))
| ~ hBOOL(hAPP(int,bool,X6037,X6038))
| hBOOL(hAPP(int,bool,X6037,hAPP(nat,int,semiring_1_of_nat(int),esk125_1(X6037)))) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk126_1(X6040)))
| ~ hBOOL(hAPP(int,bool,X6040,hAPP(nat,int,semiring_1_of_nat(int),X6041))) )
& ( hBOOL(hAPP(int,bool,X6040,esk126_1(X6040)))
| ~ hBOOL(hAPP(int,bool,X6040,hAPP(nat,int,semiring_1_of_nat(int),X6041))) ) ),
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_866_transfer__int__nat__quantifiers_I2_J])])])])])]) ).
fof(i_0_2175,plain,
! [X3341,X3342,X3343] :
( ~ hBOOL(hAPP(fun(X3341,bool),bool,hAPP(fun(X3341,bool),fun(fun(X3341,bool),bool),ord_less_eq(fun(X3341,bool)),X3342),X3343))
| ~ hBOOL(hAPP(fun(X3341,bool),bool,finite_finite(X3341),X3343))
| hBOOL(hAPP(fun(X3341,bool),bool,finite_finite(X3341),X3342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_finite__subset])]) ).
fof(i_0_2176,plain,
! [X3344,X3345,X3346] :
( ~ hBOOL(hAPP(fun(X3344,bool),bool,finite_finite(X3344),X3346))
| ~ hBOOL(hAPP(fun(X3344,bool),bool,hAPP(fun(X3344,bool),fun(fun(X3344,bool),bool),ord_less_eq(fun(X3344,bool)),X3345),X3346))
| hBOOL(hAPP(fun(X3344,bool),bool,finite_finite(X3344),X3345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_rev__finite__subset])]) ).
fof(i_0_2177,plain,
! [X5229] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5229),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5229),X5229))),
inference(variable_rename,[status(thm)],[fact_603_le__square]) ).
fof(i_0_2178,plain,
! [X4176,X4177] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4176),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4176),X4177))),
inference(variable_rename,[status(thm)],[fact_246_le__add1]) ).
fof(i_0_2179,plain,
! [X4174,X4175] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4174),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4175),X4174))),
inference(variable_rename,[status(thm)],[fact_245_le__add2]) ).
fof(i_0_2180,plain,
! [X4338,X4339,X4340] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| X4339 = X4340
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4339),X4340)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| X4339 = X4340
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4339),X4340)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4339),X4340)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4339),X4340)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| X4339 = X4340
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| X4339 = X4340
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4338,X4340),X4339)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_303_nat__less__cases])])]) ).
fof(i_0_2181,plain,
! [X5759,X5760,X5761] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5759),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5760),X5761)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5760),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5759),X5761)),
inference(variable_rename,[status(thm)],[fact_769_zadd__left__commute]) ).
fof(i_0_2182,plain,
! [X4121,X4122,X4123] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4121),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4122),X4123)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4122),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4121),X4123)),
inference(variable_rename,[status(thm)],[fact_229_nat__add__left__commute]) ).
cnf(i_0_2183,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1305]) ).
cnf(i_0_2184,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1339]) ).
cnf(i_0_2185,plain,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1340]) ).
cnf(i_0_2186,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1341]) ).
cnf(i_0_2187,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1342]) ).
cnf(i_0_2188,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1343]) ).
cnf(i_0_2189,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1344]) ).
cnf(i_0_2190,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1345]) ).
cnf(i_0_2191,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1346]) ).
fof(i_0_2192,plain,
! [X6260,X6261] :
( ~ number_ring(X6260)
| hAPP(X6260,X6260,hAPP(X6260,fun(X6260,X6260),plus_plus(X6260),hAPP(int,X6260,number_number_of(X6260),X6261)),one_one(X6260)) = hAPP(int,X6260,number_number_of(X6260),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6261),hAPP(int,int,bit1,pls))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_965_add__special_I3_J])])]) ).
fof(i_0_2193,plain,
! [X5077,X5078,X5080] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk90_2(X5077,X5078)),X5077))
| ~ hBOOL(hAPP(nat,bool,X5078,X5077))
| hBOOL(hAPP(nat,bool,X5078,zero_zero(nat))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5080),esk90_2(X5077,X5078)))
| ~ hBOOL(hAPP(nat,bool,X5078,X5080))
| ~ hBOOL(hAPP(nat,bool,X5078,X5077))
| hBOOL(hAPP(nat,bool,X5078,zero_zero(nat))) )
& ( hBOOL(hAPP(nat,bool,X5078,esk90_2(X5077,X5078)))
| ~ hBOOL(hAPP(nat,bool,X5078,X5077))
| hBOOL(hAPP(nat,bool,X5078,zero_zero(nat))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1347])])])])]) ).
cnf(i_0_2194,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
| ti(fun(X1,bool),X2) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1348]) ).
fof(i_0_2195,plain,
! [X5028,X5029,X5030,X5031] :
( ~ hBOOL(hAPP(fun(X5028,bool),bool,hAPP(fun(X5028,bool),fun(fun(X5028,bool),bool),ord_less_eq(fun(X5028,bool)),X5030),X5031))
| ~ hBOOL(hAPP(X5028,bool,X5030,X5029))
| hBOOL(hAPP(X5028,bool,X5031,X5029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_538_predicate1D])]) ).
fof(i_0_2196,plain,
! [X5024,X5025,X5026,X5027] :
( ~ hBOOL(hAPP(X5024,bool,X5026,X5027))
| ~ hBOOL(hAPP(fun(X5024,bool),bool,hAPP(fun(X5024,bool),fun(fun(X5024,bool),bool),ord_less_eq(fun(X5024,bool)),X5026),X5025))
| hBOOL(hAPP(X5024,bool,X5025,X5027)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_537_rev__predicate1D])]) ).
cnf(i_0_2197,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,abs_abs(X1),X2)))
| ti(X1,X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1349]) ).
fof(i_0_2198,plain,
! [X6091,X6092,X6093] :
( ( ~ hBOOL(X6093)
| hAPP(nat,int,semiring_1_of_nat(int),X6091) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X6093),X6091),X6092)) )
& ( hBOOL(X6093)
| hAPP(nat,int,semiring_1_of_nat(int),X6092) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X6093),X6091),X6092)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1350])]) ).
fof(i_0_2199,plain,
! [X4241,X4242,X4243] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4243),X4242) != X4241
| X4243 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4241),X4242)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4242),X4243)) )
& ( X4243 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4241),X4242)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4243),X4242) = X4241
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4242),X4243)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_268_le__imp__diff__is__add])])]) ).
cnf(i_0_2200,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| ~ ring_char_0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1351]) ).
fof(i_0_2201,plain,
! [X4619,X4620,X4622,X4623,X4624] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4619),X4620))
| X4620 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4619),esk47_2(X4619,X4620))) )
& ( X4623 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4622),X4624))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4622),X4623)) ) ),
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_395_less__iff__Suc__add])])])])]) ).
cnf(i_0_2202,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(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1301]) ).
fof(i_0_2203,plain,
! [X6335,X6336,X6337,X6338,X6339,X6340] : hAPP(X6335,X6336,hAPP(fun(X6335,X6337),fun(X6335,X6336),hAPP(fun(X6335,fun(X6337,X6336)),fun(fun(X6335,X6337),fun(X6335,X6336)),combs(X6335,X6337,X6336),X6338),X6339),X6340) = hAPP(X6337,X6336,hAPP(X6335,fun(X6337,X6336),X6338,X6340),hAPP(X6335,X6337,X6339,X6340)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_U]) ).
cnf(i_0_2204,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1352]) ).
fof(i_0_2205,plain,
! [X4729,X4730] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4729),esk59_2(X4729,X4730)))
| X4730 = hAPP(nat,nat,suc,X4729)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4729),X4730)) )
& ( X4730 = hAPP(nat,nat,suc,esk59_2(X4729,X4730))
| X4730 = hAPP(nat,nat,suc,X4729)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4729),X4730)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_429_lessE])])])]) ).
fof(i_0_2206,plain,
! [X4662,X4663] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4662),X4663))
| X4663 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4662),esk51_2(X4662,X4663))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_411_less__imp__Suc__add])])]) ).
fof(i_0_2207,plain,
! [X5056] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5056))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5056),one_one(nat))) = X5056 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_545_Suc__diff__1])]) ).
fof(i_0_2208,plain,
! [X5057] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5057))
| X5057 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X5057),one_one(nat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_546_Suc__pred_H])]) ).
cnf(i_0_2209,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),X3) = ti(X1,X2)
| ~ group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1353]) ).
cnf(i_0_2210,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X3) = ti(X1,X2)
| ~ group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1354]) ).
fof(i_0_2211,plain,
! [X5937,X5938,X5940] :
( ~ linorder(X5937)
| ~ hBOOL(hAPP(X5937,bool,hAPP(X5937,fun(X5937,bool),ord_less(X5937),esk113_2(X5937,X5938)),X5940))
| hBOOL(hAPP(X5937,bool,hAPP(X5937,fun(X5937,bool),ord_less_eq(X5937),X5938),X5940)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_823_pinf_I8_J])])])]) ).
fof(i_0_2212,plain,
! [X4292,X4293,X4294,X4295,X4296] :
( ~ hBOOL(hAPP(fun(X4292,fun(X4293,X4293)),bool,finite_comp_fun_idem(X4292,X4293),X4296))
| hAPP(X4293,X4293,hAPP(X4292,fun(X4293,X4293),X4296,X4294),hAPP(X4293,X4293,hAPP(X4292,fun(X4293,X4293),X4296,X4294),X4295)) = hAPP(X4293,X4293,hAPP(X4292,fun(X4293,X4293),X4296,X4294),X4295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_285_comp__fun__idem_Ofun__left__idem])]) ).
cnf(i_0_2213,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_1355]) ).
fof(i_0_2214,plain,
! [X5933,X5934,X5936] :
( ~ linorder(X5933)
| ~ hBOOL(hAPP(X5933,bool,hAPP(X5933,fun(X5933,bool),ord_less(X5933),X5936),esk112_2(X5933,X5934)))
| hBOOL(hAPP(X5933,bool,hAPP(X5933,fun(X5933,bool),ord_less_eq(X5933),X5936),X5934)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_822_minf_I6_J])])])]) ).
fof(i_0_2215,plain,
! [X6192,X6193,X6194] :
( ~ linordered_idom(X6192)
| hAPP(X6192,X6192,abs_abs(X6192),hAPP(X6192,X6192,hAPP(X6192,fun(X6192,X6192),times_times(X6192),X6193),X6194)) = hAPP(X6192,X6192,hAPP(X6192,fun(X6192,X6192),times_times(X6192),hAPP(X6192,X6192,abs_abs(X6192),X6193)),hAPP(X6192,X6192,abs_abs(X6192),X6194)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_921_abs__mult])])]) ).
fof(i_0_2216,plain,
! [X6264] : hAPP(int,int,bit1,X6264) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X6264)),X6264),
inference(variable_rename,[status(thm)],[fact_968_Bit1__def]) ).
fof(i_0_2217,plain,
! [X3499,X3500,X3501] : hAPP(fun(X3499,bool),fun(X3499,bool),hAPP(X3499,fun(fun(X3499,bool),fun(X3499,bool)),insert(X3499),X3500),hAPP(fun(X3499,bool),fun(X3499,bool),hAPP(X3499,fun(fun(X3499,bool),fun(X3499,bool)),insert(X3499),X3500),X3501)) = hAPP(fun(X3499,bool),fun(X3499,bool),hAPP(X3499,fun(fun(X3499,bool),fun(X3499,bool)),insert(X3499),X3500),X3501),
inference(variable_rename,[status(thm)],[fact_77_insert__absorb2]) ).
fof(i_0_2218,plain,
! [X5264,X5265,X5266] :
( ~ number_ring(X5264)
| hAPP(X5264,X5264,hAPP(X5264,fun(X5264,X5264),times_times(X5264),hAPP(int,X5264,number_number_of(X5264),X5265)),hAPP(int,X5264,number_number_of(X5264),X5266)) = hAPP(int,X5264,number_number_of(X5264),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5265),X5266)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_618_arith__simps_I32_J])])]) ).
fof(i_0_2219,plain,
! [X5297,X5298,X5299] :
( ~ number_ring(X5297)
| hAPP(X5297,X5297,hAPP(X5297,fun(X5297,X5297),plus_plus(X5297),hAPP(int,X5297,number_number_of(X5297),X5298)),hAPP(int,X5297,number_number_of(X5297),X5299)) = hAPP(int,X5297,number_number_of(X5297),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5298),X5299)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_628_add__number__of__eq])])]) ).
fof(i_0_2220,plain,
! [X5258,X5259,X5260] :
( ~ number_ring(X5258)
| hAPP(int,X5258,number_number_of(X5258),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5259),X5260)) = hAPP(X5258,X5258,hAPP(X5258,fun(X5258,X5258),times_times(X5258),hAPP(int,X5258,number_number_of(X5258),X5259)),hAPP(int,X5258,number_number_of(X5258),X5260)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_616_number__of__mult])])]) ).
fof(i_0_2221,plain,
! [X5294,X5295,X5296] :
( ~ number_ring(X5294)
| hAPP(int,X5294,number_number_of(X5294),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5295),X5296)) = hAPP(X5294,X5294,hAPP(X5294,fun(X5294,X5294),plus_plus(X5294),hAPP(int,X5294,number_number_of(X5294),X5295)),hAPP(int,X5294,number_number_of(X5294),X5296)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_627_number__of__add])])]) ).
fof(i_0_2222,plain,
! [X5280,X5281,X5282] :
( ~ number_ring(X5280)
| hAPP(int,X5280,number_number_of(X5280),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5281),X5282)) = hAPP(X5280,X5280,hAPP(X5280,fun(X5280,X5280),minus_minus(X5280),hAPP(int,X5280,number_number_of(X5280),X5281)),hAPP(int,X5280,number_number_of(X5280),X5282)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_623_number__of__diff])])]) ).
fof(i_0_2223,plain,
! [X6020,X6021,X6022] :
( ~ semiring_1(X6020)
| hAPP(nat,X6020,semiring_1_of_nat(X6020),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6021),X6022)) = hAPP(X6020,X6020,hAPP(X6020,fun(X6020,X6020),times_times(X6020),hAPP(nat,X6020,semiring_1_of_nat(X6020),X6021)),hAPP(nat,X6020,semiring_1_of_nat(X6020),X6022)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_854_of__nat__mult])])]) ).
fof(i_0_2224,plain,
! [X5986,X5987,X5988] :
( ~ semiring_1(X5986)
| hAPP(nat,X5986,semiring_1_of_nat(X5986),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5987),X5988)) = hAPP(X5986,X5986,hAPP(X5986,fun(X5986,X5986),plus_plus(X5986),hAPP(nat,X5986,semiring_1_of_nat(X5986),X5987)),hAPP(nat,X5986,semiring_1_of_nat(X5986),X5988)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_842_of__nat__add])])]) ).
fof(i_0_2225,plain,
! [X4449,X4450,X4451] :
( ~ preorder(X4449)
| ~ hBOOL(hAPP(X4449,bool,hAPP(X4449,fun(X4449,bool),ord_less(X4449),X4450),X4451))
| hBOOL(hAPP(X4449,bool,hAPP(X4449,fun(X4449,bool),ord_less_eq(X4449),X4450),X4451)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_338_order__less__imp__le])])]) ).
cnf(i_0_2226,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| ~ ring_char_0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1351]) ).
fof(i_0_2227,plain,
! [X5556,X5557] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5556)),X5557) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5557),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5556),X5557)),
inference(variable_rename,[status(thm)],[fact_703_mult__Suc]) ).
fof(i_0_2228,plain,
! [X5081,X5082] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk91_2(X5081,X5082)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5081),X5082)) )
& ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5081),esk91_2(X5081,X5082)) = X5082
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5081),X5082)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_552_less__imp__add__positive])])])]) ).
fof(i_0_2229,plain,
! [X5719,X5720] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),X5719)),hAPP(int,int,number_number_of(int),X5720)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5719),X5720)),
inference(variable_rename,[status(thm)],[fact_749_times__numeral__code_I5_J]) ).
fof(i_0_2230,plain,
! [X6023,X6024] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X6023)),hAPP(nat,int,semiring_1_of_nat(int),X6024)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6023),X6024)),
inference(variable_rename,[status(thm)],[fact_855_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_2231,plain,
! [X6016,X6017] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X6016)),hAPP(nat,int,semiring_1_of_nat(int),X6017)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6016),X6017)),
inference(variable_rename,[status(thm)],[fact_852_zmult__int]) ).
fof(i_0_2232,plain,
! [X5735,X5736] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),X5735)),hAPP(int,int,number_number_of(int),X5736)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5735),X5736)),
inference(variable_rename,[status(thm)],[fact_755_plus__numeral__code_I9_J]) ).
fof(i_0_2233,plain,
! [X6031,X6032] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X6031)),hAPP(nat,int,semiring_1_of_nat(int),X6032)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6031),X6032)),
inference(variable_rename,[status(thm)],[fact_859_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_2234,plain,
! [X6005,X6006] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X6005)),hAPP(nat,int,semiring_1_of_nat(int),X6006)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6005),X6006)),
inference(variable_rename,[status(thm)],[fact_849_zadd__int]) ).
fof(i_0_2235,plain,
! [X6018,X6019] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6018),X6019)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X6018)),hAPP(nat,int,semiring_1_of_nat(int),X6019)),
inference(variable_rename,[status(thm)],[fact_853_int__mult]) ).
fof(i_0_2236,plain,
! [X6077] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk130_1(X6077)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X6077)) )
& ( X6077 = hAPP(nat,int,semiring_1_of_nat(int),esk130_1(X6077))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X6077)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_881_zero__less__imp__eq__int])])])]) ).
fof(i_0_2237,plain,
! [X6029,X6030] : hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X6029)),hAPP(nat,int,semiring_1_of_nat(int),X6030)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X6029),X6030)),
inference(variable_rename,[status(thm)],[fact_858_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).
fof(i_0_2238,plain,
! [X5748] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X5748))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5748)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5748))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X5748)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_763_int__one__le__iff__zero__less])]) ).
cnf(i_0_2239,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),X2)),zero_zero(X1)))
| ti(X1,X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1303]) ).
fof(i_0_2240,plain,
! [X5776,X5777] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5776),X5777))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5776),X5777)) )
& ( X5776 != X5777
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5776),X5777)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5776),X5777))
| X5776 = X5777
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5776),X5777)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_777_zless__le])])]) ).
fof(i_0_2241,plain,
! [X4580,X4581] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4580),X4581))
| X4580 = X4581
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4580),X4581)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_382_le__neq__implies__less])]) ).
fof(i_0_2242,plain,
! [X4576,X4577] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4576),X4577))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4576),X4577))
| X4576 = X4577 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4576),X4577))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4576),X4577)) )
& ( X4576 != X4577
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4576),X4577)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_380_le__eq__less__or__eq])])]) ).
fof(i_0_2243,plain,
! [X4574,X4575] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4574),X4575))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4574),X4575)) )
& ( X4574 != X4575
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4574),X4575)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4574),X4575))
| X4574 = X4575
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4574),X4575)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_379_nat__less__le])])]) ).
fof(i_0_2244,plain,
! [X4584,X4585] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4584),X4585))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4584),X4585)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_384_termination__basic__simps_I5_J])]) ).
fof(i_0_2245,plain,
! [X4582,X4583] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4582),X4583))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4582),X4583)) )
& ( X4582 != X4583
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4582),X4583)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_383_less__or__eq__imp__le])])]) ).
fof(i_0_2246,plain,
! [X4578,X4579] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4578),X4579))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4578),X4579)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_381_less__imp__le__nat])]) ).
fof(i_0_2247,plain,
! [X6075,X6076] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6075),X6076))
| hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X6076),X6075) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X6076),X6075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_880_tsub__eq])]) ).
fof(i_0_2248,plain,
! [X5964,X5965] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5964),X5965))
| hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X5965),X5964) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X5965),X5964) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5964),X5965))
| hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X5965),X5964) = zero_zero(int) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1356])]) ).
fof(i_0_2249,plain,
! [X4966] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4966),hAPP(nat,nat,suc,zero_zero(nat))))
| X4966 = zero_zero(nat) )
& ( X4966 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4966),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_511_less__Suc0])]) ).
cnf(i_0_2250,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1339]) ).
cnf(i_0_2251,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,pls))),X2) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1357]) ).
fof(i_0_2252,plain,
! [X3856,X3857] : hAPP(fun(X3856,bool),fun(X3856,bool),collect(X3856),hAPP(X3856,fun(X3856,bool),hAPP(fun(X3856,fun(X3856,bool)),fun(X3856,fun(X3856,bool)),combc(X3856,X3856,bool),fequal(X3856)),X3857)) = hAPP(fun(X3856,bool),fun(X3856,bool),hAPP(X3856,fun(fun(X3856,bool),fun(X3856,bool)),insert(X3856),X3857),bot_bot(fun(X3856,bool))),
inference(variable_rename,[status(thm)],[fact_166_singleton__conv]) ).
cnf(i_0_2253,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1358]) ).
cnf(i_0_2254,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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_1338]) ).
fof(i_0_2255,plain,
! [X4644,X4645] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4644),X4645))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4645),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4644),X4645)) = X4644 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1359])]) ).
fof(i_0_2256,plain,
! [X4211,X4212] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4211),X4212)),X4211) = X4212,
inference(variable_rename,[status(thm)],[fact_257_diff__add__inverse]) ).
fof(i_0_2257,plain,
! [X4209,X4210] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4209),X4210)),X4210) = X4209,
inference(variable_rename,[status(thm)],[fact_256_diff__add__inverse2]) ).
fof(i_0_2258,plain,
! [X5256,X5257] :
( ~ number_ring(X5256)
| hBOOL(hAPP(fun(X5256,bool),bool,hAPP(X5256,fun(fun(X5256,bool),bool),member(X5256),hAPP(int,X5256,number_number_of(X5256),X5257)),ring_1_Ints(X5256))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_615_Ints__number__of])])]) ).
fof(i_0_2259,plain,
! [X5981,X5982] :
( ~ ring_1(X5981)
| hBOOL(hAPP(fun(X5981,bool),bool,hAPP(X5981,fun(fun(X5981,bool),bool),member(X5981),hAPP(nat,X5981,semiring_1_of_nat(X5981),X5982)),ring_1_Ints(X5981))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_840_Ints__of__nat])])]) ).
cnf(i_0_2260,plain,
( ti(X1,X4) = ti(X1,X5)
| ti(X1,X2) != ti(X1,X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5)
| ~ ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1360]) ).
cnf(i_0_2261,plain,
( ti(X1,X4) = ti(X1,X5)
| ti(X1,X2) != ti(X1,X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)
| ~ ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1360]) ).
cnf(i_0_2262,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),bot_bot(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_1361]) ).
fof(i_0_2263,plain,
! [X6010,X6011,X6013,X6014,X6015] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6010),X6011))
| X6011 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6010),hAPP(nat,int,semiring_1_of_nat(int),esk124_2(X6010,X6011))) )
& ( X6014 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6013),hAPP(nat,int,semiring_1_of_nat(int),X6015))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X6013),X6014)) ) ),
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_851_zle__iff__zadd])])])])]) ).
cnf(i_0_2264,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),hAPP(X3,fun(X1,X3),combk(X3,X1),X4)),X2) = hAPP(fun(X3,bool),fun(X3,bool),hAPP(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X4),bot_bot(fun(X3,bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1362]) ).
fof(i_0_2265,plain,
! [X6248] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6248),pls))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X6248)) = one_one(nat) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6248),pls))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X6248)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X6248)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1363])]) ).
fof(i_0_2266,plain,
! [X5102,X5103] :
( ( hBOOL(hAPP(nat,bool,X5103,esk98_2(X5102,X5103)))
| hBOOL(hAPP(nat,bool,X5103,X5102))
| ~ hBOOL(hAPP(nat,bool,X5103,zero_zero(nat))) )
& ( ~ hBOOL(hAPP(nat,bool,X5103,hAPP(nat,nat,suc,esk98_2(X5102,X5103))))
| hBOOL(hAPP(nat,bool,X5103,X5102))
| ~ hBOOL(hAPP(nat,bool,X5103,zero_zero(nat))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_560_nat__induct])])])]) ).
fof(i_0_2267,plain,
! [X6197,X6198,X6199] :
( ~ ordere142940540dd_abs(X6197)
| hAPP(X6197,X6197,abs_abs(X6197),hAPP(X6197,X6197,hAPP(X6197,fun(X6197,X6197),minus_minus(X6197),X6198),X6199)) = hAPP(X6197,X6197,abs_abs(X6197),hAPP(X6197,X6197,hAPP(X6197,fun(X6197,X6197),minus_minus(X6197),X6199),X6198)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_923_abs__minus__commute])])]) ).
fof(i_0_2268,plain,
! [X5743,X5744] :
( ( X5744 = one_one(int)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5744),X5743) != one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5744)) )
& ( X5743 = one_one(int)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5744),X5743) != one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5744)) )
& ( X5744 != one_one(int)
| X5743 != one_one(int)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5744),X5743) = one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X5744)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_758_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_2269,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1364]) ).
cnf(i_0_2270,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]) ).
cnf(i_0_2271,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1366]) ).
cnf(i_0_2272,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1335]) ).
cnf(i_0_2273,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1367]) ).
cnf(i_0_2274,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1368]) ).
cnf(i_0_2275,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1369]) ).
cnf(i_0_2276,plain,
( hAPP(fun(X1,bool),X1,the(X1),X3) = ti(X1,X2)
| ti(X1,esk43_4(X1,X2,X3,X4)) != ti(X1,X4)
| ~ hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1370]) ).
fof(i_0_2277,plain,
! [X5015,X5016] :
( ( ~ hBOOL(hAPP(X5015,bool,bot_bot(fun(X5015,bool)),X5016))
| hBOOL(hAPP(fun(X5015,bool),bool,hAPP(X5015,fun(fun(X5015,bool),bool),member(X5015),X5016),bot_bot(fun(X5015,bool)))) )
& ( ~ hBOOL(hAPP(fun(X5015,bool),bool,hAPP(X5015,fun(fun(X5015,bool),bool),member(X5015),X5016),bot_bot(fun(X5015,bool))))
| hBOOL(hAPP(X5015,bool,bot_bot(fun(X5015,bool)),X5016)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_532_bot__empty__eq])]) ).
fof(i_0_2278,plain,
! [X6317,X6318,X6319,X6320,X6321,X6322] : hAPP(X6317,X6318,hAPP(fun(X6317,X6319),fun(X6317,X6318),hAPP(fun(X6319,X6318),fun(fun(X6317,X6319),fun(X6317,X6318)),combb(X6319,X6318,X6317),X6320),X6321),X6322) = hAPP(X6319,X6318,X6320,hAPP(X6317,X6319,X6321,X6322)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_U]) ).
fof(i_0_2279,plain,
! [X6323,X6324,X6325,X6326,X6327,X6328] : hAPP(X6323,X6324,hAPP(X6325,fun(X6323,X6324),hAPP(fun(X6323,fun(X6325,X6324)),fun(X6325,fun(X6323,X6324)),combc(X6323,X6325,X6324),X6326),X6327),X6328) = hAPP(X6325,X6324,hAPP(X6323,fun(X6325,X6324),X6326,X6328),X6327),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_U]) ).
fof(i_0_2280,plain,
! [X5554,X5555] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5554),hAPP(nat,nat,suc,X5555)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5554),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5554),X5555)),
inference(variable_rename,[status(thm)],[fact_702_mult__Suc__right]) ).
cnf(i_0_2281,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1371]) ).
cnf(i_0_2282,plain,
( hBOOL(hAPP(X1,bool,X2,esk43_4(X1,X3,X2,X4)))
| hAPP(fun(X1,bool),X1,the(X1),X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,X2,X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1370]) ).
fof(i_0_2283,plain,
! [X4170,X4171] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X4170)),X4171) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4170),X4171)),
inference(variable_rename,[status(thm)],[fact_243_add__Suc]) ).
cnf(i_0_2284,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk30_2(X1,X2)),esk31_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1348]) ).
fof(i_0_2285,plain,
! [X4681,X4682] : ~ hBOOL(hAPP(fun(X4681,bool),bool,hAPP(fun(X4681,bool),fun(fun(X4681,bool),bool),ord_less(fun(X4681,bool)),X4682),bot_bot(fun(X4681,bool)))),
inference(variable_rename,[status(thm)],[i_0_1372]) ).
cnf(i_0_2286,plain,
( ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1373]) ).
cnf(i_0_2287,plain,
( ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1374]) ).
cnf(i_0_2288,plain,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ti(fun(X1,bool),X3) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
fof(i_0_2289,plain,
! [X6087,X6088] :
( ( X6087 != X6088
| hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6087) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6088) )
& ( hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6087) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6088)
| X6087 = X6088 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_887_transfer__nat__int__set__relations_I3_J])]) ).
fof(i_0_2290,plain,
! [X3494,X3495,X3496] :
( ( ~ hBOOL(hAPP(fun(X3494,bool),bool,hAPP(X3494,fun(fun(X3494,bool),bool),member(X3494),X3495),X3496))
| hBOOL(hAPP(X3494,bool,X3496,X3495)) )
& ( ~ hBOOL(hAPP(X3494,bool,X3496,X3495))
| hBOOL(hAPP(fun(X3494,bool),bool,hAPP(X3494,fun(fun(X3494,bool),bool),member(X3494),X3495),X3496)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_mem__def])]) ).
cnf(i_0_2291,plain,
( hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| ti(X1,esk44_3(X1,X2,X3)) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1376]) ).
cnf(i_0_2292,plain,
( hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| ti(X1,esk42_3(X1,X2,X3)) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1377]) ).
cnf(i_0_2293,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1368]) ).
cnf(i_0_2294,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1369]) ).
cnf(i_0_2295,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1369]) ).
cnf(i_0_2296,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1345]) ).
cnf(i_0_2297,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1378]) ).
cnf(i_0_2298,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1379]) ).
cnf(i_0_2299,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1380]) ).
fof(i_0_2300,plain,
! [X4178,X4179,X4181,X4182,X4183] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4178),X4179))
| X4179 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4178),esk38_2(X4178,X4179)) )
& ( X4182 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4181),X4183)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4181),X4182)) ) ),
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_247_le__iff__add])])])])]) ).
fof(i_0_2301,plain,
! [X6151] :
( ( hBOOL(hAPP(int,bool,nat_neg,X6151))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6151)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6151))
| ~ hBOOL(hAPP(int,bool,nat_neg,X6151)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1381])]) ).
fof(i_0_2302,plain,
! [X4990,X4991] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4990),X4991))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4990),X4991) = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_522_diff__is__0__eq_H])]) ).
fof(i_0_2303,plain,
! [X4988,X4989] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4988),X4989) != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4988),X4989)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4988),X4989))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4988),X4989) = zero_zero(nat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_521_diff__is__0__eq])]) ).
fof(i_0_2304,plain,
! [X5240,X5241,X5242] :
( ~ ab_sem1668676832m_mult(X5240)
| hAPP(X5240,X5240,hAPP(X5240,fun(X5240,X5240),times_times(X5240),X5241),hAPP(X5240,X5240,hAPP(X5240,fun(X5240,X5240),times_times(X5240),X5241),X5242)) = hAPP(X5240,X5240,hAPP(X5240,fun(X5240,X5240),times_times(X5240),X5241),X5242) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_608_mult__left__idem])])]) ).
fof(i_0_2305,plain,
! [X3477,X3478,X3479] :
( ~ linorder(X3477)
| hBOOL(hAPP(X3477,bool,hAPP(X3477,fun(X3477,bool),ord_less_eq(X3477),X3478),X3479))
| hBOOL(hAPP(X3477,bool,hAPP(X3477,fun(X3477,bool),ord_less_eq(X3477),X3479),X3478)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1382])])]) ).
fof(i_0_2306,plain,
! [X3435,X3436,X3437] :
( ~ linorder(X3435)
| hBOOL(hAPP(X3435,bool,hAPP(X3435,fun(X3435,bool),ord_less_eq(X3435),X3436),X3437))
| hBOOL(hAPP(X3435,bool,hAPP(X3435,fun(X3435,bool),ord_less_eq(X3435),X3437),X3436)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_58_linorder__linear])])]) ).
fof(i_0_2307,plain,
! [X4431,X4432,X4433] :
( ~ linorder(X4431)
| hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less(X4431),X4432),X4433))
| hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less_eq(X4431),X4433),X4432)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1383])])]) ).
fof(i_0_2308,plain,
! [X4434,X4435,X4436] :
( ~ linorder(X4434)
| hBOOL(hAPP(X4434,bool,hAPP(X4434,fun(X4434,bool),ord_less_eq(X4434),X4435),X4436))
| hBOOL(hAPP(X4434,bool,hAPP(X4434,fun(X4434,bool),ord_less(X4434),X4436),X4435)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1384])])]) ).
fof(i_0_2309,plain,
! [X4419,X4420,X4421] :
( ~ linorder(X4419)
| hBOOL(hAPP(X4419,bool,hAPP(X4419,fun(X4419,bool),ord_less_eq(X4419),X4420),X4421))
| hBOOL(hAPP(X4419,bool,hAPP(X4419,fun(X4419,bool),ord_less(X4419),X4421),X4420)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_328_linorder__le__less__linear])])]) ).
cnf(i_0_2310,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_1302]) ).
cnf(i_0_2311,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_1385]) ).
cnf(i_0_2312,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_1385]) ).
cnf(i_0_2313,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_1386]) ).
cnf(i_0_2314,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_1292]) ).
cnf(i_0_2315,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_1292]) ).
cnf(i_0_2316,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_1387]) ).
fof(i_0_2317,plain,
! [X4721,X4722] :
( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk56_2(X4721,X4722)),X4722))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X4722)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk56_2(X4721,X4722)),X4721))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X4722)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_427_bounded__nat__set__is__finite])])])]) ).
fof(i_0_2318,plain,
! [X6195,X6196] :
( ~ linordered_idom(X6195)
| hAPP(X6195,X6195,hAPP(X6195,fun(X6195,X6195),times_times(X6195),hAPP(X6195,X6195,abs_abs(X6195),X6196)),hAPP(X6195,X6195,abs_abs(X6195),X6196)) = hAPP(X6195,X6195,hAPP(X6195,fun(X6195,X6195),times_times(X6195),X6196),X6196) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_922_abs__mult__self])])]) ).
fof(i_0_2319,plain,
! [X5774,X5775] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5774),X5775))
| X5774 = X5775
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5775),X5774)) ),
inference(variable_rename,[status(thm)],[fact_776_zless__linear]) ).
fof(i_0_2320,plain,
! [X4331,X4332] :
( X4331 = X4332
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4331),X4332))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4332),X4331)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1388])]) ).
fof(i_0_2321,plain,
! [X4329,X4330] :
( ( X4329 = X4330
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4329),X4330))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4330),X4329)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4329),X4330))
| X4329 != X4330 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4330),X4329))
| X4329 != X4330 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_298_nat__neq__iff])])]) ).
fof(i_0_2322,plain,
! [X5765,X5766] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5765),X5766))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5766),X5765)) ),
inference(variable_rename,[status(thm)],[fact_772_zle__linear]) ).
fof(i_0_2323,plain,
! [X3329,X3330] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3329),X3330))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3330),X3329)) ),
inference(variable_rename,[status(thm)],[fact_23_nat__le__linear]) ).
fof(i_0_2324,plain,
! [X6209,X6210] :
( hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X6209),X6210)) != one_one(int)
| hAPP(int,int,abs_abs(int),X6209) = one_one(int) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_931_abs__zmult__eq__1])]) ).
fof(i_0_2325,plain,
! [X5074,X5075] :
( ( hBOOL(hAPP(fun(X5074,bool),bool,hAPP(X5074,fun(fun(X5074,bool),bool),member(X5074),esk89_2(X5074,X5075)),X5075))
| hAPP(fun(X5074,bool),nat,finite_card(X5074),X5075) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X5074,bool),bool,finite_finite(X5074),X5075)) )
& ( one_one(nat) != zero_zero(nat)
| hAPP(fun(X5074,bool),nat,finite_card(X5074),X5075) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X5074,bool),bool,finite_finite(X5074),X5075)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_550_card_Oneutral])])])]) ).
fof(i_0_2326,plain,
! [X6136,X6137] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6137)))
| hAPP(nat,X6136,semiring_1_of_nat(X6136),hAPP(int,nat,number_number_of(nat),X6137)) = zero_zero(X6136)
| ~ number_ring(X6136) )
& ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6137)))
| hAPP(nat,X6136,semiring_1_of_nat(X6136),hAPP(int,nat,number_number_of(nat),X6137)) = hAPP(int,X6136,number_number_of(X6136),X6137)
| ~ number_ring(X6136) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1389])])])]) ).
cnf(i_0_2327,plain,
hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1390]) ).
fof(i_0_2328,plain,
! [X4168,X4169] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4168),hAPP(nat,nat,suc,X4169)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4168),X4169)),
inference(variable_rename,[status(thm)],[fact_242_add__Suc__right]) ).
cnf(i_0_2329,plain,
( hAPP(X1,X1,abs_abs(X1),X2) = ti(X1,X2)
| ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1391]) ).
cnf(i_0_2330,plain,
( hAPP(X1,X1,abs_abs(X1),X2) = ti(X1,X2)
| ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1392]) ).
fof(i_0_2331,plain,
! [X6221] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6221)))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X6221)) = zero_zero(int) )
& ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6221)))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X6221)) = hAPP(int,int,number_number_of(int),X6221) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1393])]) ).
fof(i_0_2332,plain,
! [X6246] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6246)))
| hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X6246)) = one_one(nat) )
& ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6246)))
| hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X6246)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X6246)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1394])]) ).
cnf(i_0_2333,plain,
( ti(X1,X2) = ti(X1,X4)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1395]) ).
cnf(i_0_2334,plain,
( ti(X1,X2) = ti(X1,X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1396]) ).
cnf(i_0_2335,plain,
( ti(X1,X3) = ti(X1,X4)
| ~ cancel146912293up_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1397]) ).
cnf(i_0_2336,plain,
( ti(X1,X3) = ti(X1,X4)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1398]) ).
cnf(i_0_2337,plain,
( ti(X1,X3) = ti(X1,X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1399]) ).
cnf(i_0_2338,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,esk6_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk6_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1400]) ).
fof(i_0_2339,plain,
! [X3881,X3882,X3883,X3884] : hAPP(nat,X3881,hAPP(fun(nat,X3881),fun(nat,X3881),hAPP(X3881,fun(fun(nat,X3881),fun(nat,X3881)),nat_case(X3881),X3882),X3883),hAPP(nat,nat,suc,X3884)) = hAPP(nat,X3881,X3883,X3884),
inference(variable_rename,[status(thm)],[fact_174_nat__case__Suc]) ).
fof(i_0_2340,plain,
! [X3727,X3728] : ~ hBOOL(hAPP(fun(X3727,bool),bool,hAPP(X3727,fun(fun(X3727,bool),bool),member(X3727),X3728),bot_bot(fun(X3727,bool)))),
inference(variable_rename,[status(thm)],[i_0_1401]) ).
fof(i_0_2341,plain,
! [X3706,X3707] : ~ hBOOL(hAPP(fun(X3706,bool),bool,hAPP(X3706,fun(fun(X3706,bool),bool),member(X3706),X3707),bot_bot(fun(X3706,bool)))),
inference(variable_rename,[status(thm)],[i_0_1402]) ).
cnf(i_0_2342,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_1403]) ).
fof(i_0_2343,plain,
! [X3363,X3364] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X3363)),hAPP(nat,nat,suc,X3364)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3363),X3364),
inference(variable_rename,[status(thm)],[fact_38_diff__Suc__Suc]) ).
fof(i_0_2344,plain,
! [X4172,X4173] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X4172)),X4173) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4172),hAPP(nat,nat,suc,X4173)),
inference(variable_rename,[status(thm)],[fact_244_add__Suc__shift]) ).
cnf(i_0_2345,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),bot_bot(X1)),X2))
| ti(X1,X2) != bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1404]) ).
fof(i_0_2346,plain,
! [X6150] :
( ( ~ hBOOL(hAPP(int,bool,nat_neg,X6150))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6150),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6150),zero_zero(int)))
| hBOOL(hAPP(int,bool,nat_neg,X6150)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_904_neg__def])]) ).
cnf(i_0_2347,plain,
( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),hAPP(X3,fun(X1,X3),combk(X3,X1),X4)),X2) = bot_bot(fun(X3,bool))
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1362]) ).
cnf(i_0_2348,plain,
( ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,abs_abs(X1),X2)))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1349]) ).
cnf(i_0_2349,plain,
( ti(X1,X2) = bot_bot(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),bot_bot(X1)))
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1405]) ).
cnf(i_0_2350,plain,
( ti(X1,X2) = bot_bot(X1)
| ~ bot(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),bot_bot(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1406]) ).
cnf(i_0_2351,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),bot_bot(fun(X1,bool))))
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1361]) ).
fof(i_0_2352,plain,
! [X5097,X5098] :
( ( hBOOL(hAPP(nat,bool,X5097,hAPP(nat,nat,suc,esk96_1(X5097))))
| hBOOL(hAPP(nat,bool,X5097,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X5097,X5098)) )
& ( ~ hBOOL(hAPP(nat,bool,X5097,esk96_1(X5097)))
| hBOOL(hAPP(nat,bool,X5097,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X5097,X5098)) ) ),
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_558_zero__induct])])])])])]) ).
fof(i_0_2353,plain,
! [X6107] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6107))
| X6107 = hAPP(nat,int,semiring_1_of_nat(int),esk133_1(X6107)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_895_zero__le__imp__eq__int])])]) ).
fof(i_0_2354,plain,
! [X6105] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6105))
| X6105 = hAPP(nat,int,semiring_1_of_nat(int),esk132_1(X6105)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_894_nonneg__eq__int])])]) ).
fof(i_0_2355,plain,
! [X6103] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6103))
| X6103 = hAPP(nat,int,semiring_1_of_nat(int),esk131_1(X6103)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_893_nonneg__int__cases])])]) ).
fof(i_0_2356,plain,
! [X5084] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5084))
| X5084 = hAPP(nat,nat,suc,esk92_1(X5084)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_553_gr0__implies__Suc])])]) ).
fof(i_0_2357,plain,
! [X4962,X4964,X4965] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4962))
| X4962 = hAPP(nat,nat,suc,esk82_1(X4962)) )
& ( X4964 != hAPP(nat,nat,suc,X4965)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4964)) ) ),
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_510_gr0__conv__Suc])])])])]) ).
cnf(i_0_2358,plain,
hAPP(fun(X1,bool),X1,the_elem(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1407]) ).
cnf(i_0_2359,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk28_2(X1,X2)),esk27_2(X1,X2))
| ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1371]) ).
fof(i_0_2360,plain,
! [X6033] : hAPP(fun(nat,bool),nat,finite_card(nat),X6033) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X6033)),
inference(variable_rename,[status(thm)],[fact_860_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).
cnf(i_0_2361,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2) != bot_bot(fun(sum_sum(X3,X1),bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1408]) ).
cnf(i_0_2362,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4) != bot_bot(fun(sum_sum(X1,X3),bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1408]) ).
fof(i_0_2363,plain,
! [X6156,X6157] :
( ~ ordere142940540dd_abs(X6156)
| hBOOL(hAPP(X6156,bool,hAPP(X6156,fun(X6156,bool),ord_less_eq(X6156),zero_zero(X6156)),hAPP(X6156,X6156,abs_abs(X6156),X6157))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_908_abs__ge__zero])])]) ).
fof(i_0_2364,plain,
! [X5974,X5975] :
( ~ linordered_semidom(X5974)
| hBOOL(hAPP(X5974,bool,hAPP(X5974,fun(X5974,bool),ord_less_eq(X5974),zero_zero(X5974)),hAPP(nat,X5974,semiring_1_of_nat(X5974),X5975))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_833_zero__le__imp__of__nat])])]) ).
fof(i_0_2365,plain,
! [X5972,X5973] :
( ~ linordered_semidom(X5972)
| hBOOL(hAPP(X5972,bool,hAPP(X5972,fun(X5972,bool),ord_less_eq(X5972),zero_zero(X5972)),hAPP(nat,X5972,semiring_1_of_nat(X5972),X5973))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_832_of__nat__0__le__iff])])]) ).
cnf(i_0_2366,plain,
( hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4) = bot_bot(fun(sum_sum(X1,X3),bool))
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool))
| ti(fun(X3,bool),X4) != bot_bot(fun(X3,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1408]) ).
fof(i_0_2367,plain,
! [X6184,X6185] :
( ~ ordere142940540dd_abs(X6184)
| hBOOL(hAPP(X6184,bool,hAPP(X6184,fun(X6184,bool),ord_less_eq(X6184),X6185),hAPP(X6184,X6184,abs_abs(X6184),X6185))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_918_abs__ge__self])])]) ).
fof(i_0_2368,plain,
! [X4958] :
( ~ linordered_semidom(X4958)
| ~ hBOOL(hAPP(X4958,bool,hAPP(X4958,fun(X4958,bool),ord_less_eq(X4958),one_one(X4958)),zero_zero(X4958))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1409])]) ).
fof(i_0_2369,plain,
! [X4961] :
( ~ linordered_semidom(X4961)
| ~ hBOOL(hAPP(X4961,bool,hAPP(X4961,fun(X4961,bool),ord_less(X4961),one_one(X4961)),zero_zero(X4961))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1410])]) ).
cnf(i_0_2370,plain,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),zero_zero(nat)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1411]) ).
fof(i_0_2371,plain,
! [X6215] :
( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X6215)))
| hAPP(int,nat,number_number_of(nat),X6215) = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_935_neg__imp__number__of__eq__0])]) ).
fof(i_0_2372,plain,
! [X6036] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X6036))),
inference(variable_rename,[status(thm)],[fact_865_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).
fof(i_0_2373,plain,
! [X5970] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X5970))),
inference(variable_rename,[status(thm)],[fact_830_zero__zle__int]) ).
fof(i_0_2374,plain,
! [X4864] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X4864))),
inference(variable_rename,[status(thm)],[fact_456_zero__less__Suc]) ).
fof(i_0_2375,plain,
! [X4509,X4510] :
( ~ bot(X4509)
| ~ hBOOL(hAPP(X4509,bool,hAPP(X4509,fun(X4509,bool),ord_less(X4509),X4510),bot_bot(X4509))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1412])])]) ).
fof(i_0_2376,plain,
! [X4324] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4324),hAPP(nat,nat,suc,X4324))),
inference(variable_rename,[status(thm)],[fact_294_lessI]) ).
cnf(i_0_2377,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,pls))) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1413]) ).
fof(i_0_2378,plain,
! [X4341,X4342] :
( ~ preorder(X4341)
| ~ hBOOL(hAPP(X4341,bool,hAPP(X4341,fun(X4341,bool),ord_less(X4341),X4342),X4342)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1414])])]) ).
cnf(i_0_2379,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk93_3(X1,X2,X3)),esk94_3(X1,X2,X3))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1415]) ).
cnf(i_0_2380,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk87_3(X1,X2,X3)),esk88_3(X1,X2,X3))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1318]) ).
fof(i_0_2381,plain,
! [X4906] :
( ( X4906 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4906)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4906))
| X4906 != zero_zero(nat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_483_neq0__conv])]) ).
cnf(i_0_2382,plain,
( hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),X2),zero_zero(nat)),X3) = ti(X1,X3)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1416]) ).
fof(i_0_2383,plain,
! [X4865] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4865),zero_zero(nat)))
| X4865 = zero_zero(nat) )
& ( X4865 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4865),zero_zero(nat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_457_le__0__eq])]) ).
fof(i_0_2384,plain,
! [X4907] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4907),zero_zero(nat))),
inference(variable_rename,[status(thm)],[i_0_1417]) ).
fof(i_0_2385,plain,
! [X4905] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4905),zero_zero(nat))),
inference(variable_rename,[status(thm)],[i_0_1418]) ).
fof(i_0_2386,plain,
! [X4862] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4862),zero_zero(nat))),
inference(variable_rename,[status(thm)],[i_0_1419]) ).
fof(i_0_2387,plain,
! [X4867,X4868] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4867),X4868) != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4868),X4867) != zero_zero(nat)
| X4867 = X4868 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_459_diffs0__imp__equal])]) ).
fof(i_0_2388,plain,
! [X4903,X4904] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4903),X4904))
| X4904 != zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_481_gr__implies__not0])]) ).
fof(i_0_2389,plain,
! [X4336,X4337] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4336),X4337))
| X4336 != X4337 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_302_less__not__refl3])]) ).
fof(i_0_2390,plain,
! [X4334,X4335] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4334),X4335))
| X4335 != X4334 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_301_less__not__refl2])]) ).
fof(i_0_2391,plain,
! [X5188,X5189,X5190] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5188),X5189) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5190),X5189)
| X5188 = X5190
| X5189 = zero_zero(nat) )
& ( X5188 != X5190
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5188),X5189) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5190),X5189) )
& ( X5189 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5188),X5189) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5190),X5189) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_588_mult__cancel2])])]) ).
fof(i_0_2392,plain,
! [X5793,X5794,X5795] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5793),X5794) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5793),X5795)
| X5793 = zero_zero(nat)
| X5794 = X5795 )
& ( X5793 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5793),X5794) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5793),X5795) )
& ( X5794 != X5795
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5793),X5794) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5793),X5795) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_784_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_2393,plain,
! [X5185,X5186,X5187] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5185),X5186) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5185),X5187)
| X5186 = X5187
| X5185 = zero_zero(nat) )
& ( X5186 != X5187
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5185),X5186) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5185),X5187) )
& ( X5185 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5185),X5186) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5185),X5187) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_587_mult__cancel1])])]) ).
fof(i_0_2394,plain,
! [X4333] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4333),X4333)),
inference(variable_rename,[status(thm)],[i_0_1420]) ).
fof(i_0_2395,plain,
! [X4328] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4328),X4328)),
inference(variable_rename,[status(thm)],[i_0_1421]) ).
fof(i_0_2396,plain,
! [X4130,X4131,X4132] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4130),X4131) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4132),X4131)
| X4130 = X4132 )
& ( X4130 != X4132
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4130),X4131) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4132),X4131) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_232_nat__add__right__cancel])]) ).
fof(i_0_2397,plain,
! [X4127,X4128,X4129] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4127),X4128) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4127),X4129)
| X4128 = X4129 )
& ( X4128 != X4129
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4127),X4128) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4127),X4129) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_nat__add__left__cancel])]) ).
fof(i_0_2398,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(fof_simplification,[status(thm)],[fact_989_rel__simps_I2_J]) ).
fof(i_0_2399,plain,
! [X6364,X6365] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X6364),X6365))
| ~ hBOOL(X6364)
| hBOOL(X6365) ),
inference(variable_rename,[status(thm)],[i_0_1422]) ).
fof(i_0_2400,plain,
! [X6351,X6352] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X6351),X6352))
| hBOOL(X6351)
| hBOOL(X6352) ),
inference(variable_rename,[status(thm)],[i_0_1423]) ).
fof(i_0_2401,plain,
! [X6343,X6344] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X6343),X6344))
| hBOOL(X6343) ),
inference(variable_rename,[status(thm)],[i_0_1424]) ).
fof(i_0_2402,plain,
! [X6345,X6346] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X6345),X6346))
| hBOOL(X6346) ),
inference(variable_rename,[status(thm)],[i_0_1425]) ).
cnf(i_0_2403,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
| ti(X1,X2) != ti(X1,X3)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1396]) ).
cnf(i_0_2404,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
| ti(X1,X2) != ti(X1,X3)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1399]) ).
cnf(i_0_2405,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1344]) ).
cnf(i_0_2406,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1317]) ).
cnf(i_0_2407,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1317]) ).
cnf(i_0_2408,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_1426]) ).
cnf(i_0_2409,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1427]) ).
cnf(i_0_2410,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
inference(split_conjunct,[status(thm)],[i_0_1428]) ).
cnf(i_0_2411,plain,
ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1429]) ).
fof(i_0_2412,plain,
! [X4986,X4987] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4986),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4986),X4987)) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_520_diff__add__0]) ).
cnf(i_0_2413,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),finite2073411215e_idem(X1)) = finite2073411215e_idem(X1),
inference(split_conjunct,[status(thm)],[i_0_1430]) ).
cnf(i_0_2414,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),finite_folding_one(X1)) = finite_folding_one(X1),
inference(split_conjunct,[status(thm)],[i_0_1431]) ).
fof(i_0_2415,plain,
! [X6213] : ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),X6213))),
inference(variable_rename,[status(thm)],[i_0_1432]) ).
fof(i_0_2416,plain,
! [X3712,X3713] : hBOOL(hAPP(fun(X3712,bool),bool,hAPP(fun(X3712,bool),fun(fun(X3712,bool),bool),ord_less_eq(fun(X3712,bool)),bot_bot(fun(X3712,bool))),X3713)),
inference(variable_rename,[status(thm)],[fact_124_empty__subsetI]) ).
fof(i_0_2417,plain,
~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))),
inference(fof_simplification,[status(thm)],[fact_951_not__neg__number__of__Pls]) ).
cnf(i_0_2418,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk20_2(X1,X2)),X2))
| ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1373]) ).
cnf(i_0_2419,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk19_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
fof(i_0_2420,plain,
! [X6109] : X6109 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),esk134_1(X6109))),hAPP(nat,int,semiring_1_of_nat(int),esk135_1(X6109))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_896_int__diff__cases])])]) ).
cnf(i_0_2421,plain,
( hAPP(fun(X1,bool),X1,the(X1),X2) = ti(X1,X3)
| ti(X1,esk41_3(X1,X2,X3)) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1433]) ).
cnf(i_0_2422,plain,
( ti(fun(X1,bool),X4) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != bot_bot(fun(X2,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1434]) ).
cnf(i_0_2423,plain,
( ti(fun(X2,bool),X4) = bot_bot(fun(X2,bool))
| bot_bot(fun(X1,bool)) != hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1435]) ).
cnf(i_0_2424,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_1436]) ).
fof(i_0_2425,plain,
! [X4975,X4976] :
( ( X4975 = zero_zero(nat)
| X4975 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4975),X4976) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X4976 = hAPP(nat,nat,suc,zero_zero(nat))
| X4975 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4975),X4976) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X4975 = zero_zero(nat)
| X4976 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4975),X4976) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X4976 = hAPP(nat,nat,suc,zero_zero(nat))
| X4976 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4975),X4976) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X4975 != hAPP(nat,nat,suc,zero_zero(nat))
| X4976 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4975),X4976) = hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X4975 != zero_zero(nat)
| X4976 != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4975),X4976) = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_514_add__is__1])])]) ).
fof(i_0_2426,plain,
! [X4973,X4974] :
( ( X4973 = zero_zero(nat)
| X4973 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4973),X4974) )
& ( X4974 = hAPP(nat,nat,suc,zero_zero(nat))
| X4973 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4973),X4974) )
& ( X4973 = zero_zero(nat)
| X4974 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4973),X4974) )
& ( X4974 = hAPP(nat,nat,suc,zero_zero(nat))
| X4974 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4973),X4974) )
& ( X4973 != hAPP(nat,nat,suc,zero_zero(nat))
| X4974 != zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4973),X4974) )
& ( X4973 != zero_zero(nat)
| X4974 != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4973),X4974) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_513_one__is__add])])]) ).
fof(i_0_2427,plain,
! [X3525,X3526] : hBOOL(hAPP(fun(X3525,bool),bool,hAPP(fun(X3525,bool),fun(fun(X3525,bool),bool),ord_less_eq(fun(X3525,bool)),X3526),X3526)),
inference(variable_rename,[status(thm)],[fact_84_subset__refl]) ).
cnf(i_0_2428,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),pls)),X2) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1437]) ).
fof(i_0_2429,plain,
! [X6244,X6245] :
( ~ number_ring(X6244)
| hAPP(int,X6244,number_number_of(X6244),hAPP(int,int,succ,X6245)) = hAPP(X6244,X6244,hAPP(X6244,fun(X6244,X6244),plus_plus(X6244),one_one(X6244)),hAPP(int,X6244,number_number_of(X6244),X6245)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_945_number__of__succ])])]) ).
fof(i_0_2430,plain,
! [X6059,X6060] :
( ~ semiring_1(X6059)
| hAPP(nat,X6059,semiring_1_of_nat(X6059),hAPP(nat,nat,suc,X6060)) = hAPP(X6059,X6059,hAPP(X6059,fun(X6059,X6059),plus_plus(X6059),one_one(X6059)),hAPP(nat,X6059,semiring_1_of_nat(X6059),X6060)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_873_of__nat__Suc])])]) ).
cnf(i_0_2431,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),bot_bot(X1)))
| ti(X1,X2) != bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1405]) ).
cnf(i_0_2432,plain,
( hBOOL(hAPP(X1,bool,X2,esk41_3(X1,X2,X3)))
| hAPP(fun(X1,bool),X1,the(X1),X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1433]) ).
fof(i_0_2433,plain,
! [X6056] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X6056)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X6056)),
inference(variable_rename,[status(thm)],[fact_871_int__Suc]) ).
fof(i_0_2434,plain,
! [X3858,X3859] : hAPP(fun(X3858,bool),fun(X3858,bool),collect(X3858),hAPP(X3858,fun(X3858,bool),fequal(X3858),X3859)) = hAPP(fun(X3858,bool),fun(X3858,bool),hAPP(X3858,fun(fun(X3858,bool),fun(X3858,bool)),insert(X3858),X3859),bot_bot(fun(X3858,bool))),
inference(variable_rename,[status(thm)],[fact_167_singleton__conv2]) ).
cnf(i_0_2435,plain,
( ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1438]) ).
cnf(i_0_2436,plain,
( ti(X1,X2) = bot_bot(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),bot_bot(X1)),X2))
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1404]) ).
fof(i_0_2437,plain,
! [X5312] :
( ~ ring_1(X5312)
| hBOOL(hAPP(fun(X5312,bool),bool,hAPP(X5312,fun(fun(X5312,bool),bool),member(X5312),zero_zero(X5312)),ring_1_Ints(X5312))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_632_Ints__0])]) ).
fof(i_0_2438,plain,
! [X5313] :
( ~ ring_1(X5313)
| hBOOL(hAPP(fun(X5313,bool),bool,hAPP(X5313,fun(fun(X5313,bool),bool),member(X5313),one_one(X5313)),ring_1_Ints(X5313))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_633_Ints__1])]) ).
fof(i_0_2439,plain,
! [X5535,X5536] :
( ( X5535 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5535),X5536) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X5536 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5535),X5536) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X5535 != hAPP(nat,nat,suc,zero_zero(nat))
| X5536 != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5535),X5536) = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_695_mult__eq__1__iff])])]) ).
cnf(i_0_2440,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk27_2(X1,X2)))
| ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1371]) ).
cnf(i_0_2441,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk30_2(X1,X2)),esk31_2(X1,X2))
| ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1348]) ).
cnf(i_0_2442,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ ring_n68954251visors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]) ).
cnf(i_0_2443,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ no_zero_divisors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1440]) ).
cnf(i_0_2444,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ no_zero_divisors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1441]) ).
cnf(i_0_2445,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != zero_zero(X1)
| ~ group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1442]) ).
cnf(i_0_2446,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != zero_zero(X1)
| ~ ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1443]) ).
cnf(i_0_2447,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_1444]) ).
cnf(i_0_2448,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_1445]) ).
fof(i_0_2449,plain,
! [X4029] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X4029)),one_one(nat)) = X4029,
inference(variable_rename,[status(thm)],[fact_207_diff__Suc__1]) ).
cnf(i_0_2450,plain,
( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2) = bot_bot(fun(X3,bool))
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1434]) ).
cnf(i_0_2451,plain,
( bot_bot(fun(X3,bool)) = hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1435]) ).
cnf(i_0_2452,plain,
( ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1446]) ).
fof(i_0_2453,plain,
! [X3825,X3826,X3827] : hAPP(fun(X3825,bool),fun(X3825,bool),hAPP(X3825,fun(fun(X3825,bool),fun(X3825,bool)),insert(X3825),X3826),X3827) != bot_bot(fun(X3825,bool)),
inference(variable_rename,[status(thm)],[fact_155_insert__not__empty]) ).
fof(i_0_2454,plain,
! [X3828,X3829,X3830] : bot_bot(fun(X3828,bool)) != hAPP(fun(X3828,bool),fun(X3828,bool),hAPP(X3828,fun(fun(X3828,bool),fun(X3828,bool)),insert(X3828),X3829),X3830),
inference(variable_rename,[status(thm)],[fact_156_empty__not__insert]) ).
fof(i_0_2455,plain,
! [X4959] :
( ~ linordered_semidom(X4959)
| hBOOL(hAPP(X4959,bool,hAPP(X4959,fun(X4959,bool),ord_less_eq(X4959),zero_zero(X4959)),one_one(X4959))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_507_zero__le__one])]) ).
fof(i_0_2456,plain,
! [X4960] :
( ~ linordered_semidom(X4960)
| hBOOL(hAPP(X4960,bool,hAPP(X4960,fun(X4960,bool),ord_less(X4960),zero_zero(X4960)),one_one(X4960))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_508_zero__less__one])]) ).
fof(i_0_2457,plain,
! [X3848,X3849] :
( ~ bot(X3848)
| hBOOL(hAPP(X3848,bool,hAPP(X3848,fun(X3848,bool),ord_less_eq(X3848),bot_bot(X3848)),X3849)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_bot__least])])]) ).
fof(i_0_2458,plain,
! [X5318,X5319,X5320] :
( ~ comm_semiring_1(X5318)
| hAPP(X5318,X5318,hAPP(X5318,fun(X5318,X5318),times_times(X5318),X5319),X5320) = hAPP(X5318,X5318,hAPP(X5318,fun(X5318,X5318),times_times(X5318),X5320),X5319) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])]) ).
fof(i_0_2459,plain,
! [X5128,X5129,X5130] :
( ~ comm_semiring_1(X5128)
| hAPP(X5128,X5128,hAPP(X5128,fun(X5128,X5128),plus_plus(X5128),X5129),X5130) = hAPP(X5128,X5128,hAPP(X5128,fun(X5128,X5128),plus_plus(X5128),X5130),X5129) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
cnf(i_0_2460,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) = zero_zero(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1442]) ).
cnf(i_0_2461,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) = zero_zero(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1443]) ).
fof(i_0_2462,plain,
! [X3441,X3442,X3443] :
( ~ preorder(X3441)
| X3442 != X3443
| hBOOL(hAPP(X3441,bool,hAPP(X3441,fun(X3441,bool),ord_less_eq(X3441),X3442),X3443)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_60_order__eq__refl])])]) ).
fof(i_0_2463,plain,
! [X3433,X3434] :
( ~ preorder(X3433)
| hBOOL(hAPP(X3433,bool,hAPP(X3433,fun(X3433,bool),ord_less_eq(X3433),X3434),X3434)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_order__refl])])]) ).
fof(i_0_2464,plain,
! [X4902] :
( X4902 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4902)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_gr0I])]) ).
fof(i_0_2465,plain,
! [X4866] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X4866)),
inference(variable_rename,[status(thm)],[fact_458_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2466,plain,
! [X4863] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X4863)),
inference(variable_rename,[status(thm)],[fact_455_le0]) ).
cnf(i_0_2467,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),bot_bot(fun(X1,bool))) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[i_0_1447]) ).
fof(i_0_2468,plain,
! [X3327,X3328] :
( X3327 != X3328
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3327),X3328)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_eq__imp__le])]) ).
cnf(i_0_2469,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(int,X1,number_number_of(X1),pls)) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1448]) ).
fof(i_0_2470,plain,
! [X5764] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5764),X5764)),
inference(variable_rename,[status(thm)],[fact_771_zle__refl]) ).
fof(i_0_2471,plain,
! [X3331] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3331),X3331)),
inference(variable_rename,[status(thm)],[fact_24_le__refl]) ).
fof(i_0_2472,plain,
! [X5717,X5718] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5717),X5718) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5718),X5717),
inference(variable_rename,[status(thm)],[fact_748_zmult__commute]) ).
fof(i_0_2473,plain,
! [X5762,X5763] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5762),X5763) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5763),X5762),
inference(variable_rename,[status(thm)],[fact_770_zadd__commute]) ).
fof(i_0_2474,plain,
! [X5708,X5709] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5708),X5709) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5709),X5708),
inference(variable_rename,[status(thm)],[fact_743_nat__mult__commute]) ).
fof(i_0_2475,plain,
! [X4119,X4120] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4119),X4120) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4120),X4119),
inference(variable_rename,[status(thm)],[fact_228_nat__add__commute]) ).
fof(i_0_2476,plain,
! [X6341,X6342] :
( ~ hBOOL(X6342)
| ~ hBOOL(X6341)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X6342),X6341)) ),
inference(variable_rename,[status(thm)],[i_0_1449]) ).
fof(i_0_2477,plain,
! [X6362,X6363] :
( ~ hBOOL(X6363)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X6362),X6363)) ),
inference(variable_rename,[status(thm)],[i_0_1450]) ).
fof(i_0_2478,plain,
! [X6347,X6348] :
( ~ hBOOL(X6348)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X6348),X6347)) ),
inference(variable_rename,[status(thm)],[i_0_1451]) ).
fof(i_0_2479,plain,
! [X6349,X6350] :
( ~ hBOOL(X6350)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X6349),X6350)) ),
inference(variable_rename,[status(thm)],[i_0_1452]) ).
fof(i_0_2480,plain,
! [X6360,X6361] :
( hBOOL(X6361)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X6361),X6360)) ),
inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).
cnf(i_0_2481,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_1453]) ).
cnf(i_0_2482,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1454]) ).
cnf(i_0_2483,plain,
( ti(X1,X2) = zero_zero(X1)
| zero_zero(X1) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1455]) ).
cnf(i_0_2484,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_1456]) ).
cnf(i_0_2485,plain,
( ti(X1,X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
| ti(X1,X2) != zero_zero(X1)
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1438]) ).
cnf(i_0_2486,plain,
ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
inference(split_conjunct,[status(thm)],[i_0_1457]) ).
cnf(i_0_2487,plain,
ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
inference(split_conjunct,[status(thm)],[i_0_1458]) ).
fof(i_0_2488,plain,
! [X3735,X3736] : hAPP(fun(X3735,bool),fun(X3735,bool),hAPP(fun(X3735,bool),fun(fun(X3735,bool),fun(X3735,bool)),minus_minus(fun(X3735,bool)),bot_bot(fun(X3735,bool))),X3736) = bot_bot(fun(X3735,bool)),
inference(variable_rename,[status(thm)],[fact_131_empty__Diff]) ).
cnf(i_0_2489,plain,
( ti(fun(X2,bool),esk94_3(X2,X3,X1)) = bot_bot(fun(X2,bool))
| X1 != zero_zero(nat)
| hAPP(fun(X2,bool),nat,finite_card(X2),X3) != hAPP(nat,nat,suc,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1415]) ).
cnf(i_0_2490,plain,
( ti(fun(X2,bool),esk88_3(X2,X3,X1)) = bot_bot(fun(X2,bool))
| X1 != zero_zero(nat)
| hAPP(fun(X2,bool),nat,finite_card(X2),X3) != hAPP(nat,nat,suc,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1318]) ).
fof(i_0_2491,plain,
! [X3717,X3718,X3719,X3720,X3721] :
( ( hAPP(fun(X3717,bool),fun(X3717,bool),collect(X3717),X3718) != bot_bot(fun(X3717,bool))
| ~ hBOOL(hAPP(X3717,bool,X3718,X3719)) )
& ( hBOOL(hAPP(X3720,bool,X3721,esk17_2(X3720,X3721)))
| hAPP(fun(X3720,bool),fun(X3720,bool),collect(X3720),X3721) = bot_bot(fun(X3720,bool)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1459])])])])]) ).
fof(i_0_2492,plain,
! [X3729,X3730,X3731,X3732,X3733] :
( ( bot_bot(fun(X3729,bool)) != hAPP(fun(X3729,bool),fun(X3729,bool),collect(X3729),X3730)
| ~ hBOOL(hAPP(X3729,bool,X3730,X3731)) )
& ( hBOOL(hAPP(X3732,bool,X3733,esk18_2(X3732,X3733)))
| bot_bot(fun(X3732,bool)) = hAPP(fun(X3732,bool),fun(X3732,bool),collect(X3732),X3733) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1460])])])])]) ).
fof(i_0_2493,plain,
! [X5183,X5184] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5183),X5184) != zero_zero(nat)
| X5183 = zero_zero(nat)
| X5184 = zero_zero(nat) )
& ( X5183 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5183),X5184) = zero_zero(nat) )
& ( X5184 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5183),X5184) = zero_zero(nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_586_mult__is__0])])]) ).
fof(i_0_2494,plain,
! [X5561,X5562] :
( X5561 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5561),X5562)
| X5562 = one_one(nat)
| X5561 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_705_mult__eq__self__implies__10])]) ).
fof(i_0_2495,plain,
! [X4898,X4899] :
( ( X4898 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4898),X4899) != zero_zero(nat) )
& ( X4899 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4898),X4899) != zero_zero(nat) )
& ( X4898 != zero_zero(nat)
| X4899 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4898),X4899) = zero_zero(nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_477_add__is__0])])]) ).
fof(i_0_2496,plain,
! [X5247,X5248] :
( ( X5247 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5247),X5248) != one_one(nat) )
& ( X5248 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5247),X5248) != one_one(nat) )
& ( X5247 != one_one(nat)
| X5248 != one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5247),X5248) = one_one(nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_610_nat__mult__eq__1__iff])])]) ).
fof(i_0_2497,plain,
! [X5250,X5251] :
( ( X5250 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5250),X5251) )
& ( X5251 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5250),X5251) )
& ( X5250 != one_one(nat)
| X5251 != one_one(nat)
| one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5250),X5251) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_612_nat__1__eq__mult__iff])])]) ).
fof(i_0_2498,plain,
! [X4896,X4897] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4896),X4897) != X4896
| X4897 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_476_add__eq__self__zero])]) ).
cnf(i_0_2499,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ ring_n68954251visors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]) ).
cnf(i_0_2500,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ ring_n68954251visors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]) ).
cnf(i_0_2501,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1454]) ).
cnf(i_0_2502,plain,
( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
| ti(X1,X2) != zero_zero(X1)
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1455]) ).
cnf(i_0_2503,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_1461]) ).
fof(i_0_2504,plain,
! [X3837,X3838,X3839] : hAPP(fun(X3837,bool),fun(X3838,bool),hAPP(fun(X3837,X3838),fun(fun(X3837,bool),fun(X3838,bool)),image(X3837,X3838),X3839),bot_bot(fun(X3837,bool))) = bot_bot(fun(X3838,bool)),
inference(variable_rename,[status(thm)],[fact_159_image__empty]) ).
fof(i_0_2505,plain,
! [X3723,X3724] : hAPP(fun(X3723,bool),fun(X3723,bool),hAPP(fun(X3723,bool),fun(fun(X3723,bool),fun(X3723,bool)),minus_minus(fun(X3723,bool)),X3724),X3724) = bot_bot(fun(X3723,bool)),
inference(variable_rename,[status(thm)],[fact_127_Diff__cancel]) ).
cnf(i_0_2506,plain,
( ti(fun(fun(X1,X1),fun(nat,fun(X1,X1))),semiri532925092at_aux(X1)) = semiri532925092at_aux(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]) ).
fof(i_0_2507,plain,
! [X4297] : hBOOL(hAPP(fun(X4297,fun(fun(X4297,bool),fun(X4297,bool))),bool,finite_comp_fun_idem(X4297,fun(X4297,bool)),insert(X4297))),
inference(variable_rename,[status(thm)],[fact_286_comp__fun__idem__insert]) ).
cnf(i_0_2508,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1371]) ).
cnf(i_0_2509,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_1463]) ).
cnf(i_0_2510,plain,
hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1464]) ).
cnf(i_0_2511,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1465]) ).
cnf(i_0_2512,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1466]) ).
cnf(i_0_2513,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1467]) ).
cnf(i_0_2514,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]) ).
cnf(i_0_2515,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1469]) ).
cnf(i_0_2516,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1470]) ).
cnf(i_0_2517,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1471]) ).
cnf(i_0_2518,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1472]) ).
cnf(i_0_2519,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1473]) ).
cnf(i_0_2520,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1474]) ).
cnf(i_0_2521,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1475]) ).
cnf(i_0_2522,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1476]) ).
cnf(i_0_2523,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),zero_zero(X1)) = ti(X1,X2)
| ~ group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1477]) ).
cnf(i_0_2524,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1478]) ).
cnf(i_0_2525,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]) ).
fof(i_0_2526,plain,
! [X4253] : hAPP(nat,nat,suc,X4253) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X4253),
inference(variable_rename,[status(thm)],[fact_272_Suc__eq__plus1__left]) ).
fof(i_0_2527,plain,
! [X6243] : hAPP(int,int,succ,X6243) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6243),one_one(int)),
inference(variable_rename,[status(thm)],[fact_944_succ__def]) ).
fof(i_0_2528,plain,
! [X4254] : hAPP(nat,nat,suc,X4254) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4254),one_one(nat)),
inference(variable_rename,[status(thm)],[fact_273_Suc__eq__plus1]) ).
fof(i_0_2529,plain,
! [X4652] : hAPP(nat,fun(nat,bool),ord_less(nat),X4652) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X4652)),
inference(variable_rename,[status(thm)],[fact_408_less__eq__Suc__le__raw]) ).
fof(i_0_2530,plain,
! [X6203,X6204] :
( ~ ordere142940540dd_abs(X6203)
| hAPP(X6203,X6203,abs_abs(X6203),hAPP(X6203,X6203,abs_abs(X6203),X6204)) = hAPP(X6203,X6203,abs_abs(X6203),X6204) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_925_abs__idempotent])])]) ).
cnf(i_0_2531,plain,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
inference(split_conjunct,[status(thm)],[tsy_v_P_res]) ).
fof(i_0_2532,plain,
! [X6211,X6212] :
( ~ linordered_idom(X6211)
| hAPP(X6211,X6211,abs_abs(X6211),hAPP(nat,X6211,semiring_1_of_nat(X6211),X6212)) = hAPP(nat,X6211,semiring_1_of_nat(X6211),X6212) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_932_abs__of__nat])])]) ).
cnf(i_0_2533,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1480]) ).
cnf(i_0_2534,plain,
ti(fun(fun(X1,fun(X2,X2)),bool),finite_comp_fun_idem(X1,X2)) = finite_comp_fun_idem(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1481]) ).
fof(i_0_2535,plain,
! [X5968,X5969] :
( ~ number_semiring(X5968)
| hAPP(int,X5968,number_number_of(X5968),hAPP(nat,int,semiring_1_of_nat(int),X5969)) = hAPP(nat,X5968,semiring_1_of_nat(X5968),X5969) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_829_number__of__int])])]) ).
cnf(i_0_2536,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_1482]) ).
cnf(i_0_2537,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_1483]) ).
fof(i_0_2538,plain,
! [X6214] : hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),X6214)) = hAPP(nat,int,semiring_1_of_nat(int),X6214),
inference(variable_rename,[status(thm)],[fact_934_abs__int__eq]) ).
cnf(i_0_2539,plain,
ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
inference(split_conjunct,[status(thm)],[i_0_1484]) ).
cnf(i_0_2540,plain,
ti(fun(X1,fun(fun(X1,bool),X1)),partial_flat_lub(X1)) = partial_flat_lub(X1),
inference(split_conjunct,[status(thm)],[i_0_1485]) ).
cnf(i_0_2541,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(split_conjunct,[status(thm)],[i_0_1486]) ).
fof(i_0_2542,plain,
! [X3752] : bot_bot(fun(X3752,bool)) = hAPP(fun(X3752,bool),fun(X3752,bool),collect(X3752),hAPP(bool,fun(X3752,bool),combk(bool,X3752),fFalse)),
inference(variable_rename,[status(thm)],[fact_135_empty__def]) ).
cnf(i_0_2543,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
| ti(fun(X1,bool),X2) != bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1446]) ).
fof(i_0_2544,plain,
! [X4980,X4981] :
( hBOOL(hAPP(fun(X4980,bool),bool,finite_finite(X4980),X4981))
| hAPP(fun(X4980,bool),nat,finite_card(X4980),X4981) = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1487])]) ).
fof(i_0_2545,plain,
! [X5374,X5375] :
( ~ comm_semiring_1(X5374)
| hAPP(X5374,X5374,hAPP(X5374,fun(X5374,X5374),times_times(X5374),zero_zero(X5374)),X5375) = zero_zero(X5374) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])])]) ).
fof(i_0_2546,plain,
! [X5168,X5169] :
( ~ mult_zero(X5168)
| hAPP(X5168,X5168,hAPP(X5168,fun(X5168,X5168),times_times(X5168),zero_zero(X5168)),X5169) = zero_zero(X5168) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_579_mult__zero__left])])]) ).
fof(i_0_2547,plain,
! [X5376,X5377] :
( ~ comm_semiring_1(X5376)
| hAPP(X5376,X5376,hAPP(X5376,fun(X5376,X5376),times_times(X5376),X5377),zero_zero(X5376)) = zero_zero(X5376) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])]) ).
fof(i_0_2548,plain,
! [X5170,X5171] :
( ~ mult_zero(X5170)
| hAPP(X5170,X5170,hAPP(X5170,fun(X5170,X5170),times_times(X5170),X5171),zero_zero(X5170)) = zero_zero(X5170) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_580_mult__zero__right])])]) ).
fof(i_0_2549,plain,
! [X4890,X4891] :
( ~ group_add(X4890)
| hAPP(X4890,X4890,hAPP(X4890,fun(X4890,X4890),minus_minus(X4890),X4891),X4891) = zero_zero(X4890) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_472_diff__self])])]) ).
fof(i_0_2550,plain,
! [X5267,X5268,X5269] :
( ( hAPP(int,X5267,number_number_of(X5267),X5268) != hAPP(int,X5267,number_number_of(X5267),X5269)
| X5268 = X5269
| ~ number_ring(X5267)
| ~ ring_char_0(X5267) )
& ( X5268 != X5269
| hAPP(int,X5267,number_number_of(X5267),X5268) = hAPP(int,X5267,number_number_of(X5267),X5269)
| ~ number_ring(X5267)
| ~ ring_char_0(X5267) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_619_eq__number__of])])])]) ).
fof(i_0_2551,plain,
! [X5983,X5984,X5985] :
( ( hAPP(nat,X5983,semiring_1_of_nat(X5983),X5984) != hAPP(nat,X5983,semiring_1_of_nat(X5983),X5985)
| X5984 = X5985
| ~ semiring_char_0(X5983) )
& ( X5984 != X5985
| hAPP(nat,X5983,semiring_1_of_nat(X5983),X5984) = hAPP(nat,X5983,semiring_1_of_nat(X5983),X5985)
| ~ semiring_char_0(X5983) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_841_of__nat__eq__iff])])])]) ).
fof(i_0_2552,plain,
! [X5181] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X5181) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_584_mult__0]) ).
fof(i_0_2553,plain,
! [X4871] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X4871) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_462_diff__0__eq__0]) ).
fof(i_0_2554,plain,
! [X5715] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),X5715) = X5715,
inference(variable_rename,[status(thm)],[fact_746_zmult__1]) ).
fof(i_0_2555,plain,
! [X5747] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),X5747) = X5747,
inference(variable_rename,[status(thm)],[fact_761_zadd__0]) ).
fof(i_0_2556,plain,
! [X5252] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X5252) = X5252,
inference(variable_rename,[status(thm)],[fact_613_nat__mult__1]) ).
fof(i_0_2557,plain,
! [X4901] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X4901) = X4901,
inference(variable_rename,[status(thm)],[fact_479_plus__nat_Oadd__0]) ).
cnf(i_0_2558,hypothesis,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1488]) ).
fof(i_0_2559,plain,
! [X5182] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5182),zero_zero(nat)) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_585_mult__0__right]) ).
fof(i_0_2560,plain,
! [X5716] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X5716),one_one(int)) = X5716,
inference(variable_rename,[status(thm)],[fact_747_zmult__1__right]) ).
fof(i_0_2561,plain,
! [X5746] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X5746),zero_zero(int)) = X5746,
inference(variable_rename,[status(thm)],[fact_760_zadd__0__right]) ).
fof(i_0_2562,plain,
! [X5249] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5249),one_one(nat)) = X5249,
inference(variable_rename,[status(thm)],[fact_611_nat__mult__1__right]) ).
fof(i_0_2563,plain,
! [X4900] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4900),zero_zero(nat)) = X4900,
inference(variable_rename,[status(thm)],[fact_478_Nat_Oadd__0__right]) ).
fof(i_0_2564,plain,
! [X4870] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4870),zero_zero(nat)) = X4870,
inference(variable_rename,[status(thm)],[fact_461_minus__nat_Odiff__0]) ).
fof(i_0_2565,plain,
! [X4869] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4869),X4869) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_460_diff__self__eq__0]) ).
fof(i_0_2566,plain,
! [X6094,X6095] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X6094) != hAPP(nat,int,semiring_1_of_nat(int),X6095)
| X6094 = X6095 )
& ( X6094 != X6095
| hAPP(nat,int,semiring_1_of_nat(int),X6094) = hAPP(nat,int,semiring_1_of_nat(int),X6095) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_890_transfer__int__nat__relations_I1_J])]) ).
fof(i_0_2567,plain,
! [X6081,X6082] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X6081) != hAPP(nat,int,semiring_1_of_nat(int),X6082)
| X6081 = X6082 )
& ( X6081 != X6082
| hAPP(nat,int,semiring_1_of_nat(int),X6081) = hAPP(nat,int,semiring_1_of_nat(int),X6082) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_883_int__int__eq])]) ).
fof(i_0_2568,plain,
! [X6278] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X6278),pls) = X6278,
inference(variable_rename,[status(thm)],[fact_982_add__Pls__right]) ).
fof(i_0_2569,plain,
! [X6276] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X6276),pls) = X6276,
inference(variable_rename,[status(thm)],[fact_980_diff__bin__simps_I1_J]) ).
fof(i_0_2570,plain,
! [X6277] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X6277) = X6277,
inference(variable_rename,[status(thm)],[fact_981_add__Pls]) ).
fof(i_0_2571,plain,
! [X6279] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X6279) = pls,
inference(variable_rename,[status(thm)],[fact_983_mult__Pls]) ).
fof(i_0_2572,plain,
~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
inference(fof_simplification,[status(thm)],[fact_928_not__neg__0]) ).
fof(i_0_2573,plain,
~ hBOOL(hAPP(int,bool,nat_neg,one_one(int))),
inference(fof_simplification,[status(thm)],[fact_926_not__neg__1]) ).
fof(i_0_2574,plain,
! [X6315] :
( ~ hBOOL(hAPP(bool,bool,fNot,X6315))
| ~ hBOOL(X6315) ),
inference(variable_rename,[status(thm)],[i_0_1489]) ).
fof(i_0_2575,plain,
! [X6272,X6273] :
( ( hAPP(int,int,bit1,X6272) != hAPP(int,int,bit1,X6273)
| X6272 = X6273 )
& ( X6272 != X6273
| hAPP(int,int,bit1,X6272) = hAPP(int,int,bit1,X6273) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_977_rel__simps_I51_J])]) ).
fof(i_0_2576,plain,
! [X3318,X3319] :
( ( hAPP(nat,nat,suc,X3318) != hAPP(nat,nat,suc,X3319)
| X3318 = X3319 )
& ( X3318 != X3319
| hAPP(nat,nat,suc,X3318) = hAPP(nat,nat,suc,X3319) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_nat_Oinject])]) ).
fof(i_0_2577,plain,
! [X3316,X3317] :
( hAPP(nat,nat,suc,X3316) != hAPP(nat,nat,suc,X3317)
| X3316 = X3317 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_Suc__inject])]) ).
fof(i_0_2578,plain,
! [X6255] :
( ~ number_semiring(X6255)
| hAPP(int,X6255,number_number_of(X6255),hAPP(int,int,bit1,pls)) = one_one(X6255) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_962_semiring__numeral__1__eq__1])]) ).
fof(i_0_2579,plain,
! [X6254] :
( ~ number_ring(X6254)
| hAPP(int,X6254,number_number_of(X6254),hAPP(int,int,bit1,pls)) = one_one(X6254) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_961_numeral__1__eq__1])]) ).
fof(i_0_2580,plain,
! [X6253] :
( ~ number_ring(X6253)
| one_one(X6253) = hAPP(int,X6253,number_number_of(X6253),hAPP(int,int,bit1,pls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_957_semiring__norm_I110_J])]) ).
cnf(i_0_2581,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(split_conjunct,[status(thm)],[i_0_1490]) ).
fof(i_0_2582,plain,
! [X5191] :
( ~ ab_sem1668676832m_mult(X5191)
| hBOOL(hAPP(fun(X5191,fun(X5191,X5191)),bool,finite_comp_fun_idem(X5191,X5191),times_times(X5191))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_589_comp__fun__idem])]) ).
cnf(i_0_2583,plain,
( hAPP(X1,X1,abs_abs(X1),X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1491]) ).
cnf(i_0_2584,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,abs_abs(X1),X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1491]) ).
fof(i_0_2585,plain,
! [X3711] : hBOOL(hAPP(fun(X3711,bool),bool,finite_finite(X3711),bot_bot(fun(X3711,bool)))),
inference(variable_rename,[status(thm)],[fact_123_finite_OemptyI]) ).
cnf(i_0_2586,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[i_0_1492]) ).
cnf(i_0_2587,plain,
ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1493]) ).
cnf(i_0_2588,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ mult_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1494]) ).
cnf(i_0_2589,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ no_zero_divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1495]) ).
cnf(i_0_2590,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1496]) ).
cnf(i_0_2591,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1497]) ).
cnf(i_0_2592,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ ab_semigroup_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1498]) ).
cnf(i_0_2593,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ ab_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1499]) ).
cnf(i_0_2594,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1500]) ).
cnf(i_0_2595,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]) ).
cnf(i_0_2596,plain,
( ti(fun(X1,fun(X1,X1)),minus_minus(X1)) = minus_minus(X1)
| ~ minus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1502]) ).
fof(i_0_2597,plain,
! [X3314,X3315] :
( ~ finite_finite_1(X3314)
| hBOOL(hAPP(fun(X3314,bool),bool,finite_finite(X3314),X3315)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_finite])])]) ).
fof(i_0_2598,plain,
! [X3312,X3313] :
( ~ finite_finite_1(X3312)
| hBOOL(hAPP(fun(X3312,bool),bool,finite_finite(X3312),X3313)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_finite__code])])]) ).
cnf(i_0_2599,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1503]) ).
cnf(i_0_2600,plain,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1504]) ).
cnf(i_0_2601,plain,
ti(fun(fun(X1,bool),X1),the_elem(X1)) = the_elem(X1),
inference(split_conjunct,[status(thm)],[i_0_1505]) ).
cnf(i_0_2602,plain,
ti(fun(fun(X1,bool),X1),the(X1)) = the(X1),
inference(split_conjunct,[status(thm)],[i_0_1506]) ).
cnf(i_0_2603,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(split_conjunct,[status(thm)],[i_0_1507]) ).
cnf(i_0_2604,plain,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
inference(split_conjunct,[status(thm)],[i_0_1508]) ).
cnf(i_0_2605,plain,
ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
inference(split_conjunct,[status(thm)],[i_0_1509]) ).
cnf(i_0_2606,hypothesis,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1488]) ).
cnf(i_0_2607,plain,
ti(fun(int,fun(int,int)),nat_tsub) = nat_tsub,
inference(split_conjunct,[status(thm)],[tsy_c_Nat__Transfer_Otsub_res]) ).
cnf(i_0_2608,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(split_conjunct,[status(thm)],[tsy_c_fimplies_res]) ).
cnf(i_0_2609,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(split_conjunct,[status(thm)],[tsy_c_fdisj_res]) ).
cnf(i_0_2610,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(split_conjunct,[status(thm)],[tsy_c_fconj_res]) ).
cnf(i_0_2611,plain,
( ti(bool,X1) = fTrue
| ti(bool,X1) = fFalse ),
inference(split_conjunct,[status(thm)],[i_0_1510]) ).
cnf(i_0_2612,plain,
( ti(bool,X1) = fTrue
| ti(bool,X1) = fFalse ),
inference(split_conjunct,[status(thm)],[i_0_1511]) ).
fof(i_0_2613,plain,
! [X6316] :
( hBOOL(X6316)
| hBOOL(hAPP(bool,bool,fNot,X6316)) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
fof(i_0_2614,plain,
! [X5980] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X5980) != zero_zero(int)
| X5980 = zero_zero(nat) )
& ( X5980 != zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),X5980) = zero_zero(int) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_839_int__eq__0__conv])]) ).
fof(i_0_2615,plain,
! [X4911] : hAPP(nat,nat,suc,X4911) != zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_488_Suc__not__Zero]) ).
fof(i_0_2616,plain,
! [X4910] : hAPP(nat,nat,suc,X4910) != zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_487_nat_Osimps_I3_J]) ).
fof(i_0_2617,plain,
! [X4908] : hAPP(nat,nat,suc,X4908) != zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_485_Suc__neq__Zero]) ).
fof(i_0_2618,plain,
! [X4913] : zero_zero(nat) != hAPP(nat,nat,suc,X4913),
inference(variable_rename,[status(thm)],[fact_490_Zero__not__Suc]) ).
fof(i_0_2619,plain,
! [X4912] : zero_zero(nat) != hAPP(nat,nat,suc,X4912),
inference(variable_rename,[status(thm)],[fact_489_nat_Osimps_I2_J]) ).
fof(i_0_2620,plain,
! [X4909] : zero_zero(nat) != hAPP(nat,nat,suc,X4909),
inference(variable_rename,[status(thm)],[fact_486_Zero__neq__Suc]) ).
fof(i_0_2621,plain,
! [X3320] : hAPP(nat,nat,suc,X3320) != X3320,
inference(variable_rename,[status(thm)],[fact_18_Suc__n__not__n]) ).
fof(i_0_2622,plain,
! [X3321] : X3321 != hAPP(nat,nat,suc,X3321),
inference(variable_rename,[status(thm)],[fact_19_n__not__Suc__n]) ).
fof(i_0_2623,plain,
! [X6274] : hAPP(int,int,bit1,X6274) != pls,
inference(variable_rename,[status(thm)],[fact_978_rel__simps_I46_J]) ).
fof(i_0_2624,plain,
! [X6275] : pls != hAPP(int,int,bit1,X6275),
inference(variable_rename,[status(thm)],[fact_979_rel__simps_I39_J]) ).
cnf(i_0_2625,plain,
ti(fun(option(com),com),the_1(com)) = the_1(com),
inference(split_conjunct,[status(thm)],[tsy_c_Option_Othe_res]) ).
cnf(i_0_2626,plain,
( ti(fun(X1,X1),abs_abs(X1)) = abs_abs(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1512]) ).
cnf(i_0_2627,plain,
ti(fun(pname,option(com)),body) = body,
inference(split_conjunct,[status(thm)],[tsy_c_Com_Obody_res]) ).
cnf(i_0_2628,plain,
ti(fun(X1,X1),combi(X1)) = combi(X1),
inference(split_conjunct,[status(thm)],[i_0_1513]) ).
cnf(i_0_2629,plain,
( ti(fun(int,X1),number_number_of(X1)) = number_number_of(X1)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1514]) ).
cnf(i_0_2630,plain,
( ti(fun(nat,X1),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1515]) ).
cnf(i_0_2631,plain,
( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
| ~ ring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1516]) ).
cnf(i_0_2632,hypothesis,
ti(fun(x_a,bool),g) = g,
inference(split_conjunct,[status(thm)],[tsy_v_G_res]) ).
cnf(i_0_2633,plain,
ti(fun(int,int),succ) = succ,
inference(split_conjunct,[status(thm)],[tsy_c_Int_Osucc_res]) ).
cnf(i_0_2634,plain,
ti(fun(int,int),bit1) = bit1,
inference(split_conjunct,[status(thm)],[tsy_c_Int_OBit1_res]) ).
cnf(i_0_2635,plain,
ti(fun(int,bool),nat_neg) = nat_neg,
inference(split_conjunct,[status(thm)],[tsy_c_Nat__Numeral_Oneg_res]) ).
cnf(i_0_2636,hypothesis,
ti(fun(nat,nat),suc) = suc,
inference(split_conjunct,[status(thm)],[tsy_c_Nat_OSuc_res]) ).
cnf(i_0_2637,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(split_conjunct,[status(thm)],[tsy_c_fNot_res]) ).
cnf(i_0_2638,plain,
ti(fun(com,x_a),mgt) = mgt,
inference(split_conjunct,[status(thm)],[tsy_v_mgt_res]) ).
cnf(i_0_2639,plain,
ti(fun(com,bool),wt) = wt,
inference(split_conjunct,[status(thm)],[tsy_v_wt_res]) ).
cnf(i_0_2640,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
inference(split_conjunct,[status(thm)],[tsy_v_mgt__call_res]) ).
cnf(i_0_2641,hypothesis,
ti(fun(pname,bool),u) = u,
inference(split_conjunct,[status(thm)],[tsy_v_U_res]) ).
fof(i_0_2642,plain,
! [X4979] : hAPP(fun(X4979,bool),nat,finite_card(X4979),bot_bot(fun(X4979,bool))) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_516_card_Oempty]) ).
fof(i_0_2643,plain,
! [X3753,X3754,X3755] :
( ~ bot(X3754)
| hAPP(X3753,X3754,bot_bot(fun(X3753,X3754)),X3755) = bot_bot(X3754) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_bot__fun__def])])]) ).
fof(i_0_2644,plain,
! [X3749,X3750,X3751] :
( ~ bot(X3750)
| hAPP(X3749,X3750,bot_bot(fun(X3749,X3750)),X3751) = bot_bot(X3750) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_bot__apply])])]) ).
fof(i_0_2645,plain,
! [X6208] :
( ~ ordere142940540dd_abs(X6208)
| hAPP(X6208,X6208,abs_abs(X6208),zero_zero(X6208)) = zero_zero(X6208) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_930_abs__zero])]) ).
fof(i_0_2646,plain,
! [X6205] :
( ~ linordered_idom(X6205)
| hAPP(X6205,X6205,abs_abs(X6205),one_one(X6205)) = one_one(X6205) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_927_abs__one])]) ).
cnf(i_0_2647,plain,
( ti(X1,bot_bot(X1)) = bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1517]) ).
cnf(i_0_2648,plain,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1518]) ).
cnf(i_0_2649,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1519]) ).
fof(i_0_2650,plain,
! [X5978] :
( ~ semiring_1(X5978)
| hAPP(nat,X5978,semiring_1_of_nat(X5978),zero_zero(nat)) = zero_zero(X5978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_835_of__nat__0])]) ).
fof(i_0_2651,plain,
! [X5979] :
( ~ semiring_1(X5979)
| hAPP(nat,X5979,semiring_1_of_nat(X5979),one_one(nat)) = one_one(X5979) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_836_of__nat__1])]) ).
cnf(i_0_2652,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[i_0_1520]) ).
fof(i_0_2653,plain,
! [X6265] :
( ~ number_semiring(X6265)
| hAPP(int,X6265,number_number_of(X6265),pls) = zero_zero(X6265) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_969_semiring__numeral__0__eq__0])]) ).
fof(i_0_2654,plain,
! [X6266] :
( ~ number_ring(X6266)
| hAPP(int,X6266,number_number_of(X6266),pls) = zero_zero(X6266) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_970_number__of__Pls])]) ).
fof(i_0_2655,plain,
! [X6267] :
( ~ number_ring(X6267)
| zero_zero(X6267) = hAPP(int,X6267,number_number_of(X6267),pls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_971_semiring__norm_I112_J])]) ).
fof(i_0_2656,plain,
! [X5100] :
( X5100 = zero_zero(nat)
| X5100 = hAPP(nat,nat,suc,esk97_1(X5100)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_559_not0__implies__Suc])])]) ).
fof(i_0_2657,plain,
! [X5095] :
( X5095 = zero_zero(nat)
| X5095 = hAPP(nat,nat,suc,esk95_1(X5095)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_557_nat_Oexhaust])])]) ).
fof(i_0_2658,plain,
! [X5855] : hAPP(int,int,number_number_of(int),X5855) = X5855,
inference(variable_rename,[status(thm)],[fact_798_number__of__is__id]) ).
cnf(i_0_2659,plain,
ti(int,pls) = pls,
inference(split_conjunct,[status(thm)],[tsy_c_Int_OPls_res]) ).
cnf(i_0_2660,hypothesis,
ti(nat,na) = na,
inference(split_conjunct,[status(thm)],[tsy_v_na_res]) ).
cnf(i_0_2661,plain,
ti(bool,fTrue) = fTrue,
inference(split_conjunct,[status(thm)],[tsy_c_fTrue_res]) ).
cnf(i_0_2662,plain,
ti(bool,fFalse) = fFalse,
inference(split_conjunct,[status(thm)],[tsy_c_fFalse_res]) ).
cnf(i_0_2663,hypothesis,
ti(pname,pn) = pn,
inference(split_conjunct,[status(thm)],[tsy_v_pn_res]) ).
fof(i_0_2664,plain,
! [X6304,X6305] :
( ~ finite_finite_1(X6305)
| ~ finite_finite_1(X6304)
| finite_finite_1(sum_sum(X6304,X6305)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum___Finite__Set_Ofinite])]) ).
fof(i_0_2665,plain,
! [X6294,X6295] :
( ~ finite_finite_1(X6295)
| ~ finite_finite_1(X6294)
| finite_finite_1(fun(X6294,X6295)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite])]) ).
fof(i_0_2666,plain,
! [X6292,X6293] :
( ~ preorder(X6293)
| preorder(fun(X6292,X6293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Opreorder])]) ).
fof(i_0_2667,plain,
! [X6296,X6297] :
( ~ order(X6297)
| order(fun(X6296,X6297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oorder])]) ).
fof(i_0_2668,plain,
! [X6298,X6299] :
( ~ ord(X6299)
| ord(fun(X6298,X6299)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oord])]) ).
fof(i_0_2669,plain,
! [X6300,X6301] :
( ~ bot(X6301)
| bot(fun(X6300,X6301)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Obot])]) ).
fof(i_0_2670,plain,
! [X6302,X6303] :
( ~ minus(X6303)
| minus(fun(X6302,X6303)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Groups_Ominus])]) ).
fof(i_0_2671,plain,
! [X4873] :
( ~ zero_neq_one(X4873)
| zero_zero(X4873) != one_one(X4873) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_464_zero__neq__one])]) ).
fof(i_0_2672,plain,
! [X4872] :
( ~ zero_neq_one(X4872)
| one_one(X4872) != zero_zero(X4872) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_463_one__neq__zero])]) ).
fof(i_0_2673,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
cnf(i_0_2674,plain,
( hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9) = hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10)
| hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| hAPP(X2,X1,X3,hAPP(X1,X2,X8,esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X1,X1,combi(X1),esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X2,combi(X2),esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| ~ comm_monoid_mult(X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X10))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X8,esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X10))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1521,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2675,plain,
( hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9) = hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk141_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10)),X9))
| hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X2,combi(X2),esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
| ~ comm_monoid_mult(X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X10))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk142_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9)) ),
inference(rw,[status(thm)],[i_0_1523,c_0_1522]),
[final] ).
cnf(i_0_2676,plain,
( hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X6),X4),X10) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X5),X4),X9)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk142_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X10))
| hAPP(X1,X2,X7,hAPP(X2,X1,X8,esk141_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))) != hAPP(X2,X2,combi(X2),esk141_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))
| ~ comm_monoid_mult(X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X8,esk141_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))),X10)) ),
inference(rw,[status(thm)],[i_0_1524,c_0_1522]),
[final] ).
cnf(i_0_2677,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk142_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X10))
| hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X6),X4),X10) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X5),X4),X9)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk141_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X9))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
| ~ comm_monoid_mult(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1215]),
[final] ).
cnf(i_0_2678,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X4),X7),X6)),hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X5),X7),X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk140_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X3,X1,X5,esk140_7(X3,X1,X4,X5,X6,X2,X7))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk136_7(X3,X1,X4,X5,X6,X2,X7)),esk137_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk138_7(X3,X1,X4,X5,X6,X2,X7)),esk139_7(X3,X1,X4,X5,X6,X2,X7))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X7),X7))
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2679,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk140_7(X1,X2,X3,X4,X5,X6,X7)),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X7),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X7),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),esk136_7(X1,X2,X3,X4,X5,X6,X7)),esk137_7(X1,X2,X3,X4,X5,X6,X7))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),esk138_7(X1,X2,X3,X4,X5,X6,X7)),esk139_7(X1,X2,X3,X4,X5,X6,X7))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X7),X7))
| ~ comm_monoid_mult(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2680,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X4),X7),X6)),hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X5),X7),X6)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk137_7(X3,X1,X4,X5,X6,X2,X7)),esk139_7(X3,X1,X4,X5,X6,X2,X7)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk140_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X3,X1,X5,esk140_7(X3,X1,X4,X5,X6,X2,X7))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X7),X7))
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2681,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X4),X7),X6)),hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X5),X7),X6)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk136_7(X3,X1,X4,X5,X6,X2,X7)),esk138_7(X3,X1,X4,X5,X6,X2,X7)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk140_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X3,X1,X5,esk140_7(X3,X1,X4,X5,X6,X2,X7))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X7),X7))
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2682,plain,
( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_2683,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk140_7(X1,X2,X3,X4,X5,X6,X7)),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X7),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X7),X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk137_7(X1,X2,X3,X4,X5,X6,X7)),esk139_7(X1,X2,X3,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X7),X7))
| ~ comm_monoid_mult(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2684,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk140_7(X1,X2,X3,X4,X5,X6,X7)),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X7),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X7),X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk136_7(X1,X2,X3,X4,X5,X6,X7)),esk138_7(X1,X2,X3,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X7),X7))
| ~ comm_monoid_mult(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2685,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X3))),one_one(int))),X1))),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1527]),
[final] ).
cnf(i_0_2686,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_1528]),
[final] ).
cnf(i_0_2687,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1))
| hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) ),
inference(split_conjunct,[status(thm)],[i_0_1529]),
[final] ).
cnf(i_0_2688,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk148_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,X2,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X2,X4)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk147_4(X1,X2,X3,X4)),one_one(nat)))),hAPP(nat,int,X2,esk147_4(X1,X2,X3,X4))))),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2689,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk148_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X3,X4)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X3,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk147_4(X2,X3,X4,X1)),one_one(nat)))),hAPP(nat,int,X3,esk147_4(X2,X3,X4,X1))))),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2690,plain,
( hAPP(nat,int,X1,esk148_4(X2,X1,X3,X4)) = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X1,X4)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk147_4(X2,X1,X3,X4)),one_one(nat)))),hAPP(nat,int,X1,esk147_4(X2,X1,X3,X4))))),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2691,plain,
( hAPP(fun(X1,bool),X2,X7,X3) = hAPP(X2,X2,combi(X2),X5)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk34_7(X1,X2,X3,X4,X5,X6,X7)),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X4),X5),X6),X7)) ),
inference(rw,[status(thm)],[i_0_1531,c_0_1522]),
[final] ).
cnf(i_0_2692,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk146_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,X2,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X2,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk145_3(X1,X2,X3)),one_one(nat)))),hAPP(nat,int,X2,esk145_3(X1,X2,X3))))),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_2693,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk144_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,X2,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X2,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk143_3(X1,X2,X3)),one_one(nat)))),hAPP(nat,int,X2,esk143_3(X1,X2,X3))))),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1533]),
[final] ).
cnf(i_0_2694,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool)))))),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1534]),
[final] ).
cnf(i_0_2695,plain,
( hAPP(nat,int,X1,esk146_3(X2,X1,X3)) = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X1,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk145_3(X2,X1,X3)),one_one(nat)))),hAPP(nat,int,X1,esk145_3(X2,X1,X3))))),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_2696,plain,
( hAPP(nat,int,X1,esk144_3(X2,X1,X3)) = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X1,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk143_3(X2,X1,X3)),one_one(nat)))),hAPP(nat,int,X1,esk143_3(X2,X1,X3))))),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1533]),
[final] ).
cnf(i_0_2697,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X3),X2))),one_one(int))),X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_2698,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),X4)),X5)),X6))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1536]),
[final] ).
cnf(i_0_2699,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),X4)),X5)),X6))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1537]),
[final] ).
cnf(i_0_2700,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3)),X4)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_2701,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3)),X4)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1539]),
[final] ).
cnf(i_0_2702,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk65_6(X2,X1,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk64_6(X2,X1,X4,X3,X5,X6))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X5)),X6))
| ~ order(X1)
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1540]),
[final] ).
cnf(i_0_2703,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk63_6(X2,X1,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk62_6(X2,X1,X4,X3,X5,X6))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X5)),X6))
| ~ order(X1)
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_2704,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X5)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk76_6(X2,X1,X3,X4,X5,X6))),hAPP(X2,X1,X3,esk77_6(X2,X1,X3,X4,X5,X6))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X6)),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ order(X1)
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1542]),
[final] ).
cnf(i_0_2705,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X5)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk78_6(X2,X1,X3,X4,X5,X6))),hAPP(X2,X1,X3,esk79_6(X2,X1,X3,X4,X5,X6))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X6)),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ order(X1)
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1543]),
[final] ).
cnf(i_0_2706,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),hAPP(X2,X1,X3,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk75_6(X1,X2,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk74_6(X1,X2,X4,X3,X5,X6))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),hAPP(X2,X1,X3,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ order(X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1544]),
[final] ).
cnf(i_0_2707,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),hAPP(X2,X1,X3,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk73_6(X1,X2,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk72_6(X1,X2,X4,X3,X5,X6))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),hAPP(X2,X1,X3,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ order(X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2708,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk68_6(X1,X2,X4,X5,X3,X6))),hAPP(X2,X1,X3,esk69_6(X1,X2,X4,X5,X3,X6))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X6),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X3,X6)))
| ~ order(X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_2709,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk66_6(X1,X2,X4,X5,X3,X6))),hAPP(X2,X1,X3,esk67_6(X1,X2,X4,X5,X3,X6))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X6),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X3,X6)))
| ~ order(X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1547]),
[final] ).
cnf(i_0_2710,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X5)),X3)),X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1536]),
[final] ).
cnf(i_0_2711,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X5)),X3)),X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1537]),
[final] ).
cnf(i_0_2712,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X4)),X2)),X3)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X4),X2)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_2713,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X4)),X2)),X3)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X4),X2)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1539]),
[final] ).
cnf(i_0_2714,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X4)),X5)),X6)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2715,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X4)),X5)),X6)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2716,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X4)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X4)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)),X4)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2717,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X4)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X4)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)),X4)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2718,plain,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1))
| hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_1552]),
[final] ).
cnf(i_0_2719,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X5),X2)),X3)),X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2720,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X5),X2)),X3)),X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2721,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4),X1)),X2)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X4),X2)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2722,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4),X1)),X2)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X4),X2)),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2723,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X4))),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X5)))))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1553]),
[final] ).
cnf(i_0_2724,plain,
( hAPP(fun(X1,bool),X2,X7,X4) = hAPP(X2,X2,combi(X2),X6)
| hAPP(X1,X2,X3,esk34_7(X1,X2,X4,X5,X6,X3,X7)) != hAPP(X2,X2,combi(X2),X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X5),X6),X3),X7)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1554,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2725,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X4)),X5)),one_one(X1)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2726,plain,
( hAPP(X2,X2,combi(X2),X3) = hAPP(fun(X2,bool),X2,the(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X3)))),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X1))),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[i_0_1556,c_0_1522]),
[final] ).
cnf(i_0_2727,plain,
( hAPP(X2,X2,combi(X2),X3) = hAPP(fun(X2,bool),X2,the(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4)))),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X1))),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X3))))
| hBOOL(X1) ),
inference(rw,[status(thm)],[i_0_1557,c_0_1522]),
[final] ).
cnf(i_0_2728,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_1558]),
[final] ).
cnf(i_0_2729,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_1558]),
[final] ).
cnf(i_0_2730,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),X5)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X3)),X4)),X5)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1559]),
[final] ).
cnf(i_0_2731,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X2),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,X1)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,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,X1)),X2)),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(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X1)))),bot_bot(fun(x_a,bool))))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2732,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk76_6(X1,X2,X3,X4,X5,X6)),esk77_6(X1,X2,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X5)),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ order(X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1542]),
[final] ).
cnf(i_0_2733,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk78_6(X1,X2,X3,X4,X5,X6)),esk79_6(X1,X2,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X5)),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X6)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ order(X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1543]),
[final] ).
cnf(i_0_2734,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk65_6(X1,X2,X3,X4,X5,X6)),esk64_6(X1,X2,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X4,X3)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X4,X5)),X6))
| ~ order(X2)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1540]),
[final] ).
cnf(i_0_2735,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk63_6(X1,X2,X3,X4,X5,X6)),esk62_6(X1,X2,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X4,X3)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X4,X5)),X6))
| ~ order(X2)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_2736,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X4)),X5)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X3),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_2737,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X4),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X4)),X5)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X5))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_2738,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_2739,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk75_6(X2,X1,X3,X4,X5,X6)),esk74_6(X2,X1,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),hAPP(X1,X2,X4,X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),hAPP(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ order(X1)
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1544]),
[final] ).
cnf(i_0_2740,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk73_6(X2,X1,X3,X4,X5,X6)),esk72_6(X2,X1,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),hAPP(X1,X2,X4,X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),hAPP(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ order(X1)
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2741,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk68_6(X2,X1,X3,X4,X5,X6)),esk69_6(X2,X1,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),hAPP(X1,X2,X5,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X3))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),hAPP(X1,X2,X5,X6)))
| ~ order(X1)
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_2742,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk66_6(X2,X1,X3,X4,X5,X6)),esk67_6(X2,X1,X3,X4,X5,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),hAPP(X1,X2,X5,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X3))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X4),hAPP(X1,X2,X5,X6)))
| ~ order(X1)
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1547]),
[final] ).
cnf(i_0_2743,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X4) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(fun(X1,bool),X1,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,esk32_4(X1,X4,X2,X3)),esk33_4(X1,X4,X2,X3))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk32_4(X1,X4,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk33_4(X1,X4,X2,X3)),bot_bot(fun(X1,bool)))))) ),
inference(rw,[status(thm)],[i_0_1564,c_0_1522]),
[final] ).
cnf(i_0_2744,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5))),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X4),X5)))),
inference(split_conjunct,[status(thm)],[i_0_1565]),
[final] ).
cnf(i_0_2745,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_1566]),
[final] ).
cnf(i_0_2746,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),X2))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X4),X5)),X6)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X4),X5)),X6)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X3),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X6))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1567]),
[final] ).
cnf(i_0_2747,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(rw,[status(thm)],[i_0_1568,c_0_1522]),
[final] ).
cnf(i_0_2748,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))),zero_zero(X1))) ),
inference(rw,[status(thm)],[i_0_1569,c_0_1522]),
[final] ).
cnf(i_0_2749,plain,
( ~ linordered_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2750,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_1558]),
[final] ).
cnf(i_0_2751,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk104_6(X1,X2,X3,X4,X5,X6)),X6))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X3),X6) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X5),X3),X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X6))
| ~ ab_semigroup_mult(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1571]),
[final] ).
cnf(i_0_2752,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_1572]),
[final] ).
cnf(i_0_2753,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_1572]),
[final] ).
cnf(i_0_2754,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),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X2)),X1))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk29_2(X1,X2)),hAPP(nat,nat,X2,esk29_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1573]),
[final] ).
cnf(i_0_2755,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),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),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(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),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_1574]),
[final] ).
cnf(i_0_2756,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))))),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2757,plain,
( hAPP(fun(X1,bool),X2,X6,X7) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(X1,X2,X5,X8)),hAPP(fun(X1,bool),X2,X6,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X7),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X8),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X3),X4),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2758,plain,
( hAPP(fun(X1,bool),X2,X6,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X8),X7)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(X1,X2,X5,X8)),hAPP(fun(X1,bool),X2,X6,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X7),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X8),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X3),X4),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_2759,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5) = bot_bot(fun(X1,bool))
| hAPP(X1,X1,X4,hAPP(fun(X1,bool),X1,X3,X5)) = hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))
| hAPP(X1,X1,X4,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,esk39_5(X1,X5,X4,X2,X3)),esk40_5(X1,X5,X4,X2,X3))) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X1,X1,X4,esk39_5(X1,X5,X4,X2,X3))),hAPP(X1,X1,X4,esk40_5(X1,X5,X4,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X5))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1578,c_0_1522]),
[final] ).
cnf(i_0_2760,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),X5)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X3)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1579]),
[final] ).
cnf(i_0_2761,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))))),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_1580]),
[final] ).
cnf(i_0_2762,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_2763,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool))))),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2764,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X4))),X3))
| ~ linord1278240602ring_1(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),X6) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_2765,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X4))),X3))
| ~ linord626643107strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),X6) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_2766,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2767,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2768,plain,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),X6) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X5),X4),X6)
| hAPP(X1,X2,X3,esk104_6(X1,X2,X4,X3,X5,X6)) != hAPP(X1,X2,X5,esk104_6(X1,X2,X4,X3,X5,X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X6))
| ~ ab_semigroup_mult(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1571]),
[final] ).
cnf(i_0_2769,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(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool))))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2770,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2771,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))
| ~ 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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool))))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2772,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2773,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2774,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X1)),X1)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2775,plain,
hBOOL(hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),bool,finite_comp_fun_idem(X1,fun(X1,bool)),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X1,bool),fun(X1,bool))),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),X1),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool))),combc(fun(X1,bool),fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)))),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X1,fun(X1,bool))),combc(X1,fun(X1,bool),fun(X1,bool)),insert(X1)),bot_bot(fun(X1,bool)))))),
inference(split_conjunct,[status(thm)],[i_0_1589]),
[final] ).
cnf(i_0_2776,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk80_6(X2,X1,X3,X4,X5,X6)),X6))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X6) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1590,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2777,plain,
( hAPP(fun(X1,bool),X2,X6,X7) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X3),X5),X4),X7)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X3),X4),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1591]),
[final] ).
cnf(i_0_2778,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X5))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X4),X5)),X6)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X4),X5)),X6)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X6),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1592]),
[final] ).
cnf(i_0_2779,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X8),X7))
| hAPP(fun(X1,bool),X2,X6,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X8),X7)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(X1,X2,X5,X8)),hAPP(fun(X1,bool),X2,X6,X7))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X3),X4),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1593]),
[final] ).
cnf(i_0_2780,plain,
( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(fun(X1,bool),X2,X6,X8)),hAPP(fun(X1,bool),X2,X6,X7)) = hAPP(fun(X1,bool),X2,X6,X7)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1594]),
[final] ).
cnf(i_0_2781,plain,
( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(X1,X2,X5,X8)),hAPP(fun(X1,bool),X2,X6,X7)) = hAPP(fun(X1,bool),X2,X6,X7)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1595]),
[final] ).
cnf(i_0_2782,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3)))),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3))))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_2783,plain,
( hAPP(fun(X1,bool),X2,X6,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X8),X7)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(X1,X2,X5,X8)),hAPP(fun(X1,bool),X2,X6,X7))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_1597]),
[final] ).
cnf(i_0_2784,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1598,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2785,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,esk12_5(X1,X2,X3,X4,X5))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2786,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_1600]),
[final] ).
cnf(i_0_2787,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_1601]),
[final] ).
cnf(i_0_2788,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2789,plain,
( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,X7),X7) = hAPP(X2,X2,combi(X2),X7)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6)) ),
inference(rw,[status(thm)],[i_0_1602,c_0_1522]),
[final] ).
cnf(i_0_2790,plain,
( hAPP(fun(X1,bool),X2,X6,bot_bot(fun(X1,bool))) = hAPP(X2,X2,combi(X2),X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite1357897459simple(X2,X1),X3),X4),X5),X6)) ),
inference(rw,[status(thm)],[i_0_1603,c_0_1522]),
[final] ).
cnf(i_0_2791,plain,
( hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X1)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X2))
| ~ hBOOL(hAPP(int,bool,X1,esk107_2(X2,X1)))
| ~ hBOOL(hAPP(int,bool,X2,esk107_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2792,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk107_2(X1,X2)))
| hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X2)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2793,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X6)
| hAPP(X1,X2,X3,esk80_6(X2,X1,X3,X4,X5,X6)) != hAPP(X1,X2,X4,esk80_6(X2,X1,X3,X4,X5,X6))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X6) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1605,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2794,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2795,plain,
( hBOOL(hAPP(int,bool,X1,esk107_2(X2,X1)))
| hBOOL(hAPP(int,bool,X2,esk107_2(X2,X1)))
| hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X1)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2796,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_2797,plain,
( hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1606,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2798,plain,
( hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X3))),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1607]),
[final] ).
cnf(i_0_2799,plain,
( hBOOL(hAPP(X1,bool,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),fconj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X3))),X2)) = bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1607]),
[final] ).
cnf(i_0_2800,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2801,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_2802,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(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(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_1610]),
[final] ).
cnf(i_0_2803,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),X4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),X5)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3)),X4) != X5
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1611]),
[final] ).
cnf(i_0_2804,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X4)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X4)),X5)
| X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)),X4)),X5)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1612]),
[final] ).
cnf(i_0_2805,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X1)),X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2806,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),X6)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),X4)),X5) != hAPP(X1,X1,combi(X1),X6)
| ~ ring(X1) ),
inference(rw,[status(thm)],[i_0_1613,c_0_1522]),
[final] ).
cnf(i_0_2807,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)),X6) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)),X2)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X4)),X5)),X6)
| ~ ring(X1) ),
inference(rw,[status(thm)],[i_0_1614,c_0_1522]),
[final] ).
cnf(i_0_2808,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,abs_abs(X1),X2)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,abs_abs(X1),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1615]),
[final] ).
cnf(i_0_2809,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_1616]),
[final] ).
cnf(i_0_2810,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X3),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_2811,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),X6),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X2,X1,X5,X4)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),X6),X3))
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1618]),
[final] ).
cnf(i_0_2812,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),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1619]),
[final] ).
cnf(i_0_2813,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk48_3(X2,X3,X1))),hAPP(nat,nat,X1,esk49_3(X2,X3,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1620]),
[final] ).
cnf(i_0_2814,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk52_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk52_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2815,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X4)),X2)),X3) = X5
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X4),X2)),X5)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1611]),
[final] ).
cnf(i_0_2816,plain,
( X3 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X4),X1)),X2)),X5)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X4),X2)),X5)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1612]),
[final] ).
cnf(i_0_2817,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X5)),X3)),X4) = hAPP(X1,X1,combi(X1),X6)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)
| ~ ring(X1) ),
inference(rw,[status(thm)],[i_0_1622,c_0_1522]),
[final] ).
cnf(i_0_2818,plain,
( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X5),X2)),X3)),X6)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)),X6)
| ~ ring(X1) ),
inference(rw,[status(thm)],[i_0_1623,c_0_1522]),
[final] ).
cnf(i_0_2819,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_1624]),
[final] ).
cnf(i_0_2820,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk53_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk53_4(X1,X3,X4,X2)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1625]),
[final] ).
cnf(i_0_2821,plain,
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X4,X1)),hAPP(nat,X3,X4,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X4,esk52_4(X3,X1,X2,X4))),hAPP(nat,X3,X4,hAPP(nat,nat,suc,esk52_4(X3,X1,X2,X4)))))
| ~ order(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2822,plain,
( hBOOL(hAPP(int,bool,X1,esk123_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X1,esk122_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,esk122_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,X2,esk120_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2823,plain,
( hBOOL(hAPP(int,bool,X1,esk119_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X1,esk118_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,esk118_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,X2,esk116_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2824,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)),X5)
| ~ semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_2825,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),esk24_3(X1,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk23_3(X1,X2,X3)),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2826,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),esk118_4(X1,X2,X3,X4)),X4))
| hBOOL(hAPP(int,bool,X1,esk119_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,X2,esk116_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2827,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)),X4),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2828,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X3)),X1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X3)),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2829,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3))),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3))))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2830,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3))),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X2))))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2831,plain,
( hBOOL(hAPP(int,bool,X1,esk122_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X2,esk122_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X1,esk123_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,X2,esk120_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2832,plain,
( hBOOL(hAPP(int,bool,X1,esk118_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X2,esk118_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X1,esk119_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,X2,esk116_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2833,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),esk122_4(X2,X3,X4,X1)))
| hBOOL(hAPP(int,bool,X2,esk123_3(X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X3,X5))
| ~ hBOOL(hAPP(int,bool,X3,esk120_3(X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X3,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X2,X3,X4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X2,X3,X4)),X4))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2834,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X2)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,esk16_2(X1,X2))),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2835,plain,
hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),X1)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),X1),semiring_1_of_nat(int)))),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2836,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(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_1636]),
[final] ).
cnf(i_0_2837,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),X1,X4,X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X5,X3),hAPP(fun(X1,bool),X1,X4,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1248]),
[final] ).
cnf(i_0_2838,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3))))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_2839,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3))))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_2840,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1639]),
[final] ).
cnf(i_0_2841,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1640]),
[final] ).
cnf(i_0_2842,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),X1,X4,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X5,X3),hAPP(fun(X1,bool),X1,X4,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1251]),
[final] ).
cnf(i_0_2843,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(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(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)))
| ~ 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_1610]),
[final] ).
cnf(i_0_2844,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk48_3(X1,X2,X3)),esk49_3(X1,X2,X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X3,X1)),X2)),hAPP(nat,nat,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1620]),
[final] ).
cnf(i_0_2845,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2846,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_2847,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linord581940658strict(X1) ),
inference(rw,[status(thm)],[i_0_1641,c_0_1522]),
[final] ).
cnf(i_0_2848,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))))
| ~ linord581940658strict(X1) ),
inference(rw,[status(thm)],[i_0_1642,c_0_1522]),
[final] ).
cnf(i_0_2849,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),bot_bot(fun(X1,bool)))))
| hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X3),X2) = hAPP(fun(X1,bool),X1,the(X1),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)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_1267]),
[final] ).
cnf(i_0_2850,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(int,bool,X3,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))))
| ~ hBOOL(hAPP(int,bool,X3,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_2851,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_2852,plain,
( hBOOL(hAPP(int,bool,X3,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X2)),hAPP(nat,int,semiring_1_of_nat(int),X1))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_2853,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_1645]),
[final] ).
cnf(i_0_2854,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_1646]),
[final] ).
cnf(i_0_2855,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(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_1647]),
[final] ).
cnf(i_0_2856,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X4))),one_one(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1648]),
[final] ).
cnf(i_0_2857,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3))))
| ~ hBOOL(hAPP(int,bool,X1,zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X2)),hAPP(nat,int,semiring_1_of_nat(int),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_2858,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_1243]),
[final] ).
cnf(i_0_2859,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1649]),
[final] ).
cnf(i_0_2860,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3))))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk109_3(X2,X1,X3)),X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_2861,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3))))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk108_3(X2,X1,X3)),X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_2862,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk12_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_1599]),
[final] ).
cnf(i_0_2863,plain,
( hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(X1,fun(X1,bool),fequal(X1),X3))),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_2864,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_2865,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),esk9_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_1245]),
[final] ).
cnf(i_0_2866,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1654]),
[final] ).
cnf(i_0_2867,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_2868,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1656]),
[final] ).
cnf(i_0_2869,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1657]),
[final] ).
cnf(i_0_2870,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1658]),
[final] ).
cnf(i_0_2871,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1659]),
[final] ).
cnf(i_0_2872,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_2873,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1661]),
[final] ).
cnf(i_0_2874,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_2875,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_2876,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(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,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2877,plain,
( hBOOL(hAPP(int,bool,X1,esk123_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,esk120_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,X1,esk122_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,esk122_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2878,plain,
( hBOOL(hAPP(int,bool,X1,esk119_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,esk116_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,X1,esk118_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,esk118_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2879,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk10_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_1252]),
[final] ).
cnf(i_0_2880,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_1253]),
[final] ).
cnf(i_0_2881,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
| ~ ordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1664]),
[final] ).
cnf(i_0_2882,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
| ~ ordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_2883,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1666]),
[final] ).
cnf(i_0_2884,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1667]),
[final] ).
cnf(i_0_2885,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1668]),
[final] ).
cnf(i_0_2886,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_2887,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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2888,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2889,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2890,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2891,plain,
( hBOOL(hAPP(X1,bool,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),fconj),hAPP(X1,fun(X1,bool),fequal(X1),X3))),X2)) = bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_2892,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2893,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2894,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2895,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2896,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2897,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2898,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2899,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2900,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_1676]),
[final] ).
cnf(i_0_2901,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),esk118_4(X1,X2,X3,X4)),X4))
| hBOOL(hAPP(int,bool,X1,esk119_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,esk116_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2902,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk36_3(X1,X2,X3)),esk37_3(X1,X2,X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_1677,c_0_1522]),
[final] ).
cnf(i_0_2903,plain,
( hBOOL(hAPP(int,bool,X1,esk122_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X2,esk122_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X1,esk123_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,esk120_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2904,plain,
( hBOOL(hAPP(int,bool,X1,esk118_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X2,esk118_4(X1,X2,X3,X4)))
| hBOOL(hAPP(int,bool,X1,esk119_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,esk116_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk116_3(X1,X2,X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk117_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP(int,bool,X2,X5))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2905,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),esk122_4(X2,X3,X4,X1)))
| hBOOL(hAPP(int,bool,X2,esk123_3(X2,X3,X4)))
| hBOOL(hAPP(int,bool,X3,esk120_3(X2,X3,X4)))
| hBOOL(hAPP(int,bool,X3,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk120_3(X2,X3,X4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),esk121_3(X2,X3,X4)),X4))))
| ~ hBOOL(hAPP(int,bool,X3,X5))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2906,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1678]),
[final] ).
cnf(i_0_2907,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1679]),
[final] ).
cnf(i_0_2908,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1680]),
[final] ).
cnf(i_0_2909,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1681]),
[final] ).
cnf(i_0_2910,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1682]),
[final] ).
cnf(i_0_2911,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_2912,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1684]),
[final] ).
cnf(i_0_2913,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1685]),
[final] ).
cnf(i_0_2914,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1686]),
[final] ).
cnf(i_0_2915,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1687]),
[final] ).
cnf(i_0_2916,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk148_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk147_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,X2,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X2,X4)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2917,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_1688]),
[final] ).
cnf(i_0_2918,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2919,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_2920,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_2921,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_2922,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2923,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2924,plain,
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X5)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1693,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2925,plain,
( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,combi(X1),X5)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1694,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_2926,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1695]),
[final] ).
cnf(i_0_2927,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk13_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk13_4(X2,X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1696]),
[final] ).
cnf(i_0_2928,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk8_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk8_4(X2,X1,X3,X4))))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_2929,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_1698]),
[final] ).
cnf(i_0_2930,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_1646]),
[final] ).
cnf(i_0_2931,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_1647]),
[final] ).
cnf(i_0_2932,plain,
( hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))))) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1699]),
[final] ).
cnf(i_0_2933,plain,
( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1639]),
[final] ).
cnf(i_0_2934,plain,
( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1640]),
[final] ).
cnf(i_0_2935,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_1698]),
[final] ).
cnf(i_0_2936,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk148_4(X2,X3,X4,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk147_4(X2,X3,X4,X1)),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X3,X4)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X3,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2937,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk148_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),esk147_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,X2,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X2,X4)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2938,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1700]),
[final] ).
cnf(i_0_2939,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_1701]),
[final] ).
cnf(i_0_2940,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))),X4),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2941,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_2942,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_2943,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1679]),
[final] ).
cnf(i_0_2944,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1705]),
[final] ).
cnf(i_0_2945,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk148_4(X2,X3,X4,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk147_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X3,X4)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X3,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2946,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_2947,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_2948,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk100_3(X1,X2,X3)),X2)),X3))
| ~ linord1117847801e_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_2949,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_1243]),
[final] ).
cnf(i_0_2950,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_1698]),
[final] ).
cnf(i_0_2951,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ ordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1709]),
[final] ).
cnf(i_0_2952,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1656]),
[final] ).
cnf(i_0_2953,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ ordere1490568538miring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_2954,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ ordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_2955,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2956,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_2957,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2958,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord893533164strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_2959,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_2960,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1661]),
[final] ).
cnf(i_0_2961,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ ordered_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_2962,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_2963,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ ordered_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_2964,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2965,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_2966,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2967,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1718]),
[final] ).
cnf(i_0_2968,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_2969,plain,
( hBOOL(hAPP(int,bool,X1,esk109_3(X2,X1,X3)))
| hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_2970,plain,
( hBOOL(hAPP(int,bool,X1,esk108_3(X2,X1,X3)))
| hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_2971,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
| ~ ordere779506340up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_2972,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
| ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_2973,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
| ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_2974,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
| ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1722]),
[final] ).
cnf(i_0_2975,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X1))),X3)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_2976,plain,
( hAPP(nat,int,X1,esk148_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk147_4(X2,X1,X3,X4)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X1,X4)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2977,plain,
hAPP(fun(X1,bool),X1,the_elem(X1),X2) = hAPP(fun(X1,bool),X1,the(X1),hAPP(fun(X1,fun(X1,bool)),fun(X1,bool),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,fun(X1,bool)),fun(X1,bool)),combb(fun(X1,bool),bool,X1),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),fequal(fun(X1,bool)),X2)),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X1,fun(X1,bool))),combc(X1,fun(X1,bool),fun(X1,bool)),insert(X1)),bot_bot(fun(X1,bool))))),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_2978,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk57_3(X2,X3,X1))),hAPP(nat,nat,X1,esk58_3(X2,X3,X1))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_2979,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2980,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2981,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2982,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2983,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X3),X1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X3),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_2984,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2985,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2986,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_2987,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_2988,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2989,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_2990,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X4)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_2991,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2992,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2993,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1733]),
[final] ).
cnf(i_0_2994,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1734]),
[final] ).
cnf(i_0_2995,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_2996,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_2997,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_2998,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk102_3(X1,X2,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X3),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_2999,plain,
( hBOOL(hAPP(int,bool,X1,X3))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk105_3(X1,X2,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3000,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3001,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),X2))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1741]),
[final] ).
cnf(i_0_3002,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_3003,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk115_3(X2,X1,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk114_3(X2,X1,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3004,plain,
( hAPP(nat,int,X1,esk148_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),esk147_4(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X1,X4)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_3005,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)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3006,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_3007,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_1743,c_0_1522]),
[final] ).
cnf(i_0_3008,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),X4))
| ~ number(X1)
| ~ semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_3009,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),X4))
| ~ number(X1)
| ~ ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_3010,plain,
( hBOOL(hAPP(int,bool,X3,zero_zero(int)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_3011,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),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_1582]),
[final] ).
cnf(i_0_3012,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk36_3(X1,X2,X3)),esk37_3(X1,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_1746,c_0_1522]),
[final] ).
cnf(i_0_3013,plain,
( 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(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_3014,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(int,X1,number_number_of(X1),X3)),hAPP(int,X1,number_number_of(X1),X2)))
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1747]),
[final] ).
cnf(i_0_3015,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_3016,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
| ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3017,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_3018,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_3019,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3020,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),esk9_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_1753,c_0_1522]),
[final] ).
cnf(i_0_3021,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),zero_zero(X1)))
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1754]),
[final] ).
cnf(i_0_3022,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),zero_zero(X1)))
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_3023,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,suc,X2))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_3024,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),ring_1_Ints(X1)))
| ~ ring_1(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_3025,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1)))
| ~ ring_1(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_3026,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),ring_1_Ints(X1)))
| ~ ring_1(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1759]),
[final] ).
cnf(i_0_3027,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_1760]),
[final] ).
cnf(i_0_3028,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_3029,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_3030,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),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(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1761]),
[final] ).
cnf(i_0_3031,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(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1762]),
[final] ).
cnf(i_0_3032,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_3033,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X2)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_3034,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,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_3035,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,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_3036,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),plus_plus(nat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_3037,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[final] ).
cnf(i_0_3038,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3039,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
| ~ ordere779506340up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_3040,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1681]),
[final] ).
cnf(i_0_3041,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
| ~ ordere779506340up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1770]),
[final] ).
cnf(i_0_3042,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_3043,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
| ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_3044,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1685]),
[final] ).
cnf(i_0_3045,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
| ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_3046,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1687]),
[final] ).
cnf(i_0_3047,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3048,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_3049,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_1774]),
[final] ).
cnf(i_0_3050,plain,
( hAPP(fun(X1,bool),X1,X4,X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X5),X4)) ),
inference(rw,[status(thm)],[i_0_1775,c_0_1522]),
[final] ).
cnf(i_0_3051,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk101_4(X1,X2,X3,X4)),X4))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X4) = one_one(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ comm_monoid_mult(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3052,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk146_3(X1,X2,X3)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk145_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,X2,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X2,zero_zero(nat))),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_3053,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk144_3(X1,X2,X3)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk143_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,X2,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X2,zero_zero(nat))),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1533]),
[final] ).
cnf(i_0_3054,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X3)),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3))),X4)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3055,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),X3)),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3))),X4)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3056,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(int,X1,number_number_of(X1),X3)),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3))),X4)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3057,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X3),X1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X3),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_3058,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_3059,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_3060,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3061,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_3062,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1783]),
[final] ).
cnf(i_0_3063,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1784]),
[final] ).
cnf(i_0_3064,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3065,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_1785]),
[final] ).
cnf(i_0_3066,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_1786]),
[final] ).
cnf(i_0_3067,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1787]),
[final] ).
cnf(i_0_3068,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3069,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X2)),X3)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))),X3),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_3070,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_3071,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| 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(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_1582]),
[final] ).
cnf(i_0_3072,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(int,X1,number_number_of(X1),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(int,X1,number_number_of(X1),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(int,X1,number_number_of(X1),X4)))
| ~ number(X1)
| ~ semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1789]),
[final] ).
cnf(i_0_3073,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),hAPP(int,X1,number_number_of(X1),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(int,X1,number_number_of(X1),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(int,X1,number_number_of(X1),X4)))
| ~ number(X1)
| ~ ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_3074,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_3075,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_3076,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_3077,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere453448008miring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_3078,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_3079,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_3080,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),zero_zero(X1)))
| ~ ordere453448008miring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3081,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_3082,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_3083,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),zero_zero(X1)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1797]),
[final] ).
cnf(i_0_3084,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_3085,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_3086,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_3087,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3088,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,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3089,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,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_3090,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1804]),
[final] ).
cnf(i_0_3091,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_3092,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),X2) = hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),hAPP(X1,fun(X1,X1),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combc(X1,X1,X1),plus_plus(X1)),one_one(X1))),X2),zero_zero(X1))
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1805]),
[final] ).
cnf(i_0_3093,plain,
( hAPP(fun(X1,bool),X1,X4,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X2)) = hAPP(X1,X1,combi(X1),X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X5),X4)) ),
inference(rw,[status(thm)],[i_0_1806,c_0_1522]),
[final] ).
cnf(i_0_3094,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk10_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_1807,c_0_1522]),
[final] ).
cnf(i_0_3095,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_1808,c_0_1522]),
[final] ).
cnf(i_0_3096,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3097,plain,
( ~ linordered_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3098,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),one_one(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3099,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),one_one(nat))
| ~ 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_1812]),
[final] ).
cnf(i_0_3100,plain,
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),esk16_2(X1,X2)),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X2)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_3101,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_3102,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_3103,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_1813,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3104,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_3105,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_1528]),
[final] ).
cnf(i_0_3106,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3107,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3108,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_1816,c_0_1522]),
[final] ).
cnf(i_0_3109,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_1817]),
[final] ).
cnf(i_0_3110,plain,
( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),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_1762]),
[final] ).
cnf(i_0_3111,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1818,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3112,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1819,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3113,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1820,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3114,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1821,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3115,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,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3116,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,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1822]),
[final] ).
cnf(i_0_3117,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,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_3118,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3119,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3120,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))
| ~ 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),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1825,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3121,plain,
( hAPP(nat,int,X1,esk146_3(X2,X1,X3)) = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk145_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X1,zero_zero(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_3122,plain,
( hAPP(nat,int,X1,esk144_3(X2,X1,X3)) = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk143_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(nat,int,X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,X1,zero_zero(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1533]),
[final] ).
cnf(i_0_3123,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_1826]),
[final] ).
cnf(i_0_3124,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk25_3(X1,X2,X3)),esk26_3(X1,X2,X3))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3125,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3126,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_3127,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_1830,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3128,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_1831,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3129,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk37_3(X1,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_1832,c_0_1522]),
[final] ).
cnf(i_0_3130,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,X2,esk37_3(X1,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_1833,c_0_1522]),
[final] ).
cnf(i_0_3131,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),esk37_3(X1,X2,X3)) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1834,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3132,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X3)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3133,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_1836]),
[final] ).
cnf(i_0_3134,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(nat)),X1)))),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3135,plain,
( 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),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_1586]),
[final] ).
cnf(i_0_3136,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_1774]),
[final] ).
cnf(i_0_3137,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5) = bot_bot(fun(X1,bool))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X1,bool),X1,X3,X5)),hAPP(fun(X1,bool),X1,X3,X4)) = hAPP(fun(X1,bool),X1,X3,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1838,c_0_1522]),
[final] ).
cnf(i_0_3138,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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(nat)),X4))) ),
inference(rw,[status(thm)],[i_0_1839,c_0_1522]),
[final] ).
cnf(i_0_3139,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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(nat)),X4))) ),
inference(rw,[status(thm)],[i_0_1840,c_0_1522]),
[final] ).
cnf(i_0_3140,plain,
( hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X3),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ 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),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_1841,c_0_1522]),
[final] ).
cnf(i_0_3141,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_3142,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3143,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3144,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3145,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,suc,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_3146,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3147,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3148,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_1848]),
[final] ).
cnf(i_0_3149,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_1849]),
[final] ).
cnf(i_0_3150,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_3151,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),bot_bot(fun(X1,bool)))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1850,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3152,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| 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),X4),bot_bot(fun(X1,bool)))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1851,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3153,plain,
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool)))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1852,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3154,plain,
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| 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),X5),bot_bot(fun(X1,bool)))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1853,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3155,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))) = 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_1854,c_0_1522]),
[final] ).
cnf(i_0_3156,plain,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X4) = one_one(X2)
| hAPP(X1,X2,X3,esk101_4(X1,X2,X3,X4)) != one_one(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ comm_monoid_mult(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3157,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)))),
inference(split_conjunct,[status(thm)],[i_0_1855]),
[final] ).
cnf(i_0_3158,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X4) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X5),hAPP(fun(X1,bool),X1,X3,X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1856,c_0_1522]),
[final] ).
cnf(i_0_3159,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X2)),X3)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X2)))
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3160,plain,
( hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3161,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| hBOOL(hAPP(int,bool,X3,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_3162,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3163,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3164,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3165,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3166,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk103_3(X1,X2,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3167,plain,
( hBOOL(hAPP(int,bool,X1,X3))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk106_3(X1,X2,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3168,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),esk102_3(X1,X2,X3)),X3))
| hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X3),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3169,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_3170,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_3171,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3172,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1754]),
[final] ).
cnf(i_0_3173,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_3174,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3175,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3176,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X4),X2)) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ 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_1862,c_0_1522]),
[final] ).
cnf(i_0_3177,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),esk105_3(X2,X1,X3)))
| hBOOL(hAPP(int,bool,X2,X3))
| ~ hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3178,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3179,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3180,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3181,plain,
( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X4))
| ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1865]),
[final] ).
cnf(i_0_3182,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk115_3(X1,X2,X3)),X3))
| hBOOL(hAPP(int,bool,X2,X1))
| ~ hBOOL(hAPP(int,bool,X2,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk114_3(X1,X2,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3183,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1866]),
[final] ).
cnf(i_0_3184,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_3185,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X2)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_3186,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3187,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3188,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3189,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk61_3(X1,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1870]),
[final] ).
cnf(i_0_3190,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),one_one(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| X1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3191,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1872,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3192,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1873,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3193,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| X1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_3194,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),esk114_3(X2,X1,X3)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk115_3(X2,X1,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3195,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2))))
| ~ hBOOL(hAPP(int,bool,X1,zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_3196,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_1875,c_0_1522]),
[final] ).
cnf(i_0_3197,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_1876,c_0_1522]),
[final] ).
cnf(i_0_3198,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_1877,c_0_1522]),
[final] ).
cnf(i_0_3199,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3200,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_3201,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ ordere453448008miring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1879]),
[final] ).
cnf(i_0_3202,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1880]),
[final] ).
cnf(i_0_3203,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1881]),
[final] ).
cnf(i_0_3204,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3205,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3206,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3207,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3208,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))) = 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_1812]),
[final] ).
cnf(i_0_3209,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3210,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ ordered_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1886]),
[final] ).
cnf(i_0_3211,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_3212,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3213,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1888]),
[final] ).
cnf(i_0_3214,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1889]),
[final] ).
cnf(i_0_3215,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1890]),
[final] ).
cnf(i_0_3216,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3217,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3218,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),esk99_3(X1,X2,X3))))
| ~ linordered_field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3219,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_1894]),
[final] ).
cnf(i_0_3220,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk71_4(X1,X2,X3,X4)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3221,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3222,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1897]),
[final] ).
cnf(i_0_3223,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3224,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3225,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_3226,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3227,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3228,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) = 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_1903,c_0_1522]),
[final] ).
cnf(i_0_3229,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1904]),
[final] ).
cnf(i_0_3230,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_1905]),
[final] ).
cnf(i_0_3231,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk21_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_3232,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X5),hAPP(fun(X1,bool),X1,X3,X4)) = hAPP(fun(X1,bool),X1,X3,X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1906]),
[final] ).
cnf(i_0_3233,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),one_one(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1907]),
[final] ).
cnf(i_0_3234,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X2)),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X2)),X3)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3235,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X2)),X3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1908]),
[final] ).
cnf(i_0_3236,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X2)),X3) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3237,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1910]),
[final] ).
cnf(i_0_3238,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3239,plain,
( hBOOL(hAPP(int,bool,X1,esk102_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X3),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3240,plain,
( hBOOL(hAPP(int,bool,X1,esk105_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X1,X3))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3241,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),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_1861]),
[final] ).
cnf(i_0_3242,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),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_1912]),
[final] ).
cnf(i_0_3243,plain,
( ~ ring_char_0(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3244,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X3)),hAPP(X1,X1,abs_abs(X1),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordered_ring_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3245,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X3)),hAPP(X1,X1,abs_abs(X1),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordered_ring_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3246,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X3)),hAPP(X1,X1,abs_abs(X1),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ ordered_ring_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3247,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X3)),hAPP(X1,X1,abs_abs(X1),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ ordered_ring_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3248,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),X1),
inference(split_conjunct,[status(thm)],[i_0_1915]),
[final] ).
cnf(i_0_3249,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(int,X1,number_number_of(X1),X3)),hAPP(int,X1,number_number_of(X1),X2)))
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1747]),
[final] ).
cnf(i_0_3250,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3251,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3252,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3253,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X5) = hAPP(X1,X1,combi(X1),X6)
| hAPP(X1,X1,combi(X1),X3) != hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X6))
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1919,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3254,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk57_3(X1,X2,X3)),esk58_3(X1,X2,X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X3,X1)),hAPP(nat,nat,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_3255,plain,
hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X3),X4),X5),bot_bot(fun(X1,bool))) = hAPP(X2,X2,combi(X2),X5),
inference(rw,[status(thm)],[i_0_1920,c_0_1522]),
[final] ).
cnf(i_0_3256,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(rw,[status(thm)],[i_0_1921,c_0_1522]),
[final] ).
cnf(i_0_3257,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(rw,[status(thm)],[i_0_1922,c_0_1522]),
[final] ).
cnf(i_0_3258,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X4) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X5),hAPP(fun(X1,bool),X1,X3,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1923,c_0_1522]),
[final] ).
cnf(i_0_3259,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_1924]),
[final] ).
cnf(i_0_3260,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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(fun(X1,bool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3261,plain,
( hBOOL(hAPP(int,bool,X1,esk115_3(X2,X1,X3)))
| hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),esk114_3(X2,X1,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3262,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| hBOOL(hAPP(int,bool,X1,esk114_3(X2,X1,X3)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),esk115_3(X2,X1,X3)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3263,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X1))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3264,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3265,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3266,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int)))) ),
inference(split_conjunct,[status(thm)],[i_0_1927]),
[final] ).
cnf(i_0_3267,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1928]),
[final] ).
cnf(i_0_3268,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int)))) ),
inference(split_conjunct,[status(thm)],[i_0_1929]),
[final] ).
cnf(i_0_3269,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),one_one(int)))) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3270,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),one_one(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3271,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_1932]),
[final] ).
cnf(i_0_3272,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_1262]),
[final] ).
cnf(i_0_3273,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_1296]),
[final] ).
cnf(i_0_3274,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3)))
| ~ number_ring(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3275,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3)))
| ~ number_ring(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3276,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3277,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1936]),
[final] ).
cnf(i_0_3278,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3279,plain,
( hAPP(int,nat,number_number_of(nat),X2) = hAPP(int,nat,number_number_of(nat),X1)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(int,int,number_number_of(int),X2) != zero_zero(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X1)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3280,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_1939]),
[final] ).
cnf(i_0_3281,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))),
inference(split_conjunct,[status(thm)],[i_0_1940]),
[final] ).
cnf(i_0_3282,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3283,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(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))))) = 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_1942]),
[final] ).
cnf(i_0_3284,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_1943]),
[final] ).
cnf(i_0_3285,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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_1944]),
[final] ).
cnf(i_0_3286,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(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(fun(X1,bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3287,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3288,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3289,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1948]),
[final] ).
cnf(i_0_3290,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1949]),
[final] ).
cnf(i_0_3291,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X1)),hAPP(int,int,number_number_of(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3292,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),X1)),hAPP(int,int,number_number_of(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1951]),
[final] ).
cnf(i_0_3293,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3294,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1953]),
[final] ).
cnf(i_0_3295,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1954]),
[final] ).
cnf(i_0_3296,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1955]),
[final] ).
cnf(i_0_3297,plain,
( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3298,plain,
( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3299,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3300,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_3301,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3302,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_3303,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_1962]),
[final] ).
cnf(i_0_3304,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1963]),
[final] ).
cnf(i_0_3305,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3306,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3307,plain,
( hAPP(int,nat,number_number_of(nat),X1) = hAPP(int,nat,number_number_of(nat),X2)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X2)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3308,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
inference(split_conjunct,[status(thm)],[fact_984_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]),
[final] ).
cnf(i_0_3309,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_1966,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3310,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_1967]),
[final] ).
cnf(i_0_3311,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3312,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3313,plain,
( hAPP(int,nat,number_number_of(nat),X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),X1)),one_one(nat)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3314,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3315,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3316,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3317,plain,
( hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3318,plain,
( hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1974]),
[final] ).
cnf(i_0_3319,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),X4),bot_bot(fun(X1,bool)))) = 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),X5),bot_bot(fun(X1,bool))))
| hAPP(X1,X1,combi(X1),X4) != hAPP(X1,X1,combi(X1),X5)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1975,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3320,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),X4),bot_bot(fun(X1,bool)))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))))
| hAPP(X1,X1,combi(X1),X4) != hAPP(X1,X1,combi(X1),X5)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1976,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3321,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_1977]),
[final] ).
cnf(i_0_3322,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_1978]),
[final] ).
cnf(i_0_3323,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_1979]),
[final] ).
cnf(i_0_3324,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_1980]),
[final] ).
cnf(i_0_3325,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(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_1981]),
[final] ).
cnf(i_0_3326,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5)))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1982]),
[final] ).
cnf(i_0_3327,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5)))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3328,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_3329,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_1984]),
[final] ).
cnf(i_0_3330,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_1985]),
[final] ).
cnf(i_0_3331,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk55_2(X1,X2)),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(nat)),esk54_2(X1,X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[i_0_1986,c_0_1522]),
[final] ).
cnf(i_0_3332,plain,
hAPP(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),combi(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
inference(rw,[status(thm)],[i_0_1987,c_0_1522]),
[final] ).
cnf(i_0_3333,plain,
hAPP(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),combi(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))))),finite1357897459simple(X1,X2)) = finite1357897459simple(X1,X2),
inference(rw,[status(thm)],[i_0_1988,c_0_1522]),
[final] ).
cnf(i_0_3334,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_1989]),
[final] ).
cnf(i_0_3335,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_3336,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X3)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3337,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1992]),
[final] ).
cnf(i_0_3338,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_3339,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_1994]),
[final] ).
cnf(i_0_3340,plain,
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X4),X3))
| hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3341,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk71_4(X1,X2,X3,X4)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3342,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_1996,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3343,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_1997]),
[final] ).
cnf(i_0_3344,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3345,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3346,plain,
( hBOOL(hAPP(nat,bool,X4,X3))
| X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)
| ~ hBOOL(hAPP(nat,bool,X4,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3347,plain,
( hBOOL(hAPP(nat,bool,X4,X3))
| X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)
| ~ hBOOL(hAPP(nat,bool,X4,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3348,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_1998]),
[final] ).
cnf(i_0_3349,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),hAPP(int,X1,number_number_of(X1),X2))),hAPP(int,X1,number_number_of(X1),X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3350,plain,
( hAPP(fun(sum_sum(X1,X3),bool),nat,finite_card(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3351,plain,
( hAPP(fun(sum_sum(X1,X3),bool),nat,finite_card(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3352,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_2002,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3353,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_2003,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3354,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3355,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk22_4(X1,X2,X3,X4)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_3356,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk22_4(X1,X2,X3,X4)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_3357,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2005]),
[final] ).
cnf(i_0_3358,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3359,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3360,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3361,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1928]),
[final] ).
cnf(i_0_3362,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3363,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1929]),
[final] ).
cnf(i_0_3364,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1927]),
[final] ).
cnf(i_0_3365,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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_2007]),
[final] ).
cnf(i_0_3366,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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_2008]),
[final] ).
cnf(i_0_3367,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3368,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3369,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3370,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2012]),
[final] ).
cnf(i_0_3371,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2013]),
[final] ).
cnf(i_0_3372,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2014]),
[final] ).
cnf(i_0_3373,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk60_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_3374,plain,
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(int,X3,number_number_of(X3),X1)),hAPP(int,X3,number_number_of(X3),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ number_ring(X3)
| ~ linordered_idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3375,plain,
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(int,X3,number_number_of(X3),X1)),hAPP(int,X3,number_number_of(X3),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ number_ring(X3)
| ~ linordered_idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3376,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3377,plain,
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X1)),hAPP(nat,X3,semiring_1_of_nat(X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ linordered_semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3378,plain,
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X1)),hAPP(nat,X3,semiring_1_of_nat(X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ linordered_semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3379,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_2017]),
[final] ).
cnf(i_0_3380,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_2018]),
[final] ).
cnf(i_0_3381,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_2019]),
[final] ).
cnf(i_0_3382,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_2020]),
[final] ).
cnf(i_0_3383,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_3384,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3385,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_2023]),
[final] ).
cnf(i_0_3386,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X3)),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3387,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X1)),hAPP(int,int,number_number_of(int),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3388,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3389,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1953]),
[final] ).
cnf(i_0_3390,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),X1)),hAPP(int,int,number_number_of(int),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1951]),
[final] ).
cnf(i_0_3391,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1954]),
[final] ).
cnf(i_0_3392,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1955]),
[final] ).
cnf(i_0_3393,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3394,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),hAPP(int,nat,number_number_of(nat),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3395,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),bot_bot(fun(X1,bool)))))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2026,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3396,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3397,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_3398,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3399,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_3400,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_1962]),
[final] ).
cnf(i_0_3401,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3402,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3403,plain,
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X2)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3404,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3405,plain,
( ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X4),X3))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3406,plain,
( hAPP(fun(X1,bool),X1,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),bot_bot(fun(X1,bool)))) = hAPP(X1,X1,combi(X1),X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite_folding_one(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_2029,c_0_1522]),
[final] ).
cnf(i_0_3407,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_2030,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3408,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),collect(X1),X3)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
| ~ hBOOL(hAPP(X1,bool,X2,esk81_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3409,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_2032,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3410,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_2033,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3411,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2034,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3412,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk71_4(X1,X3,X2,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3413,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5)
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3414,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3415,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5)
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3416,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)
| ~ ordered_ab_group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3417,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X2)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(int,nat,number_number_of(nat),X1) != hAPP(int,nat,number_number_of(nat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3418,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(rw,[status(thm)],[i_0_2037,c_0_1522]),
[final] ).
cnf(i_0_3419,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(rw,[status(thm)],[i_0_2038,c_0_1522]),
[final] ).
cnf(i_0_3420,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2039]),
[final] ).
cnf(i_0_3421,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3422,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2041]),
[final] ).
cnf(i_0_3423,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3424,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2043]),
[final] ).
cnf(i_0_3425,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3426,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2045]),
[final] ).
cnf(i_0_3427,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3428,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X3)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))
| ~ ring_1(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3429,plain,
( hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X2)),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),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_2048]),
[final] ).
cnf(i_0_3430,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_3431,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_2050]),
[final] ).
cnf(i_0_3432,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3433,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3434,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2053,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3435,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3436,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ ab_semigroup_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_3437,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3438,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
| ~ ab_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3439,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3440,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3441,plain,
( X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3442,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3443,plain,
( hBOOL(hAPP(X1,bool,X2,esk81_3(X1,X3,X2)))
| 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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3444,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,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),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_2062]),
[final] ).
cnf(i_0_3445,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X1) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3446,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_2064]),
[final] ).
cnf(i_0_3447,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk25_3(X1,X2,X3)),esk26_3(X1,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3448,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_3449,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk85_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3450,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk84_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3451,plain,
( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),hAPP(X4,fun(X1,X4),combk(X4,X1),X5)),X3) = hAPP(fun(X4,bool),fun(X4,bool),hAPP(X4,fun(fun(X4,bool),fun(X4,bool)),insert(X4),X5),bot_bot(fun(X4,bool)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_3452,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk4_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_2066]),
[final] ).
cnf(i_0_3453,plain,
( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X1))))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X1),u)) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3454,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_2068]),
[final] ).
cnf(i_0_3455,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3),
inference(split_conjunct,[status(thm)],[i_0_2069]),
[final] ).
cnf(i_0_3456,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_3457,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X2)),X3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3458,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3459,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3460,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3461,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X3)),X2) = hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2075]),
[final] ).
cnf(i_0_3462,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_2076]),
[final] ).
cnf(i_0_3463,plain,
( hAPP(nat,nat,suc,X1) = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3464,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_2078]),
[final] ).
cnf(i_0_3465,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X1)),X1) != zero_zero(int),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3466,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3467,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(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2081,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3468,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(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2082,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3469,plain,
( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk85_3(X3,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3470,plain,
( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk84_3(X3,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3471,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_2083]),
[final] ).
cnf(i_0_3472,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),X2)),zero_zero(X1))) ),
inference(rw,[status(thm)],[i_0_2084,c_0_1522]),
[final] ).
cnf(i_0_3473,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_2085]),
[final] ).
cnf(i_0_3474,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3475,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_3476,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3477,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3478,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_2023]),
[final] ).
cnf(i_0_3479,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_2087]),
[final] ).
cnf(i_0_3480,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_2088]),
[final] ).
cnf(i_0_3481,plain,
( hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),X2),hAPP(nat,nat,suc,X3)),X4) = hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),X2),X3),hAPP(X1,X1,X2,X4))
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3482,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_2064]),
[final] ).
cnf(i_0_3483,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_2090]),
[final] ).
cnf(i_0_3484,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2091,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3485,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_2092]),
[final] ).
cnf(i_0_3486,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_2093]),
[final] ).
cnf(i_0_3487,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_2094]),
[final] ).
cnf(i_0_3488,plain,
( X1 = hAPP(nat,nat,suc,esk60_2(X2,X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_3489,plain,
( X2 = hAPP(nat,nat,suc,esk5_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_2095]),
[final] ).
cnf(i_0_3490,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,X1))))
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3491,plain,
( ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,abs_abs(X1),X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_3492,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk103_3(X1,X2,X3)),X3))
| hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3493,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk50_3(X1,X2,X3)),X3))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3494,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3495,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3496,plain,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_3497,plain,
( hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3498,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(nat)),X1))) = X1,
inference(split_conjunct,[status(thm)],[i_0_2101]),
[final] ).
cnf(i_0_3499,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk83_2(X1,X2)),X2))
| X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3500,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),esk11_3(X1,X2,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3501,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk50_3(X1,X2,X3))))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3502,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3503,plain,
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X3),X4))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3504,plain,
( X1 = zero_zero(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),X1)),one_one(int))) ),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_3505,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3506,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))),
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_3507,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_1985]),
[final] ).
cnf(i_0_3508,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_2108]),
[final] ).
cnf(i_0_3509,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3510,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3511,plain,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3512,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3513,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(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3514,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2114,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3515,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2115,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3516,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2116,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3517,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2117,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3518,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),X3) = hAPP(nat,nat,suc,X5)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != X5
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X4),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2118,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3519,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3520,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3521,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk85_3(X1,X2,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3522,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk84_3(X1,X2,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3523,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_2121]),
[final] ).
cnf(i_0_3524,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),esk106_3(X2,X1,X3)))
| hBOOL(hAPP(int,bool,X2,X3))
| ~ hBOOL(hAPP(int,bool,X2,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3525,plain,
( X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3526,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,X1,esk4_3(X2,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_3527,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_2123,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3528,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_1286]),
[final] ).
cnf(i_0_3529,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(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1301]),
[final] ).
cnf(i_0_3530,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(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_3531,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(fun(X1,bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3532,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X3)))
| X1 != hAPP(nat,nat,suc,X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3533,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),esk128_1(X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3534,plain,
hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
inference(split_conjunct,[status(thm)],[fact_952_transfer__int__nat__numerals_I4_J]),
[final] ).
cnf(i_0_3535,plain,
( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk85_3(X3,X1,X2))
| hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,X3,zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3536,plain,
( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk84_3(X3,X1,X2))
| hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,X3,zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3537,plain,
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3538,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),esk14_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_2127]),
[final] ).
cnf(i_0_3539,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),esk45_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_2128]),
[final] ).
cnf(i_0_3540,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk111_2(X1,X2)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_3541,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),one_one(nat))),X2),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3542,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X4),X4) = hAPP(X1,X1,combi(X1),X4)
| ~ hBOOL(hAPP(fun(fun(X1,bool),X1),bool,hAPP(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool),finite2073411215e_idem(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_2131,c_0_1522]),
[final] ).
cnf(i_0_3543,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),hAPP(nat,X2,semiring_1_of_nat(X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ linordered_semidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3544,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk110_2(X1,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3545,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk86_2(X2,X1)),one_one(nat))))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3546,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1))
| X1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_3547,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_3548,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_1984]),
[final] ).
cnf(i_0_3549,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),hAPP(int,X1,number_number_of(X1),X2)) = hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_3550,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_2137]),
[final] ).
cnf(i_0_3551,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3552,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk115_3(X1,X2,X3)),X3))
| hBOOL(hAPP(int,bool,X2,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),esk114_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3553,plain,
( hBOOL(X4)
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_3554,plain,
( hAPP(nat,X2,semiring_1_of_nat(X2),hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,X2,number_number_of(X2),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X1)))
| ~ number_ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_3555,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3556,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2141]),
[final] ).
cnf(i_0_3557,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3558,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1368]),
[final] ).
cnf(i_0_3559,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3560,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_3561,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2144]),
[final] ).
cnf(i_0_3562,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2145]),
[final] ).
cnf(i_0_3563,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3564,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3565,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3566,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_2093]),
[final] ).
cnf(i_0_3567,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_2148]),
[final] ).
cnf(i_0_3568,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_2149]),
[final] ).
cnf(i_0_3569,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_2113]),
[final] ).
cnf(i_0_3570,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3571,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3572,plain,
( hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),minus_minus(fun(X2,X1)),X3),X4),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5))
| ~ minus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3573,plain,
( hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),minus_minus(fun(X2,X1)),X3),X4),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5))
| ~ minus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3574,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3575,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3576,plain,
( X1 = zero_zero(nat)
| hAPP(fun(X2,bool),nat,finite_card(X2),X3) = hAPP(nat,nat,suc,X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5))
| hAPP(fun(X2,bool),nat,finite_card(X2),X5) != X1
| hAPP(fun(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X3) != hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X4),X5) ),
inference(rw,[status(thm)],[i_0_2153,c_0_1522]),
[final] ).
cnf(i_0_3577,plain,
( X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3578,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3579,plain,
( X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2156]),
[final] ).
cnf(i_0_3580,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_2157]),
[final] ).
cnf(i_0_3581,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2158,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3582,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2159,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3583,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X4)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2160,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3584,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2161,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3585,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2162,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3586,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X4)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2163,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3587,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3588,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))
| ~ linordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_3589,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3590,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2167]),
[final] ).
cnf(i_0_3591,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2168]),
[final] ).
cnf(i_0_3592,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,esk50_3(X1,X2,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3593,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk23_3(X1,X2,X3)),esk24_3(X1,X2,X3)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_3594,plain,
( hAPP(int,int,number_number_of(int),X2) = zero_zero(int)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X2)))
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(int,nat,number_number_of(nat),X2) != hAPP(int,nat,number_number_of(nat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3595,plain,
( X2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,esk129_2(X1,X2))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_3596,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_3597,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_2170]),
[final] ).
cnf(i_0_3598,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk70_3(X1,X2,X3)),X2))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_3599,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
inference(rw,[status(thm)],[i_0_2172,c_0_1522]),
[final] ).
cnf(i_0_3600,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1338]),
[final] ).
cnf(i_0_3601,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_3602,plain,
( hBOOL(hAPP(int,bool,X2,hAPP(nat,int,semiring_1_of_nat(int),esk125_1(X2))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3603,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_2175]),
[final] ).
cnf(i_0_3604,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_2176]),
[final] ).
cnf(i_0_3605,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1927]),
[final] ).
cnf(i_0_3606,plain,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk93_3(X1,X2,X3)),esk94_3(X1,X2,X3)))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1415]),
[final] ).
cnf(i_0_3607,plain,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk87_3(X1,X2,X3)),esk88_3(X1,X2,X3)))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1318]),
[final] ).
cnf(i_0_3608,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X2)))
| hAPP(int,nat,number_number_of(nat),X2) = hAPP(int,nat,number_number_of(nat),X1)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(int,int,number_number_of(int),X2) != zero_zero(int) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3609,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1))),
inference(split_conjunct,[status(thm)],[i_0_2177]),
[final] ).
cnf(i_0_3610,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_3611,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_3612,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X1),X2))
| X2 = X1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3613,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_3614,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3615,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2183,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3616,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2184,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3617,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2185,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3618,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2186,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3619,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2187,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3620,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2188,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3621,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2189,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3622,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2190,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3623,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2191,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3624,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),X2)),one_one(X1)) = hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_3625,plain,
( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk86_2(X2,X3)))
| ~ hBOOL(hAPP(nat,bool,X3,X1))
| ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3626,plain,
( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk90_2(X2,X3)))
| ~ hBOOL(hAPP(nat,bool,X3,X1))
| ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_3627,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2194,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3628,plain,
( hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2195]),
[final] ).
cnf(i_0_3629,plain,
( hBOOL(hAPP(X1,bool,X4,X3))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_3630,plain,
( hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,abs_abs(X1),X2))) ),
inference(rw,[status(thm)],[i_0_2197,c_0_1522]),
[final] ).
cnf(i_0_3631,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X1),X2),X3))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3632,plain,
( hBOOL(X1)
| hAPP(nat,int,semiring_1_of_nat(int),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3633,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X3) = X2
| X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_3634,plain,
( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) != X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_3635,plain,
( hBOOL(hAPP(int,bool,X1,esk103_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3636,plain,
( hBOOL(hAPP(int,bool,X1,esk106_3(X1,X2,X3)))
| hBOOL(hAPP(int,bool,X1,X3))
| ~ hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3637,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
| ~ ring_char_0(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1))) ),
inference(rw,[status(thm)],[i_0_2200,c_0_1522]),
[final] ).
cnf(i_0_3638,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X1 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2201]),
[final] ).
cnf(i_0_3639,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(fun(X1,bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2202,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3640,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_2203]),
[final] ).
cnf(i_0_3641,plain,
hAPP(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),combi(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
inference(rw,[status(thm)],[i_0_2204,c_0_1522]),
[final] ).
cnf(i_0_3642,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk11_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_2103]),
[final] ).
cnf(i_0_3643,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk59_2(X1,X2)))
| X2 = hAPP(nat,nat,suc,X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3644,plain,
( X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk51_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3645,plain,
( X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk47_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2201]),
[final] ).
cnf(i_0_3646,plain,
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),one_one(nat))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3647,plain,
( X1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),one_one(nat)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2208]),
[final] ).
cnf(i_0_3648,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)),X3) = hAPP(X1,X1,combi(X1),X2)
| ~ group_add(X1) ),
inference(rw,[status(thm)],[i_0_2209,c_0_1522]),
[final] ).
cnf(i_0_3649,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X3) = hAPP(X1,X1,combi(X1),X2)
| ~ group_add(X1) ),
inference(rw,[status(thm)],[i_0_2210,c_0_1522]),
[final] ).
cnf(i_0_3650,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk113_2(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2211]),
[final] ).
cnf(i_0_3651,plain,
( hAPP(X2,X2,hAPP(X1,fun(X2,X2),X3,X4),hAPP(X2,X2,hAPP(X1,fun(X2,X2),X3,X4),X5)) = hAPP(X2,X2,hAPP(X1,fun(X2,X2),X3,X4),X5)
| ~ hBOOL(hAPP(fun(X1,fun(X2,X2)),bool,finite_comp_fun_idem(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2212]),
[final] ).
cnf(i_0_3652,plain,
( X1 = hAPP(nat,nat,suc,esk83_2(X1,X2))
| X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3653,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_2213,c_0_1522]),
[final] ).
cnf(i_0_3654,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk112_2(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2214]),
[final] ).
cnf(i_0_3655,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X3))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2215]),
[final] ).
cnf(i_0_3656,plain,
hAPP(int,int,bit1,X1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X1)),X1),
inference(split_conjunct,[status(thm)],[i_0_2216]),
[final] ).
cnf(i_0_3657,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_2217]),
[final] ).
cnf(i_0_3658,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3)) = hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2218]),
[final] ).
cnf(i_0_3659,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3)) = hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2219]),
[final] ).
cnf(i_0_3660,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2220]),
[final] ).
cnf(i_0_3661,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3662,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(int,X1,number_number_of(X1),X2)),hAPP(int,X1,number_number_of(X1),X3))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3663,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_3664,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_3665,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2225]),
[final] ).
cnf(i_0_3666,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3667,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1344]),
[final] ).
cnf(i_0_3668,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1345]),
[final] ).
cnf(i_0_3669,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ ring_char_0(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1))) ),
inference(rw,[status(thm)],[i_0_2226,c_0_1522]),
[final] ).
cnf(i_0_3670,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3671,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3672,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_3673,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk91_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2228]),
[final] ).
cnf(i_0_3674,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),X1)),hAPP(int,int,number_number_of(int),X2)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_3675,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_3676,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_3677,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),X1)),hAPP(int,int,number_number_of(int),X2)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2232]),
[final] ).
cnf(i_0_3678,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_3679,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_3680,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)),
inference(split_conjunct,[status(thm)],[i_0_2235]),
[final] ).
cnf(i_0_3681,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk130_1(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2236]),
[final] ).
cnf(i_0_3682,plain,
hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2237]),
[final] ).
cnf(i_0_3683,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3684,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3685,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),X2)),zero_zero(X1)))
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(rw,[status(thm)],[i_0_2239,c_0_1522]),
[final] ).
cnf(i_0_3686,plain,
( X1 = X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_3687,plain,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_3688,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3689,plain,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_3690,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_3691,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_3692,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_3693,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3694,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3695,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(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_3696,plain,
( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X2),X1) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3697,plain,
( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X2),X1) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3698,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3699,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ linorder(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2250,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3700,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,pls))),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ number_ring(X1) ),
inference(rw,[status(thm)],[i_0_2251,c_0_1522]),
[final] ).
cnf(i_0_3701,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),esk115_3(X1,X2,X3)),X3))
| hBOOL(hAPP(int,bool,X2,X1))
| hBOOL(hAPP(int,bool,X2,esk114_3(X1,X2,X3)))
| ~ hBOOL(hAPP(int,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3702,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),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(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_3703,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),bot_bot(fun(X1,bool))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2253,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3704,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[i_0_2254,c_0_1522]),
[final] ).
cnf(i_0_3705,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk126_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3706,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3707,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X1) = X2,
inference(split_conjunct,[status(thm)],[i_0_2256]),
[final] ).
cnf(i_0_3708,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2257]),
[final] ).
cnf(i_0_3709,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(int,X1,number_number_of(X1),X2)),ring_1_Ints(X1)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2258]),
[final] ).
cnf(i_0_3710,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),ring_1_Ints(X1)))
| ~ ring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2259]),
[final] ).
cnf(i_0_3711,plain,
( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,combi(X1),X5)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5)
| ~ ab_group_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2260,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3712,plain,
( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,combi(X1),X5)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X4),X5)
| ~ ab_group_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2261,c_0_1522]),c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3713,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),bot_bot(fun(X1,bool)))) ),
inference(rw,[status(thm)],[i_0_2262,c_0_1522]),
[final] ).
cnf(i_0_3714,plain,
( X2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),esk124_2(X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3715,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),hAPP(X3,fun(X1,X3),combk(X3,X1),X4)),X2) = hAPP(fun(X3,bool),fun(X3,bool),hAPP(X3,fun(fun(X3,bool),fun(X3,bool)),insert(X3),X4),bot_bot(fun(X3,bool))) ),
inference(rw,[status(thm)],[i_0_2264,c_0_1522]),
[final] ).
cnf(i_0_3716,plain,
( hBOOL(hAPP(int,bool,X1,esk115_3(X2,X1,X3)))
| hBOOL(hAPP(int,bool,X1,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),esk114_3(X2,X1,X3)))
| ~ hBOOL(hAPP(int,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3717,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X1)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3718,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk98_2(X2,X1))))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3719,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| X2 = X1
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X2)))
| hAPP(int,nat,number_number_of(nat),X2) != hAPP(int,nat,number_number_of(nat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3720,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3)) = hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X2))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_3721,plain,
( X1 = one_one(int)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2) != one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_3722,plain,
( X1 = one_one(int)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X1) != one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_3723,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linordered_idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2269,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3724,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2270,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3725,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2271,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3726,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2272,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3727,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2273,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3728,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2274,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3729,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2275,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3730,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(sum_sum(X1,X3),bool),nat,finite_card(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)) = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3731,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2)) = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3732,plain,
( hAPP(fun(X1,bool),X1,the(X1),X3) = hAPP(X1,X1,combi(X1),X2)
| hAPP(X1,X1,combi(X1),esk43_4(X1,X2,X3,X4)) != hAPP(X1,X1,combi(X1),X4)
| ~ hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2276,c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3733,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk100_3(X1,X2,X3)),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord1117847801e_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_3734,plain,
( hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),bot_bot(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3735,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk70_3(X1,X2,X3)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_3736,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_2278]),
[final] ).
cnf(i_0_3737,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_2279]),
[final] ).
cnf(i_0_3738,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2280]),
[final] ).
cnf(i_0_3739,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(rw,[status(thm)],[i_0_2281,c_0_1522]),
[final] ).
cnf(i_0_3740,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3741,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| X1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),hAPP(nat,int,semiring_1_of_nat(int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3742,plain,
( hAPP(fun(X1,bool),X1,the(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,X2,esk43_4(X1,X3,X2,X4)))
| ~ hBOOL(hAPP(X1,bool,X2,X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(rw,[status(thm)],[i_0_2282,c_0_1522]),
[final] ).
cnf(i_0_3743,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_3744,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int)))
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3745,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),X1)),one_one(int)))
| X1 != zero_zero(int) ),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_3746,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk30_2(X1,X2)),esk31_2(X1,X2))) ),
inference(rw,[status(thm)],[i_0_2284,c_0_1522]),
[final] ).
cnf(i_0_3747,plain,
~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),bot_bot(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_3748,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(rw,[status(thm)],[i_0_2286,c_0_1522]),
[final] ).
cnf(i_0_3749,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
inference(rw,[status(thm)],[i_0_2287,c_0_1522]),
[final] ).
cnf(i_0_3750,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_2288,c_0_1522]),
[final] ).
cnf(i_0_3751,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),esk100_3(X1,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord1117847801e_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_3752,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),esk99_3(X1,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linordered_field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3753,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),
inference(split_conjunct,[status(thm)],[fact_955_numeral__3__eq__3]),
[final] ).
cnf(i_0_3754,plain,
( X1 = X2
| hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3755,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_2290]),
[final] ).
cnf(i_0_3756,plain,
( hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| hAPP(X1,X1,combi(X1),esk44_3(X1,X2,X3)) != hAPP(X1,X1,combi(X1),X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2291,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3757,plain,
( hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| hAPP(X1,X1,combi(X1),esk42_3(X1,X2,X3)) != hAPP(X1,X1,combi(X1),X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2292,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3758,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,X2,semiring_1_of_nat(X2),hAPP(int,nat,number_number_of(nat),X1)) = zero_zero(X2)
| ~ number_ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_3759,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2293,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3760,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2294,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3761,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2295,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3762,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2296,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3763,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2297,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3764,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2298,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3765,plain,
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2299,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3766,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2) = one_one(int)
| X1 != one_one(int)
| X2 != one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_3767,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk91_2(X1,X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2228]),
[final] ).
cnf(i_0_3768,plain,
( X2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk38_2(X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3769,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,nat_neg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3770,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_3771,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3772,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)
| ~ ab_sem1668676832m_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3773,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_3774,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3775,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3776,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3777,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3778,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3779,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3780,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk26_3(X1,X2,X3)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3781,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_2310,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3782,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_2311,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3783,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_2312,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3784,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_2313,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3785,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_2314,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3786,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_2315,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3787,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_2316,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3788,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk26_3(X1,X2,X3)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3789,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk15_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3790,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk46_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3791,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk56_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3792,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,abs_abs(X1),X2)),hAPP(X1,X1,abs_abs(X1),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3793,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 = X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3794,plain,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3795,plain,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3796,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk24_3(X1,X2,X3)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_3797,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3798,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_2323]),
[final] ).
cnf(i_0_3799,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk24_3(X1,X2,X3)))
| hBOOL(hAPP(fun(X1,bool),bool,X2,bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_3800,plain,
( hAPP(int,int,abs_abs(int),X1) = one_one(int)
| hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)) != one_one(int) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3801,plain,
( hBOOL(hAPP(X1,bool,X2,esk44_3(X1,X2,X3)))
| hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1376]),
[final] ).
cnf(i_0_3802,plain,
( hBOOL(hAPP(X1,bool,X2,esk42_3(X1,X2,X3)))
| hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1377]),
[final] ).
cnf(i_0_3803,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk89_2(X1,X2)),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2325]),
[final] ).
cnf(i_0_3804,plain,
( hAPP(nat,X2,semiring_1_of_nat(X2),hAPP(int,nat,number_number_of(nat),X1)) = zero_zero(X2)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| ~ number_ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3805,plain,
hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2)) = hAPP(X1,X1,combi(X1),X2),
inference(rw,[status(thm)],[i_0_2327,c_0_1522]),
[final] ).
cnf(i_0_3806,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3807,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk127_1(X1)))
| hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3808,plain,
( hAPP(X1,X1,abs_abs(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(rw,[status(thm)],[i_0_2329,c_0_1522]),
[final] ).
cnf(i_0_3809,plain,
( hAPP(X1,X1,abs_abs(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ ordere142940540dd_abs(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(rw,[status(thm)],[i_0_2330,c_0_1522]),
[final] ).
cnf(i_0_3810,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X1)) = zero_zero(int)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3811,plain,
( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X1)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3812,plain,
( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X1)) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3813,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
| ~ cancel_semigroup_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2333,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3814,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
| ~ cancel_semigroup_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2334,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3815,plain,
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
| ~ cancel146912293up_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2335,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3816,plain,
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
| ~ cancel_semigroup_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2336,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3817,plain,
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
| ~ cancel_semigroup_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2337,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3818,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,esk6_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk6_4(X1,X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2338,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3819,plain,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),hAPP(nat,nat,suc,X4)) = hAPP(nat,X1,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_2339]),
[final] ).
cnf(i_0_3820,plain,
~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),bot_bot(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[i_0_2340]),
[final] ).
cnf(i_0_3821,plain,
~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),bot_bot(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_3822,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_2342,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3823,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_2343]),
[final] ).
cnf(i_0_3824,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)),
inference(split_conjunct,[status(thm)],[i_0_2344]),
[final] ).
cnf(i_0_3825,plain,
( X1 = hAPP(nat,nat,suc,esk59_2(X2,X1))
| X1 = hAPP(nat,nat,suc,X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3826,plain,
( hAPP(X1,X1,combi(X1),X2) != bot_bot(X1)
| ~ bot(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),bot_bot(X1)),X2)) ),
inference(rw,[status(thm)],[i_0_2345,c_0_1522]),
[final] ).
cnf(i_0_3827,plain,
( hBOOL(hAPP(int,bool,nat_neg,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[i_0_2346]),
[final] ).
cnf(i_0_3828,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3829,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk90_2(X1,X2)),X1))
| hBOOL(hAPP(nat,bool,X2,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_3830,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk86_2(X1,X2)),X1))
| hBOOL(hAPP(nat,bool,X2,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3831,plain,
( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),hAPP(X3,fun(X1,X3),combk(X3,X1),X4)),X2) = bot_bot(fun(X3,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool)) ),
inference(rw,[status(thm)],[i_0_2347,c_0_1522]),
[final] ).
cnf(i_0_3832,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_2093]),
[final] ).
cnf(i_0_3833,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,abs_abs(X1),X2)))
| ~ ordere142940540dd_abs(X1) ),
inference(rw,[status(thm)],[i_0_2348,c_0_1522]),
[final] ).
cnf(i_0_3834,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),bot_bot(fun(X1,bool))))
| ~ hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3835,plain,
( hBOOL(hAPP(int,bool,X1,esk126_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3836,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),X1),X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3837,plain,
( hAPP(X1,X1,combi(X1),X2) = bot_bot(X1)
| ~ bot(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),bot_bot(X1))) ),
inference(rw,[status(thm)],[i_0_2349,c_0_1522]),
[final] ).
cnf(i_0_3838,plain,
( hAPP(X1,X1,combi(X1),X2) = bot_bot(X1)
| ~ bot(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),bot_bot(X1))) ),
inference(rw,[status(thm)],[i_0_2350,c_0_1522]),
[final] ).
cnf(i_0_3839,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3840,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),bot_bot(fun(X1,bool))))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool)) ),
inference(rw,[status(thm)],[i_0_2351,c_0_1522]),
[final] ).
cnf(i_0_3841,plain,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk96_1(X1))))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_3842,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk133_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2353]),
[final] ).
cnf(i_0_3843,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk132_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2354]),
[final] ).
cnf(i_0_3844,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk131_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2355]),
[final] ).
cnf(i_0_3845,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk130_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2236]),
[final] ).
cnf(i_0_3846,plain,
( X1 = hAPP(nat,nat,suc,esk92_1(X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2356]),
[final] ).
cnf(i_0_3847,plain,
( X1 = hAPP(nat,nat,suc,esk82_1(X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2357]),
[final] ).
cnf(i_0_3848,plain,
hAPP(fun(X1,bool),X1,the_elem(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool)))) = hAPP(X1,X1,combi(X1),X2),
inference(rw,[status(thm)],[i_0_2358,c_0_1522]),
[final] ).
cnf(i_0_3849,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk28_2(X1,X2)),esk27_2(X1,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2359,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3850,plain,
hAPP(fun(nat,bool),nat,finite_card(nat),X1) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_3851,plain,
( hBOOL(hAPP(int,bool,X1,esk115_3(X2,X1,X3)))
| hBOOL(hAPP(int,bool,X1,X2))
| hBOOL(hAPP(int,bool,X1,esk114_3(X2,X1,X3)))
| ~ hBOOL(hAPP(int,bool,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3852,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2) != bot_bot(fun(sum_sum(X3,X1),bool)) ),
inference(rw,[status(thm)],[i_0_2361,c_0_1522]),
[final] ).
cnf(i_0_3853,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4) != bot_bot(fun(sum_sum(X1,X3),bool)) ),
inference(rw,[status(thm)],[i_0_2362,c_0_1522]),
[final] ).
cnf(i_0_3854,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,abs_abs(X1),X2)))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2363]),
[final] ).
cnf(i_0_3855,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2364]),
[final] ).
cnf(i_0_3856,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2365]),
[final] ).
cnf(i_0_3857,plain,
( hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4) = bot_bot(fun(sum_sum(X1,X3),bool))
| hAPP(fun(X3,bool),fun(X3,bool),combi(fun(X3,bool)),X4) != bot_bot(fun(X3,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2366,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3858,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,abs_abs(X1),X2)))
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2367]),
[final] ).
cnf(i_0_3859,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_2290]),
[final] ).
cnf(i_0_3860,plain,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_3861,plain,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2369]),
[final] ).
cnf(i_0_3862,plain,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),zero_zero(nat)) = hAPP(X1,X1,combi(X1),X2),
inference(rw,[status(thm)],[i_0_2370,c_0_1522]),
[final] ).
cnf(i_0_3863,plain,
( hAPP(int,nat,number_number_of(nat),X1) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2371]),
[final] ).
cnf(i_0_3864,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_3865,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
inference(split_conjunct,[status(thm)],[i_0_2373]),
[final] ).
cnf(i_0_3866,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat))))
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3867,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_2374]),
[final] ).
cnf(i_0_3868,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3869,plain,
( ~ bot(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),bot_bot(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2375]),
[final] ).
cnf(i_0_3870,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3871,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_2376]),
[final] ).
cnf(i_0_3872,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,pls))) = hAPP(X1,X1,combi(X1),X2)
| ~ number_ring(X1) ),
inference(rw,[status(thm)],[i_0_2377,c_0_1522]),
[final] ).
cnf(i_0_3873,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2378]),
[final] ).
cnf(i_0_3874,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk93_3(X1,X2,X3)),esk94_3(X1,X2,X3))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(rw,[status(thm)],[i_0_2379,c_0_1522]),
[final] ).
cnf(i_0_3875,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk87_3(X1,X2,X3)),esk88_3(X1,X2,X3))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(rw,[status(thm)],[i_0_2380,c_0_1522]),
[final] ).
cnf(i_0_3876,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_3877,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,X2,semiring_1_of_nat(X2),hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,X2,number_number_of(X2),X1)
| ~ number_ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3878,plain,
( hAPP(X1,X1,hAPP(nat,fun(X1,X1),hAPP(fun(X1,X1),fun(nat,fun(X1,X1)),semiri532925092at_aux(X1),X2),zero_zero(nat)),X3) = hAPP(X1,X1,combi(X1),X3)
| ~ semiring_1(X1) ),
inference(rw,[status(thm)],[i_0_2382,c_0_1522]),
[final] ).
cnf(i_0_3879,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_3880,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[i_0_2384]),
[final] ).
cnf(i_0_3881,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[i_0_2385]),
[final] ).
cnf(i_0_3882,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_3883,plain,
( X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2387]),
[final] ).
cnf(i_0_3884,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,int,number_number_of(int),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3885,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2388]),
[final] ).
cnf(i_0_3886,plain,
( X1 != X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_3887,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_3888,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2389]),
[final] ).
cnf(i_0_3889,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2390]),
[final] ).
cnf(i_0_3890,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3891,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3892,plain,
( X1 = X3
| X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2391]),
[final] ).
cnf(i_0_3893,plain,
( X1 = zero_zero(nat)
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3894,plain,
( X2 = X3
| X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2393]),
[final] ).
cnf(i_0_3895,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2394]),
[final] ).
cnf(i_0_3896,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2395]),
[final] ).
cnf(i_0_3897,plain,
( X1 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2396]),
[final] ).
cnf(i_0_3898,plain,
( X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2397]),
[final] ).
cnf(i_0_3899,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(split_conjunct,[status(thm)],[i_0_2398]),
[final] ).
cnf(i_0_3900,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2399]),
[final] ).
cnf(i_0_3901,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2400]),
[final] ).
cnf(i_0_3902,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2401]),
[final] ).
cnf(i_0_3903,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2402]),
[final] ).
cnf(i_0_3904,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk46_2(X1,X2)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3905,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk15_2(X1,X2)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3906,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk56_2(X1,X2)),X2))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3907,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ cancel_semigroup_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2403,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3908,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ cancel_semigroup_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2404,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3909,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2405,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3910,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2406,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3911,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2407,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3912,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_2408,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3913,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = hAPP(X1,X1,combi(X1),X2),
inference(rw,[status(thm)],[i_0_2409,c_0_1522]),
[final] ).
cnf(i_0_3914,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = hAPP(X1,X1,combi(X1),X3),
inference(rw,[status(thm)],[i_0_2410,c_0_1522]),
[final] ).
cnf(i_0_3915,plain,
hAPP(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),combi(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
inference(rw,[status(thm)],[i_0_2411,c_0_1522]),
[final] ).
cnf(i_0_3916,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2412]),
[final] ).
cnf(i_0_3917,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X2),X1) = zero_zero(int) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3918,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,nat_neg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2346]),
[final] ).
cnf(i_0_3919,plain,
hAPP(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),combi(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool))),finite2073411215e_idem(X1)) = finite2073411215e_idem(X1),
inference(rw,[status(thm)],[i_0_2413,c_0_1522]),
[final] ).
cnf(i_0_3920,plain,
hAPP(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool)),combi(fun(fun(X1,fun(X1,X1)),fun(fun(fun(X1,bool),X1),bool))),finite_folding_one(X1)) = finite_folding_one(X1),
inference(rw,[status(thm)],[i_0_2414,c_0_1522]),
[final] ).
cnf(i_0_3921,plain,
~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),X1))),
inference(split_conjunct,[status(thm)],[i_0_2415]),
[final] ).
cnf(i_0_3922,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),bot_bot(fun(X1,bool))),X2)),
inference(split_conjunct,[status(thm)],[i_0_2416]),
[final] ).
cnf(i_0_3923,plain,
~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))),
inference(split_conjunct,[status(thm)],[i_0_2417]),
[final] ).
cnf(i_0_3924,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk20_2(X1,X2)),X2)) ),
inference(rw,[status(thm)],[i_0_2418,c_0_1522]),
[final] ).
cnf(i_0_3925,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk19_2(X1,X2)),X2)) ),
inference(rw,[status(thm)],[i_0_2419,c_0_1522]),
[final] ).
cnf(i_0_3926,plain,
X1 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),esk134_1(X1))),hAPP(nat,int,semiring_1_of_nat(int),esk135_1(X1))),
inference(split_conjunct,[status(thm)],[i_0_2420]),
[final] ).
cnf(i_0_3927,plain,
( hAPP(fun(X1,bool),X1,the(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,combi(X1),esk41_3(X1,X2,X3)) != hAPP(X1,X1,combi(X1),X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2421,c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3928,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(int,bool,X1,esk127_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3929,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X4) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != bot_bot(fun(X2,bool)) ),
inference(rw,[status(thm)],[i_0_2422,c_0_1522]),
[final] ).
cnf(i_0_3930,plain,
( hAPP(fun(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X4) = bot_bot(fun(X2,bool))
| bot_bot(fun(X1,bool)) != hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4) ),
inference(rw,[status(thm)],[i_0_2423,c_0_1522]),
[final] ).
cnf(i_0_3931,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_2424,c_0_1522]),
[final] ).
cnf(i_0_3932,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| X2 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_3933,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| X2 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_3934,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_2427]),
[final] ).
cnf(i_0_3935,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(int,X1,number_number_of(X1),pls)),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ number_ring(X1) ),
inference(rw,[status(thm)],[i_0_2428,c_0_1522]),
[final] ).
cnf(i_0_3936,plain,
( hBOOL(hAPP(int,bool,nat_neg,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3937,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(int,int,succ,X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),hAPP(int,X1,number_number_of(X1),X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2429]),
[final] ).
cnf(i_0_3938,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,suc,X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_3939,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,esk96_1(X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_3940,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),bot_bot(X1)))
| hAPP(X1,X1,combi(X1),X2) != bot_bot(X1)
| ~ bot(X1) ),
inference(rw,[status(thm)],[i_0_2431,c_0_1522]),
[final] ).
cnf(i_0_3941,plain,
( hAPP(fun(X1,bool),X1,the(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,X2,esk41_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(rw,[status(thm)],[i_0_2432,c_0_1522]),
[final] ).
cnf(i_0_3942,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)),
inference(split_conjunct,[status(thm)],[i_0_2433]),
[final] ).
cnf(i_0_3943,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2357]),
[final] ).
cnf(i_0_3944,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))),
inference(split_conjunct,[status(thm)],[i_0_2434]),
[final] ).
cnf(i_0_3945,plain,
( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2435,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3946,plain,
( hAPP(X1,X1,combi(X1),X2) = bot_bot(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),bot_bot(X1)),X2))
| ~ bot(X1) ),
inference(rw,[status(thm)],[i_0_2436,c_0_1522]),
[final] ).
cnf(i_0_3947,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1)))
| ~ ring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2437]),
[final] ).
cnf(i_0_3948,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1)))
| ~ ring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2438]),
[final] ).
cnf(i_0_3949,plain,
( X1 = zero_zero(nat)
| X1 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_3950,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_3951,plain,
( X1 = zero_zero(nat)
| X1 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_3952,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| X1 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_3953,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_3954,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_3955,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk27_2(X1,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[i_0_2440,c_0_1522]),
[final] ).
cnf(i_0_3956,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk30_2(X1,X2)),esk31_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2441,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3957,plain,
( hBOOL(hAPP(nat,bool,X1,esk98_2(X2,X1)))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3958,plain,
( hBOOL(hAPP(nat,bool,X1,esk90_2(X2,X1)))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_3959,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| X1 != hAPP(nat,nat,suc,zero_zero(nat))
| X2 != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_3960,plain,
( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ ring_n68954251visors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2442,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3961,plain,
( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2443,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3962,plain,
( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2444,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3963,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != zero_zero(X1)
| ~ group_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2445,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3964,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) != zero_zero(X1)
| ~ ab_group_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2446,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3965,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_3966,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_2447,c_0_1522]),
[final] ).
cnf(i_0_3967,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_2448,c_0_1522]),
[final] ).
cnf(i_0_3968,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),one_one(nat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2449]),
[final] ).
cnf(i_0_3969,plain,
( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2) = bot_bot(fun(X3,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool)) ),
inference(rw,[status(thm)],[i_0_2450,c_0_1522]),
[final] ).
cnf(i_0_3970,plain,
( bot_bot(fun(X3,bool)) = 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),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool)) ),
inference(rw,[status(thm)],[i_0_2451,c_0_1522]),
[final] ).
cnf(i_0_3971,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[i_0_2452,c_0_1522]),
[final] ).
cnf(i_0_3972,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X3) != bot_bot(fun(X1,bool)),
inference(split_conjunct,[status(thm)],[i_0_2453]),
[final] ).
cnf(i_0_3973,plain,
bot_bot(fun(X1,bool)) != 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_2454]),
[final] ).
cnf(i_0_3974,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_3975,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_3976,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),bot_bot(X1)),X2))
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2457]),
[final] ).
cnf(i_0_3977,plain,
( X1 = zero_zero(nat)
| X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_3978,plain,
( X1 = zero_zero(nat)
| X2 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_3979,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2458]),
[final] ).
cnf(i_0_3980,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2459]),
[final] ).
cnf(i_0_3981,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ group_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2460,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3982,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ ab_group_add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2461,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_3983,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2462]),
[final] ).
cnf(i_0_3984,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_2463]),
[final] ).
cnf(i_0_3985,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
inference(split_conjunct,[status(thm)],[fact_812_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]),
[final] ).
cnf(i_0_3986,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
inference(split_conjunct,[status(thm)],[fact_814_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]),
[final] ).
cnf(i_0_3987,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
inference(split_conjunct,[status(thm)],[fact_762_int__0__less__1]),
[final] ).
cnf(i_0_3988,plain,
( X1 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_3989,plain,
( X1 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2464]),
[final] ).
cnf(i_0_3990,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2465]),
[final] ).
cnf(i_0_3991,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2466]),
[final] ).
cnf(i_0_3992,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_3993,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),bot_bot(fun(X1,bool))) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
inference(rw,[status(thm)],[i_0_2467,c_0_1522]),
[final] ).
cnf(i_0_3994,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3995,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2393]),
[final] ).
cnf(i_0_3996,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2391]),
[final] ).
cnf(i_0_3997,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_2245]),
[final] ).
cnf(i_0_3998,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_2242]),
[final] ).
cnf(i_0_3999,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_2468]),
[final] ).
cnf(i_0_4000,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(int,X1,number_number_of(X1),pls)) = hAPP(X1,X1,combi(X1),X2)
| ~ number_ring(X1) ),
inference(rw,[status(thm)],[i_0_2469,c_0_1522]),
[final] ).
cnf(i_0_4001,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2470]),
[final] ).
cnf(i_0_4002,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2471]),
[final] ).
cnf(i_0_4003,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2472]),
[final] ).
cnf(i_0_4004,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2473]),
[final] ).
cnf(i_0_4005,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2474]),
[final] ).
cnf(i_0_4006,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2475]),
[final] ).
cnf(i_0_4007,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2476]),
[final] ).
cnf(i_0_4008,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
inference(split_conjunct,[status(thm)],[fact_985_rel__simps_I19_J]),
[final] ).
cnf(i_0_4009,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2477]),
[final] ).
cnf(i_0_4010,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2478]),
[final] ).
cnf(i_0_4011,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2479]),
[final] ).
cnf(i_0_4012,plain,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2480]),
[final] ).
cnf(i_0_4013,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_2481,c_0_1522]),
[final] ).
cnf(i_0_4014,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
| ~ linord219039673up_add(X1) ),
inference(rw,[status(thm)],[i_0_2482,c_0_1522]),
[final] ).
cnf(i_0_4015,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| zero_zero(X1) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
| ~ linord219039673up_add(X1) ),
inference(rw,[status(thm)],[i_0_2483,c_0_1522]),
[final] ).
cnf(i_0_4016,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_2484,c_0_1522]),
[final] ).
cnf(i_0_4017,plain,
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ semiri456707255roduct(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2485,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_4018,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| X1 != zero_zero(nat)
| X2 != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_4019,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| X1 != hAPP(nat,nat,suc,zero_zero(nat))
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_4020,plain,
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)
| X1 != zero_zero(nat)
| X2 != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_4021,plain,
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)
| X1 != hAPP(nat,nat,suc,zero_zero(nat))
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_4022,plain,
hAPP(fun(X1,fun(fun(nat,X1),fun(nat,X1))),fun(X1,fun(fun(nat,X1),fun(nat,X1))),combi(fun(X1,fun(fun(nat,X1),fun(nat,X1)))),nat_case(X1)) = nat_case(X1),
inference(rw,[status(thm)],[i_0_2486,c_0_1522]),
[final] ).
cnf(i_0_4023,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_2487,c_0_1522]),
[final] ).
cnf(i_0_4024,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),bot_bot(fun(X1,bool))),X2) = bot_bot(fun(X1,bool)),
inference(split_conjunct,[status(thm)],[i_0_2488]),
[final] ).
cnf(i_0_4025,plain,
( hAPP(fun(X2,bool),fun(X2,bool),combi(fun(X2,bool)),esk94_3(X2,X3,X1)) = bot_bot(fun(X2,bool))
| X1 != zero_zero(nat)
| hAPP(fun(X2,bool),nat,finite_card(X2),X3) != hAPP(nat,nat,suc,X1) ),
inference(rw,[status(thm)],[i_0_2489,c_0_1522]),
[final] ).
cnf(i_0_4026,plain,
( hAPP(fun(X2,bool),fun(X2,bool),combi(fun(X2,bool)),esk88_3(X2,X3,X1)) = bot_bot(fun(X2,bool))
| X1 != zero_zero(nat)
| hAPP(fun(X2,bool),nat,finite_card(X2),X3) != hAPP(nat,nat,suc,X1) ),
inference(rw,[status(thm)],[i_0_2490,c_0_1522]),
[final] ).
cnf(i_0_4027,plain,
( hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) != bot_bot(fun(X1,bool))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_4028,plain,
( bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2492]),
[final] ).
cnf(i_0_4029,plain,
( X1 = zero_zero(nat)
| X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_4030,plain,
( X2 = one_one(nat)
| X1 = zero_zero(nat)
| X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2494]),
[final] ).
cnf(i_0_4031,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2495]),
[final] ).
cnf(i_0_4032,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2495]),
[final] ).
cnf(i_0_4033,plain,
( X1 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2496]),
[final] ).
cnf(i_0_4034,plain,
( X1 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != one_one(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2496]),
[final] ).
cnf(i_0_4035,plain,
( X1 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_4036,plain,
( X1 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_4037,plain,
( X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2498]),
[final] ).
cnf(i_0_4038,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ ring_n68954251visors(X1) ),
inference(rw,[status(thm)],[i_0_2499,c_0_1522]),
[final] ).
cnf(i_0_4039,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ ring_n68954251visors(X1) ),
inference(rw,[status(thm)],[i_0_2500,c_0_1522]),
[final] ).
cnf(i_0_4040,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ linord219039673up_add(X1) ),
inference(rw,[status(thm)],[i_0_2501,c_0_1522]),
[final] ).
cnf(i_0_4041,plain,
( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ linord219039673up_add(X1) ),
inference(rw,[status(thm)],[i_0_2502,c_0_1522]),
[final] ).
cnf(i_0_4042,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_2503,c_0_1522]),
[final] ).
cnf(i_0_4043,plain,
hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),bot_bot(fun(X1,bool))) = bot_bot(fun(X2,bool)),
inference(split_conjunct,[status(thm)],[i_0_2504]),
[final] ).
cnf(i_0_4044,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),X2) = bot_bot(fun(X1,bool)),
inference(split_conjunct,[status(thm)],[i_0_2505]),
[final] ).
cnf(i_0_4045,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),esk94_3(X1,X2,X3)) = X3
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1415]),
[final] ).
cnf(i_0_4046,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),esk88_3(X1,X2,X3)) = X3
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(nat,nat,suc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1318]),
[final] ).
cnf(i_0_4047,plain,
( hAPP(fun(fun(X1,X1),fun(nat,fun(X1,X1))),fun(fun(X1,X1),fun(nat,fun(X1,X1))),combi(fun(fun(X1,X1),fun(nat,fun(X1,X1)))),semiri532925092at_aux(X1)) = semiri532925092at_aux(X1)
| ~ semiring_1(X1) ),
inference(rw,[status(thm)],[i_0_2506,c_0_1522]),
[final] ).
cnf(i_0_4048,plain,
hBOOL(hAPP(fun(X1,fun(fun(X1,bool),fun(X1,bool))),bool,finite_comp_fun_idem(X1,fun(X1,bool)),insert(X1))),
inference(split_conjunct,[status(thm)],[i_0_2507]),
[final] ).
cnf(i_0_4049,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
| one_one(nat) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2325]),
[final] ).
cnf(i_0_4050,plain,
bot_bot(fun(int,bool)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))),
inference(split_conjunct,[status(thm)],[fact_886_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]),
[final] ).
cnf(i_0_4051,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool)) ),
inference(rw,[status(thm)],[i_0_2508,c_0_1522]),
[final] ).
cnf(i_0_4052,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = hAPP(X2,X2,combi(X2),X3),
inference(rw,[status(thm)],[i_0_2509,c_0_1522]),
[final] ).
cnf(i_0_4053,plain,
hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)) = hAPP(X1,X1,combi(X1),X2),
inference(rw,[status(thm)],[i_0_2510,c_0_1522]),
[final] ).
cnf(i_0_4054,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_monoid_mult(X1) ),
inference(rw,[status(thm)],[i_0_2511,c_0_1522]),
[final] ).
cnf(i_0_4055,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_semiring_1(X1) ),
inference(rw,[status(thm)],[i_0_2512,c_0_1522]),
[final] ).
cnf(i_0_4056,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ monoid_mult(X1) ),
inference(rw,[status(thm)],[i_0_2513,c_0_1522]),
[final] ).
cnf(i_0_4057,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_semiring_1(X1) ),
inference(rw,[status(thm)],[i_0_2514,c_0_1522]),
[final] ).
cnf(i_0_4058,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_monoid_add(X1) ),
inference(rw,[status(thm)],[i_0_2515,c_0_1522]),
[final] ).
cnf(i_0_4059,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ monoid_add(X1) ),
inference(rw,[status(thm)],[i_0_2516,c_0_1522]),
[final] ).
cnf(i_0_4060,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_monoid_mult(X1) ),
inference(rw,[status(thm)],[i_0_2517,c_0_1522]),
[final] ).
cnf(i_0_4061,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_semiring_1(X1) ),
inference(rw,[status(thm)],[i_0_2518,c_0_1522]),
[final] ).
cnf(i_0_4062,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = hAPP(X1,X1,combi(X1),X2)
| ~ monoid_mult(X1) ),
inference(rw,[status(thm)],[i_0_2519,c_0_1522]),
[final] ).
cnf(i_0_4063,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_semiring_1(X1) ),
inference(rw,[status(thm)],[i_0_2520,c_0_1522]),
[final] ).
cnf(i_0_4064,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = hAPP(X1,X1,combi(X1),X2)
| ~ comm_monoid_add(X1) ),
inference(rw,[status(thm)],[i_0_2521,c_0_1522]),
[final] ).
cnf(i_0_4065,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = hAPP(X1,X1,combi(X1),X2)
| ~ monoid_add(X1) ),
inference(rw,[status(thm)],[i_0_2522,c_0_1522]),
[final] ).
cnf(i_0_4066,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),zero_zero(X1)) = hAPP(X1,X1,combi(X1),X2)
| ~ group_add(X1) ),
inference(rw,[status(thm)],[i_0_2523,c_0_1522]),
[final] ).
cnf(i_0_4067,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(rw,[status(thm)],[i_0_2524,c_0_1522]),
[final] ).
cnf(i_0_4068,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(rw,[status(thm)],[i_0_2525,c_0_1522]),
[final] ).
cnf(i_0_4069,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X1),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_4070,plain,
hAPP(int,int,succ,X1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)),
inference(split_conjunct,[status(thm)],[i_0_2527]),
[final] ).
cnf(i_0_4071,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),one_one(nat)),
inference(split_conjunct,[status(thm)],[i_0_2528]),
[final] ).
cnf(i_0_4072,plain,
hAPP(nat,fun(nat,bool),ord_less(nat),X1) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),
inference(split_conjunct,[status(thm)],[i_0_2529]),
[final] ).
cnf(i_0_4073,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(X1,X1,abs_abs(X1),X2)) = hAPP(X1,X1,abs_abs(X1),X2)
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2530]),
[final] ).
cnf(i_0_4074,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_2531,c_0_1522]),
[final] ).
cnf(i_0_4075,plain,
( hAPP(X1,X1,abs_abs(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)) = hAPP(nat,X1,semiring_1_of_nat(X1),X2)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2532]),
[final] ).
cnf(i_0_4076,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_2533,c_0_1522]),c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_4077,plain,
hAPP(fun(fun(X1,fun(X2,X2)),bool),fun(fun(X1,fun(X2,X2)),bool),combi(fun(fun(X1,fun(X2,X2)),bool)),finite_comp_fun_idem(X1,X2)) = finite_comp_fun_idem(X1,X2),
inference(rw,[status(thm)],[i_0_2534,c_0_1522]),
[final] ).
cnf(i_0_4078,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,X1,semiring_1_of_nat(X1),X2)
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2535]),
[final] ).
cnf(i_0_4079,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rw,[status(thm)],[i_0_2536,c_0_1522]),
[final] ).
cnf(i_0_4080,plain,
hAPP(X1,X1,combi(X1),hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(rw,[status(thm)],[i_0_2537,c_0_1522]),
[final] ).
cnf(i_0_4081,plain,
hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),X1),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4082,plain,
hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(bool,fun(X1,fun(X1,X1))),combi(fun(bool,fun(X1,fun(X1,X1)))),if(X1)) = if(X1),
inference(rw,[status(thm)],[i_0_2539,c_0_1522]),
[final] ).
cnf(i_0_4083,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_954_numeral__1__eq__Suc__0]),
[final] ).
cnf(i_0_4084,plain,
hAPP(fun(X1,fun(fun(X1,bool),X1)),fun(X1,fun(fun(X1,bool),X1)),combi(fun(X1,fun(fun(X1,bool),X1))),partial_flat_lub(X1)) = partial_flat_lub(X1),
inference(rw,[status(thm)],[i_0_2540,c_0_1522]),
[final] ).
cnf(i_0_4085,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_2541,c_0_1522]),
[final] ).
cnf(i_0_4086,plain,
bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse)),
inference(split_conjunct,[status(thm)],[i_0_2542]),
[final] ).
cnf(i_0_4087,plain,
( hBOOL(hAPP(X1,bool,X2,esk17_2(X1,X2)))
| hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_4088,plain,
( hBOOL(hAPP(X1,bool,X2,esk18_2(X1,X2)))
| bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2492]),
[final] ).
cnf(i_0_4089,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != bot_bot(fun(X1,bool)) ),
inference(rw,[status(thm)],[i_0_2543,c_0_1522]),
[final] ).
cnf(i_0_4090,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_4091,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_4092,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2544]),
[final] ).
cnf(i_0_4093,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2545]),
[final] ).
cnf(i_0_4094,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ mult_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2546]),
[final] ).
cnf(i_0_4095,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2547]),
[final] ).
cnf(i_0_4096,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ mult_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2548]),
[final] ).
cnf(i_0_4097,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X2) = zero_zero(X1)
| ~ group_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2549]),
[final] ).
cnf(i_0_4098,plain,
( X2 = X3
| hAPP(int,X1,number_number_of(X1),X2) != hAPP(int,X1,number_number_of(X1),X3)
| ~ number_ring(X1)
| ~ ring_char_0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2550]),
[final] ).
cnf(i_0_4099,plain,
( X2 = X3
| hAPP(nat,X1,semiring_1_of_nat(X1),X2) != hAPP(nat,X1,semiring_1_of_nat(X1),X3)
| ~ semiring_char_0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2551]),
[final] ).
cnf(i_0_4100,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X1 != one_one(nat)
| X2 != one_one(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2496]),
[final] ).
cnf(i_0_4101,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = zero_zero(nat)
| X1 != zero_zero(nat)
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2495]),
[final] ).
cnf(i_0_4102,plain,
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)
| X1 != one_one(nat)
| X2 != one_one(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_4103,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2552]),
[final] ).
cnf(i_0_4104,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X1) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2553]),
[final] ).
cnf(i_0_4105,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_1907]),
[final] ).
cnf(i_0_4106,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_4107,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) = zero_zero(nat)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_4108,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2554]),
[final] ).
cnf(i_0_4109,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2555]),
[final] ).
cnf(i_0_4110,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2556]),
[final] ).
cnf(i_0_4111,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2557]),
[final] ).
cnf(i_0_4112,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = X2
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_4113,hypothesis,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ),
inference(rw,[status(thm)],[i_0_2558,c_0_1522]),
[final] ).
cnf(i_0_4114,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2559]),
[final] ).
cnf(i_0_4115,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),one_one(int)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2560]),
[final] ).
cnf(i_0_4116,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),zero_zero(int)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2561]),
[final] ).
cnf(i_0_4117,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),one_one(nat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2562]),
[final] ).
cnf(i_0_4118,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2563]),
[final] ).
cnf(i_0_4119,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),zero_zero(nat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2564]),
[final] ).
cnf(i_0_4120,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2565]),
[final] ).
cnf(i_0_4121,plain,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2566]),
[final] ).
cnf(i_0_4122,plain,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2567]),
[final] ).
cnf(i_0_4123,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),pls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2568]),
[final] ).
cnf(i_0_4124,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),pls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2569]),
[final] ).
cnf(i_0_4125,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2570]),
[final] ).
cnf(i_0_4126,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X1) = pls,
inference(split_conjunct,[status(thm)],[i_0_2571]),
[final] ).
cnf(i_0_4127,plain,
~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
inference(split_conjunct,[status(thm)],[i_0_2572]),
[final] ).
cnf(i_0_4128,plain,
~ hBOOL(hAPP(int,bool,nat_neg,one_one(int))),
inference(split_conjunct,[status(thm)],[i_0_2573]),
[final] ).
cnf(i_0_4129,plain,
( ~ hBOOL(hAPP(bool,bool,fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2574]),
[final] ).
cnf(i_0_4130,plain,
( X1 = X2
| hAPP(int,int,bit1,X1) != hAPP(int,int,bit1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2575]),
[final] ).
cnf(i_0_4131,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2576]),
[final] ).
cnf(i_0_4132,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2577]),
[final] ).
cnf(i_0_4133,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2578]),
[final] ).
cnf(i_0_4134,plain,
( hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2579]),
[final] ).
cnf(i_0_4135,plain,
( one_one(X1) = hAPP(int,X1,number_number_of(X1),hAPP(int,int,bit1,pls))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2580]),
[final] ).
cnf(i_0_4136,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat))) = one_one(int),
inference(split_conjunct,[status(thm)],[fact_869_int__Suc0__eq__1]),
[final] ).
cnf(i_0_4137,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_2581,c_0_1522]),
[final] ).
cnf(i_0_4138,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat),
inference(split_conjunct,[status(thm)],[fact_959_nat__numeral__1__eq__1]),
[final] ).
cnf(i_0_4139,plain,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_960_one__is__num__one]),
[final] ).
cnf(i_0_4140,plain,
one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_958_Numeral1__eq1__nat]),
[final] ).
cnf(i_0_4141,plain,
( hBOOL(hAPP(fun(X1,fun(X1,X1)),bool,finite_comp_fun_idem(X1,X1),times_times(X1)))
| ~ ab_sem1668676832m_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2582]),
[final] ).
cnf(i_0_4142,plain,
( hAPP(X1,X1,abs_abs(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(rw,[status(thm)],[i_0_2583,c_0_1522]),
[final] ).
cnf(i_0_4143,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,X1,abs_abs(X1),X2) != zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(rw,[status(thm)],[i_0_2584,c_0_1522]),
[final] ).
cnf(i_0_4144,plain,
hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),bot_bot(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[i_0_2585]),
[final] ).
cnf(i_0_4145,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_2586,c_0_1522]),
[final] ).
cnf(i_0_4146,plain,
hAPP(fun(X1,fun(X2,X1)),fun(X1,fun(X2,X1)),combi(fun(X1,fun(X2,X1))),combk(X1,X2)) = combk(X1,X2),
inference(rw,[status(thm)],[i_0_2587,c_0_1522]),
[final] ).
cnf(i_0_4147,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
| ~ mult_zero(X1) ),
inference(rw,[status(thm)],[i_0_2588,c_0_1522]),
[final] ).
cnf(i_0_4148,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
| ~ no_zero_divisors(X1) ),
inference(rw,[status(thm)],[i_0_2589,c_0_1522]),
[final] ).
cnf(i_0_4149,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
| ~ semiring(X1) ),
inference(rw,[status(thm)],[i_0_2590,c_0_1522]),
[final] ).
cnf(i_0_4150,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
| ~ monoid_mult(X1) ),
inference(rw,[status(thm)],[i_0_2591,c_0_1522]),
[final] ).
cnf(i_0_4151,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
| ~ ab_semigroup_mult(X1) ),
inference(rw,[status(thm)],[i_0_2592,c_0_1522]),
[final] ).
cnf(i_0_4152,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),plus_plus(X1)) = plus_plus(X1)
| ~ ab_semigroup_add(X1) ),
inference(rw,[status(thm)],[i_0_2593,c_0_1522]),
[final] ).
cnf(i_0_4153,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),plus_plus(X1)) = plus_plus(X1)
| ~ cancel_semigroup_add(X1) ),
inference(rw,[status(thm)],[i_0_2594,c_0_1522]),
[final] ).
cnf(i_0_4154,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),plus_plus(X1)) = plus_plus(X1)
| ~ monoid_add(X1) ),
inference(rw,[status(thm)],[i_0_2595,c_0_1522]),
[final] ).
cnf(i_0_4155,plain,
( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),minus_minus(X1)) = minus_minus(X1)
| ~ minus(X1) ),
inference(rw,[status(thm)],[i_0_2596,c_0_1522]),
[final] ).
cnf(i_0_4156,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2597]),
[final] ).
cnf(i_0_4157,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2598]),
[final] ).
cnf(i_0_4158,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)
| ~ ord(X1) ),
inference(rw,[status(thm)],[i_0_2599,c_0_1522]),
[final] ).
cnf(i_0_4159,plain,
( hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
inference(rw,[status(thm)],[i_0_2600,c_0_1522]),
[final] ).
cnf(i_0_4160,plain,
hAPP(fun(fun(X1,bool),X1),fun(fun(X1,bool),X1),combi(fun(fun(X1,bool),X1)),the_elem(X1)) = the_elem(X1),
inference(rw,[status(thm)],[i_0_2601,c_0_1522]),
[final] ).
cnf(i_0_4161,plain,
hAPP(fun(fun(X1,bool),X1),fun(fun(X1,bool),X1),combi(fun(fun(X1,bool),X1)),the(X1)) = the(X1),
inference(rw,[status(thm)],[i_0_2602,c_0_1522]),
[final] ).
cnf(i_0_4162,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_2603,c_0_1522]),
[final] ).
cnf(i_0_4163,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_2604,c_0_1522]),
[final] ).
cnf(i_0_4164,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_2605,c_0_1522]),
[final] ).
cnf(i_0_4165,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
inference(split_conjunct,[status(thm)],[conj_0]),
[final] ).
cnf(i_0_4166,hypothesis,
( hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[i_0_2606,c_0_1522]),
[final] ).
cnf(i_0_4167,plain,
hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combi(fun(int,fun(int,int))),nat_tsub) = nat_tsub,
inference(rw,[status(thm)],[i_0_2607,c_0_1522]),
[final] ).
cnf(i_0_4168,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_2608,c_0_1522]),
[final] ).
cnf(i_0_4169,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_2609,c_0_1522]),
[final] ).
cnf(i_0_4170,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_2610,c_0_1522]),
[final] ).
cnf(i_0_4171,plain,
( hAPP(bool,bool,combi(bool),X1) = fFalse
| hAPP(bool,bool,combi(bool),X1) = fTrue ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2611,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_4172,plain,
( hAPP(bool,bool,combi(bool),X1) = fFalse
| hAPP(bool,bool,combi(bool),X1) = fTrue ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2612,c_0_1522]),c_0_1522]),
[final] ).
cnf(i_0_4173,plain,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2613]),
[final] ).
cnf(i_0_4174,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_949_succ__Pls]),
[final] ).
cnf(i_0_4175,plain,
( X1 = zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),X1) != zero_zero(int) ),
inference(split_conjunct,[status(thm)],[i_0_2614]),
[final] ).
cnf(i_0_4176,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2615]),
[final] ).
cnf(i_0_4177,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2616]),
[final] ).
cnf(i_0_4178,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2617]),
[final] ).
cnf(i_0_4179,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2618]),
[final] ).
cnf(i_0_4180,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2619]),
[final] ).
cnf(i_0_4181,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2620]),
[final] ).
cnf(i_0_4182,plain,
hAPP(nat,nat,suc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_2621]),
[final] ).
cnf(i_0_4183,plain,
X1 != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2622]),
[final] ).
cnf(i_0_4184,plain,
hAPP(int,int,bit1,X1) != pls,
inference(split_conjunct,[status(thm)],[i_0_2623]),
[final] ).
cnf(i_0_4185,plain,
pls != hAPP(int,int,bit1,X1),
inference(split_conjunct,[status(thm)],[i_0_2624]),
[final] ).
cnf(i_0_4186,plain,
hAPP(fun(option(com),com),fun(option(com),com),combi(fun(option(com),com)),the_1(com)) = the_1(com),
inference(rw,[status(thm)],[i_0_2625,c_0_1522]),
[final] ).
cnf(i_0_4187,plain,
( hAPP(fun(X1,X1),fun(X1,X1),combi(fun(X1,X1)),abs_abs(X1)) = abs_abs(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(rw,[status(thm)],[i_0_2626,c_0_1522]),
[final] ).
cnf(i_0_4188,plain,
hAPP(fun(pname,option(com)),fun(pname,option(com)),combi(fun(pname,option(com))),body) = body,
inference(rw,[status(thm)],[i_0_2627,c_0_1522]),
[final] ).
cnf(i_0_4189,plain,
hAPP(fun(X1,X1),fun(X1,X1),combi(fun(X1,X1)),combi(X1)) = combi(X1),
inference(rw,[status(thm)],[i_0_2628,c_0_1522]),
[final] ).
cnf(i_0_4190,plain,
( hAPP(fun(int,X1),fun(int,X1),combi(fun(int,X1)),number_number_of(X1)) = number_number_of(X1)
| ~ number(X1) ),
inference(rw,[status(thm)],[i_0_2629,c_0_1522]),
[final] ).
cnf(i_0_4191,plain,
( hAPP(fun(nat,X1),fun(nat,X1),combi(fun(nat,X1)),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1)
| ~ semiring_1(X1) ),
inference(rw,[status(thm)],[i_0_2630,c_0_1522]),
[final] ).
cnf(i_0_4192,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),ring_1_Ints(X1)) = ring_1_Ints(X1)
| ~ ring_1(X1) ),
inference(rw,[status(thm)],[i_0_2631,c_0_1522]),
[final] ).
cnf(i_0_4193,hypothesis,
hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g) = g,
inference(rw,[status(thm)],[i_0_2632,c_0_1522]),
[final] ).
cnf(i_0_4194,plain,
hAPP(fun(int,int),fun(int,int),combi(fun(int,int)),succ) = succ,
inference(rw,[status(thm)],[i_0_2633,c_0_1522]),
[final] ).
cnf(i_0_4195,plain,
hAPP(fun(int,int),fun(int,int),combi(fun(int,int)),bit1) = bit1,
inference(rw,[status(thm)],[i_0_2634,c_0_1522]),
[final] ).
cnf(i_0_4196,plain,
hAPP(fun(int,bool),fun(int,bool),combi(fun(int,bool)),nat_neg) = nat_neg,
inference(rw,[status(thm)],[i_0_2635,c_0_1522]),
[final] ).
cnf(i_0_4197,hypothesis,
hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc) = suc,
inference(rw,[status(thm)],[i_0_2636,c_0_1522]),
[final] ).
cnf(i_0_4198,plain,
hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot) = fNot,
inference(rw,[status(thm)],[i_0_2637,c_0_1522]),
[final] ).
cnf(i_0_4199,plain,
hAPP(fun(com,x_a),fun(com,x_a),combi(fun(com,x_a)),mgt) = mgt,
inference(rw,[status(thm)],[i_0_2638,c_0_1522]),
[final] ).
cnf(i_0_4200,plain,
hAPP(fun(com,bool),fun(com,bool),combi(fun(com,bool)),wt) = wt,
inference(rw,[status(thm)],[i_0_2639,c_0_1522]),
[final] ).
cnf(i_0_4201,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_2640,c_0_1522]),
[final] ).
cnf(i_0_4202,hypothesis,
hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) = u,
inference(rw,[status(thm)],[i_0_2641,c_0_1522]),
[final] ).
cnf(i_0_4203,plain,
hAPP(fun(X1,bool),nat,finite_card(X1),bot_bot(fun(X1,bool))) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_2642]),
[final] ).
cnf(i_0_4204,plain,
( hAPP(X2,X1,bot_bot(fun(X2,X1)),X3) = bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2643]),
[final] ).
cnf(i_0_4205,plain,
( hAPP(X2,X1,bot_bot(fun(X2,X1)),X3) = bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2644]),
[final] ).
cnf(i_0_4206,plain,
( hAPP(X1,X1,abs_abs(X1),zero_zero(X1)) = zero_zero(X1)
| ~ ordere142940540dd_abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2645]),
[final] ).
cnf(i_0_4207,plain,
( hAPP(X1,X1,abs_abs(X1),one_one(X1)) = one_one(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2646]),
[final] ).
cnf(i_0_4208,plain,
( hAPP(X1,X1,combi(X1),bot_bot(X1)) = bot_bot(X1)
| ~ bot(X1) ),
inference(rw,[status(thm)],[i_0_2647,c_0_1522]),
[final] ).
cnf(i_0_4209,plain,
( hAPP(X1,X1,combi(X1),zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(rw,[status(thm)],[i_0_2648,c_0_1522]),
[final] ).
cnf(i_0_4210,plain,
( hAPP(X1,X1,combi(X1),one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(rw,[status(thm)],[i_0_2649,c_0_1522]),
[final] ).
cnf(i_0_4211,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) = zero_zero(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2650]),
[final] ).
cnf(i_0_4212,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) = one_one(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2651]),
[final] ).
cnf(i_0_4213,plain,
hAPP(X1,X1,combi(X1),undefined(X1)) = undefined(X1),
inference(rw,[status(thm)],[i_0_2652,c_0_1522]),
[final] ).
cnf(i_0_4214,plain,
( hAPP(int,X1,number_number_of(X1),pls) = zero_zero(X1)
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2653]),
[final] ).
cnf(i_0_4215,plain,
( hAPP(int,X1,number_number_of(X1),pls) = zero_zero(X1)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2654]),
[final] ).
cnf(i_0_4216,plain,
( zero_zero(X1) = hAPP(int,X1,number_number_of(X1),pls)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2655]),
[final] ).
cnf(i_0_4217,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = zero_zero(int)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[i_0_2614]),
[final] ).
cnf(i_0_4218,plain,
( X1 = zero_zero(nat)
| X1 = hAPP(nat,nat,suc,esk97_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2656]),
[final] ).
cnf(i_0_4219,plain,
( X1 = zero_zero(nat)
| X1 = hAPP(nat,nat,suc,esk95_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2657]),
[final] ).
cnf(i_0_4220,plain,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_838_int__0]),
[final] ).
cnf(i_0_4221,plain,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
inference(split_conjunct,[status(thm)],[fact_837_int__1]),
[final] ).
cnf(i_0_4222,plain,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_863_transfer__int__nat__numerals_I1_J]),
[final] ).
cnf(i_0_4223,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
inference(split_conjunct,[status(thm)],[fact_862_transfer__int__nat__numerals_I2_J]),
[final] ).
cnf(i_0_4224,plain,
hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[fact_974_nat__number__of__Pls]),
[final] ).
cnf(i_0_4225,plain,
zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
inference(split_conjunct,[status(thm)],[fact_967_zero__is__num__zero]),
[final] ).
cnf(i_0_4226,plain,
zero_zero(nat) = hAPP(int,nat,number_number_of(nat),pls),
inference(split_conjunct,[status(thm)],[fact_975_semiring__norm_I113_J]),
[final] ).
cnf(i_0_4227,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_523_One__nat__def]),
[final] ).
cnf(i_0_4228,plain,
hAPP(int,int,number_number_of(int),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2658]),
[final] ).
cnf(i_0_4229,plain,
hAPP(int,int,combi(int),pls) = pls,
inference(rw,[status(thm)],[i_0_2659,c_0_1522]),
[final] ).
cnf(i_0_4230,hypothesis,
hAPP(nat,nat,combi(nat),na) = na,
inference(rw,[status(thm)],[i_0_2660,c_0_1522]),
[final] ).
cnf(i_0_4231,plain,
hAPP(bool,bool,combi(bool),fTrue) = fTrue,
inference(rw,[status(thm)],[i_0_2661,c_0_1522]),
[final] ).
cnf(i_0_4232,plain,
hAPP(bool,bool,combi(bool),fFalse) = fFalse,
inference(rw,[status(thm)],[i_0_2662,c_0_1522]),
[final] ).
cnf(i_0_4233,hypothesis,
hAPP(pname,pname,combi(pname),pn) = pn,
inference(rw,[status(thm)],[i_0_2663,c_0_1522]),
[final] ).
cnf(i_0_4234,plain,
( finite_finite_1(sum_sum(X2,X1))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2664]),
[final] ).
cnf(i_0_4235,plain,
( finite_finite_1(fun(X2,X1))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2665]),
[final] ).
cnf(i_0_4236,plain,
( preorder(fun(X2,X1))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2666]),
[final] ).
cnf(i_0_4237,plain,
( order(fun(X2,X1))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2667]),
[final] ).
cnf(i_0_4238,plain,
( ord(fun(X2,X1))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2668]),
[final] ).
cnf(i_0_4239,plain,
( bot(fun(X2,X1))
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2669]),
[final] ).
cnf(i_0_4240,plain,
( minus(fun(X2,X1))
| ~ minus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2670]),
[final] ).
cnf(i_0_4241,plain,
( ~ zero_neq_one(X1)
| zero_zero(X1) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2671]),
[final] ).
cnf(i_0_4242,plain,
( ~ zero_neq_one(X1)
| one_one(X1) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2672]),
[final] ).
cnf(i_0_4243,plain,
zero_zero(int) != one_one(int),
inference(split_conjunct,[status(thm)],[fact_799_int__0__neq__1]),
[final] ).
cnf(i_0_4244,plain,
bot_bot(nat) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[fact_475_bot__nat__def]),
[final] ).
cnf(i_0_4245,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[i_0_2673]),
[final] ).
cnf(i_0_4246,plain,
ordered_ring_abs(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_4247,plain,
semiring_char_0(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_4248,plain,
semiring_char_0(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_4249,plain,
number_semiring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__semiring]),
[final] ).
cnf(i_0_4250,plain,
number_semiring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Int_Onumber__semiring]),
[final] ).
cnf(i_0_4251,plain,
linord1278240602ring_1(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_4252,plain,
linordered_semiring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4253,plain,
linordered_semiring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4254,plain,
linord893533164strict(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_4255,plain,
linord893533164strict(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_4256,plain,
linord20386208strict(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_4257,plain,
linord20386208strict(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_4258,plain,
linordered_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4259,plain,
linord581940658strict(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__ring__strict]),
[final] ).
cnf(i_0_4260,plain,
ordere1490568538miring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_4261,plain,
ordere1490568538miring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_4262,plain,
ordered_semiring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4263,plain,
ordered_semiring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4264,plain,
ordered_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oordered__ring]),
[final] ).
cnf(i_0_4265,plain,
ordere453448008miring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_4266,plain,
ordere453448008miring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_4267,plain,
ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring]),
[final] ).
cnf(i_0_4268,plain,
ring_char_0(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Oring__char__0]),
[final] ).
cnf(i_0_4269,plain,
number_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]),
[final] ).
cnf(i_0_4270,plain,
comm_monoid_mult(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_4271,plain,
comm_monoid_mult(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_4272,plain,
comm_semiring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4273,plain,
comm_semiring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4274,plain,
ring_n68954251visors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_4275,plain,
linord626643107strict(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_4276,plain,
semiri456707255roduct(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]),
[final] ).
cnf(i_0_4277,plain,
semiri456707255roduct(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]),
[final] ).
cnf(i_0_4278,plain,
comm_semiring_1(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_4279,plain,
comm_semiring_1(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_4280,plain,
ordere216010020id_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_4281,plain,
ordere216010020id_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_4282,plain,
linord219039673up_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Olinordered__ab__group__add]),
[final] ).
cnf(i_0_4283,plain,
comm_monoid_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4284,plain,
comm_monoid_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4285,plain,
zero_neq_one(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_4286,plain,
zero_neq_one(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_4287,plain,
linordered_idom(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4288,plain,
linordered_semidom(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4289,plain,
linordered_semidom(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4290,plain,
ordere223160158up_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4291,plain,
ordere223160158up_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4292,plain,
group_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Ogroup__add]),
[final] ).
cnf(i_0_4293,plain,
ordere779506340up_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_4294,plain,
ordere779506340up_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_4295,plain,
ordere236663937imp_le(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_4296,plain,
ordere236663937imp_le(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_4297,plain,
cancel146912293up_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4298,plain,
cancel146912293up_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4299,plain,
ab_group_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oab__group__add]),
[final] ).
cnf(i_0_4300,plain,
ordered_ab_group_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__group__add]),
[final] ).
cnf(i_0_4301,plain,
linorder(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Olinorder]),
[final] ).
cnf(i_0_4302,plain,
linorder(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]),
[final] ).
cnf(i_0_4303,plain,
preorder(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Opreorder]),
[final] ).
cnf(i_0_4304,plain,
preorder(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]),
[final] ).
cnf(i_0_4305,plain,
preorder(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]),
[final] ).
cnf(i_0_4306,plain,
order(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Oorder]),
[final] ).
cnf(i_0_4307,plain,
order(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]),
[final] ).
cnf(i_0_4308,plain,
order(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]),
[final] ).
cnf(i_0_4309,plain,
finite_finite_1(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]),
[final] ).
cnf(i_0_4310,plain,
ord(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Oord]),
[final] ).
cnf(i_0_4311,plain,
ord(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oord]),
[final] ).
cnf(i_0_4312,plain,
ord(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oord]),
[final] ).
cnf(i_0_4313,plain,
bot(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Obot]),
[final] ).
cnf(i_0_4314,plain,
bot(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Obot]),
[final] ).
cnf(i_0_4315,plain,
semiring_1(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Osemiring__1]),
[final] ).
cnf(i_0_4316,plain,
semiring_1(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Osemiring__1]),
[final] ).
cnf(i_0_4317,plain,
ring_1(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__1]),
[final] ).
cnf(i_0_4318,plain,
number(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber]),
[final] ).
cnf(i_0_4319,plain,
number(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Int_Onumber]),
[final] ).
cnf(i_0_4320,plain,
zero(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Ozero]),
[final] ).
cnf(i_0_4321,plain,
zero(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ozero]),
[final] ).
cnf(i_0_4322,plain,
mult_zero(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Omult__zero]),
[final] ).
cnf(i_0_4323,plain,
mult_zero(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Omult__zero]),
[final] ).
cnf(i_0_4324,plain,
no_zero_divisors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_4325,plain,
no_zero_divisors(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_4326,plain,
semiring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Osemiring]),
[final] ).
cnf(i_0_4327,plain,
semiring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Osemiring]),
[final] ).
cnf(i_0_4328,plain,
monoid_mult(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4329,plain,
monoid_mult(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4330,plain,
ab_semigroup_mult(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_4331,plain,
ab_semigroup_mult(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_4332,plain,
ab_semigroup_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_4333,plain,
ab_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_4334,plain,
cancel_semigroup_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_4335,plain,
cancel_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_4336,plain,
monoid_add(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Omonoid__add]),
[final] ).
cnf(i_0_4337,plain,
monoid_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]),
[final] ).
cnf(i_0_4338,plain,
one(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oone]),
[final] ).
cnf(i_0_4339,plain,
one(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oone]),
[final] ).
cnf(i_0_4340,plain,
minus(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Ominus]),
[final] ).
cnf(i_0_4341,plain,
minus(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ominus]),
[final] ).
cnf(i_0_4342,plain,
minus(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Groups_Ominus]),
[final] ).
cnf(i_0_4343,plain,
ordere142940540dd_abs(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__group__add__abs]),
[final] ).
cnf(i_0_4344,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_976_Pls__def]),
[final] ).
cnf(i_0_4345,axiom,
X1 = X1 ).
cnf(i_0_4346,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4347,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4348,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_4349,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_4350,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_4351,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_4352,axiom,
( X1 != X2
| number_number_of(X1) = number_number_of(X2) ) ).
cnf(i_0_4353,axiom,
( X1 != X2
| the_elem(X1) = the_elem(X2) ) ).
cnf(i_0_4354,axiom,
( X1 != X2
| nat_case(X1) = nat_case(X2) ) ).
cnf(i_0_4355,axiom,
( X1 != X2
| semiri532925092at_aux(X1) = semiri532925092at_aux(X2) ) ).
cnf(i_0_4356,axiom,
( X1 != X2
| combk(X1,X3) = combk(X2,X3) ) ).
cnf(i_0_4357,axiom,
( X1 != X2
| combk(X3,X1) = combk(X3,X2) ) ).
cnf(i_0_4358,axiom,
( X1 != X2
| sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).
cnf(i_0_4359,axiom,
( X1 != X2
| sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).
cnf(i_0_4360,axiom,
( X1 != X2
| finite_card(X1) = finite_card(X2) ) ).
cnf(i_0_4361,axiom,
( X1 != X2
| if(X1) = if(X2) ) ).
cnf(i_0_4362,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_4363,axiom,
( X1 != X2
| combs(X1,X3,X4) = combs(X2,X3,X4) ) ).
cnf(i_0_4364,axiom,
( X1 != X2
| combs(X3,X1,X4) = combs(X3,X2,X4) ) ).
cnf(i_0_4365,axiom,
( X1 != X2
| combs(X3,X4,X1) = combs(X3,X4,X2) ) ).
cnf(i_0_4366,axiom,
( X1 != X2
| combb(X1,X3,X4) = combb(X2,X3,X4) ) ).
cnf(i_0_4367,axiom,
( X1 != X2
| combb(X3,X1,X4) = combb(X3,X2,X4) ) ).
cnf(i_0_4368,axiom,
( X1 != X2
| combb(X3,X4,X1) = combb(X3,X4,X2) ) ).
cnf(i_0_4369,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_4370,axiom,
( X1 != X2
| combc(X1,X3,X4) = combc(X2,X3,X4) ) ).
cnf(i_0_4371,axiom,
( X1 != X2
| combc(X3,X1,X4) = combc(X3,X2,X4) ) ).
cnf(i_0_4372,axiom,
( X1 != X2
| combc(X3,X4,X1) = combc(X3,X4,X2) ) ).
cnf(i_0_4373,axiom,
( X1 != X2
| ord_less(X1) = ord_less(X2) ) ).
cnf(i_0_4374,axiom,
( X1 != X2
| zero_zero(X1) = zero_zero(X2) ) ).
cnf(i_0_4375,axiom,
( X1 != X2
| minus_minus(X1) = minus_minus(X2) ) ).
cnf(i_0_4376,axiom,
( X1 != X2
| plus_plus(X1) = plus_plus(X2) ) ).
cnf(i_0_4377,axiom,
( X1 != X2
| abs_abs(X1) = abs_abs(X2) ) ).
cnf(i_0_4378,axiom,
( X1 != X2
| one_one(X1) = one_one(X2) ) ).
cnf(i_0_4379,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_4380,axiom,
( X1 != X2
| image(X1,X3) = image(X2,X3) ) ).
cnf(i_0_4381,axiom,
( X1 != X2
| image(X3,X1) = image(X3,X2) ) ).
cnf(i_0_4382,axiom,
( X1 != X2
| ord_less_eq(X1) = ord_less_eq(X2) ) ).
cnf(i_0_4383,axiom,
( X1 != X2
| finite_fold_image(X1,X3) = finite_fold_image(X2,X3) ) ).
cnf(i_0_4384,axiom,
( X1 != X2
| finite_fold_image(X3,X1) = finite_fold_image(X3,X2) ) ).
cnf(i_0_4385,axiom,
( X1 != X2
| finite1357897459simple(X1,X3) = finite1357897459simple(X2,X3) ) ).
cnf(i_0_4386,axiom,
( X1 != X2
| finite1357897459simple(X3,X1) = finite1357897459simple(X3,X2) ) ).
cnf(i_0_4387,axiom,
( X1 != X2
| insert(X1) = insert(X2) ) ).
cnf(i_0_4388,axiom,
( X1 != X2
| bot_bot(X1) = bot_bot(X2) ) ).
cnf(i_0_4389,axiom,
( X1 != X2
| times_times(X1) = times_times(X2) ) ).
cnf(i_0_4390,axiom,
( X1 != X2
| the(X1) = the(X2) ) ).
cnf(i_0_4391,axiom,
( X1 != X2
| the_1(X1) = the_1(X2) ) ).
cnf(i_0_4392,axiom,
( X1 != X2
| finite_folding_one(X1) = finite_folding_one(X2) ) ).
cnf(i_0_4393,axiom,
( X1 != X2
| finite2073411215e_idem(X1) = finite2073411215e_idem(X2) ) ).
cnf(i_0_4394,axiom,
( X1 != X2
| ring_1_Ints(X1) = ring_1_Ints(X2) ) ).
cnf(i_0_4395,axiom,
( X1 != X2
| finite_comp_fun_idem(X1,X3) = finite_comp_fun_idem(X2,X3) ) ).
cnf(i_0_4396,axiom,
( X1 != X2
| finite_comp_fun_idem(X3,X1) = finite_comp_fun_idem(X3,X2) ) ).
cnf(i_0_4397,axiom,
( X1 != X2
| combi(X1) = combi(X2) ) ).
cnf(i_0_4398,axiom,
( X1 != X2
| finite908156982e_idem(X1,X3) = finite908156982e_idem(X2,X3) ) ).
cnf(i_0_4399,axiom,
( X1 != X2
| finite908156982e_idem(X3,X1) = finite908156982e_idem(X3,X2) ) ).
cnf(i_0_4400,axiom,
( X1 != X2
| finite_finite(X1) = finite_finite(X2) ) ).
cnf(i_0_4401,axiom,
( X1 != X2
| semiring_1_of_nat(X1) = semiring_1_of_nat(X2) ) ).
cnf(i_0_4402,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_4403,axiom,
( X1 != X2
| partial_flat_lub(X1) = partial_flat_lub(X2) ) ).
cnf(i_0_4404,axiom,
( X1 != X2
| ~ comm_monoid_mult(X1)
| comm_monoid_mult(X2) ) ).
cnf(i_0_4405,axiom,
( X1 != X2
| ~ linordered_idom(X1)
| linordered_idom(X2) ) ).
cnf(i_0_4406,axiom,
( X1 != X2
| ~ linord1278240602ring_1(X1)
| linord1278240602ring_1(X2) ) ).
cnf(i_0_4407,axiom,
( X1 != X2
| ~ linord626643107strict(X1)
| linord626643107strict(X2) ) ).
cnf(i_0_4408,axiom,
( X1 != X2
| ~ ring(X1)
| ring(X2) ) ).
cnf(i_0_4409,axiom,
( X1 != X2
| ~ semiring(X1)
| semiring(X2) ) ).
cnf(i_0_4410,axiom,
( X1 != X2
| ~ linord20386208strict(X1)
| linord20386208strict(X2) ) ).
cnf(i_0_4411,axiom,
( X1 != X2
| ~ linordered_semiring(X1)
| linordered_semiring(X2) ) ).
cnf(i_0_4412,axiom,
( X1 != X2
| ~ ordered_semiring(X1)
| ordered_semiring(X2) ) ).
cnf(i_0_4413,axiom,
( X1 != X2
| ~ ordere236663937imp_le(X1)
| ordere236663937imp_le(X2) ) ).
cnf(i_0_4414,axiom,
( X1 != X2
| ~ semiri456707255roduct(X1)
| semiri456707255roduct(X2) ) ).
cnf(i_0_4415,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4416,axiom,
( X1 != X2
| ~ linord1117847801e_zero(X1)
| linord1117847801e_zero(X2) ) ).
cnf(i_0_4417,axiom,
( X1 != X2
| ~ ordere1490568538miring(X1)
| ordere1490568538miring(X2) ) ).
cnf(i_0_4418,axiom,
( X1 != X2
| ~ linord893533164strict(X1)
| linord893533164strict(X2) ) ).
cnf(i_0_4419,axiom,
( X1 != X2
| ~ ordere779506340up_add(X1)
| ordere779506340up_add(X2) ) ).
cnf(i_0_4420,axiom,
( X1 != X2
| ~ ordere223160158up_add(X1)
| ordere223160158up_add(X2) ) ).
cnf(i_0_4421,axiom,
( X1 != X2
| ~ number(X1)
| number(X2) ) ).
cnf(i_0_4422,axiom,
( X1 != X2
| ~ linorder(X1)
| linorder(X2) ) ).
cnf(i_0_4423,axiom,
( X1 != X2
| ~ comm_semiring_1(X1)
| comm_semiring_1(X2) ) ).
cnf(i_0_4424,axiom,
( X1 != X2
| ~ linord219039673up_add(X1)
| linord219039673up_add(X2) ) ).
cnf(i_0_4425,axiom,
( X1 != X2
| ~ ordered_ab_group_add(X1)
| ordered_ab_group_add(X2) ) ).
cnf(i_0_4426,axiom,
( X1 != X2
| ~ ordered_ring(X1)
| ordered_ring(X2) ) ).
cnf(i_0_4427,axiom,
( X1 != X2
| ~ ring_1(X1)
| ring_1(X2) ) ).
cnf(i_0_4428,axiom,
( X1 != X2
| ~ number_ring(X1)
| number_ring(X2) ) ).
cnf(i_0_4429,axiom,
( X1 != X2
| ~ ordere453448008miring(X1)
| ordere453448008miring(X2) ) ).
cnf(i_0_4430,axiom,
( X1 != X2
| ~ ordere216010020id_add(X1)
| ordere216010020id_add(X2) ) ).
cnf(i_0_4431,axiom,
( X1 != X2
| ~ semiring_1(X1)
| semiring_1(X2) ) ).
cnf(i_0_4432,axiom,
( X1 != X2
| ~ linordered_semidom(X1)
| linordered_semidom(X2) ) ).
cnf(i_0_4433,axiom,
( X1 != X2
| ~ linordered_field(X1)
| linordered_field(X2) ) ).
cnf(i_0_4434,axiom,
( X1 != X2
| ~ dense_linorder(X1)
| dense_linorder(X2) ) ).
cnf(i_0_4435,axiom,
( X1 != X2
| ~ comm_semiring(X1)
| comm_semiring(X2) ) ).
cnf(i_0_4436,axiom,
( X1 != X2
| ~ ring_char_0(X1)
| ring_char_0(X2) ) ).
cnf(i_0_4437,axiom,
( X1 != X2
| ~ order(X1)
| order(X2) ) ).
cnf(i_0_4438,axiom,
( X1 != X2
| ~ ordered_ring_abs(X1)
| ordered_ring_abs(X2) ) ).
cnf(i_0_4439,axiom,
( X1 != X2
| ~ preorder(X1)
| preorder(X2) ) ).
cnf(i_0_4440,axiom,
( X1 != X2
| ~ ab_semigroup_add(X1)
| ab_semigroup_add(X2) ) ).
cnf(i_0_4441,axiom,
( X1 != X2
| ~ minus(X1)
| minus(X2) ) ).
cnf(i_0_4442,axiom,
( X1 != X2
| ~ group_add(X1)
| group_add(X2) ) ).
cnf(i_0_4443,axiom,
( X1 != X2
| ~ ab_group_add(X1)
| ab_group_add(X2) ) ).
cnf(i_0_4444,axiom,
( X1 != X2
| ~ ab_sem1668676832m_mult(X1)
| ab_sem1668676832m_mult(X2) ) ).
cnf(i_0_4445,axiom,
( X1 != X2
| ~ cancel_semigroup_add(X1)
| cancel_semigroup_add(X2) ) ).
cnf(i_0_4446,axiom,
( X1 != X2
| ~ cancel146912293up_add(X1)
| cancel146912293up_add(X2) ) ).
cnf(i_0_4447,axiom,
( X1 != X2
| ~ bot(X1)
| bot(X2) ) ).
cnf(i_0_4448,axiom,
( X1 != X2
| ~ ord(X1)
| ord(X2) ) ).
cnf(i_0_4449,axiom,
( X1 != X2
| ~ ring_n68954251visors(X1)
| ring_n68954251visors(X2) ) ).
cnf(i_0_4450,axiom,
( X1 != X2
| ~ no_zero_divisors(X1)
| no_zero_divisors(X2) ) ).
cnf(i_0_4451,axiom,
( X1 != X2
| ~ monoid_mult(X1)
| monoid_mult(X2) ) ).
cnf(i_0_4452,axiom,
( X1 != X2
| ~ comm_monoid_add(X1)
| comm_monoid_add(X2) ) ).
cnf(i_0_4453,axiom,
( X1 != X2
| ~ monoid_add(X1)
| monoid_add(X2) ) ).
cnf(i_0_4454,axiom,
( X1 != X2
| ~ number_semiring(X1)
| number_semiring(X2) ) ).
cnf(i_0_4455,axiom,
( X1 != X2
| ~ mult_zero(X1)
| mult_zero(X2) ) ).
cnf(i_0_4456,axiom,
( X1 != X2
| ~ semiring_char_0(X1)
| semiring_char_0(X2) ) ).
cnf(i_0_4457,axiom,
( X1 != X2
| ~ finite_finite_1(X1)
| finite_finite_1(X2) ) ).
cnf(i_0_4458,axiom,
( X1 != X2
| ~ zero(X1)
| zero(X2) ) ).
cnf(i_0_4459,axiom,
( X1 != X2
| ~ ordere142940540dd_abs(X1)
| ordere142940540dd_abs(X2) ) ).
cnf(i_0_4460,axiom,
( X1 != X2
| ~ one(X1)
| one(X2) ) ).
cnf(i_0_4461,axiom,
( X1 != X2
| ~ zero_neq_one(X1)
| zero_neq_one(X2) ) ).
cnf(i_0_4462,axiom,
( X1 != X2
| ~ linord581940658strict(X1)
| linord581940658strict(X2) ) ).
cnf(i_0_4463,axiom,
( X1 != X2
| ~ linordered_ring(X1)
| linordered_ring(X2) ) ).
cnf(i_0_4464,axiom,
( X1 != X2
| ~ ab_semigroup_mult(X1)
| ab_semigroup_mult(X2) ) ).
cnf(i_0_4345_001,axiom,
X1 = X1 ).
cnf(i_0_4346_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4347_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4348_004,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_4349_005,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_4350_006,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_4351_007,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_4352_008,axiom,
( X1 != X2
| number_number_of(X1) = number_number_of(X2) ) ).
cnf(i_0_4353_009,axiom,
( X1 != X2
| the_elem(X1) = the_elem(X2) ) ).
cnf(i_0_4354_010,axiom,
( X1 != X2
| nat_case(X1) = nat_case(X2) ) ).
cnf(i_0_4355_011,axiom,
( X1 != X2
| semiri532925092at_aux(X1) = semiri532925092at_aux(X2) ) ).
cnf(i_0_4356_012,axiom,
( X1 != X2
| combk(X1,X3) = combk(X2,X3) ) ).
cnf(i_0_4357_013,axiom,
( X1 != X2
| combk(X3,X1) = combk(X3,X2) ) ).
cnf(i_0_4358_014,axiom,
( X1 != X2
| sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).
cnf(i_0_4359_015,axiom,
( X1 != X2
| sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).
cnf(i_0_4360_016,axiom,
( X1 != X2
| finite_card(X1) = finite_card(X2) ) ).
cnf(i_0_4361_017,axiom,
( X1 != X2
| if(X1) = if(X2) ) ).
cnf(i_0_4362_018,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_4363_019,axiom,
( X1 != X2
| combs(X1,X3,X4) = combs(X2,X3,X4) ) ).
cnf(i_0_4364_020,axiom,
( X1 != X2
| combs(X3,X1,X4) = combs(X3,X2,X4) ) ).
cnf(i_0_4365_021,axiom,
( X1 != X2
| combs(X3,X4,X1) = combs(X3,X4,X2) ) ).
cnf(i_0_4366_022,axiom,
( X1 != X2
| combb(X1,X3,X4) = combb(X2,X3,X4) ) ).
cnf(i_0_4367_023,axiom,
( X1 != X2
| combb(X3,X1,X4) = combb(X3,X2,X4) ) ).
cnf(i_0_4368_024,axiom,
( X1 != X2
| combb(X3,X4,X1) = combb(X3,X4,X2) ) ).
cnf(i_0_4369_025,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_4370_026,axiom,
( X1 != X2
| combc(X1,X3,X4) = combc(X2,X3,X4) ) ).
cnf(i_0_4371_027,axiom,
( X1 != X2
| combc(X3,X1,X4) = combc(X3,X2,X4) ) ).
cnf(i_0_4372_028,axiom,
( X1 != X2
| combc(X3,X4,X1) = combc(X3,X4,X2) ) ).
cnf(i_0_4373_029,axiom,
( X1 != X2
| ord_less(X1) = ord_less(X2) ) ).
cnf(i_0_4374_030,axiom,
( X1 != X2
| zero_zero(X1) = zero_zero(X2) ) ).
cnf(i_0_4375_031,axiom,
( X1 != X2
| minus_minus(X1) = minus_minus(X2) ) ).
cnf(i_0_4376_032,axiom,
( X1 != X2
| plus_plus(X1) = plus_plus(X2) ) ).
cnf(i_0_4377_033,axiom,
( X1 != X2
| abs_abs(X1) = abs_abs(X2) ) ).
cnf(i_0_4378_034,axiom,
( X1 != X2
| one_one(X1) = one_one(X2) ) ).
cnf(i_0_4379_035,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_4380_036,axiom,
( X1 != X2
| image(X1,X3) = image(X2,X3) ) ).
cnf(i_0_4381_037,axiom,
( X1 != X2
| image(X3,X1) = image(X3,X2) ) ).
cnf(i_0_4382_038,axiom,
( X1 != X2
| ord_less_eq(X1) = ord_less_eq(X2) ) ).
cnf(i_0_4383_039,axiom,
( X1 != X2
| finite_fold_image(X1,X3) = finite_fold_image(X2,X3) ) ).
cnf(i_0_4384_040,axiom,
( X1 != X2
| finite_fold_image(X3,X1) = finite_fold_image(X3,X2) ) ).
cnf(i_0_4385_041,axiom,
( X1 != X2
| finite1357897459simple(X1,X3) = finite1357897459simple(X2,X3) ) ).
cnf(i_0_4386_042,axiom,
( X1 != X2
| finite1357897459simple(X3,X1) = finite1357897459simple(X3,X2) ) ).
cnf(i_0_4387_043,axiom,
( X1 != X2
| insert(X1) = insert(X2) ) ).
cnf(i_0_4388_044,axiom,
( X1 != X2
| bot_bot(X1) = bot_bot(X2) ) ).
cnf(i_0_4389_045,axiom,
( X1 != X2
| times_times(X1) = times_times(X2) ) ).
cnf(i_0_4390_046,axiom,
( X1 != X2
| the(X1) = the(X2) ) ).
cnf(i_0_4391_047,axiom,
( X1 != X2
| the_1(X1) = the_1(X2) ) ).
cnf(i_0_4392_048,axiom,
( X1 != X2
| finite_folding_one(X1) = finite_folding_one(X2) ) ).
cnf(i_0_4393_049,axiom,
( X1 != X2
| finite2073411215e_idem(X1) = finite2073411215e_idem(X2) ) ).
cnf(i_0_4394_050,axiom,
( X1 != X2
| ring_1_Ints(X1) = ring_1_Ints(X2) ) ).
cnf(i_0_4395_051,axiom,
( X1 != X2
| finite_comp_fun_idem(X1,X3) = finite_comp_fun_idem(X2,X3) ) ).
cnf(i_0_4396_052,axiom,
( X1 != X2
| finite_comp_fun_idem(X3,X1) = finite_comp_fun_idem(X3,X2) ) ).
cnf(i_0_4397_053,axiom,
( X1 != X2
| combi(X1) = combi(X2) ) ).
cnf(i_0_4398_054,axiom,
( X1 != X2
| finite908156982e_idem(X1,X3) = finite908156982e_idem(X2,X3) ) ).
cnf(i_0_4399_055,axiom,
( X1 != X2
| finite908156982e_idem(X3,X1) = finite908156982e_idem(X3,X2) ) ).
cnf(i_0_4400_056,axiom,
( X1 != X2
| finite_finite(X1) = finite_finite(X2) ) ).
cnf(i_0_4401_057,axiom,
( X1 != X2
| semiring_1_of_nat(X1) = semiring_1_of_nat(X2) ) ).
cnf(i_0_4402_058,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_4403_059,axiom,
( X1 != X2
| partial_flat_lub(X1) = partial_flat_lub(X2) ) ).
cnf(i_0_4404_060,axiom,
( X1 != X2
| ~ comm_monoid_mult(X1)
| comm_monoid_mult(X2) ) ).
cnf(i_0_4405_061,axiom,
( X1 != X2
| ~ linordered_idom(X1)
| linordered_idom(X2) ) ).
cnf(i_0_4406_062,axiom,
( X1 != X2
| ~ linord1278240602ring_1(X1)
| linord1278240602ring_1(X2) ) ).
cnf(i_0_4407_063,axiom,
( X1 != X2
| ~ linord626643107strict(X1)
| linord626643107strict(X2) ) ).
cnf(i_0_4408_064,axiom,
( X1 != X2
| ~ ring(X1)
| ring(X2) ) ).
cnf(i_0_4409_065,axiom,
( X1 != X2
| ~ semiring(X1)
| semiring(X2) ) ).
cnf(i_0_4410_066,axiom,
( X1 != X2
| ~ linord20386208strict(X1)
| linord20386208strict(X2) ) ).
cnf(i_0_4411_067,axiom,
( X1 != X2
| ~ linordered_semiring(X1)
| linordered_semiring(X2) ) ).
cnf(i_0_4412_068,axiom,
( X1 != X2
| ~ ordered_semiring(X1)
| ordered_semiring(X2) ) ).
cnf(i_0_4413_069,axiom,
( X1 != X2
| ~ ordere236663937imp_le(X1)
| ordere236663937imp_le(X2) ) ).
cnf(i_0_4414_070,axiom,
( X1 != X2
| ~ semiri456707255roduct(X1)
| semiri456707255roduct(X2) ) ).
cnf(i_0_4415_071,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4416_072,axiom,
( X1 != X2
| ~ linord1117847801e_zero(X1)
| linord1117847801e_zero(X2) ) ).
cnf(i_0_4417_073,axiom,
( X1 != X2
| ~ ordere1490568538miring(X1)
| ordere1490568538miring(X2) ) ).
cnf(i_0_4418_074,axiom,
( X1 != X2
| ~ linord893533164strict(X1)
| linord893533164strict(X2) ) ).
cnf(i_0_4419_075,axiom,
( X1 != X2
| ~ ordere779506340up_add(X1)
| ordere779506340up_add(X2) ) ).
cnf(i_0_4420_076,axiom,
( X1 != X2
| ~ ordere223160158up_add(X1)
| ordere223160158up_add(X2) ) ).
cnf(i_0_4421_077,axiom,
( X1 != X2
| ~ number(X1)
| number(X2) ) ).
cnf(i_0_4422_078,axiom,
( X1 != X2
| ~ linorder(X1)
| linorder(X2) ) ).
cnf(i_0_4423_079,axiom,
( X1 != X2
| ~ comm_semiring_1(X1)
| comm_semiring_1(X2) ) ).
cnf(i_0_4424_080,axiom,
( X1 != X2
| ~ linord219039673up_add(X1)
| linord219039673up_add(X2) ) ).
cnf(i_0_4425_081,axiom,
( X1 != X2
| ~ ordered_ab_group_add(X1)
| ordered_ab_group_add(X2) ) ).
cnf(i_0_4426_082,axiom,
( X1 != X2
| ~ ordered_ring(X1)
| ordered_ring(X2) ) ).
cnf(i_0_4427_083,axiom,
( X1 != X2
| ~ ring_1(X1)
| ring_1(X2) ) ).
cnf(i_0_4428_084,axiom,
( X1 != X2
| ~ number_ring(X1)
| number_ring(X2) ) ).
cnf(i_0_4429_085,axiom,
( X1 != X2
| ~ ordere453448008miring(X1)
| ordere453448008miring(X2) ) ).
cnf(i_0_4430_086,axiom,
( X1 != X2
| ~ ordere216010020id_add(X1)
| ordere216010020id_add(X2) ) ).
cnf(i_0_4431_087,axiom,
( X1 != X2
| ~ semiring_1(X1)
| semiring_1(X2) ) ).
cnf(i_0_4432_088,axiom,
( X1 != X2
| ~ linordered_semidom(X1)
| linordered_semidom(X2) ) ).
cnf(i_0_4433_089,axiom,
( X1 != X2
| ~ linordered_field(X1)
| linordered_field(X2) ) ).
cnf(i_0_4434_090,axiom,
( X1 != X2
| ~ dense_linorder(X1)
| dense_linorder(X2) ) ).
cnf(i_0_4435_091,axiom,
( X1 != X2
| ~ comm_semiring(X1)
| comm_semiring(X2) ) ).
cnf(i_0_4436_092,axiom,
( X1 != X2
| ~ ring_char_0(X1)
| ring_char_0(X2) ) ).
cnf(i_0_4437_093,axiom,
( X1 != X2
| ~ order(X1)
| order(X2) ) ).
cnf(i_0_4438_094,axiom,
( X1 != X2
| ~ ordered_ring_abs(X1)
| ordered_ring_abs(X2) ) ).
cnf(i_0_4439_095,axiom,
( X1 != X2
| ~ preorder(X1)
| preorder(X2) ) ).
cnf(i_0_4440_096,axiom,
( X1 != X2
| ~ ab_semigroup_add(X1)
| ab_semigroup_add(X2) ) ).
cnf(i_0_4441_097,axiom,
( X1 != X2
| ~ minus(X1)
| minus(X2) ) ).
cnf(i_0_4442_098,axiom,
( X1 != X2
| ~ group_add(X1)
| group_add(X2) ) ).
cnf(i_0_4443_099,axiom,
( X1 != X2
| ~ ab_group_add(X1)
| ab_group_add(X2) ) ).
cnf(i_0_4444_100,axiom,
( X1 != X2
| ~ ab_sem1668676832m_mult(X1)
| ab_sem1668676832m_mult(X2) ) ).
cnf(i_0_4445_101,axiom,
( X1 != X2
| ~ cancel_semigroup_add(X1)
| cancel_semigroup_add(X2) ) ).
cnf(i_0_4446_102,axiom,
( X1 != X2
| ~ cancel146912293up_add(X1)
| cancel146912293up_add(X2) ) ).
cnf(i_0_4447_103,axiom,
( X1 != X2
| ~ bot(X1)
| bot(X2) ) ).
cnf(i_0_4448_104,axiom,
( X1 != X2
| ~ ord(X1)
| ord(X2) ) ).
cnf(i_0_4449_105,axiom,
( X1 != X2
| ~ ring_n68954251visors(X1)
| ring_n68954251visors(X2) ) ).
cnf(i_0_4450_106,axiom,
( X1 != X2
| ~ no_zero_divisors(X1)
| no_zero_divisors(X2) ) ).
cnf(i_0_4451_107,axiom,
( X1 != X2
| ~ monoid_mult(X1)
| monoid_mult(X2) ) ).
cnf(i_0_4452_108,axiom,
( X1 != X2
| ~ comm_monoid_add(X1)
| comm_monoid_add(X2) ) ).
cnf(i_0_4453_109,axiom,
( X1 != X2
| ~ monoid_add(X1)
| monoid_add(X2) ) ).
cnf(i_0_4454_110,axiom,
( X1 != X2
| ~ number_semiring(X1)
| number_semiring(X2) ) ).
cnf(i_0_4455_111,axiom,
( X1 != X2
| ~ mult_zero(X1)
| mult_zero(X2) ) ).
cnf(i_0_4456_112,axiom,
( X1 != X2
| ~ semiring_char_0(X1)
| semiring_char_0(X2) ) ).
cnf(i_0_4457_113,axiom,
( X1 != X2
| ~ finite_finite_1(X1)
| finite_finite_1(X2) ) ).
cnf(i_0_4458_114,axiom,
( X1 != X2
| ~ zero(X1)
| zero(X2) ) ).
cnf(i_0_4459_115,axiom,
( X1 != X2
| ~ ordere142940540dd_abs(X1)
| ordere142940540dd_abs(X2) ) ).
cnf(i_0_4460_116,axiom,
( X1 != X2
| ~ one(X1)
| one(X2) ) ).
cnf(i_0_4461_117,axiom,
( X1 != X2
| ~ zero_neq_one(X1)
| zero_neq_one(X2) ) ).
cnf(i_0_4462_118,axiom,
( X1 != X2
| ~ linord581940658strict(X1)
| linord581940658strict(X2) ) ).
cnf(i_0_4463_119,axiom,
( X1 != X2
| ~ linordered_ring(X1)
| linordered_ring(X2) ) ).
cnf(i_0_4464_120,axiom,
( X1 != X2
| ~ ab_semigroup_mult(X1)
| ab_semigroup_mult(X2) ) ).
cnf(i_0_4465,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),X3)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X3),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X2)) ),
inference(equality_inference,[],[2746]) ).
cnf(i_0_4466,plain,
( ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) ),
inference(equality_inference,[],[2768]) ).
cnf(i_0_4467,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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),X5),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk80_6(X2,X1,X3,X5,X4,X4)),X4)) ),
inference(equality_inference,[],[2776]) ).
cnf(i_0_4468,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X3)),X1))) ),
inference(equality_inference,[],[2778]) ).
cnf(i_0_4469,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X4),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X4)),X2)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X1)) ),
inference(equality_inference,[],[2803]) ).
cnf(i_0_4470,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X1)),X2)),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)),X4)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(equality_inference,[],[2804]) ).
cnf(i_0_4471,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1)),X2)),X3) = X3 ),
inference(equality_inference,[],[2815]) ).
cnf(i_0_4472,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1))
| X2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1)),X3)),X2) ),
inference(equality_inference,[],[2816]) ).
cnf(i_0_4473,plain,
( ~ ring(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X2)),X3)),X4) = hAPP(X1,X1,combi(X1),X4) ),
inference(equality_inference,[],[2817]) ).
cnf(i_0_4474,plain,
( ~ ring(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X3),X3)),X4)),X2) ),
inference(equality_inference,[],[2818]) ).
cnf(i_0_4475,plain,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4) ),
inference(equality_inference,[],[2924]) ).
cnf(i_0_4476,plain,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4) ),
inference(equality_inference,[],[2925]) ).
cnf(i_0_4477,plain,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) ),
inference(equality_inference,[],[3111]) ).
cnf(i_0_4478,plain,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) ),
inference(equality_inference,[],[3112]) ).
cnf(i_0_4479,plain,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(equality_inference,[],[3113]) ).
cnf(i_0_4480,plain,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(equality_inference,[],[3114]) ).
cnf(i_0_4481,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3) ),
inference(equality_inference,[],[3151]) ).
cnf(i_0_4482,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3) ),
inference(equality_inference,[],[3152]) ).
cnf(i_0_4483,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[3153]) ).
cnf(i_0_4484,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
| hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[3154]) ).
cnf(i_0_4485,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,[],[3198]) ).
cnf(i_0_4486,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,[],[3342]) ).
cnf(i_0_4487,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)),X3))) ),
inference(equality_inference,[],[3347]) ).
cnf(i_0_4488,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,[],[3348]) ).
cnf(i_0_4489,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,[],[3407]) ).
cnf(i_0_4490,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,[],[3410]) ).
cnf(i_0_4491,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(equality_inference,[],[3417]) ).
cnf(i_0_4492,plain,
X1 = X1,
inference(equality_inference,[],[3525]) ).
cnf(i_0_4493,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,[],[3527]) ).
cnf(i_0_4494,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(equality_inference,[],[3532]) ).
cnf(i_0_4495,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X2))))),
inference(equality_inference,[],[3546]) ).
cnf(i_0_4496,plain,
( X1 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(equality_inference,[],[3577]) ).
cnf(i_0_4497,plain,
( hAPP(int,int,number_number_of(int),X1) = zero_zero(int)
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(equality_inference,[],[3594]) ).
cnf(i_0_4498,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)))),
inference(equality_inference,[],[3605]) ).
cnf(i_0_4499,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X2) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))) ),
inference(equality_inference,[],[3633]) ).
cnf(i_0_4500,plain,
( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(equality_inference,[],[3634]) ).
cnf(i_0_4501,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))),
inference(equality_inference,[],[3638]) ).
cnf(i_0_4502,plain,
~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X2)),
inference(equality_inference,[],[3639]) ).
cnf(i_0_4503,plain,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(equality_inference,[],[3699]) ).
cnf(i_0_4504,plain,
hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2),
inference(equality_inference,[],[3703]) ).
cnf(i_0_4505,plain,
( X1 = X1
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1))) ),
inference(equality_inference,[],[3719]) ).
cnf(i_0_4506,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2)))),
inference(equality_inference,[],[3741]) ).
cnf(i_0_4507,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))),zero_zero(int))),
inference(equality_inference,[],[3744]) ).
cnf(i_0_4508,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),zero_zero(int))),one_one(int))),
inference(equality_inference,[],[3745]) ).
cnf(i_0_4509,plain,
X1 = X1,
inference(equality_inference,[],[3754]) ).
cnf(i_0_4510,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(equality_inference,[],[3761]) ).
cnf(i_0_4511,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(equality_inference,[],[3765]) ).
cnf(i_0_4512,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,[],[3786]) ).
cnf(i_0_4513,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,[],[3787]) ).
cnf(i_0_4514,plain,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[3814]) ).
cnf(i_0_4515,plain,
( ~ cancel146912293up_add(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[3815]) ).
cnf(i_0_4516,plain,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[3817]) ).
cnf(i_0_4517,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,[],[3818]) ).
cnf(i_0_4518,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))),
inference(equality_inference,[],[3839]) ).
cnf(i_0_4519,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
inference(equality_inference,[],[3868]) ).
cnf(i_0_4520,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(equality_inference,[],[3870]) ).
cnf(i_0_4521,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(equality_inference,[],[3885]) ).
cnf(i_0_4522,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(equality_inference,[],[3886]) ).
cnf(i_0_4523,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(equality_inference,[],[3890]) ).
cnf(i_0_4524,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(equality_inference,[],[3891]) ).
cnf(i_0_4525,plain,
( X1 = X1
| X2 = zero_zero(nat) ),
inference(equality_inference,[],[3892]) ).
cnf(i_0_4526,plain,
( X1 = X1
| X2 = zero_zero(nat) ),
inference(equality_inference,[],[3894]) ).
cnf(i_0_4527,plain,
X1 = X1,
inference(equality_inference,[],[3897]) ).
cnf(i_0_4528,plain,
X1 = X1,
inference(equality_inference,[],[3898]) ).
cnf(i_0_4529,plain,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) ),
inference(equality_inference,[],[3907]) ).
cnf(i_0_4530,plain,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) ),
inference(equality_inference,[],[3908]) ).
cnf(i_0_4531,plain,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
inference(equality_inference,[],[3911]) ).
cnf(i_0_4532,plain,
hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
inference(equality_inference,[],[3912]) ).
cnf(i_0_4533,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
inference(equality_inference,[],[3943]) ).
cnf(i_0_4534,plain,
( ~ group_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X2) = zero_zero(X1) ),
inference(equality_inference,[],[3981]) ).
cnf(i_0_4535,plain,
( ~ ab_group_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X2) = zero_zero(X1) ),
inference(equality_inference,[],[3982]) ).
cnf(i_0_4536,plain,
( ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
inference(equality_inference,[],[3983]) ).
cnf(i_0_4537,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X2),
inference(equality_inference,[],[3995]) ).
cnf(i_0_4538,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),zero_zero(nat)),
inference(equality_inference,[],[3996]) ).
cnf(i_0_4539,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(equality_inference,[],[3999]) ).
cnf(i_0_4540,plain,
( ~ number_ring(X1)
| ~ ring_char_0(X1)
| X2 = X2 ),
inference(equality_inference,[],[4098]) ).
cnf(i_0_4541,plain,
( ~ semiring_char_0(X1)
| X2 = X2 ),
inference(equality_inference,[],[4099]) ).
cnf(i_0_4542,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = zero_zero(nat),
inference(equality_inference,[],[4106]) ).
cnf(i_0_4543,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = zero_zero(nat),
inference(equality_inference,[],[4107]) ).
cnf(i_0_4544,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
inference(equality_inference,[],[4112]) ).
cnf(i_0_4545,plain,
X1 = X1,
inference(equality_inference,[],[4122]) ).
cnf(i_0_4546,plain,
X1 = X1,
inference(equality_inference,[],[4130]) ).
cnf(i_0_4547,plain,
X1 = X1,
inference(equality_inference,[],[4132]) ).
cnf(i_0_4548,plain,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
inference(equality_inference,[],[4217]) ).
cnf(i_0_4549,plain,
hBOOL(hAPP(pname,bool,u,pn)),
inference(scs_inference,[],[i_0_3965,i_0_3755]) ).
cnf(i_0_4550,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_3755]) ).
cnf(i_0_4551,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_2809,i_0_3965,i_0_3755,i_0_3786]) ).
cnf(i_0_4552,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_3786]) ).
cnf(i_0_4553,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_2809,i_0_3965,i_0_3755,i_0_3786,i_0_3787]) ).
cnf(i_0_4554,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_3787]) ).
cnf(i_0_4555,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)) != X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_3965,i_0_3755,i_0_3786,i_0_3787,i_0_3605]) ).
cnf(i_0_4556,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(rename_variables,[],[i_0_4522]) ).
cnf(i_0_4557,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3605]) ).
cnf(i_0_4558,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_3965,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870]) ).
cnf(i_0_4559,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_3106]) ).
cnf(i_0_4560,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3870]) ).
cnf(i_0_4561,plain,
X1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4498,i_0_3965,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886]) ).
cnf(i_0_4562,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3886]) ).
cnf(i_0_4563,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) != hAPP(nat,nat,suc,X1),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4498,i_0_3280,i_0_3965,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890]) ).
cnf(i_0_4564,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3890]) ).
cnf(i_0_4565,plain,
hAPP(nat,nat,suc,X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4498,i_0_3280,i_0_3965,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891]) ).
cnf(i_0_4566,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_3891]) ).
cnf(i_0_4567,plain,
hAPP(int,int,bit1,pls) = hAPP(int,int,succ,pls),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4498,i_0_4174,i_0_3280,i_0_3965,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346]) ).
cnf(i_0_4568,plain,
hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,X1,one_one(int))) != X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4498,i_0_4174,i_0_3280,i_0_3965,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350]) ).
cnf(i_0_4569,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_2809,i_0_4522,i_0_4498,i_0_4174,i_0_3280,i_0_3965,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351]) ).
cnf(i_0_4570,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(fun(pname,bool),fun(fun(pname,bool),bool),ord_less_eq(fun(pname,bool)),esk9_5(x_a,pname,g,mgt_call,u)),u)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4498,i_0_4174,i_0_3280,i_0_3965,i_0_3448,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865]) ).
cnf(i_0_4571,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)),esk9_5(X1,X3,X2,X4,X5)),X5)) ),
inference(rename_variables,[],[i_0_2865]) ).
cnf(i_0_4572,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X2))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3965,i_0_3448,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006]) ).
cnf(i_0_4573,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(rename_variables,[],[i_0_3882]) ).
cnf(i_0_4574,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3),X2))) ),
inference(rename_variables,[],[i_0_3006]) ).
cnf(i_0_4575,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X1)),zero_zero(int))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3965,i_0_3448,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033]) ).
cnf(i_0_4576,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X2)),zero_zero(int))) ),
inference(rename_variables,[],[i_0_3033]) ).
cnf(i_0_4577,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3965,i_0_3448,i_0_3611,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036]) ).
cnf(i_0_4578,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))),
inference(rename_variables,[],[i_0_3611]) ).
cnf(i_0_4579,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(rename_variables,[],[i_0_3036]) ).
cnf(i_0_4580,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3965,i_0_3448,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037]) ).
cnf(i_0_4581,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))),
inference(rename_variables,[],[i_0_3611]) ).
cnf(i_0_4582,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(rename_variables,[],[i_0_3037]) ).
cnf(i_0_4583,plain,
hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X2),bot_bot(fun(X1,bool))) = hAPP(X1,X1,combi(X1),X2),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3965,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140]) ).
cnf(i_0_4584,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),bot_bot(fun(X1,bool))),X2)),
inference(rename_variables,[],[i_0_3922]) ).
cnf(i_0_4585,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),bot_bot(fun(X1,bool)))))
| hAPP(fun(X1,bool),X1,hAPP(X1,fun(fun(X1,bool),X1),partial_flat_lub(X1),X3),X2) = hAPP(X1,X1,combi(X1),X3) ),
inference(rename_variables,[],[i_0_3140]) ).
cnf(i_0_4586,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3896,i_0_3965,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186]) ).
cnf(i_0_4587,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(rename_variables,[],[i_0_3896]) ).
cnf(i_0_4588,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(rename_variables,[],[i_0_3186]) ).
cnf(i_0_4589,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),pls)),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,pls))),X1),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3896,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263]) ).
cnf(i_0_4590,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X1))),X2) ),
inference(rename_variables,[],[i_0_3263]) ).
cnf(i_0_4591,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),one_one(int))),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269]) ).
cnf(i_0_4592,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X1)),
inference(rename_variables,[],[i_0_4001]) ).
cnf(i_0_4593,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(rename_variables,[],[i_0_3269]) ).
cnf(i_0_4594,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),zero_zero(nat))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3991,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288]) ).
cnf(i_0_4595,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,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) ),
inference(rename_variables,[],[i_0_3288]) ).
cnf(i_0_4596,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,hAPP(nat,int,semiring_1_of_nat(int),X1))),hAPP(int,int,bit1,zero_zero(int)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302]) ).
cnf(i_0_4597,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(rename_variables,[],[i_0_3302]) ).
cnf(i_0_4598,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,zero_zero(nat)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305]) ).
cnf(i_0_4599,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
inference(rename_variables,[],[i_0_3305]) ).
cnf(i_0_4600,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2))),X2)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329]) ).
cnf(i_0_4601,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))),
inference(rename_variables,[],[i_0_3611]) ).
cnf(i_0_4602,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_3329]) ).
cnf(i_0_4603,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363]) ).
cnf(i_0_4604,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(rename_variables,[],[i_0_4522]) ).
cnf(i_0_4605,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(rename_variables,[],[i_0_3363]) ).
cnf(i_0_4606,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4174,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364]) ).
cnf(i_0_4607,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(rename_variables,[],[i_0_4522]) ).
cnf(i_0_4608,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(rename_variables,[],[i_0_3364]) ).
cnf(i_0_4609,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk60_2(X1,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4174,i_0_3871,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373]) ).
cnf(i_0_4610,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(rename_variables,[],[i_0_3871]) ).
cnf(i_0_4611,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk60_2(X1,X2))) ),
inference(rename_variables,[],[i_0_3373]) ).
cnf(i_0_4612,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_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4174,i_0_3871,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379]) ).
cnf(i_0_4613,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(rename_variables,[],[i_0_4002]) ).
cnf(i_0_4614,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_3379]) ).
cnf(i_0_4615,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4174,i_0_3871,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382]) ).
cnf(i_0_4616,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1))),
inference(rename_variables,[],[i_0_3609]) ).
cnf(i_0_4617,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(nat),X1),X2)) ),
inference(rename_variables,[],[i_0_3382]) ).
cnf(i_0_4618,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4174,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383]) ).
cnf(i_0_4619,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(rename_variables,[],[i_0_3871]) ).
cnf(i_0_4620,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(rename_variables,[],[i_0_3383]) ).
cnf(i_0_4621,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),pls)),hAPP(int,nat,number_number_of(nat),pls))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4174,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394]) ).
cnf(i_0_4622,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,X1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),X1)),hAPP(int,nat,number_number_of(nat),X1))) ),
inference(rename_variables,[],[i_0_3394]) ).
cnf(i_0_4623,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397]) ).
cnf(i_0_4624,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(rename_variables,[],[i_0_3397]) ).
cnf(i_0_4625,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399]) ).
cnf(i_0_4626,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(rename_variables,[],[i_0_3399]) ).
cnf(i_0_4627,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400]) ).
cnf(i_0_4628,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_3400]) ).
cnf(i_0_4629,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3867,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402]) ).
cnf(i_0_4630,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
inference(rename_variables,[],[i_0_3402]) ).
cnf(i_0_4631,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),zero_zero(nat))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3867,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429]) ).
cnf(i_0_4632,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X2)),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) ),
inference(rename_variables,[],[i_0_3429]) ).
cnf(i_0_4633,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3867,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442]) ).
cnf(i_0_4634,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
inference(rename_variables,[],[i_0_3442]) ).
cnf(i_0_4635,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),zero_zero(nat))),zero_zero(nat)) = X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3867,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445]) ).
cnf(i_0_4636,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X1) = X2 ),
inference(rename_variables,[],[i_0_3445]) ).
cnf(i_0_4637,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),zero_zero(nat)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),zero_zero(nat))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3867,i_0_3871,i_0_4610,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471]) ).
cnf(i_0_4638,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_3471]) ).
cnf(i_0_4639,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,suc,esk60_2(X1,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488]) ).
cnf(i_0_4640,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(rename_variables,[],[i_0_3871]) ).
cnf(i_0_4641,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
| X2 = hAPP(nat,nat,suc,esk60_2(X1,X2)) ),
inference(rename_variables,[],[i_0_3488]) ).
cnf(i_0_4642,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,esk5_2(X1,hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489]) ).
cnf(i_0_4643,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(rename_variables,[],[i_0_4002]) ).
cnf(i_0_4644,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,esk5_2(X1,X2)) ),
inference(rename_variables,[],[i_0_3489]) ).
cnf(i_0_4645,plain,
hAPP(nat,nat,combi(nat),X1) = X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525]) ).
cnf(i_0_4646,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rename_variables,[],[i_0_4079]) ).
cnf(i_0_4647,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)
| X2 = X3 ),
inference(rename_variables,[],[i_0_3525]) ).
cnf(i_0_4648,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,suc,X1),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4498,i_0_4506,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537]) ).
cnf(i_0_4649,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) = X1 ),
inference(rename_variables,[],[i_0_3537]) ).
cnf(i_0_4650,plain,
X1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X2))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546]) ).
cnf(i_0_4651,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X3))) ),
inference(rename_variables,[],[i_0_3546]) ).
cnf(i_0_4652,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567]) ).
cnf(i_0_4653,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_3567]) ).
cnf(i_0_4654,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569]) ).
cnf(i_0_4655,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(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(rename_variables,[],[i_0_3569]) ).
cnf(i_0_4656,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571]) ).
cnf(i_0_4657,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
inference(rename_variables,[],[i_0_3571]) ).
cnf(i_0_4658,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(nat,int,semiring_1_of_nat(int),X1))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574]) ).
cnf(i_0_4659,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2)))),
inference(rename_variables,[],[i_0_4506]) ).
cnf(i_0_4660,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1))) ),
inference(rename_variables,[],[i_0_3574]) ).
cnf(i_0_4661,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(nat,int,semiring_1_of_nat(int),X1))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575]) ).
cnf(i_0_4662,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2)))),
inference(rename_variables,[],[i_0_4506]) ).
cnf(i_0_4663,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1))) ),
inference(rename_variables,[],[i_0_3575]) ).
cnf(i_0_4664,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),zero_zero(nat))) = X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596]) ).
cnf(i_0_4665,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = X2 ),
inference(rename_variables,[],[i_0_3596]) ).
cnf(i_0_4666,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),zero_zero(nat))) = zero_zero(nat),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597]) ).
cnf(i_0_4667,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_3597]) ).
cnf(i_0_4668,plain,
X1 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638]) ).
cnf(i_0_4669,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)) ),
inference(rename_variables,[],[i_0_3638]) ).
cnf(i_0_4670,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),esk51_2(zero_zero(nat),hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644]) ).
cnf(i_0_4671,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk51_2(X1,X2))) ),
inference(rename_variables,[],[i_0_3644]) ).
cnf(i_0_4672,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),esk47_2(zero_zero(nat),hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645]) ).
cnf(i_0_4673,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk47_2(X1,X2))) ),
inference(rename_variables,[],[i_0_3645]) ).
cnf(i_0_4674,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),one_one(nat))) = hAPP(nat,nat,suc,X1),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646]) ).
cnf(i_0_4675,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),one_one(nat))) = X1 ),
inference(rename_variables,[],[i_0_3646]) ).
cnf(i_0_4676,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),one_one(nat))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647]) ).
cnf(i_0_4677,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),one_one(nat))) ),
inference(rename_variables,[],[i_0_3647]) ).
cnf(i_0_4678,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_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653]) ).
cnf(i_0_4679,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_3653]) ).
cnf(i_0_4680,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk91_2(zero_zero(nat),hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673]) ).
cnf(i_0_4681,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk91_2(X1,X2))) ),
inference(rename_variables,[],[i_0_3673]) ).
cnf(i_0_4682,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk130_1(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),one_one(int))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681]) ).
cnf(i_0_4683,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)))),
inference(rename_variables,[],[i_0_4498]) ).
cnf(i_0_4684,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk130_1(X1))) ),
inference(rename_variables,[],[i_0_3681]) ).
cnf(i_0_4685,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4506,i_0_4659,i_0_4662,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684]) ).
cnf(i_0_4686,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2)))),
inference(rename_variables,[],[i_0_4506]) ).
cnf(i_0_4687,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(rename_variables,[],[i_0_3684]) ).
cnf(i_0_4688,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4506,i_0_4659,i_0_4662,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690]) ).
cnf(i_0_4689,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(rename_variables,[],[i_0_3690]) ).
cnf(i_0_4690,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)),hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4506,i_0_4659,i_0_4662,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695]) ).
cnf(i_0_4691,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(rename_variables,[],[i_0_3695]) ).
cnf(i_0_4692,plain,
hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697]) ).
cnf(i_0_4693,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X2),X1) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X1) ),
inference(rename_variables,[],[i_0_3697]) ).
cnf(i_0_4694,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk126_1(hAPP(int,fun(int,bool),fequal(int),hAPP(nat,int,semiring_1_of_nat(int),X1))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705]) ).
cnf(i_0_4695,plain,
hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
inference(rename_variables,[],[i_0_4532]) ).
cnf(i_0_4696,plain,
( ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk126_1(X1))) ),
inference(rename_variables,[],[i_0_3705]) ).
cnf(i_0_4697,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1)) = X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706]) ).
cnf(i_0_4698,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)) = X1 ),
inference(rename_variables,[],[i_0_3706]) ).
cnf(i_0_4699,plain,
hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),bot_bot(fun(X1,bool))) = bot_bot(fun(X1,bool)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713]) ).
cnf(i_0_4700,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(rename_variables,[],[i_0_3934]) ).
cnf(i_0_4701,plain,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),bot_bot(fun(X1,bool))))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool)) ),
inference(rename_variables,[],[i_0_3713]) ).
cnf(i_0_4702,plain,
zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))),hAPP(nat,int,semiring_1_of_nat(int),esk124_2(hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),zero_zero(int)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714]) ).
cnf(i_0_4703,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| X2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),esk124_2(X1,X2))) ),
inference(rename_variables,[],[i_0_3714]) ).
cnf(i_0_4704,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),one_one(int)))) = one_one(nat),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717]) ).
cnf(i_0_4705,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X1)) = one_one(nat) ),
inference(rename_variables,[],[i_0_3717]) ).
cnf(i_0_4706,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),pls)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,pls)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740]) ).
cnf(i_0_4707,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(rename_variables,[],[i_0_4522]) ).
cnf(i_0_4708,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X1)) ),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4709,plain,
X1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))),hAPP(nat,int,semiring_1_of_nat(int),X2)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741]) ).
cnf(i_0_4710,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| X2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X3)) ),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4711,plain,
hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) != bot_bot(fun(pname,bool)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750]) ).
cnf(i_0_4712,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),combi(fun(X1,bool)),X3) != bot_bot(fun(X1,bool)) ),
inference(rename_variables,[],[i_0_3750]) ).
cnf(i_0_4713,plain,
hAPP(fun(nat,bool),fun(nat,bool),combi(fun(nat,bool)),X1) = X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754]) ).
cnf(i_0_4714,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rename_variables,[],[i_0_4079]) ).
cnf(i_0_4715,plain,
( hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X1) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3754]) ).
cnf(i_0_4716,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),esk91_2(zero_zero(nat),hAPP(nat,nat,suc,X1))) = hAPP(nat,nat,suc,X1),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767]) ).
cnf(i_0_4717,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk91_2(X1,X2)) = X2 ),
inference(rename_variables,[],[i_0_3767]) ).
cnf(i_0_4718,plain,
X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),esk38_2(zero_zero(nat),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768]) ).
cnf(i_0_4719,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk38_2(X1,X2)) ),
inference(rename_variables,[],[i_0_3768]) ).
cnf(i_0_4720,plain,
~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769]) ).
cnf(i_0_4721,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2)))),
inference(rename_variables,[],[i_0_4506]) ).
cnf(i_0_4722,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,nat_neg,X1)) ),
inference(rename_variables,[],[i_0_3769]) ).
cnf(i_0_4723,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)) = zero_zero(nat),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771]) ).
cnf(i_0_4724,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),X1),X2) = zero_zero(nat) ),
inference(rename_variables,[],[i_0_3771]) ).
cnf(i_0_4725,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798]) ).
cnf(i_0_4726,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_3798]) ).
cnf(i_0_4727,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk127_1(hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807]) ).
cnf(i_0_4728,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(rename_variables,[],[i_0_4522]) ).
cnf(i_0_4729,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk127_1(X1))) ),
inference(rename_variables,[],[i_0_3807]) ).
cnf(i_0_4730,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),esk6_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),esk6_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_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818]) ).
cnf(i_0_4731,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,esk6_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk6_4(X1,X2,X3,X4)) ),
inference(rename_variables,[],[i_0_3818]) ).
cnf(i_0_4732,plain,
hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),pls)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,pls)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828]) ).
cnf(i_0_4733,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,X1)) ),
inference(rename_variables,[],[i_0_3828]) ).
cnf(i_0_4734,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),esk126_1(hAPP(int,fun(int,bool),fequal(int),hAPP(nat,int,semiring_1_of_nat(int),X1))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835]) ).
cnf(i_0_4735,plain,
hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
inference(rename_variables,[],[i_0_4532]) ).
cnf(i_0_4736,plain,
( ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,X1,esk126_1(X1))) ),
inference(rename_variables,[],[i_0_3835]) ).
cnf(i_0_4737,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X1) != zero_zero(nat),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836]) ).
cnf(i_0_4738,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),X1),X2) != zero_zero(nat) ),
inference(rename_variables,[],[i_0_3836]) ).
cnf(i_0_4739,plain,
X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839]) ).
cnf(i_0_4740,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) ),
inference(rename_variables,[],[i_0_3839]) ).
cnf(i_0_4741,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),esk133_1(one_one(int))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842]) ).
cnf(i_0_4742,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| X1 = hAPP(nat,int,semiring_1_of_nat(int),esk133_1(X1)) ),
inference(rename_variables,[],[i_0_3842]) ).
cnf(i_0_4743,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),esk132_1(one_one(int))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843]) ).
cnf(i_0_4744,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| X1 = hAPP(nat,int,semiring_1_of_nat(int),esk132_1(X1)) ),
inference(rename_variables,[],[i_0_3843]) ).
cnf(i_0_4745,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),esk131_1(one_one(int))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844]) ).
cnf(i_0_4746,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| X1 = hAPP(nat,int,semiring_1_of_nat(int),esk131_1(X1)) ),
inference(rename_variables,[],[i_0_3844]) ).
cnf(i_0_4747,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),esk130_1(one_one(int))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845]) ).
cnf(i_0_4748,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| X1 = hAPP(nat,int,semiring_1_of_nat(int),esk130_1(X1)) ),
inference(rename_variables,[],[i_0_3845]) ).
cnf(i_0_4749,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,esk92_1(hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846]) ).
cnf(i_0_4750,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = hAPP(nat,nat,suc,esk92_1(X1)) ),
inference(rename_variables,[],[i_0_3846]) ).
cnf(i_0_4751,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,esk82_1(hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847]) ).
cnf(i_0_4752,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = hAPP(nat,nat,suc,esk82_1(X1)) ),
inference(rename_variables,[],[i_0_3847]) ).
cnf(i_0_4753,plain,
~ hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X2)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859]) ).
cnf(i_0_4754,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_3859]) ).
cnf(i_0_4755,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) != zero_zero(nat),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868]) ).
cnf(i_0_4756,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_3106]) ).
cnf(i_0_4757,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != zero_zero(nat) ),
inference(rename_variables,[],[i_0_3868]) ).
cnf(i_0_4758,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),pls)) = hAPP(int,int,number_number_of(int),pls),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884]) ).
cnf(i_0_4759,plain,
( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),X1)))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),X1)) = hAPP(int,int,number_number_of(int),X1) ),
inference(rename_variables,[],[i_0_3884]) ).
cnf(i_0_4760,plain,
esk60_2(X1,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1))) != zero_zero(nat),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885]) ).
cnf(i_0_4761,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != zero_zero(nat) ),
inference(rename_variables,[],[i_0_3885]) ).
cnf(i_0_4762,plain,
X1 = esk38_2(zero_zero(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898]) ).
cnf(i_0_4763,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)
| X2 = X3 ),
inference(rename_variables,[],[i_0_3898]) ).
cnf(i_0_4764,plain,
hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))) = zero_zero(int),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917]) ).
cnf(i_0_4765,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X2),X1) = zero_zero(int) ),
inference(rename_variables,[],[i_0_3917]) ).
cnf(i_0_4766,plain,
~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),one_one(int)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918]) ).
cnf(i_0_4767,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,nat_neg,X1)) ),
inference(rename_variables,[],[i_0_3918]) ).
cnf(i_0_4768,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),esk127_1(hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1))))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928]) ).
cnf(i_0_4769,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(rename_variables,[],[i_0_4522]) ).
cnf(i_0_4770,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(int,bool,X1,esk127_1(X1))) ),
inference(rename_variables,[],[i_0_3928]) ).
cnf(i_0_4771,plain,
hAPP(fun(pname,bool),fun(X1,bool),hAPP(fun(pname,X1),fun(fun(pname,bool),fun(X1,bool)),image(pname,X1),X2),u) != bot_bot(fun(X1,bool)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929]) ).
cnf(i_0_4772,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2) != bot_bot(fun(X3,bool)) ),
inference(rename_variables,[],[i_0_3929]) ).
cnf(i_0_4773,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X1) != hAPP(nat,nat,suc,X2),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943]) ).
cnf(i_0_4774,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 != hAPP(nat,nat,suc,X2) ),
inference(rename_variables,[],[i_0_3943]) ).
cnf(i_0_4775,plain,
hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) = hAPP(fun(pname,bool),fun(pname,bool),hAPP(pname,fun(fun(pname,bool),fun(pname,bool)),insert(pname),esk30_2(pname,u)),esk31_2(pname,u)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956]) ).
cnf(i_0_4776,plain,
( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = bot_bot(fun(X1,bool))
| hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk30_2(X1,X2)),esk31_2(X1,X2)) ),
inference(rename_variables,[],[i_0_3956]) ).
cnf(i_0_4777,plain,
hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(int,fun(int,bool),ord_less(int),X1)) != bot_bot(fun(int,bool)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027]) ).
cnf(i_0_4778,plain,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) != bot_bot(fun(X1,bool)) ),
inference(rename_variables,[],[i_0_4027]) ).
cnf(i_0_4779,plain,
bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(int,fun(int,bool),ord_less(int),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028]) ).
cnf(i_0_4780,plain,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) ),
inference(rename_variables,[],[i_0_4028]) ).
cnf(i_0_4781,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),one_one(int))) = zero_zero(nat),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037]) ).
cnf(i_0_4782,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != X1
| X2 = zero_zero(nat) ),
inference(rename_variables,[],[i_0_4037]) ).
cnf(i_0_4783,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),bot_bot(fun(X1,bool))) = bot_bot(fun(X1,bool)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087]) ).
cnf(i_0_4784,plain,
( hBOOL(hAPP(X1,bool,X2,esk17_2(X1,X2)))
| hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = bot_bot(fun(X1,bool)) ),
inference(rename_variables,[],[i_0_4087]) ).
cnf(i_0_4785,plain,
hAPP(int,int,combi(int),X1) = X1,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130]) ).
cnf(i_0_4786,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rename_variables,[],[i_0_4079]) ).
cnf(i_0_4787,plain,
( hAPP(int,int,bit1,X1) != hAPP(int,int,bit1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_4130]) ).
cnf(i_0_4788,plain,
hAPP(nat,nat,suc,X1) = esk60_2(X1,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132]) ).
cnf(i_0_4789,plain,
( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_4132]) ).
cnf(i_0_4790,plain,
X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1)),X1),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500]) ).
cnf(i_0_4791,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X1) ),
inference(rename_variables,[],[i_0_4500]) ).
cnf(i_0_4792,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4296,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911]) ).
cnf(i_0_4793,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordere236663937imp_le(X1) ),
inference(rename_variables,[],[i_0_2911]) ).
cnf(i_0_4794,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_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4507,i_0_4174,i_0_4296,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950]) ).
cnf(i_0_4795,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_2950]) ).
cnf(i_0_4796,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354]) ).
cnf(i_0_4797,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2)))),
inference(rename_variables,[],[i_0_4506]) ).
cnf(i_0_4798,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,abs_abs(X1),X2)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere142940540dd_abs(X1) ),
inference(rename_variables,[],[i_0_3354]) ).
cnf(i_0_4799,plain,
hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),X1),hAPP(int,fun(int,bool),ord_less(int),X2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),one_one(int)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629]) ).
cnf(i_0_4800,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(rename_variables,[],[i_0_3462]) ).
cnf(i_0_4801,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(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(rename_variables,[],[i_0_3629]) ).
cnf(i_0_4802,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk113_2(nat,hAPP(nat,nat,suc,X1))),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650]) ).
cnf(i_0_4803,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk113_2(X1,X2)),X3))
| ~ linorder(X1) ),
inference(rename_variables,[],[i_0_3650]) ).
cnf(i_0_4804,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),esk112_2(nat,X1))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650,i_0_3654]) ).
cnf(i_0_4805,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk112_2(X1,X3)))
| ~ linorder(X1) ),
inference(rename_variables,[],[i_0_3654]) ).
cnf(i_0_4806,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X1)),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4304,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650,i_0_3654,i_0_3666]) ).
cnf(i_0_4807,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(rename_variables,[],[i_0_3666]) ).
cnf(i_0_4808,plain,
hAPP(nat,nat,combi(nat),hAPP(nat,nat,suc,X1)) != hAPP(nat,nat,combi(nat),X1),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4304,i_0_4307,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650,i_0_3654,i_0_3666,i_0_3911]) ).
cnf(i_0_4809,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| ~ order(X1) ),
inference(rename_variables,[],[i_0_3911]) ).
cnf(i_0_4810,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4304,i_0_4307,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650,i_0_3654,i_0_3666,i_0_3911,i_0_3983]) ).
cnf(i_0_4811,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1)
| X2 != X3 ),
inference(rename_variables,[],[i_0_3983]) ).
cnf(i_0_4812,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int))) != 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_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4304,i_0_4307,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650,i_0_3654,i_0_3666,i_0_3911,i_0_3983,i_0_4415]) ).
cnf(i_0_4813,plain,
ab_semigroup_mult(hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),esk134_1(int))),hAPP(nat,int,semiring_1_of_nat(int),esk135_1(int)))),
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4304,i_0_4307,i_0_4330,i_0_4343,i_0_4079,i_0_4646,i_0_4714,i_0_3926,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650,i_0_3654,i_0_3666,i_0_3911,i_0_3983,i_0_4415,i_0_4464]) ).
cnf(i_0_4814,plain,
X1 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),esk134_1(X1))),hAPP(nat,int,semiring_1_of_nat(int),esk135_1(X1))),
inference(rename_variables,[],[i_0_3926]) ).
cnf(i_0_4815,plain,
$false,
inference(scs_inference,[],[i_0_2809,i_0_4522,i_0_4556,i_0_4604,i_0_4607,i_0_4707,i_0_4728,i_0_4498,i_0_4683,i_0_4532,i_0_4695,i_0_4506,i_0_4659,i_0_4662,i_0_4686,i_0_4721,i_0_4507,i_0_4174,i_0_4296,i_0_4302,i_0_4304,i_0_4307,i_0_4330,i_0_4343,i_0_4080,i_0_4079,i_0_4646,i_0_4714,i_0_3926,i_0_3867,i_0_3986,i_0_3987,i_0_3871,i_0_4610,i_0_4619,i_0_3280,i_0_3882,i_0_4573,i_0_3506,i_0_3821,i_0_3991,i_0_3896,i_0_4587,i_0_4001,i_0_4002,i_0_4613,i_0_4643,i_0_3523,i_0_3965,i_0_3923,i_0_3448,i_0_3934,i_0_3922,i_0_3462,i_0_3609,i_0_4616,i_0_3611,i_0_4578,i_0_4581,i_0_3106,i_0_4559,i_0_3755,i_0_3786,i_0_3787,i_0_3605,i_0_3870,i_0_3886,i_0_3890,i_0_3891,i_0_4346,i_0_4350,i_0_4351,i_0_2865,i_0_3006,i_0_3033,i_0_3036,i_0_3037,i_0_3140,i_0_3186,i_0_3263,i_0_3269,i_0_3288,i_0_3302,i_0_3305,i_0_3329,i_0_3363,i_0_3364,i_0_3373,i_0_3379,i_0_3382,i_0_3383,i_0_3394,i_0_3397,i_0_3399,i_0_3400,i_0_3402,i_0_3429,i_0_3442,i_0_3445,i_0_3471,i_0_3488,i_0_3489,i_0_3525,i_0_3537,i_0_3546,i_0_3567,i_0_3569,i_0_3571,i_0_3574,i_0_3575,i_0_3596,i_0_3597,i_0_3638,i_0_3644,i_0_3645,i_0_3646,i_0_3647,i_0_3653,i_0_3673,i_0_3681,i_0_3684,i_0_3690,i_0_3695,i_0_3697,i_0_3705,i_0_3706,i_0_3713,i_0_3714,i_0_3717,i_0_3740,i_0_3741,i_0_3750,i_0_3754,i_0_3767,i_0_3768,i_0_3769,i_0_3771,i_0_3798,i_0_3807,i_0_3818,i_0_3828,i_0_3835,i_0_3836,i_0_3839,i_0_3842,i_0_3843,i_0_3844,i_0_3845,i_0_3846,i_0_3847,i_0_3859,i_0_3868,i_0_3884,i_0_3885,i_0_3898,i_0_3917,i_0_3918,i_0_3928,i_0_3929,i_0_3943,i_0_3956,i_0_4027,i_0_4028,i_0_4037,i_0_4087,i_0_4130,i_0_4132,i_0_4500,i_0_2911,i_0_2950,i_0_3354,i_0_3629,i_0_3650,i_0_3654,i_0_3666,i_0_3911,i_0_3983,i_0_4415,i_0_4464,i_0_3198]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW473+7 : TPTP v9.2.1. Released v5.3.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:56:43 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 6.59/5.91 % Version : CSE_E---1.7
% 6.59/5.91 % Problem : theBenchmark.p
% 6.59/5.91 % SZS status Theorem for theBenchmark.p
% 6.59/5.91 % SZS output start CNFRefutation
% See solution above
% 11.60/8.49 % Total time : 5.555s
%------------------------------------------------------------------------------