%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW473+6 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 0.72s 5.79s
% Output : CNFRefutation 8.09s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_844)
% Comments :
%------------------------------------------------------------------------------
fof(fact_208_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/sandbox/benchmark/theBenchmark.p',fact_208_If__def) ).
fof(fact_160_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,X55] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X55))
=> ( ti(fun(X1,bool),X55) != bot_bot(fun(X1,bool))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X55))
=> 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),X55))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_finite__ne__induct) ).
fof(fact_94_imageE,axiom,
! [X1,X2,X34,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X34),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
=> ~ ! [X33] :
( ti(X1,X34) = hAPP(X2,X1,X12,X33)
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X33),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_imageE) ).
fof(fact_217_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/sandbox/benchmark/theBenchmark.p',fact_217_flat__lub__def) ).
fof(fact_162_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/sandbox/benchmark/theBenchmark.p',fact_162_folding__one_Oinsert) ).
fof(fact_179_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/sandbox/benchmark/theBenchmark.p',fact_179_Diff__insert__absorb) ).
fof(fact_64_insert__ident,axiom,
! [X1,X13,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13))
=> ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X13)
<=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_insert__ident) ).
fof(fact_53_insertCI,axiom,
! [X1,X34,X11,X13] :
( ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> ti(X1,X11) = ti(X1,X34) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insertCI) ).
fof(fact_375_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/sandbox/benchmark/theBenchmark.p',fact_375_linorder__antisym__conv2) ).
fof(fact_334_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/sandbox/benchmark/theBenchmark.p',fact_334_linorder__antisym__conv3) ).
fof(fact_370_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/sandbox/benchmark/theBenchmark.p',fact_370_linorder__antisym__conv1) ).
fof(fact_154_nonempty__iff,axiom,
! [X1,X8] :
( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
<=> ? [X33,X59] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X59)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X59)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_nonempty__iff) ).
fof(fact_424_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/sandbox/benchmark/theBenchmark.p',fact_424_linorder__neqE__linordered__idom) ).
fof(fact_351_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/sandbox/benchmark/theBenchmark.p',fact_351_linorder__cases) ).
fof(fact_335_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/sandbox/benchmark/theBenchmark.p',fact_335_linorder__neqE) ).
fof(fact_332_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/sandbox/benchmark/theBenchmark.p',fact_332_not__less__iff__gr__or__eq) ).
fof(fact_111_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/sandbox/benchmark/theBenchmark.p',fact_111_all__not__in__conv) ).
fof(fact_106_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/sandbox/benchmark/theBenchmark.p',fact_106_equals0D) ).
fof(fact_78_equalityE,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_equalityE) ).
fof(help_fequal_1_1_T,axiom,
! [X3,X21,X22] :
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22))
| ti(X3,X21) = ti(X3,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
fof(fact_49_pigeonhole__infinite,axiom,
! [X2,X1,X12,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)))
=> ? [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
& ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X8))),hAPP(X2,fun(X1,bool),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),hAPP(fun(X1,X2),fun(X1,fun(X2,bool)),hAPP(fun(X2,fun(X2,bool)),fun(fun(X1,X2),fun(X1,fun(X2,bool))),combb(X2,fun(X2,bool),X1),fequal(X2)),X12)),hAPP(X1,X2,X12,X33)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pigeonhole__infinite) ).
fof(fact_211_folding__image__simple_Oneutral,axiom,
! [X2,X1,X8,X12,X42,X40,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),X42),X40),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,X40,X33) = ti(X1,X42) )
=> hAPP(fun(X2,bool),X1,X10,X8) = ti(X1,X42) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_folding__image__simple_Oneutral) ).
fof(help_COMBI_1_1_U,axiom,
! [X3,X80] : hAPP(X3,X3,combi(X3),X80) = ti(X3,X80),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(fact_194_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,X61] : 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),X61)),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),X61),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/sandbox/benchmark/theBenchmark.p',fact_194_folding__one_Oclosed) ).
fof(fact_193_folding__one__idem_Ohom__commute,axiom,
! [X1,X48,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,X61] : hAPP(X1,X1,X9,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,X33),X61)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X12,hAPP(X1,X1,X9,X33)),hAPP(X1,X1,X9,X61))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X48))
=> ( ti(fun(X1,bool),X48) != bot_bot(fun(X1,bool))
=> hAPP(X1,X1,X9,hAPP(fun(X1,bool),X1,X10,X48)) = 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),X48)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_folding__one__idem_Ohom__commute) ).
fof(fact_416_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/sandbox/benchmark/theBenchmark.p',fact_416_psubset__insert__iff) ).
fof(fact_185_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/sandbox/benchmark/theBenchmark.p',fact_185_subset__insert__iff) ).
fof(fact_207_folding__image__simple_Oinsert,axiom,
! [X2,X1,X14,X8,X12,X42,X40,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),X42),X40),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,X40,X14)),hAPP(fun(X2,bool),X1,X10,X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_folding__image__simple_Oinsert) ).
fof(fact_206_folding__image__simple_Oempty,axiom,
! [X2,X1,X12,X42,X40,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),X42),X40),X10))
=> hAPP(fun(X2,bool),X1,X10,bot_bot(fun(X2,bool))) = ti(X1,X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_folding__image__simple_Oempty) ).
fof(fact_128_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/sandbox/benchmark/theBenchmark.p',fact_128_Collect__conv__if) ).
fof(fact_223_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/sandbox/benchmark/theBenchmark.p',fact_223_card__Diff__insert) ).
fof(fact_129_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/sandbox/benchmark/theBenchmark.p',fact_129_Collect__conv__if2) ).
fof(fact_148_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))))
=> ( ! [X54,X55] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X54),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X54),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X55))
=> 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),X54),X55))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_finite__subset__induct) ).
fof(fact_47_finite__subset__image,axiom,
! [X2,X1,X12,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X8)))
=> ? [X30] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X30),X8))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X30))
& ti(fun(X1,bool),X13) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X30) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite__subset__image) ).
fof(fact_92_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)))
<=> ? [X47] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X47),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),X47) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_subset__image__iff) ).
fof(fact_265_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/sandbox/benchmark/theBenchmark.p',fact_265_add__leE) ).
fof(fact_87_subset__insert,axiom,
! [X1,X13,X14,X8] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X13)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subset__insert) ).
fof(fact_174_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/sandbox/benchmark/theBenchmark.p',fact_174_folding__one_Oremove) ).
fof(fact_204_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/sandbox/benchmark/theBenchmark.p',fact_204_Diff__iff) ).
fof(fact_201_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/sandbox/benchmark/theBenchmark.p',fact_201_DiffD2) ).
fof(fact_175_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/sandbox/benchmark/theBenchmark.p',fact_175_folding__one_Oinsert__remove) ).
fof(fact_79_image__iff,axiom,
! [X1,X2,X42,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X42),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,X42) = hAPP(X2,X1,X12,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_image__iff) ).
fof(fact_219_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/sandbox/benchmark/theBenchmark.p',fact_219_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/sandbox/benchmark/theBenchmark.p',fact_6_card__seteq) ).
fof(fact_303_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/sandbox/benchmark/theBenchmark.p',fact_303_not__add__less1) ).
fof(fact_302_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/sandbox/benchmark/theBenchmark.p',fact_302_not__add__less2) ).
fof(fact_132_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/sandbox/benchmark/theBenchmark.p',fact_132_subset__singletonD) ).
fof(fact_150_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,X55] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X55))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X55))
=> 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),X55))) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_finite__induct) ).
fof(fact_62_insert__iff,axiom,
! [X1,X11,X34,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X8)))
<=> ( ti(X1,X11) = ti(X1,X34)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_insert__iff) ).
fof(fact_54_insertE,axiom,
! [X1,X11,X34,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X8)))
=> ( ti(X1,X11) != ti(X1,X34)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_insertE) ).
fof(fact_158_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/sandbox/benchmark/theBenchmark.p',fact_158_folding__one__idem_Osubset__idem) ).
fof(fact_418_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/sandbox/benchmark/theBenchmark.p',fact_418_finite__conv__nat__seg__image) ).
fof(fact_384_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/sandbox/benchmark/theBenchmark.p',fact_384_nat__seg__image__imp__finite) ).
fof(fact_200_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/sandbox/benchmark/theBenchmark.p',fact_200_DiffI) ).
fof(fact_120_doubleton__eq__iff,axiom,
! [X1,X11,X34,X35,X50] :
( 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),X50),bot_bot(fun(X1,bool))))
<=> ( ( ti(X1,X11) = ti(X1,X35)
& ti(X1,X34) = ti(X1,X50) )
| ( ti(X1,X11) = ti(X1,X50)
& ti(X1,X34) = ti(X1,X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_doubleton__eq__iff) ).
fof(fact_180_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/sandbox/benchmark/theBenchmark.p',fact_180_insert__Diff) ).
fof(fact_170_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/sandbox/benchmark/theBenchmark.p',fact_170_insert__Diff__if) ).
fof(fact_171_double__diff,axiom,
! [X1,X41,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),X41))
=> 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)),X41),X8)) = ti(fun(X1,bool),X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_double__diff) ).
fof(fact_121_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/sandbox/benchmark/theBenchmark.p',fact_121_singleton__iff) ).
fof(fact_119_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/sandbox/benchmark/theBenchmark.p',fact_119_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/sandbox/benchmark/theBenchmark.p',fact_50_image__eqI) ).
fof(fact_81_rev__image__eqI,axiom,
! [X2,X1,X34,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( ti(X2,X34) = hAPP(X1,X2,X12,X14)
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X34),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rev__image__eqI) ).
fof(fact_159_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/sandbox/benchmark/theBenchmark.p',fact_159_folding__one__idem_Oinsert__idem) ).
fof(fact_63_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/sandbox/benchmark/theBenchmark.p',fact_63_insert__code) ).
fof(fact_35_not__less__eq__eq,axiom,
! [X28,X20] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X20)),X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_not__less__eq__eq) ).
fof(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/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple_res) ).
fof(fact_414_less__fun__def,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X12,X40] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X12),X40))
<=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X40))
& ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X40),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_less__fun__def) ).
fof(fact_68_set__eq__subset,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_set__eq__subset) ).
fof(fact_51_equalityI,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8))
=> ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_equalityI) ).
fof(fact_187_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/sandbox/benchmark/theBenchmark.p',fact_187_folding__one_Osingleton) ).
fof(fact_462_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/sandbox/benchmark/theBenchmark.p',fact_462_add__nonneg__eq__0__iff) ).
fof(fact_322_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/sandbox/benchmark/theBenchmark.p',fact_322_not__less__eq) ).
fof(fact_285_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/sandbox/benchmark/theBenchmark.p',fact_285_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/sandbox/benchmark/theBenchmark.p',fact_8_card__insert__if) ).
fof(fact_412_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/sandbox/benchmark/theBenchmark.p',fact_412_psubset__eq) ).
fof(fact_411_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/sandbox/benchmark/theBenchmark.p',fact_411_subset__iff__psubset__eq) ).
fof(fact_9_card__insert__disjoint,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(nat,nat,suc,hAPP(fun(X1,bool),nat,finite_card(X1),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_card__insert__disjoint) ).
fof(fact_31_le__SucE,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),hAPP(nat,nat,suc,X17)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> X18 = hAPP(nat,nat,suc,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__SucE) ).
fof(fact_366_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/sandbox/benchmark/theBenchmark.p',fact_366_less__le__not__le) ).
fof(fact_319_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/sandbox/benchmark/theBenchmark.p',fact_319_not__less__less__Suc__eq) ).
fof(fact_318_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/sandbox/benchmark/theBenchmark.p',fact_318_less__antisym) ).
fof(fact_314_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/sandbox/benchmark/theBenchmark.p',fact_314_less__SucE) ).
fof(fact_146_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/sandbox/benchmark/theBenchmark.p',fact_146_order__eq__iff) ).
fof(fact_144_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/sandbox/benchmark/theBenchmark.p',fact_144_order__antisym__conv) ).
fof(fact_139_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/sandbox/benchmark/theBenchmark.p',fact_139_order__antisym) ).
fof(fact_137_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/sandbox/benchmark/theBenchmark.p',fact_137_xt1_I5_J) ).
fof(fact_36_Suc__n__not__le__n,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Suc__n__not__le__n) ).
fof(fact_164_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/sandbox/benchmark/theBenchmark.p',fact_164_folding__one__idem_Oidem) ).
fof(fact_363_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/sandbox/benchmark/theBenchmark.p',fact_363_linorder__not__le) ).
fof(fact_373_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/sandbox/benchmark/theBenchmark.p',fact_373_leD) ).
fof(fact_362_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/sandbox/benchmark/theBenchmark.p',fact_362_linorder__not__less) ).
fof(fact_350_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/sandbox/benchmark/theBenchmark.p',fact_350_order__less__asym) ).
fof(fact_342_order__less__asym_H,axiom,
! [X3] :
( preorder(X3)
=> ! [X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X49)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_order__less__asym_H) ).
fof(fact_338_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/sandbox/benchmark/theBenchmark.p',fact_338_order__less__imp__not__less) ).
fof(fact_337_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/sandbox/benchmark/theBenchmark.p',fact_337_order__less__not__sym) ).
fof(fact_343_xt1_I9_J,axiom,
! [X3] :
( order(X3)
=> ! [X53,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X49))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_xt1_I9_J) ).
fof(fact_142_xt1_I3_J,axiom,
! [X3] :
( order(X3)
=> ! [X52,X49,X53] :
( ti(X3,X49) = ti(X3,X53)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X52),X53))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X52),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_xt1_I3_J) ).
fof(fact_140_xt1_I4_J,axiom,
! [X3] :
( order(X3)
=> ! [X52,X53,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),X49))
=> ( ti(X3,X53) = ti(X3,X52)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X52),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_xt1_I4_J) ).
fof(fact_345_xt1_I1_J,axiom,
! [X3] :
( order(X3)
=> ! [X52,X49,X53] :
( ti(X3,X49) = ti(X3,X53)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X52),X53))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X52),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_xt1_I1_J) ).
fof(fact_347_xt1_I2_J,axiom,
! [X3] :
( order(X3)
=> ! [X52,X53,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X49))
=> ( ti(X3,X53) = ti(X3,X52)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X52),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_xt1_I2_J) ).
fof(fact_378_xt1_I11_J,axiom,
! [X3] :
( order(X3)
=> ! [X53,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),X49))
=> ( ti(X3,X49) != ti(X3,X53)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_xt1_I11_J) ).
fof(fact_377_order__le__neq__trans,axiom,
! [X3] :
( order(X3)
=> ! [X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53))
=> ( ti(X3,X49) != ti(X3,X53)
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_order__le__neq__trans) ).
fof(fact_376_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/sandbox/benchmark/theBenchmark.p',fact_376_order__le__imp__less__or__eq) ).
fof(fact_371_order__neq__le__trans,axiom,
! [X3] :
( order(X3)
=> ! [X49,X53] :
( ti(X3,X49) != ti(X3,X53)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_order__neq__le__trans) ).
fof(fact_367_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/sandbox/benchmark/theBenchmark.p',fact_367_order__le__less) ).
fof(fact_365_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/sandbox/benchmark/theBenchmark.p',fact_365_order__less__le) ).
fof(fact_372_xt1_I12_J,axiom,
! [X3] :
( order(X3)
=> ! [X49,X53] :
( ti(X3,X49) != ti(X3,X53)
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),X49))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_xt1_I12_J) ).
fof(fact_266_diff__add__cancel,axiom,
! [X3] :
( group_add(X3)
=> ! [X49,X53] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X49),X53)),X53) = ti(X3,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_diff__add__cancel) ).
fof(fact_267_add__diff__cancel,axiom,
! [X3] :
( group_add(X3)
=> ! [X49,X53] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X53)),X53) = ti(X3,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_add__diff__cancel) ).
fof(fact_66_insert__absorb,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X8))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8) = ti(fun(X1,bool),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_insert__absorb) ).
fof(fact_118_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/sandbox/benchmark/theBenchmark.p',fact_118_singleton__inject) ).
fof(fact_400_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/sandbox/benchmark/theBenchmark.p',fact_400_add__diff__inverse) ).
fof(fact_186_diff__eq__diff__eq,axiom,
! [X1] :
( ab_group_add(X1)
=> ! [X11,X34,X35,X50] :
( 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),X50)
=> ( ti(X1,X11) = ti(X1,X34)
<=> ti(X1,X35) = ti(X1,X50) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_diff__eq__diff__eq) ).
fof(fact_124_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/sandbox/benchmark/theBenchmark.p',fact_124_subset__empty) ).
fof(fact_134_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/sandbox/benchmark/theBenchmark.p',fact_134_image__constant__conv) ).
fof(fact_333_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/sandbox/benchmark/theBenchmark.p',fact_333_linorder__less__linear) ).
fof(fact_331_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/sandbox/benchmark/theBenchmark.p',fact_331_linorder__neq__iff) ).
fof(fact_216_the1__equality,axiom,
! [X1,X11,X16] :
( ? [X33] :
( hBOOL(hAPP(X1,bool,X16,X33))
& ! [X61] :
( hBOOL(hAPP(X1,bool,X16,X61))
=> ti(X1,X61) = ti(X1,X33) ) )
=> ( hBOOL(hAPP(X1,bool,X16,X11))
=> hAPP(fun(X1,bool),X1,the(X1),X16) = ti(X1,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_the1__equality) ).
fof(fact_151_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))
| ? [X57,X54] :
( ti(fun(X1,bool),X11) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X54),X57)
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_finite_Osimps) ).
fof(fact_413_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/sandbox/benchmark/theBenchmark.p',fact_413_not__psubset__empty) ).
fof(fact_110_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/sandbox/benchmark/theBenchmark.p',fact_110_ex__in__conv) ).
fof(fact_215_theI_H,axiom,
! [X1,X16] :
( ? [X33] :
( hBOOL(hAPP(X1,bool,X16,X33))
& ! [X61] :
( hBOOL(hAPP(X1,bool,X16,X61))
=> ti(X1,X61) = ti(X1,X33) ) )
=> hBOOL(hAPP(X1,bool,X16,hAPP(fun(X1,bool),X1,the(X1),X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_theI_H) ).
fof(fact_214_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/sandbox/benchmark/theBenchmark.p',fact_214_theI) ).
fof(fact_340_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/sandbox/benchmark/theBenchmark.p',fact_340_order__less__imp__not__eq2) ).
fof(fact_339_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/sandbox/benchmark/theBenchmark.p',fact_339_order__less__imp__not__eq) ).
fof(fact_336_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/sandbox/benchmark/theBenchmark.p',fact_336_less__imp__neq) ).
fof(fact_135_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/sandbox/benchmark/theBenchmark.p',fact_135_linorder__le__cases) ).
fof(fact_368_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/sandbox/benchmark/theBenchmark.p',fact_368_leI) ).
fof(fact_369_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/sandbox/benchmark/theBenchmark.p',fact_369_not__leE) ).
fof(fact_69_equalityD1,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_equalityD1) ).
fof(fact_70_equalityD2,axiom,
! [X1,X8,X13] :
( ti(fun(X1,bool),X8) = ti(fun(X1,bool),X13)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_equalityD2) ).
fof(fact_355_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/sandbox/benchmark/theBenchmark.p',fact_355_linorder__neqE__nat) ).
fof(fact_209_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/sandbox/benchmark/theBenchmark.p',fact_209_the__eq__trivial) ).
fof(fact_247_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/sandbox/benchmark/theBenchmark.p',fact_247_add__right__cancel) ).
fof(fact_244_add__right__imp__eq,axiom,
! [X3] :
( cancel_semigroup_add(X3)
=> ! [X53,X49,X52] :
( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X49) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X49)
=> ti(X3,X53) = ti(X3,X52) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_add__right__imp__eq) ).
fof(fact_245_add__imp__eq,axiom,
! [X3] :
( cancel146912293up_add(X3)
=> ! [X49,X53,X52] :
( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X53) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)
=> ti(X3,X53) = ti(X3,X52) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__imp__eq) ).
fof(fact_248_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/sandbox/benchmark/theBenchmark.p',fact_248_add__left__cancel) ).
fof(fact_246_add__left__imp__eq,axiom,
! [X3] :
( cancel_semigroup_add(X3)
=> ! [X49,X53,X52] :
( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X53) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)
=> ti(X3,X53) = ti(X3,X52) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__left__imp__eq) ).
fof(fact_74_ext,axiom,
! [X1,X2,X12,X40] :
( ! [X33] : hAPP(X1,X2,X12,X33) = hAPP(X1,X2,X40,X33)
=> ti(fun(X1,X2),X12) = ti(fun(X1,X2),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
fof(fact_108_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/sandbox/benchmark/theBenchmark.p',fact_108_empty__iff) ).
fof(fact_103_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/sandbox/benchmark/theBenchmark.p',fact_103_emptyE) ).
fof(fact_361_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/sandbox/benchmark/theBenchmark.p',fact_361_bot__less) ).
fof(fact_116_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/sandbox/benchmark/theBenchmark.p',fact_116_bot__unique) ).
fof(fact_115_le__bot,axiom,
! [X3] :
( bot(X3)
=> ! [X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),bot_bot(X3)))
=> ti(X3,X49) = bot_bot(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_le__bot) ).
fof(fact_153_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/sandbox/benchmark/theBenchmark.p',fact_153_the__elem__eq) ).
fof(fact_445_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/sandbox/benchmark/theBenchmark.p',fact_445_Plus__eq__empty__conv) ).
fof(fact_455_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/sandbox/benchmark/theBenchmark.p',fact_455_not__one__le__zero) ).
fof(fact_453_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/sandbox/benchmark/theBenchmark.p',fact_453_not__one__less__zero) ).
fof(fact_491_nat__case__0,axiom,
! [X1,X65,X66] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X65),X66),zero_zero(nat)) = ti(X1,X65),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_nat__case__0) ).
fof(fact_360_not__less__bot,axiom,
! [X3] :
( bot(X3)
=> ! [X49] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),bot_bot(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_not__less__bot) ).
fof(fact_330_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/sandbox/benchmark/theBenchmark.p',fact_330_order__less__irrefl) ).
fof(fact_447_less__zeroE,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_less__zeroE) ).
fof(fact_356_less__irrefl__nat,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_less__irrefl__nat) ).
fof(fact_353_less__not__refl,axiom,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_less__not__refl) ).
fof(help_fimplies_3_1_U,axiom,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X80),X81))
| ~ hBOOL(X80)
| hBOOL(X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(help_fdisj_3_1_U,axiom,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X80),X81))
| hBOOL(X80)
| hBOOL(X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X80),X81))
| hBOOL(X80) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X80),X81))
| hBOOL(X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
fof(help_fequal_2_1_T,axiom,
! [X3,X21,X22] :
( ti(X3,X21) != ti(X3,X22)
| hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X21),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
fof(tsy_c_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one_res) ).
fof(fact_210_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/sandbox/benchmark/theBenchmark.p',fact_210_the__equality) ).
fof(fact_125_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/sandbox/benchmark/theBenchmark.p',fact_125_image__is__empty) ).
fof(fact_127_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/sandbox/benchmark/theBenchmark.p',fact_127_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/sandbox/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
fof(fact_480_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/sandbox/benchmark/theBenchmark.p',fact_480_right__minus__eq) ).
fof(fact_479_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/sandbox/benchmark/theBenchmark.p',fact_479_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/sandbox/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
fof(tsy_c_COMBB_res,axiom,
! [X1,X2,X3] : ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
fof(fact_166_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/sandbox/benchmark/theBenchmark.p',fact_166_Diff__empty) ).
fof(help_fconj_1_1_U,axiom,
! [X81,X80] :
( ~ hBOOL(X80)
| ~ hBOOL(X81)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X80),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fimplies_2_1_U,axiom,
! [X80,X81] :
( ~ hBOOL(X81)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X80),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(help_fdisj_1_1_U,axiom,
! [X81,X80] :
( ~ hBOOL(X80)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X80),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(help_fdisj_2_1_U,axiom,
! [X80,X81] :
( ~ hBOOL(X81)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X80),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
fof(tsy_c_Set_Oimage_res,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
fof(fact_494_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/sandbox/benchmark/theBenchmark.p',fact_494_double__zero__sym) ).
fof(fact_84_image__ident,axiom,
! [X1,X45] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X45) = ti(fun(X1,bool),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
fof(fact_107_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/sandbox/benchmark/theBenchmark.p',fact_107_Collect__empty__eq) ).
fof(fact_109_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/sandbox/benchmark/theBenchmark.p',fact_109_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/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(help_COMBK_1_1_U,axiom,
! [X1,X3,X80,X81] : hAPP(X1,X3,hAPP(X3,fun(X1,X3),combk(X3,X1),X80),X81) = ti(X3,X80),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(fact_198_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/sandbox/benchmark/theBenchmark.p',fact_198_the__sym__eq__trivial) ).
fof(fact_493_add__0,axiom,
! [X3] :
( comm_monoid_add(X3)
=> ! [X49] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X49) = ti(X3,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_add__0) ).
fof(fact_492_add__0__left,axiom,
! [X3] :
( monoid_add(X3)
=> ! [X49] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X49) = ti(X3,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_add__0__left) ).
fof(fact_496_add_Ocomm__neutral,axiom,
! [X3] :
( comm_monoid_add(X3)
=> ! [X49] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),zero_zero(X3)) = ti(X3,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_add_Ocomm__neutral) ).
fof(fact_495_add__0__right,axiom,
! [X3] :
( monoid_add(X3)
=> ! [X49] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),zero_zero(X3)) = ti(X3,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_add__0__right) ).
fof(fact_477_diff__0__right,axiom,
! [X3] :
( group_add(X3)
=> ! [X49] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X49),zero_zero(X3)) = ti(X3,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_diff__0__right) ).
fof(help_ti_idem,axiom,
! [X78,X79] : ti(X78,ti(X78,X79)) = ti(X78,X79),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(tsy_c_hAPP_res,axiom,
! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(tsy_c_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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
fof(fact_450_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/sandbox/benchmark/theBenchmark.p',fact_450_card__infinite) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [X4] :
( hBOOL(ti(bool,X4))
<=> hBOOL(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(help_fNot_1_1_U,axiom,
! [X80] :
( ~ hBOOL(hAPP(bool,bool,fNot,X80))
| ~ hBOOL(X80) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(tsy_c_Set_OCollect_res,axiom,
! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
fof(fact_76_Collect__def,axiom,
! [X1,X16] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = ti(fun(X1,bool),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
fof(tsy_c_COMBK_res,axiom,
! [X3,X1] : ti(fun(X3,fun(X1,X3)),combk(X3,X1)) = combk(X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
fof(tsy_c_Groups_Oplus__class_Oplus_2_res,axiom,
! [X3] :
( cancel_semigroup_add(X3)
=> ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).
fof(tsy_c_Groups_Oplus__class_Oplus_1_res,axiom,
! [X3] :
( ab_semigroup_add(X3)
=> ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
! [X2] :
( ord(X2)
=> ti(fun(X2,fun(X2,bool)),ord_less_eq(X2)) = ord_less_eq(X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
fof(tsy_c_Finite__Set_Ocard_res,axiom,
! [X2] : ti(fun(fun(X2,bool),nat),finite_card(X2)) = finite_card(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).
fof(tsy_c_Finite__Set_Ofinite_res,axiom,
! [X1] : ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
fof(help_fFalse_1_1_T,axiom,
! [X80] :
( ti(bool,X80) = fTrue
| ti(bool,X80) = fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(tsy_c_COMBI_res,axiom,
! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
fof(tsy_c_Orderings_Obot__class_Obot_res,axiom,
! [X2] :
( bot(X2)
=> ti(X2,bot_bot(X2)) = bot_bot(X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(fact_288_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/sandbox/benchmark/theBenchmark.p',fact_288_card__Diff2__less) ).
fof(fact_433_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,X61] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X61),X33))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X12,X61)),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/sandbox/benchmark/theBenchmark.p',fact_433_xt4) ).
fof(fact_430_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,X61] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X61),X33))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X12,X61)),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/sandbox/benchmark/theBenchmark.p',fact_430_xt6) ).
fof(fact_438_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,X61] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X33),X61))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X12,X61))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X11)),X35)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_order__le__less__subst2) ).
fof(fact_439_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,X61] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X33),X61))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X12,X61))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X11)),X35)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_order__less__le__subst2) ).
fof(fact_436_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,X61] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X61),X33))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X61)),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/sandbox/benchmark/theBenchmark.p',fact_436_xt7) ).
fof(fact_435_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,X61] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X61),X33))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X12,X61)),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/sandbox/benchmark/theBenchmark.p',fact_435_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,X61] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X33),X61))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X12,X33)),hAPP(X2,X1,X12,X61))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),hAPP(X2,X1,X12,X35))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_order__less__le__subst1) ).
fof(fact_434_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,X61] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X33),X61))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X12,X33)),hAPP(X2,X1,X12,X61))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),hAPP(X2,X1,X12,X35))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_order__le__less__subst1) ).
fof(fact_26_finite__Collect__disjI,axiom,
! [X1,X16,X15] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X16)),X15))))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__Collect__disjI) ).
fof(fact_149_assms_I2_J,axiom,
! [X56,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,X56)),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,X56)))),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,X56)),bot_bot(fun(x_a,bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_assms_I2_J) ).
fof(fact_386_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/sandbox/benchmark/theBenchmark.p',fact_386_finite__M__bounded__by__nat) ).
fof(fact_182_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/sandbox/benchmark/theBenchmark.p',fact_182_image__diff__subset) ).
fof(fact_59_insert__Collect,axiom,
! [X1,X11,X16] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fimplies),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11)))),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_insert__Collect) ).
fof(fact_10_finite__Collect__conjI,axiom,
! [X1,X15,X16] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X15))) )
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X16)),X15)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Collect__conjI) ).
fof(fact_152_finite__less__ub,axiom,
! [X58,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)),X58)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_finite__less__ub) ).
fof(fact_205_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/sandbox/benchmark/theBenchmark.p',fact_205_set__diff__eq) ).
fof(fact_289_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/sandbox/benchmark/theBenchmark.p',fact_289_card__Diff1__less) ).
fof(fact_196_folding__image__simple_Oremove,axiom,
! [X2,X1,X14,X8,X12,X42,X40,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),X42),X40),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,X40,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/sandbox/benchmark/theBenchmark.p',fact_196_folding__image__simple_Oremove) ).
fof(fact_197_folding__image__simple_Oinsert__remove,axiom,
! [X2,X1,X14,X8,X12,X42,X40,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),X42),X40),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,X40,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/sandbox/benchmark/theBenchmark.p',fact_197_folding__image__simple_Oinsert__remove) ).
fof(fact_192_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/sandbox/benchmark/theBenchmark.p',fact_192_card__Diff1__le) ).
fof(fact_184_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/sandbox/benchmark/theBenchmark.p',fact_184_diff__single__insert) ).
fof(fact_226_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/sandbox/benchmark/theBenchmark.p',fact_226_comp__fun__idem__remove) ).
fof(fact_96_image__subsetI,axiom,
! [X2,X1,X12,X13,X8] :
( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X33)),X13)) )
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_image__subsetI) ).
fof(fact_82_insert__compr__raw,axiom,
! [X1,X33,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X43) = 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)),X43))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_insert__compr__raw) ).
fof(fact_58_insert__compr,axiom,
! [X1,X11,X13] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X11))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_insert__compr) ).
fof(conj_6,conjecture,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
fof(fact_189_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/sandbox/benchmark/theBenchmark.p',fact_189_diff__card__le__card__Diff) ).
fof(fact_405_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/sandbox/benchmark/theBenchmark.p',fact_405_mono__nat__linear__lb) ).
fof(fact_422_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/sandbox/benchmark/theBenchmark.p',fact_422_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/sandbox/benchmark/theBenchmark.p',fact_48_lift__Suc__mono__le) ).
fof(fact_419_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/sandbox/benchmark/theBenchmark.p',fact_419_lift__Suc__mono__less) ).
fof(fact_195_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))
=> ( ! [X54,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),X54),X57))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X57))
=> 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)),X57),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X54),bot_bot(fun(X1,bool)))))) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,bot_bot(fun(X1,bool)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_finite__empty__induct) ).
fof(fact_99_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/sandbox/benchmark/theBenchmark.p',fact_99_assms_I3_J) ).
fof(fact_181_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/sandbox/benchmark/theBenchmark.p',fact_181_finite__Diff__insert) ).
fof(fact_4_card__image__le,axiom,
! [X2,X1,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))),hAPP(fun(X1,bool),nat,finite_card(X1),X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_card__image__le) ).
fof(fact_39_le__diff__iff,axiom,
! [X20,X19,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X19)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__diff__iff) ).
fof(fact_403_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/sandbox/benchmark/theBenchmark.p',fact_403_less__diff__iff) ).
fof(fact_172_Diff__mono,axiom,
! [X1,X46,X13,X8,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X41))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X46),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)),X41),X46))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Diff__mono) ).
fof(fact_1_finite__Collect__subsets,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X8)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
fof(fact_277_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/sandbox/benchmark/theBenchmark.p',fact_277_le__add__diff) ).
fof(fact_274_le__diff__conv2,axiom,
! [X36,X19,X64] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X64))
=> ( 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),X64),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)),X64)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_le__diff__conv2) ).
fof(fact_233_add__le__imp__le__right,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X49,X52,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X52)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_add__le__imp__le__right) ).
fof(fact_228_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/sandbox/benchmark/theBenchmark.p',fact_228_add__le__cancel__right) ).
fof(fact_234_add__le__imp__le__left,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X52,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X49)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X53)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_add__le__imp__le__left) ).
fof(fact_229_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/sandbox/benchmark/theBenchmark.p',fact_229_add__le__cancel__left) ).
fof(fact_310_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/sandbox/benchmark/theBenchmark.p',fact_310_add__less__cancel__right) ).
fof(fact_305_add__less__imp__less__right,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X49,X52,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X52)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_add__less__imp__less__right) ).
fof(fact_309_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/sandbox/benchmark/theBenchmark.p',fact_309_add__less__cancel__left) ).
fof(fact_304_add__less__imp__less__left,axiom,
! [X3] :
( ordere236663937imp_le(X3)
=> ! [X52,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X49)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X53)))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_add__less__imp__less__left) ).
fof(fact_93_image__mono,axiom,
! [X2,X1,X12,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_image__mono) ).
fof(fact_258_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/sandbox/benchmark/theBenchmark.p',fact_258_nat__add__left__cancel__le) ).
fof(fact_301_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/sandbox/benchmark/theBenchmark.p',fact_301_nat__add__left__cancel__less) ).
fof(fact_225_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/sandbox/benchmark/theBenchmark.p',fact_225_card_Oremove) ).
fof(fact_155_le__funI,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X12,X40] :
( ! [X33] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X40,X33)))
=> hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_le__funI) ).
fof(fact_100_le__fun__def,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X12,X40] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X40))
<=> ! [X33] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X33)),hAPP(X1,X2,X40,X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_le__fun__def) ).
fof(fact_86_insert__subset,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__subset) ).
fof(fact_190_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/sandbox/benchmark/theBenchmark.p',fact_190_card__Suc__Diff1) ).
fof(fact_224_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/sandbox/benchmark/theBenchmark.p',fact_224_card_Oinsert__remove) ).
fof(fact_89_insert__mono,axiom,
! [X1,X11,X41,X46] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X41),X46))
=> 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),X41)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__mono) ).
fof(fact_177_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/sandbox/benchmark/theBenchmark.p',fact_177_Diff__insert2) ).
fof(fact_191_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/sandbox/benchmark/theBenchmark.p',fact_191_card__insert) ).
fof(fact_278_le__diff__conv,axiom,
! [X64,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),X64),X19)),X36))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X64),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_le__diff__conv) ).
fof(fact_401_less__diff__conv,axiom,
! [X36,X64,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),X64),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)),X64)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_less__diff__conv) ).
fof(fact_232_add__mono,axiom,
! [X3] :
( ordere779506340up_add(X3)
=> ! [X52,X62,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X52),X62))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X62))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_add__mono) ).
fof(fact_388_add__less__le__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X52,X62,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X52),X62))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X62))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_add__less__le__mono) ).
fof(fact_387_add__le__less__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X52,X62,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X52),X62))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X62))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_add__le__less__mono) ).
fof(fact_306_add__strict__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X52,X62,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X52),X62))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X62))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_add__strict__mono) ).
fof(fact_161_the__elem__def,axiom,
! [X1,X60] : hAPP(fun(X1,bool),X1,the_elem(X1),X60) = 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)),X60)),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/sandbox/benchmark/theBenchmark.p',fact_161_the__elem__def) ).
fof(fact_427_less__mono__imp__le__mono,axiom,
! [X36,X64,X12] :
( ! [X69,X72] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X72))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X12,X69)),hAPP(nat,nat,X12,X72))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X64))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X12,X36)),hAPP(nat,nat,X12,X64))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_less__mono__imp__le__mono) ).
fof(fact_262_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/sandbox/benchmark/theBenchmark.p',fact_262_add__le__mono) ).
fof(fact_297_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/sandbox/benchmark/theBenchmark.p',fact_297_add__less__mono) ).
fof(fact_402_diff__less__mono,axiom,
! [X52,X49,X53] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X53))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X49))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X49),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X53),X52))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_diff__less__mono) ).
fof(fact_328_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/sandbox/benchmark/theBenchmark.p',fact_328_diff__less__mono2) ).
fof(fact_460_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/sandbox/benchmark/theBenchmark.p',fact_460_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_466_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/sandbox/benchmark/theBenchmark.p',fact_466_le__iff__diff__le__0) ).
fof(fact_7_card__insert__le,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X8)),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_card__insert__le) ).
fof(fact_417_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/sandbox/benchmark/theBenchmark.p',fact_417_card__psubset) ).
fof(fact_227_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/sandbox/benchmark/theBenchmark.p',fact_227_less__eq__nat_Osimps_I2_J) ).
fof(fact_264_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/sandbox/benchmark/theBenchmark.p',fact_264_add__leD1) ).
fof(fact_263_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/sandbox/benchmark/theBenchmark.p',fact_263_add__leD2) ).
fof(fact_295_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/sandbox/benchmark/theBenchmark.p',fact_295_add__lessD1) ).
fof(fact_230_add__right__mono,axiom,
! [X3] :
( ordere779506340up_add(X3)
=> ! [X52,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X52))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_add__right__mono) ).
fof(fact_231_add__left__mono,axiom,
! [X3] :
( ordere779506340up_add(X3)
=> ! [X52,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),X53))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X49)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X53))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_add__left__mono) ).
fof(fact_308_add__strict__right__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X52,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X52))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_add__strict__right__mono) ).
fof(fact_307_add__strict__left__mono,axiom,
! [X3] :
( ordere223160158up_add(X3)
=> ! [X52,X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X49)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X52),X53))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_add__strict__left__mono) ).
fof(fact_283_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/sandbox/benchmark/theBenchmark.p',fact_283_diff__Suc__diff__eq2) ).
fof(fact_261_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/sandbox/benchmark/theBenchmark.p',fact_261_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/sandbox/benchmark/theBenchmark.p',fact_43_diff__le__mono) ).
fof(fact_44_diff__le__mono2,axiom,
! [X29,X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X29),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_diff__le__mono2) ).
fof(fact_298_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/sandbox/benchmark/theBenchmark.p',fact_298_add__less__mono1) ).
fof(fact_465_add__nonpos__nonpos,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X53,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X49),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),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),X49),X53)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_add__nonpos__nonpos) ).
fof(fact_199_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/sandbox/benchmark/theBenchmark.p',fact_199_DiffE) ).
fof(fact_218_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/sandbox/benchmark/theBenchmark.p',fact_218_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/sandbox/benchmark/theBenchmark.p',fact_37_Suc__diff__diff) ).
fof(fact_202_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/sandbox/benchmark/theBenchmark.p',fact_202_DiffD1) ).
fof(fact_46_finite__surj,axiom,
! [X2,X1,X13,X12,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X13),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_finite__surj) ).
fof(fact_173_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/sandbox/benchmark/theBenchmark.p',fact_173_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/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__le__nat) ).
fof(fact_292_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/sandbox/benchmark/theBenchmark.p',fact_292_finite__Collect__less__nat) ).
fof(fact_176_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/sandbox/benchmark/theBenchmark.p',fact_176_Diff__insert) ).
fof(fact_284_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/sandbox/benchmark/theBenchmark.p',fact_284_diff__Suc__diff__eq1) ).
fof(fact_80_imageI,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_imageI) ).
fof(fact_40_Nat_Odiff__diff__eq,axiom,
! [X17,X25,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X18))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X25)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X25)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).
fof(fact_441_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/sandbox/benchmark/theBenchmark.p',fact_441_finite__Plus__iff) ).
fof(fact_443_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/sandbox/benchmark/theBenchmark.p',fact_443_finite__PlusD_I1_J) ).
fof(fact_444_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/sandbox/benchmark/theBenchmark.p',fact_444_finite__PlusD_I2_J) ).
fof(fact_329_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/sandbox/benchmark/theBenchmark.p',fact_329_less__imp__diff__less) ).
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/sandbox/benchmark/theBenchmark.p',fact_270_add__diff__assoc2) ).
fof(fact_269_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/sandbox/benchmark/theBenchmark.p',fact_269_diff__add__assoc2) ).
fof(fact_426_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))
=> ? [X71] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X71),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/sandbox/benchmark/theBenchmark.p',fact_426_psubset__imp__ex__mem) ).
fof(fact_461_add__nonneg__nonneg,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X53,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X49))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X53))
=> 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),X49),X53))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_add__nonneg__nonneg) ).
fof(fact_463_add__increasing,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X53,X52,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X49))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),X52))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_add__increasing) ).
fof(fact_464_add__increasing2,axiom,
! [X3] :
( ordere216010020id_add(X3)
=> ! [X53,X49,X52] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X52))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),X49))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X53),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_add__increasing2) ).
fof(fact_454_pos__add__strict,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X53,X52,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X49))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X52))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X52))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_pos__add__strict) ).
fof(fact_83_image__image,axiom,
! [X2,X1,X44,X12,X40,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(X44,bool),fun(X2,bool),hAPP(fun(X44,X2),fun(fun(X44,bool),fun(X2,bool)),image(X44,X2),X40),X8)) = hAPP(fun(X44,bool),fun(X1,bool),hAPP(fun(X44,X1),fun(fun(X44,bool),fun(X1,bool)),image(X44,X1),hAPP(fun(X44,X2),fun(X44,X1),hAPP(fun(X2,X1),fun(fun(X44,X2),fun(X44,X1)),combb(X2,X1,X44),X12),X40)),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_image__image) ).
fof(fact_432_dense__le__bounded,axiom,
! [X3] :
( dense_linorder(X3)
=> ! [X51,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),X51)) ) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X51)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_dense__le__bounded) ).
fof(fact_168_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/sandbox/benchmark/theBenchmark.p',fact_168_finite__Diff2) ).
fof(fact_88_subset__insertI2,axiom,
! [X1,X34,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_subset__insertI2) ).
fof(fact_183_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/sandbox/benchmark/theBenchmark.p',fact_183_folding__one__idem_Oin__idem) ).
fof(fact_169_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/sandbox/benchmark/theBenchmark.p',fact_169_insert__Diff1) ).
fof(fact_459_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/sandbox/benchmark/theBenchmark.p',fact_459_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_188_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/sandbox/benchmark/theBenchmark.p',fact_188_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/sandbox/benchmark/theBenchmark.p',fact_5_card__mono) ).
fof(fact_415_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/sandbox/benchmark/theBenchmark.p',fact_415_psubset__card__mono) ).
fof(fact_65_insertI2,axiom,
! [X1,X34,X11,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_insertI2) ).
fof(fact_399_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/sandbox/benchmark/theBenchmark.p',fact_399_diff__less__Suc) ).
fof(fact_389_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/sandbox/benchmark/theBenchmark.p',fact_389_less__add__Suc1) ).
fof(fact_390_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/sandbox/benchmark/theBenchmark.p',fact_390_less__add__Suc2) ).
fof(fact_178_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/sandbox/benchmark/theBenchmark.p',fact_178_insert__Diff__single) ).
fof(fact_77_subset__trans,axiom,
! [X1,X41,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),X41))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_subset__trans) ).
fof(fact_409_psubset__subset__trans,axiom,
! [X1,X41,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),X41))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_psubset__subset__trans) ).
fof(fact_408_subset__psubset__trans,axiom,
! [X1,X41,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),X41))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_subset__psubset__trans) ).
fof(fact_421_psubset__trans,axiom,
! [X1,X41,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),X41))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X8),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_psubset__trans) ).
fof(fact_271_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/sandbox/benchmark/theBenchmark.p',fact_271_diff__add__assoc) ).
fof(fact_275_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/sandbox/benchmark/theBenchmark.p',fact_275_add__diff__assoc) ).
fof(fact_279_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/sandbox/benchmark/theBenchmark.p',fact_279_diff__diff__right) ).
fof(fact_33_Suc__le__mono,axiom,
! [X20,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X20)),hAPP(nat,nat,suc,X28)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Suc__le__mono) ).
fof(fact_320_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/sandbox/benchmark/theBenchmark.p',fact_320_Suc__less__eq) ).
fof(fact_312_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/sandbox/benchmark/theBenchmark.p',fact_312_Suc__less__SucD) ).
fof(fact_315_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/sandbox/benchmark/theBenchmark.p',fact_315_less__trans__Suc) ).
fof(fact_91_insert__image,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8)) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_insert__image) ).
fof(fact_442_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/sandbox/benchmark/theBenchmark.p',fact_442_finite__Plus) ).
fof(fact_72_set__rev__mp,axiom,
! [X1,X13,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_set__rev__mp) ).
fof(fact_73_set__mp,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_set__mp) ).
fof(fact_71_in__mono,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_in__mono) ).
fof(fact_52_subsetD,axiom,
! [X1,X35,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X35),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subsetD) ).
fof(fact_420_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/sandbox/benchmark/theBenchmark.p',fact_420_psubsetD) ).
fof(fact_102_le__funE,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X14,X12,X40] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X40))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X14)),hAPP(X1,X2,X40,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_le__funE) ).
fof(fact_101_le__funD,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X14,X12,X40] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X40))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X12,X14)),hAPP(X1,X2,X40,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_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/sandbox/benchmark/theBenchmark.p',fact_27_finite__insert) ).
fof(fact_45_diff__le__self,axiom,
! [X18,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X17)),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_diff__le__self) ).
fof(fact_25_diff__commute,axiom,
! [X26,X27,X25] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X27)),X25) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X25)),X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_diff__commute) ).
fof(fact_90_image__insert,axiom,
! [X2,X1,X12,X11,X13] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X11),X13)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X2,X1,X12,X11)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X12),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_image__insert) ).
fof(fact_41_eq__diff__iff,axiom,
! [X20,X19,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X28))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X20))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X19) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X20),X19)
<=> X28 = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_eq__diff__iff) ).
fof(fact_446_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/sandbox/benchmark/theBenchmark.p',fact_446_card__Plus__conv__if) ).
fof(fact_440_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/sandbox/benchmark/theBenchmark.p',fact_440_card__Plus) ).
fof(fact_286_termination__basic__simps_I3_J,axiom,
! [X51,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),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_termination__basic__simps_I3_J) ).
fof(fact_259_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/sandbox/benchmark/theBenchmark.p',fact_259_trans__le__add1) ).
fof(fact_287_termination__basic__simps_I4_J,axiom,
! [X22,X21,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X51))
=> 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),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_termination__basic__simps_I4_J) ).
fof(fact_260_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/sandbox/benchmark/theBenchmark.p',fact_260_trans__le__add2) ).
fof(fact_300_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/sandbox/benchmark/theBenchmark.p',fact_300_trans__less__add1) ).
fof(fact_293_termination__basic__simps_I1_J,axiom,
! [X51,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),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_termination__basic__simps_I1_J) ).
fof(fact_299_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/sandbox/benchmark/theBenchmark.p',fact_299_trans__less__add2) ).
fof(fact_294_termination__basic__simps_I2_J,axiom,
! [X22,X21,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X51))
=> 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),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_termination__basic__simps_I2_J) ).
fof(fact_428_Suc__lessE,axiom,
! [X26,X25] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X26)),X25))
=> ~ ! [X72] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X72))
=> X25 != hAPP(nat,nat,suc,X72) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_Suc__lessE) ).
fof(fact_30_Suc__leD,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X18)),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Suc__leD) ).
fof(fact_398_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/sandbox/benchmark/theBenchmark.p',fact_398_Suc__le__lessD) ).
fof(fact_394_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/sandbox/benchmark/theBenchmark.p',fact_394_Suc__le__eq) ).
fof(fact_392_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/sandbox/benchmark/theBenchmark.p',fact_392_less__eq__Suc__le) ).
fof(fact_313_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/sandbox/benchmark/theBenchmark.p',fact_313_Suc__lessD) ).
fof(fact_203_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/sandbox/benchmark/theBenchmark.p',fact_203_Diff__idemp) ).
fof(fact_291_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/sandbox/benchmark/theBenchmark.p',fact_291_Suc__mono) ).
fof(fact_157_diff__eq__diff__less__eq,axiom,
! [X1] :
( ordered_ab_group_add(X1)
=> ! [X11,X34,X35,X50] :
( 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),X50)
=> ( 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),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_diff__eq__diff__less__eq) ).
fof(fact_311_diff__eq__diff__less,axiom,
! [X1] :
( ordered_ab_group_add(X1)
=> ! [X11,X34,X35,X50] :
( 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),X50)
=> ( 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),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_diff__eq__diff__less) ).
fof(fact_138_order__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X51,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),X51))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X51)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__trans) ).
fof(fact_136_xt1_I6_J,axiom,
! [X3] :
( order(X3)
=> ! [X51,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),X51),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X51),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_xt1_I6_J) ).
fof(fact_379_order__less__le__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X51,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),X51))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X51)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_order__less__le__trans) ).
fof(fact_381_order__le__less__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X51,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),X51))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X51)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_order__le__less__trans) ).
fof(fact_348_order__less__trans,axiom,
! [X3] :
( preorder(X3)
=> ! [X51,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),X51))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X51)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_order__less__trans) ).
fof(fact_380_xt1_I7_J,axiom,
! [X3] :
( order(X3)
=> ! [X51,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),X51),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X51),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_xt1_I7_J) ).
fof(fact_382_xt1_I8_J,axiom,
! [X3] :
( order(X3)
=> ! [X51,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),X51),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X51),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_xt1_I8_J) ).
fof(fact_349_xt1_I10_J,axiom,
! [X3] :
( order(X3)
=> ! [X51,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),X51),X22))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X51),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_xt1_I10_J) ).
fof(fact_21_le__trans,axiom,
! [X25,X26,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X25))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_le__trans) ).
fof(fact_296_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/sandbox/benchmark/theBenchmark.p',fact_296_less__add__eq__less) ).
fof(fact_249_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X3] :
( ab_semigroup_add(X3)
=> ! [X49,X53,X52] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),X53)),X52) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X53),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_397_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/sandbox/benchmark/theBenchmark.p',fact_397_le__less__Suc__eq) ).
fof(fact_273_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/sandbox/benchmark/theBenchmark.p',fact_273_le__add__diff__inverse2) ).
fof(fact_133_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/sandbox/benchmark/theBenchmark.p',fact_133_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/sandbox/benchmark/theBenchmark.p',fact_55_zero__induct__lemma) ).
fof(fact_156_assms_I4_J,axiom,
! [X56] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X56),u))
=> hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X56)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_assms_I4_J) ).
fof(fact_253_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/sandbox/benchmark/theBenchmark.p',fact_253_diff__cancel) ).
fof(fact_254_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/sandbox/benchmark/theBenchmark.p',fact_254_diff__cancel2) ).
fof(fact_241_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/sandbox/benchmark/theBenchmark.p',fact_241_nat__add__assoc) ).
fof(fact_252_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/sandbox/benchmark/theBenchmark.p',fact_252_diff__diff__left) ).
fof(fact_85_subset__insertI,axiom,
! [X1,X13,X11] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X13),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subset__insertI) ).
fof(fact_316_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/sandbox/benchmark/theBenchmark.p',fact_316_Suc__lessI) ).
fof(fact_61_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/sandbox/benchmark/theBenchmark.p',fact_61_insert__commute) ).
fof(fact_163_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/sandbox/benchmark/theBenchmark.p',fact_163_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/sandbox/benchmark/theBenchmark.p',fact_11_Suc__diff__le) ).
fof(fact_57_insertI1,axiom,
! [X1,X11,X13] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_insertI1) ).
fof(fact_396_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/sandbox/benchmark/theBenchmark.p',fact_396_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/sandbox/benchmark/theBenchmark.p',fact_13_card__Collect__le__nat) ).
fof(fact_2_finite__imageI,axiom,
! [X2,X1,X9,X10] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X10))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X9),X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__imageI) ).
fof(conj_5,hypothesis,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
fof(fact_34_le__Suc__eq,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),hAPP(nat,nat,suc,X20)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
| X28 = hAPP(nat,nat,suc,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_le__Suc__eq) ).
fof(fact_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/sandbox/benchmark/theBenchmark.p',fact_56_Suc__le__D) ).
fof(fact_406_inc__induct,axiom,
! [X16,X36,X64] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X64))
=> ( hBOOL(hAPP(nat,bool,X16,X64))
=> ( ! [X69] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X69),X64))
=> ( 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/sandbox/benchmark/theBenchmark.p',fact_406_inc__induct) ).
fof(fact_385_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/sandbox/benchmark/theBenchmark.p',fact_385_card__Collect__less__nat) ).
fof(fact_95_subsetI,axiom,
! [X1,X13,X8] :
( ! [X33] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X13)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_subsetI) ).
fof(fact_3_finite_OinsertI,axiom,
! [X1,X11,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X11),X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite_OinsertI) ).
fof(fact_321_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/sandbox/benchmark/theBenchmark.p',fact_321_less__Suc__eq) ).
fof(fact_393_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/sandbox/benchmark/theBenchmark.p',fact_393_less__Suc__eq__le) ).
fof(fact_410_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/sandbox/benchmark/theBenchmark.p',fact_410_psubset__imp__subset) ).
fof(fact_98_finite__nat__set__iff__bounded__le,axiom,
! [X48] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X48))
<=> ? [X38] :
! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X48))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).
fof(fact_383_finite__nat__set__iff__bounded,axiom,
! [X48] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X48))
<=> ? [X38] :
! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X48))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_finite__nat__set__iff__bounded) ).
fof(fact_221_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/sandbox/benchmark/theBenchmark.p',fact_221_diff__Suc__eq__diff__pred) ).
fof(fact_0_assms_I1_J,axiom,
! [X6,X7] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X6),X7))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
fof(fact_341_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/sandbox/benchmark/theBenchmark.p',fact_341_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/sandbox/benchmark/theBenchmark.p',fact_32_le__SucI) ).
fof(fact_395_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/sandbox/benchmark/theBenchmark.p',fact_395_le__imp__less__Suc) ).
fof(fact_317_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/sandbox/benchmark/theBenchmark.p',fact_317_less__SucI) ).
fof(fact_213_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/sandbox/benchmark/theBenchmark.p',fact_213_minus__apply) ).
fof(fact_212_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/sandbox/benchmark/theBenchmark.p',fact_212_fun__diff__def) ).
fof(fact_20_le__antisym,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18))
=> X18 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_le__antisym) ).
fof(fact_423_less__add__one,axiom,
! [X3] :
( linordered_semidom(X3)
=> ! [X49] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X49),one_one(X3)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_less__add__one) ).
fof(fact_276_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/sandbox/benchmark/theBenchmark.p',fact_276_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/sandbox/benchmark/theBenchmark.p',fact_42_diff__diff__cancel) ).
fof(fact_431_dense__le,axiom,
! [X3] :
( dense_linorder(X3)
=> ! [X51,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),X51)) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_dense__le) ).
fof(fact_28_finite__subset,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite__subset) ).
fof(fact_29_rev__finite__subset,axiom,
! [X1,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X13))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
fof(fact_256_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/sandbox/benchmark/theBenchmark.p',fact_256_le__add1) ).
fof(fact_255_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/sandbox/benchmark/theBenchmark.p',fact_255_le__add2) ).
fof(fact_359_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/sandbox/benchmark/theBenchmark.p',fact_359_nat__less__cases) ).
fof(fact_242_nat__add__left__commute,axiom,
! [X21,X22,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),X51)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X22),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_nat__add__left__commute) ).
fof(fact_272_le__imp__diff__is__add,axiom,
! [X19,X36,X64] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X64))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X64),X36) = X19
<=> X64 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X36) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_le__imp__diff__is__add) ).
fof(fact_391_less__iff__Suc__add,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X20))
<=> ? [X63] : X20 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_less__iff__Suc__add) ).
fof(help_COMBS_1_1_U,axiom,
! [X3,X2,X1,X80,X81,X82] : 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),X80),X81),X82) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X80,X82),hAPP(X3,X1,X81,X82)),
file('/export/starexec/sandbox/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)
=> ~ ! [X72] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X72))
=> X25 != hAPP(nat,nat,suc,X72) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_lessE) ).
fof(fact_407_less__imp__Suc__add,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X18),X17))
=> ? [X63] : X17 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_less__imp__Suc__add) ).
fof(fact_238_comp__fun__idem_Ofun__left__idem,axiom,
! [X1,X2,X14,X42,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),X42)) = hAPP(X2,X2,hAPP(X1,fun(X2,X2),X12,X14),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_comp__fun__idem_Ofun__left__idem) ).
fof(fact_60_insert__absorb2,axiom,
! [X1,X14,X8] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_insert__absorb2) ).
fof(fact_374_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/sandbox/benchmark/theBenchmark.p',fact_374_order__less__imp__le) ).
fof(fact_327_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/sandbox/benchmark/theBenchmark.p',fact_327_nat__less__le) ).
fof(fact_326_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/sandbox/benchmark/theBenchmark.p',fact_326_le__eq__less__or__eq) ).
fof(fact_324_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/sandbox/benchmark/theBenchmark.p',fact_324_le__neq__implies__less) ).
fof(fact_352_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/sandbox/benchmark/theBenchmark.p',fact_352_termination__basic__simps_I5_J) ).
fof(fact_325_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/sandbox/benchmark/theBenchmark.p',fact_325_less__imp__le__nat) ).
fof(fact_323_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/sandbox/benchmark/theBenchmark.p',fact_323_less__or__eq__imp__le) ).
fof(fact_130_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/sandbox/benchmark/theBenchmark.p',fact_130_singleton__conv) ).
fof(fact_251_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/sandbox/benchmark/theBenchmark.p',fact_251_diff__add__inverse) ).
fof(fact_250_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/sandbox/benchmark/theBenchmark.p',fact_250_diff__add__inverse2) ).
fof(help_COMBB_1_1_U,axiom,
! [X3,X2,X1,X80,X81,X82] : 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),X80),X81),X82) = hAPP(X1,X2,X80,hAPP(X3,X1,X81,X82)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
fof(help_COMBC_1_1_U,axiom,
! [X3,X2,X1,X80,X81,X82] : hAPP(X3,X2,hAPP(X1,fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2)),combc(X3,X1,X2),X80),X81),X82) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X80,X82),X81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
fof(fact_236_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/sandbox/benchmark/theBenchmark.p',fact_236_add__Suc) ).
fof(fact_75_mem__def,axiom,
! [X1,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
<=> hBOOL(hAPP(X1,bool,X8,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
fof(fact_257_le__iff__add,axiom,
! [X28,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X20))
<=> ? [X63] : X20 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X28),X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_le__iff__add) ).
fof(fact_471_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/sandbox/benchmark/theBenchmark.p',fact_471_diff__is__0__eq) ).
fof(fact_470_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/sandbox/benchmark/theBenchmark.p',fact_470_diff__is__0__eq_H) ).
fof(fact_147_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/sandbox/benchmark/theBenchmark.p',fact_147_linorder__linear) ).
fof(fact_364_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/sandbox/benchmark/theBenchmark.p',fact_364_linorder__le__less__linear) ).
fof(fact_425_bounded__nat__set__is__finite,axiom,
! [X20,X48] :
( ! [X33] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X33),X48))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X20)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_bounded__nat__set__is__finite) ).
fof(fact_354_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/sandbox/benchmark/theBenchmark.p',fact_354_nat__neq__iff) ).
fof(fact_23_nat__le__linear,axiom,
! [X18,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nat__le__linear) ).
fof(fact_235_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/sandbox/benchmark/theBenchmark.p',fact_235_add__Suc__right) ).
fof(fact_282_nat__case__Suc,axiom,
! [X1,X65,X66,X23] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X65),X66),hAPP(nat,nat,suc,X23)) = hAPP(nat,X1,X66,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_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/sandbox/benchmark/theBenchmark.p',fact_38_diff__Suc__Suc) ).
fof(fact_237_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/sandbox/benchmark/theBenchmark.p',fact_237_add__Suc__shift) ).
fof(fact_449_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/sandbox/benchmark/theBenchmark.p',fact_449_zero__less__Suc) ).
fof(fact_290_lessI,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,suc,X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_lessI) ).
fof(fact_489_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/sandbox/benchmark/theBenchmark.p',fact_489_le__0__eq) ).
fof(fact_473_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/sandbox/benchmark/theBenchmark.p',fact_473_diffs0__imp__equal) ).
fof(fact_358_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/sandbox/benchmark/theBenchmark.p',fact_358_less__not__refl3) ).
fof(fact_357_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/sandbox/benchmark/theBenchmark.p',fact_357_less__not__refl2) ).
fof(fact_239_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/sandbox/benchmark/theBenchmark.p',fact_239_nat__add__right__cancel) ).
fof(fact_240_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/sandbox/benchmark/theBenchmark.p',fact_240_nat__add__left__cancel) ).
fof(fact_469_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/sandbox/benchmark/theBenchmark.p',fact_469_diff__add__0) ).
fof(fact_105_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/sandbox/benchmark/theBenchmark.p',fact_105_empty__subsetI) ).
fof(fact_467_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/sandbox/benchmark/theBenchmark.p',fact_467_add__is__1) ).
fof(fact_468_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/sandbox/benchmark/theBenchmark.p',fact_468_one__is__add) ).
fof(fact_67_subset__refl,axiom,
! [X1,X8] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_subset__refl) ).
fof(fact_131_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/sandbox/benchmark/theBenchmark.p',fact_131_singleton__conv2) ).
fof(fact_222_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/sandbox/benchmark/theBenchmark.p',fact_222_diff__Suc__1) ).
fof(fact_122_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/sandbox/benchmark/theBenchmark.p',fact_122_insert__not__empty) ).
fof(fact_123_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/sandbox/benchmark/theBenchmark.p',fact_123_empty__not__insert) ).
fof(fact_456_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/sandbox/benchmark/theBenchmark.p',fact_456_zero__le__one) ).
fof(fact_452_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/sandbox/benchmark/theBenchmark.p',fact_452_zero__less__one) ).
fof(fact_117_bot__least,axiom,
! [X3] :
( bot(X3)
=> ! [X49] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),bot_bot(X3)),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_bot__least) ).
fof(fact_145_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/sandbox/benchmark/theBenchmark.p',fact_145_order__eq__refl) ).
fof(fact_97_order__refl,axiom,
! [X3] :
( preorder(X3)
=> ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_order__refl) ).
fof(fact_490_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/sandbox/benchmark/theBenchmark.p',fact_490_less__eq__nat_Osimps_I1_J) ).
fof(fact_448_le0,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_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/sandbox/benchmark/theBenchmark.p',fact_22_eq__imp__le) ).
fof(fact_24_le__refl,axiom,
! [X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_le__refl) ).
fof(fact_243_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/sandbox/benchmark/theBenchmark.p',fact_243_nat__add__commute) ).
fof(help_fimplies_1_1_U,axiom,
! [X81,X80] :
( hBOOL(X80)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X80),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(fact_167_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/sandbox/benchmark/theBenchmark.p',fact_167_empty__Diff) ).
fof(fact_126_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/sandbox/benchmark/theBenchmark.p',fact_126_image__empty) ).
fof(fact_165_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/sandbox/benchmark/theBenchmark.p',fact_165_Diff__cancel) ).
fof(fact_268_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/sandbox/benchmark/theBenchmark.p',fact_268_comp__fun__idem__insert) ).
fof(fact_281_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/sandbox/benchmark/theBenchmark.p',fact_281_Suc__eq__plus1__left) ).
fof(fact_280_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/sandbox/benchmark/theBenchmark.p',fact_280_Suc__eq__plus1) ).
fof(fact_404_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/sandbox/benchmark/theBenchmark.p',fact_404_less__eq__Suc__le__raw) ).
fof(tsy_v_P_res,axiom,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_P_res) ).
fof(fact_112_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/sandbox/benchmark/theBenchmark.p',fact_112_empty__def) ).
fof(fact_478_diff__self,axiom,
! [X3] :
( group_add(X3)
=> ! [X49] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),minus_minus(X3),X49),X49) = zero_zero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_diff__self) ).
fof(fact_476_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/sandbox/benchmark/theBenchmark.p',fact_476_diff__0__eq__0) ).
fof(fact_475_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/sandbox/benchmark/theBenchmark.p',fact_475_minus__nat_Odiff__0) ).
fof(fact_474_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/sandbox/benchmark/theBenchmark.p',fact_474_diff__self__eq__0) ).
fof(fact_17_nat_Oinject,axiom,
! [X23,X24] :
( hAPP(nat,nat,suc,X23) = hAPP(nat,nat,suc,X24)
<=> X23 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
fof(fact_16_Suc__inject,axiom,
! [X21,X22] :
( hAPP(nat,nat,suc,X21) = hAPP(nat,nat,suc,X22)
=> X21 = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Suc__inject) ).
fof(fact_104_finite_OemptyI,axiom,
! [X1] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_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/sandbox/benchmark/theBenchmark.p',fact_15_finite) ).
fof(fact_14_finite__code,axiom,
! [X1] :
( finite_finite_1(X1)
=> ! [X8] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__code) ).
fof(tsy_c_fimplies_res,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
fof(tsy_c_fdisj_res,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
fof(tsy_c_fconj_res,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
fof(help_fNot_2_1_U,axiom,
! [X80] :
( hBOOL(X80)
| hBOOL(hAPP(bool,bool,fNot,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(fact_484_Suc__not__Zero,axiom,
! [X18] : hAPP(nat,nat,suc,X18) != zero_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_Suc__not__Zero) ).
fof(fact_483_nat_Osimps_I3_J,axiom,
! [X74] : hAPP(nat,nat,suc,X74) != zero_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_nat_Osimps_I3_J) ).
fof(fact_481_Suc__neq__Zero,axiom,
! [X18] : hAPP(nat,nat,suc,X18) != zero_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_Suc__neq__Zero) ).
fof(fact_486_Zero__not__Suc,axiom,
! [X18] : zero_zero(nat) != hAPP(nat,nat,suc,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_Zero__not__Suc) ).
fof(fact_485_nat_Osimps_I2_J,axiom,
! [X75] : zero_zero(nat) != hAPP(nat,nat,suc,X75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_nat_Osimps_I2_J) ).
fof(fact_482_Zero__neq__Suc,axiom,
! [X18] : zero_zero(nat) != hAPP(nat,nat,suc,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_Zero__neq__Suc) ).
fof(fact_18_Suc__n__not__n,axiom,
! [X17] : hAPP(nat,nat,suc,X17) != X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Suc__n__not__n) ).
fof(fact_19_n__not__Suc__n,axiom,
! [X17] : X17 != hAPP(nat,nat,suc,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n__not__Suc__n) ).
fof(tsy_c_Option_Othe_res,axiom,
ti(fun(option(com),com),the_1(com)) = the_1(com),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Com_Obody_res) ).
fof(tsy_v_G_res,hypothesis,
ti(fun(x_a,bool),g) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_G_res) ).
fof(tsy_c_Nat_OSuc_res,hypothesis,
ti(fun(nat,nat),suc) = suc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).
fof(tsy_c_fNot_res,axiom,
ti(fun(bool,bool),fNot) = fNot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
fof(tsy_v_mgt_res,axiom,
ti(fun(com,x_a),mgt) = mgt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_mgt_res) ).
fof(tsy_v_wt_res,axiom,
ti(fun(com,bool),wt) = wt,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_v_mgt__call_res) ).
fof(tsy_v_U_res,hypothesis,
ti(fun(pname,bool),u) = u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_U_res) ).
fof(fact_451_card_Oempty,axiom,
! [X1] : hAPP(fun(X1,bool),nat,finite_card(X1),bot_bot(fun(X1,bool))) = zero_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_card_Oempty) ).
fof(fact_114_bot__apply,axiom,
! [X2,X1] :
( bot(X1)
=> ! [X14] : hAPP(X2,X1,bot_bot(fun(X2,X1)),X14) = bot_bot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_bot__apply) ).
fof(fact_113_bot__fun__def,axiom,
! [X1,X2] :
( bot(X2)
=> ! [X33] : hAPP(X1,X2,bot_bot(fun(X1,X2)),X33) = bot_bot(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_bot__fun__def) ).
fof(tsy_v_na_res,hypothesis,
ti(nat,na) = na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_na_res) ).
fof(tsy_c_fTrue_res,axiom,
ti(bool,fTrue) = fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
fof(tsy_c_fFalse_res,axiom,
ti(bool,fFalse) = fFalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(tsy_v_pn_res,hypothesis,
ti(pname,pn) = pn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_pn_res) ).
fof(arity_sum___Finite__Set_Ofinite,axiom,
! [X76,X77] :
( ( finite_finite_1(X77)
& finite_finite_1(X76) )
=> finite_finite_1(sum_sum(X76,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).
fof(arity_fun___Finite__Set_Ofinite,axiom,
! [X76,X77] :
( ( finite_finite_1(X77)
& finite_finite_1(X76) )
=> finite_finite_1(fun(X76,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
fof(arity_fun___Orderings_Opreorder,axiom,
! [X76,X77] :
( preorder(X77)
=> preorder(fun(X76,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
fof(arity_fun___Orderings_Oorder,axiom,
! [X76,X77] :
( order(X77)
=> order(fun(X76,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
fof(arity_fun___Orderings_Oord,axiom,
! [X76,X77] :
( ord(X77)
=> ord(fun(X76,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
fof(arity_fun___Orderings_Obot,axiom,
! [X76,X77] :
( bot(X77)
=> bot(fun(X76,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
fof(arity_fun___Groups_Ominus,axiom,
! [X76,X77] :
( minus(X77)
=> minus(fun(X76,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
fof(fact_458_zero__neq__one,axiom,
! [X3] :
( zero_neq_one(X3)
=> zero_zero(X3) != one_one(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_zero__neq__one) ).
fof(fact_457_one__neq__zero,axiom,
! [X3] :
( zero_neq_one(X3)
=> one_one(X3) != zero_zero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_one__neq__zero) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(conj_3,hypothesis,
hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(conj_4,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(conj_0,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_472_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_One__nat__def) ).
fof(fact_488_bot__nat__def,axiom,
bot_bot(nat) = zero_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_bot__nat__def) ).
fof(arity_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
fof(arity_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
ordere216010020id_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat_Onat___Rings_Ozero__neq__one,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
fof(arity_Nat_Onat___Rings_Olinordered__semidom,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
fof(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
ordere223160158up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
ordere779506340up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
fof(arity_Nat_Onat___Orderings_Opreorder,axiom,
preorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
fof(arity_HOL_Obool___Orderings_Opreorder,axiom,
preorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
fof(arity_Nat_Onat___Orderings_Oorder,axiom,
order(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
fof(arity_HOL_Obool___Orderings_Oorder,axiom,
order(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
finite_finite_1(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(arity_Nat_Onat___Orderings_Oord,axiom,
ord(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
fof(arity_HOL_Obool___Orderings_Oord,axiom,
ord(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
fof(arity_Nat_Onat___Orderings_Obot,axiom,
bot(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
fof(arity_HOL_Obool___Orderings_Obot,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
fof(arity_Nat_Onat___Groups_Ozero,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
fof(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
fof(arity_Nat_Onat___Groups_Omonoid__add,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
fof(arity_Nat_Onat___Groups_Oone,axiom,
one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
fof(arity_Nat_Onat___Groups_Ominus,axiom,
minus(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ominus) ).
fof(arity_HOL_Obool___Groups_Ominus,axiom,
minus(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
fof(i_0_603,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_208_If__def]) ).
fof(i_0_604,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,X55] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X55))
=> ( ti(fun(X1,bool),X55) != bot_bot(fun(X1,bool))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X55))
=> 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),X55))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_160_finite__ne__induct]) ).
fof(i_0_605,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_94_imageE]) ).
fof(i_0_606,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_217_flat__lub__def]) ).
fof(i_0_607,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_162_folding__one_Oinsert]) ).
fof(i_0_608,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_179_Diff__insert__absorb]) ).
fof(i_0_609,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_64_insert__ident]) ).
fof(i_0_610,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_611,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_375_linorder__antisym__conv2]) ).
fof(i_0_612,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_334_linorder__antisym__conv3]) ).
fof(i_0_613,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_370_linorder__antisym__conv1]) ).
fof(i_0_614,plain,
! [X1,X8] :
( ti(fun(X1,bool),X8) != bot_bot(fun(X1,bool))
<=> ? [X33,X59] :
( ti(fun(X1,bool),X8) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X33),X59)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X59)) ) ),
inference(fof_simplification,[status(thm)],[fact_154_nonempty__iff]) ).
fof(i_0_615,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_424_linorder__neqE__linordered__idom]) ).
fof(i_0_616,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_351_linorder__cases]) ).
fof(i_0_617,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_335_linorder__neqE]) ).
fof(i_0_618,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_332_not__less__iff__gr__or__eq]) ).
fof(i_0_619,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_111_all__not__in__conv]) ).
fof(i_0_620,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_106_equals0D]) ).
fof(i_0_621,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_78_equalityE]) ).
fof(i_0_622,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_623,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_624,plain,
! [X2607,X2608,X2609,X2610,X2611,X2612,X2613] :
( ( hBOOL(hAPP(fun(X2607,bool),bool,hAPP(X2607,fun(fun(X2607,bool),bool),member(X2607),esk40_7(X2607,X2608,X2609,X2610,X2611,X2612,X2613)),X2609))
| hAPP(fun(X2607,bool),X2608,X2613,X2609) = ti(X2608,X2611)
| ~ hBOOL(hAPP(fun(X2607,bool),bool,finite_finite(X2607),X2609))
| ~ hBOOL(hAPP(fun(fun(X2607,bool),X2608),bool,hAPP(fun(X2607,X2608),fun(fun(fun(X2607,bool),X2608),bool),hAPP(X2608,fun(fun(X2607,X2608),fun(fun(fun(X2607,bool),X2608),bool)),hAPP(fun(X2608,fun(X2608,X2608)),fun(X2608,fun(fun(X2607,X2608),fun(fun(fun(X2607,bool),X2608),bool))),finite1357897459simple(X2608,X2607),X2610),X2611),X2612),X2613)) )
& ( hAPP(X2607,X2608,X2612,esk40_7(X2607,X2608,X2609,X2610,X2611,X2612,X2613)) != ti(X2608,X2611)
| hAPP(fun(X2607,bool),X2608,X2613,X2609) = ti(X2608,X2611)
| ~ hBOOL(hAPP(fun(X2607,bool),bool,finite_finite(X2607),X2609))
| ~ hBOOL(hAPP(fun(fun(X2607,bool),X2608),bool,hAPP(fun(X2607,X2608),fun(fun(fun(X2607,bool),X2608),bool),hAPP(X2608,fun(fun(X2607,X2608),fun(fun(fun(X2607,bool),X2608),bool)),hAPP(fun(X2608,fun(X2608,X2608)),fun(X2608,fun(fun(X2607,X2608),fun(fun(fun(X2607,bool),X2608),bool))),finite1357897459simple(X2608,X2607),X2610),X2611),X2612),X2613)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_folding__image__simple_Oneutral])])])]) ).
fof(i_0_625,plain,
! [X3499,X3500] : hAPP(X3499,X3499,combi(X3499),X3500) = ti(X3499,X3500),
inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).
fof(i_0_626,plain,
! [X2597,X2598,X2599,X2600] :
( ( ~ hBOOL(X2600)
| ti(X2597,X2598) = hAPP(fun(X2597,bool),X2597,the(X2597),hAPP(fun(X2597,bool),fun(X2597,bool),hAPP(fun(X2597,fun(bool,bool)),fun(fun(X2597,bool),fun(X2597,bool)),combs(X2597,bool,bool),hAPP(fun(X2597,bool),fun(X2597,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2597,bool),fun(X2597,fun(bool,bool))),combb(bool,fun(bool,bool),X2597),fconj),hAPP(fun(X2597,bool),fun(X2597,bool),hAPP(fun(bool,bool),fun(fun(X2597,bool),fun(X2597,bool)),combb(bool,bool,X2597),hAPP(bool,fun(bool,bool),fimplies,X2600)),hAPP(X2597,fun(X2597,bool),hAPP(fun(X2597,fun(X2597,bool)),fun(X2597,fun(X2597,bool)),combc(X2597,X2597,bool),fequal(X2597)),X2598)))),hAPP(fun(X2597,bool),fun(X2597,bool),hAPP(fun(bool,bool),fun(fun(X2597,bool),fun(X2597,bool)),combb(bool,bool,X2597),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X2600))),hAPP(X2597,fun(X2597,bool),hAPP(fun(X2597,fun(X2597,bool)),fun(X2597,fun(X2597,bool)),combc(X2597,X2597,bool),fequal(X2597)),X2599)))) )
& ( hBOOL(X2600)
| ti(X2597,X2599) = hAPP(fun(X2597,bool),X2597,the(X2597),hAPP(fun(X2597,bool),fun(X2597,bool),hAPP(fun(X2597,fun(bool,bool)),fun(fun(X2597,bool),fun(X2597,bool)),combs(X2597,bool,bool),hAPP(fun(X2597,bool),fun(X2597,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2597,bool),fun(X2597,fun(bool,bool))),combb(bool,fun(bool,bool),X2597),fconj),hAPP(fun(X2597,bool),fun(X2597,bool),hAPP(fun(bool,bool),fun(fun(X2597,bool),fun(X2597,bool)),combb(bool,bool,X2597),hAPP(bool,fun(bool,bool),fimplies,X2600)),hAPP(X2597,fun(X2597,bool),hAPP(fun(X2597,fun(X2597,bool)),fun(X2597,fun(X2597,bool)),combc(X2597,X2597,bool),fequal(X2597)),X2598)))),hAPP(fun(X2597,bool),fun(X2597,bool),hAPP(fun(bool,bool),fun(fun(X2597,bool),fun(X2597,bool)),combb(bool,bool,X2597),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X2600))),hAPP(X2597,fun(X2597,bool),hAPP(fun(X2597,fun(X2597,bool)),fun(X2597,fun(X2597,bool)),combc(X2597,X2597,bool),fequal(X2597)),X2599)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_603])]) ).
fof(i_0_627,plain,
! [X2528,X2529,X2530,X2531] :
( ~ hBOOL(hAPP(fun(fun(X2528,bool),X2528),bool,hAPP(fun(X2528,fun(X2528,X2528)),fun(fun(fun(X2528,bool),X2528),bool),finite_folding_one(X2528),X2530),X2531))
| ~ hBOOL(hAPP(fun(X2528,bool),bool,finite_finite(X2528),X2529))
| ti(fun(X2528,bool),X2529) = bot_bot(fun(X2528,bool))
| ~ hBOOL(hAPP(fun(X2528,bool),bool,hAPP(X2528,fun(fun(X2528,bool),bool),member(X2528),hAPP(X2528,X2528,hAPP(X2528,fun(X2528,X2528),X2530,esk35_4(X2528,X2529,X2530,X2531)),esk36_4(X2528,X2529,X2530,X2531))),hAPP(fun(X2528,bool),fun(X2528,bool),hAPP(X2528,fun(fun(X2528,bool),fun(X2528,bool)),insert(X2528),esk35_4(X2528,X2529,X2530,X2531)),hAPP(fun(X2528,bool),fun(X2528,bool),hAPP(X2528,fun(fun(X2528,bool),fun(X2528,bool)),insert(X2528),esk36_4(X2528,X2529,X2530,X2531)),bot_bot(fun(X2528,bool))))))
| hBOOL(hAPP(fun(X2528,bool),bool,hAPP(X2528,fun(fun(X2528,bool),bool),member(X2528),hAPP(fun(X2528,bool),X2528,X2531,X2529)),X2529)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_194_folding__one_Oclosed])])]) ).
fof(i_0_628,plain,
! [X2521,X2522,X2523,X2524,X2525] :
( ~ hBOOL(hAPP(fun(fun(X2521,bool),X2521),bool,hAPP(fun(X2521,fun(X2521,X2521)),fun(fun(fun(X2521,bool),X2521),bool),finite2073411215e_idem(X2521),X2524),X2525))
| hAPP(X2521,X2521,X2523,hAPP(X2521,X2521,hAPP(X2521,fun(X2521,X2521),X2524,esk33_5(X2521,X2522,X2523,X2524,X2525)),esk34_5(X2521,X2522,X2523,X2524,X2525))) != hAPP(X2521,X2521,hAPP(X2521,fun(X2521,X2521),X2524,hAPP(X2521,X2521,X2523,esk33_5(X2521,X2522,X2523,X2524,X2525))),hAPP(X2521,X2521,X2523,esk34_5(X2521,X2522,X2523,X2524,X2525)))
| ~ hBOOL(hAPP(fun(X2521,bool),bool,finite_finite(X2521),X2522))
| ti(fun(X2521,bool),X2522) = bot_bot(fun(X2521,bool))
| hAPP(X2521,X2521,X2523,hAPP(fun(X2521,bool),X2521,X2525,X2522)) = hAPP(fun(X2521,bool),X2521,X2525,hAPP(fun(X2521,bool),fun(X2521,bool),hAPP(fun(X2521,X2521),fun(fun(X2521,bool),fun(X2521,bool)),image(X2521,X2521),X2523),X2522)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_193_folding__one__idem_Ohom__commute])])]) ).
fof(i_0_629,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_416_psubset__insert__iff]) ).
fof(i_0_630,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_185_subset__insert__iff]) ).
fof(i_0_631,plain,
! [X2,X1,X14,X8,X12,X42,X40,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),X42),X40),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,X40,X14)),hAPP(fun(X2,bool),X1,X10,X8)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_207_folding__image__simple_Oinsert]) ).
fof(i_0_632,plain,
! [X2583,X2584,X2585,X2586,X2587,X2588] :
( ~ hBOOL(hAPP(fun(fun(X2583,bool),X2584),bool,hAPP(fun(X2583,X2584),fun(fun(fun(X2583,bool),X2584),bool),hAPP(X2584,fun(fun(X2583,X2584),fun(fun(fun(X2583,bool),X2584),bool)),hAPP(fun(X2584,fun(X2584,X2584)),fun(X2584,fun(fun(X2583,X2584),fun(fun(fun(X2583,bool),X2584),bool))),finite1357897459simple(X2584,X2583),X2585),X2586),X2587),X2588))
| hAPP(fun(X2583,bool),X2584,X2588,bot_bot(fun(X2583,bool))) = ti(X2584,X2586) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_206_folding__image__simple_Oempty])]) ).
fof(i_0_633,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_128_Collect__conv__if]) ).
fof(i_0_634,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_223_card__Diff__insert]) ).
fof(i_0_635,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_129_Collect__conv__if2]) ).
fof(i_0_636,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))))
=> ( ! [X54,X55] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X54),X8))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X54),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X55))
=> 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),X54),X55))) ) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_148_finite__subset__induct]) ).
fof(i_0_637,plain,
! [X2399,X2400,X2401] :
( ( hBOOL(hAPP(fun(X2399,bool),bool,finite_finite(X2399),esk32_3(X2399,X2400,X2401)))
| hBOOL(hAPP(fun(X2399,bool),bool,X2400,X2401))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,X2400,hAPP(fun(X2399,bool),fun(X2399,bool),hAPP(X2399,fun(fun(X2399,bool),fun(X2399,bool)),insert(X2399),esk30_3(X2399,X2400,X2401)),bot_bot(fun(X2399,bool)))))
| ti(fun(X2399,bool),X2401) = bot_bot(fun(X2399,bool))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,finite_finite(X2399),X2401)) )
& ( ti(fun(X2399,bool),esk32_3(X2399,X2400,X2401)) != bot_bot(fun(X2399,bool))
| hBOOL(hAPP(fun(X2399,bool),bool,X2400,X2401))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,X2400,hAPP(fun(X2399,bool),fun(X2399,bool),hAPP(X2399,fun(fun(X2399,bool),fun(X2399,bool)),insert(X2399),esk30_3(X2399,X2400,X2401)),bot_bot(fun(X2399,bool)))))
| ti(fun(X2399,bool),X2401) = bot_bot(fun(X2399,bool))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,finite_finite(X2399),X2401)) )
& ( ~ hBOOL(hAPP(fun(X2399,bool),bool,hAPP(X2399,fun(fun(X2399,bool),bool),member(X2399),esk31_3(X2399,X2400,X2401)),esk32_3(X2399,X2400,X2401)))
| hBOOL(hAPP(fun(X2399,bool),bool,X2400,X2401))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,X2400,hAPP(fun(X2399,bool),fun(X2399,bool),hAPP(X2399,fun(fun(X2399,bool),fun(X2399,bool)),insert(X2399),esk30_3(X2399,X2400,X2401)),bot_bot(fun(X2399,bool)))))
| ti(fun(X2399,bool),X2401) = bot_bot(fun(X2399,bool))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,finite_finite(X2399),X2401)) )
& ( hBOOL(hAPP(fun(X2399,bool),bool,X2400,esk32_3(X2399,X2400,X2401)))
| hBOOL(hAPP(fun(X2399,bool),bool,X2400,X2401))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,X2400,hAPP(fun(X2399,bool),fun(X2399,bool),hAPP(X2399,fun(fun(X2399,bool),fun(X2399,bool)),insert(X2399),esk30_3(X2399,X2400,X2401)),bot_bot(fun(X2399,bool)))))
| ti(fun(X2399,bool),X2401) = bot_bot(fun(X2399,bool))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,finite_finite(X2399),X2401)) )
& ( ~ hBOOL(hAPP(fun(X2399,bool),bool,X2400,hAPP(fun(X2399,bool),fun(X2399,bool),hAPP(X2399,fun(fun(X2399,bool),fun(X2399,bool)),insert(X2399),esk31_3(X2399,X2400,X2401)),esk32_3(X2399,X2400,X2401))))
| hBOOL(hAPP(fun(X2399,bool),bool,X2400,X2401))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,X2400,hAPP(fun(X2399,bool),fun(X2399,bool),hAPP(X2399,fun(fun(X2399,bool),fun(X2399,bool)),insert(X2399),esk30_3(X2399,X2400,X2401)),bot_bot(fun(X2399,bool)))))
| ti(fun(X2399,bool),X2401) = bot_bot(fun(X2399,bool))
| ~ hBOOL(hAPP(fun(X2399,bool),bool,finite_finite(X2399),X2401)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_604])])])]) ).
fof(i_0_638,plain,
! [X1953,X1954,X1955,X1956,X1957] :
( ( hBOOL(hAPP(fun(X1953,bool),bool,hAPP(fun(X1953,bool),fun(fun(X1953,bool),bool),ord_less_eq(fun(X1953,bool)),esk1_5(X1953,X1954,X1955,X1956,X1957)),X1956))
| ~ hBOOL(hAPP(fun(X1954,bool),bool,hAPP(fun(X1954,bool),fun(fun(X1954,bool),bool),ord_less_eq(fun(X1954,bool)),X1957),hAPP(fun(X1953,bool),fun(X1954,bool),hAPP(fun(X1953,X1954),fun(fun(X1953,bool),fun(X1954,bool)),image(X1953,X1954),X1955),X1956)))
| ~ hBOOL(hAPP(fun(X1954,bool),bool,finite_finite(X1954),X1957)) )
& ( hBOOL(hAPP(fun(X1953,bool),bool,finite_finite(X1953),esk1_5(X1953,X1954,X1955,X1956,X1957)))
| ~ hBOOL(hAPP(fun(X1954,bool),bool,hAPP(fun(X1954,bool),fun(fun(X1954,bool),bool),ord_less_eq(fun(X1954,bool)),X1957),hAPP(fun(X1953,bool),fun(X1954,bool),hAPP(fun(X1953,X1954),fun(fun(X1953,bool),fun(X1954,bool)),image(X1953,X1954),X1955),X1956)))
| ~ hBOOL(hAPP(fun(X1954,bool),bool,finite_finite(X1954),X1957)) )
& ( ti(fun(X1954,bool),X1957) = hAPP(fun(X1953,bool),fun(X1954,bool),hAPP(fun(X1953,X1954),fun(fun(X1953,bool),fun(X1954,bool)),image(X1953,X1954),X1955),esk1_5(X1953,X1954,X1955,X1956,X1957))
| ~ hBOOL(hAPP(fun(X1954,bool),bool,hAPP(fun(X1954,bool),fun(fun(X1954,bool),bool),ord_less_eq(fun(X1954,bool)),X1957),hAPP(fun(X1953,bool),fun(X1954,bool),hAPP(fun(X1953,X1954),fun(fun(X1953,bool),fun(X1954,bool)),image(X1953,X1954),X1955),X1956)))
| ~ hBOOL(hAPP(fun(X1954,bool),bool,finite_finite(X1954),X1957)) ) ),
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_639,plain,
! [X2135,X2136,X2137,X2138,X2139,X2141,X2142,X2143,X2144,X2145,X2146] :
( ( hBOOL(hAPP(fun(X2136,bool),bool,hAPP(fun(X2136,bool),fun(fun(X2136,bool),bool),ord_less_eq(fun(X2136,bool)),esk8_5(X2135,X2136,X2137,X2138,X2139)),X2139))
| ~ hBOOL(hAPP(fun(X2135,bool),bool,hAPP(fun(X2135,bool),fun(fun(X2135,bool),bool),ord_less_eq(fun(X2135,bool)),X2137),hAPP(fun(X2136,bool),fun(X2135,bool),hAPP(fun(X2136,X2135),fun(fun(X2136,bool),fun(X2135,bool)),image(X2136,X2135),X2138),X2139))) )
& ( ti(fun(X2135,bool),X2137) = hAPP(fun(X2136,bool),fun(X2135,bool),hAPP(fun(X2136,X2135),fun(fun(X2136,bool),fun(X2135,bool)),image(X2136,X2135),X2138),esk8_5(X2135,X2136,X2137,X2138,X2139))
| ~ hBOOL(hAPP(fun(X2135,bool),bool,hAPP(fun(X2135,bool),fun(fun(X2135,bool),bool),ord_less_eq(fun(X2135,bool)),X2137),hAPP(fun(X2136,bool),fun(X2135,bool),hAPP(fun(X2136,X2135),fun(fun(X2136,bool),fun(X2135,bool)),image(X2136,X2135),X2138),X2139))) )
& ( ~ hBOOL(hAPP(fun(X2142,bool),bool,hAPP(fun(X2142,bool),fun(fun(X2142,bool),bool),ord_less_eq(fun(X2142,bool)),X2146),X2145))
| ti(fun(X2141,bool),X2143) != hAPP(fun(X2142,bool),fun(X2141,bool),hAPP(fun(X2142,X2141),fun(fun(X2142,bool),fun(X2141,bool)),image(X2142,X2141),X2144),X2146)
| hBOOL(hAPP(fun(X2141,bool),bool,hAPP(fun(X2141,bool),fun(fun(X2141,bool),bool),ord_less_eq(fun(X2141,bool)),X2143),hAPP(fun(X2142,bool),fun(X2141,bool),hAPP(fun(X2142,X2141),fun(fun(X2142,bool),fun(X2141,bool)),image(X2142,X2141),X2144),X2145))) ) ),
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_92_subset__image__iff])])])])])]) ).
fof(i_0_640,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_265_add__leE]) ).
fof(i_0_641,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_87_subset__insert]) ).
fof(i_0_642,plain,
! [X2448,X2449,X2450,X2451,X2452] :
( ( hAPP(fun(X2448,bool),fun(X2448,bool),hAPP(fun(X2448,bool),fun(fun(X2448,bool),fun(X2448,bool)),minus_minus(fun(X2448,bool)),X2450),hAPP(fun(X2448,bool),fun(X2448,bool),hAPP(X2448,fun(fun(X2448,bool),fun(X2448,bool)),insert(X2448),X2449),bot_bot(fun(X2448,bool)))) != bot_bot(fun(X2448,bool))
| hAPP(fun(X2448,bool),X2448,X2452,X2450) = ti(X2448,X2449)
| ~ hBOOL(hAPP(fun(X2448,bool),bool,hAPP(X2448,fun(fun(X2448,bool),bool),member(X2448),X2449),X2450))
| ~ hBOOL(hAPP(fun(X2448,bool),bool,finite_finite(X2448),X2450))
| ~ hBOOL(hAPP(fun(fun(X2448,bool),X2448),bool,hAPP(fun(X2448,fun(X2448,X2448)),fun(fun(fun(X2448,bool),X2448),bool),finite_folding_one(X2448),X2451),X2452)) )
& ( hAPP(fun(X2448,bool),fun(X2448,bool),hAPP(fun(X2448,bool),fun(fun(X2448,bool),fun(X2448,bool)),minus_minus(fun(X2448,bool)),X2450),hAPP(fun(X2448,bool),fun(X2448,bool),hAPP(X2448,fun(fun(X2448,bool),fun(X2448,bool)),insert(X2448),X2449),bot_bot(fun(X2448,bool)))) = bot_bot(fun(X2448,bool))
| hAPP(fun(X2448,bool),X2448,X2452,X2450) = hAPP(X2448,X2448,hAPP(X2448,fun(X2448,X2448),X2451,X2449),hAPP(fun(X2448,bool),X2448,X2452,hAPP(fun(X2448,bool),fun(X2448,bool),hAPP(fun(X2448,bool),fun(fun(X2448,bool),fun(X2448,bool)),minus_minus(fun(X2448,bool)),X2450),hAPP(fun(X2448,bool),fun(X2448,bool),hAPP(X2448,fun(fun(X2448,bool),fun(X2448,bool)),insert(X2448),X2449),bot_bot(fun(X2448,bool))))))
| ~ hBOOL(hAPP(fun(X2448,bool),bool,hAPP(X2448,fun(fun(X2448,bool),bool),member(X2448),X2449),X2450))
| ~ hBOOL(hAPP(fun(X2448,bool),bool,finite_finite(X2448),X2450))
| ~ hBOOL(hAPP(fun(fun(X2448,bool),X2448),bool,hAPP(fun(X2448,fun(X2448,X2448)),fun(fun(fun(X2448,bool),X2448),bool),finite_folding_one(X2448),X2451),X2452)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_174_folding__one_Oremove])])]) ).
fof(i_0_643,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_204_Diff__iff]) ).
fof(i_0_644,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_201_DiffD2]) ).
fof(i_0_645,plain,
! [X2453,X2454,X2455,X2456,X2457] :
( ( hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(fun(X2453,bool),fun(fun(X2453,bool),fun(X2453,bool)),minus_minus(fun(X2453,bool)),X2455),hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(X2453,fun(fun(X2453,bool),fun(X2453,bool)),insert(X2453),X2454),bot_bot(fun(X2453,bool)))) != bot_bot(fun(X2453,bool))
| hAPP(fun(X2453,bool),X2453,X2457,hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(X2453,fun(fun(X2453,bool),fun(X2453,bool)),insert(X2453),X2454),X2455)) = ti(X2453,X2454)
| ~ hBOOL(hAPP(fun(X2453,bool),bool,finite_finite(X2453),X2455))
| ~ hBOOL(hAPP(fun(fun(X2453,bool),X2453),bool,hAPP(fun(X2453,fun(X2453,X2453)),fun(fun(fun(X2453,bool),X2453),bool),finite_folding_one(X2453),X2456),X2457)) )
& ( hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(fun(X2453,bool),fun(fun(X2453,bool),fun(X2453,bool)),minus_minus(fun(X2453,bool)),X2455),hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(X2453,fun(fun(X2453,bool),fun(X2453,bool)),insert(X2453),X2454),bot_bot(fun(X2453,bool)))) = bot_bot(fun(X2453,bool))
| hAPP(fun(X2453,bool),X2453,X2457,hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(X2453,fun(fun(X2453,bool),fun(X2453,bool)),insert(X2453),X2454),X2455)) = hAPP(X2453,X2453,hAPP(X2453,fun(X2453,X2453),X2456,X2454),hAPP(fun(X2453,bool),X2453,X2457,hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(fun(X2453,bool),fun(fun(X2453,bool),fun(X2453,bool)),minus_minus(fun(X2453,bool)),X2455),hAPP(fun(X2453,bool),fun(X2453,bool),hAPP(X2453,fun(fun(X2453,bool),fun(X2453,bool)),insert(X2453),X2454),bot_bot(fun(X2453,bool))))))
| ~ hBOOL(hAPP(fun(X2453,bool),bool,finite_finite(X2453),X2455))
| ~ hBOOL(hAPP(fun(fun(X2453,bool),X2453),bool,hAPP(fun(X2453,fun(X2453,X2453)),fun(fun(fun(X2453,bool),X2453),bool),finite_folding_one(X2453),X2456),X2457)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_175_folding__one_Oinsert__remove])])]) ).
fof(i_0_646,plain,
! [X2152,X2153,X2154,X2155,X2156] :
( ( ti(X2152,X2154) = hAPP(X2153,X2152,X2155,esk9_5(X2152,X2153,X2154,X2155,X2156))
| ~ hBOOL(hAPP(fun(X2152,bool),bool,hAPP(X2152,fun(fun(X2152,bool),bool),member(X2152),X2154),hAPP(fun(X2153,bool),fun(X2152,bool),hAPP(fun(X2153,X2152),fun(fun(X2153,bool),fun(X2152,bool)),image(X2153,X2152),X2155),X2156))) )
& ( hBOOL(hAPP(fun(X2153,bool),bool,hAPP(X2153,fun(fun(X2153,bool),bool),member(X2153),esk9_5(X2152,X2153,X2154,X2155,X2156)),X2156))
| ~ hBOOL(hAPP(fun(X2152,bool),bool,hAPP(X2152,fun(fun(X2152,bool),bool),member(X2152),X2154),hAPP(fun(X2153,bool),fun(X2152,bool),hAPP(fun(X2153,X2152),fun(fun(X2153,bool),fun(X2152,bool)),image(X2153,X2152),X2155),X2156))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_605])])])]) ).
fof(i_0_647,plain,
! [X2072,X2073,X2074,X2075,X2076,X2078,X2079,X2080,X2081,X2082,X2083] :
( ( hBOOL(hAPP(fun(X2073,bool),bool,hAPP(X2073,fun(fun(X2073,bool),bool),member(X2073),esk7_5(X2072,X2073,X2074,X2075,X2076)),X2076))
| ~ hBOOL(hAPP(fun(X2072,bool),bool,hAPP(X2072,fun(fun(X2072,bool),bool),member(X2072),X2074),hAPP(fun(X2073,bool),fun(X2072,bool),hAPP(fun(X2073,X2072),fun(fun(X2073,bool),fun(X2072,bool)),image(X2073,X2072),X2075),X2076))) )
& ( ti(X2072,X2074) = hAPP(X2073,X2072,X2075,esk7_5(X2072,X2073,X2074,X2075,X2076))
| ~ hBOOL(hAPP(fun(X2072,bool),bool,hAPP(X2072,fun(fun(X2072,bool),bool),member(X2072),X2074),hAPP(fun(X2073,bool),fun(X2072,bool),hAPP(fun(X2073,X2072),fun(fun(X2073,bool),fun(X2072,bool)),image(X2073,X2072),X2075),X2076))) )
& ( ~ hBOOL(hAPP(fun(X2079,bool),bool,hAPP(X2079,fun(fun(X2079,bool),bool),member(X2079),X2083),X2082))
| ti(X2078,X2080) != hAPP(X2079,X2078,X2081,X2083)
| hBOOL(hAPP(fun(X2078,bool),bool,hAPP(X2078,fun(fun(X2078,bool),bool),member(X2078),X2080),hAPP(fun(X2079,bool),fun(X2078,bool),hAPP(fun(X2079,X2078),fun(fun(X2079,bool),fun(X2078,bool)),image(X2079,X2078),X2081),X2082))) ) ),
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_79_image__iff])])])])])]) ).
fof(i_0_648,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_219_card__Diff__singleton__if]) ).
fof(i_0_649,plain,
! [X1857,X1858,X1859] :
( ~ hBOOL(hAPP(fun(X1857,bool),bool,finite_finite(X1857),X1859))
| ~ hBOOL(hAPP(fun(X1857,bool),bool,hAPP(fun(X1857,bool),fun(fun(X1857,bool),bool),ord_less_eq(fun(X1857,bool)),X1858),X1859))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1857,bool),nat,finite_card(X1857),X1859)),hAPP(fun(X1857,bool),nat,finite_card(X1857),X1858)))
| ti(fun(X1857,bool),X1858) = ti(fun(X1857,bool),X1859) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_card__seteq])]) ).
fof(i_0_650,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_303_not__add__less1]) ).
fof(i_0_651,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_302_not__add__less2]) ).
fof(i_0_652,plain,
! [X2287,X2288,X2289] :
( ~ hBOOL(hAPP(fun(X2287,bool),bool,hAPP(fun(X2287,bool),fun(fun(X2287,bool),bool),ord_less_eq(fun(X2287,bool)),X2288),hAPP(fun(X2287,bool),fun(X2287,bool),hAPP(X2287,fun(fun(X2287,bool),fun(X2287,bool)),insert(X2287),X2289),bot_bot(fun(X2287,bool)))))
| ti(fun(X2287,bool),X2288) = bot_bot(fun(X2287,bool))
| ti(fun(X2287,bool),X2288) = hAPP(fun(X2287,bool),fun(X2287,bool),hAPP(X2287,fun(fun(X2287,bool),fun(X2287,bool)),insert(X2287),X2289),bot_bot(fun(X2287,bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_132_subset__singletonD])]) ).
fof(i_0_653,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,X55] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X55))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X33),X55))
=> ( hBOOL(hAPP(fun(X1,bool),bool,X16,X55))
=> 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),X55))) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,X16,X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_150_finite__induct]) ).
fof(i_0_654,plain,
! [X2013,X2014,X2015,X2016] :
( ( ~ hBOOL(hAPP(fun(X2013,bool),bool,hAPP(X2013,fun(fun(X2013,bool),bool),member(X2013),X2014),hAPP(fun(X2013,bool),fun(X2013,bool),hAPP(X2013,fun(fun(X2013,bool),fun(X2013,bool)),insert(X2013),X2015),X2016)))
| ti(X2013,X2014) = ti(X2013,X2015)
| hBOOL(hAPP(fun(X2013,bool),bool,hAPP(X2013,fun(fun(X2013,bool),bool),member(X2013),X2014),X2016)) )
& ( ti(X2013,X2014) != ti(X2013,X2015)
| hBOOL(hAPP(fun(X2013,bool),bool,hAPP(X2013,fun(fun(X2013,bool),bool),member(X2013),X2014),hAPP(fun(X2013,bool),fun(X2013,bool),hAPP(X2013,fun(fun(X2013,bool),fun(X2013,bool)),insert(X2013),X2015),X2016))) )
& ( ~ hBOOL(hAPP(fun(X2013,bool),bool,hAPP(X2013,fun(fun(X2013,bool),bool),member(X2013),X2014),X2016))
| hBOOL(hAPP(fun(X2013,bool),bool,hAPP(X2013,fun(fun(X2013,bool),bool),member(X2013),X2014),hAPP(fun(X2013,bool),fun(X2013,bool),hAPP(X2013,fun(fun(X2013,bool),fun(X2013,bool)),insert(X2013),X2015),X2016))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_62_insert__iff])])]) ).
fof(i_0_655,plain,
! [X1986,X1987,X1988,X1989] :
( ~ hBOOL(hAPP(fun(X1986,bool),bool,hAPP(X1986,fun(fun(X1986,bool),bool),member(X1986),X1987),hAPP(fun(X1986,bool),fun(X1986,bool),hAPP(X1986,fun(fun(X1986,bool),fun(X1986,bool)),insert(X1986),X1988),X1989)))
| ti(X1986,X1987) = ti(X1986,X1988)
| hBOOL(hAPP(fun(X1986,bool),bool,hAPP(X1986,fun(fun(X1986,bool),bool),member(X1986),X1987),X1989)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_insertE])]) ).
fof(i_0_656,plain,
! [X2389,X2390,X2391,X2392,X2393] :
( ~ hBOOL(hAPP(fun(fun(X2389,bool),X2389),bool,hAPP(fun(X2389,fun(X2389,X2389)),fun(fun(fun(X2389,bool),X2389),bool),finite2073411215e_idem(X2389),X2392),X2393))
| ~ hBOOL(hAPP(fun(X2389,bool),bool,finite_finite(X2389),X2391))
| ti(fun(X2389,bool),X2390) = bot_bot(fun(X2389,bool))
| ~ hBOOL(hAPP(fun(X2389,bool),bool,hAPP(fun(X2389,bool),fun(fun(X2389,bool),bool),ord_less_eq(fun(X2389,bool)),X2390),X2391))
| hAPP(X2389,X2389,hAPP(X2389,fun(X2389,X2389),X2392,hAPP(fun(X2389,bool),X2389,X2393,X2390)),hAPP(fun(X2389,bool),X2389,X2393,X2391)) = hAPP(fun(X2389,bool),X2389,X2393,X2391) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_158_folding__one__idem_Osubset__idem])]) ).
fof(i_0_657,plain,
! [X3231,X3232,X3235,X3236,X3237,X3238] :
( ( ~ hBOOL(hAPP(fun(X3231,bool),bool,finite_finite(X3231),X3232))
| ti(fun(X3231,bool),X3232) = hAPP(fun(nat,bool),fun(X3231,bool),hAPP(fun(nat,X3231),fun(fun(nat,bool),fun(X3231,bool)),image(nat,X3231),esk53_2(X3231,X3232)),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)),esk52_2(X3231,X3232)))) )
& ( ti(fun(X3235,bool),X3236) != hAPP(fun(nat,bool),fun(X3235,bool),hAPP(fun(nat,X3235),fun(fun(nat,bool),fun(X3235,bool)),image(nat,X3235),X3238),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)),X3237)))
| hBOOL(hAPP(fun(X3235,bool),bool,finite_finite(X3235),X3236)) ) ),
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_418_finite__conv__nat__seg__image])])])])]) ).
fof(i_0_658,plain,
! [X3131,X3132,X3133,X3134] :
( ti(fun(X3131,bool),X3132) != hAPP(fun(nat,bool),fun(X3131,bool),hAPP(fun(nat,X3131),fun(fun(nat,bool),fun(X3131,bool)),image(nat,X3131),X3133),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)),X3134)))
| hBOOL(hAPP(fun(X3131,bool),bool,finite_finite(X3131),X3132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_384_nat__seg__image__imp__finite])]) ).
fof(i_0_659,plain,
! [X2638,X2639,X2640] :
( ( ~ hBOOL(hAPP(fun(X2638,bool),bool,hAPP(fun(X2638,bool),fun(fun(X2638,bool),bool),ord_less_eq(fun(X2638,bool)),X2639),hAPP(fun(X2638,bool),fun(X2638,bool),hAPP(X2638,fun(fun(X2638,bool),fun(X2638,bool)),insert(X2638),X2640),bot_bot(fun(X2638,bool)))))
| hAPP(fun(X2638,bool),X2638,hAPP(X2638,fun(fun(X2638,bool),X2638),partial_flat_lub(X2638),X2640),X2639) = ti(X2638,X2640) )
& ( hBOOL(hAPP(fun(X2638,bool),bool,hAPP(fun(X2638,bool),fun(fun(X2638,bool),bool),ord_less_eq(fun(X2638,bool)),X2639),hAPP(fun(X2638,bool),fun(X2638,bool),hAPP(X2638,fun(fun(X2638,bool),fun(X2638,bool)),insert(X2638),X2640),bot_bot(fun(X2638,bool)))))
| hAPP(fun(X2638,bool),X2638,hAPP(X2638,fun(fun(X2638,bool),X2638),partial_flat_lub(X2638),X2640),X2639) = hAPP(fun(X2638,bool),X2638,the(X2638),hAPP(fun(X2638,bool),fun(X2638,bool),hAPP(fun(X2638,fun(fun(X2638,bool),bool)),fun(fun(X2638,bool),fun(X2638,bool)),combc(X2638,fun(X2638,bool),bool),member(X2638)),hAPP(fun(X2638,bool),fun(X2638,bool),hAPP(fun(X2638,bool),fun(fun(X2638,bool),fun(X2638,bool)),minus_minus(fun(X2638,bool)),X2639),hAPP(fun(X2638,bool),fun(X2638,bool),hAPP(X2638,fun(fun(X2638,bool),fun(X2638,bool)),insert(X2638),X2640),bot_bot(fun(X2638,bool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_606])]) ).
fof(i_0_660,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_200_DiffI]) ).
fof(i_0_661,plain,
! [X2250,X2251,X2252,X2253,X2254] :
( ( ti(X2250,X2251) = ti(X2250,X2254)
| ti(X2250,X2251) = ti(X2250,X2253)
| hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2251),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2252),bot_bot(fun(X2250,bool)))) != hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2253),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2254),bot_bot(fun(X2250,bool)))) )
& ( ti(X2250,X2252) = ti(X2250,X2253)
| ti(X2250,X2251) = ti(X2250,X2253)
| hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2251),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2252),bot_bot(fun(X2250,bool)))) != hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2253),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2254),bot_bot(fun(X2250,bool)))) )
& ( ti(X2250,X2251) = ti(X2250,X2254)
| ti(X2250,X2252) = ti(X2250,X2254)
| hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2251),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2252),bot_bot(fun(X2250,bool)))) != hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2253),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2254),bot_bot(fun(X2250,bool)))) )
& ( ti(X2250,X2252) = ti(X2250,X2253)
| ti(X2250,X2252) = ti(X2250,X2254)
| hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2251),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2252),bot_bot(fun(X2250,bool)))) != hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2253),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2254),bot_bot(fun(X2250,bool)))) )
& ( ti(X2250,X2251) != ti(X2250,X2253)
| ti(X2250,X2252) != ti(X2250,X2254)
| hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2251),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2252),bot_bot(fun(X2250,bool)))) = hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2253),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2254),bot_bot(fun(X2250,bool)))) )
& ( ti(X2250,X2251) != ti(X2250,X2254)
| ti(X2250,X2252) != ti(X2250,X2253)
| hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2251),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2252),bot_bot(fun(X2250,bool)))) = hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2253),hAPP(fun(X2250,bool),fun(X2250,bool),hAPP(X2250,fun(fun(X2250,bool),fun(X2250,bool)),insert(X2250),X2254),bot_bot(fun(X2250,bool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_120_doubleton__eq__iff])])]) ).
fof(i_0_662,plain,
! [X2472,X2473,X2474] :
( ~ hBOOL(hAPP(fun(X2472,bool),bool,hAPP(X2472,fun(fun(X2472,bool),bool),member(X2472),X2473),X2474))
| hAPP(fun(X2472,bool),fun(X2472,bool),hAPP(X2472,fun(fun(X2472,bool),fun(X2472,bool)),insert(X2472),X2473),hAPP(fun(X2472,bool),fun(X2472,bool),hAPP(fun(X2472,bool),fun(fun(X2472,bool),fun(X2472,bool)),minus_minus(fun(X2472,bool)),X2474),hAPP(fun(X2472,bool),fun(X2472,bool),hAPP(X2472,fun(fun(X2472,bool),fun(X2472,bool)),insert(X2472),X2473),bot_bot(fun(X2472,bool))))) = ti(fun(X2472,bool),X2474) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_insert__Diff])]) ).
fof(i_0_663,plain,
! [X2407,X2408,X2409,X2410,X2411] :
( ~ hBOOL(hAPP(fun(fun(X2407,bool),X2407),bool,hAPP(fun(X2407,fun(X2407,X2407)),fun(fun(fun(X2407,bool),X2407),bool),finite_folding_one(X2407),X2410),X2411))
| ~ hBOOL(hAPP(fun(X2407,bool),bool,finite_finite(X2407),X2409))
| hBOOL(hAPP(fun(X2407,bool),bool,hAPP(X2407,fun(fun(X2407,bool),bool),member(X2407),X2408),X2409))
| ti(fun(X2407,bool),X2409) = bot_bot(fun(X2407,bool))
| hAPP(fun(X2407,bool),X2407,X2411,hAPP(fun(X2407,bool),fun(X2407,bool),hAPP(X2407,fun(fun(X2407,bool),fun(X2407,bool)),insert(X2407),X2408),X2409)) = hAPP(X2407,X2407,hAPP(X2407,fun(X2407,X2407),X2410,X2408),hAPP(fun(X2407,bool),X2407,X2411,X2409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_607])]) ).
fof(i_0_664,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_170_insert__Diff__if]) ).
fof(i_0_665,plain,
! [X2436,X2437,X2438,X2439] :
( ~ hBOOL(hAPP(fun(X2436,bool),bool,hAPP(fun(X2436,bool),fun(fun(X2436,bool),bool),ord_less_eq(fun(X2436,bool)),X2438),X2439))
| ~ hBOOL(hAPP(fun(X2436,bool),bool,hAPP(fun(X2436,bool),fun(fun(X2436,bool),bool),ord_less_eq(fun(X2436,bool)),X2439),X2437))
| hAPP(fun(X2436,bool),fun(X2436,bool),hAPP(fun(X2436,bool),fun(fun(X2436,bool),fun(X2436,bool)),minus_minus(fun(X2436,bool)),X2439),hAPP(fun(X2436,bool),fun(X2436,bool),hAPP(fun(X2436,bool),fun(fun(X2436,bool),fun(X2436,bool)),minus_minus(fun(X2436,bool)),X2437),X2438)) = ti(fun(X2436,bool),X2438) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_171_double__diff])]) ).
fof(i_0_666,plain,
! [X2255,X2256,X2257] :
( ( ~ hBOOL(hAPP(fun(X2255,bool),bool,hAPP(X2255,fun(fun(X2255,bool),bool),member(X2255),X2256),hAPP(fun(X2255,bool),fun(X2255,bool),hAPP(X2255,fun(fun(X2255,bool),fun(X2255,bool)),insert(X2255),X2257),bot_bot(fun(X2255,bool)))))
| ti(X2255,X2256) = ti(X2255,X2257) )
& ( ti(X2255,X2256) != ti(X2255,X2257)
| hBOOL(hAPP(fun(X2255,bool),bool,hAPP(X2255,fun(fun(X2255,bool),bool),member(X2255),X2256),hAPP(fun(X2255,bool),fun(X2255,bool),hAPP(X2255,fun(fun(X2255,bool),fun(X2255,bool)),insert(X2255),X2257),bot_bot(fun(X2255,bool))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_121_singleton__iff])]) ).
fof(i_0_667,plain,
! [X2247,X2248,X2249] :
( ~ hBOOL(hAPP(fun(X2247,bool),bool,hAPP(X2247,fun(fun(X2247,bool),bool),member(X2247),X2248),hAPP(fun(X2247,bool),fun(X2247,bool),hAPP(X2247,fun(fun(X2247,bool),fun(X2247,bool)),insert(X2247),X2249),bot_bot(fun(X2247,bool)))))
| ti(X2247,X2248) = ti(X2247,X2249) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_119_singletonE])]) ).
fof(i_0_668,plain,
! [X1969,X1970,X1971,X1972,X1973,X1974] :
( ti(X1969,X1972) != hAPP(X1970,X1969,X1973,X1974)
| ~ hBOOL(hAPP(fun(X1970,bool),bool,hAPP(X1970,fun(fun(X1970,bool),bool),member(X1970),X1974),X1971))
| hBOOL(hAPP(fun(X1969,bool),bool,hAPP(X1969,fun(fun(X1969,bool),bool),member(X1969),X1972),hAPP(fun(X1970,bool),fun(X1969,bool),hAPP(fun(X1970,X1969),fun(fun(X1970,bool),fun(X1969,bool)),image(X1970,X1969),X1973),X1971))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_image__eqI])]) ).
fof(i_0_669,plain,
! [X2089,X2090,X2091,X2092,X2093,X2094] :
( ~ hBOOL(hAPP(fun(X2090,bool),bool,hAPP(X2090,fun(fun(X2090,bool),bool),member(X2090),X2093),X2094))
| ti(X2089,X2091) != hAPP(X2090,X2089,X2092,X2093)
| hBOOL(hAPP(fun(X2089,bool),bool,hAPP(X2089,fun(fun(X2089,bool),bool),member(X2089),X2091),hAPP(fun(X2090,bool),fun(X2089,bool),hAPP(fun(X2090,X2089),fun(fun(X2090,bool),fun(X2089,bool)),image(X2090,X2089),X2092),X2094))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_81_rev__image__eqI])]) ).
fof(i_0_670,plain,
! [X2469,X2470,X2471] :
( hBOOL(hAPP(fun(X2469,bool),bool,hAPP(X2469,fun(fun(X2469,bool),bool),member(X2469),X2470),X2471))
| hAPP(fun(X2469,bool),fun(X2469,bool),hAPP(fun(X2469,bool),fun(fun(X2469,bool),fun(X2469,bool)),minus_minus(fun(X2469,bool)),hAPP(fun(X2469,bool),fun(X2469,bool),hAPP(X2469,fun(fun(X2469,bool),fun(X2469,bool)),insert(X2469),X2470),X2471)),hAPP(fun(X2469,bool),fun(X2469,bool),hAPP(X2469,fun(fun(X2469,bool),fun(X2469,bool)),insert(X2469),X2470),bot_bot(fun(X2469,bool)))) = ti(fun(X2469,bool),X2471) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_608])]) ).
fof(i_0_671,plain,
! [X2394,X2395,X2396,X2397,X2398] :
( ~ hBOOL(hAPP(fun(fun(X2394,bool),X2394),bool,hAPP(fun(X2394,fun(X2394,X2394)),fun(fun(fun(X2394,bool),X2394),bool),finite2073411215e_idem(X2394),X2397),X2398))
| ~ hBOOL(hAPP(fun(X2394,bool),bool,finite_finite(X2394),X2396))
| ti(fun(X2394,bool),X2396) = bot_bot(fun(X2394,bool))
| hAPP(fun(X2394,bool),X2394,X2398,hAPP(fun(X2394,bool),fun(X2394,bool),hAPP(X2394,fun(fun(X2394,bool),fun(X2394,bool)),insert(X2394),X2395),X2396)) = hAPP(X2394,X2394,hAPP(X2394,fun(X2394,X2394),X2397,X2395),hAPP(fun(X2394,bool),X2394,X2398,X2396)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_159_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_672,plain,
! [X2017,X2018,X2019,X2020] :
( ( ~ hBOOL(hAPP(X2017,bool,hAPP(fun(X2017,bool),fun(X2017,bool),hAPP(X2017,fun(fun(X2017,bool),fun(X2017,bool)),insert(X2017),X2018),X2019),X2020))
| ti(X2017,X2018) = ti(X2017,X2020)
| hBOOL(hAPP(X2017,bool,X2019,X2020)) )
& ( ti(X2017,X2018) != ti(X2017,X2020)
| hBOOL(hAPP(X2017,bool,hAPP(fun(X2017,bool),fun(X2017,bool),hAPP(X2017,fun(fun(X2017,bool),fun(X2017,bool)),insert(X2017),X2018),X2019),X2020)) )
& ( ~ hBOOL(hAPP(X2017,bool,X2019,X2020))
| hBOOL(hAPP(X2017,bool,hAPP(fun(X2017,bool),fun(X2017,bool),hAPP(X2017,fun(fun(X2017,bool),fun(X2017,bool)),insert(X2017),X2018),X2019),X2020)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_insert__code])])]) ).
fof(i_0_673,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_674,plain,
! [X1800,X1801] : ti(fun(fun(X1800,fun(X1800,X1800)),fun(X1800,fun(fun(X1801,X1800),fun(fun(fun(X1801,bool),X1800),bool)))),finite1357897459simple(X1800,X1801)) = finite1357897459simple(X1800,X1801),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple_res]) ).
fof(i_0_675,plain,
! [X1,X2] :
( ord(X2)
=> ! [X12,X40] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X12),X40))
<=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X12),X40))
& ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X40),X12)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_414_less__fun__def]) ).
fof(i_0_676,plain,
! [X2021,X2022,X2023,X2024] :
( ( hAPP(fun(X2021,bool),fun(X2021,bool),hAPP(X2021,fun(fun(X2021,bool),fun(X2021,bool)),insert(X2021),X2023),X2024) != hAPP(fun(X2021,bool),fun(X2021,bool),hAPP(X2021,fun(fun(X2021,bool),fun(X2021,bool)),insert(X2021),X2023),X2022)
| ti(fun(X2021,bool),X2024) = ti(fun(X2021,bool),X2022)
| hBOOL(hAPP(fun(X2021,bool),bool,hAPP(X2021,fun(fun(X2021,bool),bool),member(X2021),X2023),X2022))
| hBOOL(hAPP(fun(X2021,bool),bool,hAPP(X2021,fun(fun(X2021,bool),bool),member(X2021),X2023),X2024)) )
& ( ti(fun(X2021,bool),X2024) != ti(fun(X2021,bool),X2022)
| hAPP(fun(X2021,bool),fun(X2021,bool),hAPP(X2021,fun(fun(X2021,bool),fun(X2021,bool)),insert(X2021),X2023),X2024) = hAPP(fun(X2021,bool),fun(X2021,bool),hAPP(X2021,fun(fun(X2021,bool),fun(X2021,bool)),insert(X2021),X2023),X2022)
| hBOOL(hAPP(fun(X2021,bool),bool,hAPP(X2021,fun(fun(X2021,bool),bool),member(X2021),X2023),X2022))
| hBOOL(hAPP(fun(X2021,bool),bool,hAPP(X2021,fun(fun(X2021,bool),bool),member(X2021),X2023),X2024)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_609])])]) ).
fof(i_0_677,plain,
! [X2034,X2035,X2036] :
( ( hBOOL(hAPP(fun(X2034,bool),bool,hAPP(fun(X2034,bool),fun(fun(X2034,bool),bool),ord_less_eq(fun(X2034,bool)),X2035),X2036))
| ti(fun(X2034,bool),X2035) != ti(fun(X2034,bool),X2036) )
& ( hBOOL(hAPP(fun(X2034,bool),bool,hAPP(fun(X2034,bool),fun(fun(X2034,bool),bool),ord_less_eq(fun(X2034,bool)),X2036),X2035))
| ti(fun(X2034,bool),X2035) != ti(fun(X2034,bool),X2036) )
& ( ~ hBOOL(hAPP(fun(X2034,bool),bool,hAPP(fun(X2034,bool),fun(fun(X2034,bool),bool),ord_less_eq(fun(X2034,bool)),X2035),X2036))
| ~ hBOOL(hAPP(fun(X2034,bool),bool,hAPP(fun(X2034,bool),fun(fun(X2034,bool),bool),ord_less_eq(fun(X2034,bool)),X2036),X2035))
| ti(fun(X2034,bool),X2035) = ti(fun(X2034,bool),X2036) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_set__eq__subset])])]) ).
fof(i_0_678,plain,
! [X1975,X1976,X1977] :
( ~ hBOOL(hAPP(fun(X1975,bool),bool,hAPP(fun(X1975,bool),fun(fun(X1975,bool),bool),ord_less_eq(fun(X1975,bool)),X1976),X1977))
| ~ hBOOL(hAPP(fun(X1975,bool),bool,hAPP(fun(X1975,bool),fun(fun(X1975,bool),bool),ord_less_eq(fun(X1975,bool)),X1977),X1976))
| ti(fun(X1975,bool),X1976) = ti(fun(X1975,bool),X1977) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_equalityI])]) ).
fof(i_0_679,plain,
! [X2502,X2503,X2504,X2505] :
( ~ hBOOL(hAPP(fun(fun(X2502,bool),X2502),bool,hAPP(fun(X2502,fun(X2502,X2502)),fun(fun(fun(X2502,bool),X2502),bool),finite_folding_one(X2502),X2504),X2505))
| hAPP(fun(X2502,bool),X2502,X2505,hAPP(fun(X2502,bool),fun(X2502,bool),hAPP(X2502,fun(fun(X2502,bool),fun(X2502,bool)),insert(X2502),X2503),bot_bot(fun(X2502,bool)))) = ti(X2502,X2503) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_187_folding__one_Osingleton])]) ).
fof(i_0_680,plain,
! [X1982,X1983,X1984,X1985] :
( ( ~ hBOOL(hAPP(fun(X1982,bool),bool,hAPP(X1982,fun(fun(X1982,bool),bool),member(X1982),X1984),X1985))
| hBOOL(hAPP(fun(X1982,bool),bool,hAPP(X1982,fun(fun(X1982,bool),bool),member(X1982),X1984),hAPP(fun(X1982,bool),fun(X1982,bool),hAPP(X1982,fun(fun(X1982,bool),fun(X1982,bool)),insert(X1982),X1983),X1985))) )
& ( ti(X1982,X1984) != ti(X1982,X1983)
| hBOOL(hAPP(fun(X1982,bool),bool,hAPP(X1982,fun(fun(X1982,bool),bool),member(X1982),X1984),hAPP(fun(X1982,bool),fun(X1982,bool),hAPP(X1982,fun(fun(X1982,bool),fun(X1982,bool)),insert(X1982),X1983),X1985))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_610])])]) ).
fof(i_0_681,plain,
! [X3404,X3405,X3406] :
( ( ti(X3404,X3406) = zero_zero(X3404)
| hAPP(X3404,X3404,hAPP(X3404,fun(X3404,X3404),plus_plus(X3404),X3406),X3405) != zero_zero(X3404)
| ~ hBOOL(hAPP(X3404,bool,hAPP(X3404,fun(X3404,bool),ord_less_eq(X3404),zero_zero(X3404)),X3405))
| ~ hBOOL(hAPP(X3404,bool,hAPP(X3404,fun(X3404,bool),ord_less_eq(X3404),zero_zero(X3404)),X3406))
| ~ ordere216010020id_add(X3404) )
& ( ti(X3404,X3405) = zero_zero(X3404)
| hAPP(X3404,X3404,hAPP(X3404,fun(X3404,X3404),plus_plus(X3404),X3406),X3405) != zero_zero(X3404)
| ~ hBOOL(hAPP(X3404,bool,hAPP(X3404,fun(X3404,bool),ord_less_eq(X3404),zero_zero(X3404)),X3405))
| ~ hBOOL(hAPP(X3404,bool,hAPP(X3404,fun(X3404,bool),ord_less_eq(X3404),zero_zero(X3404)),X3406))
| ~ ordere216010020id_add(X3404) )
& ( ti(X3404,X3406) != zero_zero(X3404)
| ti(X3404,X3405) != zero_zero(X3404)
| hAPP(X3404,X3404,hAPP(X3404,fun(X3404,X3404),plus_plus(X3404),X3406),X3405) = zero_zero(X3404)
| ~ hBOOL(hAPP(X3404,bool,hAPP(X3404,fun(X3404,bool),ord_less_eq(X3404),zero_zero(X3404)),X3405))
| ~ hBOOL(hAPP(X3404,bool,hAPP(X3404,fun(X3404,bool),ord_less_eq(X3404),zero_zero(X3404)),X3406))
| ~ ordere216010020id_add(X3404) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_462_add__nonneg__eq__0__iff])])])]) ).
fof(i_0_682,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_322_not__less__eq]) ).
fof(i_0_683,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_285_card_Oinsert]) ).
fof(i_0_684,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_685,plain,
! [X3212,X3213,X3214] :
( ( hBOOL(hAPP(fun(X3212,bool),bool,hAPP(fun(X3212,bool),fun(fun(X3212,bool),bool),ord_less_eq(fun(X3212,bool)),X3213),X3214))
| ~ hBOOL(hAPP(fun(X3212,bool),bool,hAPP(fun(X3212,bool),fun(fun(X3212,bool),bool),ord_less(fun(X3212,bool)),X3213),X3214)) )
& ( ti(fun(X3212,bool),X3213) != ti(fun(X3212,bool),X3214)
| ~ hBOOL(hAPP(fun(X3212,bool),bool,hAPP(fun(X3212,bool),fun(fun(X3212,bool),bool),ord_less(fun(X3212,bool)),X3213),X3214)) )
& ( ~ hBOOL(hAPP(fun(X3212,bool),bool,hAPP(fun(X3212,bool),fun(fun(X3212,bool),bool),ord_less_eq(fun(X3212,bool)),X3213),X3214))
| ti(fun(X3212,bool),X3213) = ti(fun(X3212,bool),X3214)
| hBOOL(hAPP(fun(X3212,bool),bool,hAPP(fun(X3212,bool),fun(fun(X3212,bool),bool),ord_less(fun(X3212,bool)),X3213),X3214)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_412_psubset__eq])])]) ).
fof(i_0_686,plain,
! [X3209,X3210,X3211] :
( ( ~ hBOOL(hAPP(fun(X3209,bool),bool,hAPP(fun(X3209,bool),fun(fun(X3209,bool),bool),ord_less_eq(fun(X3209,bool)),X3210),X3211))
| hBOOL(hAPP(fun(X3209,bool),bool,hAPP(fun(X3209,bool),fun(fun(X3209,bool),bool),ord_less(fun(X3209,bool)),X3210),X3211))
| ti(fun(X3209,bool),X3210) = ti(fun(X3209,bool),X3211) )
& ( ~ hBOOL(hAPP(fun(X3209,bool),bool,hAPP(fun(X3209,bool),fun(fun(X3209,bool),bool),ord_less(fun(X3209,bool)),X3210),X3211))
| hBOOL(hAPP(fun(X3209,bool),bool,hAPP(fun(X3209,bool),fun(fun(X3209,bool),bool),ord_less_eq(fun(X3209,bool)),X3210),X3211)) )
& ( ti(fun(X3209,bool),X3210) != ti(fun(X3209,bool),X3211)
| hBOOL(hAPP(fun(X3209,bool),bool,hAPP(fun(X3209,bool),fun(fun(X3209,bool),bool),ord_less_eq(fun(X3209,bool)),X3210),X3211)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_411_subset__iff__psubset__eq])])]) ).
fof(i_0_687,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_688,plain,
! [X3097,X3098,X3099] :
( ( hBOOL(hAPP(X3097,bool,hAPP(X3097,fun(X3097,bool),ord_less(X3097),X3098),X3099))
| ti(X3097,X3098) = ti(X3097,X3099)
| ~ hBOOL(hAPP(X3097,bool,hAPP(X3097,fun(X3097,bool),ord_less_eq(X3097),X3098),X3099))
| ~ linorder(X3097) )
& ( ti(X3097,X3098) != ti(X3097,X3099)
| ~ hBOOL(hAPP(X3097,bool,hAPP(X3097,fun(X3097,bool),ord_less(X3097),X3098),X3099))
| ~ hBOOL(hAPP(X3097,bool,hAPP(X3097,fun(X3097,bool),ord_less_eq(X3097),X3098),X3099))
| ~ linorder(X3097) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_611])])])]) ).
fof(i_0_689,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_690,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_366_less__le__not__le]) ).
fof(i_0_691,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_319_not__less__less__Suc__eq]) ).
fof(i_0_692,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_318_less__antisym]) ).
fof(i_0_693,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_314_less__SucE]) ).
fof(i_0_694,plain,
! [X2338,X2339,X2340] :
( ( hBOOL(hAPP(X2338,bool,hAPP(X2338,fun(X2338,bool),ord_less_eq(X2338),X2339),X2340))
| ti(X2338,X2339) != ti(X2338,X2340)
| ~ order(X2338) )
& ( hBOOL(hAPP(X2338,bool,hAPP(X2338,fun(X2338,bool),ord_less_eq(X2338),X2340),X2339))
| ti(X2338,X2339) != ti(X2338,X2340)
| ~ order(X2338) )
& ( ~ hBOOL(hAPP(X2338,bool,hAPP(X2338,fun(X2338,bool),ord_less_eq(X2338),X2339),X2340))
| ~ hBOOL(hAPP(X2338,bool,hAPP(X2338,fun(X2338,bool),ord_less_eq(X2338),X2340),X2339))
| ti(X2338,X2339) = ti(X2338,X2340)
| ~ order(X2338) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_order__eq__iff])])])]) ).
fof(i_0_695,plain,
! [X2332,X2333,X2334] :
( ( ~ hBOOL(hAPP(X2332,bool,hAPP(X2332,fun(X2332,bool),ord_less_eq(X2332),X2334),X2333))
| ti(X2332,X2334) = ti(X2332,X2333)
| ~ hBOOL(hAPP(X2332,bool,hAPP(X2332,fun(X2332,bool),ord_less_eq(X2332),X2333),X2334))
| ~ order(X2332) )
& ( ti(X2332,X2334) != ti(X2332,X2333)
| hBOOL(hAPP(X2332,bool,hAPP(X2332,fun(X2332,bool),ord_less_eq(X2332),X2334),X2333))
| ~ hBOOL(hAPP(X2332,bool,hAPP(X2332,fun(X2332,bool),ord_less_eq(X2332),X2333),X2334))
| ~ order(X2332) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_144_order__antisym__conv])])])]) ).
fof(i_0_696,plain,
! [X2313,X2314,X2315] :
( ~ order(X2313)
| ~ hBOOL(hAPP(X2313,bool,hAPP(X2313,fun(X2313,bool),ord_less_eq(X2313),X2314),X2315))
| ~ hBOOL(hAPP(X2313,bool,hAPP(X2313,fun(X2313,bool),ord_less_eq(X2313),X2315),X2314))
| ti(X2313,X2314) = ti(X2313,X2315) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_139_order__antisym])])]) ).
fof(i_0_697,plain,
! [X2306,X2307,X2308] :
( ~ order(X2306)
| ~ hBOOL(hAPP(X2306,bool,hAPP(X2306,fun(X2306,bool),ord_less_eq(X2306),X2307),X2308))
| ~ hBOOL(hAPP(X2306,bool,hAPP(X2306,fun(X2306,bool),ord_less_eq(X2306),X2308),X2307))
| ti(X2306,X2308) = ti(X2306,X2307) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_xt1_I5_J])])]) ).
fof(i_0_698,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_699,plain,
! [X2415,X2416,X2417,X2418] :
( ~ hBOOL(hAPP(fun(fun(X2415,bool),X2415),bool,hAPP(fun(X2415,fun(X2415,X2415)),fun(fun(fun(X2415,bool),X2415),bool),finite2073411215e_idem(X2415),X2417),X2418))
| hAPP(X2415,X2415,hAPP(X2415,fun(X2415,X2415),X2417,X2416),X2416) = ti(X2415,X2416) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_164_folding__one__idem_Oidem])]) ).
fof(i_0_700,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_363_linorder__not__le]) ).
fof(i_0_701,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_373_leD]) ).
fof(i_0_702,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_362_linorder__not__less]) ).
fof(i_0_703,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_350_order__less__asym]) ).
fof(i_0_704,plain,
! [X3] :
( preorder(X3)
=> ! [X49,X53] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X49)) ) ),
inference(fof_simplification,[status(thm)],[fact_342_order__less__asym_H]) ).
fof(i_0_705,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_338_order__less__imp__not__less]) ).
fof(i_0_706,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_337_order__less__not__sym]) ).
fof(i_0_707,plain,
! [X3] :
( order(X3)
=> ! [X53,X49] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X53),X49))
=> ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),X53)) ) ),
inference(fof_simplification,[status(thm)],[fact_343_xt1_I9_J]) ).
fof(i_0_708,plain,
! [X2324,X2325,X2326,X2327] :
( ~ order(X2324)
| ti(X2324,X2326) != ti(X2324,X2327)
| ~ hBOOL(hAPP(X2324,bool,hAPP(X2324,fun(X2324,bool),ord_less_eq(X2324),X2325),X2327))
| hBOOL(hAPP(X2324,bool,hAPP(X2324,fun(X2324,bool),ord_less_eq(X2324),X2325),X2326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_142_xt1_I3_J])])]) ).
fof(i_0_709,plain,
! [X2316,X2317,X2318,X2319] :
( ~ order(X2316)
| ~ hBOOL(hAPP(X2316,bool,hAPP(X2316,fun(X2316,bool),ord_less_eq(X2316),X2318),X2319))
| ti(X2316,X2318) != ti(X2316,X2317)
| hBOOL(hAPP(X2316,bool,hAPP(X2316,fun(X2316,bool),ord_less_eq(X2316),X2317),X2319)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_xt1_I4_J])])]) ).
fof(i_0_710,plain,
! [X2978,X2979,X2980] :
( ( hBOOL(hAPP(X2978,bool,hAPP(X2978,fun(X2978,bool),ord_less(X2978),X2980),X2979))
| ti(X2978,X2980) = ti(X2978,X2979)
| hBOOL(hAPP(X2978,bool,hAPP(X2978,fun(X2978,bool),ord_less(X2978),X2979),X2980))
| ~ linorder(X2978) )
& ( ti(X2978,X2980) != ti(X2978,X2979)
| ~ hBOOL(hAPP(X2978,bool,hAPP(X2978,fun(X2978,bool),ord_less(X2978),X2980),X2979))
| hBOOL(hAPP(X2978,bool,hAPP(X2978,fun(X2978,bool),ord_less(X2978),X2979),X2980))
| ~ linorder(X2978) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_612])])])]) ).
fof(i_0_711,plain,
! [X3013,X3014,X3015,X3016] :
( ~ order(X3013)
| ti(X3013,X3015) != ti(X3013,X3016)
| ~ hBOOL(hAPP(X3013,bool,hAPP(X3013,fun(X3013,bool),ord_less(X3013),X3014),X3016))
| hBOOL(hAPP(X3013,bool,hAPP(X3013,fun(X3013,bool),ord_less(X3013),X3014),X3015)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_345_xt1_I1_J])])]) ).
fof(i_0_712,plain,
! [X3021,X3022,X3023,X3024] :
( ~ order(X3021)
| ~ hBOOL(hAPP(X3021,bool,hAPP(X3021,fun(X3021,bool),ord_less(X3021),X3023),X3024))
| ti(X3021,X3023) != ti(X3021,X3022)
| hBOOL(hAPP(X3021,bool,hAPP(X3021,fun(X3021,bool),ord_less(X3021),X3022),X3024)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_347_xt1_I2_J])])]) ).
fof(i_0_713,plain,
! [X3082,X3083,X3084] :
( ( ~ hBOOL(hAPP(X3082,bool,hAPP(X3082,fun(X3082,bool),ord_less_eq(X3082),X3083),X3084))
| ti(X3082,X3083) = ti(X3082,X3084)
| hBOOL(hAPP(X3082,bool,hAPP(X3082,fun(X3082,bool),ord_less(X3082),X3083),X3084))
| ~ linorder(X3082) )
& ( ti(X3082,X3083) != ti(X3082,X3084)
| hBOOL(hAPP(X3082,bool,hAPP(X3082,fun(X3082,bool),ord_less_eq(X3082),X3083),X3084))
| hBOOL(hAPP(X3082,bool,hAPP(X3082,fun(X3082,bool),ord_less(X3082),X3083),X3084))
| ~ linorder(X3082) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_613])])])]) ).
fof(i_0_714,plain,
! [X3106,X3107,X3108] :
( ~ order(X3106)
| ~ hBOOL(hAPP(X3106,bool,hAPP(X3106,fun(X3106,bool),ord_less_eq(X3106),X3107),X3108))
| ti(X3106,X3108) = ti(X3106,X3107)
| hBOOL(hAPP(X3106,bool,hAPP(X3106,fun(X3106,bool),ord_less(X3106),X3107),X3108)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_378_xt1_I11_J])])]) ).
fof(i_0_715,plain,
! [X3103,X3104,X3105] :
( ~ order(X3103)
| ~ hBOOL(hAPP(X3103,bool,hAPP(X3103,fun(X3103,bool),ord_less_eq(X3103),X3104),X3105))
| ti(X3103,X3104) = ti(X3103,X3105)
| hBOOL(hAPP(X3103,bool,hAPP(X3103,fun(X3103,bool),ord_less(X3103),X3104),X3105)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_377_order__le__neq__trans])])]) ).
fof(i_0_716,plain,
! [X3100,X3101,X3102] :
( ~ order(X3100)
| ~ hBOOL(hAPP(X3100,bool,hAPP(X3100,fun(X3100,bool),ord_less_eq(X3100),X3101),X3102))
| hBOOL(hAPP(X3100,bool,hAPP(X3100,fun(X3100,bool),ord_less(X3100),X3101),X3102))
| ti(X3100,X3101) = ti(X3100,X3102) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_376_order__le__imp__less__or__eq])])]) ).
fof(i_0_717,plain,
! [X3085,X3086,X3087] :
( ~ order(X3085)
| ti(X3085,X3086) = ti(X3085,X3087)
| ~ hBOOL(hAPP(X3085,bool,hAPP(X3085,fun(X3085,bool),ord_less_eq(X3085),X3086),X3087))
| hBOOL(hAPP(X3085,bool,hAPP(X3085,fun(X3085,bool),ord_less(X3085),X3086),X3087)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_371_order__neq__le__trans])])]) ).
fof(i_0_718,plain,
! [X3073,X3074,X3075] :
( ( ~ hBOOL(hAPP(X3073,bool,hAPP(X3073,fun(X3073,bool),ord_less_eq(X3073),X3074),X3075))
| hBOOL(hAPP(X3073,bool,hAPP(X3073,fun(X3073,bool),ord_less(X3073),X3074),X3075))
| ti(X3073,X3074) = ti(X3073,X3075)
| ~ order(X3073) )
& ( ~ hBOOL(hAPP(X3073,bool,hAPP(X3073,fun(X3073,bool),ord_less(X3073),X3074),X3075))
| hBOOL(hAPP(X3073,bool,hAPP(X3073,fun(X3073,bool),ord_less_eq(X3073),X3074),X3075))
| ~ order(X3073) )
& ( ti(X3073,X3074) != ti(X3073,X3075)
| hBOOL(hAPP(X3073,bool,hAPP(X3073,fun(X3073,bool),ord_less_eq(X3073),X3074),X3075))
| ~ order(X3073) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_367_order__le__less])])])]) ).
fof(i_0_719,plain,
! [X3067,X3068,X3069] :
( ( hBOOL(hAPP(X3067,bool,hAPP(X3067,fun(X3067,bool),ord_less_eq(X3067),X3068),X3069))
| ~ hBOOL(hAPP(X3067,bool,hAPP(X3067,fun(X3067,bool),ord_less(X3067),X3068),X3069))
| ~ order(X3067) )
& ( ti(X3067,X3068) != ti(X3067,X3069)
| ~ hBOOL(hAPP(X3067,bool,hAPP(X3067,fun(X3067,bool),ord_less(X3067),X3068),X3069))
| ~ order(X3067) )
& ( ~ hBOOL(hAPP(X3067,bool,hAPP(X3067,fun(X3067,bool),ord_less_eq(X3067),X3068),X3069))
| ti(X3067,X3068) = ti(X3067,X3069)
| hBOOL(hAPP(X3067,bool,hAPP(X3067,fun(X3067,bool),ord_less(X3067),X3068),X3069))
| ~ order(X3067) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_365_order__less__le])])])]) ).
fof(i_0_720,plain,
! [X3088,X3089,X3090] :
( ~ order(X3088)
| ti(X3088,X3089) = ti(X3088,X3090)
| ~ hBOOL(hAPP(X3088,bool,hAPP(X3088,fun(X3088,bool),ord_less_eq(X3088),X3090),X3089))
| hBOOL(hAPP(X3088,bool,hAPP(X3088,fun(X3088,bool),ord_less(X3088),X3090),X3089)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_372_xt1_I12_J])])]) ).
fof(i_0_721,plain,
! [X2370,X2371,X2374,X2375,X2376,X2377] :
( ( ti(fun(X2370,bool),X2371) = hAPP(fun(X2370,bool),fun(X2370,bool),hAPP(X2370,fun(fun(X2370,bool),fun(X2370,bool)),insert(X2370),esk27_2(X2370,X2371)),esk28_2(X2370,X2371))
| ti(fun(X2370,bool),X2371) = bot_bot(fun(X2370,bool)) )
& ( ~ hBOOL(hAPP(fun(X2370,bool),bool,hAPP(X2370,fun(fun(X2370,bool),bool),member(X2370),esk27_2(X2370,X2371)),esk28_2(X2370,X2371)))
| ti(fun(X2370,bool),X2371) = bot_bot(fun(X2370,bool)) )
& ( ti(fun(X2374,bool),X2375) != hAPP(fun(X2374,bool),fun(X2374,bool),hAPP(X2374,fun(fun(X2374,bool),fun(X2374,bool)),insert(X2374),X2376),X2377)
| hBOOL(hAPP(fun(X2374,bool),bool,hAPP(X2374,fun(fun(X2374,bool),bool),member(X2374),X2376),X2377))
| ti(fun(X2374,bool),X2375) != bot_bot(fun(X2374,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_614])])])])])]) ).
fof(i_0_722,plain,
! [X2791,X2792,X2793] :
( ~ group_add(X2791)
| hAPP(X2791,X2791,hAPP(X2791,fun(X2791,X2791),plus_plus(X2791),hAPP(X2791,X2791,hAPP(X2791,fun(X2791,X2791),minus_minus(X2791),X2792),X2793)),X2793) = ti(X2791,X2792) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_266_diff__add__cancel])])]) ).
fof(i_0_723,plain,
! [X2794,X2795,X2796] :
( ~ group_add(X2794)
| hAPP(X2794,X2794,hAPP(X2794,fun(X2794,X2794),minus_minus(X2794),hAPP(X2794,X2794,hAPP(X2794,fun(X2794,X2794),plus_plus(X2794),X2795),X2796)),X2796) = ti(X2794,X2795) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_267_add__diff__cancel])])]) ).
fof(i_0_724,plain,
! [X2029,X2030,X2031] :
( ~ hBOOL(hAPP(fun(X2029,bool),bool,hAPP(X2029,fun(fun(X2029,bool),bool),member(X2029),X2030),X2031))
| hAPP(fun(X2029,bool),fun(X2029,bool),hAPP(X2029,fun(fun(X2029,bool),fun(X2029,bool)),insert(X2029),X2030),X2031) = ti(fun(X2029,bool),X2031) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_insert__absorb])]) ).
fof(i_0_725,plain,
! [X2244,X2245,X2246] :
( hAPP(fun(X2244,bool),fun(X2244,bool),hAPP(X2244,fun(fun(X2244,bool),fun(X2244,bool)),insert(X2244),X2245),bot_bot(fun(X2244,bool))) != hAPP(fun(X2244,bool),fun(X2244,bool),hAPP(X2244,fun(fun(X2244,bool),fun(X2244,bool)),insert(X2244),X2246),bot_bot(fun(X2244,bool)))
| ti(X2244,X2245) = ti(X2244,X2246) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_118_singleton__inject])]) ).
fof(i_0_726,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_400_add__diff__inverse]) ).
fof(i_0_727,plain,
! [X2497,X2498,X2499,X2500,X2501] :
( ( ti(X2497,X2498) != ti(X2497,X2499)
| ti(X2497,X2500) = ti(X2497,X2501)
| hAPP(X2497,X2497,hAPP(X2497,fun(X2497,X2497),minus_minus(X2497),X2498),X2499) != hAPP(X2497,X2497,hAPP(X2497,fun(X2497,X2497),minus_minus(X2497),X2500),X2501)
| ~ ab_group_add(X2497) )
& ( ti(X2497,X2500) != ti(X2497,X2501)
| ti(X2497,X2498) = ti(X2497,X2499)
| hAPP(X2497,X2497,hAPP(X2497,fun(X2497,X2497),minus_minus(X2497),X2498),X2499) != hAPP(X2497,X2497,hAPP(X2497,fun(X2497,X2497),minus_minus(X2497),X2500),X2501)
| ~ ab_group_add(X2497) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_diff__eq__diff__eq])])])]) ).
fof(i_0_728,plain,
! [X2264,X2265] :
( ( ~ hBOOL(hAPP(fun(X2264,bool),bool,hAPP(fun(X2264,bool),fun(fun(X2264,bool),bool),ord_less_eq(fun(X2264,bool)),X2265),bot_bot(fun(X2264,bool))))
| ti(fun(X2264,bool),X2265) = bot_bot(fun(X2264,bool)) )
& ( ti(fun(X2264,bool),X2265) != bot_bot(fun(X2264,bool))
| hBOOL(hAPP(fun(X2264,bool),bool,hAPP(fun(X2264,bool),fun(fun(X2264,bool),bool),ord_less_eq(fun(X2264,bool)),X2265),bot_bot(fun(X2264,bool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_124_subset__empty])]) ).
fof(i_0_729,plain,
! [X2295,X2296,X2297,X2298] :
( ( ti(fun(X2296,bool),X2298) != bot_bot(fun(X2296,bool))
| hAPP(fun(X2296,bool),fun(X2295,bool),hAPP(fun(X2296,X2295),fun(fun(X2296,bool),fun(X2295,bool)),image(X2296,X2295),hAPP(X2295,fun(X2296,X2295),combk(X2295,X2296),X2297)),X2298) = bot_bot(fun(X2295,bool)) )
& ( ti(fun(X2296,bool),X2298) = bot_bot(fun(X2296,bool))
| hAPP(fun(X2296,bool),fun(X2295,bool),hAPP(fun(X2296,X2295),fun(fun(X2296,bool),fun(X2295,bool)),image(X2296,X2295),hAPP(X2295,fun(X2296,X2295),combk(X2295,X2296),X2297)),X2298) = hAPP(fun(X2295,bool),fun(X2295,bool),hAPP(X2295,fun(fun(X2295,bool),fun(X2295,bool)),insert(X2295),X2297),bot_bot(fun(X2295,bool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_image__constant__conv])]) ).
fof(i_0_730,plain,
! [X3259,X3260,X3261] :
( ~ linordered_idom(X3259)
| ti(X3259,X3260) = ti(X3259,X3261)
| hBOOL(hAPP(X3259,bool,hAPP(X3259,fun(X3259,bool),ord_less(X3259),X3260),X3261))
| hBOOL(hAPP(X3259,bool,hAPP(X3259,fun(X3259,bool),ord_less(X3259),X3261),X3260)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_615])])]) ).
fof(i_0_731,plain,
! [X3036,X3037,X3038] :
( ~ linorder(X3036)
| hBOOL(hAPP(X3036,bool,hAPP(X3036,fun(X3036,bool),ord_less(X3036),X3037),X3038))
| ti(X3036,X3037) = ti(X3036,X3038)
| hBOOL(hAPP(X3036,bool,hAPP(X3036,fun(X3036,bool),ord_less(X3036),X3038),X3037)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_616])])]) ).
fof(i_0_732,plain,
! [X2981,X2982,X2983] :
( ~ linorder(X2981)
| ti(X2981,X2982) = ti(X2981,X2983)
| hBOOL(hAPP(X2981,bool,hAPP(X2981,fun(X2981,bool),ord_less(X2981),X2982),X2983))
| hBOOL(hAPP(X2981,bool,hAPP(X2981,fun(X2981,bool),ord_less(X2981),X2983),X2982)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_617])])]) ).
fof(i_0_733,plain,
! [X2975,X2976,X2977] :
( ~ linorder(X2975)
| hBOOL(hAPP(X2975,bool,hAPP(X2975,fun(X2975,bool),ord_less(X2975),X2976),X2977))
| ti(X2975,X2976) = ti(X2975,X2977)
| hBOOL(hAPP(X2975,bool,hAPP(X2975,fun(X2975,bool),ord_less(X2975),X2977),X2976)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_333_linorder__less__linear])])]) ).
fof(i_0_734,plain,
! [X2972,X2973,X2974] :
( ( hBOOL(hAPP(X2972,bool,hAPP(X2972,fun(X2972,bool),ord_less(X2972),X2973),X2974))
| hBOOL(hAPP(X2972,bool,hAPP(X2972,fun(X2972,bool),ord_less(X2972),X2974),X2973))
| ti(X2972,X2973) = ti(X2972,X2974)
| ~ linorder(X2972) )
& ( ~ hBOOL(hAPP(X2972,bool,hAPP(X2972,fun(X2972,bool),ord_less(X2972),X2974),X2973))
| ~ hBOOL(hAPP(X2972,bool,hAPP(X2972,fun(X2972,bool),ord_less(X2972),X2973),X2974))
| ~ linorder(X2972) )
& ( ti(X2972,X2973) != ti(X2972,X2974)
| ~ hBOOL(hAPP(X2972,bool,hAPP(X2972,fun(X2972,bool),ord_less(X2972),X2973),X2974))
| ~ linorder(X2972) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_618])])])]) ).
fof(i_0_735,plain,
! [X2969,X2970,X2971] :
( ( ti(X2969,X2970) = ti(X2969,X2971)
| hBOOL(hAPP(X2969,bool,hAPP(X2969,fun(X2969,bool),ord_less(X2969),X2970),X2971))
| hBOOL(hAPP(X2969,bool,hAPP(X2969,fun(X2969,bool),ord_less(X2969),X2971),X2970))
| ~ linorder(X2969) )
& ( ~ hBOOL(hAPP(X2969,bool,hAPP(X2969,fun(X2969,bool),ord_less(X2969),X2970),X2971))
| ti(X2969,X2970) != ti(X2969,X2971)
| ~ linorder(X2969) )
& ( ~ hBOOL(hAPP(X2969,bool,hAPP(X2969,fun(X2969,bool),ord_less(X2969),X2971),X2970))
| ti(X2969,X2970) != ti(X2969,X2971)
| ~ linorder(X2969) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_331_linorder__neq__iff])])])]) ).
fof(i_0_736,plain,
! [X2633,X2634,X2635,X2636] :
( ( hBOOL(hAPP(X2633,bool,X2635,esk43_4(X2633,X2634,X2635,X2636)))
| ~ hBOOL(hAPP(X2633,bool,X2635,X2636))
| ~ hBOOL(hAPP(X2633,bool,X2635,X2634))
| hAPP(fun(X2633,bool),X2633,the(X2633),X2635) = ti(X2633,X2634) )
& ( ti(X2633,esk43_4(X2633,X2634,X2635,X2636)) != ti(X2633,X2636)
| ~ hBOOL(hAPP(X2633,bool,X2635,X2636))
| ~ hBOOL(hAPP(X2633,bool,X2635,X2634))
| hAPP(fun(X2633,bool),X2633,the(X2633),X2635) = ti(X2633,X2634) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_216_the1__equality])])])])]) ).
fof(i_0_737,plain,
! [X2357,X2358,X2361,X2362,X2363,X2364] :
( ( ti(fun(X2357,bool),X2358) = hAPP(fun(X2357,bool),fun(X2357,bool),hAPP(X2357,fun(fun(X2357,bool),fun(X2357,bool)),insert(X2357),esk25_2(X2357,X2358)),esk24_2(X2357,X2358))
| ti(fun(X2357,bool),X2358) = bot_bot(fun(X2357,bool))
| ~ hBOOL(hAPP(fun(X2357,bool),bool,finite_finite(X2357),X2358)) )
& ( hBOOL(hAPP(fun(X2357,bool),bool,finite_finite(X2357),esk24_2(X2357,X2358)))
| ti(fun(X2357,bool),X2358) = bot_bot(fun(X2357,bool))
| ~ hBOOL(hAPP(fun(X2357,bool),bool,finite_finite(X2357),X2358)) )
& ( ti(fun(X2361,bool),X2362) != bot_bot(fun(X2361,bool))
| hBOOL(hAPP(fun(X2361,bool),bool,finite_finite(X2361),X2362)) )
& ( ti(fun(X2361,bool),X2362) != hAPP(fun(X2361,bool),fun(X2361,bool),hAPP(X2361,fun(fun(X2361,bool),fun(X2361,bool)),insert(X2361),X2364),X2363)
| ~ hBOOL(hAPP(fun(X2361,bool),bool,finite_finite(X2361),X2363))
| hBOOL(hAPP(fun(X2361,bool),bool,finite_finite(X2361),X2362)) ) ),
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_151_finite_Osimps])])])])])]) ).
fof(i_0_738,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_413_not__psubset__empty]) ).
fof(i_0_739,plain,
! [X2225,X2226,X2228,X2229,X2230] :
( ( hBOOL(hAPP(fun(X2225,bool),bool,hAPP(X2225,fun(fun(X2225,bool),bool),member(X2225),esk19_2(X2225,X2226)),X2226))
| ti(fun(X2225,bool),X2226) = bot_bot(fun(X2225,bool)) )
& ( ti(fun(X2228,bool),X2229) != bot_bot(fun(X2228,bool))
| ~ hBOOL(hAPP(fun(X2228,bool),bool,hAPP(X2228,fun(fun(X2228,bool),bool),member(X2228),X2230),X2229)) ) ),
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_619])])])])]) ).
fof(i_0_740,plain,
! [X2202,X2203,X2204] :
( ti(fun(X2202,bool),X2204) != bot_bot(fun(X2202,bool))
| ~ hBOOL(hAPP(fun(X2202,bool),bool,hAPP(X2202,fun(fun(X2202,bool),bool),member(X2202),X2203),X2204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_620])]) ).
fof(i_0_741,plain,
! [X2219,X2220,X2221,X2222,X2223] :
( ( ~ hBOOL(hAPP(fun(X2219,bool),bool,hAPP(X2219,fun(fun(X2219,bool),bool),member(X2219),X2221),X2220))
| ti(fun(X2219,bool),X2220) != bot_bot(fun(X2219,bool)) )
& ( ti(fun(X2222,bool),X2223) = bot_bot(fun(X2222,bool))
| hBOOL(hAPP(fun(X2222,bool),bool,hAPP(X2222,fun(fun(X2222,bool),bool),member(X2222),esk18_2(X2222,X2223)),X2223)) ) ),
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_110_ex__in__conv])])])])]) ).
fof(i_0_742,plain,
! [X2629,X2630,X2631] :
( ( hBOOL(hAPP(X2629,bool,X2630,esk42_3(X2629,X2630,X2631)))
| ~ hBOOL(hAPP(X2629,bool,X2630,X2631))
| hBOOL(hAPP(X2629,bool,X2630,hAPP(fun(X2629,bool),X2629,the(X2629),X2630))) )
& ( ti(X2629,esk42_3(X2629,X2630,X2631)) != ti(X2629,X2631)
| ~ hBOOL(hAPP(X2629,bool,X2630,X2631))
| hBOOL(hAPP(X2629,bool,X2630,hAPP(fun(X2629,bool),X2629,the(X2629),X2630))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_215_theI_H])])])])]) ).
fof(i_0_743,plain,
! [X2625,X2626,X2627] :
( ( hBOOL(hAPP(X2625,bool,X2626,esk41_3(X2625,X2626,X2627)))
| hBOOL(hAPP(X2625,bool,X2626,hAPP(fun(X2625,bool),X2625,the(X2625),X2626)))
| ~ hBOOL(hAPP(X2625,bool,X2626,X2627)) )
& ( ti(X2625,esk41_3(X2625,X2626,X2627)) != ti(X2625,X2627)
| hBOOL(hAPP(X2625,bool,X2626,hAPP(fun(X2625,bool),X2625,the(X2625),X2626)))
| ~ hBOOL(hAPP(X2625,bool,X2626,X2627)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_214_theI])])])]) ).
fof(i_0_744,plain,
! [X2996,X2997,X2998] :
( ~ order(X2996)
| ~ hBOOL(hAPP(X2996,bool,hAPP(X2996,fun(X2996,bool),ord_less(X2996),X2997),X2998))
| ti(X2996,X2998) != ti(X2996,X2997) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_340_order__less__imp__not__eq2])])]) ).
fof(i_0_745,plain,
! [X2993,X2994,X2995] :
( ~ order(X2993)
| ~ hBOOL(hAPP(X2993,bool,hAPP(X2993,fun(X2993,bool),ord_less(X2993),X2994),X2995))
| ti(X2993,X2994) != ti(X2993,X2995) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_339_order__less__imp__not__eq])])]) ).
fof(i_0_746,plain,
! [X2984,X2985,X2986] :
( ~ order(X2984)
| ~ hBOOL(hAPP(X2984,bool,hAPP(X2984,fun(X2984,bool),ord_less(X2984),X2985),X2986))
| ti(X2984,X2985) != ti(X2984,X2986) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_336_less__imp__neq])])]) ).
fof(i_0_747,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_135_linorder__le__cases]) ).
fof(i_0_748,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_368_leI]) ).
fof(i_0_749,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_369_not__leE]) ).
fof(i_0_750,plain,
! [X2069,X2070,X2071] :
( ( hBOOL(hAPP(fun(X2069,bool),bool,hAPP(fun(X2069,bool),fun(fun(X2069,bool),bool),ord_less_eq(fun(X2069,bool)),X2070),X2071))
| ti(fun(X2069,bool),X2070) != ti(fun(X2069,bool),X2071) )
& ( hBOOL(hAPP(fun(X2069,bool),bool,hAPP(fun(X2069,bool),fun(fun(X2069,bool),bool),ord_less_eq(fun(X2069,bool)),X2071),X2070))
| ti(fun(X2069,bool),X2070) != ti(fun(X2069,bool),X2071) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_621])])]) ).
fof(i_0_751,plain,
! [X2037,X2038,X2039] :
( ti(fun(X2037,bool),X2038) != ti(fun(X2037,bool),X2039)
| hBOOL(hAPP(fun(X2037,bool),bool,hAPP(fun(X2037,bool),fun(fun(X2037,bool),bool),ord_less_eq(fun(X2037,bool)),X2038),X2039)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_equalityD1])]) ).
fof(i_0_752,plain,
! [X2040,X2041,X2042] :
( ti(fun(X2040,bool),X2041) != ti(fun(X2040,bool),X2042)
| hBOOL(hAPP(fun(X2040,bool),bool,hAPP(fun(X2040,bool),fun(fun(X2040,bool),bool),ord_less_eq(fun(X2040,bool)),X2042),X2041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_equalityD2])]) ).
fof(i_0_753,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_355_linorder__neqE__nat]) ).
fof(i_0_754,plain,
! [X2601,X2602] : hAPP(fun(X2601,bool),X2601,the(X2601),hAPP(X2601,fun(X2601,bool),hAPP(fun(X2601,fun(X2601,bool)),fun(X2601,fun(X2601,bool)),combc(X2601,X2601,bool),fequal(X2601)),X2602)) = ti(X2601,X2602),
inference(variable_rename,[status(thm)],[fact_209_the__eq__trivial]) ).
fof(i_0_755,plain,
! [X2731,X2732,X2733,X2734] :
( ( hAPP(X2731,X2731,hAPP(X2731,fun(X2731,X2731),plus_plus(X2731),X2732),X2733) != hAPP(X2731,X2731,hAPP(X2731,fun(X2731,X2731),plus_plus(X2731),X2734),X2733)
| ti(X2731,X2732) = ti(X2731,X2734)
| ~ cancel_semigroup_add(X2731) )
& ( ti(X2731,X2732) != ti(X2731,X2734)
| hAPP(X2731,X2731,hAPP(X2731,fun(X2731,X2731),plus_plus(X2731),X2732),X2733) = hAPP(X2731,X2731,hAPP(X2731,fun(X2731,X2731),plus_plus(X2731),X2734),X2733)
| ~ cancel_semigroup_add(X2731) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_247_add__right__cancel])])])]) ).
fof(i_0_756,plain,
! [X2719,X2720,X2721,X2722] :
( ~ cancel_semigroup_add(X2719)
| hAPP(X2719,X2719,hAPP(X2719,fun(X2719,X2719),plus_plus(X2719),X2720),X2721) != hAPP(X2719,X2719,hAPP(X2719,fun(X2719,X2719),plus_plus(X2719),X2722),X2721)
| ti(X2719,X2720) = ti(X2719,X2722) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_244_add__right__imp__eq])])]) ).
fof(i_0_757,plain,
! [X2723,X2724,X2725,X2726] :
( ~ cancel146912293up_add(X2723)
| hAPP(X2723,X2723,hAPP(X2723,fun(X2723,X2723),plus_plus(X2723),X2724),X2725) != hAPP(X2723,X2723,hAPP(X2723,fun(X2723,X2723),plus_plus(X2723),X2724),X2726)
| ti(X2723,X2725) = ti(X2723,X2726) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_245_add__imp__eq])])]) ).
fof(i_0_758,plain,
! [X2735,X2736,X2737,X2738] :
( ( hAPP(X2735,X2735,hAPP(X2735,fun(X2735,X2735),plus_plus(X2735),X2736),X2737) != hAPP(X2735,X2735,hAPP(X2735,fun(X2735,X2735),plus_plus(X2735),X2736),X2738)
| ti(X2735,X2737) = ti(X2735,X2738)
| ~ cancel_semigroup_add(X2735) )
& ( ti(X2735,X2737) != ti(X2735,X2738)
| hAPP(X2735,X2735,hAPP(X2735,fun(X2735,X2735),plus_plus(X2735),X2736),X2737) = hAPP(X2735,X2735,hAPP(X2735,fun(X2735,X2735),plus_plus(X2735),X2736),X2738)
| ~ cancel_semigroup_add(X2735) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_248_add__left__cancel])])])]) ).
fof(i_0_759,plain,
! [X2727,X2728,X2729,X2730] :
( ~ cancel_semigroup_add(X2727)
| hAPP(X2727,X2727,hAPP(X2727,fun(X2727,X2727),plus_plus(X2727),X2728),X2729) != hAPP(X2727,X2727,hAPP(X2727,fun(X2727,X2727),plus_plus(X2727),X2728),X2730)
| ti(X2727,X2729) = ti(X2727,X2730) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_246_add__left__imp__eq])])]) ).
fof(i_0_760,plain,
! [X2055,X2056,X2057,X2058] :
( hAPP(X2055,X2056,X2057,esk6_4(X2055,X2056,X2057,X2058)) != hAPP(X2055,X2056,X2058,esk6_4(X2055,X2056,X2057,X2058))
| ti(fun(X2055,X2056),X2057) = ti(fun(X2055,X2056),X2058) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_74_ext])])]) ).
fof(i_0_761,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_108_empty__iff]) ).
fof(i_0_762,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_103_emptyE]) ).
fof(i_0_763,plain,
! [X3524,X3525,X3526] :
( ~ hBOOL(hAPP(X3524,bool,hAPP(X3524,fun(X3524,bool),fequal(X3524),X3525),X3526))
| ti(X3524,X3525) = ti(X3524,X3526) ),
inference(variable_rename,[status(thm)],[i_0_622]) ).
fof(i_0_764,plain,
! [X3056,X3057] :
( ( ti(X3056,X3057) = bot_bot(X3056)
| hBOOL(hAPP(X3056,bool,hAPP(X3056,fun(X3056,bool),ord_less(X3056),bot_bot(X3056)),X3057))
| ~ bot(X3056) )
& ( ~ hBOOL(hAPP(X3056,bool,hAPP(X3056,fun(X3056,bool),ord_less(X3056),bot_bot(X3056)),X3057))
| ti(X3056,X3057) != bot_bot(X3056)
| ~ bot(X3056) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_361_bot__less])])])]) ).
fof(i_0_765,plain,
! [X2240,X2241] :
( ( ~ hBOOL(hAPP(X2240,bool,hAPP(X2240,fun(X2240,bool),ord_less_eq(X2240),X2241),bot_bot(X2240)))
| ti(X2240,X2241) = bot_bot(X2240)
| ~ bot(X2240) )
& ( ti(X2240,X2241) != bot_bot(X2240)
| hBOOL(hAPP(X2240,bool,hAPP(X2240,fun(X2240,bool),ord_less_eq(X2240),X2241),bot_bot(X2240)))
| ~ bot(X2240) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_116_bot__unique])])])]) ).
fof(i_0_766,plain,
! [X2238,X2239] :
( ~ bot(X2238)
| ~ hBOOL(hAPP(X2238,bool,hAPP(X2238,fun(X2238,bool),ord_less_eq(X2238),X2239),bot_bot(X2238)))
| ti(X2238,X2239) = bot_bot(X2238) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_115_le__bot])])]) ).
fof(i_0_767,plain,
! [X2368,X2369] : hAPP(fun(X2368,bool),X2368,the_elem(X2368),hAPP(fun(X2368,bool),fun(X2368,bool),hAPP(X2368,fun(fun(X2368,bool),fun(X2368,bool)),insert(X2368),X2369),bot_bot(fun(X2368,bool)))) = ti(X2368,X2369),
inference(variable_rename,[status(thm)],[fact_153_the__elem__eq]) ).
fof(i_0_768,plain,
! [X3373,X3374,X3375,X3376] :
( ( ti(fun(X3374,bool),X3375) = bot_bot(fun(X3374,bool))
| hAPP(fun(X3373,bool),fun(sum_sum(X3374,X3373),bool),hAPP(fun(X3374,bool),fun(fun(X3373,bool),fun(sum_sum(X3374,X3373),bool)),sum_Plus(X3374,X3373),X3375),X3376) != bot_bot(fun(sum_sum(X3374,X3373),bool)) )
& ( ti(fun(X3373,bool),X3376) = bot_bot(fun(X3373,bool))
| hAPP(fun(X3373,bool),fun(sum_sum(X3374,X3373),bool),hAPP(fun(X3374,bool),fun(fun(X3373,bool),fun(sum_sum(X3374,X3373),bool)),sum_Plus(X3374,X3373),X3375),X3376) != bot_bot(fun(sum_sum(X3374,X3373),bool)) )
& ( ti(fun(X3374,bool),X3375) != bot_bot(fun(X3374,bool))
| ti(fun(X3373,bool),X3376) != bot_bot(fun(X3373,bool))
| hAPP(fun(X3373,bool),fun(sum_sum(X3374,X3373),bool),hAPP(fun(X3374,bool),fun(fun(X3373,bool),fun(sum_sum(X3374,X3373),bool)),sum_Plus(X3374,X3373),X3375),X3376) = bot_bot(fun(sum_sum(X3374,X3373),bool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_445_Plus__eq__empty__conv])])]) ).
fof(i_0_769,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_455_not__one__le__zero]) ).
fof(i_0_770,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_453_not__one__less__zero]) ).
fof(i_0_771,plain,
! [X3456,X3457,X3458] : hAPP(nat,X3456,hAPP(fun(nat,X3456),fun(nat,X3456),hAPP(X3456,fun(fun(nat,X3456),fun(nat,X3456)),nat_case(X3456),X3457),X3458),zero_zero(nat)) = ti(X3456,X3457),
inference(variable_rename,[status(thm)],[fact_491_nat__case__0]) ).
fof(i_0_772,plain,
! [X3] :
( bot(X3)
=> ! [X49] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X49),bot_bot(X3))) ),
inference(fof_simplification,[status(thm)],[fact_360_not__less__bot]) ).
fof(i_0_773,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_330_order__less__irrefl]) ).
fof(i_0_774,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[fact_447_less__zeroE]) ).
fof(i_0_775,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_356_less__irrefl__nat]) ).
fof(i_0_776,plain,
! [X17] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_353_less__not__refl]) ).
fof(i_0_777,plain,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X80),X81))
| ~ hBOOL(X80)
| hBOOL(X81) ),
inference(fof_simplification,[status(thm)],[help_fimplies_3_1_U]) ).
fof(i_0_778,plain,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X80),X81))
| hBOOL(X80)
| hBOOL(X81) ),
inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).
fof(i_0_779,plain,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X80),X81))
| hBOOL(X80) ),
inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).
fof(i_0_780,plain,
! [X80,X81] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X80),X81))
| hBOOL(X81) ),
inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).
fof(i_0_781,plain,
! [X3527,X3528,X3529] :
( ti(X3527,X3528) != ti(X3527,X3529)
| hBOOL(hAPP(X3527,bool,hAPP(X3527,fun(X3527,bool),fequal(X3527),X3528),X3529)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_T]) ).
fof(i_0_782,plain,
! [X1822,X1823] : ti(fun(fun(X1822,bool),fun(fun(X1823,bool),fun(sum_sum(X1822,X1823),bool))),sum_Plus(X1822,X1823)) = sum_Plus(X1822,X1823),
inference(variable_rename,[status(thm)],[tsy_c_Sum__Type_OPlus_res]) ).
fof(i_0_783,plain,
! [X1803] : ti(fun(fun(X1803,fun(X1803,X1803)),fun(fun(fun(X1803,bool),X1803),bool)),finite2073411215e_idem(X1803)) = finite2073411215e_idem(X1803),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__one__idem_res]) ).
fof(i_0_784,plain,
! [X1802] : ti(fun(fun(X1802,fun(X1802,X1802)),fun(fun(fun(X1802,bool),X1802),bool)),finite_folding_one(X1802)) = finite_folding_one(X1802),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__one_res]) ).
fof(i_0_785,plain,
! [X2603,X2604,X2605] :
( ( hBOOL(hAPP(X2603,bool,X2604,esk39_3(X2603,X2604,X2605)))
| hAPP(fun(X2603,bool),X2603,the(X2603),X2604) = ti(X2603,X2605)
| ~ hBOOL(hAPP(X2603,bool,X2604,X2605)) )
& ( ti(X2603,esk39_3(X2603,X2604,X2605)) != ti(X2603,X2605)
| hAPP(fun(X2603,bool),X2603,the(X2603),X2604) = ti(X2603,X2605)
| ~ hBOOL(hAPP(X2603,bool,X2604,X2605)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_210_the__equality])])])]) ).
fof(i_0_786,plain,
! [X2266,X2267,X2268,X2269] :
( ( hAPP(fun(X2266,bool),fun(X2267,bool),hAPP(fun(X2266,X2267),fun(fun(X2266,bool),fun(X2267,bool)),image(X2266,X2267),X2268),X2269) != bot_bot(fun(X2267,bool))
| ti(fun(X2266,bool),X2269) = bot_bot(fun(X2266,bool)) )
& ( ti(fun(X2266,bool),X2269) != bot_bot(fun(X2266,bool))
| hAPP(fun(X2266,bool),fun(X2267,bool),hAPP(fun(X2266,X2267),fun(fun(X2266,bool),fun(X2267,bool)),image(X2266,X2267),X2268),X2269) = bot_bot(fun(X2267,bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_125_image__is__empty])]) ).
fof(i_0_787,plain,
! [X2273,X2274,X2275,X2276] :
( ( bot_bot(fun(X2273,bool)) != hAPP(fun(X2274,bool),fun(X2273,bool),hAPP(fun(X2274,X2273),fun(fun(X2274,bool),fun(X2273,bool)),image(X2274,X2273),X2275),X2276)
| ti(fun(X2274,bool),X2276) = bot_bot(fun(X2274,bool)) )
& ( ti(fun(X2274,bool),X2276) != bot_bot(fun(X2274,bool))
| bot_bot(fun(X2273,bool)) = hAPP(fun(X2274,bool),fun(X2273,bool),hAPP(fun(X2274,X2273),fun(fun(X2274,bool),fun(X2273,bool)),image(X2274,X2273),X2275),X2276) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_127_empty__is__image])]) ).
fof(i_0_788,plain,
! [X1793,X1794,X1795] : ti(fun(fun(X1793,fun(X1794,X1795)),fun(fun(X1793,X1794),fun(X1793,X1795))),combs(X1793,X1794,X1795)) = combs(X1793,X1794,X1795),
inference(variable_rename,[status(thm)],[tsy_c_COMBS_res]) ).
fof(i_0_789,plain,
! [X3443,X3444,X3445] :
( ( hAPP(X3443,X3443,hAPP(X3443,fun(X3443,X3443),minus_minus(X3443),X3444),X3445) != zero_zero(X3443)
| ti(X3443,X3444) = ti(X3443,X3445)
| ~ group_add(X3443) )
& ( ti(X3443,X3444) != ti(X3443,X3445)
| hAPP(X3443,X3443,hAPP(X3443,fun(X3443,X3443),minus_minus(X3443),X3444),X3445) = zero_zero(X3443)
| ~ group_add(X3443) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_right__minus__eq])])])]) ).
fof(i_0_790,plain,
! [X3440,X3441,X3442] :
( ( ti(X3440,X3441) != ti(X3440,X3442)
| hAPP(X3440,X3440,hAPP(X3440,fun(X3440,X3440),minus_minus(X3440),X3441),X3442) = zero_zero(X3440)
| ~ ab_group_add(X3440) )
& ( hAPP(X3440,X3440,hAPP(X3440,fun(X3440,X3440),minus_minus(X3440),X3441),X3442) != zero_zero(X3440)
| ti(X3440,X3441) = ti(X3440,X3442)
| ~ ab_group_add(X3440) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_479_eq__iff__diff__eq__0])])])]) ).
fof(i_0_791,plain,
! [X1787,X1788,X1789] : ti(fun(fun(X1787,fun(X1788,X1789)),fun(X1788,fun(X1787,X1789))),combc(X1787,X1788,X1789)) = combc(X1787,X1788,X1789),
inference(variable_rename,[status(thm)],[tsy_c_COMBC_res]) ).
fof(i_0_792,plain,
! [X1784,X1785,X1786] : ti(fun(fun(X1784,X1785),fun(fun(X1786,X1784),fun(X1786,X1785))),combb(X1784,X1785,X1786)) = combb(X1784,X1785,X1786),
inference(variable_rename,[status(thm)],[tsy_c_COMBB_res]) ).
fof(i_0_793,plain,
! [X2421,X2422] : hAPP(fun(X2421,bool),fun(X2421,bool),hAPP(fun(X2421,bool),fun(fun(X2421,bool),fun(X2421,bool)),minus_minus(fun(X2421,bool)),X2422),bot_bot(fun(X2421,bool))) = ti(fun(X2421,bool),X2422),
inference(variable_rename,[status(thm)],[fact_166_Diff__empty]) ).
fof(i_0_794,plain,
! [X81,X80] :
( ~ hBOOL(X80)
| ~ hBOOL(X81)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X80),X81)) ),
inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).
fof(i_0_795,plain,
! [X80,X81] :
( ~ hBOOL(X81)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X80),X81)) ),
inference(fof_simplification,[status(thm)],[help_fimplies_2_1_U]) ).
fof(i_0_796,plain,
! [X81,X80] :
( ~ hBOOL(X80)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X80),X81)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).
fof(i_0_797,plain,
! [X80,X81] :
( ~ hBOOL(X81)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X80),X81)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).
fof(i_0_798,plain,
! [X1818,X1819] : ti(fun(fun(X1818,X1819),fun(fun(X1818,bool),fun(X1819,bool))),image(X1818,X1819)) = image(X1818,X1819),
inference(variable_rename,[status(thm)],[tsy_c_Set_Oimage_res]) ).
fof(i_0_799,plain,
! [X3463,X3464] :
( ( zero_zero(X3463) != hAPP(X3463,X3463,hAPP(X3463,fun(X3463,X3463),plus_plus(X3463),X3464),X3464)
| ti(X3463,X3464) = zero_zero(X3463)
| ~ linord219039673up_add(X3463) )
& ( ti(X3463,X3464) != zero_zero(X3463)
| zero_zero(X3463) = hAPP(X3463,X3463,hAPP(X3463,fun(X3463,X3463),plus_plus(X3463),X3464),X3464)
| ~ linord219039673up_add(X3463) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_494_double__zero__sym])])])]) ).
fof(i_0_800,plain,
! [X2104,X2105] : hAPP(fun(X2104,bool),fun(X2104,bool),hAPP(fun(X2104,X2104),fun(fun(X2104,bool),fun(X2104,bool)),image(X2104,X2104),combi(X2104)),X2105) = ti(fun(X2104,bool),X2105),
inference(variable_rename,[status(thm)],[fact_84_image__ident]) ).
fof(i_0_801,plain,
! [X1812] : ti(fun(X1812,fun(fun(nat,X1812),fun(nat,X1812))),nat_case(X1812)) = nat_case(X1812),
inference(variable_rename,[status(thm)],[tsy_c_Nat_Onat_Onat__case_res]) ).
fof(i_0_802,plain,
! [X1820] : ti(fun(X1820,fun(fun(X1820,bool),fun(X1820,bool))),insert(X1820)) = insert(X1820),
inference(variable_rename,[status(thm)],[tsy_c_Set_Oinsert_res]) ).
fof(i_0_803,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_107_Collect__empty__eq]) ).
fof(i_0_804,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_109_empty__Collect__eq]) ).
fof(i_0_805,plain,
! [X1825,X1826,X1827,X1828] : hAPP(X1825,X1826,ti(fun(X1825,X1826),X1827),X1828) = hAPP(X1825,X1826,X1827,X1828),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).
fof(i_0_806,plain,
! [X3501,X3502,X3503,X3504] : hAPP(X3501,X3502,hAPP(X3502,fun(X3501,X3502),combk(X3502,X3501),X3503),X3504) = ti(X3502,X3503),
inference(variable_rename,[status(thm)],[help_COMBK_1_1_U]) ).
fof(i_0_807,plain,
! [X2555,X2556] : hAPP(fun(X2555,bool),X2555,the(X2555),hAPP(X2555,fun(X2555,bool),fequal(X2555),X2556)) = ti(X2555,X2556),
inference(variable_rename,[status(thm)],[fact_198_the__sym__eq__trivial]) ).
fof(i_0_808,plain,
! [X3461,X3462] :
( ~ comm_monoid_add(X3461)
| hAPP(X3461,X3461,hAPP(X3461,fun(X3461,X3461),plus_plus(X3461),zero_zero(X3461)),X3462) = ti(X3461,X3462) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_493_add__0])])]) ).
fof(i_0_809,plain,
! [X3459,X3460] :
( ~ monoid_add(X3459)
| hAPP(X3459,X3459,hAPP(X3459,fun(X3459,X3459),plus_plus(X3459),zero_zero(X3459)),X3460) = ti(X3459,X3460) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_492_add__0__left])])]) ).
fof(i_0_810,plain,
! [X3467,X3468] :
( ~ comm_monoid_add(X3467)
| hAPP(X3467,X3467,hAPP(X3467,fun(X3467,X3467),plus_plus(X3467),X3468),zero_zero(X3467)) = ti(X3467,X3468) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_496_add_Ocomm__neutral])])]) ).
fof(i_0_811,plain,
! [X3465,X3466] :
( ~ monoid_add(X3465)
| hAPP(X3465,X3465,hAPP(X3465,fun(X3465,X3465),plus_plus(X3465),X3466),zero_zero(X3465)) = ti(X3465,X3466) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_495_add__0__right])])]) ).
fof(i_0_812,plain,
! [X3436,X3437] :
( ~ group_add(X3436)
| hAPP(X3436,X3436,hAPP(X3436,fun(X3436,X3436),minus_minus(X3436),X3437),zero_zero(X3436)) = ti(X3436,X3437) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_477_diff__0__right])])]) ).
fof(i_0_813,plain,
! [X3483,X3484] : ti(X3483,ti(X3483,X3484)) = ti(X3483,X3484),
inference(variable_rename,[status(thm)],[help_ti_idem]) ).
fof(i_0_814,plain,
! [X1797,X1798] : ti(fun(fun(X1797,fun(X1798,X1798)),bool),finite_comp_fun_idem(X1797,X1798)) = finite_comp_fun_idem(X1797,X1798),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ocomp__fun__idem_res]) ).
fof(i_0_815,plain,
! [X1829,X1830,X1831,X1832] : hAPP(X1829,X1830,X1831,ti(X1829,X1832)) = hAPP(X1829,X1830,X1831,X1832),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).
fof(i_0_816,plain,
! [X1833,X1834,X1835,X1836] : ti(X1833,hAPP(X1834,X1833,X1835,X1836)) = hAPP(X1834,X1833,X1835,X1836),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
fof(i_0_817,plain,
! [X1816] : ti(fun(X1816,fun(fun(X1816,bool),X1816)),partial_flat_lub(X1816)) = partial_flat_lub(X1816),
inference(variable_rename,[status(thm)],[tsy_c_Partial__Function_Oflat__lub_res]) ).
fof(i_0_818,plain,
! [X1838] : ti(fun(X1838,fun(fun(X1838,bool),bool)),member(X1838)) = member(X1838),
inference(variable_rename,[status(thm)],[tsy_c_member_res]) ).
fof(i_0_819,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_450_card__infinite]) ).
fof(i_0_820,hypothesis,
! [X1837] :
( ( ~ hBOOL(ti(bool,X1837))
| hBOOL(X1837) )
& ( ~ hBOOL(X1837)
| hBOOL(ti(bool,X1837)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1])]) ).
fof(i_0_821,plain,
! [X80] :
( ~ hBOOL(hAPP(bool,bool,fNot,X80))
| ~ hBOOL(X80) ),
inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).
fof(i_0_822,plain,
! [X1817] : ti(fun(fun(X1817,bool),fun(X1817,bool)),collect(X1817)) = collect(X1817),
inference(variable_rename,[status(thm)],[tsy_c_Set_OCollect_res]) ).
fof(i_0_823,plain,
! [X2063,X2064] : hAPP(fun(X2063,bool),fun(X2063,bool),collect(X2063),X2064) = ti(fun(X2063,bool),X2064),
inference(variable_rename,[status(thm)],[fact_76_Collect__def]) ).
fof(i_0_824,plain,
! [X1791,X1792] : ti(fun(X1791,fun(X1792,X1791)),combk(X1791,X1792)) = combk(X1791,X1792),
inference(variable_rename,[status(thm)],[tsy_c_COMBK_res]) ).
fof(i_0_825,plain,
! [X1808] :
( ~ cancel_semigroup_add(X1808)
| ti(fun(X1808,fun(X1808,X1808)),plus_plus(X1808)) = plus_plus(X1808) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_2_res])]) ).
fof(i_0_826,plain,
! [X1807] :
( ~ ab_semigroup_add(X1807)
| ti(fun(X1807,fun(X1807,X1807)),plus_plus(X1807)) = plus_plus(X1807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_1_res])]) ).
fof(i_0_827,plain,
! [X1806] :
( ~ monoid_add(X1806)
| ti(fun(X1806,fun(X1806,X1806)),plus_plus(X1806)) = plus_plus(X1806) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_0_res])]) ).
fof(i_0_828,plain,
! [X1804] :
( ~ minus(X1804)
| ti(fun(X1804,fun(X1804,X1804)),minus_minus(X1804)) = minus_minus(X1804) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ominus__class_Ominus_res])]) ).
fof(i_0_829,plain,
! [X1815] :
( ~ ord(X1815)
| ti(fun(X1815,fun(X1815,bool)),ord_less_eq(X1815)) = ord_less_eq(X1815) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res])]) ).
fof(i_0_830,plain,
! [X1814] :
( ~ ord(X1814)
| ti(fun(X1814,fun(X1814,bool)),ord_less(X1814)) = ord_less(X1814) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_res])]) ).
fof(i_0_831,plain,
! [X1821] : ti(fun(fun(X1821,bool),X1821),the_elem(X1821)) = the_elem(X1821),
inference(variable_rename,[status(thm)],[tsy_c_Set_Othe__elem_res]) ).
fof(i_0_832,plain,
! [X1810] : ti(fun(fun(X1810,bool),X1810),the(X1810)) = the(X1810),
inference(variable_rename,[status(thm)],[tsy_c_HOL_OThe_res]) ).
fof(i_0_833,plain,
! [X1824] : ti(fun(X1824,fun(X1824,bool)),fequal(X1824)) = fequal(X1824),
inference(variable_rename,[status(thm)],[tsy_c_fequal_res]) ).
fof(i_0_834,plain,
! [X1796] : ti(fun(fun(X1796,bool),nat),finite_card(X1796)) = finite_card(X1796),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).
fof(i_0_835,plain,
! [X1799] : ti(fun(fun(X1799,bool),bool),finite_finite(X1799)) = finite_finite(X1799),
inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).
fof(i_0_836,plain,
! [X3523] :
( ti(bool,X3523) = fTrue
| ti(bool,X3523) = fFalse ),
inference(variable_rename,[status(thm)],[help_fFalse_1_1_T]) ).
fof(i_0_837,plain,
! [X1790] : ti(fun(X1790,X1790),combi(X1790)) = combi(X1790),
inference(variable_rename,[status(thm)],[tsy_c_COMBI_res]) ).
fof(i_0_838,plain,
! [X1813] :
( ~ bot(X1813)
| ti(X1813,bot_bot(X1813)) = bot_bot(X1813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Obot__class_Obot_res])]) ).
fof(i_0_839,plain,
! [X1809] :
( ~ zero(X1809)
| ti(X1809,zero_zero(X1809)) = zero_zero(X1809) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ozero__class_Ozero_res])]) ).
fof(i_0_840,plain,
! [X1805] :
( ~ one(X1805)
| ti(X1805,one_one(X1805)) = one_one(X1805) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_res])]) ).
fof(i_0_841,plain,
! [X1811] : ti(X1811,undefined(X1811)) = undefined(X1811),
inference(variable_rename,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).
fof(i_0_842,plain,
! [X1964,X1965,X1966,X1967] :
( ( hBOOL(hAPP(fun(X1965,bool),bool,hAPP(X1965,fun(fun(X1965,bool),bool),member(X1965),esk3_4(X1964,X1965,X1966,X1967)),X1967))
| ~ hBOOL(hAPP(fun(X1964,bool),bool,finite_finite(X1964),hAPP(fun(X1965,bool),fun(X1964,bool),hAPP(fun(X1965,X1964),fun(fun(X1965,bool),fun(X1964,bool)),image(X1965,X1964),X1966),X1967)))
| hBOOL(hAPP(fun(X1965,bool),bool,finite_finite(X1965),X1967)) )
& ( ~ hBOOL(hAPP(fun(X1965,bool),bool,finite_finite(X1965),hAPP(fun(X1965,bool),fun(X1965,bool),collect(X1965),hAPP(fun(X1965,bool),fun(X1965,bool),hAPP(fun(X1965,fun(bool,bool)),fun(fun(X1965,bool),fun(X1965,bool)),combs(X1965,bool,bool),hAPP(fun(X1965,bool),fun(X1965,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1965,bool),fun(X1965,fun(bool,bool))),combb(bool,fun(bool,bool),X1965),fconj),hAPP(fun(X1965,bool),fun(X1965,bool),hAPP(fun(X1965,fun(fun(X1965,bool),bool)),fun(fun(X1965,bool),fun(X1965,bool)),combc(X1965,fun(X1965,bool),bool),member(X1965)),X1967))),hAPP(X1964,fun(X1965,bool),hAPP(fun(X1965,fun(X1964,bool)),fun(X1964,fun(X1965,bool)),combc(X1965,X1964,bool),hAPP(fun(X1965,X1964),fun(X1965,fun(X1964,bool)),hAPP(fun(X1964,fun(X1964,bool)),fun(fun(X1965,X1964),fun(X1965,fun(X1964,bool))),combb(X1964,fun(X1964,bool),X1965),fequal(X1964)),X1966)),hAPP(X1965,X1964,X1966,esk3_4(X1964,X1965,X1966,X1967)))))))
| ~ hBOOL(hAPP(fun(X1964,bool),bool,finite_finite(X1964),hAPP(fun(X1965,bool),fun(X1964,bool),hAPP(fun(X1965,X1964),fun(fun(X1965,bool),fun(X1964,bool)),image(X1965,X1964),X1966),X1967)))
| hBOOL(hAPP(fun(X1965,bool),bool,finite_finite(X1965),X1967)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_623])])])]) ).
cnf(i_0_843,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk40_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_624]) ).
cnf(i_0_844,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_625]) ).
fof(i_0_845,plain,
! [X2850,X2851,X2852,X2853] :
( ~ hBOOL(hAPP(fun(X2850,bool),bool,finite_finite(X2850),X2853))
| ~ hBOOL(hAPP(fun(X2850,bool),bool,hAPP(X2850,fun(fun(X2850,bool),bool),member(X2850),X2852),X2853))
| ~ hBOOL(hAPP(fun(X2850,bool),bool,hAPP(X2850,fun(fun(X2850,bool),bool),member(X2850),X2851),X2853))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2850,bool),nat,finite_card(X2850),hAPP(fun(X2850,bool),fun(X2850,bool),hAPP(fun(X2850,bool),fun(fun(X2850,bool),fun(X2850,bool)),minus_minus(fun(X2850,bool)),hAPP(fun(X2850,bool),fun(X2850,bool),hAPP(fun(X2850,bool),fun(fun(X2850,bool),fun(X2850,bool)),minus_minus(fun(X2850,bool)),X2853),hAPP(fun(X2850,bool),fun(X2850,bool),hAPP(X2850,fun(fun(X2850,bool),fun(X2850,bool)),insert(X2850),X2852),bot_bot(fun(X2850,bool))))),hAPP(fun(X2850,bool),fun(X2850,bool),hAPP(X2850,fun(fun(X2850,bool),fun(X2850,bool)),insert(X2850),X2851),bot_bot(fun(X2850,bool)))))),hAPP(fun(X2850,bool),nat,finite_card(X2850),X2853))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_288_card__Diff2__less])]) ).
fof(i_0_846,plain,
! [X3297,X3298,X3299,X3300,X3301,X3302] :
( ( hBOOL(hAPP(X3297,bool,hAPP(X3297,fun(X3297,bool),ord_less_eq(X3297),esk67_6(X3297,X3298,X3299,X3300,X3301,X3302)),esk66_6(X3297,X3298,X3299,X3300,X3301,X3302)))
| hBOOL(hAPP(X3298,bool,hAPP(X3298,fun(X3298,bool),ord_less(X3298),hAPP(X3297,X3298,X3300,X3299)),X3302))
| ~ hBOOL(hAPP(X3297,bool,hAPP(X3297,fun(X3297,bool),ord_less_eq(X3297),X3299),X3301))
| ~ hBOOL(hAPP(X3298,bool,hAPP(X3298,fun(X3298,bool),ord_less(X3298),hAPP(X3297,X3298,X3300,X3301)),X3302))
| ~ order(X3298)
| ~ order(X3297) )
& ( ~ hBOOL(hAPP(X3298,bool,hAPP(X3298,fun(X3298,bool),ord_less_eq(X3298),hAPP(X3297,X3298,X3300,esk67_6(X3297,X3298,X3299,X3300,X3301,X3302))),hAPP(X3297,X3298,X3300,esk66_6(X3297,X3298,X3299,X3300,X3301,X3302))))
| hBOOL(hAPP(X3298,bool,hAPP(X3298,fun(X3298,bool),ord_less(X3298),hAPP(X3297,X3298,X3300,X3299)),X3302))
| ~ hBOOL(hAPP(X3297,bool,hAPP(X3297,fun(X3297,bool),ord_less_eq(X3297),X3299),X3301))
| ~ hBOOL(hAPP(X3298,bool,hAPP(X3298,fun(X3298,bool),ord_less(X3298),hAPP(X3297,X3298,X3300,X3301)),X3302))
| ~ order(X3298)
| ~ order(X3297) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_xt4])])])])]) ).
fof(i_0_847,plain,
! [X3280,X3281,X3282,X3283,X3284,X3285] :
( ( hBOOL(hAPP(X3280,bool,hAPP(X3280,fun(X3280,bool),ord_less(X3280),esk63_6(X3280,X3281,X3282,X3283,X3284,X3285)),esk62_6(X3280,X3281,X3282,X3283,X3284,X3285)))
| hBOOL(hAPP(X3281,bool,hAPP(X3281,fun(X3281,bool),ord_less(X3281),hAPP(X3280,X3281,X3283,X3282)),X3285))
| ~ hBOOL(hAPP(X3280,bool,hAPP(X3280,fun(X3280,bool),ord_less(X3280),X3282),X3284))
| ~ hBOOL(hAPP(X3281,bool,hAPP(X3281,fun(X3281,bool),ord_less_eq(X3281),hAPP(X3280,X3281,X3283,X3284)),X3285))
| ~ order(X3281)
| ~ ord(X3280) )
& ( ~ hBOOL(hAPP(X3281,bool,hAPP(X3281,fun(X3281,bool),ord_less(X3281),hAPP(X3280,X3281,X3283,esk63_6(X3280,X3281,X3282,X3283,X3284,X3285))),hAPP(X3280,X3281,X3283,esk62_6(X3280,X3281,X3282,X3283,X3284,X3285))))
| hBOOL(hAPP(X3281,bool,hAPP(X3281,fun(X3281,bool),ord_less(X3281),hAPP(X3280,X3281,X3283,X3282)),X3285))
| ~ hBOOL(hAPP(X3280,bool,hAPP(X3280,fun(X3280,bool),ord_less(X3280),X3282),X3284))
| ~ hBOOL(hAPP(X3281,bool,hAPP(X3281,fun(X3281,bool),ord_less_eq(X3281),hAPP(X3280,X3281,X3283,X3284)),X3285))
| ~ order(X3281)
| ~ ord(X3280) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_430_xt6])])])])]) ).
fof(i_0_848,plain,
! [X3337,X3338,X3339,X3340,X3341,X3342] :
( ( hBOOL(hAPP(X3337,bool,hAPP(X3337,fun(X3337,bool),ord_less_eq(X3337),esk76_6(X3337,X3338,X3339,X3340,X3341,X3342)),esk77_6(X3337,X3338,X3339,X3340,X3341,X3342)))
| hBOOL(hAPP(X3338,bool,hAPP(X3338,fun(X3338,bool),ord_less(X3338),hAPP(X3337,X3338,X3339,X3341)),X3340))
| ~ hBOOL(hAPP(X3338,bool,hAPP(X3338,fun(X3338,bool),ord_less(X3338),hAPP(X3337,X3338,X3339,X3342)),X3340))
| ~ hBOOL(hAPP(X3337,bool,hAPP(X3337,fun(X3337,bool),ord_less_eq(X3337),X3341),X3342))
| ~ order(X3338)
| ~ order(X3337) )
& ( ~ hBOOL(hAPP(X3338,bool,hAPP(X3338,fun(X3338,bool),ord_less_eq(X3338),hAPP(X3337,X3338,X3339,esk76_6(X3337,X3338,X3339,X3340,X3341,X3342))),hAPP(X3337,X3338,X3339,esk77_6(X3337,X3338,X3339,X3340,X3341,X3342))))
| hBOOL(hAPP(X3338,bool,hAPP(X3338,fun(X3338,bool),ord_less(X3338),hAPP(X3337,X3338,X3339,X3341)),X3340))
| ~ hBOOL(hAPP(X3338,bool,hAPP(X3338,fun(X3338,bool),ord_less(X3338),hAPP(X3337,X3338,X3339,X3342)),X3340))
| ~ hBOOL(hAPP(X3337,bool,hAPP(X3337,fun(X3337,bool),ord_less_eq(X3337),X3341),X3342))
| ~ order(X3338)
| ~ order(X3337) ) ),
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_order__le__less__subst2])])])])]) ).
fof(i_0_849,plain,
! [X3345,X3346,X3347,X3348,X3349,X3350] :
( ( hBOOL(hAPP(X3345,bool,hAPP(X3345,fun(X3345,bool),ord_less(X3345),esk78_6(X3345,X3346,X3347,X3348,X3349,X3350)),esk79_6(X3345,X3346,X3347,X3348,X3349,X3350)))
| hBOOL(hAPP(X3346,bool,hAPP(X3346,fun(X3346,bool),ord_less(X3346),hAPP(X3345,X3346,X3347,X3349)),X3348))
| ~ hBOOL(hAPP(X3346,bool,hAPP(X3346,fun(X3346,bool),ord_less_eq(X3346),hAPP(X3345,X3346,X3347,X3350)),X3348))
| ~ hBOOL(hAPP(X3345,bool,hAPP(X3345,fun(X3345,bool),ord_less(X3345),X3349),X3350))
| ~ order(X3346)
| ~ order(X3345) )
& ( ~ hBOOL(hAPP(X3346,bool,hAPP(X3346,fun(X3346,bool),ord_less(X3346),hAPP(X3345,X3346,X3347,esk78_6(X3345,X3346,X3347,X3348,X3349,X3350))),hAPP(X3345,X3346,X3347,esk79_6(X3345,X3346,X3347,X3348,X3349,X3350))))
| hBOOL(hAPP(X3346,bool,hAPP(X3346,fun(X3346,bool),ord_less(X3346),hAPP(X3345,X3346,X3347,X3349)),X3348))
| ~ hBOOL(hAPP(X3346,bool,hAPP(X3346,fun(X3346,bool),ord_less_eq(X3346),hAPP(X3345,X3346,X3347,X3350)),X3348))
| ~ hBOOL(hAPP(X3345,bool,hAPP(X3345,fun(X3345,bool),ord_less(X3345),X3349),X3350))
| ~ order(X3346)
| ~ order(X3345) ) ),
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_order__less__le__subst2])])])])]) ).
fof(i_0_850,plain,
! [X3321,X3322,X3323,X3324,X3325,X3326] :
( ( hBOOL(hAPP(X3322,bool,hAPP(X3322,fun(X3322,bool),ord_less_eq(X3322),esk73_6(X3321,X3322,X3323,X3324,X3325,X3326)),esk72_6(X3321,X3322,X3323,X3324,X3325,X3326)))
| hBOOL(hAPP(X3321,bool,hAPP(X3321,fun(X3321,bool),ord_less(X3321),X3323),hAPP(X3322,X3321,X3324,X3326)))
| ~ hBOOL(hAPP(X3321,bool,hAPP(X3321,fun(X3321,bool),ord_less(X3321),X3323),hAPP(X3322,X3321,X3324,X3325)))
| ~ hBOOL(hAPP(X3322,bool,hAPP(X3322,fun(X3322,bool),ord_less_eq(X3322),X3325),X3326))
| ~ order(X3322)
| ~ order(X3321) )
& ( ~ hBOOL(hAPP(X3321,bool,hAPP(X3321,fun(X3321,bool),ord_less_eq(X3321),hAPP(X3322,X3321,X3324,esk73_6(X3321,X3322,X3323,X3324,X3325,X3326))),hAPP(X3322,X3321,X3324,esk72_6(X3321,X3322,X3323,X3324,X3325,X3326))))
| hBOOL(hAPP(X3321,bool,hAPP(X3321,fun(X3321,bool),ord_less(X3321),X3323),hAPP(X3322,X3321,X3324,X3326)))
| ~ hBOOL(hAPP(X3321,bool,hAPP(X3321,fun(X3321,bool),ord_less(X3321),X3323),hAPP(X3322,X3321,X3324,X3325)))
| ~ hBOOL(hAPP(X3322,bool,hAPP(X3322,fun(X3322,bool),ord_less_eq(X3322),X3325),X3326))
| ~ order(X3322)
| ~ order(X3321) ) ),
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_xt7])])])])]) ).
fof(i_0_851,plain,
! [X3313,X3314,X3315,X3316,X3317,X3318] :
( ( hBOOL(hAPP(X3314,bool,hAPP(X3314,fun(X3314,bool),ord_less(X3314),esk71_6(X3313,X3314,X3315,X3316,X3317,X3318)),esk70_6(X3313,X3314,X3315,X3316,X3317,X3318)))
| hBOOL(hAPP(X3313,bool,hAPP(X3313,fun(X3313,bool),ord_less(X3313),X3315),hAPP(X3314,X3313,X3316,X3318)))
| ~ hBOOL(hAPP(X3313,bool,hAPP(X3313,fun(X3313,bool),ord_less_eq(X3313),X3315),hAPP(X3314,X3313,X3316,X3317)))
| ~ hBOOL(hAPP(X3314,bool,hAPP(X3314,fun(X3314,bool),ord_less(X3314),X3317),X3318))
| ~ order(X3314)
| ~ order(X3313) )
& ( ~ hBOOL(hAPP(X3313,bool,hAPP(X3313,fun(X3313,bool),ord_less(X3313),hAPP(X3314,X3313,X3316,esk71_6(X3313,X3314,X3315,X3316,X3317,X3318))),hAPP(X3314,X3313,X3316,esk70_6(X3313,X3314,X3315,X3316,X3317,X3318))))
| hBOOL(hAPP(X3313,bool,hAPP(X3313,fun(X3313,bool),ord_less(X3313),X3315),hAPP(X3314,X3313,X3316,X3318)))
| ~ hBOOL(hAPP(X3313,bool,hAPP(X3313,fun(X3313,bool),ord_less_eq(X3313),X3315),hAPP(X3314,X3313,X3316,X3317)))
| ~ hBOOL(hAPP(X3314,bool,hAPP(X3314,fun(X3314,bool),ord_less(X3314),X3317),X3318))
| ~ order(X3314)
| ~ order(X3313) ) ),
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_xt5])])])])]) ).
fof(i_0_852,plain,
! [X3329,X3330,X3331,X3332,X3333,X3334] :
( ( hBOOL(hAPP(X3330,bool,hAPP(X3330,fun(X3330,bool),ord_less_eq(X3330),esk74_6(X3329,X3330,X3331,X3332,X3333,X3334)),esk75_6(X3329,X3330,X3331,X3332,X3333,X3334)))
| hBOOL(hAPP(X3329,bool,hAPP(X3329,fun(X3329,bool),ord_less(X3329),X3332),hAPP(X3330,X3329,X3333,X3331)))
| ~ hBOOL(hAPP(X3330,bool,hAPP(X3330,fun(X3330,bool),ord_less_eq(X3330),X3334),X3331))
| ~ hBOOL(hAPP(X3329,bool,hAPP(X3329,fun(X3329,bool),ord_less(X3329),X3332),hAPP(X3330,X3329,X3333,X3334)))
| ~ order(X3330)
| ~ order(X3329) )
& ( ~ hBOOL(hAPP(X3329,bool,hAPP(X3329,fun(X3329,bool),ord_less_eq(X3329),hAPP(X3330,X3329,X3333,esk74_6(X3329,X3330,X3331,X3332,X3333,X3334))),hAPP(X3330,X3329,X3333,esk75_6(X3329,X3330,X3331,X3332,X3333,X3334))))
| hBOOL(hAPP(X3329,bool,hAPP(X3329,fun(X3329,bool),ord_less(X3329),X3332),hAPP(X3330,X3329,X3333,X3331)))
| ~ hBOOL(hAPP(X3330,bool,hAPP(X3330,fun(X3330,bool),ord_less_eq(X3330),X3334),X3331))
| ~ hBOOL(hAPP(X3329,bool,hAPP(X3329,fun(X3329,bool),ord_less(X3329),X3332),hAPP(X3330,X3329,X3333,X3334)))
| ~ order(X3330)
| ~ order(X3329) ) ),
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_853,plain,
! [X3305,X3306,X3307,X3308,X3309,X3310] :
( ( hBOOL(hAPP(X3306,bool,hAPP(X3306,fun(X3306,bool),ord_less(X3306),esk68_6(X3305,X3306,X3307,X3308,X3309,X3310)),esk69_6(X3305,X3306,X3307,X3308,X3309,X3310)))
| hBOOL(hAPP(X3305,bool,hAPP(X3305,fun(X3305,bool),ord_less(X3305),X3308),hAPP(X3306,X3305,X3309,X3307)))
| ~ hBOOL(hAPP(X3306,bool,hAPP(X3306,fun(X3306,bool),ord_less(X3306),X3310),X3307))
| ~ hBOOL(hAPP(X3305,bool,hAPP(X3305,fun(X3305,bool),ord_less_eq(X3305),X3308),hAPP(X3306,X3305,X3309,X3310)))
| ~ order(X3306)
| ~ order(X3305) )
& ( ~ hBOOL(hAPP(X3305,bool,hAPP(X3305,fun(X3305,bool),ord_less(X3305),hAPP(X3306,X3305,X3309,esk68_6(X3305,X3306,X3307,X3308,X3309,X3310))),hAPP(X3306,X3305,X3309,esk69_6(X3305,X3306,X3307,X3308,X3309,X3310))))
| hBOOL(hAPP(X3305,bool,hAPP(X3305,fun(X3305,bool),ord_less(X3305),X3308),hAPP(X3306,X3305,X3309,X3307)))
| ~ hBOOL(hAPP(X3306,bool,hAPP(X3306,fun(X3306,bool),ord_less(X3306),X3310),X3307))
| ~ hBOOL(hAPP(X3305,bool,hAPP(X3305,fun(X3305,bool),ord_less_eq(X3305),X3308),hAPP(X3306,X3305,X3309,X3310)))
| ~ order(X3306)
| ~ order(X3305) ) ),
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_order__le__less__subst1])])])])]) ).
cnf(i_0_854,plain,
( hAPP(fun(X1,bool),X2,X7,X4) = ti(X2,X6)
| hAPP(X1,X2,X3,esk40_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_624]) ).
cnf(i_0_855,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_626]) ).
cnf(i_0_856,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_626]) ).
fof(i_0_857,plain,
! [X1899,X1900,X1901] :
( ( hBOOL(hAPP(fun(X1899,bool),bool,finite_finite(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),collect(X1899),X1900)))
| ~ hBOOL(hAPP(fun(X1899,bool),bool,finite_finite(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),collect(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),hAPP(fun(X1899,fun(bool,bool)),fun(fun(X1899,bool),fun(X1899,bool)),combs(X1899,bool,bool),hAPP(fun(X1899,bool),fun(X1899,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1899,bool),fun(X1899,fun(bool,bool))),combb(bool,fun(bool,bool),X1899),fdisj),X1900)),X1901)))) )
& ( hBOOL(hAPP(fun(X1899,bool),bool,finite_finite(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),collect(X1899),X1901)))
| ~ hBOOL(hAPP(fun(X1899,bool),bool,finite_finite(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),collect(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),hAPP(fun(X1899,fun(bool,bool)),fun(fun(X1899,bool),fun(X1899,bool)),combs(X1899,bool,bool),hAPP(fun(X1899,bool),fun(X1899,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1899,bool),fun(X1899,fun(bool,bool))),combb(bool,fun(bool,bool),X1899),fdisj),X1900)),X1901)))) )
& ( ~ hBOOL(hAPP(fun(X1899,bool),bool,finite_finite(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),collect(X1899),X1900)))
| ~ hBOOL(hAPP(fun(X1899,bool),bool,finite_finite(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),collect(X1899),X1901)))
| hBOOL(hAPP(fun(X1899,bool),bool,finite_finite(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),collect(X1899),hAPP(fun(X1899,bool),fun(X1899,bool),hAPP(fun(X1899,fun(bool,bool)),fun(fun(X1899,bool),fun(X1899,bool)),combs(X1899,bool,bool),hAPP(fun(X1899,bool),fun(X1899,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1899,bool),fun(X1899,fun(bool,bool))),combb(bool,fun(bool,bool),X1899),fdisj),X1900)),X1901)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_26_finite__Collect__disjI])])]) ).
fof(i_0_858,plain,
! [X2350,X2351] :
( ~ 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,X2350)),X2351)),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,X2350)))),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,X2351),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,X2350)),bot_bot(fun(x_a,bool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_assms_I2_J])]) ).
fof(i_0_859,plain,
! [X3136,X3137] : 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),X3136)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X3137))))),
inference(variable_rename,[status(thm)],[fact_386_finite__M__bounded__by__nat]) ).
cnf(i_0_860,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,esk35_4(X1,X4,X2,X3)),esk36_4(X1,X4,X2,X3))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_4(X1,X4,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk36_4(X1,X4,X2,X3)),bot_bot(fun(X1,bool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_627]) ).
fof(i_0_861,plain,
! [X2479,X2480,X2481,X2482,X2483] : hBOOL(hAPP(fun(X2479,bool),bool,hAPP(fun(X2479,bool),fun(fun(X2479,bool),bool),ord_less_eq(fun(X2479,bool)),hAPP(fun(X2479,bool),fun(X2479,bool),hAPP(fun(X2479,bool),fun(fun(X2479,bool),fun(X2479,bool)),minus_minus(fun(X2479,bool)),hAPP(fun(X2480,bool),fun(X2479,bool),hAPP(fun(X2480,X2479),fun(fun(X2480,bool),fun(X2479,bool)),image(X2480,X2479),X2481),X2482)),hAPP(fun(X2480,bool),fun(X2479,bool),hAPP(fun(X2480,X2479),fun(fun(X2480,bool),fun(X2479,bool)),image(X2480,X2479),X2481),X2483))),hAPP(fun(X2480,bool),fun(X2479,bool),hAPP(fun(X2480,X2479),fun(fun(X2480,bool),fun(X2479,bool)),image(X2480,X2479),X2481),hAPP(fun(X2480,bool),fun(X2480,bool),hAPP(fun(X2480,bool),fun(fun(X2480,bool),fun(X2480,bool)),minus_minus(fun(X2480,bool)),X2482),X2483)))),
inference(variable_rename,[status(thm)],[fact_182_image__diff__subset]) ).
fof(i_0_862,plain,
! [X2003,X2004,X2005] : hAPP(fun(X2003,bool),fun(X2003,bool),hAPP(X2003,fun(fun(X2003,bool),fun(X2003,bool)),insert(X2003),X2004),hAPP(fun(X2003,bool),fun(X2003,bool),collect(X2003),X2005)) = hAPP(fun(X2003,bool),fun(X2003,bool),collect(X2003),hAPP(fun(X2003,bool),fun(X2003,bool),hAPP(fun(X2003,fun(bool,bool)),fun(fun(X2003,bool),fun(X2003,bool)),combs(X2003,bool,bool),hAPP(fun(X2003,bool),fun(X2003,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2003,bool),fun(X2003,fun(bool,bool))),combb(bool,fun(bool,bool),X2003),fimplies),hAPP(fun(X2003,bool),fun(X2003,bool),hAPP(fun(bool,bool),fun(fun(X2003,bool),fun(X2003,bool)),combb(bool,bool,X2003),fNot),hAPP(X2003,fun(X2003,bool),hAPP(fun(X2003,fun(X2003,bool)),fun(X2003,fun(X2003,bool)),combc(X2003,X2003,bool),fequal(X2003)),X2004)))),X2005)),
inference(variable_rename,[status(thm)],[fact_59_insert__Collect]) ).
fof(i_0_863,plain,
! [X1869,X1870,X1871] :
( ( ~ hBOOL(hAPP(fun(X1869,bool),bool,finite_finite(X1869),hAPP(fun(X1869,bool),fun(X1869,bool),collect(X1869),X1871)))
| hBOOL(hAPP(fun(X1869,bool),bool,finite_finite(X1869),hAPP(fun(X1869,bool),fun(X1869,bool),collect(X1869),hAPP(fun(X1869,bool),fun(X1869,bool),hAPP(fun(X1869,fun(bool,bool)),fun(fun(X1869,bool),fun(X1869,bool)),combs(X1869,bool,bool),hAPP(fun(X1869,bool),fun(X1869,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1869,bool),fun(X1869,fun(bool,bool))),combb(bool,fun(bool,bool),X1869),fconj),X1871)),X1870)))) )
& ( ~ hBOOL(hAPP(fun(X1869,bool),bool,finite_finite(X1869),hAPP(fun(X1869,bool),fun(X1869,bool),collect(X1869),X1870)))
| hBOOL(hAPP(fun(X1869,bool),bool,finite_finite(X1869),hAPP(fun(X1869,bool),fun(X1869,bool),collect(X1869),hAPP(fun(X1869,bool),fun(X1869,bool),hAPP(fun(X1869,fun(bool,bool)),fun(fun(X1869,bool),fun(X1869,bool)),combs(X1869,bool,bool),hAPP(fun(X1869,bool),fun(X1869,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1869,bool),fun(X1869,fun(bool,bool))),combb(bool,fun(bool,bool),X1869),fconj),X1871)),X1870)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_finite__Collect__conjI])])]) ).
fof(i_0_864,plain,
! [X2365,X2366] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk26_2(X2365,X2366)),hAPP(nat,nat,X2366,esk26_2(X2365,X2366))))
| 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)),X2366)),X2365)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_finite__less__ub])])]) ).
fof(i_0_865,plain,
! [X2580,X2581,X2582] : hAPP(fun(X2580,bool),fun(X2580,bool),hAPP(fun(X2580,bool),fun(fun(X2580,bool),fun(X2580,bool)),minus_minus(fun(X2580,bool)),X2581),X2582) = hAPP(fun(X2580,bool),fun(X2580,bool),collect(X2580),hAPP(fun(X2580,bool),fun(X2580,bool),hAPP(fun(X2580,fun(bool,bool)),fun(fun(X2580,bool),fun(X2580,bool)),combs(X2580,bool,bool),hAPP(fun(X2580,bool),fun(X2580,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2580,bool),fun(X2580,fun(bool,bool))),combb(bool,fun(bool,bool),X2580),fconj),hAPP(fun(X2580,bool),fun(X2580,bool),hAPP(fun(X2580,fun(fun(X2580,bool),bool)),fun(fun(X2580,bool),fun(X2580,bool)),combc(X2580,fun(X2580,bool),bool),member(X2580)),X2581))),hAPP(fun(X2580,bool),fun(X2580,bool),hAPP(fun(bool,bool),fun(fun(X2580,bool),fun(X2580,bool)),combb(bool,bool,X2580),fNot),hAPP(fun(X2580,bool),fun(X2580,bool),hAPP(fun(X2580,fun(fun(X2580,bool),bool)),fun(fun(X2580,bool),fun(X2580,bool)),combc(X2580,fun(X2580,bool),bool),member(X2580)),X2582)))),
inference(variable_rename,[status(thm)],[fact_205_set__diff__eq]) ).
fof(i_0_866,plain,
! [X2854,X2855,X2856] :
( ~ hBOOL(hAPP(fun(X2854,bool),bool,finite_finite(X2854),X2856))
| ~ hBOOL(hAPP(fun(X2854,bool),bool,hAPP(X2854,fun(fun(X2854,bool),bool),member(X2854),X2855),X2856))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2854,bool),nat,finite_card(X2854),hAPP(fun(X2854,bool),fun(X2854,bool),hAPP(fun(X2854,bool),fun(fun(X2854,bool),fun(X2854,bool)),minus_minus(fun(X2854,bool)),X2856),hAPP(fun(X2854,bool),fun(X2854,bool),hAPP(X2854,fun(fun(X2854,bool),fun(X2854,bool)),insert(X2854),X2855),bot_bot(fun(X2854,bool)))))),hAPP(fun(X2854,bool),nat,finite_card(X2854),X2856))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_289_card__Diff1__less])]) ).
fof(i_0_867,plain,
! [X2539,X2540,X2541,X2542,X2543,X2544,X2545,X2546] :
( ~ hBOOL(hAPP(fun(fun(X2539,bool),X2540),bool,hAPP(fun(X2539,X2540),fun(fun(fun(X2539,bool),X2540),bool),hAPP(X2540,fun(fun(X2539,X2540),fun(fun(fun(X2539,bool),X2540),bool)),hAPP(fun(X2540,fun(X2540,X2540)),fun(X2540,fun(fun(X2539,X2540),fun(fun(fun(X2539,bool),X2540),bool))),finite1357897459simple(X2540,X2539),X2543),X2544),X2545),X2546))
| ~ hBOOL(hAPP(fun(X2539,bool),bool,finite_finite(X2539),X2542))
| ~ hBOOL(hAPP(fun(X2539,bool),bool,hAPP(X2539,fun(fun(X2539,bool),bool),member(X2539),X2541),X2542))
| hAPP(fun(X2539,bool),X2540,X2546,X2542) = hAPP(X2540,X2540,hAPP(X2540,fun(X2540,X2540),X2543,hAPP(X2539,X2540,X2545,X2541)),hAPP(fun(X2539,bool),X2540,X2546,hAPP(fun(X2539,bool),fun(X2539,bool),hAPP(fun(X2539,bool),fun(fun(X2539,bool),fun(X2539,bool)),minus_minus(fun(X2539,bool)),X2542),hAPP(fun(X2539,bool),fun(X2539,bool),hAPP(X2539,fun(fun(X2539,bool),fun(X2539,bool)),insert(X2539),X2541),bot_bot(fun(X2539,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_196_folding__image__simple_Oremove])]) ).
fof(i_0_868,plain,
! [X2547,X2548,X2549,X2550,X2551,X2552,X2553,X2554] :
( ~ hBOOL(hAPP(fun(fun(X2547,bool),X2548),bool,hAPP(fun(X2547,X2548),fun(fun(fun(X2547,bool),X2548),bool),hAPP(X2548,fun(fun(X2547,X2548),fun(fun(fun(X2547,bool),X2548),bool)),hAPP(fun(X2548,fun(X2548,X2548)),fun(X2548,fun(fun(X2547,X2548),fun(fun(fun(X2547,bool),X2548),bool))),finite1357897459simple(X2548,X2547),X2551),X2552),X2553),X2554))
| ~ hBOOL(hAPP(fun(X2547,bool),bool,finite_finite(X2547),X2550))
| hAPP(fun(X2547,bool),X2548,X2554,hAPP(fun(X2547,bool),fun(X2547,bool),hAPP(X2547,fun(fun(X2547,bool),fun(X2547,bool)),insert(X2547),X2549),X2550)) = hAPP(X2548,X2548,hAPP(X2548,fun(X2548,X2548),X2551,hAPP(X2547,X2548,X2553,X2549)),hAPP(fun(X2547,bool),X2548,X2554,hAPP(fun(X2547,bool),fun(X2547,bool),hAPP(fun(X2547,bool),fun(fun(X2547,bool),fun(X2547,bool)),minus_minus(fun(X2547,bool)),X2550),hAPP(fun(X2547,bool),fun(X2547,bool),hAPP(X2547,fun(fun(X2547,bool),fun(X2547,bool)),insert(X2547),X2549),bot_bot(fun(X2547,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_197_folding__image__simple_Oinsert__remove])]) ).
cnf(i_0_869,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,esk33_5(X1,X5,X4,X2,X3)),esk34_5(X1,X5,X4,X2,X3))) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X1,X1,X4,esk33_5(X1,X5,X4,X2,X3))),hAPP(X1,X1,X4,esk34_5(X1,X5,X4,X2,X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_628]) ).
fof(i_0_870,plain,
! [X2518,X2519,X2520] :
( ~ hBOOL(hAPP(fun(X2518,bool),bool,finite_finite(X2518),X2520))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2518,bool),nat,finite_card(X2518),hAPP(fun(X2518,bool),fun(X2518,bool),hAPP(fun(X2518,bool),fun(fun(X2518,bool),fun(X2518,bool)),minus_minus(fun(X2518,bool)),X2520),hAPP(fun(X2518,bool),fun(X2518,bool),hAPP(X2518,fun(fun(X2518,bool),fun(X2518,bool)),insert(X2518),X2519),bot_bot(fun(X2518,bool)))))),hAPP(fun(X2518,bool),nat,finite_card(X2518),X2520))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_192_card__Diff1__le])]) ).
fof(i_0_871,plain,
! [X3224,X3225,X3226,X3227] :
( ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(fun(X3224,bool),fun(fun(X3224,bool),fun(X3224,bool)),minus_minus(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),bot_bot(fun(X3224,bool))))),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less_eq(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less_eq(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(fun(X3224,bool),fun(fun(X3224,bool),fun(X3224,bool)),minus_minus(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),bot_bot(fun(X3224,bool))))),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less_eq(fun(X3224,bool)),X3225),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(fun(X3224,bool),fun(fun(X3224,bool),fun(X3224,bool)),minus_minus(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),bot_bot(fun(X3224,bool))))),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less_eq(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(X3224,fun(fun(X3224,bool),bool),member(X3224),X3226),X3225))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(fun(X3224,bool),fun(fun(X3224,bool),fun(X3224,bool)),minus_minus(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),bot_bot(fun(X3224,bool))))),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) )
& ( ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less_eq(fun(X3224,bool)),X3225),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(fun(X3224,bool),fun(fun(X3224,bool),fun(X3224,bool)),minus_minus(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),bot_bot(fun(X3224,bool))))),X3227))
| ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),X3227))
| hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,bool),fun(fun(X3224,bool),bool),ord_less(fun(X3224,bool)),X3225),hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(X3224,fun(fun(X3224,bool),fun(X3224,bool)),insert(X3224),X3226),X3227))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_629])])]) ).
fof(i_0_872,plain,
! [X2493,X2494,X2495,X2496] :
( ( ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(X2493,fun(fun(X2493,bool),bool),member(X2493),X2495),X2494))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(fun(X2493,bool),fun(fun(X2493,bool),fun(X2493,bool)),minus_minus(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),bot_bot(fun(X2493,bool))))),X2496))
| ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),X2496))) )
& ( hBOOL(hAPP(fun(X2493,bool),bool,hAPP(X2493,fun(fun(X2493,bool),bool),member(X2493),X2495),X2494))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),X2496))
| ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),X2496))) )
& ( ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(X2493,fun(fun(X2493,bool),bool),member(X2493),X2495),X2494))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(X2493,fun(fun(X2493,bool),bool),member(X2493),X2495),X2494))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),X2496))) )
& ( ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),X2496))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(X2493,fun(fun(X2493,bool),bool),member(X2493),X2495),X2494))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),X2496))) )
& ( ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(X2493,fun(fun(X2493,bool),bool),member(X2493),X2495),X2494))
| ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(fun(X2493,bool),fun(fun(X2493,bool),fun(X2493,bool)),minus_minus(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),bot_bot(fun(X2493,bool))))),X2496))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),X2496))) )
& ( ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),X2496))
| ~ hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(fun(X2493,bool),fun(fun(X2493,bool),fun(X2493,bool)),minus_minus(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),bot_bot(fun(X2493,bool))))),X2496))
| hBOOL(hAPP(fun(X2493,bool),bool,hAPP(fun(X2493,bool),fun(fun(X2493,bool),bool),ord_less_eq(fun(X2493,bool)),X2494),hAPP(fun(X2493,bool),fun(X2493,bool),hAPP(X2493,fun(fun(X2493,bool),fun(X2493,bool)),insert(X2493),X2495),X2496))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_630])])]) ).
fof(i_0_873,plain,
! [X2489,X2490,X2491,X2492] :
( ~ hBOOL(hAPP(fun(X2489,bool),bool,hAPP(fun(X2489,bool),fun(fun(X2489,bool),bool),ord_less_eq(fun(X2489,bool)),hAPP(fun(X2489,bool),fun(X2489,bool),hAPP(fun(X2489,bool),fun(fun(X2489,bool),fun(X2489,bool)),minus_minus(fun(X2489,bool)),X2490),hAPP(fun(X2489,bool),fun(X2489,bool),hAPP(X2489,fun(fun(X2489,bool),fun(X2489,bool)),insert(X2489),X2491),bot_bot(fun(X2489,bool))))),X2492))
| ~ hBOOL(hAPP(fun(X2489,bool),bool,hAPP(X2489,fun(fun(X2489,bool),bool),member(X2489),X2491),X2490))
| hBOOL(hAPP(fun(X2489,bool),bool,hAPP(fun(X2489,bool),fun(fun(X2489,bool),bool),ord_less_eq(fun(X2489,bool)),X2490),hAPP(fun(X2489,bool),fun(X2489,bool),hAPP(X2489,fun(fun(X2489,bool),fun(X2489,bool)),insert(X2489),X2491),X2492))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_184_diff__single__insert])]) ).
fof(i_0_874,plain,
! [X2662] : hBOOL(hAPP(fun(X2662,fun(fun(X2662,bool),fun(X2662,bool))),bool,finite_comp_fun_idem(X2662,fun(X2662,bool)),hAPP(fun(X2662,fun(X2662,bool)),fun(X2662,fun(fun(X2662,bool),fun(X2662,bool))),hAPP(fun(fun(X2662,bool),fun(fun(X2662,bool),fun(X2662,bool))),fun(fun(X2662,fun(X2662,bool)),fun(X2662,fun(fun(X2662,bool),fun(X2662,bool)))),combb(fun(X2662,bool),fun(fun(X2662,bool),fun(X2662,bool)),X2662),hAPP(fun(fun(X2662,bool),fun(fun(X2662,bool),fun(X2662,bool))),fun(fun(X2662,bool),fun(fun(X2662,bool),fun(X2662,bool))),combc(fun(X2662,bool),fun(X2662,bool),fun(X2662,bool)),minus_minus(fun(X2662,bool)))),hAPP(fun(X2662,bool),fun(X2662,fun(X2662,bool)),hAPP(fun(X2662,fun(fun(X2662,bool),fun(X2662,bool))),fun(fun(X2662,bool),fun(X2662,fun(X2662,bool))),combc(X2662,fun(X2662,bool),fun(X2662,bool)),insert(X2662)),bot_bot(fun(X2662,bool)))))),
inference(variable_rename,[status(thm)],[fact_226_comp__fun__idem__remove]) ).
fof(i_0_875,plain,
! [X2589,X2590,X2591,X2592,X2593,X2594,X2595,X2596] :
( ~ hBOOL(hAPP(fun(fun(X2589,bool),X2590),bool,hAPP(fun(X2589,X2590),fun(fun(fun(X2589,bool),X2590),bool),hAPP(X2590,fun(fun(X2589,X2590),fun(fun(fun(X2589,bool),X2590),bool)),hAPP(fun(X2590,fun(X2590,X2590)),fun(X2590,fun(fun(X2589,X2590),fun(fun(fun(X2589,bool),X2590),bool))),finite1357897459simple(X2590,X2589),X2593),X2594),X2595),X2596))
| ~ hBOOL(hAPP(fun(X2589,bool),bool,finite_finite(X2589),X2592))
| hBOOL(hAPP(fun(X2589,bool),bool,hAPP(X2589,fun(fun(X2589,bool),bool),member(X2589),X2591),X2592))
| hAPP(fun(X2589,bool),X2590,X2596,hAPP(fun(X2589,bool),fun(X2589,bool),hAPP(X2589,fun(fun(X2589,bool),fun(X2589,bool)),insert(X2589),X2591),X2592)) = hAPP(X2590,X2590,hAPP(X2590,fun(X2590,X2590),X2593,hAPP(X2589,X2590,X2595,X2591)),hAPP(fun(X2589,bool),X2590,X2596,X2592)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_631])]) ).
fof(i_0_876,plain,
! [X2162,X2163,X2164,X2165,X2166] :
( ( hBOOL(hAPP(fun(X2163,bool),bool,hAPP(X2163,fun(fun(X2163,bool),bool),member(X2163),esk11_5(X2162,X2163,X2164,X2165,X2166)),X2166))
| hBOOL(hAPP(fun(X2162,bool),bool,hAPP(fun(X2162,bool),fun(fun(X2162,bool),bool),ord_less_eq(fun(X2162,bool)),hAPP(fun(X2163,bool),fun(X2162,bool),hAPP(fun(X2163,X2162),fun(fun(X2163,bool),fun(X2162,bool)),image(X2163,X2162),X2164),X2166)),X2165)) )
& ( ~ hBOOL(hAPP(fun(X2162,bool),bool,hAPP(X2162,fun(fun(X2162,bool),bool),member(X2162),hAPP(X2163,X2162,X2164,esk11_5(X2162,X2163,X2164,X2165,X2166))),X2165))
| hBOOL(hAPP(fun(X2162,bool),bool,hAPP(fun(X2162,bool),fun(fun(X2162,bool),bool),ord_less_eq(fun(X2162,bool)),hAPP(fun(X2163,bool),fun(X2162,bool),hAPP(fun(X2163,X2162),fun(fun(X2163,bool),fun(X2162,bool)),image(X2163,X2162),X2164),X2166)),X2165)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_image__subsetI])])])]) ).
fof(i_0_877,plain,
! [X2095,X2096,X2097] : hAPP(fun(X2095,bool),fun(X2095,bool),hAPP(X2095,fun(fun(X2095,bool),fun(X2095,bool)),insert(X2095),X2096),X2097) = hAPP(fun(X2095,bool),fun(X2095,bool),collect(X2095),hAPP(fun(X2095,bool),fun(X2095,bool),hAPP(fun(X2095,fun(bool,bool)),fun(fun(X2095,bool),fun(X2095,bool)),combs(X2095,bool,bool),hAPP(fun(X2095,bool),fun(X2095,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2095,bool),fun(X2095,fun(bool,bool))),combb(bool,fun(bool,bool),X2095),fdisj),hAPP(X2095,fun(X2095,bool),hAPP(fun(X2095,fun(X2095,bool)),fun(X2095,fun(X2095,bool)),combc(X2095,X2095,bool),fequal(X2095)),X2096))),hAPP(fun(X2095,bool),fun(X2095,bool),hAPP(fun(X2095,fun(fun(X2095,bool),bool)),fun(fun(X2095,bool),fun(X2095,bool)),combc(X2095,fun(X2095,bool),bool),member(X2095)),X2097))),
inference(variable_rename,[status(thm)],[fact_82_insert__compr__raw]) ).
fof(i_0_878,plain,
! [X2000,X2001,X2002] : hAPP(fun(X2000,bool),fun(X2000,bool),hAPP(X2000,fun(fun(X2000,bool),fun(X2000,bool)),insert(X2000),X2001),X2002) = hAPP(fun(X2000,bool),fun(X2000,bool),collect(X2000),hAPP(fun(X2000,bool),fun(X2000,bool),hAPP(fun(X2000,fun(bool,bool)),fun(fun(X2000,bool),fun(X2000,bool)),combs(X2000,bool,bool),hAPP(fun(X2000,bool),fun(X2000,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2000,bool),fun(X2000,fun(bool,bool))),combb(bool,fun(bool,bool),X2000),fdisj),hAPP(X2000,fun(X2000,bool),hAPP(fun(X2000,fun(X2000,bool)),fun(X2000,fun(X2000,bool)),combc(X2000,X2000,bool),fequal(X2000)),X2001))),hAPP(fun(X2000,bool),fun(X2000,bool),hAPP(fun(X2000,fun(fun(X2000,bool),bool)),fun(fun(X2000,bool),fun(X2000,bool)),combc(X2000,fun(X2000,bool),bool),member(X2000)),X2002))),
inference(variable_rename,[status(thm)],[fact_58_insert__compr]) ).
cnf(i_0_879,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_632]) ).
fof(i_0_880,plain,
! [X2277,X2278,X2279] :
( ( ~ hBOOL(hAPP(X2277,bool,X2278,X2279))
| hAPP(fun(X2277,bool),fun(X2277,bool),collect(X2277),hAPP(fun(X2277,bool),fun(X2277,bool),hAPP(fun(X2277,fun(bool,bool)),fun(fun(X2277,bool),fun(X2277,bool)),combs(X2277,bool,bool),hAPP(fun(X2277,bool),fun(X2277,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2277,bool),fun(X2277,fun(bool,bool))),combb(bool,fun(bool,bool),X2277),fconj),hAPP(X2277,fun(X2277,bool),hAPP(fun(X2277,fun(X2277,bool)),fun(X2277,fun(X2277,bool)),combc(X2277,X2277,bool),fequal(X2277)),X2279))),X2278)) = hAPP(fun(X2277,bool),fun(X2277,bool),hAPP(X2277,fun(fun(X2277,bool),fun(X2277,bool)),insert(X2277),X2279),bot_bot(fun(X2277,bool))) )
& ( hBOOL(hAPP(X2277,bool,X2278,X2279))
| hAPP(fun(X2277,bool),fun(X2277,bool),collect(X2277),hAPP(fun(X2277,bool),fun(X2277,bool),hAPP(fun(X2277,fun(bool,bool)),fun(fun(X2277,bool),fun(X2277,bool)),combs(X2277,bool,bool),hAPP(fun(X2277,bool),fun(X2277,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2277,bool),fun(X2277,fun(bool,bool))),combb(bool,fun(bool,bool),X2277),fconj),hAPP(X2277,fun(X2277,bool),hAPP(fun(X2277,fun(X2277,bool)),fun(X2277,fun(X2277,bool)),combc(X2277,X2277,bool),fequal(X2277)),X2279))),X2278)) = bot_bot(fun(X2277,bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_633])]) ).
fof(i_0_881,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_882,plain,
! [X2509,X2510,X2511] :
( ~ hBOOL(hAPP(fun(X2509,bool),bool,finite_finite(X2509),X2511))
| 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(X2509,bool),nat,finite_card(X2509),X2510)),hAPP(fun(X2509,bool),nat,finite_card(X2509),X2511))),hAPP(fun(X2509,bool),nat,finite_card(X2509),hAPP(fun(X2509,bool),fun(X2509,bool),hAPP(fun(X2509,bool),fun(fun(X2509,bool),fun(X2509,bool)),minus_minus(fun(X2509,bool)),X2510),X2511)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_189_diff__card__le__card__Diff])]) ).
fof(i_0_883,plain,
! [X3186,X3187,X3188] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk48_3(X3186,X3187,X3188)),esk49_3(X3186,X3187,X3188)))
| 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,X3188,X3186)),X3187)),hAPP(nat,nat,X3188,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3186),X3187)))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X3188,esk48_3(X3186,X3187,X3188))),hAPP(nat,nat,X3188,esk49_3(X3186,X3187,X3188))))
| 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,X3188,X3186)),X3187)),hAPP(nat,nat,X3188,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3186),X3187)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_405_mono__nat__linear__lb])])])]) ).
fof(i_0_884,plain,
! [X3252,X3253,X3254,X3255] :
( ( ~ hBOOL(hAPP(X3252,bool,hAPP(X3252,fun(X3252,bool),ord_less(X3252),hAPP(nat,X3252,X3255,X3253)),hAPP(nat,X3252,X3255,X3254)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3253),X3254))
| ~ hBOOL(hAPP(X3252,bool,hAPP(X3252,fun(X3252,bool),ord_less(X3252),hAPP(nat,X3252,X3255,esk55_4(X3252,X3253,X3254,X3255))),hAPP(nat,X3252,X3255,hAPP(nat,nat,suc,esk55_4(X3252,X3253,X3254,X3255)))))
| ~ order(X3252) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3253),X3254))
| hBOOL(hAPP(X3252,bool,hAPP(X3252,fun(X3252,bool),ord_less(X3252),hAPP(nat,X3252,X3255,X3253)),hAPP(nat,X3252,X3255,X3254)))
| ~ hBOOL(hAPP(X3252,bool,hAPP(X3252,fun(X3252,bool),ord_less(X3252),hAPP(nat,X3252,X3255,esk55_4(X3252,X3253,X3254,X3255))),hAPP(nat,X3252,X3255,hAPP(nat,nat,suc,esk55_4(X3252,X3253,X3254,X3255)))))
| ~ order(X3252) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_422_lift__Suc__mono__less__iff])])])])]) ).
fof(i_0_885,plain,
! [X1959,X1960,X1961,X1962] :
( ~ order(X1959)
| ~ hBOOL(hAPP(X1959,bool,hAPP(X1959,fun(X1959,bool),ord_less_eq(X1959),hAPP(nat,X1959,X1962,esk2_4(X1959,X1960,X1961,X1962))),hAPP(nat,X1959,X1962,hAPP(nat,nat,suc,esk2_4(X1959,X1960,X1961,X1962)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1960),X1961))
| hBOOL(hAPP(X1959,bool,hAPP(X1959,fun(X1959,bool),ord_less_eq(X1959),hAPP(nat,X1959,X1962,X1960)),hAPP(nat,X1959,X1962,X1961))) ),
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_886,plain,
! [X3239,X3240,X3241,X3242] :
( ~ order(X3239)
| ~ hBOOL(hAPP(X3239,bool,hAPP(X3239,fun(X3239,bool),ord_less(X3239),hAPP(nat,X3239,X3242,esk54_4(X3239,X3240,X3241,X3242))),hAPP(nat,X3239,X3242,hAPP(nat,nat,suc,esk54_4(X3239,X3240,X3241,X3242)))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3240),X3241))
| hBOOL(hAPP(X3239,bool,hAPP(X3239,fun(X3239,bool),ord_less(X3239),hAPP(nat,X3239,X3242,X3240)),hAPP(nat,X3239,X3242,X3241))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_419_lift__Suc__mono__less])])])]) ).
fof(i_0_887,plain,
! [X2534,X2535,X2536] :
( ( hBOOL(hAPP(fun(X2534,bool),bool,finite_finite(X2534),esk38_3(X2534,X2535,X2536)))
| hBOOL(hAPP(fun(X2534,bool),bool,X2535,bot_bot(fun(X2534,bool))))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,X2535,X2536))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,finite_finite(X2534),X2536)) )
& ( hBOOL(hAPP(fun(X2534,bool),bool,hAPP(X2534,fun(fun(X2534,bool),bool),member(X2534),esk37_3(X2534,X2535,X2536)),esk38_3(X2534,X2535,X2536)))
| hBOOL(hAPP(fun(X2534,bool),bool,X2535,bot_bot(fun(X2534,bool))))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,X2535,X2536))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,finite_finite(X2534),X2536)) )
& ( hBOOL(hAPP(fun(X2534,bool),bool,X2535,esk38_3(X2534,X2535,X2536)))
| hBOOL(hAPP(fun(X2534,bool),bool,X2535,bot_bot(fun(X2534,bool))))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,X2535,X2536))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,finite_finite(X2534),X2536)) )
& ( ~ hBOOL(hAPP(fun(X2534,bool),bool,X2535,hAPP(fun(X2534,bool),fun(X2534,bool),hAPP(fun(X2534,bool),fun(fun(X2534,bool),fun(X2534,bool)),minus_minus(fun(X2534,bool)),esk38_3(X2534,X2535,X2536)),hAPP(fun(X2534,bool),fun(X2534,bool),hAPP(X2534,fun(fun(X2534,bool),fun(X2534,bool)),insert(X2534),esk37_3(X2534,X2535,X2536)),bot_bot(fun(X2534,bool))))))
| hBOOL(hAPP(fun(X2534,bool),bool,X2535,bot_bot(fun(X2534,bool))))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,X2535,X2536))
| ~ hBOOL(hAPP(fun(X2534,bool),bool,finite_finite(X2534),X2536)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_195_finite__empty__induct])])])]) ).
fof(i_0_888,plain,
! [X2176,X2177] :
( ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),esk14_2(X2176,X2177)),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X2176),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,X2177)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X2177)) )
& ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X2176),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,esk14_2(X2176,X2177))),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,X2176),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,X2177)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X2177)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_99_assms_I3_J])])])]) ).
fof(i_0_889,plain,
! [X2475,X2476,X2477,X2478] :
( ( ~ hBOOL(hAPP(fun(X2475,bool),bool,finite_finite(X2475),hAPP(fun(X2475,bool),fun(X2475,bool),hAPP(fun(X2475,bool),fun(fun(X2475,bool),fun(X2475,bool)),minus_minus(fun(X2475,bool)),X2476),hAPP(fun(X2475,bool),fun(X2475,bool),hAPP(X2475,fun(fun(X2475,bool),fun(X2475,bool)),insert(X2475),X2477),X2478))))
| hBOOL(hAPP(fun(X2475,bool),bool,finite_finite(X2475),hAPP(fun(X2475,bool),fun(X2475,bool),hAPP(fun(X2475,bool),fun(fun(X2475,bool),fun(X2475,bool)),minus_minus(fun(X2475,bool)),X2476),X2478))) )
& ( ~ hBOOL(hAPP(fun(X2475,bool),bool,finite_finite(X2475),hAPP(fun(X2475,bool),fun(X2475,bool),hAPP(fun(X2475,bool),fun(fun(X2475,bool),fun(X2475,bool)),minus_minus(fun(X2475,bool)),X2476),X2478)))
| hBOOL(hAPP(fun(X2475,bool),bool,finite_finite(X2475),hAPP(fun(X2475,bool),fun(X2475,bool),hAPP(fun(X2475,bool),fun(fun(X2475,bool),fun(X2475,bool)),minus_minus(fun(X2475,bool)),X2476),hAPP(fun(X2475,bool),fun(X2475,bool),hAPP(X2475,fun(fun(X2475,bool),fun(X2475,bool)),insert(X2475),X2477),X2478)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_finite__Diff__insert])]) ).
fof(i_0_890,plain,
! [X1850,X1851,X1852,X1853] :
( ~ hBOOL(hAPP(fun(X1851,bool),bool,finite_finite(X1851),X1853))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1850,bool),nat,finite_card(X1850),hAPP(fun(X1851,bool),fun(X1850,bool),hAPP(fun(X1851,X1850),fun(fun(X1851,bool),fun(X1850,bool)),image(X1851,X1850),X1852),X1853))),hAPP(fun(X1851,bool),nat,finite_card(X1851),X1853))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_card__image__le])]) ).
fof(i_0_891,plain,
! [X1929,X1930,X1931] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1931),X1930)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1929),X1930)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1931),X1929))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1930),X1929))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1930),X1931)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1931),X1929))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1931),X1930)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1929),X1930)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1930),X1929))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1930),X1931)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_le__diff__iff])])]) ).
fof(i_0_892,plain,
! [X3182,X3183,X3184] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3184),X3183)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3182),X3183)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3184),X3182))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3183),X3182))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3183),X3184)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3184),X3182))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3184),X3183)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3182),X3183)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3183),X3182))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3183),X3184)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_403_less__diff__iff])])]) ).
fof(i_0_893,plain,
! [X2652,X2653,X2654,X2655] :
( ~ hBOOL(hAPP(fun(X2652,bool),bool,finite_finite(X2652),X2655))
| ~ hBOOL(hAPP(fun(X2652,bool),bool,hAPP(X2652,fun(fun(X2652,bool),bool),member(X2652),X2654),X2655))
| hBOOL(hAPP(fun(X2652,bool),bool,hAPP(X2652,fun(fun(X2652,bool),bool),member(X2652),X2654),X2653))
| hAPP(fun(X2652,bool),nat,finite_card(X2652),hAPP(fun(X2652,bool),fun(X2652,bool),hAPP(fun(X2652,bool),fun(fun(X2652,bool),fun(X2652,bool)),minus_minus(fun(X2652,bool)),X2655),hAPP(fun(X2652,bool),fun(X2652,bool),hAPP(X2652,fun(fun(X2652,bool),fun(X2652,bool)),insert(X2652),X2654),X2653))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X2652,bool),nat,finite_card(X2652),hAPP(fun(X2652,bool),fun(X2652,bool),hAPP(fun(X2652,bool),fun(fun(X2652,bool),fun(X2652,bool)),minus_minus(fun(X2652,bool)),X2655),X2653))),one_one(nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_634])]) ).
fof(i_0_894,plain,
! [X2440,X2441,X2442,X2443,X2444] :
( ~ hBOOL(hAPP(fun(X2440,bool),bool,hAPP(fun(X2440,bool),fun(fun(X2440,bool),bool),ord_less_eq(fun(X2440,bool)),X2443),X2444))
| ~ hBOOL(hAPP(fun(X2440,bool),bool,hAPP(fun(X2440,bool),fun(fun(X2440,bool),bool),ord_less_eq(fun(X2440,bool)),X2441),X2442))
| hBOOL(hAPP(fun(X2440,bool),bool,hAPP(fun(X2440,bool),fun(fun(X2440,bool),bool),ord_less_eq(fun(X2440,bool)),hAPP(fun(X2440,bool),fun(X2440,bool),hAPP(fun(X2440,bool),fun(fun(X2440,bool),fun(X2440,bool)),minus_minus(fun(X2440,bool)),X2443),X2442)),hAPP(fun(X2440,bool),fun(X2440,bool),hAPP(fun(X2440,bool),fun(fun(X2440,bool),fun(X2440,bool)),minus_minus(fun(X2440,bool)),X2444),X2441))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_172_Diff__mono])]) ).
fof(i_0_895,plain,
! [X2280,X2281,X2282] :
( ( ~ hBOOL(hAPP(X2280,bool,X2281,X2282))
| hAPP(fun(X2280,bool),fun(X2280,bool),collect(X2280),hAPP(fun(X2280,bool),fun(X2280,bool),hAPP(fun(X2280,fun(bool,bool)),fun(fun(X2280,bool),fun(X2280,bool)),combs(X2280,bool,bool),hAPP(fun(X2280,bool),fun(X2280,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2280,bool),fun(X2280,fun(bool,bool))),combb(bool,fun(bool,bool),X2280),fconj),hAPP(X2280,fun(X2280,bool),fequal(X2280),X2282))),X2281)) = hAPP(fun(X2280,bool),fun(X2280,bool),hAPP(X2280,fun(fun(X2280,bool),fun(X2280,bool)),insert(X2280),X2282),bot_bot(fun(X2280,bool))) )
& ( hBOOL(hAPP(X2280,bool,X2281,X2282))
| hAPP(fun(X2280,bool),fun(X2280,bool),collect(X2280),hAPP(fun(X2280,bool),fun(X2280,bool),hAPP(fun(X2280,fun(bool,bool)),fun(fun(X2280,bool),fun(X2280,bool)),combs(X2280,bool,bool),hAPP(fun(X2280,bool),fun(X2280,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2280,bool),fun(X2280,fun(bool,bool))),combb(bool,fun(bool,bool),X2280),fconj),hAPP(X2280,fun(X2280,bool),fequal(X2280),X2282))),X2281)) = bot_bot(fun(X2280,bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_635])]) ).
fof(i_0_896,plain,
! [X2344,X2345,X2346,X2347] :
( ( hBOOL(hAPP(fun(X2344,bool),bool,finite_finite(X2344),esk21_4(X2344,X2345,X2346,X2347)))
| hBOOL(hAPP(fun(X2344,bool),bool,X2345,X2347))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,X2345,bot_bot(fun(X2344,bool))))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,hAPP(fun(X2344,bool),fun(fun(X2344,bool),bool),ord_less_eq(fun(X2344,bool)),X2347),X2346))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,finite_finite(X2344),X2347)) )
& ( hBOOL(hAPP(fun(X2344,bool),bool,hAPP(X2344,fun(fun(X2344,bool),bool),member(X2344),esk20_4(X2344,X2345,X2346,X2347)),X2346))
| hBOOL(hAPP(fun(X2344,bool),bool,X2345,X2347))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,X2345,bot_bot(fun(X2344,bool))))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,hAPP(fun(X2344,bool),fun(fun(X2344,bool),bool),ord_less_eq(fun(X2344,bool)),X2347),X2346))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,finite_finite(X2344),X2347)) )
& ( ~ hBOOL(hAPP(fun(X2344,bool),bool,hAPP(X2344,fun(fun(X2344,bool),bool),member(X2344),esk20_4(X2344,X2345,X2346,X2347)),esk21_4(X2344,X2345,X2346,X2347)))
| hBOOL(hAPP(fun(X2344,bool),bool,X2345,X2347))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,X2345,bot_bot(fun(X2344,bool))))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,hAPP(fun(X2344,bool),fun(fun(X2344,bool),bool),ord_less_eq(fun(X2344,bool)),X2347),X2346))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,finite_finite(X2344),X2347)) )
& ( hBOOL(hAPP(fun(X2344,bool),bool,X2345,esk21_4(X2344,X2345,X2346,X2347)))
| hBOOL(hAPP(fun(X2344,bool),bool,X2345,X2347))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,X2345,bot_bot(fun(X2344,bool))))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,hAPP(fun(X2344,bool),fun(fun(X2344,bool),bool),ord_less_eq(fun(X2344,bool)),X2347),X2346))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,finite_finite(X2344),X2347)) )
& ( ~ hBOOL(hAPP(fun(X2344,bool),bool,X2345,hAPP(fun(X2344,bool),fun(X2344,bool),hAPP(X2344,fun(fun(X2344,bool),fun(X2344,bool)),insert(X2344),esk20_4(X2344,X2345,X2346,X2347)),esk21_4(X2344,X2345,X2346,X2347))))
| hBOOL(hAPP(fun(X2344,bool),bool,X2345,X2347))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,X2345,bot_bot(fun(X2344,bool))))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,hAPP(fun(X2344,bool),fun(fun(X2344,bool),bool),ord_less_eq(fun(X2344,bool)),X2347),X2346))
| ~ hBOOL(hAPP(fun(X2344,bool),bool,finite_finite(X2344),X2347)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_636])])])]) ).
fof(i_0_897,plain,
! [X1841,X1842] :
( ~ hBOOL(hAPP(fun(X1841,bool),bool,finite_finite(X1841),X1842))
| hBOOL(hAPP(fun(fun(X1841,bool),bool),bool,finite_finite(fun(X1841,bool)),hAPP(fun(fun(X1841,bool),bool),fun(fun(X1841,bool),bool),collect(fun(X1841,bool)),hAPP(fun(X1841,bool),fun(fun(X1841,bool),bool),hAPP(fun(fun(X1841,bool),fun(fun(X1841,bool),bool)),fun(fun(X1841,bool),fun(fun(X1841,bool),bool)),combc(fun(X1841,bool),fun(X1841,bool),bool),ord_less_eq(fun(X1841,bool))),X1842)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets])]) ).
cnf(i_0_898,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),esk31_3(X1,X2,X3)),esk32_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),esk30_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_637]) ).
fof(i_0_899,plain,
! [X2820,X2821,X2822] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2821),X2822))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2820),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2822),X2820)),X2821))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_277_le__add__diff])]) ).
fof(i_0_900,plain,
! [X2812,X2813,X2814] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2812),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2814),X2813)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2812),X2813)),X2814))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2813),X2814)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2812),X2813)),X2814))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2812),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2814),X2813)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2813),X2814)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_274_le__diff__conv2])])]) ).
fof(i_0_901,plain,
! [X2686,X2687,X2688,X2689] :
( ~ ordere236663937imp_le(X2686)
| ~ hBOOL(hAPP(X2686,bool,hAPP(X2686,fun(X2686,bool),ord_less_eq(X2686),hAPP(X2686,X2686,hAPP(X2686,fun(X2686,X2686),plus_plus(X2686),X2687),X2688)),hAPP(X2686,X2686,hAPP(X2686,fun(X2686,X2686),plus_plus(X2686),X2689),X2688)))
| hBOOL(hAPP(X2686,bool,hAPP(X2686,fun(X2686,bool),ord_less_eq(X2686),X2687),X2689)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_233_add__le__imp__le__right])])]) ).
fof(i_0_902,plain,
! [X2665,X2666,X2667,X2668] :
( ( ~ hBOOL(hAPP(X2665,bool,hAPP(X2665,fun(X2665,bool),ord_less_eq(X2665),hAPP(X2665,X2665,hAPP(X2665,fun(X2665,X2665),plus_plus(X2665),X2666),X2667)),hAPP(X2665,X2665,hAPP(X2665,fun(X2665,X2665),plus_plus(X2665),X2668),X2667)))
| hBOOL(hAPP(X2665,bool,hAPP(X2665,fun(X2665,bool),ord_less_eq(X2665),X2666),X2668))
| ~ ordere236663937imp_le(X2665) )
& ( ~ hBOOL(hAPP(X2665,bool,hAPP(X2665,fun(X2665,bool),ord_less_eq(X2665),X2666),X2668))
| hBOOL(hAPP(X2665,bool,hAPP(X2665,fun(X2665,bool),ord_less_eq(X2665),hAPP(X2665,X2665,hAPP(X2665,fun(X2665,X2665),plus_plus(X2665),X2666),X2667)),hAPP(X2665,X2665,hAPP(X2665,fun(X2665,X2665),plus_plus(X2665),X2668),X2667)))
| ~ ordere236663937imp_le(X2665) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_228_add__le__cancel__right])])])]) ).
fof(i_0_903,plain,
! [X2690,X2691,X2692,X2693] :
( ~ ordere236663937imp_le(X2690)
| ~ hBOOL(hAPP(X2690,bool,hAPP(X2690,fun(X2690,bool),ord_less_eq(X2690),hAPP(X2690,X2690,hAPP(X2690,fun(X2690,X2690),plus_plus(X2690),X2691),X2692)),hAPP(X2690,X2690,hAPP(X2690,fun(X2690,X2690),plus_plus(X2690),X2691),X2693)))
| hBOOL(hAPP(X2690,bool,hAPP(X2690,fun(X2690,bool),ord_less_eq(X2690),X2692),X2693)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_234_add__le__imp__le__left])])]) ).
fof(i_0_904,plain,
! [X2669,X2670,X2671,X2672] :
( ( ~ hBOOL(hAPP(X2669,bool,hAPP(X2669,fun(X2669,bool),ord_less_eq(X2669),hAPP(X2669,X2669,hAPP(X2669,fun(X2669,X2669),plus_plus(X2669),X2670),X2671)),hAPP(X2669,X2669,hAPP(X2669,fun(X2669,X2669),plus_plus(X2669),X2670),X2672)))
| hBOOL(hAPP(X2669,bool,hAPP(X2669,fun(X2669,bool),ord_less_eq(X2669),X2671),X2672))
| ~ ordere236663937imp_le(X2669) )
& ( ~ hBOOL(hAPP(X2669,bool,hAPP(X2669,fun(X2669,bool),ord_less_eq(X2669),X2671),X2672))
| hBOOL(hAPP(X2669,bool,hAPP(X2669,fun(X2669,bool),ord_less_eq(X2669),hAPP(X2669,X2669,hAPP(X2669,fun(X2669,X2669),plus_plus(X2669),X2670),X2671)),hAPP(X2669,X2669,hAPP(X2669,fun(X2669,X2669),plus_plus(X2669),X2670),X2672)))
| ~ ordere236663937imp_le(X2669) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_229_add__le__cancel__left])])])]) ).
fof(i_0_905,plain,
! [X2919,X2920,X2921,X2922] :
( ( ~ hBOOL(hAPP(X2919,bool,hAPP(X2919,fun(X2919,bool),ord_less(X2919),hAPP(X2919,X2919,hAPP(X2919,fun(X2919,X2919),plus_plus(X2919),X2920),X2921)),hAPP(X2919,X2919,hAPP(X2919,fun(X2919,X2919),plus_plus(X2919),X2922),X2921)))
| hBOOL(hAPP(X2919,bool,hAPP(X2919,fun(X2919,bool),ord_less(X2919),X2920),X2922))
| ~ ordere236663937imp_le(X2919) )
& ( ~ hBOOL(hAPP(X2919,bool,hAPP(X2919,fun(X2919,bool),ord_less(X2919),X2920),X2922))
| hBOOL(hAPP(X2919,bool,hAPP(X2919,fun(X2919,bool),ord_less(X2919),hAPP(X2919,X2919,hAPP(X2919,fun(X2919,X2919),plus_plus(X2919),X2920),X2921)),hAPP(X2919,X2919,hAPP(X2919,fun(X2919,X2919),plus_plus(X2919),X2922),X2921)))
| ~ ordere236663937imp_le(X2919) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_310_add__less__cancel__right])])])]) ).
fof(i_0_906,plain,
! [X2898,X2899,X2900,X2901] :
( ~ ordere236663937imp_le(X2898)
| ~ hBOOL(hAPP(X2898,bool,hAPP(X2898,fun(X2898,bool),ord_less(X2898),hAPP(X2898,X2898,hAPP(X2898,fun(X2898,X2898),plus_plus(X2898),X2899),X2900)),hAPP(X2898,X2898,hAPP(X2898,fun(X2898,X2898),plus_plus(X2898),X2901),X2900)))
| hBOOL(hAPP(X2898,bool,hAPP(X2898,fun(X2898,bool),ord_less(X2898),X2899),X2901)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_305_add__less__imp__less__right])])]) ).
fof(i_0_907,plain,
! [X2915,X2916,X2917,X2918] :
( ( ~ hBOOL(hAPP(X2915,bool,hAPP(X2915,fun(X2915,bool),ord_less(X2915),hAPP(X2915,X2915,hAPP(X2915,fun(X2915,X2915),plus_plus(X2915),X2916),X2917)),hAPP(X2915,X2915,hAPP(X2915,fun(X2915,X2915),plus_plus(X2915),X2916),X2918)))
| hBOOL(hAPP(X2915,bool,hAPP(X2915,fun(X2915,bool),ord_less(X2915),X2917),X2918))
| ~ ordere236663937imp_le(X2915) )
& ( ~ hBOOL(hAPP(X2915,bool,hAPP(X2915,fun(X2915,bool),ord_less(X2915),X2917),X2918))
| hBOOL(hAPP(X2915,bool,hAPP(X2915,fun(X2915,bool),ord_less(X2915),hAPP(X2915,X2915,hAPP(X2915,fun(X2915,X2915),plus_plus(X2915),X2916),X2917)),hAPP(X2915,X2915,hAPP(X2915,fun(X2915,X2915),plus_plus(X2915),X2916),X2918)))
| ~ ordere236663937imp_le(X2915) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_309_add__less__cancel__left])])])]) ).
fof(i_0_908,plain,
! [X2894,X2895,X2896,X2897] :
( ~ ordere236663937imp_le(X2894)
| ~ hBOOL(hAPP(X2894,bool,hAPP(X2894,fun(X2894,bool),ord_less(X2894),hAPP(X2894,X2894,hAPP(X2894,fun(X2894,X2894),plus_plus(X2894),X2895),X2896)),hAPP(X2894,X2894,hAPP(X2894,fun(X2894,X2894),plus_plus(X2894),X2895),X2897)))
| hBOOL(hAPP(X2894,bool,hAPP(X2894,fun(X2894,bool),ord_less(X2894),X2896),X2897)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_304_add__less__imp__less__left])])]) ).
fof(i_0_909,plain,
! [X2147,X2148,X2149,X2150,X2151] :
( ~ hBOOL(hAPP(fun(X2148,bool),bool,hAPP(fun(X2148,bool),fun(fun(X2148,bool),bool),ord_less_eq(fun(X2148,bool)),X2150),X2151))
| hBOOL(hAPP(fun(X2147,bool),bool,hAPP(fun(X2147,bool),fun(fun(X2147,bool),bool),ord_less_eq(fun(X2147,bool)),hAPP(fun(X2148,bool),fun(X2147,bool),hAPP(fun(X2148,X2147),fun(fun(X2148,bool),fun(X2147,bool)),image(X2148,X2147),X2149),X2150)),hAPP(fun(X2148,bool),fun(X2147,bool),hAPP(fun(X2148,X2147),fun(fun(X2148,bool),fun(X2147,bool)),image(X2148,X2147),X2149),X2151))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_image__mono])]) ).
fof(i_0_910,plain,
! [X2766,X2767,X2768] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2766),X2767)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2766),X2768)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2767),X2768)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2767),X2768))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2766),X2767)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2766),X2768))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_258_nat__add__left__cancel__le])]) ).
fof(i_0_911,plain,
! [X2887,X2888,X2889] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2887),X2888)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2887),X2889)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2888),X2889)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2888),X2889))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2887),X2888)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2887),X2889))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_301_nat__add__left__cancel__less])]) ).
fof(i_0_912,plain,
! [X2659,X2660,X2661] :
( ~ hBOOL(hAPP(fun(X2659,bool),bool,finite_finite(X2659),X2661))
| ~ hBOOL(hAPP(fun(X2659,bool),bool,hAPP(X2659,fun(fun(X2659,bool),bool),member(X2659),X2660),X2661))
| hAPP(fun(X2659,bool),nat,finite_card(X2659),X2661) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X2659,bool),nat,finite_card(X2659),hAPP(fun(X2659,bool),fun(X2659,bool),hAPP(fun(X2659,bool),fun(fun(X2659,bool),fun(X2659,bool)),minus_minus(fun(X2659,bool)),X2661),hAPP(fun(X2659,bool),fun(X2659,bool),hAPP(X2659,fun(fun(X2659,bool),fun(X2659,bool)),insert(X2659),X2660),bot_bot(fun(X2659,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_225_card_Oremove])]) ).
fof(i_0_913,plain,
! [X2378,X2379,X2380,X2381] :
( ~ ord(X2379)
| ~ hBOOL(hAPP(X2379,bool,hAPP(X2379,fun(X2379,bool),ord_less_eq(X2379),hAPP(X2378,X2379,X2380,esk29_4(X2378,X2379,X2380,X2381))),hAPP(X2378,X2379,X2381,esk29_4(X2378,X2379,X2380,X2381))))
| hBOOL(hAPP(fun(X2378,X2379),bool,hAPP(fun(X2378,X2379),fun(fun(X2378,X2379),bool),ord_less_eq(fun(X2378,X2379)),X2380),X2381)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_155_le__funI])])])]) ).
fof(i_0_914,plain,
! [X2179,X2180,X2181,X2182,X2183,X2184,X2185] :
( ( ~ hBOOL(hAPP(fun(X2179,X2180),bool,hAPP(fun(X2179,X2180),fun(fun(X2179,X2180),bool),ord_less_eq(fun(X2179,X2180)),X2181),X2182))
| hBOOL(hAPP(X2180,bool,hAPP(X2180,fun(X2180,bool),ord_less_eq(X2180),hAPP(X2179,X2180,X2181,X2183)),hAPP(X2179,X2180,X2182,X2183)))
| ~ ord(X2180) )
& ( ~ hBOOL(hAPP(X2180,bool,hAPP(X2180,fun(X2180,bool),ord_less_eq(X2180),hAPP(X2179,X2180,X2184,esk15_4(X2179,X2180,X2184,X2185))),hAPP(X2179,X2180,X2185,esk15_4(X2179,X2180,X2184,X2185))))
| hBOOL(hAPP(fun(X2179,X2180),bool,hAPP(fun(X2179,X2180),fun(fun(X2179,X2180),bool),ord_less_eq(fun(X2179,X2180)),X2184),X2185))
| ~ ord(X2180) ) ),
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_100_le__fun__def])])])])])]) ).
fof(i_0_915,plain,
! [X2109,X2110,X2111,X2112] :
( ( hBOOL(hAPP(fun(X2109,bool),bool,hAPP(X2109,fun(fun(X2109,bool),bool),member(X2109),X2110),X2112))
| ~ hBOOL(hAPP(fun(X2109,bool),bool,hAPP(fun(X2109,bool),fun(fun(X2109,bool),bool),ord_less_eq(fun(X2109,bool)),hAPP(fun(X2109,bool),fun(X2109,bool),hAPP(X2109,fun(fun(X2109,bool),fun(X2109,bool)),insert(X2109),X2110),X2111)),X2112)) )
& ( hBOOL(hAPP(fun(X2109,bool),bool,hAPP(fun(X2109,bool),fun(fun(X2109,bool),bool),ord_less_eq(fun(X2109,bool)),X2111),X2112))
| ~ hBOOL(hAPP(fun(X2109,bool),bool,hAPP(fun(X2109,bool),fun(fun(X2109,bool),bool),ord_less_eq(fun(X2109,bool)),hAPP(fun(X2109,bool),fun(X2109,bool),hAPP(X2109,fun(fun(X2109,bool),fun(X2109,bool)),insert(X2109),X2110),X2111)),X2112)) )
& ( ~ hBOOL(hAPP(fun(X2109,bool),bool,hAPP(X2109,fun(fun(X2109,bool),bool),member(X2109),X2110),X2112))
| ~ hBOOL(hAPP(fun(X2109,bool),bool,hAPP(fun(X2109,bool),fun(fun(X2109,bool),bool),ord_less_eq(fun(X2109,bool)),X2111),X2112))
| hBOOL(hAPP(fun(X2109,bool),bool,hAPP(fun(X2109,bool),fun(fun(X2109,bool),bool),ord_less_eq(fun(X2109,bool)),hAPP(fun(X2109,bool),fun(X2109,bool),hAPP(X2109,fun(fun(X2109,bool),fun(X2109,bool)),insert(X2109),X2110),X2111)),X2112)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_insert__subset])])]) ).
fof(i_0_916,plain,
! [X2512,X2513,X2514] :
( ~ hBOOL(hAPP(fun(X2512,bool),bool,finite_finite(X2512),X2514))
| ~ hBOOL(hAPP(fun(X2512,bool),bool,hAPP(X2512,fun(fun(X2512,bool),bool),member(X2512),X2513),X2514))
| hAPP(nat,nat,suc,hAPP(fun(X2512,bool),nat,finite_card(X2512),hAPP(fun(X2512,bool),fun(X2512,bool),hAPP(fun(X2512,bool),fun(fun(X2512,bool),fun(X2512,bool)),minus_minus(fun(X2512,bool)),X2514),hAPP(fun(X2512,bool),fun(X2512,bool),hAPP(X2512,fun(fun(X2512,bool),fun(X2512,bool)),insert(X2512),X2513),bot_bot(fun(X2512,bool)))))) = hAPP(fun(X2512,bool),nat,finite_card(X2512),X2514) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_190_card__Suc__Diff1])]) ).
fof(i_0_917,plain,
! [X2656,X2657,X2658] :
( ~ hBOOL(hAPP(fun(X2656,bool),bool,finite_finite(X2656),X2658))
| hAPP(fun(X2656,bool),nat,finite_card(X2656),hAPP(fun(X2656,bool),fun(X2656,bool),hAPP(X2656,fun(fun(X2656,bool),fun(X2656,bool)),insert(X2656),X2657),X2658)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X2656,bool),nat,finite_card(X2656),hAPP(fun(X2656,bool),fun(X2656,bool),hAPP(fun(X2656,bool),fun(fun(X2656,bool),fun(X2656,bool)),minus_minus(fun(X2656,bool)),X2658),hAPP(fun(X2656,bool),fun(X2656,bool),hAPP(X2656,fun(fun(X2656,bool),fun(X2656,bool)),insert(X2656),X2657),bot_bot(fun(X2656,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_224_card_Oinsert__remove])]) ).
fof(i_0_918,plain,
! [X2121,X2122,X2123,X2124] :
( ~ hBOOL(hAPP(fun(X2121,bool),bool,hAPP(fun(X2121,bool),fun(fun(X2121,bool),bool),ord_less_eq(fun(X2121,bool)),X2123),X2124))
| hBOOL(hAPP(fun(X2121,bool),bool,hAPP(fun(X2121,bool),fun(fun(X2121,bool),bool),ord_less_eq(fun(X2121,bool)),hAPP(fun(X2121,bool),fun(X2121,bool),hAPP(X2121,fun(fun(X2121,bool),fun(X2121,bool)),insert(X2121),X2122),X2123)),hAPP(fun(X2121,bool),fun(X2121,bool),hAPP(X2121,fun(fun(X2121,bool),fun(X2121,bool)),insert(X2121),X2122),X2124))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_89_insert__mono])]) ).
fof(i_0_919,plain,
! [X2462,X2463,X2464,X2465] : hAPP(fun(X2462,bool),fun(X2462,bool),hAPP(fun(X2462,bool),fun(fun(X2462,bool),fun(X2462,bool)),minus_minus(fun(X2462,bool)),X2463),hAPP(fun(X2462,bool),fun(X2462,bool),hAPP(X2462,fun(fun(X2462,bool),fun(X2462,bool)),insert(X2462),X2464),X2465)) = hAPP(fun(X2462,bool),fun(X2462,bool),hAPP(fun(X2462,bool),fun(fun(X2462,bool),fun(X2462,bool)),minus_minus(fun(X2462,bool)),hAPP(fun(X2462,bool),fun(X2462,bool),hAPP(fun(X2462,bool),fun(fun(X2462,bool),fun(X2462,bool)),minus_minus(fun(X2462,bool)),X2463),hAPP(fun(X2462,bool),fun(X2462,bool),hAPP(X2462,fun(fun(X2462,bool),fun(X2462,bool)),insert(X2462),X2464),bot_bot(fun(X2462,bool))))),X2465),
inference(variable_rename,[status(thm)],[fact_177_Diff__insert2]) ).
fof(i_0_920,plain,
! [X2515,X2516,X2517] :
( ~ hBOOL(hAPP(fun(X2515,bool),bool,finite_finite(X2515),X2517))
| hAPP(fun(X2515,bool),nat,finite_card(X2515),hAPP(fun(X2515,bool),fun(X2515,bool),hAPP(X2515,fun(fun(X2515,bool),fun(X2515,bool)),insert(X2515),X2516),X2517)) = hAPP(nat,nat,suc,hAPP(fun(X2515,bool),nat,finite_card(X2515),hAPP(fun(X2515,bool),fun(X2515,bool),hAPP(fun(X2515,bool),fun(fun(X2515,bool),fun(X2515,bool)),minus_minus(fun(X2515,bool)),X2517),hAPP(fun(X2515,bool),fun(X2515,bool),hAPP(X2515,fun(fun(X2515,bool),fun(X2515,bool)),insert(X2515),X2516),bot_bot(fun(X2515,bool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_191_card__insert])]) ).
fof(i_0_921,plain,
! [X2823,X2824,X2825] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2823),X2824)),X2825))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2823),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2825),X2824))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2823),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2825),X2824)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2823),X2824)),X2825)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_278_le__diff__conv])]) ).
fof(i_0_922,plain,
! [X3176,X3177,X3178] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3176),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3177),X3178)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3176),X3178)),X3177)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3176),X3178)),X3177))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3176),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3177),X3178))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_401_less__diff__conv])]) ).
fof(i_0_923,plain,
! [X2681,X2682,X2683,X2684,X2685] :
( ~ ordere779506340up_add(X2681)
| ~ hBOOL(hAPP(X2681,bool,hAPP(X2681,fun(X2681,bool),ord_less_eq(X2681),X2684),X2685))
| ~ hBOOL(hAPP(X2681,bool,hAPP(X2681,fun(X2681,bool),ord_less_eq(X2681),X2682),X2683))
| hBOOL(hAPP(X2681,bool,hAPP(X2681,fun(X2681,bool),ord_less_eq(X2681),hAPP(X2681,X2681,hAPP(X2681,fun(X2681,X2681),plus_plus(X2681),X2684),X2682)),hAPP(X2681,X2681,hAPP(X2681,fun(X2681,X2681),plus_plus(X2681),X2685),X2683))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_232_add__mono])])]) ).
fof(i_0_924,plain,
! [X3143,X3144,X3145,X3146,X3147] :
( ~ ordere223160158up_add(X3143)
| ~ hBOOL(hAPP(X3143,bool,hAPP(X3143,fun(X3143,bool),ord_less(X3143),X3146),X3147))
| ~ hBOOL(hAPP(X3143,bool,hAPP(X3143,fun(X3143,bool),ord_less_eq(X3143),X3144),X3145))
| hBOOL(hAPP(X3143,bool,hAPP(X3143,fun(X3143,bool),ord_less(X3143),hAPP(X3143,X3143,hAPP(X3143,fun(X3143,X3143),plus_plus(X3143),X3146),X3144)),hAPP(X3143,X3143,hAPP(X3143,fun(X3143,X3143),plus_plus(X3143),X3147),X3145))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_388_add__less__le__mono])])]) ).
fof(i_0_925,plain,
! [X3138,X3139,X3140,X3141,X3142] :
( ~ ordere223160158up_add(X3138)
| ~ hBOOL(hAPP(X3138,bool,hAPP(X3138,fun(X3138,bool),ord_less_eq(X3138),X3141),X3142))
| ~ hBOOL(hAPP(X3138,bool,hAPP(X3138,fun(X3138,bool),ord_less(X3138),X3139),X3140))
| hBOOL(hAPP(X3138,bool,hAPP(X3138,fun(X3138,bool),ord_less(X3138),hAPP(X3138,X3138,hAPP(X3138,fun(X3138,X3138),plus_plus(X3138),X3141),X3139)),hAPP(X3138,X3138,hAPP(X3138,fun(X3138,X3138),plus_plus(X3138),X3142),X3140))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_387_add__le__less__mono])])]) ).
fof(i_0_926,plain,
! [X2902,X2903,X2904,X2905,X2906] :
( ~ ordere223160158up_add(X2902)
| ~ hBOOL(hAPP(X2902,bool,hAPP(X2902,fun(X2902,bool),ord_less(X2902),X2905),X2906))
| ~ hBOOL(hAPP(X2902,bool,hAPP(X2902,fun(X2902,bool),ord_less(X2902),X2903),X2904))
| hBOOL(hAPP(X2902,bool,hAPP(X2902,fun(X2902,bool),ord_less(X2902),hAPP(X2902,X2902,hAPP(X2902,fun(X2902,X2902),plus_plus(X2902),X2905),X2903)),hAPP(X2902,X2902,hAPP(X2902,fun(X2902,X2902),plus_plus(X2902),X2906),X2904))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_306_add__strict__mono])])]) ).
fof(i_0_927,plain,
! [X2405,X2406] : hAPP(fun(X2405,bool),X2405,the_elem(X2405),X2406) = hAPP(fun(X2405,bool),X2405,the(X2405),hAPP(fun(X2405,fun(X2405,bool)),fun(X2405,bool),hAPP(fun(fun(X2405,bool),bool),fun(fun(X2405,fun(X2405,bool)),fun(X2405,bool)),combb(fun(X2405,bool),bool,X2405),hAPP(fun(X2405,bool),fun(fun(X2405,bool),bool),fequal(fun(X2405,bool)),X2406)),hAPP(fun(X2405,bool),fun(X2405,fun(X2405,bool)),hAPP(fun(X2405,fun(fun(X2405,bool),fun(X2405,bool))),fun(fun(X2405,bool),fun(X2405,fun(X2405,bool))),combc(X2405,fun(X2405,bool),fun(X2405,bool)),insert(X2405)),bot_bot(fun(X2405,bool))))),
inference(variable_rename,[status(thm)],[fact_161_the__elem__def]) ).
fof(i_0_928,plain,
! [X3269,X3270,X3271] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk58_3(X3269,X3270,X3271)),esk59_3(X3269,X3270,X3271)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3269),X3270))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X3271,X3269)),hAPP(nat,nat,X3271,X3270))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X3271,esk58_3(X3269,X3270,X3271))),hAPP(nat,nat,X3271,esk59_3(X3269,X3270,X3271))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3269),X3270))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X3271,X3269)),hAPP(nat,nat,X3271,X3270))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_427_less__mono__imp__le__mono])])])]) ).
fof(i_0_929,plain,
! [X2778,X2779,X2780,X2781] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2780),X2781))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2778),X2779))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2780),X2778)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2781),X2779))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_add__le__mono])]) ).
fof(i_0_930,plain,
! [X2874,X2875,X2876,X2877] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2876),X2877))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2874),X2875))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2876),X2874)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2877),X2875))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_297_add__less__mono])]) ).
fof(i_0_931,plain,
! [X3179,X3180,X3181] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3180),X3181))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3179),X3180))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3180),X3179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3181),X3179))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_402_diff__less__mono])]) ).
fof(i_0_932,plain,
! [X2961,X2962,X2963] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2962),X2963))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2962),X2961))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2961),X2963)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2961),X2962))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_328_diff__less__mono2])]) ).
cnf(i_0_933,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_638]) ).
cnf(i_0_934,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),esk31_3(X1,X2,X3)),esk32_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),esk30_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_637]) ).
fof(i_0_935,plain,
! [X3399,X3400] :
( ( ~ hBOOL(hAPP(X3399,bool,hAPP(X3399,fun(X3399,bool),ord_less_eq(X3399),hAPP(X3399,X3399,hAPP(X3399,fun(X3399,X3399),plus_plus(X3399),X3400),X3400)),zero_zero(X3399)))
| hBOOL(hAPP(X3399,bool,hAPP(X3399,fun(X3399,bool),ord_less_eq(X3399),X3400),zero_zero(X3399)))
| ~ linord219039673up_add(X3399) )
& ( ~ hBOOL(hAPP(X3399,bool,hAPP(X3399,fun(X3399,bool),ord_less_eq(X3399),X3400),zero_zero(X3399)))
| hBOOL(hAPP(X3399,bool,hAPP(X3399,fun(X3399,bool),ord_less_eq(X3399),hAPP(X3399,X3399,hAPP(X3399,fun(X3399,X3399),plus_plus(X3399),X3400),X3400)),zero_zero(X3399)))
| ~ linord219039673up_add(X3399) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_460_double__add__le__zero__iff__single__add__le__zero])])])]) ).
cnf(i_0_936,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),esk8_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_639]) ).
fof(i_0_937,plain,
! [X3418,X3419,X3420] :
( ( ~ hBOOL(hAPP(X3418,bool,hAPP(X3418,fun(X3418,bool),ord_less_eq(X3418),X3419),X3420))
| hBOOL(hAPP(X3418,bool,hAPP(X3418,fun(X3418,bool),ord_less_eq(X3418),hAPP(X3418,X3418,hAPP(X3418,fun(X3418,X3418),minus_minus(X3418),X3419),X3420)),zero_zero(X3418)))
| ~ ordered_ab_group_add(X3418) )
& ( ~ hBOOL(hAPP(X3418,bool,hAPP(X3418,fun(X3418,bool),ord_less_eq(X3418),hAPP(X3418,X3418,hAPP(X3418,fun(X3418,X3418),minus_minus(X3418),X3419),X3420)),zero_zero(X3418)))
| hBOOL(hAPP(X3418,bool,hAPP(X3418,fun(X3418,bool),ord_less_eq(X3418),X3419),X3420))
| ~ ordered_ab_group_add(X3418) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_466_le__iff__diff__le__0])])])]) ).
fof(i_0_938,plain,
! [X1860,X1861,X1862] :
( ~ hBOOL(hAPP(fun(X1860,bool),bool,finite_finite(X1860),X1862))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1860,bool),nat,finite_card(X1860),X1862)),hAPP(fun(X1860,bool),nat,finite_card(X1860),hAPP(fun(X1860,bool),fun(X1860,bool),hAPP(X1860,fun(fun(X1860,bool),fun(X1860,bool)),insert(X1860),X1861),X1862)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7_card__insert__le])]) ).
fof(i_0_939,plain,
! [X3228,X3229,X3230] :
( ~ hBOOL(hAPP(fun(X3228,bool),bool,finite_finite(X3228),X3230))
| ~ hBOOL(hAPP(fun(X3228,bool),bool,hAPP(fun(X3228,bool),fun(fun(X3228,bool),bool),ord_less_eq(fun(X3228,bool)),X3229),X3230))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3228,bool),nat,finite_card(X3228),X3229)),hAPP(fun(X3228,bool),nat,finite_card(X3228),X3230)))
| hBOOL(hAPP(fun(X3228,bool),bool,hAPP(fun(X3228,bool),fun(fun(X3228,bool),bool),ord_less(fun(X3228,bool)),X3229),X3230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_417_card__psubset])]) ).
fof(i_0_940,plain,
! [X2663,X2664] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2663)),X2664))
| 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),X2663)),X2664)) )
& ( ~ 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),X2663)),X2664))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2663)),X2664)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_227_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_941,plain,
! [X2788,X2789,X2790] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2788),X2790))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2788),X2789)),X2790)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2789),X2790))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2788),X2789)),X2790)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_640])])]) ).
fof(i_0_942,plain,
! [X2785,X2786,X2787] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2785),X2786)),X2787))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2785),X2787)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_add__leD1])]) ).
fof(i_0_943,plain,
! [X2782,X2783,X2784] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2782),X2783)),X2784))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2783),X2784)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_263_add__leD2])]) ).
fof(i_0_944,plain,
! [X2867,X2868,X2869] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2867),X2868)),X2869))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2867),X2869)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_295_add__lessD1])]) ).
fof(i_0_945,plain,
! [X2673,X2674,X2675,X2676] :
( ~ ordere779506340up_add(X2673)
| ~ hBOOL(hAPP(X2673,bool,hAPP(X2673,fun(X2673,bool),ord_less_eq(X2673),X2675),X2676))
| hBOOL(hAPP(X2673,bool,hAPP(X2673,fun(X2673,bool),ord_less_eq(X2673),hAPP(X2673,X2673,hAPP(X2673,fun(X2673,X2673),plus_plus(X2673),X2675),X2674)),hAPP(X2673,X2673,hAPP(X2673,fun(X2673,X2673),plus_plus(X2673),X2676),X2674))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_230_add__right__mono])])]) ).
fof(i_0_946,plain,
! [X2677,X2678,X2679,X2680] :
( ~ ordere779506340up_add(X2677)
| ~ hBOOL(hAPP(X2677,bool,hAPP(X2677,fun(X2677,bool),ord_less_eq(X2677),X2679),X2680))
| hBOOL(hAPP(X2677,bool,hAPP(X2677,fun(X2677,bool),ord_less_eq(X2677),hAPP(X2677,X2677,hAPP(X2677,fun(X2677,X2677),plus_plus(X2677),X2678),X2679)),hAPP(X2677,X2677,hAPP(X2677,fun(X2677,X2677),plus_plus(X2677),X2678),X2680))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_add__left__mono])])]) ).
fof(i_0_947,plain,
! [X2911,X2912,X2913,X2914] :
( ~ ordere223160158up_add(X2911)
| ~ hBOOL(hAPP(X2911,bool,hAPP(X2911,fun(X2911,bool),ord_less(X2911),X2913),X2914))
| hBOOL(hAPP(X2911,bool,hAPP(X2911,fun(X2911,bool),ord_less(X2911),hAPP(X2911,X2911,hAPP(X2911,fun(X2911,X2911),plus_plus(X2911),X2913),X2912)),hAPP(X2911,X2911,hAPP(X2911,fun(X2911,X2911),plus_plus(X2911),X2914),X2912))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_308_add__strict__right__mono])])]) ).
fof(i_0_948,plain,
! [X2907,X2908,X2909,X2910] :
( ~ ordere223160158up_add(X2907)
| ~ hBOOL(hAPP(X2907,bool,hAPP(X2907,fun(X2907,bool),ord_less(X2907),X2909),X2910))
| hBOOL(hAPP(X2907,bool,hAPP(X2907,fun(X2907,bool),ord_less(X2907),hAPP(X2907,X2907,hAPP(X2907,fun(X2907,X2907),plus_plus(X2907),X2908),X2909)),hAPP(X2907,X2907,hAPP(X2907,fun(X2907,X2907),plus_plus(X2907),X2908),X2910))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_307_add__strict__left__mono])])]) ).
fof(i_0_949,plain,
! [X2835,X2836,X2837] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2836),X2837))
| 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),X2837),X2836))),X2835) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2837)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2836),X2835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_283_diff__Suc__diff__eq2])]) ).
fof(i_0_950,plain,
! [X2113,X2114,X2115,X2116] :
( ( ~ hBOOL(hAPP(fun(X2113,bool),bool,hAPP(fun(X2113,bool),fun(fun(X2113,bool),bool),ord_less_eq(fun(X2113,bool)),X2116),hAPP(fun(X2113,bool),fun(X2113,bool),hAPP(X2113,fun(fun(X2113,bool),fun(X2113,bool)),insert(X2113),X2115),X2114)))
| hBOOL(hAPP(fun(X2113,bool),bool,hAPP(fun(X2113,bool),fun(fun(X2113,bool),bool),ord_less_eq(fun(X2113,bool)),X2116),X2114))
| hBOOL(hAPP(fun(X2113,bool),bool,hAPP(X2113,fun(fun(X2113,bool),bool),member(X2113),X2115),X2116)) )
& ( ~ hBOOL(hAPP(fun(X2113,bool),bool,hAPP(fun(X2113,bool),fun(fun(X2113,bool),bool),ord_less_eq(fun(X2113,bool)),X2116),X2114))
| hBOOL(hAPP(fun(X2113,bool),bool,hAPP(fun(X2113,bool),fun(fun(X2113,bool),bool),ord_less_eq(fun(X2113,bool)),X2116),hAPP(fun(X2113,bool),fun(X2113,bool),hAPP(X2113,fun(fun(X2113,bool),fun(X2113,bool)),insert(X2113),X2115),X2114)))
| hBOOL(hAPP(fun(X2113,bool),bool,hAPP(X2113,fun(fun(X2113,bool),bool),member(X2113),X2115),X2116)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_641])])]) ).
cnf(i_0_951,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_642]) ).
fof(i_0_952,plain,
! [X2775,X2776,X2777] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2776),X2777))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2776),X2775)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2777),X2775))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_add__le__mono1])]) ).
fof(i_0_953,plain,
! [X1940,X1941,X1942] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1941),X1942))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1941),X1940)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1942),X1940))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_diff__le__mono])]) ).
fof(i_0_954,plain,
! [X1943,X1944,X1945] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1944),X1945))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1943),X1945)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1943),X1944))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_44_diff__le__mono2])]) ).
fof(i_0_955,plain,
! [X2878,X2879,X2880] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2879),X2880))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2879),X2878)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2880),X2878))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_298_add__less__mono1])]) ).
fof(i_0_956,plain,
! [X3415,X3416,X3417] :
( ~ ordere216010020id_add(X3415)
| ~ hBOOL(hAPP(X3415,bool,hAPP(X3415,fun(X3415,bool),ord_less_eq(X3415),X3417),zero_zero(X3415)))
| ~ hBOOL(hAPP(X3415,bool,hAPP(X3415,fun(X3415,bool),ord_less_eq(X3415),X3416),zero_zero(X3415)))
| hBOOL(hAPP(X3415,bool,hAPP(X3415,fun(X3415,bool),ord_less_eq(X3415),hAPP(X3415,X3415,hAPP(X3415,fun(X3415,X3415),plus_plus(X3415),X3417),X3416)),zero_zero(X3415))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_465_add__nonpos__nonpos])])]) ).
fof(i_0_957,plain,
! [X2576,X2577,X2578,X2579] :
( ( hBOOL(hAPP(fun(X2576,bool),bool,hAPP(X2576,fun(fun(X2576,bool),bool),member(X2576),X2577),X2578))
| ~ hBOOL(hAPP(fun(X2576,bool),bool,hAPP(X2576,fun(fun(X2576,bool),bool),member(X2576),X2577),hAPP(fun(X2576,bool),fun(X2576,bool),hAPP(fun(X2576,bool),fun(fun(X2576,bool),fun(X2576,bool)),minus_minus(fun(X2576,bool)),X2578),X2579))) )
& ( ~ hBOOL(hAPP(fun(X2576,bool),bool,hAPP(X2576,fun(fun(X2576,bool),bool),member(X2576),X2577),X2579))
| ~ hBOOL(hAPP(fun(X2576,bool),bool,hAPP(X2576,fun(fun(X2576,bool),bool),member(X2576),X2577),hAPP(fun(X2576,bool),fun(X2576,bool),hAPP(fun(X2576,bool),fun(fun(X2576,bool),fun(X2576,bool)),minus_minus(fun(X2576,bool)),X2578),X2579))) )
& ( ~ hBOOL(hAPP(fun(X2576,bool),bool,hAPP(X2576,fun(fun(X2576,bool),bool),member(X2576),X2577),X2578))
| hBOOL(hAPP(fun(X2576,bool),bool,hAPP(X2576,fun(fun(X2576,bool),bool),member(X2576),X2577),X2579))
| hBOOL(hAPP(fun(X2576,bool),bool,hAPP(X2576,fun(fun(X2576,bool),bool),member(X2576),X2577),hAPP(fun(X2576,bool),fun(X2576,bool),hAPP(fun(X2576,bool),fun(fun(X2576,bool),fun(X2576,bool)),minus_minus(fun(X2576,bool)),X2578),X2579))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_643])])]) ).
fof(i_0_958,plain,
! [X2557,X2558,X2559,X2560] :
( ( hBOOL(hAPP(fun(X2557,bool),bool,hAPP(X2557,fun(fun(X2557,bool),bool),member(X2557),X2558),X2559))
| ~ hBOOL(hAPP(fun(X2557,bool),bool,hAPP(X2557,fun(fun(X2557,bool),bool),member(X2557),X2558),hAPP(fun(X2557,bool),fun(X2557,bool),hAPP(fun(X2557,bool),fun(fun(X2557,bool),fun(X2557,bool)),minus_minus(fun(X2557,bool)),X2559),X2560))) )
& ( ~ hBOOL(hAPP(fun(X2557,bool),bool,hAPP(X2557,fun(fun(X2557,bool),bool),member(X2557),X2558),X2560))
| ~ hBOOL(hAPP(fun(X2557,bool),bool,hAPP(X2557,fun(fun(X2557,bool),bool),member(X2557),X2558),hAPP(fun(X2557,bool),fun(X2557,bool),hAPP(fun(X2557,bool),fun(fun(X2557,bool),fun(X2557,bool)),minus_minus(fun(X2557,bool)),X2559),X2560))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_199_DiffE])])]) ).
fof(i_0_959,plain,
! [X2565,X2566,X2567,X2568] :
( ~ hBOOL(hAPP(fun(X2565,bool),bool,hAPP(X2565,fun(fun(X2565,bool),bool),member(X2565),X2566),hAPP(fun(X2565,bool),fun(X2565,bool),hAPP(fun(X2565,bool),fun(fun(X2565,bool),fun(X2565,bool)),minus_minus(fun(X2565,bool)),X2567),X2568)))
| ~ hBOOL(hAPP(fun(X2565,bool),bool,hAPP(X2565,fun(fun(X2565,bool),bool),member(X2565),X2566),X2568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_644])]) ).
cnf(i_0_960,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_645]) ).
cnf(i_0_961,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk9_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_646]) ).
cnf(i_0_962,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_647]) ).
fof(i_0_963,plain,
! [X2641,X2642,X2643] :
( ~ hBOOL(hAPP(fun(X2641,bool),bool,finite_finite(X2641),X2643))
| ~ hBOOL(hAPP(fun(X2641,bool),bool,hAPP(X2641,fun(fun(X2641,bool),bool),member(X2641),X2642),X2643))
| hAPP(fun(X2641,bool),nat,finite_card(X2641),hAPP(fun(X2641,bool),fun(X2641,bool),hAPP(fun(X2641,bool),fun(fun(X2641,bool),fun(X2641,bool)),minus_minus(fun(X2641,bool)),X2643),hAPP(fun(X2641,bool),fun(X2641,bool),hAPP(X2641,fun(fun(X2641,bool),fun(X2641,bool)),insert(X2641),X2642),bot_bot(fun(X2641,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X2641,bool),nat,finite_card(X2641),X2643)),one_one(nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_218_card__Diff__singleton])]) ).
fof(i_0_964,plain,
! [X2644,X2645,X2646] :
( ( ~ hBOOL(hAPP(fun(X2644,bool),bool,hAPP(X2644,fun(fun(X2644,bool),bool),member(X2644),X2645),X2646))
| hAPP(fun(X2644,bool),nat,finite_card(X2644),hAPP(fun(X2644,bool),fun(X2644,bool),hAPP(fun(X2644,bool),fun(fun(X2644,bool),fun(X2644,bool)),minus_minus(fun(X2644,bool)),X2646),hAPP(fun(X2644,bool),fun(X2644,bool),hAPP(X2644,fun(fun(X2644,bool),fun(X2644,bool)),insert(X2644),X2645),bot_bot(fun(X2644,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X2644,bool),nat,finite_card(X2644),X2646)),one_one(nat))
| ~ hBOOL(hAPP(fun(X2644,bool),bool,finite_finite(X2644),X2646)) )
& ( hBOOL(hAPP(fun(X2644,bool),bool,hAPP(X2644,fun(fun(X2644,bool),bool),member(X2644),X2645),X2646))
| hAPP(fun(X2644,bool),nat,finite_card(X2644),hAPP(fun(X2644,bool),fun(X2644,bool),hAPP(fun(X2644,bool),fun(fun(X2644,bool),fun(X2644,bool)),minus_minus(fun(X2644,bool)),X2646),hAPP(fun(X2644,bool),fun(X2644,bool),hAPP(X2644,fun(fun(X2644,bool),fun(X2644,bool)),insert(X2644),X2645),bot_bot(fun(X2644,bool))))) = hAPP(fun(X2644,bool),nat,finite_card(X2644),X2646)
| ~ hBOOL(hAPP(fun(X2644,bool),bool,finite_finite(X2644),X2646)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_648])])]) ).
cnf(i_0_965,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_649]) ).
fof(i_0_966,plain,
! [X2892,X2893] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2892),X2893)),X2892)),
inference(variable_rename,[status(thm)],[i_0_650]) ).
fof(i_0_967,plain,
! [X2890,X2891] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2890),X2891)),X2891)),
inference(variable_rename,[status(thm)],[i_0_651]) ).
cnf(i_0_968,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_639]) ).
fof(i_0_969,plain,
! [X1924,X1925,X1926] : 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,X1924)),X1925)),hAPP(nat,nat,suc,X1926)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1924),X1925)),X1926),
inference(variable_rename,[status(thm)],[fact_37_Suc__diff__diff]) ).
fof(i_0_970,plain,
! [X2569,X2570,X2571,X2572] :
( ~ hBOOL(hAPP(fun(X2569,bool),bool,hAPP(X2569,fun(fun(X2569,bool),bool),member(X2569),X2570),hAPP(fun(X2569,bool),fun(X2569,bool),hAPP(fun(X2569,bool),fun(fun(X2569,bool),fun(X2569,bool)),minus_minus(fun(X2569,bool)),X2571),X2572)))
| hBOOL(hAPP(fun(X2569,bool),bool,hAPP(X2569,fun(fun(X2569,bool),bool),member(X2569),X2570),X2571)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_202_DiffD1])]) ).
cnf(i_0_971,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_652]) ).
fof(i_0_972,plain,
! [X1948,X1949,X1950,X1951,X1952] :
( ~ hBOOL(hAPP(fun(X1949,bool),bool,finite_finite(X1949),X1952))
| ~ hBOOL(hAPP(fun(X1948,bool),bool,hAPP(fun(X1948,bool),fun(fun(X1948,bool),bool),ord_less_eq(fun(X1948,bool)),X1950),hAPP(fun(X1949,bool),fun(X1948,bool),hAPP(fun(X1949,X1948),fun(fun(X1949,bool),fun(X1948,bool)),image(X1949,X1948),X1951),X1952)))
| hBOOL(hAPP(fun(X1948,bool),bool,finite_finite(X1948),X1950)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_finite__surj])]) ).
fof(i_0_973,plain,
! [X2352,X2353,X2354] :
( ( hBOOL(hAPP(fun(X2352,bool),bool,finite_finite(X2352),esk23_3(X2352,X2353,X2354)))
| hBOOL(hAPP(fun(X2352,bool),bool,X2353,X2354))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,X2353,bot_bot(fun(X2352,bool))))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,finite_finite(X2352),X2354)) )
& ( ~ hBOOL(hAPP(fun(X2352,bool),bool,hAPP(X2352,fun(fun(X2352,bool),bool),member(X2352),esk22_3(X2352,X2353,X2354)),esk23_3(X2352,X2353,X2354)))
| hBOOL(hAPP(fun(X2352,bool),bool,X2353,X2354))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,X2353,bot_bot(fun(X2352,bool))))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,finite_finite(X2352),X2354)) )
& ( hBOOL(hAPP(fun(X2352,bool),bool,X2353,esk23_3(X2352,X2353,X2354)))
| hBOOL(hAPP(fun(X2352,bool),bool,X2353,X2354))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,X2353,bot_bot(fun(X2352,bool))))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,finite_finite(X2352),X2354)) )
& ( ~ hBOOL(hAPP(fun(X2352,bool),bool,X2353,hAPP(fun(X2352,bool),fun(X2352,bool),hAPP(X2352,fun(fun(X2352,bool),fun(X2352,bool)),insert(X2352),esk22_3(X2352,X2353,X2354)),esk23_3(X2352,X2353,X2354))))
| hBOOL(hAPP(fun(X2352,bool),bool,X2353,X2354))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,X2353,bot_bot(fun(X2352,bool))))
| ~ hBOOL(hAPP(fun(X2352,bool),bool,finite_finite(X2352),X2354)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_653])])])]) ).
cnf(i_0_974,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_654]) ).
cnf(i_0_975,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_655]) ).
cnf(i_0_976,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk32_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),esk30_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_637]) ).
cnf(i_0_977,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk32_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),esk30_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_637]) ).
cnf(i_0_978,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ti(fun(X1,bool),X3) = bot_bot(fun(X1,bool))
| ti(fun(X1,bool),esk32_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),esk30_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_637]) ).
fof(i_0_979,plain,
! [X2445,X2446,X2447] : hBOOL(hAPP(fun(X2445,bool),bool,hAPP(fun(X2445,bool),fun(fun(X2445,bool),bool),ord_less_eq(fun(X2445,bool)),hAPP(fun(X2445,bool),fun(X2445,bool),hAPP(fun(X2445,bool),fun(fun(X2445,bool),fun(X2445,bool)),minus_minus(fun(X2445,bool)),X2446),X2447)),X2446)),
inference(variable_rename,[status(thm)],[fact_173_Diff__subset]) ).
fof(i_0_980,plain,
! [X1874] : 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)),X1874)))),
inference(variable_rename,[status(thm)],[fact_12_finite__Collect__le__nat]) ).
fof(i_0_981,plain,
! [X2860] : 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)),X2860)))),
inference(variable_rename,[status(thm)],[fact_292_finite__Collect__less__nat]) ).
cnf(i_0_982,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_656]) ).
cnf(i_0_983,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_657]) ).
cnf(i_0_984,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_658]) ).
cnf(i_0_985,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_659]) ).
fof(i_0_986,plain,
! [X2458,X2459,X2460,X2461] : hAPP(fun(X2458,bool),fun(X2458,bool),hAPP(fun(X2458,bool),fun(fun(X2458,bool),fun(X2458,bool)),minus_minus(fun(X2458,bool)),X2459),hAPP(fun(X2458,bool),fun(X2458,bool),hAPP(X2458,fun(fun(X2458,bool),fun(X2458,bool)),insert(X2458),X2460),X2461)) = hAPP(fun(X2458,bool),fun(X2458,bool),hAPP(fun(X2458,bool),fun(fun(X2458,bool),fun(X2458,bool)),minus_minus(fun(X2458,bool)),hAPP(fun(X2458,bool),fun(X2458,bool),hAPP(fun(X2458,bool),fun(fun(X2458,bool),fun(X2458,bool)),minus_minus(fun(X2458,bool)),X2459),X2461)),hAPP(fun(X2458,bool),fun(X2458,bool),hAPP(X2458,fun(fun(X2458,bool),fun(X2458,bool)),insert(X2458),X2460),bot_bot(fun(X2458,bool)))),
inference(variable_rename,[status(thm)],[fact_176_Diff__insert]) ).
fof(i_0_987,plain,
! [X2838,X2839,X2840] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2839),X2840))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2838),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2840),X2839))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2838),X2839)),hAPP(nat,nat,suc,X2840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_284_diff__Suc__diff__eq1])]) ).
fof(i_0_988,plain,
! [X2561,X2562,X2563,X2564] :
( ~ hBOOL(hAPP(fun(X2561,bool),bool,hAPP(X2561,fun(fun(X2561,bool),bool),member(X2561),X2563),X2564))
| hBOOL(hAPP(fun(X2561,bool),bool,hAPP(X2561,fun(fun(X2561,bool),bool),member(X2561),X2563),X2562))
| hBOOL(hAPP(fun(X2561,bool),bool,hAPP(X2561,fun(fun(X2561,bool),bool),member(X2561),X2563),hAPP(fun(X2561,bool),fun(X2561,bool),hAPP(fun(X2561,bool),fun(fun(X2561,bool),fun(X2561,bool)),minus_minus(fun(X2561,bool)),X2564),X2562))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_660])]) ).
fof(i_0_989,plain,
! [X2084,X2085,X2086,X2087,X2088] :
( ~ hBOOL(hAPP(fun(X2085,bool),bool,hAPP(X2085,fun(fun(X2085,bool),bool),member(X2085),X2087),X2088))
| hBOOL(hAPP(fun(X2084,bool),bool,hAPP(X2084,fun(fun(X2084,bool),bool),member(X2084),hAPP(X2085,X2084,X2086,X2087)),hAPP(fun(X2085,bool),fun(X2084,bool),hAPP(fun(X2085,X2084),fun(fun(X2085,bool),fun(X2084,bool)),image(X2085,X2084),X2086),X2088))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_80_imageI])]) ).
fof(i_0_990,plain,
! [X1932,X1933,X1934] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1933),X1934))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1933),X1932))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1934),X1933)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1932),X1933)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1934),X1932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_40_Nat_Odiff__diff__eq])]) ).
cnf(i_0_991,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_661]) ).
cnf(i_0_992,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_661]) ).
cnf(i_0_993,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_661]) ).
cnf(i_0_994,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_661]) ).
cnf(i_0_995,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_662]) ).
cnf(i_0_996,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_663]) ).
fof(i_0_997,plain,
! [X2432,X2433,X2434,X2435] :
( ( ~ hBOOL(hAPP(fun(X2432,bool),bool,hAPP(X2432,fun(fun(X2432,bool),bool),member(X2432),X2434),X2435))
| hAPP(fun(X2432,bool),fun(X2432,bool),hAPP(fun(X2432,bool),fun(fun(X2432,bool),fun(X2432,bool)),minus_minus(fun(X2432,bool)),hAPP(fun(X2432,bool),fun(X2432,bool),hAPP(X2432,fun(fun(X2432,bool),fun(X2432,bool)),insert(X2432),X2434),X2433)),X2435) = hAPP(fun(X2432,bool),fun(X2432,bool),hAPP(fun(X2432,bool),fun(fun(X2432,bool),fun(X2432,bool)),minus_minus(fun(X2432,bool)),X2433),X2435) )
& ( hBOOL(hAPP(fun(X2432,bool),bool,hAPP(X2432,fun(fun(X2432,bool),bool),member(X2432),X2434),X2435))
| hAPP(fun(X2432,bool),fun(X2432,bool),hAPP(fun(X2432,bool),fun(fun(X2432,bool),fun(X2432,bool)),minus_minus(fun(X2432,bool)),hAPP(fun(X2432,bool),fun(X2432,bool),hAPP(X2432,fun(fun(X2432,bool),fun(X2432,bool)),insert(X2432),X2434),X2433)),X2435) = hAPP(fun(X2432,bool),fun(X2432,bool),hAPP(X2432,fun(fun(X2432,bool),fun(X2432,bool)),insert(X2432),X2434),hAPP(fun(X2432,bool),fun(X2432,bool),hAPP(fun(X2432,bool),fun(fun(X2432,bool),fun(X2432,bool)),minus_minus(fun(X2432,bool)),X2433),X2435)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_664])]) ).
cnf(i_0_998,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_665]) ).
fof(i_0_999,plain,
! [X3357,X3358,X3359,X3360] :
( ( hBOOL(hAPP(fun(X3357,bool),bool,finite_finite(X3357),X3359))
| ~ hBOOL(hAPP(fun(sum_sum(X3357,X3358),bool),bool,finite_finite(sum_sum(X3357,X3358)),hAPP(fun(X3358,bool),fun(sum_sum(X3357,X3358),bool),hAPP(fun(X3357,bool),fun(fun(X3358,bool),fun(sum_sum(X3357,X3358),bool)),sum_Plus(X3357,X3358),X3359),X3360))) )
& ( hBOOL(hAPP(fun(X3358,bool),bool,finite_finite(X3358),X3360))
| ~ hBOOL(hAPP(fun(sum_sum(X3357,X3358),bool),bool,finite_finite(sum_sum(X3357,X3358)),hAPP(fun(X3358,bool),fun(sum_sum(X3357,X3358),bool),hAPP(fun(X3357,bool),fun(fun(X3358,bool),fun(sum_sum(X3357,X3358),bool)),sum_Plus(X3357,X3358),X3359),X3360))) )
& ( ~ hBOOL(hAPP(fun(X3357,bool),bool,finite_finite(X3357),X3359))
| ~ hBOOL(hAPP(fun(X3358,bool),bool,finite_finite(X3358),X3360))
| hBOOL(hAPP(fun(sum_sum(X3357,X3358),bool),bool,finite_finite(sum_sum(X3357,X3358)),hAPP(fun(X3358,bool),fun(sum_sum(X3357,X3358),bool),hAPP(fun(X3357,bool),fun(fun(X3358,bool),fun(sum_sum(X3357,X3358),bool)),sum_Plus(X3357,X3358),X3359),X3360))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_441_finite__Plus__iff])])]) ).
fof(i_0_1000,plain,
! [X3365,X3366,X3367,X3368] :
( ~ hBOOL(hAPP(fun(sum_sum(X3365,X3366),bool),bool,finite_finite(sum_sum(X3365,X3366)),hAPP(fun(X3366,bool),fun(sum_sum(X3365,X3366),bool),hAPP(fun(X3365,bool),fun(fun(X3366,bool),fun(sum_sum(X3365,X3366),bool)),sum_Plus(X3365,X3366),X3367),X3368)))
| hBOOL(hAPP(fun(X3365,bool),bool,finite_finite(X3365),X3367)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_443_finite__PlusD_I1_J])]) ).
fof(i_0_1001,plain,
! [X3369,X3370,X3371,X3372] :
( ~ hBOOL(hAPP(fun(sum_sum(X3369,X3370),bool),bool,finite_finite(sum_sum(X3369,X3370)),hAPP(fun(X3370,bool),fun(sum_sum(X3369,X3370),bool),hAPP(fun(X3369,bool),fun(fun(X3370,bool),fun(sum_sum(X3369,X3370),bool)),sum_Plus(X3369,X3370),X3371),X3372)))
| hBOOL(hAPP(fun(X3370,bool),bool,finite_finite(X3370),X3372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_444_finite__PlusD_I2_J])]) ).
fof(i_0_1002,plain,
! [X2964,X2965,X2966] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2965),X2966))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2965),X2964)),X2966)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_329_less__imp__diff__less])]) ).
fof(i_0_1003,plain,
! [X2801,X2802,X2803] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2802),X2803))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2803),X2802)),X2801) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2803),X2801)),X2802) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_270_add__diff__assoc2])]) ).
fof(i_0_1004,plain,
! [X2798,X2799,X2800] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2799),X2800))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2800),X2798)),X2799) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2800),X2799)),X2798) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_269_diff__add__assoc2])]) ).
fof(i_0_1005,plain,
! [X3265,X3266,X3267] :
( ~ hBOOL(hAPP(fun(X3265,bool),bool,hAPP(fun(X3265,bool),fun(fun(X3265,bool),bool),ord_less(fun(X3265,bool)),X3266),X3267))
| hBOOL(hAPP(fun(X3265,bool),bool,hAPP(X3265,fun(fun(X3265,bool),bool),member(X3265),esk57_3(X3265,X3266,X3267)),hAPP(fun(X3265,bool),fun(X3265,bool),hAPP(fun(X3265,bool),fun(fun(X3265,bool),fun(X3265,bool)),minus_minus(fun(X3265,bool)),X3267),X3266))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_426_psubset__imp__ex__mem])])]) ).
cnf(i_0_1006,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_666]) ).
cnf(i_0_1007,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_667]) ).
cnf(i_0_1008,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_668]) ).
cnf(i_0_1009,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_669]) ).
cnf(i_0_1010,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_647]) ).
fof(i_0_1011,plain,
! [X3401,X3402,X3403] :
( ~ ordere216010020id_add(X3401)
| ~ hBOOL(hAPP(X3401,bool,hAPP(X3401,fun(X3401,bool),ord_less_eq(X3401),zero_zero(X3401)),X3403))
| ~ hBOOL(hAPP(X3401,bool,hAPP(X3401,fun(X3401,bool),ord_less_eq(X3401),zero_zero(X3401)),X3402))
| hBOOL(hAPP(X3401,bool,hAPP(X3401,fun(X3401,bool),ord_less_eq(X3401),zero_zero(X3401)),hAPP(X3401,X3401,hAPP(X3401,fun(X3401,X3401),plus_plus(X3401),X3403),X3402))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_461_add__nonneg__nonneg])])]) ).
fof(i_0_1012,plain,
! [X3407,X3408,X3409,X3410] :
( ~ ordere216010020id_add(X3407)
| ~ hBOOL(hAPP(X3407,bool,hAPP(X3407,fun(X3407,bool),ord_less_eq(X3407),zero_zero(X3407)),X3410))
| ~ hBOOL(hAPP(X3407,bool,hAPP(X3407,fun(X3407,bool),ord_less_eq(X3407),X3408),X3409))
| hBOOL(hAPP(X3407,bool,hAPP(X3407,fun(X3407,bool),ord_less_eq(X3407),X3408),hAPP(X3407,X3407,hAPP(X3407,fun(X3407,X3407),plus_plus(X3407),X3410),X3409))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_463_add__increasing])])]) ).
fof(i_0_1013,plain,
! [X3411,X3412,X3413,X3414] :
( ~ ordere216010020id_add(X3411)
| ~ hBOOL(hAPP(X3411,bool,hAPP(X3411,fun(X3411,bool),ord_less_eq(X3411),zero_zero(X3411)),X3414))
| ~ hBOOL(hAPP(X3411,bool,hAPP(X3411,fun(X3411,bool),ord_less_eq(X3411),X3412),X3413))
| hBOOL(hAPP(X3411,bool,hAPP(X3411,fun(X3411,bool),ord_less_eq(X3411),X3412),hAPP(X3411,X3411,hAPP(X3411,fun(X3411,X3411),plus_plus(X3411),X3413),X3414))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_464_add__increasing2])])]) ).
fof(i_0_1014,plain,
! [X3389,X3390,X3391,X3392] :
( ~ linordered_semidom(X3389)
| ~ hBOOL(hAPP(X3389,bool,hAPP(X3389,fun(X3389,bool),ord_less(X3389),zero_zero(X3389)),X3392))
| ~ hBOOL(hAPP(X3389,bool,hAPP(X3389,fun(X3389,bool),ord_less(X3389),X3390),X3391))
| hBOOL(hAPP(X3389,bool,hAPP(X3389,fun(X3389,bool),ord_less(X3389),X3390),hAPP(X3389,X3389,hAPP(X3389,fun(X3389,X3389),plus_plus(X3389),X3392),X3391))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_454_pos__add__strict])])]) ).
fof(i_0_1015,plain,
! [X2098,X2099,X2100,X2101,X2102,X2103] : hAPP(fun(X2098,bool),fun(X2099,bool),hAPP(fun(X2098,X2099),fun(fun(X2098,bool),fun(X2099,bool)),image(X2098,X2099),X2101),hAPP(fun(X2100,bool),fun(X2098,bool),hAPP(fun(X2100,X2098),fun(fun(X2100,bool),fun(X2098,bool)),image(X2100,X2098),X2102),X2103)) = hAPP(fun(X2100,bool),fun(X2099,bool),hAPP(fun(X2100,X2099),fun(fun(X2100,bool),fun(X2099,bool)),image(X2100,X2099),hAPP(fun(X2100,X2098),fun(X2100,X2099),hAPP(fun(X2098,X2099),fun(fun(X2100,X2098),fun(X2100,X2099)),combb(X2098,X2099,X2100),X2101),X2102)),X2103),
inference(variable_rename,[status(thm)],[fact_83_image__image]) ).
fof(i_0_1016,plain,
! [X3292,X3293,X3294,X3295] :
( ( hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less(X3292),X3294),esk65_4(X3292,X3293,X3294,X3295)))
| hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less_eq(X3292),X3295),X3293))
| ~ hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less(X3292),X3294),X3295))
| ~ dense_linorder(X3292) )
& ( hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less(X3292),esk65_4(X3292,X3293,X3294,X3295)),X3295))
| hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less_eq(X3292),X3295),X3293))
| ~ hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less(X3292),X3294),X3295))
| ~ dense_linorder(X3292) )
& ( ~ hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less_eq(X3292),esk65_4(X3292,X3293,X3294,X3295)),X3293))
| hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less_eq(X3292),X3295),X3293))
| ~ hBOOL(hAPP(X3292,bool,hAPP(X3292,fun(X3292,bool),ord_less(X3292),X3294),X3295))
| ~ dense_linorder(X3292) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_432_dense__le__bounded])])])])]) ).
fof(i_0_1017,plain,
! [X2425,X2426,X2427] :
( ( ~ hBOOL(hAPP(fun(X2425,bool),bool,finite_finite(X2425),hAPP(fun(X2425,bool),fun(X2425,bool),hAPP(fun(X2425,bool),fun(fun(X2425,bool),fun(X2425,bool)),minus_minus(fun(X2425,bool)),X2426),X2427)))
| hBOOL(hAPP(fun(X2425,bool),bool,finite_finite(X2425),X2426))
| ~ hBOOL(hAPP(fun(X2425,bool),bool,finite_finite(X2425),X2427)) )
& ( ~ hBOOL(hAPP(fun(X2425,bool),bool,finite_finite(X2425),X2426))
| hBOOL(hAPP(fun(X2425,bool),bool,finite_finite(X2425),hAPP(fun(X2425,bool),fun(X2425,bool),hAPP(fun(X2425,bool),fun(fun(X2425,bool),fun(X2425,bool)),minus_minus(fun(X2425,bool)),X2426),X2427)))
| ~ hBOOL(hAPP(fun(X2425,bool),bool,finite_finite(X2425),X2427)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_finite__Diff2])])]) ).
cnf(i_0_1018,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_670]) ).
fof(i_0_1019,plain,
! [X2117,X2118,X2119,X2120] :
( ~ hBOOL(hAPP(fun(X2117,bool),bool,hAPP(fun(X2117,bool),fun(fun(X2117,bool),bool),ord_less_eq(fun(X2117,bool)),X2119),X2120))
| hBOOL(hAPP(fun(X2117,bool),bool,hAPP(fun(X2117,bool),fun(fun(X2117,bool),bool),ord_less_eq(fun(X2117,bool)),X2119),hAPP(fun(X2117,bool),fun(X2117,bool),hAPP(X2117,fun(fun(X2117,bool),fun(X2117,bool)),insert(X2117),X2118),X2120))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_88_subset__insertI2])]) ).
fof(i_0_1020,plain,
! [X2484,X2485,X2486,X2487,X2488] :
( ~ hBOOL(hAPP(fun(fun(X2484,bool),X2484),bool,hAPP(fun(X2484,fun(X2484,X2484)),fun(fun(fun(X2484,bool),X2484),bool),finite2073411215e_idem(X2484),X2487),X2488))
| ~ hBOOL(hAPP(fun(X2484,bool),bool,finite_finite(X2484),X2486))
| ~ hBOOL(hAPP(fun(X2484,bool),bool,hAPP(X2484,fun(fun(X2484,bool),bool),member(X2484),X2485),X2486))
| hAPP(X2484,X2484,hAPP(X2484,fun(X2484,X2484),X2487,X2485),hAPP(fun(X2484,bool),X2484,X2488,X2486)) = hAPP(fun(X2484,bool),X2484,X2488,X2486) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_183_folding__one__idem_Oin__idem])]) ).
fof(i_0_1021,plain,
! [X2428,X2429,X2430,X2431] :
( ~ hBOOL(hAPP(fun(X2428,bool),bool,hAPP(X2428,fun(fun(X2428,bool),bool),member(X2428),X2430),X2431))
| hAPP(fun(X2428,bool),fun(X2428,bool),hAPP(fun(X2428,bool),fun(fun(X2428,bool),fun(X2428,bool)),minus_minus(fun(X2428,bool)),hAPP(fun(X2428,bool),fun(X2428,bool),hAPP(X2428,fun(fun(X2428,bool),fun(X2428,bool)),insert(X2428),X2430),X2429)),X2431) = hAPP(fun(X2428,bool),fun(X2428,bool),hAPP(fun(X2428,bool),fun(fun(X2428,bool),fun(X2428,bool)),minus_minus(fun(X2428,bool)),X2429),X2431) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_169_insert__Diff1])]) ).
fof(i_0_1022,plain,
! [X3397,X3398] :
( ( ~ hBOOL(hAPP(X3397,bool,hAPP(X3397,fun(X3397,bool),ord_less_eq(X3397),zero_zero(X3397)),hAPP(X3397,X3397,hAPP(X3397,fun(X3397,X3397),plus_plus(X3397),X3398),X3398)))
| hBOOL(hAPP(X3397,bool,hAPP(X3397,fun(X3397,bool),ord_less_eq(X3397),zero_zero(X3397)),X3398))
| ~ linord219039673up_add(X3397) )
& ( ~ hBOOL(hAPP(X3397,bool,hAPP(X3397,fun(X3397,bool),ord_less_eq(X3397),zero_zero(X3397)),X3398))
| hBOOL(hAPP(X3397,bool,hAPP(X3397,fun(X3397,bool),ord_less_eq(X3397),zero_zero(X3397)),hAPP(X3397,X3397,hAPP(X3397,fun(X3397,X3397),plus_plus(X3397),X3398),X3398)))
| ~ linord219039673up_add(X3397) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_459_zero__le__double__add__iff__zero__le__single__add])])])]) ).
fof(i_0_1023,plain,
! [X2506,X2507,X2508] :
( ~ hBOOL(hAPP(fun(X2506,bool),bool,finite_finite(X2506),X2508))
| ~ hBOOL(hAPP(fun(X2506,bool),bool,hAPP(fun(X2506,bool),fun(fun(X2506,bool),bool),ord_less_eq(fun(X2506,bool)),X2508),X2507))
| hAPP(fun(X2506,bool),nat,finite_card(X2506),hAPP(fun(X2506,bool),fun(X2506,bool),hAPP(fun(X2506,bool),fun(fun(X2506,bool),fun(X2506,bool)),minus_minus(fun(X2506,bool)),X2507),X2508)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X2506,bool),nat,finite_card(X2506),X2507)),hAPP(fun(X2506,bool),nat,finite_card(X2506),X2508)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_card__Diff__subset])]) ).
cnf(i_0_1024,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_671]) ).
fof(i_0_1025,plain,
! [X1854,X1855,X1856] :
( ~ hBOOL(hAPP(fun(X1854,bool),bool,finite_finite(X1854),X1856))
| ~ hBOOL(hAPP(fun(X1854,bool),bool,hAPP(fun(X1854,bool),fun(fun(X1854,bool),bool),ord_less_eq(fun(X1854,bool)),X1855),X1856))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1854,bool),nat,finite_card(X1854),X1855)),hAPP(fun(X1854,bool),nat,finite_card(X1854),X1856))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_card__mono])]) ).
fof(i_0_1026,plain,
! [X3221,X3222,X3223] :
( ~ hBOOL(hAPP(fun(X3221,bool),bool,finite_finite(X3221),X3223))
| ~ hBOOL(hAPP(fun(X3221,bool),bool,hAPP(fun(X3221,bool),fun(fun(X3221,bool),bool),ord_less(fun(X3221,bool)),X3222),X3223))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3221,bool),nat,finite_card(X3221),X3222)),hAPP(fun(X3221,bool),nat,finite_card(X3221),X3223))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_415_psubset__card__mono])]) ).
fof(i_0_1027,plain,
! [X2025,X2026,X2027,X2028] :
( ~ hBOOL(hAPP(fun(X2025,bool),bool,hAPP(X2025,fun(fun(X2025,bool),bool),member(X2025),X2027),X2028))
| hBOOL(hAPP(fun(X2025,bool),bool,hAPP(X2025,fun(fun(X2025,bool),bool),member(X2025),X2027),hAPP(fun(X2025,bool),fun(X2025,bool),hAPP(X2025,fun(fun(X2025,bool),fun(X2025,bool)),insert(X2025),X2026),X2028))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_insertI2])]) ).
fof(i_0_1028,plain,
! [X3172,X3173] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3172),X3173)),hAPP(nat,nat,suc,X3172))),
inference(variable_rename,[status(thm)],[fact_399_diff__less__Suc]) ).
fof(i_0_1029,plain,
! [X3148,X3149] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3148),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3148),X3149)))),
inference(variable_rename,[status(thm)],[fact_389_less__add__Suc1]) ).
fof(i_0_1030,plain,
! [X3150,X3151] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3150),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3151),X3150)))),
inference(variable_rename,[status(thm)],[fact_390_less__add__Suc2]) ).
fof(i_0_1031,plain,
! [X2466,X2467,X2468] : hAPP(fun(X2466,bool),fun(X2466,bool),hAPP(X2466,fun(fun(X2466,bool),fun(X2466,bool)),insert(X2466),X2467),hAPP(fun(X2466,bool),fun(X2466,bool),hAPP(fun(X2466,bool),fun(fun(X2466,bool),fun(X2466,bool)),minus_minus(fun(X2466,bool)),X2468),hAPP(fun(X2466,bool),fun(X2466,bool),hAPP(X2466,fun(fun(X2466,bool),fun(X2466,bool)),insert(X2466),X2467),bot_bot(fun(X2466,bool))))) = hAPP(fun(X2466,bool),fun(X2466,bool),hAPP(X2466,fun(fun(X2466,bool),fun(X2466,bool)),insert(X2466),X2467),X2468),
inference(variable_rename,[status(thm)],[fact_178_insert__Diff__single]) ).
fof(i_0_1032,plain,
! [X2065,X2066,X2067,X2068] :
( ~ hBOOL(hAPP(fun(X2065,bool),bool,hAPP(fun(X2065,bool),fun(fun(X2065,bool),bool),ord_less_eq(fun(X2065,bool)),X2067),X2068))
| ~ hBOOL(hAPP(fun(X2065,bool),bool,hAPP(fun(X2065,bool),fun(fun(X2065,bool),bool),ord_less_eq(fun(X2065,bool)),X2068),X2066))
| hBOOL(hAPP(fun(X2065,bool),bool,hAPP(fun(X2065,bool),fun(fun(X2065,bool),bool),ord_less_eq(fun(X2065,bool)),X2067),X2066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_77_subset__trans])]) ).
fof(i_0_1033,plain,
! [X3202,X3203,X3204,X3205] :
( ~ hBOOL(hAPP(fun(X3202,bool),bool,hAPP(fun(X3202,bool),fun(fun(X3202,bool),bool),ord_less(fun(X3202,bool)),X3204),X3205))
| ~ hBOOL(hAPP(fun(X3202,bool),bool,hAPP(fun(X3202,bool),fun(fun(X3202,bool),bool),ord_less_eq(fun(X3202,bool)),X3205),X3203))
| hBOOL(hAPP(fun(X3202,bool),bool,hAPP(fun(X3202,bool),fun(fun(X3202,bool),bool),ord_less(fun(X3202,bool)),X3204),X3203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_409_psubset__subset__trans])]) ).
fof(i_0_1034,plain,
! [X3198,X3199,X3200,X3201] :
( ~ hBOOL(hAPP(fun(X3198,bool),bool,hAPP(fun(X3198,bool),fun(fun(X3198,bool),bool),ord_less_eq(fun(X3198,bool)),X3200),X3201))
| ~ hBOOL(hAPP(fun(X3198,bool),bool,hAPP(fun(X3198,bool),fun(fun(X3198,bool),bool),ord_less(fun(X3198,bool)),X3201),X3199))
| hBOOL(hAPP(fun(X3198,bool),bool,hAPP(fun(X3198,bool),fun(fun(X3198,bool),bool),ord_less(fun(X3198,bool)),X3200),X3199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_408_subset__psubset__trans])]) ).
fof(i_0_1035,plain,
! [X3248,X3249,X3250,X3251] :
( ~ hBOOL(hAPP(fun(X3248,bool),bool,hAPP(fun(X3248,bool),fun(fun(X3248,bool),bool),ord_less(fun(X3248,bool)),X3250),X3251))
| ~ hBOOL(hAPP(fun(X3248,bool),bool,hAPP(fun(X3248,bool),fun(fun(X3248,bool),bool),ord_less(fun(X3248,bool)),X3251),X3249))
| hBOOL(hAPP(fun(X3248,bool),bool,hAPP(fun(X3248,bool),fun(fun(X3248,bool),bool),ord_less(fun(X3248,bool)),X3250),X3249)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_421_psubset__trans])]) ).
fof(i_0_1036,plain,
! [X2804,X2805,X2806] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2805),X2806))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2804),X2806)),X2805) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2804),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2806),X2805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_271_diff__add__assoc])]) ).
fof(i_0_1037,plain,
! [X2815,X2816,X2817] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2816),X2817))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2815),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2817),X2816)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2815),X2817)),X2816) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_275_add__diff__assoc])]) ).
fof(i_0_1038,plain,
! [X2826,X2827,X2828] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2827),X2828))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2826),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2828),X2827)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2826),X2827)),X2828) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_diff__diff__right])]) ).
fof(i_0_1039,plain,
! [X1917,X1918] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1917)),hAPP(nat,nat,suc,X1918)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1917),X1918)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1917),X1918))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1917)),hAPP(nat,nat,suc,X1918))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_Suc__le__mono])]) ).
fof(i_0_1040,plain,
! [X2945,X2946] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2945)),hAPP(nat,nat,suc,X2946)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2945),X2946)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2945),X2946))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2945)),hAPP(nat,nat,suc,X2946))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_320_Suc__less__eq])]) ).
fof(i_0_1041,plain,
! [X2928,X2929] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2928)),hAPP(nat,nat,suc,X2929)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2928),X2929)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_312_Suc__less__SucD])]) ).
fof(i_0_1042,plain,
! [X2934,X2935,X2936] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2935),X2936))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2936),X2934))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2935)),X2934)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_315_less__trans__Suc])]) ).
cnf(i_0_1043,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_672]) ).
fof(i_0_1044,plain,
! [X2130,X2131,X2132,X2133,X2134] :
( ~ hBOOL(hAPP(fun(X2131,bool),bool,hAPP(X2131,fun(fun(X2131,bool),bool),member(X2131),X2133),X2134))
| hAPP(fun(X2130,bool),fun(X2130,bool),hAPP(X2130,fun(fun(X2130,bool),fun(X2130,bool)),insert(X2130),hAPP(X2131,X2130,X2132,X2133)),hAPP(fun(X2131,bool),fun(X2130,bool),hAPP(fun(X2131,X2130),fun(fun(X2131,bool),fun(X2130,bool)),image(X2131,X2130),X2132),X2134)) = hAPP(fun(X2131,bool),fun(X2130,bool),hAPP(fun(X2131,X2130),fun(fun(X2131,bool),fun(X2130,bool)),image(X2131,X2130),X2132),X2134) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_insert__image])]) ).
fof(i_0_1045,plain,
! [X3361,X3362,X3363,X3364] :
( ~ hBOOL(hAPP(fun(X3362,bool),bool,finite_finite(X3362),X3364))
| ~ hBOOL(hAPP(fun(X3361,bool),bool,finite_finite(X3361),X3363))
| hBOOL(hAPP(fun(sum_sum(X3362,X3361),bool),bool,finite_finite(sum_sum(X3362,X3361)),hAPP(fun(X3361,bool),fun(sum_sum(X3362,X3361),bool),hAPP(fun(X3362,bool),fun(fun(X3361,bool),fun(sum_sum(X3362,X3361),bool)),sum_Plus(X3362,X3361),X3364),X3363))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_442_finite__Plus])]) ).
cnf(i_0_1046,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_661]) ).
cnf(i_0_1047,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_661]) ).
fof(i_0_1048,plain,
! [X2047,X2048,X2049,X2050] :
( ~ hBOOL(hAPP(fun(X2047,bool),bool,hAPP(X2047,fun(fun(X2047,bool),bool),member(X2047),X2049),X2050))
| ~ hBOOL(hAPP(fun(X2047,bool),bool,hAPP(fun(X2047,bool),fun(fun(X2047,bool),bool),ord_less_eq(fun(X2047,bool)),X2050),X2048))
| hBOOL(hAPP(fun(X2047,bool),bool,hAPP(X2047,fun(fun(X2047,bool),bool),member(X2047),X2049),X2048)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_set__rev__mp])]) ).
fof(i_0_1049,plain,
! [X2051,X2052,X2053,X2054] :
( ~ hBOOL(hAPP(fun(X2051,bool),bool,hAPP(fun(X2051,bool),fun(fun(X2051,bool),bool),ord_less_eq(fun(X2051,bool)),X2053),X2054))
| ~ hBOOL(hAPP(fun(X2051,bool),bool,hAPP(X2051,fun(fun(X2051,bool),bool),member(X2051),X2052),X2053))
| hBOOL(hAPP(fun(X2051,bool),bool,hAPP(X2051,fun(fun(X2051,bool),bool),member(X2051),X2052),X2054)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_set__mp])]) ).
fof(i_0_1050,plain,
! [X2043,X2044,X2045,X2046] :
( ~ hBOOL(hAPP(fun(X2043,bool),bool,hAPP(fun(X2043,bool),fun(fun(X2043,bool),bool),ord_less_eq(fun(X2043,bool)),X2045),X2046))
| ~ hBOOL(hAPP(fun(X2043,bool),bool,hAPP(X2043,fun(fun(X2043,bool),bool),member(X2043),X2044),X2045))
| hBOOL(hAPP(fun(X2043,bool),bool,hAPP(X2043,fun(fun(X2043,bool),bool),member(X2043),X2044),X2046)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_in__mono])]) ).
fof(i_0_1051,plain,
! [X1978,X1979,X1980,X1981] :
( ~ hBOOL(hAPP(fun(X1978,bool),bool,hAPP(fun(X1978,bool),fun(fun(X1978,bool),bool),ord_less_eq(fun(X1978,bool)),X1980),X1981))
| ~ hBOOL(hAPP(fun(X1978,bool),bool,hAPP(X1978,fun(fun(X1978,bool),bool),member(X1978),X1979),X1980))
| hBOOL(hAPP(fun(X1978,bool),bool,hAPP(X1978,fun(fun(X1978,bool),bool),member(X1978),X1979),X1981)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_subsetD])]) ).
fof(i_0_1052,plain,
! [X3244,X3245,X3246,X3247] :
( ~ hBOOL(hAPP(fun(X3244,bool),bool,hAPP(fun(X3244,bool),fun(fun(X3244,bool),bool),ord_less(fun(X3244,bool)),X3246),X3247))
| ~ hBOOL(hAPP(fun(X3244,bool),bool,hAPP(X3244,fun(fun(X3244,bool),bool),member(X3244),X3245),X3246))
| hBOOL(hAPP(fun(X3244,bool),bool,hAPP(X3244,fun(fun(X3244,bool),bool),member(X3244),X3245),X3247)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_420_psubsetD])]) ).
fof(i_0_1053,plain,
! [X2192,X2193,X2194,X2195,X2196] :
( ~ ord(X2193)
| ~ hBOOL(hAPP(fun(X2192,X2193),bool,hAPP(fun(X2192,X2193),fun(fun(X2192,X2193),bool),ord_less_eq(fun(X2192,X2193)),X2195),X2196))
| hBOOL(hAPP(X2193,bool,hAPP(X2193,fun(X2193,bool),ord_less_eq(X2193),hAPP(X2192,X2193,X2195,X2194)),hAPP(X2192,X2193,X2196,X2194))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_102_le__funE])])]) ).
fof(i_0_1054,plain,
! [X2187,X2188,X2189,X2190,X2191] :
( ~ ord(X2188)
| ~ hBOOL(hAPP(fun(X2187,X2188),bool,hAPP(fun(X2187,X2188),fun(fun(X2187,X2188),bool),ord_less_eq(fun(X2187,X2188)),X2190),X2191))
| hBOOL(hAPP(X2188,bool,hAPP(X2188,fun(X2188,bool),ord_less_eq(X2188),hAPP(X2187,X2188,X2190,X2189)),hAPP(X2187,X2188,X2191,X2189))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_101_le__funD])])]) ).
fof(i_0_1055,plain,
! [X1921,X1922] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1921),X1922))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1922)),X1921)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1922)),X1921))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1921),X1922)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_673])]) ).
fof(i_0_1056,plain,
! [X1902,X1903,X1904] :
( ( ~ hBOOL(hAPP(fun(X1902,bool),bool,finite_finite(X1902),hAPP(fun(X1902,bool),fun(X1902,bool),hAPP(X1902,fun(fun(X1902,bool),fun(X1902,bool)),insert(X1902),X1903),X1904)))
| hBOOL(hAPP(fun(X1902,bool),bool,finite_finite(X1902),X1904)) )
& ( ~ hBOOL(hAPP(fun(X1902,bool),bool,finite_finite(X1902),X1904))
| hBOOL(hAPP(fun(X1902,bool),bool,finite_finite(X1902),hAPP(fun(X1902,bool),fun(X1902,bool),hAPP(X1902,fun(fun(X1902,bool),fun(X1902,bool)),insert(X1902),X1903),X1904))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_finite__insert])]) ).
cnf(i_0_1057,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),esk53_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)),esk52_2(X1,X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_657]) ).
cnf(i_0_1058,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_674]) ).
fof(i_0_1059,plain,
! [X1946,X1947] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1946),X1947)),X1946)),
inference(variable_rename,[status(thm)],[fact_45_diff__le__self]) ).
fof(i_0_1060,plain,
! [X1896,X1897,X1898] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1896),X1897)),X1898) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1896),X1898)),X1897),
inference(variable_rename,[status(thm)],[fact_25_diff__commute]) ).
fof(i_0_1061,plain,
! [X3217,X3218,X3219,X3220] :
( ( hBOOL(hAPP(fun(X3217,X3218),bool,hAPP(fun(X3217,X3218),fun(fun(X3217,X3218),bool),ord_less_eq(fun(X3217,X3218)),X3219),X3220))
| ~ hBOOL(hAPP(fun(X3217,X3218),bool,hAPP(fun(X3217,X3218),fun(fun(X3217,X3218),bool),ord_less(fun(X3217,X3218)),X3219),X3220))
| ~ ord(X3218) )
& ( ~ hBOOL(hAPP(fun(X3217,X3218),bool,hAPP(fun(X3217,X3218),fun(fun(X3217,X3218),bool),ord_less_eq(fun(X3217,X3218)),X3220),X3219))
| ~ hBOOL(hAPP(fun(X3217,X3218),bool,hAPP(fun(X3217,X3218),fun(fun(X3217,X3218),bool),ord_less(fun(X3217,X3218)),X3219),X3220))
| ~ ord(X3218) )
& ( ~ hBOOL(hAPP(fun(X3217,X3218),bool,hAPP(fun(X3217,X3218),fun(fun(X3217,X3218),bool),ord_less_eq(fun(X3217,X3218)),X3219),X3220))
| hBOOL(hAPP(fun(X3217,X3218),bool,hAPP(fun(X3217,X3218),fun(fun(X3217,X3218),bool),ord_less_eq(fun(X3217,X3218)),X3220),X3219))
| hBOOL(hAPP(fun(X3217,X3218),bool,hAPP(fun(X3217,X3218),fun(fun(X3217,X3218),bool),ord_less(fun(X3217,X3218)),X3219),X3220))
| ~ ord(X3218) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_675])])])]) ).
cnf(i_0_1062,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_676]) ).
fof(i_0_1063,plain,
! [X2125,X2126,X2127,X2128,X2129] : hAPP(fun(X2125,bool),fun(X2126,bool),hAPP(fun(X2125,X2126),fun(fun(X2125,bool),fun(X2126,bool)),image(X2125,X2126),X2127),hAPP(fun(X2125,bool),fun(X2125,bool),hAPP(X2125,fun(fun(X2125,bool),fun(X2125,bool)),insert(X2125),X2128),X2129)) = hAPP(fun(X2126,bool),fun(X2126,bool),hAPP(X2126,fun(fun(X2126,bool),fun(X2126,bool)),insert(X2126),hAPP(X2125,X2126,X2127,X2128)),hAPP(fun(X2125,bool),fun(X2126,bool),hAPP(fun(X2125,X2126),fun(fun(X2125,bool),fun(X2126,bool)),image(X2125,X2126),X2127),X2129)),
inference(variable_rename,[status(thm)],[fact_90_image__insert]) ).
fof(i_0_1064,plain,
! [X1935,X1936,X1937] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1937),X1936) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1935),X1936)
| X1937 = X1935
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1936),X1935))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1936),X1937)) )
& ( X1937 != X1935
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1937),X1936) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1935),X1936)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1936),X1935))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1936),X1937)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_eq__diff__iff])])]) ).
fof(i_0_1065,plain,
! [X3377,X3378,X3379,X3380] :
( ( ~ hBOOL(hAPP(fun(X3378,bool),bool,finite_finite(X3378),X3380))
| ~ hBOOL(hAPP(fun(X3377,bool),bool,finite_finite(X3377),X3379))
| hAPP(fun(sum_sum(X3378,X3377),bool),nat,finite_card(sum_sum(X3378,X3377)),hAPP(fun(X3377,bool),fun(sum_sum(X3378,X3377),bool),hAPP(fun(X3378,bool),fun(fun(X3377,bool),fun(sum_sum(X3378,X3377),bool)),sum_Plus(X3378,X3377),X3380),X3379)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3378,bool),nat,finite_card(X3378),X3380)),hAPP(fun(X3377,bool),nat,finite_card(X3377),X3379)) )
& ( hBOOL(hAPP(fun(X3378,bool),bool,finite_finite(X3378),X3380))
| hAPP(fun(sum_sum(X3378,X3377),bool),nat,finite_card(sum_sum(X3378,X3377)),hAPP(fun(X3377,bool),fun(sum_sum(X3378,X3377),bool),hAPP(fun(X3378,bool),fun(fun(X3377,bool),fun(sum_sum(X3378,X3377),bool)),sum_Plus(X3378,X3377),X3380),X3379)) = zero_zero(nat) )
& ( hBOOL(hAPP(fun(X3377,bool),bool,finite_finite(X3377),X3379))
| hAPP(fun(sum_sum(X3378,X3377),bool),nat,finite_card(sum_sum(X3378,X3377)),hAPP(fun(X3377,bool),fun(sum_sum(X3378,X3377),bool),hAPP(fun(X3378,bool),fun(fun(X3377,bool),fun(sum_sum(X3378,X3377),bool)),sum_Plus(X3378,X3377),X3380),X3379)) = zero_zero(nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_446_card__Plus__conv__if])])]) ).
fof(i_0_1066,plain,
! [X3353,X3354,X3355,X3356] :
( ~ hBOOL(hAPP(fun(X3354,bool),bool,finite_finite(X3354),X3356))
| ~ hBOOL(hAPP(fun(X3353,bool),bool,finite_finite(X3353),X3355))
| hAPP(fun(sum_sum(X3354,X3353),bool),nat,finite_card(sum_sum(X3354,X3353)),hAPP(fun(X3353,bool),fun(sum_sum(X3354,X3353),bool),hAPP(fun(X3354,bool),fun(fun(X3353,bool),fun(sum_sum(X3354,X3353),bool)),sum_Plus(X3354,X3353),X3356),X3355)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3354,bool),nat,finite_card(X3354),X3356)),hAPP(fun(X3353,bool),nat,finite_card(X3353),X3355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_440_card__Plus])]) ).
cnf(i_0_1067,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_677]) ).
cnf(i_0_1068,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_678]) ).
fof(i_0_1069,plain,
! [X2844,X2845,X2846] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2845),X2846))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2845),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2846),X2844))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_286_termination__basic__simps_I3_J])]) ).
fof(i_0_1070,plain,
! [X2769,X2770,X2771] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2770),X2771))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2770),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2771),X2769))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_259_trans__le__add1])]) ).
fof(i_0_1071,plain,
! [X2847,X2848,X2849] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2848),X2849))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2848),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2847),X2849))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_termination__basic__simps_I4_J])]) ).
fof(i_0_1072,plain,
! [X2772,X2773,X2774] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2773),X2774))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2773),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2772),X2774))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_260_trans__le__add2])]) ).
fof(i_0_1073,plain,
! [X2884,X2885,X2886] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2885),X2886))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2885),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2886),X2884))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_300_trans__less__add1])]) ).
fof(i_0_1074,plain,
! [X2861,X2862,X2863] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2862),X2863))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2862),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2863),X2861))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_293_termination__basic__simps_I1_J])]) ).
fof(i_0_1075,plain,
! [X2881,X2882,X2883] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2882),X2883))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2882),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2881),X2883))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_299_trans__less__add2])]) ).
fof(i_0_1076,plain,
! [X2864,X2865,X2866] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2865),X2866))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2865),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2864),X2866))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_294_termination__basic__simps_I2_J])]) ).
fof(i_0_1077,plain,
! [X3274,X3275] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3274),esk60_2(X3274,X3275)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3274)),X3275)) )
& ( X3275 = hAPP(nat,nat,suc,esk60_2(X3274,X3275))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3274)),X3275)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_428_Suc__lessE])])])]) ).
fof(i_0_1078,plain,
! [X1911,X1912] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1911)),X1912))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1911),X1912)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_Suc__leD])]) ).
fof(i_0_1079,plain,
! [X3170,X3171] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3170)),X3171))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3170),X3171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_398_Suc__le__lessD])]) ).
fof(i_0_1080,plain,
! [X3162,X3163] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3162)),X3163))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3162),X3163)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3162),X3163))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3162)),X3163)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_394_Suc__le__eq])]) ).
fof(i_0_1081,plain,
! [X3158,X3159] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3158),X3159))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3158)),X3159)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3158)),X3159))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3158),X3159)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_392_less__eq__Suc__le])]) ).
fof(i_0_1082,plain,
! [X2930,X2931] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2930)),X2931))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2930),X2931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_313_Suc__lessD])]) ).
fof(i_0_1083,plain,
! [X2573,X2574,X2575] : hAPP(fun(X2573,bool),fun(X2573,bool),hAPP(fun(X2573,bool),fun(fun(X2573,bool),fun(X2573,bool)),minus_minus(fun(X2573,bool)),hAPP(fun(X2573,bool),fun(X2573,bool),hAPP(fun(X2573,bool),fun(fun(X2573,bool),fun(X2573,bool)),minus_minus(fun(X2573,bool)),X2574),X2575)),X2575) = hAPP(fun(X2573,bool),fun(X2573,bool),hAPP(fun(X2573,bool),fun(fun(X2573,bool),fun(X2573,bool)),minus_minus(fun(X2573,bool)),X2574),X2575),
inference(variable_rename,[status(thm)],[fact_203_Diff__idemp]) ).
cnf(i_0_1084,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_666]) ).
fof(i_0_1085,plain,
! [X2858,X2859] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2858),X2859))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2858)),hAPP(nat,nat,suc,X2859))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_291_Suc__mono])]) ).
cnf(i_0_1086,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_679]) ).
cnf(i_0_1087,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_676]) ).
cnf(i_0_1088,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_654]) ).
cnf(i_0_1089,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_680]) ).
cnf(i_0_1090,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_681]) ).
fof(i_0_1091,plain,
! [X2384,X2385,X2386,X2387,X2388] :
( ( ~ hBOOL(hAPP(X2384,bool,hAPP(X2384,fun(X2384,bool),ord_less_eq(X2384),X2385),X2386))
| hBOOL(hAPP(X2384,bool,hAPP(X2384,fun(X2384,bool),ord_less_eq(X2384),X2387),X2388))
| hAPP(X2384,X2384,hAPP(X2384,fun(X2384,X2384),minus_minus(X2384),X2385),X2386) != hAPP(X2384,X2384,hAPP(X2384,fun(X2384,X2384),minus_minus(X2384),X2387),X2388)
| ~ ordered_ab_group_add(X2384) )
& ( ~ hBOOL(hAPP(X2384,bool,hAPP(X2384,fun(X2384,bool),ord_less_eq(X2384),X2387),X2388))
| hBOOL(hAPP(X2384,bool,hAPP(X2384,fun(X2384,bool),ord_less_eq(X2384),X2385),X2386))
| hAPP(X2384,X2384,hAPP(X2384,fun(X2384,X2384),minus_minus(X2384),X2385),X2386) != hAPP(X2384,X2384,hAPP(X2384,fun(X2384,X2384),minus_minus(X2384),X2387),X2388)
| ~ ordered_ab_group_add(X2384) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_diff__eq__diff__less__eq])])])]) ).
fof(i_0_1092,plain,
! [X2923,X2924,X2925,X2926,X2927] :
( ( ~ hBOOL(hAPP(X2923,bool,hAPP(X2923,fun(X2923,bool),ord_less(X2923),X2924),X2925))
| hBOOL(hAPP(X2923,bool,hAPP(X2923,fun(X2923,bool),ord_less(X2923),X2926),X2927))
| hAPP(X2923,X2923,hAPP(X2923,fun(X2923,X2923),minus_minus(X2923),X2924),X2925) != hAPP(X2923,X2923,hAPP(X2923,fun(X2923,X2923),minus_minus(X2923),X2926),X2927)
| ~ ordered_ab_group_add(X2923) )
& ( ~ hBOOL(hAPP(X2923,bool,hAPP(X2923,fun(X2923,bool),ord_less(X2923),X2926),X2927))
| hBOOL(hAPP(X2923,bool,hAPP(X2923,fun(X2923,bool),ord_less(X2923),X2924),X2925))
| hAPP(X2923,X2923,hAPP(X2923,fun(X2923,X2923),minus_minus(X2923),X2924),X2925) != hAPP(X2923,X2923,hAPP(X2923,fun(X2923,X2923),minus_minus(X2923),X2926),X2927)
| ~ ordered_ab_group_add(X2923) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_311_diff__eq__diff__less])])])]) ).
cnf(i_0_1093,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_681]) ).
cnf(i_0_1094,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_681]) ).
fof(i_0_1095,plain,
! [X2309,X2310,X2311,X2312] :
( ~ preorder(X2309)
| ~ hBOOL(hAPP(X2309,bool,hAPP(X2309,fun(X2309,bool),ord_less_eq(X2309),X2311),X2312))
| ~ hBOOL(hAPP(X2309,bool,hAPP(X2309,fun(X2309,bool),ord_less_eq(X2309),X2312),X2310))
| hBOOL(hAPP(X2309,bool,hAPP(X2309,fun(X2309,bool),ord_less_eq(X2309),X2311),X2310)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_138_order__trans])])]) ).
fof(i_0_1096,plain,
! [X2302,X2303,X2304,X2305] :
( ~ order(X2302)
| ~ hBOOL(hAPP(X2302,bool,hAPP(X2302,fun(X2302,bool),ord_less_eq(X2302),X2304),X2305))
| ~ hBOOL(hAPP(X2302,bool,hAPP(X2302,fun(X2302,bool),ord_less_eq(X2302),X2303),X2304))
| hBOOL(hAPP(X2302,bool,hAPP(X2302,fun(X2302,bool),ord_less_eq(X2302),X2303),X2305)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_xt1_I6_J])])]) ).
fof(i_0_1097,plain,
! [X3109,X3110,X3111,X3112] :
( ~ preorder(X3109)
| ~ hBOOL(hAPP(X3109,bool,hAPP(X3109,fun(X3109,bool),ord_less(X3109),X3111),X3112))
| ~ hBOOL(hAPP(X3109,bool,hAPP(X3109,fun(X3109,bool),ord_less_eq(X3109),X3112),X3110))
| hBOOL(hAPP(X3109,bool,hAPP(X3109,fun(X3109,bool),ord_less(X3109),X3111),X3110)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_379_order__less__le__trans])])]) ).
fof(i_0_1098,plain,
! [X3117,X3118,X3119,X3120] :
( ~ preorder(X3117)
| ~ hBOOL(hAPP(X3117,bool,hAPP(X3117,fun(X3117,bool),ord_less_eq(X3117),X3119),X3120))
| ~ hBOOL(hAPP(X3117,bool,hAPP(X3117,fun(X3117,bool),ord_less(X3117),X3120),X3118))
| hBOOL(hAPP(X3117,bool,hAPP(X3117,fun(X3117,bool),ord_less(X3117),X3119),X3118)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_381_order__le__less__trans])])]) ).
fof(i_0_1099,plain,
! [X3025,X3026,X3027,X3028] :
( ~ preorder(X3025)
| ~ hBOOL(hAPP(X3025,bool,hAPP(X3025,fun(X3025,bool),ord_less(X3025),X3027),X3028))
| ~ hBOOL(hAPP(X3025,bool,hAPP(X3025,fun(X3025,bool),ord_less(X3025),X3028),X3026))
| hBOOL(hAPP(X3025,bool,hAPP(X3025,fun(X3025,bool),ord_less(X3025),X3027),X3026)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_348_order__less__trans])])]) ).
fof(i_0_1100,plain,
! [X3113,X3114,X3115,X3116] :
( ~ order(X3113)
| ~ hBOOL(hAPP(X3113,bool,hAPP(X3113,fun(X3113,bool),ord_less(X3113),X3115),X3116))
| ~ hBOOL(hAPP(X3113,bool,hAPP(X3113,fun(X3113,bool),ord_less_eq(X3113),X3114),X3115))
| hBOOL(hAPP(X3113,bool,hAPP(X3113,fun(X3113,bool),ord_less(X3113),X3114),X3116)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_380_xt1_I7_J])])]) ).
fof(i_0_1101,plain,
! [X3121,X3122,X3123,X3124] :
( ~ order(X3121)
| ~ hBOOL(hAPP(X3121,bool,hAPP(X3121,fun(X3121,bool),ord_less_eq(X3121),X3123),X3124))
| ~ hBOOL(hAPP(X3121,bool,hAPP(X3121,fun(X3121,bool),ord_less(X3121),X3122),X3123))
| hBOOL(hAPP(X3121,bool,hAPP(X3121,fun(X3121,bool),ord_less(X3121),X3122),X3124)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_382_xt1_I8_J])])]) ).
fof(i_0_1102,plain,
! [X3029,X3030,X3031,X3032] :
( ~ order(X3029)
| ~ hBOOL(hAPP(X3029,bool,hAPP(X3029,fun(X3029,bool),ord_less(X3029),X3031),X3032))
| ~ hBOOL(hAPP(X3029,bool,hAPP(X3029,fun(X3029,bool),ord_less(X3029),X3030),X3031))
| hBOOL(hAPP(X3029,bool,hAPP(X3029,fun(X3029,bool),ord_less(X3029),X3030),X3032)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_349_xt1_I10_J])])]) ).
fof(i_0_1103,plain,
! [X1888,X1889,X1890] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1889),X1890))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1890),X1888))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1889),X1888)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_le__trans])]) ).
fof(i_0_1104,plain,
! [X2870,X2871,X2872,X2873] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2872),X2873))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2870),X2873) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2872),X2871)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2870),X2871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_296_less__add__eq__less])]) ).
fof(i_0_1105,plain,
! [X2739,X2740,X2741,X2742] :
( ~ ab_semigroup_add(X2739)
| hAPP(X2739,X2739,hAPP(X2739,fun(X2739,X2739),plus_plus(X2739),hAPP(X2739,X2739,hAPP(X2739,fun(X2739,X2739),plus_plus(X2739),X2740),X2741)),X2742) = hAPP(X2739,X2739,hAPP(X2739,fun(X2739,X2739),plus_plus(X2739),X2740),hAPP(X2739,X2739,hAPP(X2739,fun(X2739,X2739),plus_plus(X2739),X2741),X2742)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_249_ab__semigroup__add__class_Oadd__ac_I1_J])])]) ).
fof(i_0_1106,plain,
! [X3168,X3169] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3169),hAPP(nat,nat,suc,X3168)))
| X3169 = X3168
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3168),X3169)) )
& ( X3169 != X3168
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3169),hAPP(nat,nat,suc,X3168)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3168),X3169)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_397_le__less__Suc__eq])])]) ).
fof(i_0_1107,plain,
! [X2949,X2950] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2949),X2950))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2950),hAPP(nat,nat,suc,X2949))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2950),hAPP(nat,nat,suc,X2949)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2949),X2950)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_682])]) ).
fof(i_0_1108,plain,
! [X2841,X2842,X2843] :
( ~ hBOOL(hAPP(fun(X2841,bool),bool,finite_finite(X2841),X2843))
| hBOOL(hAPP(fun(X2841,bool),bool,hAPP(X2841,fun(fun(X2841,bool),bool),member(X2841),X2842),X2843))
| hAPP(fun(X2841,bool),nat,finite_card(X2841),hAPP(fun(X2841,bool),fun(X2841,bool),hAPP(X2841,fun(fun(X2841,bool),fun(X2841,bool)),insert(X2841),X2842),X2843)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X2841,bool),nat,finite_card(X2841),X2843)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_683])]) ).
fof(i_0_1109,plain,
! [X2810,X2811] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2810),X2811))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2811),X2810)),X2810) = X2811 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_273_le__add__diff__inverse2])]) ).
fof(i_0_1110,plain,
! [X1863,X1864,X1865] :
( ( ~ hBOOL(hAPP(fun(X1863,bool),bool,hAPP(X1863,fun(fun(X1863,bool),bool),member(X1863),X1864),X1865))
| hAPP(fun(X1863,bool),nat,finite_card(X1863),hAPP(fun(X1863,bool),fun(X1863,bool),hAPP(X1863,fun(fun(X1863,bool),fun(X1863,bool)),insert(X1863),X1864),X1865)) = hAPP(fun(X1863,bool),nat,finite_card(X1863),X1865)
| ~ hBOOL(hAPP(fun(X1863,bool),bool,finite_finite(X1863),X1865)) )
& ( hBOOL(hAPP(fun(X1863,bool),bool,hAPP(X1863,fun(fun(X1863,bool),bool),member(X1863),X1864),X1865))
| hAPP(fun(X1863,bool),nat,finite_card(X1863),hAPP(fun(X1863,bool),fun(X1863,bool),hAPP(X1863,fun(fun(X1863,bool),fun(X1863,bool)),insert(X1863),X1864),X1865)) = hAPP(nat,nat,suc,hAPP(fun(X1863,bool),nat,finite_card(X1863),X1865))
| ~ hBOOL(hAPP(fun(X1863,bool),bool,finite_finite(X1863),X1865)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_684])])]) ).
fof(i_0_1111,plain,
! [X2290,X2291,X2292,X2293,X2294] :
( ~ hBOOL(hAPP(fun(X2291,bool),bool,hAPP(X2291,fun(fun(X2291,bool),bool),member(X2291),X2293),X2294))
| hAPP(fun(X2291,bool),fun(X2290,bool),hAPP(fun(X2291,X2290),fun(fun(X2291,bool),fun(X2290,bool)),image(X2291,X2290),hAPP(X2290,fun(X2291,X2290),combk(X2290,X2291),X2292)),X2294) = hAPP(fun(X2290,bool),fun(X2290,bool),hAPP(X2290,fun(fun(X2290,bool),fun(X2290,bool)),insert(X2290),X2292),bot_bot(fun(X2290,bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_133_image__constant])]) ).
fof(i_0_1112,plain,
! [X1990,X1991,X1992] :
( ( hBOOL(hAPP(nat,bool,X1991,hAPP(nat,nat,suc,esk4_3(X1990,X1991,X1992))))
| hBOOL(hAPP(nat,bool,X1991,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1992),X1990)))
| ~ hBOOL(hAPP(nat,bool,X1991,X1992)) )
& ( ~ hBOOL(hAPP(nat,bool,X1991,esk4_3(X1990,X1991,X1992)))
| hBOOL(hAPP(nat,bool,X1991,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1992),X1990)))
| ~ hBOOL(hAPP(nat,bool,X1991,X1992)) ) ),
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_1113,plain,
! [X2383] :
( ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X2383),u))
| hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X2383)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_156_assms_I4_J])]) ).
fof(i_0_1114,plain,
! [X2750,X2751,X2752] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2750),X2751)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2750),X2752)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2751),X2752),
inference(variable_rename,[status(thm)],[fact_253_diff__cancel]) ).
fof(i_0_1115,plain,
! [X2753,X2754,X2755] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2753),X2754)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2755),X2754)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2753),X2755),
inference(variable_rename,[status(thm)],[fact_254_diff__cancel2]) ).
fof(i_0_1116,plain,
! [X2711,X2712,X2713] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2711),X2712)),X2713) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2711),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2712),X2713)),
inference(variable_rename,[status(thm)],[fact_241_nat__add__assoc]) ).
fof(i_0_1117,plain,
! [X2747,X2748,X2749] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2747),X2748)),X2749) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2747),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2748),X2749)),
inference(variable_rename,[status(thm)],[fact_252_diff__diff__left]) ).
fof(i_0_1118,plain,
! [X2106,X2107,X2108] : hBOOL(hAPP(fun(X2106,bool),bool,hAPP(fun(X2106,bool),fun(fun(X2106,bool),bool),ord_less_eq(fun(X2106,bool)),X2107),hAPP(fun(X2106,bool),fun(X2106,bool),hAPP(X2106,fun(fun(X2106,bool),fun(X2106,bool)),insert(X2106),X2108),X2107))),
inference(variable_rename,[status(thm)],[fact_85_subset__insertI]) ).
fof(i_0_1119,plain,
! [X2937,X2938] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2937),X2938))
| hAPP(nat,nat,suc,X2937) = X2938
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2937)),X2938)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_316_Suc__lessI])]) ).
fof(i_0_1120,plain,
! [X2009,X2010,X2011,X2012] : hAPP(fun(X2009,bool),fun(X2009,bool),hAPP(X2009,fun(fun(X2009,bool),fun(X2009,bool)),insert(X2009),X2010),hAPP(fun(X2009,bool),fun(X2009,bool),hAPP(X2009,fun(fun(X2009,bool),fun(X2009,bool)),insert(X2009),X2011),X2012)) = hAPP(fun(X2009,bool),fun(X2009,bool),hAPP(X2009,fun(fun(X2009,bool),fun(X2009,bool)),insert(X2009),X2011),hAPP(fun(X2009,bool),fun(X2009,bool),hAPP(X2009,fun(fun(X2009,bool),fun(X2009,bool)),insert(X2009),X2010),X2012)),
inference(variable_rename,[status(thm)],[fact_61_insert__commute]) ).
fof(i_0_1121,plain,
! [X2412,X2413,X2414] :
( ~ hBOOL(hAPP(fun(X2412,bool),bool,finite_finite(X2412),X2414))
| hBOOL(hAPP(fun(X2412,bool),bool,finite_finite(X2412),hAPP(fun(X2412,bool),fun(X2412,bool),hAPP(fun(X2412,bool),fun(fun(X2412,bool),fun(X2412,bool)),minus_minus(fun(X2412,bool)),X2414),X2413))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_finite__Diff])]) ).
cnf(i_0_1122,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_685]) ).
cnf(i_0_1123,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_686]) ).
fof(i_0_1124,plain,
! [X1872,X1873] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1872),X1873))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1873)),X1872) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1873),X1872)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_Suc__diff__le])]) ).
fof(i_0_1125,plain,
! [X1997,X1998,X1999] : hBOOL(hAPP(fun(X1997,bool),bool,hAPP(X1997,fun(fun(X1997,bool),bool),member(X1997),X1998),hAPP(fun(X1997,bool),fun(X1997,bool),hAPP(X1997,fun(fun(X1997,bool),fun(X1997,bool)),insert(X1997),X1998),X1999))),
inference(variable_rename,[status(thm)],[fact_57_insertI1]) ).
fof(i_0_1126,plain,
! [X3166,X3167] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3166),X3167))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3166)),X3167)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_396_Suc__leI])]) ).
fof(i_0_1127,plain,
! [X1875] : 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)),X1875))) = hAPP(nat,nat,suc,X1875),
inference(variable_rename,[status(thm)],[fact_13_card__Collect__le__nat]) ).
fof(i_0_1128,plain,
! [X1843,X1844,X1845,X1846] :
( ~ hBOOL(hAPP(fun(X1844,bool),bool,finite_finite(X1844),X1846))
| hBOOL(hAPP(fun(X1843,bool),bool,finite_finite(X1843),hAPP(fun(X1844,bool),fun(X1843,bool),hAPP(fun(X1844,X1843),fun(fun(X1844,bool),fun(X1843,bool)),image(X1844,X1843),X1845),X1846))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_finite__imageI])]) ).
fof(i_0_1129,plain,
! [X1866,X1867,X1868] :
( ~ hBOOL(hAPP(fun(X1866,bool),bool,finite_finite(X1866),X1868))
| hBOOL(hAPP(fun(X1866,bool),bool,hAPP(X1866,fun(fun(X1866,bool),bool),member(X1866),X1867),X1868))
| hAPP(fun(X1866,bool),nat,finite_card(X1866),hAPP(fun(X1866,bool),fun(X1866,bool),hAPP(X1866,fun(fun(X1866,bool),fun(X1866,bool)),insert(X1866),X1867),X1868)) = hAPP(nat,nat,suc,hAPP(fun(X1866,bool),nat,finite_card(X1866),X1868)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_687])]) ).
cnf(i_0_1130,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_688]) ).
fof(i_0_1131,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_1132,plain,
! [X1919,X1920] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1919),hAPP(nat,nat,suc,X1920)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1919),X1920))
| X1919 = hAPP(nat,nat,suc,X1920) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1919),X1920))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1919),hAPP(nat,nat,suc,X1920))) )
& ( X1919 != hAPP(nat,nat,suc,X1920)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1919),hAPP(nat,nat,suc,X1920))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_34_le__Suc__eq])])]) ).
fof(i_0_1133,plain,
! [X1913,X1914] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1913),hAPP(nat,nat,suc,X1914)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1913),X1914))
| X1913 = hAPP(nat,nat,suc,X1914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_689])]) ).
fof(i_0_1134,plain,
! [X1994,X1995] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1994)),X1995))
| X1995 = hAPP(nat,nat,suc,esk5_2(X1994,X1995)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_Suc__le__D])])]) ).
fof(i_0_1135,plain,
! [X3191,X3192,X3193] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk50_3(X3191,X3192,X3193)),X3193))
| hBOOL(hAPP(nat,bool,X3191,X3192))
| ~ hBOOL(hAPP(nat,bool,X3191,X3193))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3192),X3193)) )
& ( hBOOL(hAPP(nat,bool,X3191,hAPP(nat,nat,suc,esk50_3(X3191,X3192,X3193))))
| hBOOL(hAPP(nat,bool,X3191,X3192))
| ~ hBOOL(hAPP(nat,bool,X3191,X3193))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3192),X3193)) )
& ( ~ hBOOL(hAPP(nat,bool,X3191,esk50_3(X3191,X3192,X3193)))
| hBOOL(hAPP(nat,bool,X3191,X3192))
| ~ hBOOL(hAPP(nat,bool,X3191,X3193))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3192),X3193)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_406_inc__induct])])])]) ).
fof(i_0_1136,plain,
! [X3070,X3071,X3072] :
( ( hBOOL(hAPP(X3070,bool,hAPP(X3070,fun(X3070,bool),ord_less_eq(X3070),X3071),X3072))
| ~ hBOOL(hAPP(X3070,bool,hAPP(X3070,fun(X3070,bool),ord_less(X3070),X3071),X3072))
| ~ preorder(X3070) )
& ( ~ hBOOL(hAPP(X3070,bool,hAPP(X3070,fun(X3070,bool),ord_less_eq(X3070),X3072),X3071))
| ~ hBOOL(hAPP(X3070,bool,hAPP(X3070,fun(X3070,bool),ord_less(X3070),X3071),X3072))
| ~ preorder(X3070) )
& ( ~ hBOOL(hAPP(X3070,bool,hAPP(X3070,fun(X3070,bool),ord_less_eq(X3070),X3071),X3072))
| hBOOL(hAPP(X3070,bool,hAPP(X3070,fun(X3070,bool),ord_less_eq(X3070),X3072),X3071))
| hBOOL(hAPP(X3070,bool,hAPP(X3070,fun(X3070,bool),ord_less(X3070),X3071),X3072))
| ~ preorder(X3070) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_690])])])]) ).
fof(i_0_1137,plain,
! [X3135] : 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)),X3135))) = X3135,
inference(variable_rename,[status(thm)],[fact_385_card__Collect__less__nat]) ).
fof(i_0_1138,plain,
! [X2158,X2159,X2160] :
( ( hBOOL(hAPP(fun(X2158,bool),bool,hAPP(X2158,fun(fun(X2158,bool),bool),member(X2158),esk10_3(X2158,X2159,X2160)),X2160))
| hBOOL(hAPP(fun(X2158,bool),bool,hAPP(fun(X2158,bool),fun(fun(X2158,bool),bool),ord_less_eq(fun(X2158,bool)),X2160),X2159)) )
& ( ~ hBOOL(hAPP(fun(X2158,bool),bool,hAPP(X2158,fun(fun(X2158,bool),bool),member(X2158),esk10_3(X2158,X2159,X2160)),X2159))
| hBOOL(hAPP(fun(X2158,bool),bool,hAPP(fun(X2158,bool),fun(fun(X2158,bool),bool),ord_less_eq(fun(X2158,bool)),X2160),X2159)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_95_subsetI])])])]) ).
fof(i_0_1139,plain,
! [X1847,X1848,X1849] :
( ~ hBOOL(hAPP(fun(X1847,bool),bool,finite_finite(X1847),X1849))
| hBOOL(hAPP(fun(X1847,bool),bool,finite_finite(X1847),hAPP(fun(X1847,bool),fun(X1847,bool),hAPP(X1847,fun(fun(X1847,bool),fun(X1847,bool)),insert(X1847),X1848),X1849))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_finite_OinsertI])]) ).
fof(i_0_1140,plain,
! [X2947,X2948] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2947),hAPP(nat,nat,suc,X2948)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2947),X2948))
| X2947 = X2948 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2947),X2948))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2947),hAPP(nat,nat,suc,X2948))) )
& ( X2947 != X2948
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2947),hAPP(nat,nat,suc,X2948))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_321_less__Suc__eq])])]) ).
fof(i_0_1141,plain,
! [X2943,X2944] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2943),hAPP(nat,nat,suc,X2944)))
| X2943 = X2944
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2943),X2944)) )
& ( X2943 != X2944
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2943),hAPP(nat,nat,suc,X2944)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2943),X2944)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_691])])]) ).
fof(i_0_1142,plain,
! [X2941,X2942] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2941),X2942))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2941),hAPP(nat,nat,suc,X2942)))
| X2942 = X2941 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_692])]) ).
fof(i_0_1143,plain,
! [X2932,X2933] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2932),hAPP(nat,nat,suc,X2933)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2932),X2933))
| X2932 = X2933 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_693])]) ).
fof(i_0_1144,plain,
! [X3160,X3161] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3160),hAPP(nat,nat,suc,X3161)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3160),X3161)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3160),X3161))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3160),hAPP(nat,nat,suc,X3161))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_393_less__Suc__eq__le])]) ).
cnf(i_0_1145,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_694]) ).
cnf(i_0_1146,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_695]) ).
cnf(i_0_1147,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_696]) ).
cnf(i_0_1148,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_697]) ).
fof(i_0_1149,plain,
! [X1923] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1923)),X1923)),
inference(variable_rename,[status(thm)],[i_0_698]) ).
cnf(i_0_1150,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_672]) ).
fof(i_0_1151,plain,
! [X3206,X3207,X3208] :
( ~ hBOOL(hAPP(fun(X3206,bool),bool,hAPP(fun(X3206,bool),fun(fun(X3206,bool),bool),ord_less(fun(X3206,bool)),X3207),X3208))
| hBOOL(hAPP(fun(X3206,bool),bool,hAPP(fun(X3206,bool),fun(fun(X3206,bool),bool),ord_less_eq(fun(X3206,bool)),X3207),X3208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_410_psubset__imp__subset])]) ).
fof(i_0_1152,plain,
! [X2170,X2172,X2173,X2174] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2170))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2172),X2170))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2172),esk12_1(X2170))) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk13_2(X2173,X2174)),X2173))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2173)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk13_2(X2173,X2174)),X2174))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X2173)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_1153,plain,
! [X3125,X3127,X3128,X3129] :
( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3125))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3127),X3125))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3127),esk45_1(X3125))) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk46_2(X3128,X3129)),X3128))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3128)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk46_2(X3128,X3129)),X3129))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3128)) ) ),
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_383_finite__nat__set__iff__bounded])])])])])]) ).
fof(i_0_1154,plain,
! [X2649,X2650] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2649),hAPP(nat,nat,suc,X2650)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2649),one_one(nat))),X2650),
inference(variable_rename,[status(thm)],[fact_221_diff__Suc__eq__diff__pred]) ).
cnf(i_0_1155,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_699]) ).
fof(i_0_1156,plain,
! [X1839,X1840] :
( ~ 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)),X1839),X1840))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1840),X1839)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J])]) ).
fof(i_0_1157,plain,
! [X2999,X3000,X3001,X3002] :
( ~ preorder(X2999)
| ~ hBOOL(hAPP(X2999,bool,hAPP(X2999,fun(X2999,bool),ord_less(X2999),X3001),X3002))
| ~ hBOOL(hAPP(X2999,bool,hAPP(X2999,fun(X2999,bool),ord_less(X2999),X3002),X3001))
| hBOOL(X3000) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_341_order__less__imp__triv])])]) ).
fof(i_0_1158,plain,
! [X3061,X3062,X3063] :
( ( hBOOL(hAPP(X3061,bool,hAPP(X3061,fun(X3061,bool),ord_less_eq(X3061),X3062),X3063))
| hBOOL(hAPP(X3061,bool,hAPP(X3061,fun(X3061,bool),ord_less(X3061),X3063),X3062))
| ~ linorder(X3061) )
& ( ~ hBOOL(hAPP(X3061,bool,hAPP(X3061,fun(X3061,bool),ord_less(X3061),X3063),X3062))
| ~ hBOOL(hAPP(X3061,bool,hAPP(X3061,fun(X3061,bool),ord_less_eq(X3061),X3062),X3063))
| ~ linorder(X3061) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_700])])])]) ).
fof(i_0_1159,plain,
! [X3091,X3092,X3093] :
( ~ linorder(X3091)
| ~ hBOOL(hAPP(X3091,bool,hAPP(X3091,fun(X3091,bool),ord_less_eq(X3091),X3092),X3093))
| ~ hBOOL(hAPP(X3091,bool,hAPP(X3091,fun(X3091,bool),ord_less(X3091),X3093),X3092)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_701])])]) ).
fof(i_0_1160,plain,
! [X3058,X3059,X3060] :
( ( hBOOL(hAPP(X3058,bool,hAPP(X3058,fun(X3058,bool),ord_less(X3058),X3059),X3060))
| hBOOL(hAPP(X3058,bool,hAPP(X3058,fun(X3058,bool),ord_less_eq(X3058),X3060),X3059))
| ~ linorder(X3058) )
& ( ~ hBOOL(hAPP(X3058,bool,hAPP(X3058,fun(X3058,bool),ord_less_eq(X3058),X3060),X3059))
| ~ hBOOL(hAPP(X3058,bool,hAPP(X3058,fun(X3058,bool),ord_less(X3058),X3059),X3060))
| ~ linorder(X3058) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_702])])])]) ).
fof(i_0_1161,plain,
! [X3033,X3034,X3035] :
( ~ preorder(X3033)
| ~ hBOOL(hAPP(X3033,bool,hAPP(X3033,fun(X3033,bool),ord_less(X3033),X3034),X3035))
| ~ hBOOL(hAPP(X3033,bool,hAPP(X3033,fun(X3033,bool),ord_less(X3033),X3035),X3034)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_703])])]) ).
fof(i_0_1162,plain,
! [X3003,X3004,X3005] :
( ~ preorder(X3003)
| ~ hBOOL(hAPP(X3003,bool,hAPP(X3003,fun(X3003,bool),ord_less(X3003),X3004),X3005))
| ~ hBOOL(hAPP(X3003,bool,hAPP(X3003,fun(X3003,bool),ord_less(X3003),X3005),X3004)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_704])])]) ).
fof(i_0_1163,plain,
! [X2990,X2991,X2992] :
( ~ preorder(X2990)
| ~ hBOOL(hAPP(X2990,bool,hAPP(X2990,fun(X2990,bool),ord_less(X2990),X2991),X2992))
| ~ hBOOL(hAPP(X2990,bool,hAPP(X2990,fun(X2990,bool),ord_less(X2990),X2992),X2991)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_705])])]) ).
fof(i_0_1164,plain,
! [X2987,X2988,X2989] :
( ~ preorder(X2987)
| ~ hBOOL(hAPP(X2987,bool,hAPP(X2987,fun(X2987,bool),ord_less(X2987),X2988),X2989))
| ~ hBOOL(hAPP(X2987,bool,hAPP(X2987,fun(X2987,bool),ord_less(X2987),X2989),X2988)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_706])])]) ).
fof(i_0_1165,plain,
! [X3006,X3007,X3008] :
( ~ order(X3006)
| ~ hBOOL(hAPP(X3006,bool,hAPP(X3006,fun(X3006,bool),ord_less(X3006),X3007),X3008))
| ~ hBOOL(hAPP(X3006,bool,hAPP(X3006,fun(X3006,bool),ord_less(X3006),X3008),X3007)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_707])])]) ).
fof(i_0_1166,plain,
! [X1915,X1916] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1915),X1916))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1915),hAPP(nat,nat,suc,X1916))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_32_le__SucI])]) ).
fof(i_0_1167,plain,
! [X3164,X3165] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3164),X3165))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3164),hAPP(nat,nat,suc,X3165))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_395_le__imp__less__Suc])]) ).
fof(i_0_1168,plain,
! [X2939,X2940] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2939),X2940))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2939),hAPP(nat,nat,suc,X2940))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_317_less__SucI])]) ).
fof(i_0_1169,plain,
! [X2620,X2621,X2622,X2623,X2624] :
( ~ minus(X2621)
| hAPP(X2620,X2621,hAPP(fun(X2620,X2621),fun(X2620,X2621),hAPP(fun(X2620,X2621),fun(fun(X2620,X2621),fun(X2620,X2621)),minus_minus(fun(X2620,X2621)),X2622),X2623),X2624) = hAPP(X2621,X2621,hAPP(X2621,fun(X2621,X2621),minus_minus(X2621),hAPP(X2620,X2621,X2622,X2624)),hAPP(X2620,X2621,X2623,X2624)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_213_minus__apply])])]) ).
fof(i_0_1170,plain,
! [X2615,X2616,X2617,X2618,X2619] :
( ~ minus(X2616)
| hAPP(X2615,X2616,hAPP(fun(X2615,X2616),fun(X2615,X2616),hAPP(fun(X2615,X2616),fun(fun(X2615,X2616),fun(X2615,X2616)),minus_minus(fun(X2615,X2616)),X2617),X2618),X2619) = hAPP(X2616,X2616,hAPP(X2616,fun(X2616,X2616),minus_minus(X2616),hAPP(X2615,X2616,X2617,X2619)),hAPP(X2615,X2616,X2618,X2619)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_212_fun__diff__def])])]) ).
fof(i_0_1171,plain,
! [X1886,X1887] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1886),X1887))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1887),X1886))
| X1886 = X1887 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_20_le__antisym])]) ).
cnf(i_0_1172,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_695]) ).
cnf(i_0_1173,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_708]) ).
cnf(i_0_1174,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_709]) ).
cnf(i_0_1175,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_710]) ).
cnf(i_0_1176,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_711]) ).
cnf(i_0_1177,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_712]) ).
fof(i_0_1178,plain,
! [X3257,X3258] :
( ~ linordered_semidom(X3257)
| hBOOL(hAPP(X3257,bool,hAPP(X3257,fun(X3257,bool),ord_less(X3257),X3258),hAPP(X3257,X3257,hAPP(X3257,fun(X3257,X3257),plus_plus(X3257),X3258),one_one(X3257)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_423_less__add__one])])]) ).
fof(i_0_1179,plain,
! [X2818,X2819] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2818),X2819))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2818),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2819),X2818)) = X2819 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_276_le__add__diff__inverse])]) ).
fof(i_0_1180,plain,
! [X1938,X1939] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1938),X1939))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1939),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1939),X1938)) = X1938 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_42_diff__diff__cancel])]) ).
fof(i_0_1181,plain,
! [X3288,X3289,X3290] :
( ( hBOOL(hAPP(X3288,bool,hAPP(X3288,fun(X3288,bool),ord_less(X3288),esk64_3(X3288,X3289,X3290)),X3290))
| hBOOL(hAPP(X3288,bool,hAPP(X3288,fun(X3288,bool),ord_less_eq(X3288),X3290),X3289))
| ~ dense_linorder(X3288) )
& ( ~ hBOOL(hAPP(X3288,bool,hAPP(X3288,fun(X3288,bool),ord_less_eq(X3288),esk64_3(X3288,X3289,X3290)),X3289))
| hBOOL(hAPP(X3288,bool,hAPP(X3288,fun(X3288,bool),ord_less_eq(X3288),X3290),X3289))
| ~ dense_linorder(X3288) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_431_dense__le])])])])]) ).
fof(i_0_1182,plain,
! [X1905,X1906,X1907] :
( ~ hBOOL(hAPP(fun(X1905,bool),bool,hAPP(fun(X1905,bool),fun(fun(X1905,bool),bool),ord_less_eq(fun(X1905,bool)),X1906),X1907))
| ~ hBOOL(hAPP(fun(X1905,bool),bool,finite_finite(X1905),X1907))
| hBOOL(hAPP(fun(X1905,bool),bool,finite_finite(X1905),X1906)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_finite__subset])]) ).
fof(i_0_1183,plain,
! [X1908,X1909,X1910] :
( ~ hBOOL(hAPP(fun(X1908,bool),bool,finite_finite(X1908),X1910))
| ~ hBOOL(hAPP(fun(X1908,bool),bool,hAPP(fun(X1908,bool),fun(fun(X1908,bool),bool),ord_less_eq(fun(X1908,bool)),X1909),X1910))
| hBOOL(hAPP(fun(X1908,bool),bool,finite_finite(X1908),X1909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_rev__finite__subset])]) ).
fof(i_0_1184,plain,
! [X2758,X2759] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2758),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2758),X2759))),
inference(variable_rename,[status(thm)],[fact_256_le__add1]) ).
fof(i_0_1185,plain,
! [X2756,X2757] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2756),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2757),X2756))),
inference(variable_rename,[status(thm)],[fact_255_le__add2]) ).
fof(i_0_1186,plain,
! [X3051,X3052,X3053] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| X3052 = X3053
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3052),X3053)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| X3052 = X3053
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3052),X3053)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3052),X3053)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3052),X3053)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| X3052 = X3053
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| X3052 = X3053
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3051,X3053),X3052)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_359_nat__less__cases])])]) ).
fof(i_0_1187,plain,
! [X2714,X2715,X2716] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2714),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2715),X2716)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2715),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2714),X2716)),
inference(variable_rename,[status(thm)],[fact_242_nat__add__left__commute]) ).
cnf(i_0_1188,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_688]) ).
cnf(i_0_1189,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_713]) ).
cnf(i_0_1190,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_714]) ).
cnf(i_0_1191,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_715]) ).
cnf(i_0_1192,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_716]) ).
cnf(i_0_1193,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_717]) ).
cnf(i_0_1194,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_718]) ).
cnf(i_0_1195,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_719]) ).
cnf(i_0_1196,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_720]) ).
cnf(i_0_1197,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_721]) ).
fof(i_0_1198,plain,
! [X2807,X2808,X2809] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2809),X2808) != X2807
| X2809 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2807),X2808)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2808),X2809)) )
& ( X2809 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2807),X2808)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2809),X2808) = X2807
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2808),X2809)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_272_le__imp__diff__is__add])])]) ).
fof(i_0_1199,plain,
! [X3152,X3153,X3155,X3156,X3157] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3152),X3153))
| X3153 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3152),esk47_2(X3152,X3153))) )
& ( X3156 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3155),X3157))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3155),X3156)) ) ),
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_391_less__iff__Suc__add])])])])]) ).
cnf(i_0_1200,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_685]) ).
fof(i_0_1201,plain,
! [X3505,X3506,X3507,X3508,X3509,X3510] : hAPP(X3505,X3506,hAPP(fun(X3505,X3507),fun(X3505,X3506),hAPP(fun(X3505,fun(X3507,X3506)),fun(fun(X3505,X3507),fun(X3505,X3506)),combs(X3505,X3507,X3506),X3508),X3509),X3510) = hAPP(X3507,X3506,hAPP(X3505,fun(X3507,X3506),X3508,X3510),hAPP(X3505,X3507,X3509,X3510)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_U]) ).
fof(i_0_1202,plain,
! [X3277,X3278] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3277),esk61_2(X3277,X3278)))
| X3278 = hAPP(nat,nat,suc,X3277)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3277),X3278)) )
& ( X3278 = hAPP(nat,nat,suc,esk61_2(X3277,X3278))
| X3278 = hAPP(nat,nat,suc,X3277)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3277),X3278)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_429_lessE])])])]) ).
fof(i_0_1203,plain,
! [X3195,X3196] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3195),X3196))
| X3196 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3195),esk51_2(X3195,X3196))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_407_less__imp__Suc__add])])]) ).
cnf(i_0_1204,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_722]) ).
cnf(i_0_1205,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_723]) ).
fof(i_0_1206,plain,
! [X2700,X2701,X2702,X2703,X2704] :
( ~ hBOOL(hAPP(fun(X2700,fun(X2701,X2701)),bool,finite_comp_fun_idem(X2700,X2701),X2704))
| hAPP(X2701,X2701,hAPP(X2700,fun(X2701,X2701),X2704,X2702),hAPP(X2701,X2701,hAPP(X2700,fun(X2701,X2701),X2704,X2702),X2703)) = hAPP(X2701,X2701,hAPP(X2700,fun(X2701,X2701),X2704,X2702),X2703) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_238_comp__fun__idem_Ofun__left__idem])]) ).
cnf(i_0_1207,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_724]) ).
fof(i_0_1208,plain,
! [X2006,X2007,X2008] : hAPP(fun(X2006,bool),fun(X2006,bool),hAPP(X2006,fun(fun(X2006,bool),fun(X2006,bool)),insert(X2006),X2007),hAPP(fun(X2006,bool),fun(X2006,bool),hAPP(X2006,fun(fun(X2006,bool),fun(X2006,bool)),insert(X2006),X2007),X2008)) = hAPP(fun(X2006,bool),fun(X2006,bool),hAPP(X2006,fun(fun(X2006,bool),fun(X2006,bool)),insert(X2006),X2007),X2008),
inference(variable_rename,[status(thm)],[fact_60_insert__absorb2]) ).
fof(i_0_1209,plain,
! [X3094,X3095,X3096] :
( ~ preorder(X3094)
| ~ hBOOL(hAPP(X3094,bool,hAPP(X3094,fun(X3094,bool),ord_less(X3094),X3095),X3096))
| hBOOL(hAPP(X3094,bool,hAPP(X3094,fun(X3094,bool),ord_less_eq(X3094),X3095),X3096)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_374_order__less__imp__le])])]) ).
fof(i_0_1210,plain,
! [X2959,X2960] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2959),X2960))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2959),X2960)) )
& ( X2959 != X2960
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2959),X2960)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2959),X2960))
| X2959 = X2960
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2959),X2960)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_327_nat__less__le])])]) ).
fof(i_0_1211,plain,
! [X2957,X2958] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2957),X2958))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2957),X2958))
| X2957 = X2958 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2957),X2958))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2957),X2958)) )
& ( X2957 != X2958
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2957),X2958)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_326_le__eq__less__or__eq])])]) ).
fof(i_0_1212,plain,
! [X2953,X2954] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2953),X2954))
| X2953 = X2954
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2953),X2954)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_324_le__neq__implies__less])]) ).
fof(i_0_1213,plain,
! [X3039,X3040] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3039),X3040))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3039),X3040)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_352_termination__basic__simps_I5_J])]) ).
fof(i_0_1214,plain,
! [X2955,X2956] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2955),X2956))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2955),X2956)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_325_less__imp__le__nat])]) ).
fof(i_0_1215,plain,
! [X2951,X2952] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2951),X2952))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2951),X2952)) )
& ( X2951 != X2952
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2951),X2952)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_323_less__or__eq__imp__le])])]) ).
cnf(i_0_1216,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_713]) ).
fof(i_0_1217,plain,
! [X2283,X2284] : hAPP(fun(X2283,bool),fun(X2283,bool),collect(X2283),hAPP(X2283,fun(X2283,bool),hAPP(fun(X2283,fun(X2283,bool)),fun(X2283,fun(X2283,bool)),combc(X2283,X2283,bool),fequal(X2283)),X2284)) = hAPP(fun(X2283,bool),fun(X2283,bool),hAPP(X2283,fun(fun(X2283,bool),fun(X2283,bool)),insert(X2283),X2284),bot_bot(fun(X2283,bool))),
inference(variable_rename,[status(thm)],[fact_130_singleton__conv]) ).
cnf(i_0_1218,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_725]) ).
fof(i_0_1219,plain,
! [X3174,X3175] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3174),X3175))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3175),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3174),X3175)) = X3174 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_726])]) ).
fof(i_0_1220,plain,
! [X2745,X2746] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2745),X2746)),X2745) = X2746,
inference(variable_rename,[status(thm)],[fact_251_diff__add__inverse]) ).
fof(i_0_1221,plain,
! [X2743,X2744] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2743),X2744)),X2744) = X2743,
inference(variable_rename,[status(thm)],[fact_250_diff__add__inverse2]) ).
cnf(i_0_1222,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_727]) ).
cnf(i_0_1223,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_727]) ).
cnf(i_0_1224,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_728]) ).
cnf(i_0_1225,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_729]) ).
cnf(i_0_1226,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_730]) ).
cnf(i_0_1227,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_731]) ).
cnf(i_0_1228,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_732]) ).
cnf(i_0_1229,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_710]) ).
cnf(i_0_1230,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_733]) ).
cnf(i_0_1231,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_734]) ).
cnf(i_0_1232,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_735]) ).
cnf(i_0_1233,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_736]) ).
fof(i_0_1234,plain,
! [X3487,X3488,X3489,X3490,X3491,X3492] : hAPP(X3487,X3488,hAPP(fun(X3487,X3489),fun(X3487,X3488),hAPP(fun(X3489,X3488),fun(fun(X3487,X3489),fun(X3487,X3488)),combb(X3489,X3488,X3487),X3490),X3491),X3492) = hAPP(X3489,X3488,X3490,hAPP(X3487,X3489,X3491,X3492)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_U]) ).
fof(i_0_1235,plain,
! [X3493,X3494,X3495,X3496,X3497,X3498] : hAPP(X3493,X3494,hAPP(X3495,fun(X3493,X3494),hAPP(fun(X3493,fun(X3495,X3494)),fun(X3495,fun(X3493,X3494)),combc(X3493,X3495,X3494),X3496),X3497),X3498) = hAPP(X3495,X3494,hAPP(X3493,fun(X3495,X3494),X3496,X3498),X3497),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_U]) ).
cnf(i_0_1236,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_737]) ).
cnf(i_0_1237,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_736]) ).
fof(i_0_1238,plain,
! [X2696,X2697] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X2696)),X2697) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2696),X2697)),
inference(variable_rename,[status(thm)],[fact_236_add__Suc]) ).
cnf(i_0_1239,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),esk27_2(X1,X2)),esk28_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
fof(i_0_1240,plain,
! [X3215,X3216] : ~ hBOOL(hAPP(fun(X3215,bool),bool,hAPP(fun(X3215,bool),fun(fun(X3215,bool),bool),ord_less(fun(X3215,bool)),X3216),bot_bot(fun(X3215,bool)))),
inference(variable_rename,[status(thm)],[i_0_738]) ).
cnf(i_0_1241,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_739]) ).
cnf(i_0_1242,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_740]) ).
cnf(i_0_1243,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_741]) ).
fof(i_0_1244,plain,
! [X2060,X2061,X2062] :
( ( ~ hBOOL(hAPP(fun(X2060,bool),bool,hAPP(X2060,fun(fun(X2060,bool),bool),member(X2060),X2061),X2062))
| hBOOL(hAPP(X2060,bool,X2062,X2061)) )
& ( ~ hBOOL(hAPP(X2060,bool,X2062,X2061))
| hBOOL(hAPP(fun(X2060,bool),bool,hAPP(X2060,fun(fun(X2060,bool),bool),member(X2060),X2061),X2062)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_mem__def])]) ).
cnf(i_0_1245,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_742]) ).
cnf(i_0_1246,plain,
( hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| ti(X1,esk41_3(X1,X2,X3)) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_743]) ).
cnf(i_0_1247,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_734]) ).
cnf(i_0_1248,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_735]) ).
cnf(i_0_1249,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_735]) ).
cnf(i_0_1250,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_719]) ).
cnf(i_0_1251,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_744]) ).
cnf(i_0_1252,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_745]) ).
cnf(i_0_1253,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_746]) ).
fof(i_0_1254,plain,
! [X2760,X2761,X2763,X2764,X2765] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2760),X2761))
| X2761 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2760),esk44_2(X2760,X2761)) )
& ( X2764 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2763),X2765)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2763),X2764)) ) ),
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_257_le__iff__add])])])])]) ).
fof(i_0_1255,plain,
! [X3429,X3430] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3429),X3430) != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3429),X3430)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3429),X3430))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3429),X3430) = zero_zero(nat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_471_diff__is__0__eq])]) ).
fof(i_0_1256,plain,
! [X3427,X3428] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3427),X3428))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3427),X3428) = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_470_diff__is__0__eq_H])]) ).
fof(i_0_1257,plain,
! [X2341,X2342,X2343] :
( ~ linorder(X2341)
| hBOOL(hAPP(X2341,bool,hAPP(X2341,fun(X2341,bool),ord_less_eq(X2341),X2342),X2343))
| hBOOL(hAPP(X2341,bool,hAPP(X2341,fun(X2341,bool),ord_less_eq(X2341),X2343),X2342)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_147_linorder__linear])])]) ).
fof(i_0_1258,plain,
! [X2299,X2300,X2301] :
( ~ linorder(X2299)
| hBOOL(hAPP(X2299,bool,hAPP(X2299,fun(X2299,bool),ord_less_eq(X2299),X2300),X2301))
| hBOOL(hAPP(X2299,bool,hAPP(X2299,fun(X2299,bool),ord_less_eq(X2299),X2301),X2300)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_747])])]) ).
fof(i_0_1259,plain,
! [X3076,X3077,X3078] :
( ~ linorder(X3076)
| hBOOL(hAPP(X3076,bool,hAPP(X3076,fun(X3076,bool),ord_less(X3076),X3077),X3078))
| hBOOL(hAPP(X3076,bool,hAPP(X3076,fun(X3076,bool),ord_less_eq(X3076),X3078),X3077)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_748])])]) ).
fof(i_0_1260,plain,
! [X3079,X3080,X3081] :
( ~ linorder(X3079)
| hBOOL(hAPP(X3079,bool,hAPP(X3079,fun(X3079,bool),ord_less_eq(X3079),X3080),X3081))
| hBOOL(hAPP(X3079,bool,hAPP(X3079,fun(X3079,bool),ord_less(X3079),X3081),X3080)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_749])])]) ).
fof(i_0_1261,plain,
! [X3064,X3065,X3066] :
( ~ linorder(X3064)
| hBOOL(hAPP(X3064,bool,hAPP(X3064,fun(X3064,bool),ord_less_eq(X3064),X3065),X3066))
| hBOOL(hAPP(X3064,bool,hAPP(X3064,fun(X3064,bool),ord_less(X3064),X3066),X3065)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_364_linorder__le__less__linear])])]) ).
cnf(i_0_1262,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_686]) ).
cnf(i_0_1263,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_750]) ).
cnf(i_0_1264,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_750]) ).
cnf(i_0_1265,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_751]) ).
cnf(i_0_1266,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_677]) ).
cnf(i_0_1267,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_677]) ).
cnf(i_0_1268,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_752]) ).
fof(i_0_1269,plain,
! [X3262,X3263] :
( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk56_2(X3262,X3263)),X3263))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3263)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk56_2(X3262,X3263)),X3262))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X3263)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_425_bounded__nat__set__is__finite])])])]) ).
fof(i_0_1270,plain,
! [X3044,X3045] :
( X3044 = X3045
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3044),X3045))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3045),X3044)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_753])]) ).
fof(i_0_1271,plain,
! [X3042,X3043] :
( ( X3042 = X3043
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3042),X3043))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3043),X3042)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3042),X3043))
| X3042 != X3043 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3043),X3042))
| X3042 != X3043 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_354_nat__neq__iff])])]) ).
fof(i_0_1272,plain,
! [X1893,X1894] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1893),X1894))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1894),X1893)) ),
inference(variable_rename,[status(thm)],[fact_23_nat__le__linear]) ).
cnf(i_0_1273,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_754]) ).
fof(i_0_1274,plain,
! [X2694,X2695] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2694),hAPP(nat,nat,suc,X2695)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2694),X2695)),
inference(variable_rename,[status(thm)],[fact_235_add__Suc__right]) ).
cnf(i_0_1275,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_755]) ).
cnf(i_0_1276,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_756]) ).
cnf(i_0_1277,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_757]) ).
cnf(i_0_1278,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_758]) ).
cnf(i_0_1279,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_759]) ).
cnf(i_0_1280,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_760]) ).
fof(i_0_1281,plain,
! [X2831,X2832,X2833,X2834] : hAPP(nat,X2831,hAPP(fun(nat,X2831),fun(nat,X2831),hAPP(X2831,fun(fun(nat,X2831),fun(nat,X2831)),nat_case(X2831),X2832),X2833),hAPP(nat,nat,suc,X2834)) = hAPP(nat,X2831,X2833,X2834),
inference(variable_rename,[status(thm)],[fact_282_nat__case__Suc]) ).
fof(i_0_1282,plain,
! [X2211,X2212] : ~ hBOOL(hAPP(fun(X2211,bool),bool,hAPP(X2211,fun(fun(X2211,bool),bool),member(X2211),X2212),bot_bot(fun(X2211,bool)))),
inference(variable_rename,[status(thm)],[i_0_761]) ).
fof(i_0_1283,plain,
! [X2197,X2198] : ~ hBOOL(hAPP(fun(X2197,bool),bool,hAPP(X2197,fun(fun(X2197,bool),bool),member(X2197),X2198),bot_bot(fun(X2197,bool)))),
inference(variable_rename,[status(thm)],[i_0_762]) ).
cnf(i_0_1284,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_763]) ).
fof(i_0_1285,plain,
! [X1927,X1928] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1927)),hAPP(nat,nat,suc,X1928)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1927),X1928),
inference(variable_rename,[status(thm)],[fact_38_diff__Suc__Suc]) ).
fof(i_0_1286,plain,
! [X2698,X2699] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X2698)),X2699) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2698),hAPP(nat,nat,suc,X2699)),
inference(variable_rename,[status(thm)],[fact_237_add__Suc__shift]) ).
cnf(i_0_1287,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_764]) ).
cnf(i_0_1288,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_729]) ).
cnf(i_0_1289,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_765]) ).
cnf(i_0_1290,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_766]) ).
cnf(i_0_1291,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_728]) ).
cnf(i_0_1292,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_767]) ).
cnf(i_0_1293,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk25_2(X1,X2)),esk24_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_737]) ).
cnf(i_0_1294,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_768]) ).
cnf(i_0_1295,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_768]) ).
cnf(i_0_1296,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_768]) ).
fof(i_0_1297,plain,
! [X3393] :
( ~ linordered_semidom(X3393)
| ~ hBOOL(hAPP(X3393,bool,hAPP(X3393,fun(X3393,bool),ord_less_eq(X3393),one_one(X3393)),zero_zero(X3393))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_769])]) ).
fof(i_0_1298,plain,
! [X3388] :
( ~ linordered_semidom(X3388)
| ~ hBOOL(hAPP(X3388,bool,hAPP(X3388,fun(X3388,bool),ord_less(X3388),one_one(X3388)),zero_zero(X3388))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_770])]) ).
cnf(i_0_1299,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_771]) ).
fof(i_0_1300,plain,
! [X3383] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X3383))),
inference(variable_rename,[status(thm)],[fact_449_zero__less__Suc]) ).
fof(i_0_1301,plain,
! [X3054,X3055] :
( ~ bot(X3054)
| ~ hBOOL(hAPP(X3054,bool,hAPP(X3054,fun(X3054,bool),ord_less(X3054),X3055),bot_bot(X3054))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_772])])]) ).
fof(i_0_1302,plain,
! [X2857] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2857),hAPP(nat,nat,suc,X2857))),
inference(variable_rename,[status(thm)],[fact_290_lessI]) ).
fof(i_0_1303,plain,
! [X2967,X2968] :
( ~ preorder(X2967)
| ~ hBOOL(hAPP(X2967,bool,hAPP(X2967,fun(X2967,bool),ord_less(X2967),X2968),X2968)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_773])])]) ).
fof(i_0_1304,plain,
! [X3454] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3454),zero_zero(nat)))
| X3454 = zero_zero(nat) )
& ( X3454 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3454),zero_zero(nat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_489_le__0__eq])]) ).
fof(i_0_1305,plain,
! [X3381] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3381),zero_zero(nat))),
inference(variable_rename,[status(thm)],[i_0_774]) ).
fof(i_0_1306,plain,
! [X3431,X3432] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3431),X3432) != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3432),X3431) != zero_zero(nat)
| X3431 = X3432 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_473_diffs0__imp__equal])]) ).
fof(i_0_1307,plain,
! [X3049,X3050] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3049),X3050))
| X3049 != X3050 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_358_less__not__refl3])]) ).
fof(i_0_1308,plain,
! [X3047,X3048] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3047),X3048))
| X3048 != X3047 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_357_less__not__refl2])]) ).
fof(i_0_1309,plain,
! [X3046] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3046),X3046)),
inference(variable_rename,[status(thm)],[i_0_775]) ).
fof(i_0_1310,plain,
! [X3041] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3041),X3041)),
inference(variable_rename,[status(thm)],[i_0_776]) ).
fof(i_0_1311,plain,
! [X2705,X2706,X2707] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2705),X2706) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2707),X2706)
| X2705 = X2707 )
& ( X2705 != X2707
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2705),X2706) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2707),X2706) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_239_nat__add__right__cancel])]) ).
fof(i_0_1312,plain,
! [X2708,X2709,X2710] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2708),X2709) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2708),X2710)
| X2709 = X2710 )
& ( X2709 != X2710
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2708),X2709) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2708),X2710) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_240_nat__add__left__cancel])]) ).
fof(i_0_1313,plain,
! [X3534,X3535] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X3534),X3535))
| ~ hBOOL(X3534)
| hBOOL(X3535) ),
inference(variable_rename,[status(thm)],[i_0_777]) ).
fof(i_0_1314,plain,
! [X3521,X3522] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X3521),X3522))
| hBOOL(X3521)
| hBOOL(X3522) ),
inference(variable_rename,[status(thm)],[i_0_778]) ).
fof(i_0_1315,plain,
! [X3513,X3514] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X3513),X3514))
| hBOOL(X3513) ),
inference(variable_rename,[status(thm)],[i_0_779]) ).
fof(i_0_1316,plain,
! [X3515,X3516] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X3515),X3516))
| hBOOL(X3516) ),
inference(variable_rename,[status(thm)],[i_0_780]) ).
cnf(i_0_1317,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_755]) ).
cnf(i_0_1318,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_758]) ).
cnf(i_0_1319,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_718]) ).
cnf(i_0_1320,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_694]) ).
cnf(i_0_1321,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_694]) ).
cnf(i_0_1322,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_781]) ).
cnf(i_0_1323,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_782]) ).
fof(i_0_1324,plain,
! [X3425,X3426] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3425),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3425),X3426)) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_469_diff__add__0]) ).
cnf(i_0_1325,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_783]) ).
cnf(i_0_1326,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_784]) ).
fof(i_0_1327,plain,
! [X2200,X2201] : hBOOL(hAPP(fun(X2200,bool),bool,hAPP(fun(X2200,bool),fun(fun(X2200,bool),bool),ord_less_eq(fun(X2200,bool)),bot_bot(fun(X2200,bool))),X2201)),
inference(variable_rename,[status(thm)],[fact_105_empty__subsetI]) ).
cnf(i_0_1328,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk19_2(X1,X2)),X2))
| ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_739]) ).
cnf(i_0_1329,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),esk18_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_741]) ).
cnf(i_0_1330,plain,
( hAPP(fun(X1,bool),X1,the(X1),X2) = ti(X1,X3)
| ti(X1,esk39_3(X1,X2,X3)) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_785]) ).
cnf(i_0_1331,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_786]) ).
cnf(i_0_1332,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_787]) ).
cnf(i_0_1333,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_788]) ).
fof(i_0_1334,plain,
! [X3421,X3422] :
( ( X3421 = zero_zero(nat)
| X3421 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3421),X3422) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X3422 = hAPP(nat,nat,suc,zero_zero(nat))
| X3421 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3421),X3422) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X3421 = zero_zero(nat)
| X3422 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3421),X3422) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X3422 = hAPP(nat,nat,suc,zero_zero(nat))
| X3422 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3421),X3422) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X3421 != hAPP(nat,nat,suc,zero_zero(nat))
| X3422 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3421),X3422) = hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X3421 != zero_zero(nat)
| X3422 != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3421),X3422) = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_467_add__is__1])])]) ).
fof(i_0_1335,plain,
! [X3423,X3424] :
( ( X3423 = zero_zero(nat)
| X3423 = 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),X3423),X3424) )
& ( X3424 = hAPP(nat,nat,suc,zero_zero(nat))
| X3423 = 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),X3423),X3424) )
& ( X3423 = zero_zero(nat)
| X3424 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3423),X3424) )
& ( X3424 = hAPP(nat,nat,suc,zero_zero(nat))
| X3424 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3423),X3424) )
& ( X3423 != hAPP(nat,nat,suc,zero_zero(nat))
| X3424 != zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3423),X3424) )
& ( X3423 != zero_zero(nat)
| X3424 != 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),X3423),X3424) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_468_one__is__add])])]) ).
fof(i_0_1336,plain,
! [X2032,X2033] : hBOOL(hAPP(fun(X2032,bool),bool,hAPP(fun(X2032,bool),fun(fun(X2032,bool),bool),ord_less_eq(fun(X2032,bool)),X2033),X2033)),
inference(variable_rename,[status(thm)],[fact_67_subset__refl]) ).
cnf(i_0_1337,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_765]) ).
cnf(i_0_1338,plain,
( hBOOL(hAPP(X1,bool,X2,esk39_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_785]) ).
fof(i_0_1339,plain,
! [X2285,X2286] : hAPP(fun(X2285,bool),fun(X2285,bool),collect(X2285),hAPP(X2285,fun(X2285,bool),fequal(X2285),X2286)) = hAPP(fun(X2285,bool),fun(X2285,bool),hAPP(X2285,fun(fun(X2285,bool),fun(X2285,bool)),insert(X2285),X2286),bot_bot(fun(X2285,bool))),
inference(variable_rename,[status(thm)],[fact_131_singleton__conv2]) ).
cnf(i_0_1340,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_764]) ).
cnf(i_0_1341,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk24_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_737]) ).
cnf(i_0_1342,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk27_2(X1,X2)),esk28_2(X1,X2))
| ti(fun(X1,bool),X2) = bot_bot(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
cnf(i_0_1343,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_789]) ).
cnf(i_0_1344,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_790]) ).
cnf(i_0_1345,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_791]) ).
cnf(i_0_1346,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_792]) ).
fof(i_0_1347,plain,
! [X2651] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2651)),one_one(nat)) = X2651,
inference(variable_rename,[status(thm)],[fact_222_diff__Suc__1]) ).
cnf(i_0_1348,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_786]) ).
cnf(i_0_1349,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_787]) ).
fof(i_0_1350,plain,
! [X2258,X2259,X2260] : hAPP(fun(X2258,bool),fun(X2258,bool),hAPP(X2258,fun(fun(X2258,bool),fun(X2258,bool)),insert(X2258),X2259),X2260) != bot_bot(fun(X2258,bool)),
inference(variable_rename,[status(thm)],[fact_122_insert__not__empty]) ).
fof(i_0_1351,plain,
! [X2261,X2262,X2263] : bot_bot(fun(X2261,bool)) != hAPP(fun(X2261,bool),fun(X2261,bool),hAPP(X2261,fun(fun(X2261,bool),fun(X2261,bool)),insert(X2261),X2262),X2263),
inference(variable_rename,[status(thm)],[fact_123_empty__not__insert]) ).
fof(i_0_1352,plain,
! [X3394] :
( ~ linordered_semidom(X3394)
| hBOOL(hAPP(X3394,bool,hAPP(X3394,fun(X3394,bool),ord_less_eq(X3394),zero_zero(X3394)),one_one(X3394))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_456_zero__le__one])]) ).
fof(i_0_1353,plain,
! [X3387] :
( ~ linordered_semidom(X3387)
| hBOOL(hAPP(X3387,bool,hAPP(X3387,fun(X3387,bool),ord_less(X3387),zero_zero(X3387)),one_one(X3387))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_452_zero__less__one])]) ).
fof(i_0_1354,plain,
! [X2242,X2243] :
( ~ bot(X2242)
| hBOOL(hAPP(X2242,bool,hAPP(X2242,fun(X2242,bool),ord_less_eq(X2242),bot_bot(X2242)),X2243)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_117_bot__least])])]) ).
cnf(i_0_1355,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_789]) ).
cnf(i_0_1356,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_790]) ).
fof(i_0_1357,plain,
! [X2335,X2336,X2337] :
( ~ preorder(X2335)
| X2336 != X2337
| hBOOL(hAPP(X2335,bool,hAPP(X2335,fun(X2335,bool),ord_less_eq(X2335),X2336),X2337)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_order__eq__refl])])]) ).
fof(i_0_1358,plain,
! [X2168,X2169] :
( ~ preorder(X2168)
| hBOOL(hAPP(X2168,bool,hAPP(X2168,fun(X2168,bool),ord_less_eq(X2168),X2169),X2169)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_order__refl])])]) ).
fof(i_0_1359,plain,
! [X3455] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X3455)),
inference(variable_rename,[status(thm)],[fact_490_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1360,plain,
! [X3382] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X3382)),
inference(variable_rename,[status(thm)],[fact_448_le0]) ).
cnf(i_0_1361,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_793]) ).
fof(i_0_1362,plain,
! [X1891,X1892] :
( X1891 != X1892
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1891),X1892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_eq__imp__le])]) ).
fof(i_0_1363,plain,
! [X1895] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1895),X1895)),
inference(variable_rename,[status(thm)],[fact_24_le__refl]) ).
fof(i_0_1364,plain,
! [X2717,X2718] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2717),X2718) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2718),X2717),
inference(variable_rename,[status(thm)],[fact_243_nat__add__commute]) ).
fof(i_0_1365,plain,
! [X3511,X3512] :
( ~ hBOOL(X3512)
| ~ hBOOL(X3511)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X3512),X3511)) ),
inference(variable_rename,[status(thm)],[i_0_794]) ).
fof(i_0_1366,plain,
! [X3532,X3533] :
( ~ hBOOL(X3533)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X3532),X3533)) ),
inference(variable_rename,[status(thm)],[i_0_795]) ).
fof(i_0_1367,plain,
! [X3517,X3518] :
( ~ hBOOL(X3518)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X3518),X3517)) ),
inference(variable_rename,[status(thm)],[i_0_796]) ).
fof(i_0_1368,plain,
! [X3519,X3520] :
( ~ hBOOL(X3520)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X3519),X3520)) ),
inference(variable_rename,[status(thm)],[i_0_797]) ).
fof(i_0_1369,plain,
! [X3530,X3531] :
( hBOOL(X3531)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X3531),X3530)) ),
inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).
cnf(i_0_1370,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_798]) ).
cnf(i_0_1371,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_799]) ).
cnf(i_0_1372,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_800]) ).
cnf(i_0_1373,plain,
ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
inference(split_conjunct,[status(thm)],[i_0_801]) ).
cnf(i_0_1374,plain,
ti(fun(X1,fun(fun(X1,bool),fun(X1,bool))),insert(X1)) = insert(X1),
inference(split_conjunct,[status(thm)],[i_0_802]) ).
fof(i_0_1375,plain,
! [X2423,X2424] : hAPP(fun(X2423,bool),fun(X2423,bool),hAPP(fun(X2423,bool),fun(fun(X2423,bool),fun(X2423,bool)),minus_minus(fun(X2423,bool)),bot_bot(fun(X2423,bool))),X2424) = bot_bot(fun(X2423,bool)),
inference(variable_rename,[status(thm)],[fact_167_empty__Diff]) ).
fof(i_0_1376,plain,
! [X2205,X2206,X2207,X2208,X2209] :
( ( hAPP(fun(X2205,bool),fun(X2205,bool),collect(X2205),X2206) != bot_bot(fun(X2205,bool))
| ~ hBOOL(hAPP(X2205,bool,X2206,X2207)) )
& ( hBOOL(hAPP(X2208,bool,X2209,esk16_2(X2208,X2209)))
| hAPP(fun(X2208,bool),fun(X2208,bool),collect(X2208),X2209) = bot_bot(fun(X2208,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_803])])])])]) ).
fof(i_0_1377,plain,
! [X2213,X2214,X2215,X2216,X2217] :
( ( bot_bot(fun(X2213,bool)) != hAPP(fun(X2213,bool),fun(X2213,bool),collect(X2213),X2214)
| ~ hBOOL(hAPP(X2213,bool,X2214,X2215)) )
& ( hBOOL(hAPP(X2216,bool,X2217,esk17_2(X2216,X2217)))
| bot_bot(fun(X2216,bool)) = hAPP(fun(X2216,bool),fun(X2216,bool),collect(X2216),X2217) ) ),
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_804])])])])]) ).
cnf(i_0_1378,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_799]) ).
cnf(i_0_1379,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_805]) ).
fof(i_0_1380,plain,
! [X2270,X2271,X2272] : hAPP(fun(X2270,bool),fun(X2271,bool),hAPP(fun(X2270,X2271),fun(fun(X2270,bool),fun(X2271,bool)),image(X2270,X2271),X2272),bot_bot(fun(X2270,bool))) = bot_bot(fun(X2271,bool)),
inference(variable_rename,[status(thm)],[fact_126_image__empty]) ).
fof(i_0_1381,plain,
! [X2419,X2420] : hAPP(fun(X2419,bool),fun(X2419,bool),hAPP(fun(X2419,bool),fun(fun(X2419,bool),fun(X2419,bool)),minus_minus(fun(X2419,bool)),X2420),X2420) = bot_bot(fun(X2419,bool)),
inference(variable_rename,[status(thm)],[fact_165_Diff__cancel]) ).
fof(i_0_1382,plain,
! [X2797] : hBOOL(hAPP(fun(X2797,fun(fun(X2797,bool),fun(X2797,bool))),bool,finite_comp_fun_idem(X2797,fun(X2797,bool)),insert(X2797))),
inference(variable_rename,[status(thm)],[fact_268_comp__fun__idem__insert]) ).
cnf(i_0_1383,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_737]) ).
cnf(i_0_1384,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_806]) ).
cnf(i_0_1385,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_807]) ).
cnf(i_0_1386,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_808]) ).
cnf(i_0_1387,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_809]) ).
cnf(i_0_1388,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_810]) ).
cnf(i_0_1389,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_811]) ).
cnf(i_0_1390,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_812]) ).
fof(i_0_1391,plain,
! [X2830] : hAPP(nat,nat,suc,X2830) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X2830),
inference(variable_rename,[status(thm)],[fact_281_Suc__eq__plus1__left]) ).
fof(i_0_1392,plain,
! [X2829] : hAPP(nat,nat,suc,X2829) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2829),one_one(nat)),
inference(variable_rename,[status(thm)],[fact_280_Suc__eq__plus1]) ).
fof(i_0_1393,plain,
! [X3185] : hAPP(nat,fun(nat,bool),ord_less(nat),X3185) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3185)),
inference(variable_rename,[status(thm)],[fact_404_less__eq__Suc__le__raw]) ).
cnf(i_0_1394,plain,
ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
inference(split_conjunct,[status(thm)],[tsy_v_P_res]) ).
cnf(i_0_1395,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_813]) ).
cnf(i_0_1396,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_814]) ).
cnf(i_0_1397,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_815]) ).
cnf(i_0_1398,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_816]) ).
cnf(i_0_1399,plain,
ti(fun(X1,fun(fun(X1,bool),X1)),partial_flat_lub(X1)) = partial_flat_lub(X1),
inference(split_conjunct,[status(thm)],[i_0_817]) ).
cnf(i_0_1400,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(split_conjunct,[status(thm)],[i_0_818]) ).
fof(i_0_1401,plain,
! [X2231] : bot_bot(fun(X2231,bool)) = hAPP(fun(X2231,bool),fun(X2231,bool),collect(X2231),hAPP(bool,fun(X2231,bool),combk(bool,X2231),fFalse)),
inference(variable_rename,[status(thm)],[fact_112_empty__def]) ).
fof(i_0_1402,plain,
! [X3384,X3385] :
( hBOOL(hAPP(fun(X3384,bool),bool,finite_finite(X3384),X3385))
| hAPP(fun(X3384,bool),nat,finite_card(X3384),X3385) = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_819])]) ).
fof(i_0_1403,plain,
! [X3438,X3439] :
( ~ group_add(X3438)
| hAPP(X3438,X3438,hAPP(X3438,fun(X3438,X3438),minus_minus(X3438),X3439),X3439) = zero_zero(X3438) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_478_diff__self])])]) ).
fof(i_0_1404,plain,
! [X3435] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X3435) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_476_diff__0__eq__0]) ).
cnf(i_0_1405,hypothesis,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_820]) ).
fof(i_0_1406,plain,
! [X3434] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3434),zero_zero(nat)) = X3434,
inference(variable_rename,[status(thm)],[fact_475_minus__nat_Odiff__0]) ).
fof(i_0_1407,plain,
! [X3433] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X3433),X3433) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_474_diff__self__eq__0]) ).
fof(i_0_1408,plain,
! [X3485] :
( ~ hBOOL(hAPP(bool,bool,fNot,X3485))
| ~ hBOOL(X3485) ),
inference(variable_rename,[status(thm)],[i_0_821]) ).
fof(i_0_1409,plain,
! [X1882,X1883] :
( ( hAPP(nat,nat,suc,X1882) != hAPP(nat,nat,suc,X1883)
| X1882 = X1883 )
& ( X1882 != X1883
| hAPP(nat,nat,suc,X1882) = hAPP(nat,nat,suc,X1883) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_nat_Oinject])]) ).
fof(i_0_1410,plain,
! [X1880,X1881] :
( hAPP(nat,nat,suc,X1880) != hAPP(nat,nat,suc,X1881)
| X1880 = X1881 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_Suc__inject])]) ).
cnf(i_0_1411,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(split_conjunct,[status(thm)],[i_0_822]) ).
fof(i_0_1412,plain,
! [X2199] : hBOOL(hAPP(fun(X2199,bool),bool,finite_finite(X2199),bot_bot(fun(X2199,bool)))),
inference(variable_rename,[status(thm)],[fact_104_finite_OemptyI]) ).
cnf(i_0_1413,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[i_0_823]) ).
cnf(i_0_1414,plain,
ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_824]) ).
cnf(i_0_1415,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_825]) ).
cnf(i_0_1416,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ ab_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_826]) ).
cnf(i_0_1417,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_827]) ).
cnf(i_0_1418,plain,
( ti(fun(X1,fun(X1,X1)),minus_minus(X1)) = minus_minus(X1)
| ~ minus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_1419,plain,
! [X1878,X1879] :
( ~ finite_finite_1(X1878)
| hBOOL(hAPP(fun(X1878,bool),bool,finite_finite(X1878),X1879)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_finite])])]) ).
fof(i_0_1420,plain,
! [X1876,X1877] :
( ~ finite_finite_1(X1876)
| hBOOL(hAPP(fun(X1876,bool),bool,finite_finite(X1876),X1877)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_finite__code])])]) ).
cnf(i_0_1421,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1422,plain,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_830]) ).
cnf(i_0_1423,plain,
ti(fun(fun(X1,bool),X1),the_elem(X1)) = the_elem(X1),
inference(split_conjunct,[status(thm)],[i_0_831]) ).
cnf(i_0_1424,plain,
ti(fun(fun(X1,bool),X1),the(X1)) = the(X1),
inference(split_conjunct,[status(thm)],[i_0_832]) ).
cnf(i_0_1425,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(split_conjunct,[status(thm)],[i_0_833]) ).
cnf(i_0_1426,plain,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
inference(split_conjunct,[status(thm)],[i_0_834]) ).
cnf(i_0_1427,plain,
ti(fun(fun(X1,bool),bool),finite_finite(X1)) = finite_finite(X1),
inference(split_conjunct,[status(thm)],[i_0_835]) ).
cnf(i_0_1428,hypothesis,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_820]) ).
cnf(i_0_1429,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(split_conjunct,[status(thm)],[tsy_c_fimplies_res]) ).
cnf(i_0_1430,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(split_conjunct,[status(thm)],[tsy_c_fdisj_res]) ).
cnf(i_0_1431,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(split_conjunct,[status(thm)],[tsy_c_fconj_res]) ).
cnf(i_0_1432,plain,
( ti(bool,X1) = fTrue
| ti(bool,X1) = fFalse ),
inference(split_conjunct,[status(thm)],[i_0_836]) ).
fof(i_0_1433,plain,
! [X3486] :
( hBOOL(X3486)
| hBOOL(hAPP(bool,bool,fNot,X3486)) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
fof(i_0_1434,plain,
! [X3449] : hAPP(nat,nat,suc,X3449) != zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_484_Suc__not__Zero]) ).
fof(i_0_1435,plain,
! [X3448] : hAPP(nat,nat,suc,X3448) != zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_483_nat_Osimps_I3_J]) ).
fof(i_0_1436,plain,
! [X3446] : hAPP(nat,nat,suc,X3446) != zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_481_Suc__neq__Zero]) ).
fof(i_0_1437,plain,
! [X3451] : zero_zero(nat) != hAPP(nat,nat,suc,X3451),
inference(variable_rename,[status(thm)],[fact_486_Zero__not__Suc]) ).
fof(i_0_1438,plain,
! [X3450] : zero_zero(nat) != hAPP(nat,nat,suc,X3450),
inference(variable_rename,[status(thm)],[fact_485_nat_Osimps_I2_J]) ).
fof(i_0_1439,plain,
! [X3447] : zero_zero(nat) != hAPP(nat,nat,suc,X3447),
inference(variable_rename,[status(thm)],[fact_482_Zero__neq__Suc]) ).
fof(i_0_1440,plain,
! [X1884] : hAPP(nat,nat,suc,X1884) != X1884,
inference(variable_rename,[status(thm)],[fact_18_Suc__n__not__n]) ).
fof(i_0_1441,plain,
! [X1885] : X1885 != hAPP(nat,nat,suc,X1885),
inference(variable_rename,[status(thm)],[fact_19_n__not__Suc__n]) ).
cnf(i_0_1442,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_1443,plain,
ti(fun(pname,option(com)),body) = body,
inference(split_conjunct,[status(thm)],[tsy_c_Com_Obody_res]) ).
cnf(i_0_1444,plain,
ti(fun(X1,X1),combi(X1)) = combi(X1),
inference(split_conjunct,[status(thm)],[i_0_837]) ).
cnf(i_0_1445,hypothesis,
ti(fun(x_a,bool),g) = g,
inference(split_conjunct,[status(thm)],[tsy_v_G_res]) ).
cnf(i_0_1446,hypothesis,
ti(fun(nat,nat),suc) = suc,
inference(split_conjunct,[status(thm)],[tsy_c_Nat_OSuc_res]) ).
cnf(i_0_1447,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(split_conjunct,[status(thm)],[tsy_c_fNot_res]) ).
cnf(i_0_1448,plain,
ti(fun(com,x_a),mgt) = mgt,
inference(split_conjunct,[status(thm)],[tsy_v_mgt_res]) ).
cnf(i_0_1449,plain,
ti(fun(com,bool),wt) = wt,
inference(split_conjunct,[status(thm)],[tsy_v_wt_res]) ).
cnf(i_0_1450,hypothesis,
ti(fun(pname,x_a),mgt_call) = mgt_call,
inference(split_conjunct,[status(thm)],[tsy_v_mgt__call_res]) ).
cnf(i_0_1451,hypothesis,
ti(fun(pname,bool),u) = u,
inference(split_conjunct,[status(thm)],[tsy_v_U_res]) ).
fof(i_0_1452,plain,
! [X3386] : hAPP(fun(X3386,bool),nat,finite_card(X3386),bot_bot(fun(X3386,bool))) = zero_zero(nat),
inference(variable_rename,[status(thm)],[fact_451_card_Oempty]) ).
fof(i_0_1453,plain,
! [X2235,X2236,X2237] :
( ~ bot(X2236)
| hAPP(X2235,X2236,bot_bot(fun(X2235,X2236)),X2237) = bot_bot(X2236) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_bot__apply])])]) ).
fof(i_0_1454,plain,
! [X2232,X2233,X2234] :
( ~ bot(X2233)
| hAPP(X2232,X2233,bot_bot(fun(X2232,X2233)),X2234) = bot_bot(X2233) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_113_bot__fun__def])])]) ).
cnf(i_0_1455,plain,
( ti(X1,bot_bot(X1)) = bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_838]) ).
cnf(i_0_1456,plain,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_839]) ).
cnf(i_0_1457,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_840]) ).
cnf(i_0_1458,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[i_0_841]) ).
cnf(i_0_1459,hypothesis,
ti(nat,na) = na,
inference(split_conjunct,[status(thm)],[tsy_v_na_res]) ).
cnf(i_0_1460,plain,
ti(bool,fTrue) = fTrue,
inference(split_conjunct,[status(thm)],[tsy_c_fTrue_res]) ).
cnf(i_0_1461,plain,
ti(bool,fFalse) = fFalse,
inference(split_conjunct,[status(thm)],[tsy_c_fFalse_res]) ).
cnf(i_0_1462,hypothesis,
ti(pname,pn) = pn,
inference(split_conjunct,[status(thm)],[tsy_v_pn_res]) ).
fof(i_0_1463,plain,
! [X3481,X3482] :
( ~ finite_finite_1(X3482)
| ~ finite_finite_1(X3481)
| finite_finite_1(sum_sum(X3481,X3482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum___Finite__Set_Ofinite])]) ).
fof(i_0_1464,plain,
! [X3471,X3472] :
( ~ finite_finite_1(X3472)
| ~ finite_finite_1(X3471)
| finite_finite_1(fun(X3471,X3472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite])]) ).
fof(i_0_1465,plain,
! [X3469,X3470] :
( ~ preorder(X3470)
| preorder(fun(X3469,X3470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Opreorder])]) ).
fof(i_0_1466,plain,
! [X3473,X3474] :
( ~ order(X3474)
| order(fun(X3473,X3474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oorder])]) ).
fof(i_0_1467,plain,
! [X3475,X3476] :
( ~ ord(X3476)
| ord(fun(X3475,X3476)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oord])]) ).
fof(i_0_1468,plain,
! [X3477,X3478] :
( ~ bot(X3478)
| bot(fun(X3477,X3478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Obot])]) ).
fof(i_0_1469,plain,
! [X3479,X3480] :
( ~ minus(X3480)
| minus(fun(X3479,X3480)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Groups_Ominus])]) ).
fof(i_0_1470,plain,
! [X3396] :
( ~ zero_neq_one(X3396)
| zero_zero(X3396) != one_one(X3396) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_458_zero__neq__one])]) ).
fof(i_0_1471,plain,
! [X3395] :
( ~ zero_neq_one(X3395)
| one_one(X3395) != zero_zero(X3395) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_457_one__neq__zero])]) ).
fof(i_0_1472,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
cnf(i_0_1473,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_842]),
[final] ).
cnf(i_0_1474,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),esk40_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_843,c_0_844]),
[final] ).
cnf(i_0_1475,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_845]),
[final] ).
cnf(i_0_1476,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,esk67_6(X2,X1,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk66_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_846]),
[final] ).
cnf(i_0_1477,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_847]),
[final] ).
cnf(i_0_1478,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_848]),
[final] ).
cnf(i_0_1479,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_849]),
[final] ).
cnf(i_0_1480,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,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(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_850]),
[final] ).
cnf(i_0_1481,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,esk71_6(X1,X2,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk70_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_851]),
[final] ).
cnf(i_0_1482,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,esk74_6(X1,X2,X4,X5,X3,X6))),hAPP(X2,X1,X3,esk75_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_852]),
[final] ).
cnf(i_0_1483,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,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(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_853]),
[final] ).
cnf(i_0_1484,plain,
( hAPP(fun(X1,bool),X2,X7,X4) = hAPP(X2,X2,combi(X2),X6)
| hAPP(X1,X2,X3,esk40_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_854,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1485,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_855,c_0_844]),
[final] ).
cnf(i_0_1486,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_856,c_0_844]),
[final] ).
cnf(i_0_1487,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_857]),
[final] ).
cnf(i_0_1488,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_857]),
[final] ).
cnf(i_0_1489,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_858]),
[final] ).
cnf(i_0_1490,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_848]),
[final] ).
cnf(i_0_1491,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_849]),
[final] ).
cnf(i_0_1492,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk67_6(X1,X2,X3,X4,X5,X6)),esk66_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_846]),
[final] ).
cnf(i_0_1493,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_847]),
[final] ).
cnf(i_0_1494,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_859]),
[final] ).
cnf(i_0_1495,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(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_850]),
[final] ).
cnf(i_0_1496,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk71_6(X2,X1,X3,X4,X5,X6)),esk70_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_851]),
[final] ).
cnf(i_0_1497,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk74_6(X2,X1,X3,X4,X5,X6)),esk75_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_852]),
[final] ).
cnf(i_0_1498,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(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_853]),
[final] ).
cnf(i_0_1499,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,esk35_4(X1,X4,X2,X3)),esk36_4(X1,X4,X2,X3))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk35_4(X1,X4,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk36_4(X1,X4,X2,X3)),bot_bot(fun(X1,bool)))))) ),
inference(rw,[status(thm)],[i_0_860,c_0_844]),
[final] ).
cnf(i_0_1500,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_861]),
[final] ).
cnf(i_0_1501,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_862]),
[final] ).
cnf(i_0_1502,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_857]),
[final] ).
cnf(i_0_1503,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_863]),
[final] ).
cnf(i_0_1504,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_863]),
[final] ).
cnf(i_0_1505,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),esk26_2(X1,X2)),hAPP(nat,nat,X2,esk26_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1506,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_865]),
[final] ).
cnf(i_0_1507,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_866]),
[final] ).
cnf(i_0_1508,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_867]),
[final] ).
cnf(i_0_1509,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_868]),
[final] ).
cnf(i_0_1510,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,esk33_5(X1,X5,X4,X2,X3)),esk34_5(X1,X5,X4,X2,X3))) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X1,X1,X4,esk33_5(X1,X5,X4,X2,X3))),hAPP(X1,X1,X4,esk34_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_869,c_0_844]),
[final] ).
cnf(i_0_1511,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_870]),
[final] ).
cnf(i_0_1512,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_871]),
[final] ).
cnf(i_0_1513,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_871]),
[final] ).
cnf(i_0_1514,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_871]),
[final] ).
cnf(i_0_1515,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_871]),
[final] ).
cnf(i_0_1516,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_872]),
[final] ).
cnf(i_0_1517,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_873]),
[final] ).
cnf(i_0_1518,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_872]),
[final] ).
cnf(i_0_1519,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_874]),
[final] ).
cnf(i_0_1520,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_875]),
[final] ).
cnf(i_0_1521,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk11_5(X1,X2,X3,X4,X5))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_876]),
[final] ).
cnf(i_0_1522,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_877]),
[final] ).
cnf(i_0_1523,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_878]),
[final] ).
cnf(i_0_1524,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_871]),
[final] ).
cnf(i_0_1525,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_879,c_0_844]),
[final] ).
cnf(i_0_1526,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_872]),
[final] ).
cnf(i_0_1527,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_880]),
[final] ).
cnf(i_0_1528,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_880]),
[final] ).
cnf(i_0_1529,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_881]),
[final] ).
cnf(i_0_1530,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_882]),
[final] ).
cnf(i_0_1531,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_883]),
[final] ).
cnf(i_0_1532,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,esk55_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk55_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1533,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_885]),
[final] ).
cnf(i_0_1534,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,esk54_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk54_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_886]),
[final] ).
cnf(i_0_1535,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,esk55_4(X3,X1,X2,X4))),hAPP(nat,X3,X4,hAPP(nat,nat,suc,esk55_4(X3,X1,X2,X4)))))
| ~ order(X3) ),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1536,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)),esk38_3(X1,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),esk37_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_887]),
[final] ).
cnf(i_0_1537,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,esk14_2(X1,X2))),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1538,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_889]),
[final] ).
cnf(i_0_1539,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_642]),
[final] ).
cnf(i_0_1540,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_645]),
[final] ).
cnf(i_0_1541,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_883]),
[final] ).
cnf(i_0_1542,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_659]),
[final] ).
cnf(i_0_1543,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_890]),
[final] ).
cnf(i_0_1544,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_891]),
[final] ).
cnf(i_0_1545,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_892]),
[final] ).
cnf(i_0_1546,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_893]),
[final] ).
cnf(i_0_1547,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_638]),
[final] ).
cnf(i_0_1548,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_894]),
[final] ).
cnf(i_0_1549,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk11_5(X2,X1,X3,X4,X5)),X5))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_876]),
[final] ).
cnf(i_0_1550,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_895]),
[final] ).
cnf(i_0_1551,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),esk20_4(X1,X2,X3,X4)),esk21_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_896]),
[final] ).
cnf(i_0_1552,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),esk8_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_639]),
[final] ).
cnf(i_0_1553,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_889]),
[final] ).
cnf(i_0_1554,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk9_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_646]),
[final] ).
cnf(i_0_1555,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_647]),
[final] ).
cnf(i_0_1556,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_895]),
[final] ).
cnf(i_0_1557,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_897]),
[final] ).
cnf(i_0_1558,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),esk31_3(X1,X2,X3)),esk32_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),esk30_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_898,c_0_844]),
[final] ).
cnf(i_0_1559,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_899]),
[final] ).
cnf(i_0_1560,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_900]),
[final] ).
cnf(i_0_1561,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_901]),
[final] ).
cnf(i_0_1562,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_902]),
[final] ).
cnf(i_0_1563,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_903]),
[final] ).
cnf(i_0_1564,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_904]),
[final] ).
cnf(i_0_1565,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_905]),
[final] ).
cnf(i_0_1566,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_906]),
[final] ).
cnf(i_0_1567,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_907]),
[final] ).
cnf(i_0_1568,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_908]),
[final] ).
cnf(i_0_1569,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_909]),
[final] ).
cnf(i_0_1570,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_910]),
[final] ).
cnf(i_0_1571,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_911]),
[final] ).
cnf(i_0_1572,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_912]),
[final] ).
cnf(i_0_1573,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,esk29_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk29_4(X2,X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1574,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,esk15_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk15_4(X2,X1,X3,X4))))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1575,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_915]),
[final] ).
cnf(i_0_1576,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_891]),
[final] ).
cnf(i_0_1577,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_892]),
[final] ).
cnf(i_0_1578,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_916]),
[final] ).
cnf(i_0_1579,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_915]),
[final] ).
cnf(i_0_1580,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_917]),
[final] ).
cnf(i_0_1581,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_918]),
[final] ).
cnf(i_0_1582,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_919]),
[final] ).
cnf(i_0_1583,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_900]),
[final] ).
cnf(i_0_1584,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_920]),
[final] ).
cnf(i_0_1585,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_921]),
[final] ).
cnf(i_0_1586,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_922]),
[final] ).
cnf(i_0_1587,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_638]),
[final] ).
cnf(i_0_1588,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_915]),
[final] ).
cnf(i_0_1589,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_923]),
[final] ).
cnf(i_0_1590,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_924]),
[final] ).
cnf(i_0_1591,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_925]),
[final] ).
cnf(i_0_1592,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_926]),
[final] ).
cnf(i_0_1593,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_927]),
[final] ).
cnf(i_0_1594,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,esk58_3(X2,X3,X1))),hAPP(nat,nat,X1,esk59_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_928]),
[final] ).
cnf(i_0_1595,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_929]),
[final] ).
cnf(i_0_1596,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_930]),
[final] ).
cnf(i_0_1597,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_931]),
[final] ).
cnf(i_0_1598,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_932]),
[final] ).
cnf(i_0_1599,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_871]),
[final] ).
cnf(i_0_1600,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_921]),
[final] ).
cnf(i_0_1601,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_922]),
[final] ).
cnf(i_0_1602,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_933,c_0_844]),
[final] ).
cnf(i_0_1603,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_871]),
[final] ).
cnf(i_0_1604,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),esk31_3(X1,X2,X3)),esk32_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),esk30_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_934,c_0_844]),
[final] ).
cnf(i_0_1605,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_871]),
[final] ).
cnf(i_0_1606,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_935]),
[final] ).
cnf(i_0_1607,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),esk8_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_936,c_0_844]),
[final] ).
cnf(i_0_1608,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_937]),
[final] ).
cnf(i_0_1609,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_938]),
[final] ).
cnf(i_0_1610,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_939]),
[final] ).
cnf(i_0_1611,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_940]),
[final] ).
cnf(i_0_1612,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_941]),
[final] ).
cnf(i_0_1613,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_941]),
[final] ).
cnf(i_0_1614,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_942]),
[final] ).
cnf(i_0_1615,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_943]),
[final] ).
cnf(i_0_1616,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_944]),
[final] ).
cnf(i_0_1617,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_945]),
[final] ).
cnf(i_0_1618,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_902]),
[final] ).
cnf(i_0_1619,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_946]),
[final] ).
cnf(i_0_1620,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_904]),
[final] ).
cnf(i_0_1621,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_947]),
[final] ).
cnf(i_0_1622,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_905]),
[final] ).
cnf(i_0_1623,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_948]),
[final] ).
cnf(i_0_1624,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_907]),
[final] ).
cnf(i_0_1625,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_949]),
[final] ).
cnf(i_0_1626,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_872]),
[final] ).
cnf(i_0_1627,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_950]),
[final] ).
cnf(i_0_1628,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_951,c_0_844]),
[final] ).
cnf(i_0_1629,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_952]),
[final] ).
cnf(i_0_1630,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_910]),
[final] ).
cnf(i_0_1631,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_953]),
[final] ).
cnf(i_0_1632,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_954]),
[final] ).
cnf(i_0_1633,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_955]),
[final] ).
cnf(i_0_1634,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_911]),
[final] ).
cnf(i_0_1635,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk20_4(X1,X2,X3,X4)),esk21_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_896]),
[final] ).
cnf(i_0_1636,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_871]),
[final] ).
cnf(i_0_1637,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_956]),
[final] ).
cnf(i_0_1638,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_957]),
[final] ).
cnf(i_0_1639,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_958]),
[final] ).
cnf(i_0_1640,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_959]),
[final] ).
cnf(i_0_1641,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_1642,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_960,c_0_844]),
[final] ).
cnf(i_0_1643,plain,
( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk9_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_961,c_0_844]),
[final] ).
cnf(i_0_1644,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_962,c_0_844]),
[final] ).
cnf(i_0_1645,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_963]),
[final] ).
cnf(i_0_1646,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_964]),
[final] ).
cnf(i_0_1647,plain,
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),esk14_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_888]),
[final] ).
cnf(i_0_1648,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_965,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1649,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_871]),
[final] ).
cnf(i_0_1650,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_842]),
[final] ).
cnf(i_0_1651,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_966]),
[final] ).
cnf(i_0_1652,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_967]),
[final] ).
cnf(i_0_1653,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_968,c_0_844]),
[final] ).
cnf(i_0_1654,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_969]),
[final] ).
cnf(i_0_1655,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_940]),
[final] ).
cnf(i_0_1656,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_957]),
[final] ).
cnf(i_0_1657,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_970]),
[final] ).
cnf(i_0_1658,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_958]),
[final] ).
cnf(i_0_1659,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_971,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1660,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_972]),
[final] ).
cnf(i_0_1661,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),esk22_3(X1,X2,X3)),esk23_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_973]),
[final] ).
cnf(i_0_1662,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_974,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1663,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_975,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1664,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),esk32_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),esk30_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_976,c_0_844]),
[final] ).
cnf(i_0_1665,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,esk32_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),esk30_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[i_0_977,c_0_844]),
[final] ).
cnf(i_0_1666,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)),esk32_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),esk30_3(X1,X2,X3)),bot_bot(fun(X1,bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_978,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1667,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_979]),
[final] ).
cnf(i_0_1668,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_980]),
[final] ).
cnf(i_0_1669,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_981]),
[final] ).
cnf(i_0_1670,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_872]),
[final] ).
cnf(i_0_1671,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_950]),
[final] ).
cnf(i_0_1672,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_982,c_0_844]),
[final] ).
cnf(i_0_1673,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_983,c_0_844]),
[final] ).
cnf(i_0_1674,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_984,c_0_844]),
[final] ).
cnf(i_0_1675,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_985,c_0_844]),
[final] ).
cnf(i_0_1676,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_986]),
[final] ).
cnf(i_0_1677,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_987]),
[final] ).
cnf(i_0_1678,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_957]),
[final] ).
cnf(i_0_1679,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_988]),
[final] ).
cnf(i_0_1680,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_989]),
[final] ).
cnf(i_0_1681,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_990]),
[final] ).
cnf(i_0_1682,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_1683,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_991,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1684,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_992,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1685,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_993,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1686,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_994,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1687,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_995,c_0_844]),
[final] ).
cnf(i_0_1688,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_996,c_0_844]),
[final] ).
cnf(i_0_1689,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_935]),
[final] ).
cnf(i_0_1690,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_937]),
[final] ).
cnf(i_0_1691,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_997]),
[final] ).
cnf(i_0_1692,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_998,c_0_844]),
[final] ).
cnf(i_0_1693,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_999]),
[final] ).
cnf(i_0_1694,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_999]),
[final] ).
cnf(i_0_1695,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_1000]),
[final] ).
cnf(i_0_1696,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_1001]),
[final] ).
cnf(i_0_1697,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_1002]),
[final] ).
cnf(i_0_1698,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_1003]),
[final] ).
cnf(i_0_1699,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_1004]),
[final] ).
cnf(i_0_1700,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk57_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_1005]),
[final] ).
cnf(i_0_1701,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_1006,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1702,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_1007,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1703,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_1008,c_0_844]),
[final] ).
cnf(i_0_1704,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_1009,c_0_844]),
[final] ).
cnf(i_0_1705,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_1010,c_0_844]),
[final] ).
cnf(i_0_1706,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_1011]),
[final] ).
cnf(i_0_1707,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_964]),
[final] ).
cnf(i_0_1708,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_1012]),
[final] ).
cnf(i_0_1709,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_1013]),
[final] ).
cnf(i_0_1710,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_1014]),
[final] ).
cnf(i_0_1711,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_1015]),
[final] ).
cnf(i_0_1712,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),esk65_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_1016]),
[final] ).
cnf(i_0_1713,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_1017]),
[final] ).
cnf(i_0_1714,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_1018,c_0_844]),
[final] ).
cnf(i_0_1715,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_1019]),
[final] ).
cnf(i_0_1716,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk20_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_896]),
[final] ).
cnf(i_0_1717,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_1020]),
[final] ).
cnf(i_0_1718,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_997]),
[final] ).
cnf(i_0_1719,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_1021]),
[final] ).
cnf(i_0_1720,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_1022]),
[final] ).
cnf(i_0_1721,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_1023]),
[final] ).
cnf(i_0_1722,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk58_3(X1,X2,X3)),esk59_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_928]),
[final] ).
cnf(i_0_1723,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_1024,c_0_844]),
[final] ).
cnf(i_0_1724,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_1025]),
[final] ).
cnf(i_0_1725,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_1026]),
[final] ).
cnf(i_0_1726,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_1027]),
[final] ).
cnf(i_0_1727,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_654]),
[final] ).
cnf(i_0_1728,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_680]),
[final] ).
cnf(i_0_1729,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_1028]),
[final] ).
cnf(i_0_1730,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_1029]),
[final] ).
cnf(i_0_1731,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_1030]),
[final] ).
cnf(i_0_1732,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_1031]),
[final] ).
cnf(i_0_1733,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_1032]),
[final] ).
cnf(i_0_1734,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_1033]),
[final] ).
cnf(i_0_1735,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_1034]),
[final] ).
cnf(i_0_1736,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_1035]),
[final] ).
cnf(i_0_1737,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_1036]),
[final] ).
cnf(i_0_1738,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_1037]),
[final] ).
cnf(i_0_1739,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_1038]),
[final] ).
cnf(i_0_1740,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_1039]),
[final] ).
cnf(i_0_1741,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_1040]),
[final] ).
cnf(i_0_1742,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_1041]),
[final] ).
cnf(i_0_1743,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_1042]),
[final] ).
cnf(i_0_1744,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_1043,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1745,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_1044]),
[final] ).
cnf(i_0_1746,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_1045]),
[final] ).
cnf(i_0_1747,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_999]),
[final] ).
cnf(i_0_1748,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_1046,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1749,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_1047,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1750,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_1048]),
[final] ).
cnf(i_0_1751,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_1049]),
[final] ).
cnf(i_0_1752,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_1050]),
[final] ).
cnf(i_0_1753,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_1051]),
[final] ).
cnf(i_0_1754,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_1052]),
[final] ).
cnf(i_0_1755,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_1053]),
[final] ).
cnf(i_0_1756,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_1054]),
[final] ).
cnf(i_0_1757,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_914]),
[final] ).
cnf(i_0_1758,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_1055]),
[final] ).
cnf(i_0_1759,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_1056]),
[final] ).
cnf(i_0_1760,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),esk53_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)),esk52_2(X1,X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[i_0_1057,c_0_844]),
[final] ).
cnf(i_0_1761,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_1058,c_0_844]),
[final] ).
cnf(i_0_1762,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_1059]),
[final] ).
cnf(i_0_1763,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_1060]),
[final] ).
cnf(i_0_1764,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_1061]),
[final] ).
cnf(i_0_1765,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk65_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_1016]),
[final] ).
cnf(i_0_1766,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_1062,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1767,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_1063]),
[final] ).
cnf(i_0_1768,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_1022]),
[final] ).
cnf(i_0_1769,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_1064]),
[final] ).
cnf(i_0_1770,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_1065]),
[final] ).
cnf(i_0_1771,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_1066]),
[final] ).
cnf(i_0_1772,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_1067,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1773,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_1068,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1774,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk21_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_896]),
[final] ).
cnf(i_0_1775,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk21_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_896]),
[final] ).
cnf(i_0_1776,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_1069]),
[final] ).
cnf(i_0_1777,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_1070]),
[final] ).
cnf(i_0_1778,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_1071]),
[final] ).
cnf(i_0_1779,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_1072]),
[final] ).
cnf(i_0_1780,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_1073]),
[final] ).
cnf(i_0_1781,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_1074]),
[final] ).
cnf(i_0_1782,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_1075]),
[final] ).
cnf(i_0_1783,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_1076]),
[final] ).
cnf(i_0_1784,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_1077]),
[final] ).
cnf(i_0_1785,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_1078]),
[final] ).
cnf(i_0_1786,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_1079]),
[final] ).
cnf(i_0_1787,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_1080]),
[final] ).
cnf(i_0_1788,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_1081]),
[final] ).
cnf(i_0_1789,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_1082]),
[final] ).
cnf(i_0_1790,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_1083]),
[final] ).
cnf(i_0_1791,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_1017]),
[final] ).
cnf(i_0_1792,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_1084,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1793,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_1039]),
[final] ).
cnf(i_0_1794,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_1040]),
[final] ).
cnf(i_0_1795,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_1085]),
[final] ).
cnf(i_0_1796,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_1061]),
[final] ).
cnf(i_0_1797,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_1086,c_0_844]),
[final] ).
cnf(i_0_1798,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_1087,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1799,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_1088,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1800,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_1089,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1801,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_1090,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1802,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk65_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_1016]),
[final] ).
cnf(i_0_1803,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_1091]),
[final] ).
cnf(i_0_1804,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_1091]),
[final] ).
cnf(i_0_1805,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_1092]),
[final] ).
cnf(i_0_1806,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_1092]),
[final] ).
cnf(i_0_1807,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_1093,c_0_844]),
[final] ).
cnf(i_0_1808,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_1094,c_0_844]),
[final] ).
cnf(i_0_1809,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_1095]),
[final] ).
cnf(i_0_1810,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_1096]),
[final] ).
cnf(i_0_1811,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_1097]),
[final] ).
cnf(i_0_1812,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_1098]),
[final] ).
cnf(i_0_1813,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_1099]),
[final] ).
cnf(i_0_1814,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_1100]),
[final] ).
cnf(i_0_1815,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_1101]),
[final] ).
cnf(i_0_1816,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_1102]),
[final] ).
cnf(i_0_1817,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_1103]),
[final] ).
cnf(i_0_1818,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_1104]),
[final] ).
cnf(i_0_1819,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_1105]),
[final] ).
cnf(i_0_1820,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_1106]),
[final] ).
cnf(i_0_1821,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_1107]),
[final] ).
cnf(i_0_1822,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_1108]),
[final] ).
cnf(i_0_1823,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_1109]),
[final] ).
cnf(i_0_1824,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_1110]),
[final] ).
cnf(i_0_1825,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk22_3(X1,X2,X3)),esk23_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_973]),
[final] ).
cnf(i_0_1826,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_1827,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_1111]),
[final] ).
cnf(i_0_1828,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_1112]),
[final] ).
cnf(i_0_1829,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_1113]),
[final] ).
cnf(i_0_1830,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_1114]),
[final] ).
cnf(i_0_1831,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_1115]),
[final] ).
cnf(i_0_1832,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_1116]),
[final] ).
cnf(i_0_1833,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_1117]),
[final] ).
cnf(i_0_1834,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_1118]),
[final] ).
cnf(i_0_1835,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_1119]),
[final] ).
cnf(i_0_1836,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_1120]),
[final] ).
cnf(i_0_1837,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_1121]),
[final] ).
cnf(i_0_1838,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_1122,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1839,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_1123,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1840,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_1124]),
[final] ).
cnf(i_0_1841,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_1125]),
[final] ).
cnf(i_0_1842,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_1126]),
[final] ).
cnf(i_0_1843,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_1080]),
[final] ).
cnf(i_0_1844,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_1081]),
[final] ).
cnf(i_0_1845,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_1127]),
[final] ).
cnf(i_0_1846,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_1128]),
[final] ).
cnf(i_0_1847,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_1110]),
[final] ).
cnf(i_0_1848,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_1129]),
[final] ).
cnf(i_0_1849,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_1130,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1850,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_1131]),
[final] ).
cnf(i_0_1851,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_1132]),
[final] ).
cnf(i_0_1852,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_1133]),
[final] ).
cnf(i_0_1853,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_1077]),
[final] ).
cnf(i_0_1854,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_1134]),
[final] ).
cnf(i_0_1855,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_1135]),
[final] ).
cnf(i_0_1856,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_1136]),
[final] ).
cnf(i_0_1857,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_1137]),
[final] ).
cnf(i_0_1858,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),esk10_3(X1,X2,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1138]),
[final] ).
cnf(i_0_1859,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_1135]),
[final] ).
cnf(i_0_1860,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_1061]),
[final] ).
cnf(i_0_1861,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_1056]),
[final] ).
cnf(i_0_1862,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_1139]),
[final] ).
cnf(i_0_1863,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_1140]),
[final] ).
cnf(i_0_1864,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_1141]),
[final] ).
cnf(i_0_1865,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_1142]),
[final] ).
cnf(i_0_1866,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_1143]),
[final] ).
cnf(i_0_1867,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_1144]),
[final] ).
cnf(i_0_1868,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_1145,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1869,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_1146,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1870,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_1147,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1871,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_1148,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1872,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_1149]),
[final] ).
cnf(i_0_1873,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_1112]),
[final] ).
cnf(i_0_1874,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_1150,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1875,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_672]),
[final] ).
cnf(i_0_1876,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_685]),
[final] ).
cnf(i_0_1877,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_686]),
[final] ).
cnf(i_0_1878,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_1151]),
[final] ).
cnf(i_0_1879,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),esk12_1(X1)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1152]),
[final] ).
cnf(i_0_1880,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_1153]),
[final] ).
cnf(i_0_1881,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_1154]),
[final] ).
cnf(i_0_1882,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_1155,c_0_844]),
[final] ).
cnf(i_0_1883,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_1055]),
[final] ).
cnf(i_0_1884,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_1156]),
[final] ).
cnf(i_0_1885,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_1157]),
[final] ).
cnf(i_0_1886,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_1158]),
[final] ).
cnf(i_0_1887,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_1159]),
[final] ).
cnf(i_0_1888,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_1160]),
[final] ).
cnf(i_0_1889,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_734]),
[final] ).
cnf(i_0_1890,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_1136]),
[final] ).
cnf(i_0_1891,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_1161]),
[final] ).
cnf(i_0_1892,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_1162]),
[final] ).
cnf(i_0_1893,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_1163]),
[final] ).
cnf(i_0_1894,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_1164]),
[final] ).
cnf(i_0_1895,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_1165]),
[final] ).
cnf(i_0_1896,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_1106]),
[final] ).
cnf(i_0_1897,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_1132]),
[final] ).
cnf(i_0_1898,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_1166]),
[final] ).
cnf(i_0_1899,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_1167]),
[final] ).
cnf(i_0_1900,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_1144]),
[final] ).
cnf(i_0_1901,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_1140]),
[final] ).
cnf(i_0_1902,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_1168]),
[final] ).
cnf(i_0_1903,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_1169]),
[final] ).
cnf(i_0_1904,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_1170]),
[final] ).
cnf(i_0_1905,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_1171]),
[final] ).
cnf(i_0_1906,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_1172,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1907,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_1173,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1908,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_1174,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1909,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_1175,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1910,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_1176,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1911,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_1177,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1912,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_1178]),
[final] ).
cnf(i_0_1913,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_1135]),
[final] ).
cnf(i_0_1914,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk37_3(X1,X2,X3)),esk38_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_887]),
[final] ).
cnf(i_0_1915,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_1179]),
[final] ).
cnf(i_0_1916,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_1180]),
[final] ).
cnf(i_0_1917,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),esk64_3(X1,X2,X3)),X2))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1181]),
[final] ).
cnf(i_0_1918,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_1182]),
[final] ).
cnf(i_0_1919,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_1183]),
[final] ).
cnf(i_0_1920,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_1184]),
[final] ).
cnf(i_0_1921,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_1185]),
[final] ).
cnf(i_0_1922,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_1186]),
[final] ).
cnf(i_0_1923,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_1187]),
[final] ).
cnf(i_0_1924,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_1188,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1925,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_1189,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1926,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_1190,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1927,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_1191,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1928,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_1192,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1929,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_1193,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1930,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_1194,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1931,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_1195,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1932,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_1196,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1933,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_1197,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1934,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_1198]),
[final] ).
cnf(i_0_1935,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_1198]),
[final] ).
cnf(i_0_1936,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_1199]),
[final] ).
cnf(i_0_1937,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_1200,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1938,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_1201]),
[final] ).
cnf(i_0_1939,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk10_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_1138]),
[final] ).
cnf(i_0_1940,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk61_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_1202]),
[final] ).
cnf(i_0_1941,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_1203]),
[final] ).
cnf(i_0_1942,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_1199]),
[final] ).
cnf(i_0_1943,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_1204,c_0_844]),
[final] ).
cnf(i_0_1944,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_1205,c_0_844]),
[final] ).
cnf(i_0_1945,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_1206]),
[final] ).
cnf(i_0_1946,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_1207,c_0_844]),
[final] ).
cnf(i_0_1947,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_1208]),
[final] ).
cnf(i_0_1948,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_1209]),
[final] ).
cnf(i_0_1949,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_1136]),
[final] ).
cnf(i_0_1950,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_718]),
[final] ).
cnf(i_0_1951,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_719]),
[final] ).
cnf(i_0_1952,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_1141]),
[final] ).
cnf(i_0_1953,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_1107]),
[final] ).
cnf(i_0_1954,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_1210]),
[final] ).
cnf(i_0_1955,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_1211]),
[final] ).
cnf(i_0_1956,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_1212]),
[final] ).
cnf(i_0_1957,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_1213]),
[final] ).
cnf(i_0_1958,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_1210]),
[final] ).
cnf(i_0_1959,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_1211]),
[final] ).
cnf(i_0_1960,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_1214]),
[final] ).
cnf(i_0_1961,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_1215]),
[final] ).
cnf(i_0_1962,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_1216,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1963,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_1217]),
[final] ).
cnf(i_0_1964,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_1218,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1965,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_1219]),
[final] ).
cnf(i_0_1966,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_1220]),
[final] ).
cnf(i_0_1967,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_1221]),
[final] ).
cnf(i_0_1968,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_1222,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1969,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_1223,c_0_844]),c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1970,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_1224,c_0_844]),
[final] ).
cnf(i_0_1971,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_1225,c_0_844]),
[final] ).
cnf(i_0_1972,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_1226,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1973,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_1227,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1974,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_1228,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1975,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_1229,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1976,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_1230,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1977,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_1231,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1978,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_1232,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1979,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_1065]),
[final] ).
cnf(i_0_1980,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_1065]),
[final] ).
cnf(i_0_1981,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_1233,c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1982,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk64_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_1181]),
[final] ).
cnf(i_0_1983,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_1234]),
[final] ).
cnf(i_0_1984,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_1235]),
[final] ).
cnf(i_0_1985,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_1236,c_0_844]),
[final] ).
cnf(i_0_1986,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_1237,c_0_844]),
[final] ).
cnf(i_0_1987,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_1238]),
[final] ).
cnf(i_0_1988,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),esk27_2(X1,X2)),esk28_2(X1,X2))) ),
inference(rw,[status(thm)],[i_0_1239,c_0_844]),
[final] ).
cnf(i_0_1989,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_1240]),
[final] ).
cnf(i_0_1990,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_1241,c_0_844]),
[final] ).
cnf(i_0_1991,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_1242,c_0_844]),
[final] ).
cnf(i_0_1992,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_1243,c_0_844]),
[final] ).
cnf(i_0_1993,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_1244]),
[final] ).
cnf(i_0_1994,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_1245,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1995,plain,
( hBOOL(hAPP(X1,bool,X2,hAPP(fun(X1,bool),X1,the(X1),X2)))
| 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)],[i_0_1246,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1996,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_1247,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1997,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_1248,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1998,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_1249,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_1999,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_1250,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2000,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_1251,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2001,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_1252,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2002,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_1253,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2003,plain,
( X2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk44_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_1254]),
[final] ).
cnf(i_0_2004,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_1255]),
[final] ).
cnf(i_0_2005,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_1256]),
[final] ).
cnf(i_0_2006,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_1257]),
[final] ).
cnf(i_0_2007,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_1258]),
[final] ).
cnf(i_0_2008,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_1259]),
[final] ).
cnf(i_0_2009,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_1160]),
[final] ).
cnf(i_0_2010,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_1260]),
[final] ).
cnf(i_0_2011,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_1261]),
[final] ).
cnf(i_0_2012,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_1158]),
[final] ).
cnf(i_0_2013,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk23_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_973]),
[final] ).
cnf(i_0_2014,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_1262,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2015,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_1263,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2016,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_1264,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2017,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_1265,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2018,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_1266,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2019,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_1267,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2020,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_1268,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2021,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk23_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_973]),
[final] ).
cnf(i_0_2022,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk13_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1152]),
[final] ).
cnf(i_0_2023,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_1153]),
[final] ).
cnf(i_0_2024,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_1269]),
[final] ).
cnf(i_0_2025,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_1270]),
[final] ).
cnf(i_0_2026,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_1271]),
[final] ).
cnf(i_0_2027,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),esk38_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_887]),
[final] ).
cnf(i_0_2028,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_1272]),
[final] ).
cnf(i_0_2029,plain,
( hBOOL(hAPP(fun(X1,bool),bool,X2,esk38_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_887]),
[final] ).
cnf(i_0_2030,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_742]),
[final] ).
cnf(i_0_2031,plain,
( hBOOL(hAPP(X1,bool,X2,esk41_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_743]),
[final] ).
cnf(i_0_2032,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_1273,c_0_844]),
[final] ).
cnf(i_0_2033,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_1274]),
[final] ).
cnf(i_0_2034,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_1275,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2035,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_1276,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2036,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_1277,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2037,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_1278,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2038,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_1279,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2039,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_1280,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2040,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_1281]),
[final] ).
cnf(i_0_2041,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_1282]),
[final] ).
cnf(i_0_2042,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_1283]),
[final] ).
cnf(i_0_2043,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_1284,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2044,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_1285]),
[final] ).
cnf(i_0_2045,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_1286]),
[final] ).
cnf(i_0_2046,plain,
( X1 = hAPP(nat,nat,suc,esk61_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_1202]),
[final] ).
cnf(i_0_2047,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_1287,c_0_844]),
[final] ).
cnf(i_0_2048,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_1288,c_0_844]),
[final] ).
cnf(i_0_2049,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_1132]),
[final] ).
cnf(i_0_2050,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_1255]),
[final] ).
cnf(i_0_2051,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_1289,c_0_844]),
[final] ).
cnf(i_0_2052,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_1290,c_0_844]),
[final] ).
cnf(i_0_2053,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_1254]),
[final] ).
cnf(i_0_2054,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_1291,c_0_844]),
[final] ).
cnf(i_0_2055,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_1292,c_0_844]),
[final] ).
cnf(i_0_2056,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),esk25_2(X1,X2)),esk24_2(X1,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1293,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2057,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_1294,c_0_844]),
[final] ).
cnf(i_0_2058,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_1295,c_0_844]),
[final] ).
cnf(i_0_2059,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_1296,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2060,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_1244]),
[final] ).
cnf(i_0_2061,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_1297]),
[final] ).
cnf(i_0_2062,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_1298]),
[final] ).
cnf(i_0_2063,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_1299,c_0_844]),
[final] ).
cnf(i_0_2064,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_1300]),
[final] ).
cnf(i_0_2065,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_1301]),
[final] ).
cnf(i_0_2066,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_1140]),
[final] ).
cnf(i_0_2067,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_1302]),
[final] ).
cnf(i_0_2068,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2069,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_1304]),
[final] ).
cnf(i_0_2070,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[i_0_1305]),
[final] ).
cnf(i_0_2071,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_1306]),
[final] ).
cnf(i_0_2072,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1307]),
[final] ).
cnf(i_0_2073,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1308]),
[final] ).
cnf(i_0_2074,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1271]),
[final] ).
cnf(i_0_2075,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1271]),
[final] ).
cnf(i_0_2076,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1210]),
[final] ).
cnf(i_0_2077,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2078,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1310]),
[final] ).
cnf(i_0_2079,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_1311]),
[final] ).
cnf(i_0_2080,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_1312]),
[final] ).
cnf(i_0_2081,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1313]),
[final] ).
cnf(i_0_2082,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1314]),
[final] ).
cnf(i_0_2083,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1315]),
[final] ).
cnf(i_0_2084,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1316]),
[final] ).
cnf(i_0_2085,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_1153]),
[final] ).
cnf(i_0_2086,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk13_2(X1,X2)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1152]),
[final] ).
cnf(i_0_2087,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_1269]),
[final] ).
cnf(i_0_2088,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_1317,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2089,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_1318,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2090,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_1319,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2091,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_1320,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2092,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_1321,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2093,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_1322,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2094,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_1323,c_0_844]),
[final] ).
cnf(i_0_2095,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_1324]),
[final] ).
cnf(i_0_2096,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_1325,c_0_844]),
[final] ).
cnf(i_0_2097,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_1326,c_0_844]),
[final] ).
cnf(i_0_2098,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_1327]),
[final] ).
cnf(i_0_2099,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_1328,c_0_844]),
[final] ).
cnf(i_0_2100,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),esk18_2(X1,X2)),X2)) ),
inference(rw,[status(thm)],[i_0_1329,c_0_844]),
[final] ).
cnf(i_0_2101,plain,
( hAPP(fun(X1,bool),X1,the(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,combi(X1),esk39_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_1330,c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2102,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_1331,c_0_844]),
[final] ).
cnf(i_0_2103,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_1332,c_0_844]),
[final] ).
cnf(i_0_2104,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_1333,c_0_844]),
[final] ).
cnf(i_0_2105,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_1334]),
[final] ).
cnf(i_0_2106,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_1335]),
[final] ).
cnf(i_0_2107,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_1336]),
[final] ).
cnf(i_0_2108,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_1337,c_0_844]),
[final] ).
cnf(i_0_2109,plain,
( hAPP(fun(X1,bool),X1,the(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| hBOOL(hAPP(X1,bool,X2,esk39_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1338,c_0_844]),
[final] ).
cnf(i_0_2110,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_1339]),
[final] ).
cnf(i_0_2111,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_1340,c_0_844]),
[final] ).
cnf(i_0_2112,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_1334]),
[final] ).
cnf(i_0_2113,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_1334]),
[final] ).
cnf(i_0_2114,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_1335]),
[final] ).
cnf(i_0_2115,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_1335]),
[final] ).
cnf(i_0_2116,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),esk24_2(X1,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2)) ),
inference(rw,[status(thm)],[i_0_1341,c_0_844]),
[final] ).
cnf(i_0_2117,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),esk27_2(X1,X2)),esk28_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1342,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2118,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_1343,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2119,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_1344,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2120,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_2121,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_1345,c_0_844]),
[final] ).
cnf(i_0_2122,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_1346,c_0_844]),
[final] ).
cnf(i_0_2123,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_1347]),
[final] ).
cnf(i_0_2124,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_1348,c_0_844]),
[final] ).
cnf(i_0_2125,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_1349,c_0_844]),
[final] ).
cnf(i_0_2126,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_1350]),
[final] ).
cnf(i_0_2127,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_1351]),
[final] ).
cnf(i_0_2128,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_1352]),
[final] ).
cnf(i_0_2129,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_1353]),
[final] ).
cnf(i_0_2130,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_1354]),
[final] ).
cnf(i_0_2131,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_1334]),
[final] ).
cnf(i_0_2132,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_1335]),
[final] ).
cnf(i_0_2133,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_1355,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2134,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_1356,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2135,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_1357]),
[final] ).
cnf(i_0_2136,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_1358]),
[final] ).
cnf(i_0_2137,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_1359]),
[final] ).
cnf(i_0_2138,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_1360]),
[final] ).
cnf(i_0_2139,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_1304]),
[final] ).
cnf(i_0_2140,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_1361,c_0_844]),
[final] ).
cnf(i_0_2141,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_1211]),
[final] ).
cnf(i_0_2142,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_1215]),
[final] ).
cnf(i_0_2143,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_1362]),
[final] ).
cnf(i_0_2144,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1363]),
[final] ).
cnf(i_0_2145,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_1364]),
[final] ).
cnf(i_0_2146,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_2147,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1366]),
[final] ).
cnf(i_0_2148,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1367]),
[final] ).
cnf(i_0_2149,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1368]),
[final] ).
cnf(i_0_2150,plain,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1369]),
[final] ).
cnf(i_0_2151,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_1370,c_0_844]),
[final] ).
cnf(i_0_2152,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_1371,c_0_844]),
[final] ).
cnf(i_0_2153,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_1372,c_0_844]),
[final] ).
cnf(i_0_2154,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_1334]),
[final] ).
cnf(i_0_2155,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_1334]),
[final] ).
cnf(i_0_2156,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_1335]),
[final] ).
cnf(i_0_2157,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_1335]),
[final] ).
cnf(i_0_2158,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_1373,c_0_844]),
[final] ).
cnf(i_0_2159,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_1374,c_0_844]),
[final] ).
cnf(i_0_2160,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_1375]),
[final] ).
cnf(i_0_2161,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_1376]),
[final] ).
cnf(i_0_2162,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_1377]),
[final] ).
cnf(i_0_2163,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_1378,c_0_844]),
[final] ).
cnf(i_0_2164,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_1379,c_0_844]),
[final] ).
cnf(i_0_2165,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_1380]),
[final] ).
cnf(i_0_2166,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_1381]),
[final] ).
cnf(i_0_2167,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_1382]),
[final] ).
cnf(i_0_2168,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_1383,c_0_844]),
[final] ).
cnf(i_0_2169,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_1384,c_0_844]),
[final] ).
cnf(i_0_2170,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_1385,c_0_844]),
[final] ).
cnf(i_0_2171,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_1386,c_0_844]),
[final] ).
cnf(i_0_2172,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_1387,c_0_844]),
[final] ).
cnf(i_0_2173,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_1388,c_0_844]),
[final] ).
cnf(i_0_2174,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_1389,c_0_844]),
[final] ).
cnf(i_0_2175,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_1390,c_0_844]),
[final] ).
cnf(i_0_2176,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_1391]),
[final] ).
cnf(i_0_2177,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_1392]),
[final] ).
cnf(i_0_2178,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_1393]),
[final] ).
cnf(i_0_2179,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_1394,c_0_844]),
[final] ).
cnf(i_0_2180,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_1395,c_0_844]),c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2181,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_1396,c_0_844]),
[final] ).
cnf(i_0_2182,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rw,[status(thm)],[i_0_1397,c_0_844]),
[final] ).
cnf(i_0_2183,plain,
hAPP(X1,X1,combi(X1),hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(rw,[status(thm)],[i_0_1398,c_0_844]),
[final] ).
cnf(i_0_2184,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_1399,c_0_844]),
[final] ).
cnf(i_0_2185,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_1400,c_0_844]),
[final] ).
cnf(i_0_2186,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_1401]),
[final] ).
cnf(i_0_2187,plain,
( hBOOL(hAPP(X1,bool,X2,esk16_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_1376]),
[final] ).
cnf(i_0_2188,plain,
( hBOOL(hAPP(X1,bool,X2,esk17_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_1377]),
[final] ).
cnf(i_0_2189,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_1402]),
[final] ).
cnf(i_0_2190,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_1403]),
[final] ).
cnf(i_0_2191,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_1404]),
[final] ).
cnf(i_0_2192,hypothesis,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ),
inference(rw,[status(thm)],[i_0_1405,c_0_844]),
[final] ).
cnf(i_0_2193,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),zero_zero(nat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_1406]),
[final] ).
cnf(i_0_2194,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X1) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_2195,plain,
( ~ hBOOL(hAPP(bool,bool,fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1408]),
[final] ).
cnf(i_0_2196,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1409]),
[final] ).
cnf(i_0_2197,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1410]),
[final] ).
cnf(i_0_2198,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_1411,c_0_844]),
[final] ).
cnf(i_0_2199,plain,
hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),bot_bot(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[i_0_1412]),
[final] ).
cnf(i_0_2200,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_1413,c_0_844]),
[final] ).
cnf(i_0_2201,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_1414,c_0_844]),
[final] ).
cnf(i_0_2202,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_1415,c_0_844]),
[final] ).
cnf(i_0_2203,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_1416,c_0_844]),
[final] ).
cnf(i_0_2204,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_1417,c_0_844]),
[final] ).
cnf(i_0_2205,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_1418,c_0_844]),
[final] ).
cnf(i_0_2206,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1419]),
[final] ).
cnf(i_0_2207,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X2))
| ~ finite_finite_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2208,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_1421,c_0_844]),
[final] ).
cnf(i_0_2209,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_1422,c_0_844]),
[final] ).
cnf(i_0_2210,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_1423,c_0_844]),
[final] ).
cnf(i_0_2211,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_1424,c_0_844]),
[final] ).
cnf(i_0_2212,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_1425,c_0_844]),
[final] ).
cnf(i_0_2213,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_1426,c_0_844]),
[final] ).
cnf(i_0_2214,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_1427,c_0_844]),
[final] ).
cnf(i_0_2215,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
inference(split_conjunct,[status(thm)],[conj_0]),
[final] ).
cnf(i_0_2216,hypothesis,
( hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[i_0_1428,c_0_844]),
[final] ).
cnf(i_0_2217,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_1429,c_0_844]),
[final] ).
cnf(i_0_2218,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_1430,c_0_844]),
[final] ).
cnf(i_0_2219,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_1431,c_0_844]),
[final] ).
cnf(i_0_2220,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_1432,c_0_844]),c_0_844]),
[final] ).
cnf(i_0_2221,plain,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2222,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2223,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2224,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_2225,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_1437]),
[final] ).
cnf(i_0_2226,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_1438]),
[final] ).
cnf(i_0_2227,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_1439]),
[final] ).
cnf(i_0_2228,plain,
hAPP(nat,nat,suc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1440]),
[final] ).
cnf(i_0_2229,plain,
X1 != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[i_0_1441]),
[final] ).
cnf(i_0_2230,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_1442,c_0_844]),
[final] ).
cnf(i_0_2231,plain,
hAPP(fun(pname,option(com)),fun(pname,option(com)),combi(fun(pname,option(com))),body) = body,
inference(rw,[status(thm)],[i_0_1443,c_0_844]),
[final] ).
cnf(i_0_2232,plain,
hAPP(fun(X1,X1),fun(X1,X1),combi(fun(X1,X1)),combi(X1)) = combi(X1),
inference(rw,[status(thm)],[i_0_1444,c_0_844]),
[final] ).
cnf(i_0_2233,hypothesis,
hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g) = g,
inference(rw,[status(thm)],[i_0_1445,c_0_844]),
[final] ).
cnf(i_0_2234,hypothesis,
hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc) = suc,
inference(rw,[status(thm)],[i_0_1446,c_0_844]),
[final] ).
cnf(i_0_2235,plain,
hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot) = fNot,
inference(rw,[status(thm)],[i_0_1447,c_0_844]),
[final] ).
cnf(i_0_2236,plain,
hAPP(fun(com,x_a),fun(com,x_a),combi(fun(com,x_a)),mgt) = mgt,
inference(rw,[status(thm)],[i_0_1448,c_0_844]),
[final] ).
cnf(i_0_2237,plain,
hAPP(fun(com,bool),fun(com,bool),combi(fun(com,bool)),wt) = wt,
inference(rw,[status(thm)],[i_0_1449,c_0_844]),
[final] ).
cnf(i_0_2238,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_1450,c_0_844]),
[final] ).
cnf(i_0_2239,hypothesis,
hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) = u,
inference(rw,[status(thm)],[i_0_1451,c_0_844]),
[final] ).
cnf(i_0_2240,plain,
hAPP(fun(X1,bool),nat,finite_card(X1),bot_bot(fun(X1,bool))) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[i_0_1452]),
[final] ).
cnf(i_0_2241,plain,
( hAPP(X2,X1,bot_bot(fun(X2,X1)),X3) = bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1453]),
[final] ).
cnf(i_0_2242,plain,
( hAPP(X2,X1,bot_bot(fun(X2,X1)),X3) = bot_bot(X1)
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1454]),
[final] ).
cnf(i_0_2243,plain,
( hAPP(X1,X1,combi(X1),bot_bot(X1)) = bot_bot(X1)
| ~ bot(X1) ),
inference(rw,[status(thm)],[i_0_1455,c_0_844]),
[final] ).
cnf(i_0_2244,plain,
( hAPP(X1,X1,combi(X1),zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(rw,[status(thm)],[i_0_1456,c_0_844]),
[final] ).
cnf(i_0_2245,plain,
( hAPP(X1,X1,combi(X1),one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(rw,[status(thm)],[i_0_1457,c_0_844]),
[final] ).
cnf(i_0_2246,plain,
hAPP(X1,X1,combi(X1),undefined(X1)) = undefined(X1),
inference(rw,[status(thm)],[i_0_1458,c_0_844]),
[final] ).
cnf(i_0_2247,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_472_One__nat__def]),
[final] ).
cnf(i_0_2248,hypothesis,
hAPP(nat,nat,combi(nat),na) = na,
inference(rw,[status(thm)],[i_0_1459,c_0_844]),
[final] ).
cnf(i_0_2249,plain,
hAPP(bool,bool,combi(bool),fTrue) = fTrue,
inference(rw,[status(thm)],[i_0_1460,c_0_844]),
[final] ).
cnf(i_0_2250,plain,
hAPP(bool,bool,combi(bool),fFalse) = fFalse,
inference(rw,[status(thm)],[i_0_1461,c_0_844]),
[final] ).
cnf(i_0_2251,hypothesis,
hAPP(pname,pname,combi(pname),pn) = pn,
inference(rw,[status(thm)],[i_0_1462,c_0_844]),
[final] ).
cnf(i_0_2252,plain,
( finite_finite_1(sum_sum(X2,X1))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1463]),
[final] ).
cnf(i_0_2253,plain,
( finite_finite_1(fun(X2,X1))
| ~ finite_finite_1(X1)
| ~ finite_finite_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1464]),
[final] ).
cnf(i_0_2254,plain,
( preorder(fun(X2,X1))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_2255,plain,
( order(fun(X2,X1))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1466]),
[final] ).
cnf(i_0_2256,plain,
( ord(fun(X2,X1))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1467]),
[final] ).
cnf(i_0_2257,plain,
( bot(fun(X2,X1))
| ~ bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_2258,plain,
( minus(fun(X2,X1))
| ~ minus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1469]),
[final] ).
cnf(i_0_2259,plain,
( ~ zero_neq_one(X1)
| zero_zero(X1) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1470]),
[final] ).
cnf(i_0_2260,plain,
( ~ zero_neq_one(X1)
| one_one(X1) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1471]),
[final] ).
cnf(i_0_2261,plain,
bot_bot(nat) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[fact_488_bot__nat__def]),
[final] ).
cnf(i_0_2262,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[i_0_1472]),
[final] ).
cnf(i_0_2263,plain,
comm_monoid_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_2264,plain,
ordere216010020id_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_2265,plain,
zero_neq_one(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_2266,plain,
linordered_semidom(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_2267,plain,
ordere223160158up_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_2268,plain,
cancel146912293up_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_2269,plain,
ordere779506340up_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_2270,plain,
ordere236663937imp_le(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_2271,plain,
linorder(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]),
[final] ).
cnf(i_0_2272,plain,
preorder(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]),
[final] ).
cnf(i_0_2273,plain,
preorder(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]),
[final] ).
cnf(i_0_2274,plain,
order(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]),
[final] ).
cnf(i_0_2275,plain,
order(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]),
[final] ).
cnf(i_0_2276,plain,
finite_finite_1(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]),
[final] ).
cnf(i_0_2277,plain,
ord(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oord]),
[final] ).
cnf(i_0_2278,plain,
ord(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oord]),
[final] ).
cnf(i_0_2279,plain,
bot(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Obot]),
[final] ).
cnf(i_0_2280,plain,
bot(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Obot]),
[final] ).
cnf(i_0_2281,plain,
zero(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ozero]),
[final] ).
cnf(i_0_2282,plain,
cancel_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_2283,plain,
ab_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_2284,plain,
monoid_add(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]),
[final] ).
cnf(i_0_2285,plain,
one(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oone]),
[final] ).
cnf(i_0_2286,plain,
minus(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ominus]),
[final] ).
cnf(i_0_2287,plain,
minus(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Groups_Ominus]),
[final] ).
cnf(i_0_2288,axiom,
X1 = X1 ).
cnf(i_0_2289,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2290,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2291,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_2292,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_2293,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_2294,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_2295,axiom,
( X1 != X2
| image(X1,X3) = image(X2,X3) ) ).
cnf(i_0_2296,axiom,
( X1 != X2
| image(X3,X1) = image(X3,X2) ) ).
cnf(i_0_2297,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_2298,axiom,
( X1 != X2
| combi(X1) = combi(X2) ) ).
cnf(i_0_2299,axiom,
( X1 != X2
| finite1357897459simple(X1,X3) = finite1357897459simple(X2,X3) ) ).
cnf(i_0_2300,axiom,
( X1 != X2
| finite1357897459simple(X3,X1) = finite1357897459simple(X3,X2) ) ).
cnf(i_0_2301,axiom,
( X1 != X2
| ord_less(X1) = ord_less(X2) ) ).
cnf(i_0_2302,axiom,
( X1 != X2
| finite_card(X1) = finite_card(X2) ) ).
cnf(i_0_2303,axiom,
( X1 != X2
| minus_minus(X1) = minus_minus(X2) ) ).
cnf(i_0_2304,axiom,
( X1 != X2
| insert(X1) = insert(X2) ) ).
cnf(i_0_2305,axiom,
( X1 != X2
| bot_bot(X1) = bot_bot(X2) ) ).
cnf(i_0_2306,axiom,
( X1 != X2
| ord_less_eq(X1) = ord_less_eq(X2) ) ).
cnf(i_0_2307,axiom,
( X1 != X2
| finite_finite(X1) = finite_finite(X2) ) ).
cnf(i_0_2308,axiom,
( X1 != X2
| the(X1) = the(X2) ) ).
cnf(i_0_2309,axiom,
( X1 != X2
| the_1(X1) = the_1(X2) ) ).
cnf(i_0_2310,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_2311,axiom,
( X1 != X2
| finite_folding_one(X1) = finite_folding_one(X2) ) ).
cnf(i_0_2312,axiom,
( X1 != X2
| finite2073411215e_idem(X1) = finite2073411215e_idem(X2) ) ).
cnf(i_0_2313,axiom,
( X1 != X2
| finite_comp_fun_idem(X1,X3) = finite_comp_fun_idem(X2,X3) ) ).
cnf(i_0_2314,axiom,
( X1 != X2
| finite_comp_fun_idem(X3,X1) = finite_comp_fun_idem(X3,X2) ) ).
cnf(i_0_2315,axiom,
( X1 != X2
| plus_plus(X1) = plus_plus(X2) ) ).
cnf(i_0_2316,axiom,
( X1 != X2
| combs(X1,X3,X4) = combs(X2,X3,X4) ) ).
cnf(i_0_2317,axiom,
( X1 != X2
| combs(X3,X1,X4) = combs(X3,X2,X4) ) ).
cnf(i_0_2318,axiom,
( X1 != X2
| combs(X3,X4,X1) = combs(X3,X4,X2) ) ).
cnf(i_0_2319,axiom,
( X1 != X2
| partial_flat_lub(X1) = partial_flat_lub(X2) ) ).
cnf(i_0_2320,axiom,
( X1 != X2
| one_one(X1) = one_one(X2) ) ).
cnf(i_0_2321,axiom,
( X1 != X2
| combb(X1,X3,X4) = combb(X2,X3,X4) ) ).
cnf(i_0_2322,axiom,
( X1 != X2
| combb(X3,X1,X4) = combb(X3,X2,X4) ) ).
cnf(i_0_2323,axiom,
( X1 != X2
| combb(X3,X4,X1) = combb(X3,X4,X2) ) ).
cnf(i_0_2324,axiom,
( X1 != X2
| combc(X1,X3,X4) = combc(X2,X3,X4) ) ).
cnf(i_0_2325,axiom,
( X1 != X2
| combc(X3,X1,X4) = combc(X3,X2,X4) ) ).
cnf(i_0_2326,axiom,
( X1 != X2
| combc(X3,X4,X1) = combc(X3,X4,X2) ) ).
cnf(i_0_2327,axiom,
( X1 != X2
| the_elem(X1) = the_elem(X2) ) ).
cnf(i_0_2328,axiom,
( X1 != X2
| zero_zero(X1) = zero_zero(X2) ) ).
cnf(i_0_2329,axiom,
( X1 != X2
| nat_case(X1) = nat_case(X2) ) ).
cnf(i_0_2330,axiom,
( X1 != X2
| sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).
cnf(i_0_2331,axiom,
( X1 != X2
| sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).
cnf(i_0_2332,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_2333,axiom,
( X1 != X2
| combk(X1,X3) = combk(X2,X3) ) ).
cnf(i_0_2334,axiom,
( X1 != X2
| combk(X3,X1) = combk(X3,X2) ) ).
cnf(i_0_2335,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_2336,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2337,axiom,
( X1 != X2
| ~ linordered_semidom(X1)
| linordered_semidom(X2) ) ).
cnf(i_0_2338,axiom,
( X1 != X2
| ~ dense_linorder(X1)
| dense_linorder(X2) ) ).
cnf(i_0_2339,axiom,
( X1 != X2
| ~ preorder(X1)
| preorder(X2) ) ).
cnf(i_0_2340,axiom,
( X1 != X2
| ~ ab_semigroup_add(X1)
| ab_semigroup_add(X2) ) ).
cnf(i_0_2341,axiom,
( X1 != X2
| ~ linorder(X1)
| linorder(X2) ) ).
cnf(i_0_2342,axiom,
( X1 != X2
| ~ minus(X1)
| minus(X2) ) ).
cnf(i_0_2343,axiom,
( X1 != X2
| ~ group_add(X1)
| group_add(X2) ) ).
cnf(i_0_2344,axiom,
( X1 != X2
| ~ ab_group_add(X1)
| ab_group_add(X2) ) ).
cnf(i_0_2345,axiom,
( X1 != X2
| ~ linordered_idom(X1)
| linordered_idom(X2) ) ).
cnf(i_0_2346,axiom,
( X1 != X2
| ~ cancel_semigroup_add(X1)
| cancel_semigroup_add(X2) ) ).
cnf(i_0_2347,axiom,
( X1 != X2
| ~ order(X1)
| order(X2) ) ).
cnf(i_0_2348,axiom,
( X1 != X2
| ~ cancel146912293up_add(X1)
| cancel146912293up_add(X2) ) ).
cnf(i_0_2349,axiom,
( X1 != X2
| ~ bot(X1)
| bot(X2) ) ).
cnf(i_0_2350,axiom,
( X1 != X2
| ~ comm_monoid_add(X1)
| comm_monoid_add(X2) ) ).
cnf(i_0_2351,axiom,
( X1 != X2
| ~ monoid_add(X1)
| monoid_add(X2) ) ).
cnf(i_0_2352,axiom,
( X1 != X2
| ~ finite_finite_1(X1)
| finite_finite_1(X2) ) ).
cnf(i_0_2353,axiom,
( X1 != X2
| ~ zero(X1)
| zero(X2) ) ).
cnf(i_0_2354,axiom,
( X1 != X2
| ~ one(X1)
| one(X2) ) ).
cnf(i_0_2355,axiom,
( X1 != X2
| ~ zero_neq_one(X1)
| zero_neq_one(X2) ) ).
cnf(i_0_2356,axiom,
( X1 != X2
| ~ ord(X1)
| ord(X2) ) ).
cnf(i_0_2357,axiom,
( X1 != X2
| ~ ordere236663937imp_le(X1)
| ordere236663937imp_le(X2) ) ).
cnf(i_0_2358,axiom,
( X1 != X2
| ~ ordere779506340up_add(X1)
| ordere779506340up_add(X2) ) ).
cnf(i_0_2359,axiom,
( X1 != X2
| ~ ordere223160158up_add(X1)
| ordere223160158up_add(X2) ) ).
cnf(i_0_2360,axiom,
( X1 != X2
| ~ linord219039673up_add(X1)
| linord219039673up_add(X2) ) ).
cnf(i_0_2361,axiom,
( X1 != X2
| ~ ordered_ab_group_add(X1)
| ordered_ab_group_add(X2) ) ).
cnf(i_0_2362,axiom,
( X1 != X2
| ~ ordere216010020id_add(X1)
| ordere216010020id_add(X2) ) ).
cnf(i_0_2288_001,axiom,
X1 = X1 ).
cnf(i_0_2289_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2290_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2291_004,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_2292_005,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_2293_006,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_2294_007,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_2295_008,axiom,
( X1 != X2
| image(X1,X3) = image(X2,X3) ) ).
cnf(i_0_2296_009,axiom,
( X1 != X2
| image(X3,X1) = image(X3,X2) ) ).
cnf(i_0_2297_010,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_2298_011,axiom,
( X1 != X2
| combi(X1) = combi(X2) ) ).
cnf(i_0_2299_012,axiom,
( X1 != X2
| finite1357897459simple(X1,X3) = finite1357897459simple(X2,X3) ) ).
cnf(i_0_2300_013,axiom,
( X1 != X2
| finite1357897459simple(X3,X1) = finite1357897459simple(X3,X2) ) ).
cnf(i_0_2301_014,axiom,
( X1 != X2
| ord_less(X1) = ord_less(X2) ) ).
cnf(i_0_2302_015,axiom,
( X1 != X2
| finite_card(X1) = finite_card(X2) ) ).
cnf(i_0_2303_016,axiom,
( X1 != X2
| minus_minus(X1) = minus_minus(X2) ) ).
cnf(i_0_2304_017,axiom,
( X1 != X2
| insert(X1) = insert(X2) ) ).
cnf(i_0_2305_018,axiom,
( X1 != X2
| bot_bot(X1) = bot_bot(X2) ) ).
cnf(i_0_2306_019,axiom,
( X1 != X2
| ord_less_eq(X1) = ord_less_eq(X2) ) ).
cnf(i_0_2307_020,axiom,
( X1 != X2
| finite_finite(X1) = finite_finite(X2) ) ).
cnf(i_0_2308_021,axiom,
( X1 != X2
| the(X1) = the(X2) ) ).
cnf(i_0_2309_022,axiom,
( X1 != X2
| the_1(X1) = the_1(X2) ) ).
cnf(i_0_2310_023,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_2311_024,axiom,
( X1 != X2
| finite_folding_one(X1) = finite_folding_one(X2) ) ).
cnf(i_0_2312_025,axiom,
( X1 != X2
| finite2073411215e_idem(X1) = finite2073411215e_idem(X2) ) ).
cnf(i_0_2313_026,axiom,
( X1 != X2
| finite_comp_fun_idem(X1,X3) = finite_comp_fun_idem(X2,X3) ) ).
cnf(i_0_2314_027,axiom,
( X1 != X2
| finite_comp_fun_idem(X3,X1) = finite_comp_fun_idem(X3,X2) ) ).
cnf(i_0_2315_028,axiom,
( X1 != X2
| plus_plus(X1) = plus_plus(X2) ) ).
cnf(i_0_2316_029,axiom,
( X1 != X2
| combs(X1,X3,X4) = combs(X2,X3,X4) ) ).
cnf(i_0_2317_030,axiom,
( X1 != X2
| combs(X3,X1,X4) = combs(X3,X2,X4) ) ).
cnf(i_0_2318_031,axiom,
( X1 != X2
| combs(X3,X4,X1) = combs(X3,X4,X2) ) ).
cnf(i_0_2319_032,axiom,
( X1 != X2
| partial_flat_lub(X1) = partial_flat_lub(X2) ) ).
cnf(i_0_2320_033,axiom,
( X1 != X2
| one_one(X1) = one_one(X2) ) ).
cnf(i_0_2321_034,axiom,
( X1 != X2
| combb(X1,X3,X4) = combb(X2,X3,X4) ) ).
cnf(i_0_2322_035,axiom,
( X1 != X2
| combb(X3,X1,X4) = combb(X3,X2,X4) ) ).
cnf(i_0_2323_036,axiom,
( X1 != X2
| combb(X3,X4,X1) = combb(X3,X4,X2) ) ).
cnf(i_0_2324_037,axiom,
( X1 != X2
| combc(X1,X3,X4) = combc(X2,X3,X4) ) ).
cnf(i_0_2325_038,axiom,
( X1 != X2
| combc(X3,X1,X4) = combc(X3,X2,X4) ) ).
cnf(i_0_2326_039,axiom,
( X1 != X2
| combc(X3,X4,X1) = combc(X3,X4,X2) ) ).
cnf(i_0_2327_040,axiom,
( X1 != X2
| the_elem(X1) = the_elem(X2) ) ).
cnf(i_0_2328_041,axiom,
( X1 != X2
| zero_zero(X1) = zero_zero(X2) ) ).
cnf(i_0_2329_042,axiom,
( X1 != X2
| nat_case(X1) = nat_case(X2) ) ).
cnf(i_0_2330_043,axiom,
( X1 != X2
| sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).
cnf(i_0_2331_044,axiom,
( X1 != X2
| sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).
cnf(i_0_2332_045,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_2333_046,axiom,
( X1 != X2
| combk(X1,X3) = combk(X2,X3) ) ).
cnf(i_0_2334_047,axiom,
( X1 != X2
| combk(X3,X1) = combk(X3,X2) ) ).
cnf(i_0_2335_048,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_2336_049,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2337_050,axiom,
( X1 != X2
| ~ linordered_semidom(X1)
| linordered_semidom(X2) ) ).
cnf(i_0_2338_051,axiom,
( X1 != X2
| ~ dense_linorder(X1)
| dense_linorder(X2) ) ).
cnf(i_0_2339_052,axiom,
( X1 != X2
| ~ preorder(X1)
| preorder(X2) ) ).
cnf(i_0_2340_053,axiom,
( X1 != X2
| ~ ab_semigroup_add(X1)
| ab_semigroup_add(X2) ) ).
cnf(i_0_2341_054,axiom,
( X1 != X2
| ~ linorder(X1)
| linorder(X2) ) ).
cnf(i_0_2342_055,axiom,
( X1 != X2
| ~ minus(X1)
| minus(X2) ) ).
cnf(i_0_2343_056,axiom,
( X1 != X2
| ~ group_add(X1)
| group_add(X2) ) ).
cnf(i_0_2344_057,axiom,
( X1 != X2
| ~ ab_group_add(X1)
| ab_group_add(X2) ) ).
cnf(i_0_2345_058,axiom,
( X1 != X2
| ~ linordered_idom(X1)
| linordered_idom(X2) ) ).
cnf(i_0_2346_059,axiom,
( X1 != X2
| ~ cancel_semigroup_add(X1)
| cancel_semigroup_add(X2) ) ).
cnf(i_0_2347_060,axiom,
( X1 != X2
| ~ order(X1)
| order(X2) ) ).
cnf(i_0_2348_061,axiom,
( X1 != X2
| ~ cancel146912293up_add(X1)
| cancel146912293up_add(X2) ) ).
cnf(i_0_2349_062,axiom,
( X1 != X2
| ~ bot(X1)
| bot(X2) ) ).
cnf(i_0_2350_063,axiom,
( X1 != X2
| ~ comm_monoid_add(X1)
| comm_monoid_add(X2) ) ).
cnf(i_0_2351_064,axiom,
( X1 != X2
| ~ monoid_add(X1)
| monoid_add(X2) ) ).
cnf(i_0_2352_065,axiom,
( X1 != X2
| ~ finite_finite_1(X1)
| finite_finite_1(X2) ) ).
cnf(i_0_2353_066,axiom,
( X1 != X2
| ~ zero(X1)
| zero(X2) ) ).
cnf(i_0_2354_067,axiom,
( X1 != X2
| ~ one(X1)
| one(X2) ) ).
cnf(i_0_2355_068,axiom,
( X1 != X2
| ~ zero_neq_one(X1)
| zero_neq_one(X2) ) ).
cnf(i_0_2356_069,axiom,
( X1 != X2
| ~ ord(X1)
| ord(X2) ) ).
cnf(i_0_2357_070,axiom,
( X1 != X2
| ~ ordere236663937imp_le(X1)
| ordere236663937imp_le(X2) ) ).
cnf(i_0_2358_071,axiom,
( X1 != X2
| ~ ordere779506340up_add(X1)
| ordere779506340up_add(X2) ) ).
cnf(i_0_2359_072,axiom,
( X1 != X2
| ~ ordere223160158up_add(X1)
| ordere223160158up_add(X2) ) ).
cnf(i_0_2360_073,axiom,
( X1 != X2
| ~ linord219039673up_add(X1)
| linord219039673up_add(X2) ) ).
cnf(i_0_2361_074,axiom,
( X1 != X2
| ~ ordered_ab_group_add(X1)
| ordered_ab_group_add(X2) ) ).
cnf(i_0_2362_075,axiom,
( X1 != X2
| ~ ordere216010020id_add(X1)
| ordere216010020id_add(X2) ) ).
cnf(i_0_2363,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,[],[1683]) ).
cnf(i_0_2364,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,[],[1684]) ).
cnf(i_0_2365,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,[],[1685]) ).
cnf(i_0_2366,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,[],[1686]) ).
cnf(i_0_2367,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,[],[1705]) ).
cnf(i_0_2368,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,[],[1766]) ).
cnf(i_0_2369,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,[],[1769]) ).
cnf(i_0_2370,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,[],[1798]) ).
cnf(i_0_2371,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,[],[1800]) ).
cnf(i_0_2372,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,[],[1874]) ).
cnf(i_0_2373,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,[],[1934]) ).
cnf(i_0_2374,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,[],[1935]) ).
cnf(i_0_2375,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,[],[1936]) ).
cnf(i_0_2376,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,[],[1937]) ).
cnf(i_0_2377,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,[],[1962]) ).
cnf(i_0_2378,plain,
hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2),
inference(equality_inference,[],[1964]) ).
cnf(i_0_2379,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(equality_inference,[],[1998]) ).
cnf(i_0_2380,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(equality_inference,[],[2002]) ).
cnf(i_0_2381,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,[],[2019]) ).
cnf(i_0_2382,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,[],[2020]) ).
cnf(i_0_2383,plain,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[2035]) ).
cnf(i_0_2384,plain,
( ~ cancel146912293up_add(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[2036]) ).
cnf(i_0_2385,plain,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
inference(equality_inference,[],[2038]) ).
cnf(i_0_2386,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,[],[2039]) ).
cnf(i_0_2387,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,[],[2053]) ).
cnf(i_0_2388,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(equality_inference,[],[2066]) ).
cnf(i_0_2389,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(equality_inference,[],[2075]) ).
cnf(i_0_2390,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(equality_inference,[],[2076]) ).
cnf(i_0_2391,plain,
X1 = X1,
inference(equality_inference,[],[2079]) ).
cnf(i_0_2392,plain,
X1 = X1,
inference(equality_inference,[],[2080]) ).
cnf(i_0_2393,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,[],[2088]) ).
cnf(i_0_2394,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,[],[2089]) ).
cnf(i_0_2395,plain,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
inference(equality_inference,[],[2092]) ).
cnf(i_0_2396,plain,
hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
inference(equality_inference,[],[2093]) ).
cnf(i_0_2397,plain,
( ~ group_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X2) = zero_zero(X1) ),
inference(equality_inference,[],[2133]) ).
cnf(i_0_2398,plain,
( ~ ab_group_add(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),X2),X2) = zero_zero(X1) ),
inference(equality_inference,[],[2134]) ).
cnf(i_0_2399,plain,
( ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
inference(equality_inference,[],[2135]) ).
cnf(i_0_2400,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(equality_inference,[],[2143]) ).
cnf(i_0_2401,plain,
X1 = X1,
inference(equality_inference,[],[2197]) ).
cnf(i_0_2402,plain,
hBOOL(hAPP(pname,bool,u,pn)),
inference(scs_inference,[],[i_0_2120,i_0_1993]) ).
cnf(i_0_2403,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_1993]) ).
cnf(i_0_2404,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_1529,i_0_2120,i_0_1993,i_0_2019]) ).
cnf(i_0_2405,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_2019]) ).
cnf(i_0_2406,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_1529,i_0_2120,i_0_1993,i_0_2019,i_0_2020]) ).
cnf(i_0_2407,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_2020]) ).
cnf(i_0_2408,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_1529,i_0_2120,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066]) ).
cnf(i_0_2409,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_1651]) ).
cnf(i_0_2410,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_2066]) ).
cnf(i_0_2411,plain,
hAPP(nat,nat,suc,X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2),
inference(scs_inference,[],[i_0_1529,i_0_1729,i_0_2120,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075]) ).
cnf(i_0_2412,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_2075]) ).
cnf(i_0_2413,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) != hAPP(nat,nat,suc,X1),
inference(scs_inference,[],[i_0_1529,i_0_1729,i_0_2120,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076]) ).
cnf(i_0_2414,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_2076]) ).
cnf(i_0_2415,plain,
zero_zero(nat) = bot_bot(nat),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_1729,i_0_2120,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289]) ).
cnf(i_0_2416,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(fun(pname,bool),fun(fun(pname,bool),bool),ord_less_eq(fun(pname,bool)),esk8_5(x_a,pname,g,mgt_call,u)),u)),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_1729,i_0_2120,i_0_1826,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552]) ).
cnf(i_0_2417,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)),esk8_5(X1,X3,X2,X4,X5)),X5)) ),
inference(rename_variables,[],[i_0_1552]) ).
cnf(i_0_2418,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2120,i_0_1826,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601]) ).
cnf(i_0_2419,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(rename_variables,[],[i_0_2070]) ).
cnf(i_0_2420,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_1601]) ).
cnf(i_0_2421,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2120,i_0_1826,i_0_1921,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614]) ).
cnf(i_0_2422,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_1921]) ).
cnf(i_0_2423,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_1614]) ).
cnf(i_0_2424,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2120,i_0_1826,i_0_1921,i_0_2422,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615]) ).
cnf(i_0_2425,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_1921]) ).
cnf(i_0_2426,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_1615]) ).
cnf(i_0_2427,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2120,i_0_1826,i_0_2098,i_0_1921,i_0_2422,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675]) ).
cnf(i_0_2428,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_2098]) ).
cnf(i_0_2429,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_1675]) ).
cnf(i_0_2430,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2078,i_0_2120,i_0_1826,i_0_2098,i_0_1921,i_0_2422,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697]) ).
cnf(i_0_2431,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(rename_variables,[],[i_0_2078]) ).
cnf(i_0_2432,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_1697]) ).
cnf(i_0_2433,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2138,i_0_2078,i_0_2120,i_0_1826,i_0_2098,i_0_1921,i_0_2422,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737]) ).
cnf(i_0_2434,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_1737]) ).
cnf(i_0_2435,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2120,i_0_1826,i_0_2098,i_0_1921,i_0_2422,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742]) ).
cnf(i_0_2436,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_1742]) ).
cnf(i_0_2437,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_1529,i_0_2261,i_0_1729,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2120,i_0_1826,i_0_2098,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758]) ).
cnf(i_0_2438,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_1921]) ).
cnf(i_0_2439,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_1758]) ).
cnf(i_0_2440,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_1529,i_0_2261,i_0_2067,i_0_1729,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2120,i_0_1826,i_0_2098,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784]) ).
cnf(i_0_2441,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(rename_variables,[],[i_0_2067]) ).
cnf(i_0_2442,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_1784]) ).
cnf(i_0_2443,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_1529,i_0_2261,i_0_2067,i_0_1729,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785]) ).
cnf(i_0_2444,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(rename_variables,[],[i_0_2144]) ).
cnf(i_0_2445,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_1785]) ).
cnf(i_0_2446,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),hAPP(nat,nat,suc,X1)),X2))),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_1729,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788]) ).
cnf(i_0_2447,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(rename_variables,[],[i_0_1920]) ).
cnf(i_0_2448,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_1788]) ).
cnf(i_0_2449,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_1729,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789]) ).
cnf(i_0_2450,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(rename_variables,[],[i_0_2067]) ).
cnf(i_0_2451,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_1789]) ).
cnf(i_0_2452,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_1729,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793]) ).
cnf(i_0_2453,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_1793]) ).
cnf(i_0_2454,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795]) ).
cnf(i_0_2455,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_1795]) ).
cnf(i_0_2456,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821]) ).
cnf(i_0_2457,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_1821]) ).
cnf(i_0_2458,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823]) ).
cnf(i_0_2459,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_1823]) ).
cnf(i_0_2460,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840]) ).
cnf(i_0_2461,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_1840]) ).
cnf(i_0_2462,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853]) ).
cnf(i_0_2463,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
inference(rename_variables,[],[i_0_2067]) ).
cnf(i_0_2464,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_1853]) ).
cnf(i_0_2465,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,esk5_2(X1,hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854]) ).
cnf(i_0_2466,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(rename_variables,[],[i_0_2144]) ).
cnf(i_0_2467,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_1854]) ).
cnf(i_0_2468,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),X1),X2)))),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898]) ).
cnf(i_0_2469,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_1898]) ).
cnf(i_0_2470,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,na)),hAPP(nat,nat,suc,hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))))),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900]) ).
cnf(i_0_2471,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_1900]) ).
cnf(i_0_2472,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902]) ).
cnf(i_0_2473,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_1902]) ).
cnf(i_0_2474,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915]) ).
cnf(i_0_2475,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_1915]) ).
cnf(i_0_2476,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916]) ).
cnf(i_0_2477,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_1916]) ).
cnf(i_0_2478,plain,
X1 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936]) ).
cnf(i_0_2479,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_1936]) ).
cnf(i_0_2480,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk51_2(X1,hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941]) ).
cnf(i_0_2481,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_1941]) ).
cnf(i_0_2482,plain,
hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk47_2(X1,hAPP(nat,nat,suc,X1)))),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942]) ).
cnf(i_0_2483,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_1942]) ).
cnf(i_0_2484,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946]) ).
cnf(i_0_2485,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_1946]) ).
cnf(i_0_2486,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961]) ).
cnf(i_0_2487,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_1961]) ).
cnf(i_0_2488,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965]) ).
cnf(i_0_2489,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_1965]) ).
cnf(i_0_2490,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970]) ).
cnf(i_0_2491,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_2107]) ).
cnf(i_0_2492,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_1970]) ).
cnf(i_0_2493,plain,
hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) != bot_bot(fun(pname,bool)),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992]) ).
cnf(i_0_2494,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_1992]) ).
cnf(i_0_2495,plain,
X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),esk44_2(zero_zero(nat),X1)),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003]) ).
cnf(i_0_2496,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),esk44_2(X1,X2)) ),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2497,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)) = zero_zero(nat),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005]) ).
cnf(i_0_2498,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_2005]) ).
cnf(i_0_2499,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028]) ).
cnf(i_0_2500,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_2028]) ).
cnf(i_0_2501,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039]) ).
cnf(i_0_2502,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_2039]) ).
cnf(i_0_2503,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_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050]) ).
cnf(i_0_2504,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_2050]) ).
cnf(i_0_2505,plain,
X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053]) ).
cnf(i_0_2506,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_2053]) ).
cnf(i_0_2507,plain,
~ hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X2)),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060]) ).
cnf(i_0_2508,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_2060]) ).
cnf(i_0_2509,plain,
hAPP(nat,nat,combi(nat),X1) = X1,
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080]) ).
cnf(i_0_2510,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rename_variables,[],[i_0_2182]) ).
cnf(i_0_2511,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_2080]) ).
cnf(i_0_2512,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_1529,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102]) ).
cnf(i_0_2513,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_2102]) ).
cnf(i_0_2514,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),esk27_2(pname,u)),esk28_2(pname,u)),
inference(scs_inference,[],[i_0_1529,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117]) ).
cnf(i_0_2515,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),esk27_2(X1,X2)),esk28_2(X1,X2)) ),
inference(rename_variables,[],[i_0_2117]) ).
cnf(i_0_2516,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)) != bot_bot(fun(X1,bool)),
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161]) ).
cnf(i_0_2517,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_2161]) ).
cnf(i_0_2518,plain,
bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)),
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162]) ).
cnf(i_0_2519,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_2162]) ).
cnf(i_0_2520,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_1529,i_0_2396,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187]) ).
cnf(i_0_2521,plain,
( hBOOL(hAPP(X1,bool,X2,esk16_2(X1,X2)))
| hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = bot_bot(fun(X1,bool)) ),
inference(rename_variables,[],[i_0_2187]) ).
cnf(i_0_2522,plain,
hAPP(nat,nat,suc,X1) = esk60_2(X1,hAPP(nat,nat,suc,hAPP(nat,nat,suc,X1))),
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197]) ).
cnf(i_0_2523,plain,
( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_2197]) ).
cnf(i_0_2524,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),zero_zero(nat))),zero_zero(nat)),
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374]) ).
cnf(i_0_2525,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_2374]) ).
cnf(i_0_2526,plain,
hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,X1,X2))) != X1,
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293]) ).
cnf(i_0_2527,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_1529,i_0_2396,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294]) ).
cnf(i_0_2528,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_1529,i_0_2396,i_0_2270,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564]) ).
cnf(i_0_2529,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_1564]) ).
cnf(i_0_2530,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_1529,i_0_2396,i_0_2270,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564,i_0_1588]) ).
cnf(i_0_2531,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_1588]) ).
cnf(i_0_2532,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X1)),
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2270,i_0_2272,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564,i_0_1588,i_0_1949]) ).
cnf(i_0_2533,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_1949]) ).
cnf(i_0_2534,plain,
hAPP(nat,nat,combi(nat),hAPP(nat,nat,suc,X1)) != hAPP(nat,nat,combi(nat),X1),
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2270,i_0_2272,i_0_2274,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564,i_0_1588,i_0_1949,i_0_2092]) ).
cnf(i_0_2535,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_2092]) ).
cnf(i_0_2536,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_1529,i_0_2396,i_0_2270,i_0_2272,i_0_2274,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564,i_0_1588,i_0_1949,i_0_2092,i_0_2135]) ).
cnf(i_0_2537,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_2135]) ).
cnf(i_0_2538,plain,
hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2) != 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_1529,i_0_2396,i_0_2270,i_0_2272,i_0_2274,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564,i_0_1588,i_0_1949,i_0_2092,i_0_2135,i_0_2336]) ).
cnf(i_0_2539,plain,
ordere216010020id_add(hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),esk44_2(zero_zero(nat),nat))),
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2264,i_0_2270,i_0_2272,i_0_2274,i_0_2261,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564,i_0_1588,i_0_1949,i_0_2092,i_0_2135,i_0_2336,i_0_2362]) ).
cnf(i_0_2540,plain,
$false,
inference(scs_inference,[],[i_0_1529,i_0_2396,i_0_2264,i_0_2270,i_0_2272,i_0_2274,i_0_2261,i_0_2183,i_0_2182,i_0_2067,i_0_2441,i_0_2450,i_0_2463,i_0_1729,i_0_2064,i_0_2070,i_0_2419,i_0_2042,i_0_2138,i_0_2078,i_0_2431,i_0_2144,i_0_2444,i_0_1872,i_0_2120,i_0_1826,i_0_2107,i_0_2098,i_0_1920,i_0_2447,i_0_1921,i_0_2422,i_0_2425,i_0_2438,i_0_1651,i_0_1641,i_0_1993,i_0_2019,i_0_2020,i_0_2066,i_0_2075,i_0_2076,i_0_2289,i_0_1552,i_0_1601,i_0_1614,i_0_1615,i_0_1675,i_0_1697,i_0_1737,i_0_1742,i_0_1758,i_0_1784,i_0_1785,i_0_1788,i_0_1789,i_0_1793,i_0_1795,i_0_1821,i_0_1823,i_0_1840,i_0_1853,i_0_1854,i_0_1898,i_0_1900,i_0_1902,i_0_1915,i_0_1916,i_0_1936,i_0_1941,i_0_1942,i_0_1946,i_0_1961,i_0_1965,i_0_1970,i_0_1992,i_0_2003,i_0_2005,i_0_2028,i_0_2039,i_0_2050,i_0_2053,i_0_2060,i_0_2080,i_0_2102,i_0_2117,i_0_2161,i_0_2162,i_0_2187,i_0_2197,i_0_2374,i_0_2293,i_0_2294,i_0_1564,i_0_1588,i_0_1949,i_0_2092,i_0_2135,i_0_2336,i_0_2362,i_0_1705]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+6 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 06:55:36 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.72/5.79 % Version : CSE_E---1.7
% 0.72/5.79 % Problem : theBenchmark.p
% 0.72/5.79 % SZS status Theorem for theBenchmark.p
% 0.72/5.79 % SZS output start CNFRefutation
% See solution above
% 8.09/6.95 % Total time : 5.444s
%------------------------------------------------------------------------------