TSTP Solution File: SWW470+5 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW470+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 : Mon Jun 24 18:17:17 EDT 2024
% Result : Theorem 24.60s 4.17s
% Output : CNFRefutation 24.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 29
% Syntax : Number of formulae : 227 ( 106 unt; 0 def)
% Number of atoms : 422 ( 182 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 307 ( 112 ~; 139 |; 33 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 12 con; 0-7 aty)
% Number of variables : 431 ( 10 sgn 237 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0] :
( bot(X0)
=> bot_bot(X0) = ti(X0,bot_bot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
fof(f25,axiom,
fTrue = ti(bool,fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
fof(f31,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,X3,X4) = hAPP(X2,X1,X3,ti(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(f32,axiom,
! [X1,X2,X3,X4] : hAPP(X2,X1,X3,X4) = ti(X1,hAPP(X2,X1,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(f33,axiom,
! [X3] :
( hBOOL(ti(bool,X3))
<=> hBOOL(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(f51,axiom,
! [X0,X25] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X25)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X25),bot_bot(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
fof(f57,axiom,
! [X0,X15] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15)
<=> ! [X30] : ~ hBOOL(hAPP(X0,bool,X15,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Collect__empty__eq) ).
fof(f58,axiom,
! [X0,X16] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X16),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__iff) ).
fof(f62,axiom,
! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_empty__def) ).
fof(f80,axiom,
! [X0,X31] : ti(X0,X31) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X31),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_the__elem__eq) ).
fof(f83,axiom,
! [X0,X1] :
( bot(X1)
=> ! [X30] : hAPP(X0,X1,bot_bot(fun(X0,X1)),X30) = bot_bot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_bot__fun__def) ).
fof(f93,axiom,
! [X0,X31] : ti(X0,X31) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X31)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_the__sym__eq__trivial) ).
fof(f101,axiom,
! [X0,X17,X5,X16,X15] :
( ! [X19,X20] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X15,X19),X20))
=> ? [X48,X49] :
( ! [X23] :
( ! [X24] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X48,X24),X20))
=> hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X49,X24),X23)) )
=> hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X17,X19),X23)) )
& hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X5),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X48),X16),X49)),bot_bot(fun(hoare_509422987triple(X0),bool))))) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X5),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X15),X16),X17)),bot_bot(fun(hoare_509422987triple(X0),bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_conseq) ).
fof(f105,axiom,
! [X0,X30] :
( hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X30))
<=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X30),bot_bot(fun(X0,bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_bot__empty__eq) ).
fof(f112,axiom,
! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_finite_OemptyI) ).
fof(f116,axiom,
! [X0,X15] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15) = ti(fun(X0,bool),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
fof(f131,axiom,
! [X0,X25] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X25))
<=> ( ? [X55,X54] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X55))
& hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X54),X55) = ti(fun(X0,bool),X25) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite_Osimps) ).
fof(f142,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
fof(f144,axiom,
! [X64] :
( ~ hBOOL(X64)
| ~ hBOOL(hAPP(bool,bool,fNot,X64)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(f145,axiom,
! [X64] :
( hBOOL(hAPP(bool,bool,fNot,X64))
| hBOOL(X64) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(f148,axiom,
! [X0,X2,X64,X65] : hAPP(X0,X2,hAPP(X2,fun(X0,X2),combk(X2,X0),X64),X65) = ti(X2,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(f151,axiom,
! [X64,X65] :
( hBOOL(X64)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X64),X65)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(f156,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f157,axiom,
! [X64] :
( fFalse = ti(bool,X64)
| fTrue = ti(bool,X64) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(f163,conjecture,
hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f164,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(negated_conjecture,[],[f163]) ).
fof(f173,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(rectify,[],[f31]) ).
fof(f174,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(rectify,[],[f32]) ).
fof(f175,plain,
! [X0] :
( hBOOL(ti(bool,X0))
<=> hBOOL(X0) ),
inference(rectify,[],[f33]) ).
fof(f188,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))),
inference(rectify,[],[f51]) ).
fof(f194,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
<=> ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(rectify,[],[f57]) ).
fof(f195,plain,
! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f58]) ).
fof(f216,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f80]) ).
fof(f219,plain,
! [X0,X1] :
( bot(X1)
=> ! [X2] : bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2) ),
inference(rectify,[],[f83]) ).
fof(f229,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(rectify,[],[f93]) ).
fof(f237,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6))
=> ? [X7,X8] :
( ! [X9] :
( ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),X6))
=> hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),X9)) )
=> hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,X5),X9)) )
& hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(X0),bool))))) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool))))) ),
inference(rectify,[],[f101]) ).
fof(f241,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1))
<=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) ),
inference(rectify,[],[f105]) ).
fof(f251,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(rectify,[],[f116]) ).
fof(f266,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
<=> ( ? [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X2))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ) ),
inference(rectify,[],[f131]) ).
fof(f277,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(rectify,[],[f144]) ).
fof(f278,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f145]) ).
fof(f281,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = ti(X1,X2),
inference(rectify,[],[f148]) ).
fof(f284,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(rectify,[],[f151]) ).
fof(f289,plain,
! [X0] :
( fFalse = ti(bool,X0)
| fTrue = ti(bool,X0) ),
inference(rectify,[],[f157]) ).
fof(f295,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(flattening,[],[f164]) ).
fof(f296,plain,
! [X0] :
( bot_bot(X0) = ti(X0,bot_bot(X0))
| ~ bot(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f322,plain,
! [X0,X1] :
( ! [X2] : bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2)
| ~ bot(X1) ),
inference(ennf_transformation,[],[f219]) ).
fof(f337,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| ? [X5,X6] :
( ! [X7,X8] :
( ? [X9] :
( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,X5),X9))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),X9))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),X6)) ) )
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(X0),bool))))) )
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6)) ) ),
inference(ennf_transformation,[],[f237]) ).
fof(f376,plain,
! [X0] :
( ( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) )
& ( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ) ),
inference(nnf_transformation,[],[f175]) ).
fof(f388,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(nnf_transformation,[],[f194]) ).
fof(f389,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(rectify,[],[f388]) ).
fof(f390,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X0,bool,X1,X2))
=> hBOOL(hAPP(X0,bool,X1,sK10(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f391,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK10(X0,X1))) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f389,f390]) ).
fof(f430,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5,X6] :
( ! [X7,X8] :
( ? [X9] :
( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,X5),X9))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),X9))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),X6)) ) )
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(X0),bool))))) )
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6)) )
=> ( ! [X8,X7] :
( ? [X9] :
( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,sK24(X0,X1,X2,X3,X4)),X9))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),X9))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),sK25(X0,X1,X2,X3,X4))) ) )
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(X0),bool))))) )
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK24(X0,X1,X2,X3,X4)),sK25(X0,X1,X2,X3,X4))) ) ),
introduced(choice_axiom,[]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X7,X8] :
( ? [X9] :
( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,sK24(X0,X1,X2,X3,X4)),X9))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),X9))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),sK25(X0,X1,X2,X3,X4))) ) )
=> ( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,sK24(X0,X1,X2,X3,X4)),sK26(X0,X1,X2,X3,X4,X7,X8)))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),sK26(X0,X1,X2,X3,X4,X7,X8)))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),sK25(X0,X1,X2,X3,X4))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f432,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| ( ! [X7,X8] :
( ( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,sK24(X0,X1,X2,X3,X4)),sK26(X0,X1,X2,X3,X4,X7,X8)))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),sK26(X0,X1,X2,X3,X4,X7,X8)))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),sK25(X0,X1,X2,X3,X4))) ) )
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(X0),bool))))) )
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK24(X0,X1,X2,X3,X4)),sK25(X0,X1,X2,X3,X4))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f337,f431,f430]) ).
fof(f438,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f453,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ? [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X2))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ) ),
inference(nnf_transformation,[],[f266]) ).
fof(f454,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ? [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X2))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ) ),
inference(flattening,[],[f453]) ).
fof(f455,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ? [X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X4))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X4) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ) ),
inference(rectify,[],[f454]) ).
fof(f456,plain,
! [X0,X1] :
( ? [X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X4))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X4) )
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),sK37(X0,X1)))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK38(X0,X1)),sK37(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f457,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),sK37(X0,X1)))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK38(X0,X1)),sK37(X0,X1)) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f455,f456]) ).
fof(f492,plain,
! [X0] :
( bot_bot(X0) = ti(X0,bot_bot(X0))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f498,plain,
fTrue = ti(bool,fTrue),
inference(cnf_transformation,[],[f25]) ).
fof(f504,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(cnf_transformation,[],[f173]) ).
fof(f505,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f174]) ).
fof(f506,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ),
inference(cnf_transformation,[],[f376]) ).
fof(f507,plain,
! [X0] :
( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f535,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))),
inference(cnf_transformation,[],[f188]) ).
fof(f544,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK10(X0,X1))) ),
inference(cnf_transformation,[],[f391]) ).
fof(f545,plain,
! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f195]) ).
fof(f552,plain,
! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse)),
inference(cnf_transformation,[],[f62]) ).
fof(f581,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f216]) ).
fof(f584,plain,
! [X2,X0,X1] :
( bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2)
| ~ bot(X1) ),
inference(cnf_transformation,[],[f322]) ).
fof(f598,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(cnf_transformation,[],[f229]) ).
fof(f611,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK24(X0,X1,X2,X3,X4)),sK25(X0,X1,X2,X3,X4))) ),
inference(cnf_transformation,[],[f432]) ).
fof(f620,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)) ),
inference(cnf_transformation,[],[f438]) ).
fof(f629,plain,
! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f112]) ).
fof(f634,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(cnf_transformation,[],[f251]) ).
fof(f659,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ),
inference(cnf_transformation,[],[f457]) ).
fof(f690,plain,
bot(bool),
inference(cnf_transformation,[],[f142]) ).
fof(f692,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(cnf_transformation,[],[f277]) ).
fof(f693,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f696,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = ti(X1,X2),
inference(cnf_transformation,[],[f281]) ).
fof(f699,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(cnf_transformation,[],[f284]) ).
fof(f704,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f156]) ).
fof(f705,plain,
! [X0] :
( fFalse = ti(bool,X0)
| fTrue = ti(bool,X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f711,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(cnf_transformation,[],[f295]) ).
fof(f730,plain,
! [X0] :
( bot_bot(X0) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),bot_bot(X0)),bot_bot(fun(X0,bool))))
| ~ bot(X0) ),
inference(definition_unfolding,[],[f492,f581]) ).
fof(f736,plain,
fTrue = hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),fTrue),bot_bot(fun(bool,bool)))),
inference(definition_unfolding,[],[f498,f581]) ).
fof(f742,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))),
inference(definition_unfolding,[],[f504,f581]) ).
fof(f743,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(X1,X0,X2,X3)),bot_bot(fun(X0,bool)))),
inference(definition_unfolding,[],[f505,f581]) ).
fof(f744,plain,
! [X0] :
( hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))))
| ~ hBOOL(X0) ),
inference(definition_unfolding,[],[f507,f581]) ).
fof(f745,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool))))) ),
inference(definition_unfolding,[],[f506,f581]) ).
fof(f777,plain,
! [X0,X1] : hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(definition_unfolding,[],[f598,f581]) ).
fof(f797,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(fun(X0,bool),bool),fun(X0,bool),the_elem(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),hAPP(fun(X0,bool),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),insert(fun(X0,bool)),X1),bot_bot(fun(fun(X0,bool),bool)))),
inference(definition_unfolding,[],[f634,f581]) ).
fof(f804,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| bot_bot(fun(X0,bool)) != hAPP(fun(fun(X0,bool),bool),fun(X0,bool),the_elem(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),hAPP(fun(X0,bool),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),insert(fun(X0,bool)),X1),bot_bot(fun(fun(X0,bool),bool)))) ),
inference(definition_unfolding,[],[f659,f581]) ).
fof(f828,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = 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)))),
inference(definition_unfolding,[],[f696,f581]) ).
fof(f829,plain,
! [X0] :
( fFalse = hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool))))
| fTrue = hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))) ),
inference(definition_unfolding,[],[f705,f581,f581]) ).
cnf(c_67,plain,
( ~ bot(X0)
| hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),bot_bot(X0)),bot_bot(fun(X0,bool)))) = bot_bot(X0) ),
inference(cnf_transformation,[],[f730]) ).
cnf(c_73,plain,
hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),fTrue),bot_bot(fun(bool,bool)))) = fTrue,
inference(cnf_transformation,[],[f736]) ).
cnf(c_79,plain,
hAPP(X0,X1,X2,hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))) = hAPP(X0,X1,X2,X3),
inference(cnf_transformation,[],[f742]) ).
cnf(c_80,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(X1,X0,X2,X3)),bot_bot(fun(X0,bool)))) = hAPP(X1,X0,X2,X3),
inference(cnf_transformation,[],[f743]) ).
cnf(c_81,plain,
( ~ hBOOL(X0)
| hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool))))) ),
inference(cnf_transformation,[],[f744]) ).
cnf(c_82,plain,
( ~ hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f745]) ).
cnf(c_109,plain,
hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(cnf_transformation,[],[f535]) ).
cnf(c_117,plain,
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = bot_bot(fun(X0,bool))
| hBOOL(hAPP(X0,bool,X1,sK10(X0,X1))) ),
inference(cnf_transformation,[],[f544]) ).
cnf(c_119,plain,
~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f545]) ).
cnf(c_126,plain,
hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse)) = bot_bot(fun(X0,bool)),
inference(cnf_transformation,[],[f552]) ).
cnf(c_157,plain,
( ~ bot(X0)
| hAPP(X1,X0,bot_bot(fun(X1,X0)),X2) = bot_bot(X0) ),
inference(cnf_transformation,[],[f584]) ).
cnf(c_170,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(cnf_transformation,[],[f777]) ).
cnf(c_185,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X2),X3),X4)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X2,sK24(X0,X4,X1,X3,X2)),sK25(X0,X4,X1,X3,X2))) ),
inference(cnf_transformation,[],[f611]) ).
cnf(c_193,plain,
( ~ hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) ),
inference(cnf_transformation,[],[f620]) ).
cnf(c_201,plain,
hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f629]) ).
cnf(c_206,plain,
hAPP(fun(fun(X0,bool),bool),fun(X0,bool),the_elem(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),hAPP(fun(X0,bool),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),insert(fun(X0,bool)),X1),bot_bot(fun(fun(X0,bool),bool)))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1),
inference(cnf_transformation,[],[f797]) ).
cnf(c_230,plain,
( hAPP(fun(fun(X0,bool),bool),fun(X0,bool),the_elem(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),hAPP(fun(X0,bool),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),insert(fun(X0,bool)),X1),bot_bot(fun(fun(X0,bool),bool)))) != bot_bot(fun(X0,bool))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ),
inference(cnf_transformation,[],[f804]) ).
cnf(c_262,plain,
bot(bool),
inference(cnf_transformation,[],[f690]) ).
cnf(c_264,plain,
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f692]) ).
cnf(c_265,plain,
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f693]) ).
cnf(c_268,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = hAPP(X2,X0,hAPP(X0,fun(X2,X0),combk(X0,X2),X1),X3),
inference(cnf_transformation,[],[f828]) ).
cnf(c_271,plain,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f699]) ).
cnf(c_276,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f704]) ).
cnf(c_277,plain,
( hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))) = fFalse
| hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))) = fTrue ),
inference(cnf_transformation,[],[f829]) ).
cnf(c_283,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(cnf_transformation,[],[f711]) ).
cnf(c_460,plain,
~ hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)),
inference(global_subsumption_just,[status(thm)],[c_193,c_119,c_193]) ).
cnf(c_465,plain,
( hBOOL(X0)
| ~ hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool))))) ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
cnf(c_466,plain,
( ~ hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))))
| hBOOL(X0) ),
inference(renaming,[status(thm)],[c_465]) ).
cnf(c_467,plain,
( ~ hBOOL(X0)
| hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool))))) ),
inference(prop_impl_just,[status(thm)],[c_81]) ).
cnf(c_481,plain,
( ~ bot(X0)
| hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),bot_bot(X0)),bot_bot(fun(X0,bool)))) = bot_bot(X0) ),
inference(prop_impl_just,[status(thm)],[c_67]) ).
cnf(c_509,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X2),X3),X4)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X2,sK24(X0,X4,X1,X3,X2)),sK25(X0,X4,X1,X3,X2))) ),
inference(prop_impl_just,[status(thm)],[c_185]) ).
cnf(c_543,plain,
( hAPP(fun(fun(X0,bool),bool),fun(X0,bool),the_elem(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),hAPP(fun(X0,bool),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),insert(fun(X0,bool)),X1),bot_bot(fun(fun(X0,bool),bool)))) != bot_bot(fun(X0,bool))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ),
inference(prop_impl_just,[status(thm)],[c_230]) ).
cnf(c_699,plain,
( hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))) = fFalse
| hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),X0),bot_bot(fun(bool,bool)))) = fTrue ),
inference(prop_impl_just,[status(thm)],[c_277]) ).
cnf(c_2171,plain,
( ~ bot(X0)
| hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),bot_bot(X0)))) = bot_bot(X0) ),
inference(demodulation,[status(thm)],[c_481,c_109]) ).
cnf(c_2172,plain,
hAPP(X0,X1,X2,hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X3)))) = hAPP(X0,X1,X2,X3),
inference(demodulation,[status(thm)],[c_79,c_109]) ).
cnf(c_2173,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),hAPP(X1,X0,X2,X3)))) = hAPP(X1,X0,X2,X3),
inference(demodulation,[status(thm)],[c_80,c_109]) ).
cnf(c_2174,plain,
( ~ hBOOL(X0)
| hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),collect(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)))) ),
inference(demodulation,[status(thm)],[c_467,c_109]) ).
cnf(c_2175,plain,
( ~ hBOOL(hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),collect(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0))))
| hBOOL(X0) ),
inference(demodulation,[status(thm)],[c_466,c_109]) ).
cnf(c_2177,plain,
hAPP(fun(bool,bool),bool,the_elem(bool),hAPP(fun(bool,bool),fun(bool,bool),collect(bool),hAPP(bool,fun(bool,bool),fequal(bool),fTrue))) = fTrue,
inference(demodulation,[status(thm)],[c_73,c_109]) ).
cnf(c_2192,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))) = hAPP(X2,X0,hAPP(X0,fun(X2,X0),combk(X0,X2),X1),X3),
inference(light_normalisation,[status(thm)],[c_268,c_109]) ).
cnf(c_2193,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(light_normalisation,[status(thm)],[c_170,c_109]) ).
cnf(c_2195,plain,
( ~ bot(X0)
| hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),bot_bot(X0))) = bot_bot(X0) ),
inference(demodulation,[status(thm)],[c_2171,c_2193]) ).
cnf(c_2196,plain,
hAPP(X0,X1,X2,hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X3))) = hAPP(X0,X1,X2,X3),
inference(demodulation,[status(thm)],[c_2172,c_2193]) ).
cnf(c_2197,plain,
hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),hAPP(X1,X0,X2,X3))) = hAPP(X1,X0,X2,X3),
inference(demodulation,[status(thm)],[c_2173,c_2193]) ).
cnf(c_2198,plain,
( ~ hBOOL(X0)
| hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0))) ),
inference(demodulation,[status(thm)],[c_2174,c_2193]) ).
cnf(c_2199,plain,
( ~ hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)))
| hBOOL(X0) ),
inference(demodulation,[status(thm)],[c_2175,c_2193]) ).
cnf(c_2201,plain,
hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),fTrue)) = fTrue,
inference(demodulation,[status(thm)],[c_2177,c_2193]) ).
cnf(c_2289,plain,
hAPP(fun(fun(X0,bool),bool),fun(X0,bool),the(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1),
inference(demodulation,[status(thm)],[c_206,c_109,c_2193]) ).
cnf(c_2320,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fFalse
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fTrue ),
inference(demodulation,[status(thm)],[c_699,c_109,c_2193]) ).
cnf(c_2327,plain,
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != bot_bot(fun(X0,bool))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ),
inference(demodulation,[status(thm)],[c_543,c_109,c_2193,c_2289]) ).
cnf(c_2638,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),collect(hoare_509422987triple(X0)),hAPP(hoare_509422987triple(X0),fun(hoare_509422987triple(X0),bool),fequal(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X2),X3),X4)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X2,sK24(X0,X4,X1,X3,X2)),sK25(X0,X4,X1,X3,X2))) ),
inference(demodulation,[status(thm)],[c_509,c_109]) ).
cnf(c_3201,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))),
inference(demodulation,[status(thm)],[c_283,c_109]) ).
cnf(c_3786,plain,
( hBOOL(X0)
| ~ hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0))) ),
inference(prop_impl_just,[status(thm)],[c_2199]) ).
cnf(c_3787,plain,
( ~ hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)))
| hBOOL(X0) ),
inference(renaming,[status(thm)],[c_3786]) ).
cnf(c_3788,plain,
( ~ hBOOL(X0)
| hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0))) ),
inference(prop_impl_just,[status(thm)],[c_2198]) ).
cnf(c_3794,plain,
( ~ bot(X0)
| hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),bot_bot(X0))) = bot_bot(X0) ),
inference(prop_impl_just,[status(thm)],[c_2195]) ).
cnf(c_3850,plain,
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != bot_bot(fun(X0,bool))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ),
inference(prop_impl_just,[status(thm)],[c_2327]) ).
cnf(c_4024,plain,
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X2,sK24(X0,X4,X1,X3,X2)),sK25(X0,X4,X1,X3,X2)))
| hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),collect(hoare_509422987triple(X0)),hAPP(hoare_509422987triple(X0),fun(hoare_509422987triple(X0),bool),fequal(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X2),X3),X4))))) ),
inference(prop_impl_just,[status(thm)],[c_2638]) ).
cnf(c_4025,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),collect(hoare_509422987triple(X0)),hAPP(hoare_509422987triple(X0),fun(hoare_509422987triple(X0),bool),fequal(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X2),X3),X4)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X2,sK24(X0,X4,X1,X3,X2)),sK25(X0,X4,X1,X3,X2))) ),
inference(renaming,[status(thm)],[c_4024]) ).
cnf(c_4040,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fFalse
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fTrue ),
inference(prop_impl_just,[status(thm)],[c_2320]) ).
cnf(c_9972,plain,
hAPP(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool),
inference(superposition,[status(thm)],[c_262,c_157]) ).
cnf(c_9975,plain,
~ hBOOL(bot_bot(bool)),
inference(demodulation,[status(thm)],[c_460,c_9972]) ).
cnf(c_10058,plain,
hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),bot_bot(bool))) = bot_bot(bool),
inference(superposition,[status(thm)],[c_262,c_3794]) ).
cnf(c_10080,plain,
( hAPP(fun(bool,bool),fun(bool,bool),collect(bool),hAPP(bool,fun(bool,bool),fconj,X0)) = bot_bot(fun(bool,bool))
| hBOOL(X0) ),
inference(superposition,[status(thm)],[c_117,c_271]) ).
cnf(c_10203,plain,
hAPP(fun(bool,bool),fun(bool,bool),collect(bool),hAPP(bool,fun(bool,bool),fconj,fFalse)) = bot_bot(fun(bool,bool)),
inference(superposition,[status(thm)],[c_10080,c_276]) ).
cnf(c_10207,plain,
hAPP(fun(bool,bool),fun(bool,bool),collect(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = bot_bot(fun(bool,bool)),
inference(superposition,[status(thm)],[c_10080,c_3201]) ).
cnf(c_10438,plain,
hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))))),
inference(superposition,[status(thm)],[c_10207,c_3850]) ).
cnf(c_11142,plain,
( ~ hBOOL(X0)
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fFalse
| hBOOL(fTrue) ),
inference(superposition,[status(thm)],[c_4040,c_3788]) ).
cnf(c_11143,plain,
( ~ hBOOL(fTrue)
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fFalse
| hBOOL(X0) ),
inference(superposition,[status(thm)],[c_4040,c_3787]) ).
cnf(c_11145,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),bot_bot(bool))) = fFalse
| bot_bot(bool) = fTrue ),
inference(superposition,[status(thm)],[c_4040,c_10058]) ).
cnf(c_11152,plain,
( bot_bot(bool) = fFalse
| bot_bot(bool) = fTrue ),
inference(light_normalisation,[status(thm)],[c_11145,c_10058]) ).
cnf(c_11192,plain,
( ~ hBOOL(fTrue)
| bot_bot(bool) = fFalse ),
inference(superposition,[status(thm)],[c_11152,c_9975]) ).
cnf(c_11873,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))))) = fFalse
| hBOOL(fTrue) ),
inference(superposition,[status(thm)],[c_10438,c_11142]) ).
cnf(c_12251,plain,
( hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse
| hBOOL(fTrue) ),
inference(demodulation,[status(thm)],[c_11873,c_2197]) ).
cnf(c_12259,plain,
( hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fFalse
| hBOOL(X0) ),
inference(superposition,[status(thm)],[c_12251,c_11143]) ).
cnf(c_12260,plain,
( hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse
| bot_bot(bool) = fFalse ),
inference(superposition,[status(thm)],[c_12251,c_11192]) ).
cnf(c_12277,plain,
( bot_bot(bool) = fFalse
| hBOOL(fFalse) ),
inference(superposition,[status(thm)],[c_12260,c_10438]) ).
cnf(c_12278,plain,
bot_bot(bool) = fFalse,
inference(forward_subsumption_resolution,[status(thm)],[c_12277,c_276]) ).
cnf(c_12312,plain,
( ~ hBOOL(X0)
| hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),hAPP(bool,bool,fNot,X0))) = fFalse ),
inference(superposition,[status(thm)],[c_12259,c_264]) ).
cnf(c_12327,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse
| hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse ),
inference(superposition,[status(thm)],[c_12259,c_3201]) ).
cnf(c_12582,plain,
( hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse
| hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))) = fFalse ),
inference(demodulation,[status(thm)],[c_12327,c_2197]) ).
cnf(c_12591,plain,
( hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))) = fFalse
| hBOOL(fFalse) ),
inference(superposition,[status(thm)],[c_12582,c_10438]) ).
cnf(c_12592,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))) = fFalse,
inference(forward_subsumption_resolution,[status(thm)],[c_12591,c_276]) ).
cnf(c_12594,plain,
( hAPP(fun(bool,bool),bool,finite_finite_1(bool),hAPP(bool,fun(bool,bool),fconj,fFalse)) = fFalse
| hBOOL(fTrue) ),
inference(demodulation,[status(thm)],[c_12251,c_12592]) ).
cnf(c_12826,plain,
hAPP(fun(X0,bool),X1,X2,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)) = hAPP(fun(X0,bool),X1,X2,X3),
inference(superposition,[status(thm)],[c_2289,c_2196]) ).
cnf(c_12827,plain,
hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X1,fun(X0,bool),X2,X3)) = hAPP(X1,fun(X0,bool),X2,X3),
inference(superposition,[status(thm)],[c_2289,c_2197]) ).
cnf(c_12836,plain,
hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse) = bot_bot(fun(X0,bool)),
inference(demodulation,[status(thm)],[c_126,c_12827]) ).
cnf(c_12838,plain,
hAPP(bool,fun(bool,bool),fconj,fFalse) = bot_bot(fun(bool,bool)),
inference(demodulation,[status(thm)],[c_10203,c_12827]) ).
cnf(c_12849,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))) = fFalse,
inference(demodulation,[status(thm)],[c_12592,c_12827]) ).
cnf(c_12987,plain,
( hAPP(fun(bool,bool),bool,finite_finite_1(bool),bot_bot(fun(bool,bool))) = fFalse
| hBOOL(fTrue) ),
inference(light_normalisation,[status(thm)],[c_12594,c_12838]) ).
cnf(c_13106,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(demodulation,[status(thm)],[c_2193,c_12826]) ).
cnf(c_13110,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(X0,fun(X0,bool),fequal(X0),hAPP(X1,X0,X2,X3))) = hAPP(X1,X0,X2,X3),
inference(demodulation,[status(thm)],[c_2197,c_13106]) ).
cnf(c_14229,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))) = fFalse,
inference(demodulation,[status(thm)],[c_12849,c_12836]) ).
cnf(c_14942,plain,
( ~ hBOOL(X0)
| hAPP(fun(bool,bool),bool,finite_finite_1(bool),bot_bot(fun(bool,bool))) = fFalse
| hAPP(bool,bool,fNot,X0) = fFalse ),
inference(demodulation,[status(thm)],[c_12312,c_12826,c_12836,c_12838,c_13106,c_13110,c_14229]) ).
cnf(c_14981,plain,
( hAPP(fun(bool,bool),bool,finite_finite_1(bool),bot_bot(fun(bool,bool))) = fFalse
| hAPP(bool,bool,fNot,fTrue) = fFalse ),
inference(superposition,[status(thm)],[c_12987,c_14942]) ).
cnf(c_15594,plain,
hAPP(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool),
inference(superposition,[status(thm)],[c_262,c_157]) ).
cnf(c_15597,plain,
~ hBOOL(bot_bot(bool)),
inference(demodulation,[status(thm)],[c_460,c_15594]) ).
cnf(c_15836,plain,
hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),bot_bot(bool))) = bot_bot(bool),
inference(superposition,[status(thm)],[c_262,c_3794]) ).
cnf(c_15902,plain,
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),bot_bot(fun(X0,bool))) = bot_bot(fun(X0,bool))
| hBOOL(bot_bot(bool)) ),
inference(superposition,[status(thm)],[c_15594,c_117]) ).
cnf(c_15911,plain,
hAPP(fun(X0,bool),fun(X0,bool),collect(X0),bot_bot(fun(X0,bool))) = bot_bot(fun(X0,bool)),
inference(forward_subsumption_resolution,[status(thm)],[c_15902,c_15597]) ).
cnf(c_17142,plain,
( hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)))
| hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(superposition,[status(thm)],[c_2196,c_265]) ).
cnf(c_19706,plain,
( hAPP(bool,bool,fNot,fTrue) = fFalse
| hBOOL(fFalse) ),
inference(superposition,[status(thm)],[c_14981,c_201]) ).
cnf(c_19710,plain,
hAPP(bool,bool,fNot,fTrue) = fFalse,
inference(forward_subsumption_resolution,[status(thm)],[c_19706,c_276]) ).
cnf(c_19715,plain,
( hBOOL(fFalse)
| hBOOL(fTrue) ),
inference(superposition,[status(thm)],[c_19710,c_265]) ).
cnf(c_19716,plain,
hBOOL(fTrue),
inference(forward_subsumption_resolution,[status(thm)],[c_19715,c_276]) ).
cnf(c_20124,plain,
( hBOOL(hAPP(bool,bool,fNot,fTrue))
| hBOOL(fTrue) ),
inference(superposition,[status(thm)],[c_2201,c_17142]) ).
cnf(c_21931,plain,
hBOOL(fTrue),
inference(global_subsumption_just,[status(thm)],[c_20124,c_19716]) ).
cnf(c_22645,plain,
( ~ hBOOL(fTrue)
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fFalse
| hBOOL(X0) ),
inference(superposition,[status(thm)],[c_4040,c_3787]) ).
cnf(c_22647,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),bot_bot(bool))) = fFalse
| bot_bot(bool) = fTrue ),
inference(superposition,[status(thm)],[c_4040,c_15836]) ).
cnf(c_22648,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X0)) = fFalse
| hBOOL(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22645,c_21931]) ).
cnf(c_22651,plain,
( bot_bot(bool) = fFalse
| bot_bot(bool) = fTrue ),
inference(light_normalisation,[status(thm)],[c_22647,c_15836]) ).
cnf(c_22967,plain,
bot_bot(bool) = fFalse,
inference(global_subsumption_just,[status(thm)],[c_22651,c_12278]) ).
cnf(c_22971,plain,
hAPP(X0,bool,bot_bot(fun(X0,bool)),X1) = fFalse,
inference(demodulation,[status(thm)],[c_15594,c_22967]) ).
cnf(c_23004,plain,
hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))))) = fFalse,
inference(superposition,[status(thm)],[c_22648,c_3201]) ).
cnf(c_23831,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))) = fFalse,
inference(demodulation,[status(thm)],[c_23004,c_2197]) ).
cnf(c_26585,plain,
hAPP(fun(X0,bool),X1,X2,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)) = hAPP(fun(X0,bool),X1,X2,X3),
inference(superposition,[status(thm)],[c_2289,c_2196]) ).
cnf(c_26586,plain,
hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X1,fun(X0,bool),X2,X3)) = hAPP(X1,fun(X0,bool),X2,X3),
inference(superposition,[status(thm)],[c_2289,c_2197]) ).
cnf(c_26594,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(X2,X0,hAPP(X0,fun(X2,X0),combk(X0,X2),X1),X3),
inference(demodulation,[status(thm)],[c_2192,c_26586]) ).
cnf(c_26595,plain,
hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse) = bot_bot(fun(X0,bool)),
inference(demodulation,[status(thm)],[c_126,c_26586]) ).
cnf(c_26608,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))) = fFalse,
inference(demodulation,[status(thm)],[c_23831,c_26586]) ).
cnf(c_27382,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))) = fFalse,
inference(demodulation,[status(thm)],[c_26608,c_26595]) ).
cnf(c_27524,plain,
hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(demodulation,[status(thm)],[c_2193,c_26585]) ).
cnf(c_27540,plain,
hAPP(fun(fun(X0,bool),bool),fun(X0,bool),the_elem(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1),
inference(demodulation,[status(thm)],[c_2289,c_27524]) ).
cnf(c_30804,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),hAPP(hoare_509422987triple(X0),fun(hoare_509422987triple(X0),bool),fequal(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X2),X3),X4))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X2,sK24(X0,X4,X1,X3,X2)),sK25(X0,X4,X1,X3,X2))) ),
inference(demodulation,[status(thm)],[c_4025,c_26585]) ).
cnf(c_30817,plain,
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),sK24(x_a,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),g,c,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))))),sK25(x_a,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),g,c,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))))))
| hBOOL(fFalse) ),
inference(superposition,[status(thm)],[c_27382,c_30804]) ).
cnf(c_30845,plain,
hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),sK24(x_a,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),g,c,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))))),sK25(x_a,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),g,c,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))))),
inference(forward_subsumption_resolution,[status(thm)],[c_30817,c_276]) ).
cnf(c_34684,plain,
hBOOL(fFalse),
inference(demodulation,[status(thm)],[c_30845,c_15911,c_22971,c_26594,c_27540]) ).
cnf(c_34685,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_34684,c_276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW470+5 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 05:05:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.60/4.17 % SZS status Started for theBenchmark.p
% 24.60/4.17 % SZS status Theorem for theBenchmark.p
% 24.60/4.17
% 24.60/4.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.60/4.17
% 24.60/4.17 ------ iProver source info
% 24.60/4.17
% 24.60/4.17 git: date: 2024-06-12 09:56:46 +0000
% 24.60/4.17 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 24.60/4.17 git: non_committed_changes: false
% 24.60/4.17
% 24.60/4.17 ------ Parsing...
% 24.60/4.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 24.60/4.17
% 24.60/4.17 ------ Preprocessing... sup_sim: 142 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 24.60/4.17
% 24.60/4.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 24.60/4.17
% 24.60/4.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.60/4.17 ------ Proving...
% 24.60/4.17 ------ Problem Properties
% 24.60/4.17
% 24.60/4.17
% 24.60/4.17 clauses 217
% 24.60/4.17 conjectures 0
% 24.60/4.17 EPR 3
% 24.60/4.17 Horn 161
% 24.60/4.17 unary 70
% 24.60/4.17 binary 80
% 24.60/4.17 lits 461
% 24.60/4.17 lits eq 170
% 24.60/4.17 fd_pure 0
% 24.60/4.17 fd_pseudo 0
% 24.60/4.17 fd_cond 0
% 24.60/4.17 fd_pseudo_cond 5
% 24.60/4.17 AC symbols 0
% 24.60/4.17
% 24.60/4.17 ------ Schedule dynamic 5 is on
% 24.60/4.17
% 24.60/4.17 ------ no conjectures: strip conj schedule
% 24.60/4.17
% 24.60/4.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 24.60/4.17
% 24.60/4.17
% 24.60/4.17 ------
% 24.60/4.17 Current options:
% 24.60/4.17 ------
% 24.60/4.17
% 24.60/4.17
% 24.60/4.17
% 24.60/4.17
% 24.60/4.17 ------ Proving...
% 24.60/4.17
% 24.60/4.17
% 24.60/4.17 % SZS status Theorem for theBenchmark.p
% 24.60/4.17
% 24.60/4.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.60/4.17
% 24.60/4.18
%------------------------------------------------------------------------------