TSTP Solution File: SWW296+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWW296+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n016.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 : Fri Sep 1 01:00:46 EDT 2023
% Result : Theorem 10.03s 2.68s
% Output : Refutation 10.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 118
% Syntax : Number of formulae : 168 ( 136 unt; 0 def)
% Number of atoms : 277 ( 186 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 164 ( 55 ~; 47 |; 37 &)
% ( 7 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 135 ( 135 usr; 115 con; 0-4 aty)
% Number of variables : 209 (; 187 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37889,plain,
$false,
inference(unit_resulting_resolution,[],[f17725,f19394,f17760,f37325,f22043]) ).
fof(f22043,plain,
! [X2,X3,X0,X1,X7] :
( hAPP(hAPP(c_Set_Oimage(X1,X2),sK395(X0,X1,X2,X3)),X0) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X7),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X7,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(cnf_transformation,[],[f15989]) ).
fof(f15989,plain,
! [X0,X1,X2,X3] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),sK394(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK394(X0,X1,X2,X3),X3) )
| ! [X5] : hAPP(hAPP(c_Set_Oimage(X1,X2),X5),X0) != X3 )
& ( hAPP(hAPP(c_Set_Oimage(X1,X2),sK395(X0,X1,X2,X3)),X0) = X3
| ! [X7] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X7),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X7,X3) ) ) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK394,sK395])],[f15986,f15988,f15987]) ).
fof(f15987,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),sK394(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK394(X0,X1,X2,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f15988,plain,
! [X0,X1,X2,X3] :
( ? [X6] : hAPP(hAPP(c_Set_Oimage(X1,X2),X6),X0) = X3
=> hAPP(hAPP(c_Set_Oimage(X1,X2),sK395(X0,X1,X2,X3)),X0) = X3 ),
introduced(choice_axiom,[]) ).
fof(f15986,plain,
! [X0,X1,X2,X3] :
( ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
| ! [X5] : hAPP(hAPP(c_Set_Oimage(X1,X2),X5),X0) != X3 )
& ( ? [X6] : hAPP(hAPP(c_Set_Oimage(X1,X2),X6),X0) = X3
| ! [X7] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X7),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X7,X3) ) ) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(rectify,[],[f15985]) ).
fof(f15985,plain,
! [X0,X1,X2,X3] :
( ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
| ! [X5] : hAPP(hAPP(c_Set_Oimage(X1,X2),X5),X0) != X3 )
& ( ? [X5] : hAPP(hAPP(c_Set_Oimage(X1,X2),X5),X0) = X3
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X4),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X4,X3) ) ) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(nnf_transformation,[],[f13155]) ).
fof(f13155,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
<=> ? [X5] : hAPP(hAPP(c_Set_Oimage(X1,X2),X5),X0) = X3 )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(ennf_transformation,[],[f8852]) ).
fof(f8852,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X3
=> ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X2,X1),X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
<=> ? [X5] : hAPP(hAPP(c_Set_Oimage(X1,X2),X5),X0) = X3 ) ),
inference(rectify,[],[f4419]) ).
fof(f4419,axiom,
! [X261,X18,X5,X128] :
( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) != X128
=> ( ? [X172] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oimage(X5,X18),X172),X128)),X261))
& c_Fun_Oinj__on(X5,X18,X172,X128) )
<=> ? [X309] : hAPP(hAPP(c_Set_Oimage(X18,X5),X309),X261) = X128 ) ),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_inj__on__iff__surj) ).
fof(f37325,plain,
! [X333,X336,X334] : c_Fun_Oinj__on(X334,X336,c_fequal,X333),
inference(subsumption_resolution,[],[f37324,f22388]) ).
fof(f22388,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| sK456(X0,X1,X3) != sK457(X0,X1,X3) ),
inference(cnf_transformation,[],[f16139]) ).
fof(f16139,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ( sK456(X0,X1,X3) != sK457(X0,X1,X3)
& hAPP(X1,sK456(X0,X1,X3)) = hAPP(X1,sK457(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK457(X0,X1,X3)),X0))
& hBOOL(hAPP(hAPP(c_member(X3),sK456(X0,X1,X3)),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X6) != hAPP(X1,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X7),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK456,sK457])],[f16136,f16138,f16137]) ).
fof(f16137,plain,
! [X0,X1,X3] :
( ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X4) = hAPP(X1,X5)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) )
=> ( ? [X5] :
( sK456(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK456(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),sK456(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16138,plain,
! [X0,X1,X3] :
( ? [X5] :
( sK456(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK456(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
=> ( sK456(X0,X1,X3) != sK457(X0,X1,X3)
& hAPP(X1,sK456(X0,X1,X3)) = hAPP(X1,sK457(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK457(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16136,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X4) = hAPP(X1,X5)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X6) != hAPP(X1,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X7),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(rectify,[],[f16135]) ).
fof(f16135,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X4) = hAPP(X1,X5)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X4) != hAPP(X1,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f13476]) ).
fof(f13476,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X4) != hAPP(X1,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(flattening,[],[f13475]) ).
fof(f13475,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X4) != hAPP(X1,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(ennf_transformation,[],[f9087]) ).
fof(f9087,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),X0))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X3),X5),X0))
=> ( hAPP(X1,X4) = hAPP(X1,X5)
=> X4 = X5 ) ) ) ),
inference(rectify,[],[f4409]) ).
fof(f4409,axiom,
! [X128,X1,X18,X5] :
( c_Fun_Oinj__on(X5,X18,X1,X128)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X5),X2),X128))
=> ! [X145] :
( hBOOL(hAPP(hAPP(c_member(X5),X145),X128))
=> ( hAPP(X1,X2) = hAPP(X1,X145)
=> X2 = X145 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_inj__on__def) ).
fof(f37324,plain,
! [X333,X336,X334] :
( sK457(X333,c_fequal,X334) = sK456(X333,c_fequal,X334)
| c_Fun_Oinj__on(X334,X336,c_fequal,X333) ),
inference(forward_demodulation,[],[f37300,f36904]) ).
fof(f36904,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(c_fequal,X0)) = X0,
inference(backward_demodulation,[],[f17785,f36896]) ).
fof(f36896,plain,
! [X351,X352] : hAPP(hAPP(c_Set_Oinsert(X351),X352),c_Orderings_Obot__class_Obot(tc_fun(X351,tc_HOL_Obool))) = hAPP(c_fequal,X352),
inference(forward_demodulation,[],[f36895,f36600]) ).
fof(f36600,plain,
! [X0,X1] : hAPP(c_fequal,X1) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,sF647,X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),hAPP(c_fimplies,sF710))),
inference(forward_demodulation,[],[f36599,f17653]) ).
fof(f17653,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5667]) ).
fof(f5667,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f2455]) ).
fof(f2455,axiom,
! [X22,X5] : hAPP(c_Set_OCollect(X5),X22) = X22,
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_Collect__def) ).
fof(f36599,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X0),hAPP(c_fequal,X1)) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,sF647,X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),hAPP(c_fimplies,sF710))),
inference(forward_demodulation,[],[f36598,f17850]) ).
fof(f17850,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(cnf_transformation,[],[f5864]) ).
fof(f5864,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(rectify,[],[f3932]) ).
fof(f3932,axiom,
! [X30,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X30),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X30)),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_singleton__conv2) ).
fof(f36598,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,sF647,X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),hAPP(c_fimplies,sF710))),
inference(forward_demodulation,[],[f31476,f24695]) ).
fof(f24695,plain,
tc_fun(tc_HOL_Obool,tc_HOL_Obool) = sF647,
introduced(function_definition,[]) ).
fof(f31476,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),hAPP(c_fimplies,sF710))),
inference(unit_resulting_resolution,[],[f24775,f19705]) ).
fof(f19705,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f11278]) ).
fof(f11278,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2))
| hBOOL(hAPP(X2,X1)) )
& ( hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2))
| ~ hBOOL(hAPP(X2,X1)) ) ),
inference(ennf_transformation,[],[f7198]) ).
fof(f7198,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,X1))
=> c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2)) )
& ( hBOOL(hAPP(X2,X1))
=> hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2)) ) ),
inference(rectify,[],[f3929]) ).
fof(f3929,axiom,
! [X5,X30,X22] :
( ( ~ hBOOL(hAPP(X22,X30))
=> c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X30))),X22)) )
& ( hBOOL(hAPP(X22,X30))
=> hAPP(hAPP(c_Set_Oinsert(X5),X30),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X30))),X22)) ) ),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_Collect__conv__if) ).
fof(f24775,plain,
! [X0] : hBOOL(hAPP(hAPP(c_fimplies,sF710),X0)),
inference(unit_resulting_resolution,[],[f24759,f18142]) ).
fof(f18142,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f6098]) ).
fof(f6098,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f5219]) ).
fof(f5219,axiom,
! [X38,X22] :
( hBOOL(hAPP(hAPP(c_fimplies,X22),X38))
| hBOOL(X22) ),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',help_c__fimplies__1) ).
fof(f24759,plain,
~ hBOOL(sF710),
inference(definition_folding,[],[f16803,f24758,f24757,f24756,f24755,f24754,f24753,f24752,f24751,f24750,f24749,f24748,f24747,f24746,f24745,f24656,f24744,f24743,f24712,f24656,f24742,f24741,f24656,f24740,f24712,f24656,f24739,f24738,f24705,f24704,f24695,f24737,f24696,f24695,f24656,f24736,f24731,f24696,f24695,f24712,f24656,f24735,f24734,f24700,f24733,f24690,f24656,f24656,f24696,f24695,f24732,f24727,f24690,f24656,f24656,f24731,f24696,f24695,f24730,f24729,f24656,f24656,f24728,f24723,f24712,f24656,f24656,f24727,f24690,f24656,f24656,f24726,f24725,f24712,f24656,f24656,f24724,f24714,f24713,f24712,f24656,f24657,f24656,f24723,f24712,f24656,f24656,f24722,f24721,f24720,f24719,f24676,f24718,f24656,f24717,f24656,f24712,f24656,f24716,f24657,f24656,f24657,f24656,f24713,f24712,f24656,f24715,f24670,f24657,f24656,f24657,f24656,f24714,f24713,f24712,f24656,f24657,f24656,f24711,f24710,f24709,f24708,f24707,f24706,f24705,f24704,f24695,f24703,f24696,f24695,f24656,f24702,f24701,f24700,f24699,f24690,f24656,f24656,f24696,f24695,f24698,f24657,f24656,f24691,f24690,f24656,f24656,f24697,f24696,f24695,f24694,f24693,f24656,f24656,f24692,f24657,f24656,f24670,f24657,f24656,f24657,f24656,f24691,f24690,f24656,f24656,f24689,f24688,f24657,f24656,f24657,f24656,f24657,f24656,f24687,f24657,f24656,f24682,f24670,f24657,f24656,f24657,f24656,f24670,f24657,f24656,f24657,f24656,f24670,f24657,f24656,f24657,f24656,f24686,f24685,f24670,f24657,f24656,f24657,f24656,f24670,f24657,f24656,f24657,f24656,f24684,f24657,f24656,f24683,f24671,f24670,f24657,f24656,f24657,f24656,f24671,f24670,f24657,f24656,f24657,f24656,f24682,f24670,f24657,f24656,f24657,f24656,f24670,f24657,f24656,f24657,f24656,f24681,f24671,f24670,f24657,f24656,f24657,f24656,f24671,f24670,f24657,f24656,f24657,f24656,f24657,f24656,f24680,f24679,f24678,f24677,f24676,f24675,f24656,f24674,f24657,f24656,f24658,f24657,f24656,f24673,f24659,f24658,f24657,f24656,f24670,f24657,f24656,f24657,f24656,f24672,f24657,f24656,f24660,f24659,f24658,f24657,f24656,f24671,f24670,f24657,f24656,f24657,f24656,f24669,f24668,f24667,f24666,f24665,f24657,f24656,f24658,f24664,f24661,f24657,f24656,f24659,f24658,f24657,f24656,f24663,f24657,f24656,f24662,f24661,f24657,f24656,f24660,f24659,f24658,f24657,f24656]) ).
fof(f24662,plain,
tc_fun(tc_Com_Ocom,sF613) = sF614,
introduced(function_definition,[]) ).
fof(f24663,plain,
c_COMBB(sF612,sF614,sF609) = sF615,
introduced(function_definition,[]) ).
fof(f24661,plain,
tc_fun(sF609,tc_HOL_Obool) = sF613,
introduced(function_definition,[]) ).
fof(f24664,plain,
c_COMBB(sF611,sF613,tc_Com_Ocom) = sF616,
introduced(function_definition,[]) ).
fof(f24665,plain,
c_COMBB(sF610,tc_HOL_Obool,sF609) = sF617,
introduced(function_definition,[]) ).
fof(f24666,plain,
c_HOL_OAll(t_a) = sF618,
introduced(function_definition,[]) ).
fof(f24667,plain,
hAPP(sF617,sF618) = sF619,
introduced(function_definition,[]) ).
fof(f24668,plain,
hAPP(sF616,sF619) = sF620,
introduced(function_definition,[]) ).
fof(f24669,plain,
hAPP(sF615,sF620) = sF621,
introduced(function_definition,[]) ).
fof(f24660,plain,
tc_fun(tc_Com_Ocom,sF611) = sF612,
introduced(function_definition,[]) ).
fof(f24672,plain,
c_COMBB(sF623,sF612,sF609) = sF624,
introduced(function_definition,[]) ).
fof(f24659,plain,
tc_fun(sF609,sF610) = sF611,
introduced(function_definition,[]) ).
fof(f24673,plain,
c_COMBB(sF622,sF611,tc_Com_Ocom) = sF625,
introduced(function_definition,[]) ).
fof(f24658,plain,
tc_fun(t_a,tc_HOL_Obool) = sF610,
introduced(function_definition,[]) ).
fof(f24674,plain,
c_COMBB(sF609,sF610,sF609) = sF626,
introduced(function_definition,[]) ).
fof(f24675,plain,
c_COMBB(sF608,tc_HOL_Obool,t_a) = sF627,
introduced(function_definition,[]) ).
fof(f24677,plain,
hAPP(sF627,sF628) = sF629,
introduced(function_definition,[]) ).
fof(f24678,plain,
hAPP(sF626,sF629) = sF630,
introduced(function_definition,[]) ).
fof(f24679,plain,
hAPP(sF625,sF630) = sF631,
introduced(function_definition,[]) ).
fof(f24680,plain,
hAPP(sF624,sF631) = sF632,
introduced(function_definition,[]) ).
fof(f24681,plain,
c_COMBC(sF609,sF623,sF623) = sF633,
introduced(function_definition,[]) ).
fof(f24671,plain,
tc_fun(tc_Com_Ocom,sF622) = sF623,
introduced(function_definition,[]) ).
fof(f24683,plain,
tc_fun(sF623,sF623) = sF635,
introduced(function_definition,[]) ).
fof(f24684,plain,
c_COMBB(sF634,sF635,sF609) = sF636,
introduced(function_definition,[]) ).
fof(f24685,plain,
c_COMBB(sF622,sF622,tc_Com_Ocom) = sF637,
introduced(function_definition,[]) ).
fof(f24686,plain,
hAPP(sF636,sF637) = sF638,
introduced(function_definition,[]) ).
fof(f24682,plain,
tc_fun(sF622,sF622) = sF634,
introduced(function_definition,[]) ).
fof(f24687,plain,
c_COMBB(sF622,sF634,sF609) = sF639,
introduced(function_definition,[]) ).
fof(f24688,plain,
c_COMBB(sF609,sF609,sF609) = sF640,
introduced(function_definition,[]) ).
fof(f24689,plain,
hAPP(sF639,sF640) = sF641,
introduced(function_definition,[]) ).
fof(f24692,plain,
c_COMBB(sF643,sF622,sF609) = sF644,
introduced(function_definition,[]) ).
fof(f24693,plain,
c_COMBS(t_a,sF608,sF608) = sF645,
introduced(function_definition,[]) ).
fof(f24694,plain,
hAPP(sF644,sF645) = sF646,
introduced(function_definition,[]) ).
fof(f24697,plain,
tc_fun(t_a,sF648) = sF649,
introduced(function_definition,[]) ).
fof(f24691,plain,
tc_fun(t_a,sF642) = sF643,
introduced(function_definition,[]) ).
fof(f24698,plain,
c_COMBB(sF649,sF643,sF609) = sF650,
introduced(function_definition,[]) ).
fof(f24699,plain,
c_COMBB(sF648,sF642,t_a) = sF651,
introduced(function_definition,[]) ).
fof(f24701,plain,
hAPP(sF651,sF652) = sF653,
introduced(function_definition,[]) ).
fof(f24702,plain,
hAPP(sF650,sF653) = sF654,
introduced(function_definition,[]) ).
fof(f24703,plain,
c_COMBB(sF608,sF648,t_a) = sF655,
introduced(function_definition,[]) ).
fof(f24706,plain,
hAPP(sF655,sF657) = sF658,
introduced(function_definition,[]) ).
fof(f24707,plain,
hAPP(sF654,sF658) = sF659,
introduced(function_definition,[]) ).
fof(f24708,plain,
hAPP(sF646,sF659) = sF660,
introduced(function_definition,[]) ).
fof(f24709,plain,
hAPP(sF641,sF660) = sF661,
introduced(function_definition,[]) ).
fof(f24710,plain,
hAPP(sF638,sF661) = sF662,
introduced(function_definition,[]) ).
fof(f24711,plain,
hAPP(sF633,sF662) = sF663,
introduced(function_definition,[]) ).
fof(f24670,plain,
tc_fun(sF609,sF609) = sF622,
introduced(function_definition,[]) ).
fof(f24715,plain,
c_COMBB(sF666,sF622,tc_Com_Ocom) = sF667,
introduced(function_definition,[]) ).
fof(f24716,plain,
c_COMBB(sF665,sF609,sF609) = sF668,
introduced(function_definition,[]) ).
fof(f24717,plain,
c_COMBB(sF664,sF608,t_a) = sF669,
introduced(function_definition,[]) ).
fof(f24718,plain,
c_COMBB(sF608,tc_HOL_Obool,tc_Com_Ostate) = sF670,
introduced(function_definition,[]) ).
fof(f24676,plain,
c_HOL_OAll(tc_Com_Ostate) = sF628,
introduced(function_definition,[]) ).
fof(f24719,plain,
hAPP(sF670,sF628) = sF671,
introduced(function_definition,[]) ).
fof(f24720,plain,
hAPP(sF669,sF671) = sF672,
introduced(function_definition,[]) ).
fof(f24721,plain,
hAPP(sF668,sF672) = sF673,
introduced(function_definition,[]) ).
fof(f24722,plain,
hAPP(sF667,sF673) = sF674,
introduced(function_definition,[]) ).
fof(f24657,plain,
tc_fun(t_a,sF608) = sF609,
introduced(function_definition,[]) ).
fof(f24713,plain,
tc_fun(t_a,sF664) = sF665,
introduced(function_definition,[]) ).
fof(f24714,plain,
tc_fun(sF609,sF665) = sF666,
introduced(function_definition,[]) ).
fof(f24724,plain,
c_COMBB(sF675,sF666,tc_Com_Ocom) = sF676,
introduced(function_definition,[]) ).
fof(f24725,plain,
c_COMBB(sF608,sF664,t_a) = sF677,
introduced(function_definition,[]) ).
fof(f24726,plain,
hAPP(sF676,sF677) = sF678,
introduced(function_definition,[]) ).
fof(f24723,plain,
tc_fun(sF608,sF664) = sF675,
introduced(function_definition,[]) ).
fof(f24728,plain,
c_COMBB(sF679,sF675,tc_Com_Ocom) = sF680,
introduced(function_definition,[]) ).
fof(f24729,plain,
c_COMBC(tc_Com_Ostate,sF608,sF608) = sF681,
introduced(function_definition,[]) ).
fof(f24730,plain,
hAPP(sF680,sF681) = sF682,
introduced(function_definition,[]) ).
fof(f24727,plain,
tc_fun(tc_Com_Ostate,sF642) = sF679,
introduced(function_definition,[]) ).
fof(f24732,plain,
c_COMBB(sF683,sF679,tc_Com_Ocom) = sF684,
introduced(function_definition,[]) ).
fof(f24690,plain,
tc_fun(sF608,sF608) = sF642,
introduced(function_definition,[]) ).
fof(f24733,plain,
c_COMBB(sF648,sF642,tc_Com_Ostate) = sF685,
introduced(function_definition,[]) ).
fof(f24700,plain,
c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool) = sF652,
introduced(function_definition,[]) ).
fof(f24734,plain,
hAPP(sF685,sF652) = sF686,
introduced(function_definition,[]) ).
fof(f24735,plain,
hAPP(sF684,sF686) = sF687,
introduced(function_definition,[]) ).
fof(f24731,plain,
tc_fun(tc_Com_Ostate,sF648) = sF683,
introduced(function_definition,[]) ).
fof(f24736,plain,
c_COMBB(sF664,sF683,tc_Com_Ocom) = sF688,
introduced(function_definition,[]) ).
fof(f24696,plain,
tc_fun(tc_Com_Ostate,sF647) = sF648,
introduced(function_definition,[]) ).
fof(f24737,plain,
c_COMBB(sF608,sF648,tc_Com_Ostate) = sF689,
introduced(function_definition,[]) ).
fof(f24704,plain,
c_COMBB(tc_HOL_Obool,sF647,tc_Com_Ostate) = sF656,
introduced(function_definition,[]) ).
fof(f24705,plain,
hAPP(sF656,c_fimplies) = sF657,
introduced(function_definition,[]) ).
fof(f24738,plain,
hAPP(sF689,sF657) = sF690,
introduced(function_definition,[]) ).
fof(f24739,plain,
hAPP(sF688,sF690) = sF691,
introduced(function_definition,[]) ).
fof(f24740,plain,
c_COMBC(tc_Com_Ocom,tc_Nat_Onat,sF664) = sF692,
introduced(function_definition,[]) ).
fof(f24741,plain,
tc_fun(tc_Nat_Onat,sF608) = sF693,
introduced(function_definition,[]) ).
fof(f24742,plain,
tc_fun(tc_Com_Ostate,sF693) = sF694,
introduced(function_definition,[]) ).
fof(f24712,plain,
tc_fun(tc_Com_Ostate,sF608) = sF664,
introduced(function_definition,[]) ).
fof(f24743,plain,
tc_fun(tc_Nat_Onat,sF664) = sF695,
introduced(function_definition,[]) ).
fof(f24744,plain,
c_COMBB(sF694,sF695,tc_Com_Ocom) = sF696,
introduced(function_definition,[]) ).
fof(f24656,plain,
tc_fun(tc_Com_Ostate,tc_HOL_Obool) = sF608,
introduced(function_definition,[]) ).
fof(f24745,plain,
c_COMBC(tc_Com_Ostate,tc_Nat_Onat,sF608) = sF697,
introduced(function_definition,[]) ).
fof(f24746,plain,
hAPP(sF696,sF697) = sF698,
introduced(function_definition,[]) ).
fof(f24747,plain,
hAPP(sF698,c_Natural_Oevaln) = sF699,
introduced(function_definition,[]) ).
fof(f24748,plain,
hAPP(sF692,sF699) = sF700,
introduced(function_definition,[]) ).
fof(f24749,plain,
hAPP(sF700,v_n) = sF701,
introduced(function_definition,[]) ).
fof(f24750,plain,
hAPP(sF691,sF701) = sF702,
introduced(function_definition,[]) ).
fof(f24751,plain,
hAPP(sF687,sF702) = sF703,
introduced(function_definition,[]) ).
fof(f24752,plain,
hAPP(sF682,sF703) = sF704,
introduced(function_definition,[]) ).
fof(f24753,plain,
hAPP(sF678,sF704) = sF705,
introduced(function_definition,[]) ).
fof(f24754,plain,
hAPP(sF674,sF705) = sF706,
introduced(function_definition,[]) ).
fof(f24755,plain,
hAPP(sF663,sF706) = sF707,
introduced(function_definition,[]) ).
fof(f24756,plain,
hAPP(sF632,sF707) = sF708,
introduced(function_definition,[]) ).
fof(f24757,plain,
hAPP(sF621,sF708) = sF709,
introduced(function_definition,[]) ).
fof(f24758,plain,
c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,sF709,v_t) = sF710,
introduced(function_definition,[]) ).
fof(f16803,plain,
~ hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(t_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,t_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),v_n))))))))),v_t)),
inference(cnf_transformation,[],[f10289]) ).
fof(f10289,plain,
( ~ hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(t_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,t_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),v_n))))))))),v_t))
& hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(t_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,t_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),hAPP(c_Nat_OSuc,v_n)))))))))),v_t)) ),
inference(ennf_transformation,[],[f5223]) ).
fof(f5223,negated_conjecture,
~ ( hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(t_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,t_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),hAPP(c_Nat_OSuc,v_n)))))))))),v_t))
=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(t_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,t_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),v_n))))))))),v_t)) ),
inference(negated_conjecture,[],[f5222]) ).
fof(f5222,conjecture,
( hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(t_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,t_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),hAPP(c_Nat_OSuc,v_n)))))))))),v_t))
=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(t_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(t_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_HOL_Obool),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,t_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),v_n))))))))),v_t)) ),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',conj_0) ).
fof(f36895,plain,
! [X351,X352] : hAPP(hAPP(c_Set_Oinsert(X351),X352),c_Orderings_Obot__class_Obot(tc_fun(X351,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X351),hAPP(hAPP(c_COMBS(X351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,sF647,X351),c_fconj),hAPP(hAPP(c_COMBC(X351,X351,tc_HOL_Obool),c_fequal),X352))),hAPP(c_fimplies,sF710))),
inference(forward_demodulation,[],[f35206,f24695]) ).
fof(f35206,plain,
! [X351,X352] : hAPP(hAPP(c_Set_Oinsert(X351),X352),c_Orderings_Obot__class_Obot(tc_fun(X351,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X351),hAPP(hAPP(c_COMBS(X351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X351),c_fconj),hAPP(hAPP(c_COMBC(X351,X351,tc_HOL_Obool),c_fequal),X352))),hAPP(c_fimplies,sF710))),
inference(resolution,[],[f24775,f19705]) ).
fof(f17785,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0,
inference(cnf_transformation,[],[f5799]) ).
fof(f5799,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0,
inference(rectify,[],[f4046]) ).
fof(f4046,axiom,
! [X37,X5] : c_Set_Othe__elem(X5,hAPP(hAPP(c_Set_Oinsert(X5),X37),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X37,
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_the__elem__eq) ).
fof(f37300,plain,
! [X333,X335,X336,X334] :
( sK457(X333,c_fequal,X334) = c_Set_Othe__elem(X335,hAPP(c_fequal,sK456(X333,c_fequal,X334)))
| c_Fun_Oinj__on(X334,X336,c_fequal,X333) ),
inference(superposition,[],[f36904,f22387]) ).
fof(f22387,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| hAPP(X1,sK456(X0,X1,X3)) = hAPP(X1,sK457(X0,X1,X3)) ),
inference(cnf_transformation,[],[f16139]) ).
fof(f17760,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5774]) ).
fof(f5774,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f2148]) ).
fof(f2148,axiom,
! [X128,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X128),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_subset__UNIV) ).
fof(f19394,plain,
! [X2,X0,X1] : hAPP(c_Set_OPow(X1),X0) != hAPP(hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool)),X2),X0),
inference(cnf_transformation,[],[f11268]) ).
fof(f11268,plain,
! [X0,X1,X2] : hAPP(c_Set_OPow(X1),X0) != hAPP(hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool)),X2),X0),
inference(flattening,[],[f11267]) ).
fof(f11267,plain,
! [X0,X1,X2] : hAPP(c_Set_OPow(X1),X0) != hAPP(hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool)),X2),X0),
inference(ennf_transformation,[],[f6894]) ).
fof(f6894,plain,
! [X0,X1] :
~ ? [X2] : hAPP(c_Set_OPow(X1),X0) = hAPP(hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool)),X2),X0),
inference(rectify,[],[f2192]) ).
fof(f2192,axiom,
! [X128,X5] :
~ ? [X172] : hAPP(c_Set_OPow(X5),X128) = hAPP(hAPP(c_Set_Oimage(X5,tc_fun(X5,tc_HOL_Obool)),X172),X128),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_Cantors__paradox) ).
fof(f17725,plain,
! [X0,X1] : hAPP(c_Set_OPow(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(cnf_transformation,[],[f5739]) ).
fof(f5739,plain,
! [X0,X1] : hAPP(c_Set_OPow(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(rectify,[],[f3852]) ).
fof(f3852,axiom,
! [X128,X5] : hAPP(c_Set_OPow(X5),X128) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275',fact_Pow__not__empty) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.90 % Problem : SWW296+1 : TPTP v8.1.2. Released v5.2.0.
% 0.71/0.91 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.90/1.12 % Computer : n016.cluster.edu
% 0.90/1.12 % Model : x86_64 x86_64
% 0.90/1.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.90/1.12 % Memory : 8042.1875MB
% 0.90/1.12 % OS : Linux 3.10.0-693.el7.x86_64
% 0.90/1.12 % CPULimit : 300
% 0.90/1.12 % WCLimit : 300
% 0.90/1.12 % DateTime : Sun Aug 27 22:51:59 EDT 2023
% 0.90/1.12 % CPUTime :
% 0.90/1.12 This is a FOF_CAX_RFO_SEQ problem
% 0.90/1.13 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.8cTrzMT6nK/Vampire---4.8_1275
% 0.90/1.13 % (1387)Running in auto input_syntax mode. Trying TPTP
% 0.98/1.40 % (1394)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_394 on Vampire---4 for (394ds/0Mi)
% 0.98/1.42 % (1392)dis+3_3:2_aac=none:fsd=off:fde=none:lcm=reverse:nm=32:nicw=on:sos=on:sac=on:sp=occurrence_419 on Vampire---4 for (419ds/0Mi)
% 0.98/1.42 % (1393)dis+1011_2:1_add=off:afr=on:er=known:fde=unused:nwc=1.3:nicw=on:sas=z3:sims=off:sos=on:sac=on:tgt=full_398 on Vampire---4 for (398ds/0Mi)
% 0.98/1.42 % (1391)ott+1010_3_aac=none:bs=unit_only:bce=on:ep=R:er=filter:fsd=off:fde=none:gsp=on:irw=on:lcm=predicate:nwc=10.0:sos=all:sp=occurrence_449 on Vampire---4 for (449ds/0Mi)
% 0.98/1.42 % (1389)dis-1002_1_bd=off:fsd=off:fsr=off:fde=none:nwc=1.3:sims=off:sos=all_501 on Vampire---4 for (501ds/0Mi)
% 0.98/1.42 % (1390)ott-11_3:1_afr=on:anc=all_dependent:bd=preordered:bce=on:er=filter:fsd=off:fde=unused:nm=4:sos=all:sac=on:tgt=full:urr=on_476 on Vampire---4 for (476ds/0Mi)
% 0.98/1.42 % (1388)dis+1011_3_av=off:bd=off:er=known:fsd=off:fde=unused:irw=on:nm=64:nwc=1.3:sos=on:sp=reverse_arity_577 on Vampire---4 for (577ds/0Mi)
% 4.18/1.90 % (1392)Refutation not found, incomplete strategy% (1392)------------------------------
% 4.18/1.90 % (1392)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 4.18/1.90 % (1392)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 4.18/1.90 % (1392)Termination reason: Refutation not found, incomplete strategy
% 4.18/1.90
% 4.18/1.90 % (1392)Memory used [KB]: 40169
% 4.18/1.90 % (1392)Time elapsed: 0.476 s
% 4.18/1.90 % (1392)------------------------------
% 4.18/1.90 % (1392)------------------------------
% 4.80/1.93 % (1395)lrs+1010_5:1_bd=off:fsd=off:fde=unused:lcm=predicate:nm=64:nwc=1.7:sac=on:sp=frequency:tgt=ground:stl=62_392 on Vampire---4 for (392ds/0Mi)
% 9.00/2.53 % (1388)Refutation not found, incomplete strategy% (1388)------------------------------
% 9.00/2.53 % (1388)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 9.00/2.53 % (1388)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 9.00/2.53 % (1388)Termination reason: Refutation not found, incomplete strategy
% 9.00/2.53
% 9.00/2.53 % (1388)Memory used [KB]: 27249
% 9.00/2.53 % (1388)Time elapsed: 1.093 s
% 9.00/2.53 % (1388)------------------------------
% 9.00/2.53 % (1388)------------------------------
% 9.00/2.56 % (1396)dis+1011_3:2_av=off:ep=RST:fsd=off:fde=none:gsp=on:nm=2:nwc=2.0:sos=on:sp=reverse_frequency_373 on Vampire---4 for (373ds/0Mi)
% 9.49/2.67 % (1390)First to succeed.
% 10.03/2.68 % (1390)Refutation found. Thanks to Tanya!
% 10.03/2.68 % SZS status Theorem for Vampire---4
% 10.03/2.68 % SZS output start Proof for Vampire---4
% See solution above
% 10.10/2.69 % (1390)------------------------------
% 10.10/2.69 % (1390)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 10.10/2.69 % (1390)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 10.10/2.69 % (1390)Termination reason: Refutation
% 10.10/2.69
% 10.10/2.69 % (1390)Memory used [KB]: 66267
% 10.10/2.69 % (1390)Time elapsed: 1.256 s
% 10.10/2.69 % (1390)------------------------------
% 10.10/2.69 % (1390)------------------------------
% 10.10/2.69 % (1387)Success in time 1.552 s
% 10.10/2.69 % Vampire---4.8 exiting
%------------------------------------------------------------------------------