TSTP Solution File: SWV849-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV849-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 May 19 12:18:55 EDT 2023
% Result : Unsatisfiable 257.37s 56.26s
% Output : Refutation 258.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 590
% Syntax : Number of formulae : 1247 ( 459 unt; 88 typ; 0 def)
% Number of atoms : 2275 ( 869 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 15250 (1225 ~;1104 |; 0 &;12921 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% Number of symbols : 90 ( 88 usr; 18 con; 0-10 aty)
% Number of variables : 4163 ( 0 ^;4163 !; 0 ?;4163 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(v_ba_type,type,
v_ba: $i ).
thf(v_s0_type,type,
v_s0: $i ).
thf(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(v_ca_type,type,
v_ca: $i ).
thf(v_na_type,type,
v_na: $i ).
thf(v_s1_type,type,
v_s1: $i ).
thf(c_Com_Ocom_OWhile_type,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(v_s2_type,type,
v_s2: $i ).
thf(v_b_type,type,
v_b: $i ).
thf(v_c_type,type,
v_c: $i ).
thf(v_P_type,type,
v_P: $i ).
thf(v_xb_type,type,
v_xb: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(t_a_type,type,
t_a: $i ).
thf(c_in_type,type,
c_in: $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(v_G_type,type,
v_G: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(v_xa_type,type,
v_xa: $i ).
thf(v_n_type,type,
v_n: $i > $i ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Com_Ocom_OLocal_type,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(c_Com_Ocom_OAss_type,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Com_Ocom_OCall_type,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_OCond_type,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Com_OWT_type,type,
c_Com_OWT: $i > $o ).
thf(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_Ocom__rec_type,type,
c_Com_Ocom_Ocom__rec: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_Ocom__case_type,type,
c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Ofcomp_type,type,
c_Fun_Ofcomp: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Oid_type,type,
c_Fun_Oid: $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice_type,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XbexI__1__1_type,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XballE__1__1_type,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: $i > $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1_type,type,
c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XbexE__1__1_type,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: $i > $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevaln__max2__1__1_type,type,
c_Natural_Osko__Natural__Xevaln__max2__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1_type,type,
v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1_type,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__valids_type,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2_type,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__2: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3_type,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__1_type,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__1: $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk15_type,type,
sk15: $i > $i ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(892,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[626]) ).
thf(628,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[627]) ).
thf(629,plain,
! [A: $i] :
( ( sk3 @ ( c_Suc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Suc),[sk3])]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ A @ B @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ A @ B ) @ C @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_2) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ A @ B @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ A @ B ) @ C @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(173,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(909,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(343,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OBODY @ I ) @ J )
= ( hAPP @ G @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).
thf(1315,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OBODY @ I ) @ J )
= ( hAPP @ G @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ C )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
thf(1295,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ C )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(447,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(1549,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(218,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
thf(1024,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(412,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1469,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(757,plain,
! [B: $i,A: $i] :
( ( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(758,plain,
! [B: $i,A: $i] :
( ( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[757]) ).
thf(759,plain,
! [B: $i,A: $i] :
( ( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[758]) ).
thf(760,plain,
! [A: $i] :
( ( sk10 @ ( c_Com_Ocom_OBODY @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Com_Ocom_OBODY),[sk10])]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1554,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
inference(lifteq,[status(thm)],[1553]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(410,axiom,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(1465,plain,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1466,plain,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
inference(lifteq,[status(thm)],[1465]) ).
thf(6,negated_conjecture,
hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(502,plain,
hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1840,plain,
( ( hBOOL @ ( hAPP @ v_x @ v_s0 ) )
| ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
!= ( hAPP @ v_P @ v_xb ) ) ),
inference(paramod_ordered,[status(thm)],[1466,502]) ).
thf(1855,plain,
( ( hBOOL @ ( hAPP @ v_x @ v_s0 ) )
| ( ( c_Fun_Oid @ t_a )
!= v_P )
| ( v_x != v_xb ) ),
inference(simp,[status(thm)],[1840]) ).
thf(200,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I26_J_0) ).
thf(977,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1005,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_1) ).
thf(1406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
thf(683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(99,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( C = G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(730,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( C = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(434,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1618,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
thf(1422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(466,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_1) ).
thf(1591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(16,negated_conjecture,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_15) ).
thf(511,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ A @ B @ C ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ A @ B @ C ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
thf(1437,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(473,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1608,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(494,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OBODY @ I ) @ J )
= ( hAPP @ G @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I7_J_0) ).
thf(1655,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OBODY @ I ) @ J )
= ( hAPP @ G @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(266,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(341,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ E )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ F @ D @ E )
| ~ ( c_Natural_Oevaln @ B @ C @ D @ F )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).
thf(1310,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ E )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ F @ D @ E )
| ~ ( c_Natural_Oevaln @ B @ C @ D @ F )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(124,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(797,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(487,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(1640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(945,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).
thf(1076,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(polarity_switch,[status(thm)],[1076]) ).
thf(1078,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[1077]) ).
thf(401,axiom,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1444,plain,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1445,plain,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
inference(lifteq,[status(thm)],[1444]) ).
thf(1777,plain,
( ( hBOOL @ ( hAPP @ v_P @ v_s0 ) )
| ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
!= ( hAPP @ v_P @ v_xb ) ) ),
inference(paramod_ordered,[status(thm)],[1445,502]) ).
thf(1788,plain,
( ( hBOOL @ ( hAPP @ v_P @ v_s0 ) )
| ( ( c_COMBI @ t_a )
!= v_P )
| ( v_xb != v_P ) ),
inference(simp,[status(thm)],[1777]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ D @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ballE_1) ).
thf(1426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ D @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(1839,plain,
( ( hBOOL @ v_x )
| ( ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 )
!= ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x ) ) ),
inference(paramod_ordered,[status(thm)],[1466,502]) ).
thf(1867,plain,
( ( hBOOL @ v_x )
| ( ( hAPP @ v_P @ v_xb )
!= ( c_Fun_Oid @ t_a ) )
| ( v_x != v_s0 ) ),
inference(simp,[status(thm)],[1839]) ).
thf(14,negated_conjecture,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_13) ).
thf(500,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(349,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ D )
| ( c_Natural_Oevaln @ E @ B @ C @ D )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ A ) @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).
thf(1327,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ D )
| ( c_Natural_Oevaln @ E @ B @ C @ D )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ A ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(347,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1323,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1324,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
inference(lifteq,[status(thm)],[1323]) ).
thf(378,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1397,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(polarity_switch,[status(thm)],[1396]) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
!= ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1324,1397]) ).
thf(2096,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
inference(pattern_uni,[status(thm)],[2095:[bind(A,$thf( t_a )),bind(B,$thf( v_x ))]]) ).
thf(2411,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
!= ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[502,2096]) ).
thf(2419,plain,
( ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) ),
inference(simp,[status(thm)],[2411]) ).
thf(3628,plain,
( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
!= ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) )
| ( ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1324,2419]) ).
thf(3629,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
!= ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) ),
inference(pattern_uni,[status(thm)],[3628:[]]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(8,negated_conjecture,
( ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(513,plain,
( ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(530,plain,
( ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 ) ) ),
inference(cnf,[status(esa)],[513]) ).
thf(4,negated_conjecture,
v_ba = v_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(514,plain,
v_ba = v_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(522,plain,
v_b = v_ba,
inference(lifteq,[status(thm)],[514]) ).
thf(1663,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 ) ) ),
inference(rewrite,[status(thm)],[530,522]) ).
thf(1664,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 ) )
!= ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[502,1663]) ).
thf(1666,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 )
!= ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) ) ),
inference(simp,[status(thm)],[1664]) ).
thf(1713,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( ( hAPP @ v_P @ v_xb )
!= ( hAPP @ v_P @ v_xb ) )
| ( v_s2 != v_s0 ) ),
inference(simp,[status(thm)],[1666]) ).
thf(1714,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( v_s2 != v_s0 ) ),
inference(simp,[status(thm)],[1713]) ).
thf(2847,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( v_s2 != v_s0 )
| ( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
!= ( hAPP @ v_ba @ v_s2 ) ) ),
inference(paramod_ordered,[status(thm)],[1554,1714]) ).
thf(2955,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( v_s2 != v_s0 )
| ( ( c_Fun_Oid @ A )
!= v_ba )
| ( B != v_s2 ) ),
inference(simp,[status(thm)],[2847]) ).
thf(2972,plain,
! [A: $i] :
( ( hBOOL @ v_s2 )
| ( v_s2 != v_s0 )
| ( ( c_Fun_Oid @ A )
!= v_ba ) ),
inference(simp,[status(thm)],[2955]) ).
thf(376,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ B @ ( hAPP @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
thf(1391,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ B @ ( hAPP @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(144,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
thf(841,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(1359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(415,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ E @ D )
| ~ ( c_Natural_Oevalc @ B @ C @ E )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
thf(1475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ E @ D )
| ~ ( c_Natural_Oevalc @ B @ C @ E )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(565,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(432,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_3) ).
thf(1518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(320,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ D @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_4) ).
thf(1265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ D @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(305,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP2__I_0) ).
thf(1228,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(479,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1623,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(418,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(1482,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(15,negated_conjecture,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_14) ).
thf(515,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(534,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(cnf,[status(esa)],[515]) ).
thf(535,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(lifteq,[status(thm)],[534]) ).
thf(5,negated_conjecture,
v_ca = v_c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(498,plain,
v_ca = v_c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(531,plain,
v_c = v_ca,
inference(lifteq,[status(thm)],[498]) ).
thf(3262,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(rewrite,[status(thm)],[535,531,522]) ).
thf(3263,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(simp,[status(thm)],[3262]) ).
thf(34,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(570,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,negated_conjecture,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).
thf(512,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(525,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(cnf,[status(esa)],[512]) ).
thf(526,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= v_ca )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(lifteq,[status(thm)],[525]) ).
thf(1985,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= v_ca )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(rewrite,[status(thm)],[526,531,522]) ).
thf(95,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(719,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(13,negated_conjecture,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_12) ).
thf(504,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(429,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1511,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(702,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1132,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(61,axiom,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(638,plain,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(270,axiom,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(1147,plain,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(312,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).
thf(1247,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(345,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ C @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).
thf(1319,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ C @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(1477,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(polarity_switch,[status(thm)],[1477]) ).
thf(1479,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(lifteq,[status(thm)],[1478]) ).
thf(358,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
thf(1347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(256,axiom,
! [A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(1115,plain,
! [A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(1,negated_conjecture,
hBOOL @ ( hAPP @ v_ba @ v_s0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(501,plain,
hBOOL @ ( hAPP @ v_ba @ v_s0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2886,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
!= ( hAPP @ v_ba @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[1554,501]) ).
thf(2903,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( c_Fun_Oid @ A )
!= v_ba )
| ( B != v_s0 ) ),
inference(simp,[status(thm)],[2886]) ).
thf(2989,plain,
! [A: $i] :
( ( hBOOL @ v_s0 )
| ( ( c_Fun_Oid @ A )
!= v_ba ) ),
inference(simp,[status(thm)],[2903]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(924,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).
thf(754,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(755,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ A @ B ) ),
inference(polarity_switch,[status(thm)],[754]) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[755]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(373,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
thf(1383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1581,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(905,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(766,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(370,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1377,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OLocal @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OLocal @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(436,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OSemi @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ D @ I ) @ J ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ I @ K ) ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ J @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I4_J_0) ).
thf(1526,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OSemi @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ D @ I ) @ J ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ I @ K ) ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ J @ K ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(660,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(396,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xevaln__max2__1__1 @ A @ C @ B @ D @ E @ F ) @ E )
| ~ ( c_Natural_Oevaln @ C @ D @ G @ F )
| ~ ( c_Natural_Oevaln @ A @ B @ H @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__max2_0) ).
thf(1433,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xevaln__max2__1__1 @ A @ C @ B @ D @ E @ F ) @ E )
| ~ ( c_Natural_Oevaln @ C @ D @ G @ F )
| ~ ( c_Natural_Oevaln @ A @ B @ H @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(12,negated_conjecture,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_11) ).
thf(507,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(492,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCall @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ H @ I ) @ J ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).
thf(1651,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCall @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ H @ I ) @ J ) @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1074,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ A @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(508,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ A @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(529,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ A @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) ) ),
inference(cnf,[status(esa)],[508]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(1551,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
inference(lifteq,[status(thm)],[1551]) ).
thf(2542,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( hAPP @ ( c_COMBI @ A ) @ B )
!= ( hAPP @ v_ba @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[1552,501]) ).
thf(2551,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( c_COMBI @ A )
!= v_ba )
| ( B != v_s0 ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2646,plain,
! [A: $i] :
( ( hBOOL @ v_s0 )
| ( ( c_COMBI @ A )
!= v_ba ) ),
inference(simp,[status(thm)],[2551]) ).
thf(339,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
| ~ ( c_Natural_Oevalc @ B @ D @ E )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
thf(1306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
| ~ ( c_Natural_Oevalc @ B @ D @ E )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(2539,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( hAPP @ ( c_COMBI @ A ) @ B )
!= ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[1552,502]) ).
thf(2602,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( c_COMBI @ A )
!= ( hAPP @ v_P @ v_xb ) )
| ( B != v_s0 ) ),
inference(simp,[status(thm)],[2539]) ).
thf(2641,plain,
! [A: $i] :
( ( hBOOL @ v_s0 )
| ( ( c_COMBI @ A )
!= ( hAPP @ v_P @ v_xb ) ) ),
inference(simp,[status(thm)],[2602]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(485,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ D @ A @ C @ B @ E ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ A ) @ B @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_3) ).
thf(1636,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ D @ A @ C @ B @ E ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ A ) @ B @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(123,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
thf(793,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(226,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
thf(1047,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_0) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1343,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(217,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).
thf(1021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(315,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_1) ).
thf(1255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(152,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(862,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(457,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(1570,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(820,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(367,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCall @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ H @ I ) @ J ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I8_J_0) ).
thf(1370,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCall @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ H @ I ) @ J ) @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(452,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1560,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
inference(polarity_switch,[status(thm)],[892]) ).
thf(894,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
inference(lifteq,[status(thm)],[893]) ).
thf(224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(1042,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(916,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ A @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_0) ).
thf(1365,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ A @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
thf(879,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(73,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Ovimage @ B @ ( c_Set_Ovimage @ A @ F @ C @ D ) @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__compose_0) ).
thf(665,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Ovimage @ B @ ( c_Set_Ovimage @ A @ F @ C @ D ) @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(484,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
thf(1634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(332,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OSemi @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ D @ I ) @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).
thf(1291,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OSemi @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ D @ I ) @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(polarity_switch,[status(thm)],[1104]) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(lifteq,[status(thm)],[1105]) ).
thf(2412,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
!= ( hBOOL @ ( hAPP @ v_ba @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[501,2096]) ).
thf(2413,plain,
( ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) )
!= ( hAPP @ v_ba @ v_s0 ) ),
inference(simp,[status(thm)],[2412]) ).
thf(2463,plain,
( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
!= ( hAPP @ v_ba @ v_s0 ) )
| ( ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1324,2413]) ).
thf(2464,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
!= ( hAPP @ v_ba @ v_s0 ) ),
inference(pattern_uni,[status(thm)],[2463:[]]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(847,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(471,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1602,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCall @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).
thf(852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCall @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(450,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
| ~ ( c_Natural_Oevaln @ C @ D @ E @ F )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).
thf(1555,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
| ~ ( c_Natural_Oevaln @ C @ D @ E @ F )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(241,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(1079,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(10,negated_conjecture,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(499,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(527,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(cnf,[status(esa)],[499]) ).
thf(528,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= v_ca )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(lifteq,[status(thm)],[527]) ).
thf(2327,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= v_ca )
| ~ ( hBOOL @ ( hAPP @ v_ba @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(rewrite,[status(thm)],[528,531,522]) ).
thf(458,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ B @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).
thf(1573,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ B @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(199,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
thf(974,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1402,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(359,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(1350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I22_J_0) ).
thf(1096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I30_J_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(742,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(322,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(1270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ballE_0) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(980,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(464,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_7) ).
thf(1587,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(455,axiom,
! [B: $i,A: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(1567,plain,
! [B: $i,A: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(496,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1659,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(554,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(286,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(1182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(408,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ D )
| ( hBOOL @ ( hAPP @ E @ B ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ E @ F @ A ) @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).
thf(1461,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ D )
| ( hBOOL @ ( hAPP @ E @ B ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ E @ F @ A ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(17,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_c @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_b @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_n @ D ) ) @ v_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_16) ).
thf(506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_c @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_b @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_n @ D ) ) @ v_G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_c @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_b @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_n @ D ) ) @ v_G ) ) ),
inference(cnf,[status(esa)],[506]) ).
thf(3032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_ca @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_ba @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_n @ D ) ) @ v_G ) ) ),
inference(rewrite,[status(thm)],[533,531,522]) ).
thf(299,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1214,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(489,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP2__iff_2) ).
thf(1644,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(389,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCond @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ E @ I ) @ J ) @ K ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ J @ L ) ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I5_J_0) ).
thf(1419,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCond @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ E @ I ) @ J ) @ K ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ J @ L ) ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ K @ L ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(2460,plain,
( ( ( hAPP @ ( c_in @ t_a ) @ v_x )
!= v_ba )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) )
!= v_s0 ) ),
inference(simp,[status(thm)],[2413]) ).
thf(518,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(cnf,[status(esa)],[500]) ).
thf(519,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(lifteq,[status(thm)],[518]) ).
thf(1682,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ~ ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(rewrite,[status(thm)],[519,531,522]) ).
thf(1683,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(simp,[status(thm)],[1682]) ).
thf(161,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(884,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) )
| ~ ( c_Com_OWT @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_While_0) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) )
| ~ ( c_Com_OWT @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(219,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(1028,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(901,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(215,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(1016,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(296,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(1207,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(79,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
thf(679,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(250,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1099,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(335,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastLessThan @ A @ E @ B @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).
thf(1297,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastLessThan @ A @ E @ B @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1456,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(1192,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ofcomp @ A @ ( c_Fun_Oid @ B ) @ C @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ofcomp @ A @ ( c_Fun_Oid @ B ) @ C @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(33,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(569,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatMost @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).
thf(1627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatMost @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(56,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(622,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(647,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(1263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(1451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(102,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(738,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(203,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I33_J_0) ).
thf(984,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(377,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1393,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(503,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(605,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(310,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).
thf(1241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1515,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OAss @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OAss @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OAss @ B @ C ) ),
inference(polarity_switch,[status(thm)],[1084]) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OAss @ B @ C ) ),
inference(lifteq,[status(thm)],[1085]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(1286,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(77,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
thf(674,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(1278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(491,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(1648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(3660,plain,
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) )
!= ( hAPP @ v_P @ v_xb ) )
| ( v_x != v_s0 ) ),
inference(simp,[status(thm)],[3629]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OBODY @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OBODY @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(824,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(2050,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
!= ( hBOOL @ ( hAPP @ v_ba @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[501,1397]) ).
thf(2060,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B )
!= ( hAPP @ v_ba @ v_s0 ) ),
inference(simp,[status(thm)],[2050]) ).
thf(3385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( hAPP @ v_ba @ v_s0 ) )
| ( ( hAPP @ ( c_COMBI @ A ) @ B )
!= ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1552,2060]) ).
thf(3387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_COMBI @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ v_ba @ v_s0 )
!= C ) ),
inference(simp,[status(thm)],[3385]) ).
thf(3396,plain,
! [B: $i,A: $i] :
( ( c_COMBI @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(simp,[status(thm)],[3387]) ).
thf(483,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(618,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(337,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).
thf(1301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(468,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(169,axiom,
! [B: $i,A: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).
thf(904,plain,
! [B: $i,A: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(523,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(cnf,[status(esa)],[507]) ).
thf(524,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= v_ca )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(lifteq,[status(thm)],[523]) ).
thf(1897,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= v_ca )
| ~ ( hBOOL @ ( hAPP @ v_ba @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(rewrite,[status(thm)],[524,531,522]) ).
thf(1915,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= v_ca )
| ~ ( hBOOL @ ( hAPP @ v_ba @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) )
!= ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[502,1897]) ).
thf(1916,plain,
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= v_ca )
| ~ ( hBOOL @ ( hAPP @ v_ba @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_x @ t_a ) ),
inference(pattern_uni,[status(thm)],[1915:[bind(A,$thf( v_xb ))]]) ).
thf(260,axiom,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(1124,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1125,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
inference(polarity_switch,[status(thm)],[1124]) ).
thf(2883,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
!= ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[1554,502]) ).
thf(2895,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( ( c_Fun_Oid @ A )
!= ( hAPP @ v_P @ v_xb ) )
| ( B != v_s0 ) ),
inference(simp,[status(thm)],[2883]) ).
thf(2981,plain,
! [A: $i] :
( ( hBOOL @ v_s0 )
| ( ( c_Fun_Oid @ A )
!= ( hAPP @ v_P @ v_xb ) ) ),
inference(simp,[status(thm)],[2895]) ).
thf(478,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(1620,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Suc @ C ) @ D )
| ~ ( c_Natural_Oevaln @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(1535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Suc @ C ) @ D )
| ~ ( c_Natural_Oevaln @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C )
| ~ ( c_Com_OWT @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
thf(958,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C )
| ~ ( c_Com_OWT @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(433,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OLocal @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ I ) @ J ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).
thf(1520,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OLocal @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ I ) @ J ) @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(40,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
thf(584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(84,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(476,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).
thf(1615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D @ E )
| ~ ( c_Natural_Oevaln @ B @ F @ D @ E )
| ~ ( c_Natural_Oevaln @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(1389,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D @ E )
| ~ ( c_Natural_Oevaln @ B @ F @ D @ E )
| ~ ( c_Natural_Oevaln @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(137,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(91,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ c_Com_Ocom_OSKIP @ I )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I1_J_0) ).
thf(711,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ c_Com_Ocom_OSKIP @ I )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(426,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1503,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(516,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(cnf,[status(esa)],[511]) ).
thf(517,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(lifteq,[status(thm)],[516]) ).
thf(1668,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ~ ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(rewrite,[status(thm)],[517,531,522]) ).
thf(1669,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_na @ v_xa @ t_a ) ),
inference(simp,[status(thm)],[1668]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OWhile @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OWhile @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(309,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ D @ E @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
thf(1239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ D @ E @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(248,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(1092,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(177,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(919,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).
thf(704,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatMost @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_0) ).
thf(1638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatMost @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(63,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I43_J_0) ).
thf(641,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(394,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(787,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(92,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ c_Com_Ocom_OSKIP @ I )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).
thf(713,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ c_Com_Ocom_OSKIP @ I )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ( c_Natural_Oevalc @ D @ B @ C )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
thf(1194,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ( c_Natural_Oevalc @ D @ B @ C )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(167,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(900,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).
thf(1282,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(2408,plain,
( ~ ( hBOOL @ ( hAPP @ v_P @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
| ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
!= ( hAPP @ ( c_in @ t_a ) @ v_x ) ) ),
inference(paramod_ordered,[status(thm)],[1445,2096]) ).
thf(2415,plain,
( ~ ( hBOOL @ ( hAPP @ v_P @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
| ( ( c_COMBI @ t_a )
!= ( c_in @ t_a ) )
| ( v_x != v_P ) ),
inference(simp,[status(thm)],[2408]) ).
thf(435,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ D @ A @ C @ B @ E ) )
| ( E = B )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ A ) @ B @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_1) ).
thf(1492,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ D @ A @ C @ B @ E ) )
| ( E = B )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ A ) @ B @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(990,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(207,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D )
| ~ ( c_Natural_Oevalc @ B @ E @ D )
| ~ ( c_Natural_Oevalc @ A @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(996,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D )
| ~ ( c_Natural_Oevalc @ B @ E @ D )
| ~ ( c_Natural_Oevalc @ A @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(3,negated_conjecture,
c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) @ v_s1 @ v_na @ v_s2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(509,plain,
c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) @ v_s1 @ v_na @ v_s2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(648,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(polarity_switch,[status(thm)],[647]) ).
thf(649,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[648]) ).
thf(1776,plain,
( ( hBOOL @ v_P )
| ( ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s0 )
!= ( hAPP @ ( c_COMBI @ t_a ) @ v_P ) ) ),
inference(paramod_ordered,[status(thm)],[1445,502]) ).
thf(1801,plain,
( ( hBOOL @ v_P )
| ( ( hAPP @ v_P @ v_xb )
!= ( c_COMBI @ t_a ) )
| ( v_P != v_s0 ) ),
inference(simp,[status(thm)],[1776]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1122,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).
thf(808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( B = D ) ),
inference(cnf,[status(esa)],[808]) ).
thf(810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( B = D ) ),
inference(lifteq,[status(thm)],[809]) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( sk12 @ A @ ( c_Com_Ocom_OAss @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(c_Com_Ocom_OAss),[sk12])]) ).
thf(413,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1471,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(242,axiom,
c_Com_OWT @ c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(1080,plain,
c_Com_OWT @ c_Com_Ocom_OSKIP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(451,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1557,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Oid @ B ) @ B @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Oid @ B ) @ B @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(50,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(609,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(348,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCond @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ E @ I ) @ J ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).
thf(1325,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCond @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ E @ I ) @ J ) @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).
thf(1293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ A @ B @ C ) ),
inference(polarity_switch,[status(thm)],[930]) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[931]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1112,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(890,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1665,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 ) )
!= ( hBOOL @ ( hAPP @ v_ba @ v_s0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[501,1663]) ).
thf(1667,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( ( hAPP @ ( hAPP @ v_P @ v_xb ) @ v_s2 )
!= ( hAPP @ v_ba @ v_s0 ) ) ),
inference(simp,[status(thm)],[1665]) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(polarity_switch,[status(thm)],[913]) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[914]) ).
thf(202,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(983,plain,
class_HOL_Ominus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(437,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I32_J_0) ).
thf(780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(563,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(313,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(1250,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(2,negated_conjecture,
c_Natural_Oevaln @ v_ca @ v_s0 @ v_na @ v_s1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(505,plain,
c_Natural_Oevaln @ v_ca @ v_s0 @ v_na @ v_s1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(411,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ D @ E @ A ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ G ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UN_3) ).
thf(1467,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ D @ E @ A ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ G ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(25,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(553,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(386,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).
thf(1413,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(243,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(1081,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(106,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I27_J_0) ).
thf(749,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1018,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(141,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(836,plain,
class_Lattices_Odistrib__lattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(446,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(1547,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(27,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(557,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(149,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(855,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(275,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
thf(1156,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(1605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(314,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ D ) @ F @ D @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ G ) )
= ( hAPP @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(1252,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ D ) @ F @ D @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ G ) )
= ( hAPP @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(321,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(1267,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(438,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1531,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(991,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[990]) ).
thf(992,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[991]) ).
thf(993,plain,
! [A: $i] :
( ( sk15 @ ( c_Suc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Suc),[sk15])]) ).
thf(83,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
thf(690,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(469,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(1598,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Com_OWT @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Com_OWT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).
thf(872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(380,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).
thf(1400,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[704]) ).
thf(706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[705]) ).
thf(707,plain,
! [B: $i,A: $i] :
( ( sk6 @ A @ ( c_Com_Ocom_OAss @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(c_Com_Ocom_OAss),[sk6])]) ).
thf(306,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(1230,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(419,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(1484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(520,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(cnf,[status(esa)],[504]) ).
thf(521,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(lifteq,[status(thm)],[520]) ).
thf(1715,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(rewrite,[status(thm)],[521,531,522]) ).
thf(1716,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ v_G ) ) ),
inference(simp,[status(thm)],[1715]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(344,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1317,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(3623,plain,
( ( ( hAPP @ ( c_in @ t_a ) @ v_x )
!= ( hAPP @ v_P @ v_xb ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) )
!= v_s0 ) ),
inference(simp,[status(thm)],[2419]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I28_J_0) ).
thf(1218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(442,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(1538,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(544,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(171,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(907,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
| ~ ( c_Natural_Oevalc @ C @ D @ E )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
thf(1404,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
| ~ ( c_Natural_Oevalc @ C @ D @ E )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(744,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(444,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_5) ).
thf(1543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1778,plain,
( ( hBOOL @ v_P )
| ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
!= ( hAPP @ v_ba @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[1445,501]) ).
thf(1797,plain,
( ( hBOOL @ v_P )
| ( ( c_COMBI @ t_a )
!= v_ba )
| ( v_P != v_s0 ) ),
inference(simp,[status(thm)],[1778]) ).
thf(35,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(571,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(368,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1372,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(323,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_Natural_Oevaln @ D @ E @ F @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ B ) @ E ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ F @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ D @ A @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__def2_0) ).
thf(1272,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_Natural_Oevaln @ D @ E @ F @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ B ) @ E ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ F @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ D @ A @ t_a ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(3381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( hAPP @ v_ba @ v_s0 ) )
| ( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
!= ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1554,2060]) ).
thf(3389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Oid @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ v_ba @ v_s0 )
!= C ) ),
inference(simp,[status(thm)],[3381]) ).
thf(3398,plain,
! [B: $i,A: $i] :
( ( c_Fun_Oid @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(simp,[status(thm)],[3389]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(859,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_0) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(329,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OWhile @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ ( hAPP @ F @ I ) @ J ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ J @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I6_J_0) ).
thf(1284,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OWhile @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ ( hAPP @ F @ I ) @ J ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ J @ K ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(1353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(600,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(1052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(407,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Natural_Oevaln @ C @ B @ D @ E )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ C @ F ) @ B @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).
thf(1459,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Natural_Oevaln @ C @ B @ D @ E )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ C @ F ) @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(671,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(39,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I23_J_0) ).
thf(581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_0) ).
thf(1216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1126,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(114,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(2467,plain,
( ( ( hAPP @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) )
!= ( hAPP @ v_ba @ v_s0 ) )
| ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
!= ( hAPP @ ( c_in @ t_a ) @ v_x ) ) ),
inference(paramod_ordered,[status(thm)],[1466,2413]) ).
thf(2486,plain,
( ( v_x != v_ba )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) )
!= v_s0 )
| ( ( c_Fun_Oid @ t_a )
!= ( c_in @ t_a ) )
| ( v_x != v_x ) ),
inference(simp,[status(thm)],[2467]) ).
thf(2490,plain,
( ( v_x != v_ba )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) )
!= v_s0 )
| ( ( c_Fun_Oid @ t_a )
!= ( c_in @ t_a ) ) ),
inference(simp,[status(thm)],[2486]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OBODY @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(1189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OBODY @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(1289,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(2540,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ B @ v_s0 ) )
| ( ( hAPP @ ( c_COMBI @ A ) @ B )
!= ( hAPP @ v_P @ v_xb ) ) ),
inference(paramod_ordered,[status(thm)],[1552,502]) ).
thf(2546,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ B @ v_s0 ) )
| ( ( c_COMBI @ A )
!= v_P )
| ( B != v_xb ) ),
inference(simp,[status(thm)],[2540]) ).
thf(2643,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ v_xb @ v_s0 ) )
| ( ( c_COMBI @ A )
!= v_P ) ),
inference(simp,[status(thm)],[2546]) ).
thf(325,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xevaln__max2__1__1 @ C @ A @ D @ B @ E @ F ) @ F )
| ~ ( c_Natural_Oevaln @ A @ B @ G @ F )
| ~ ( c_Natural_Oevaln @ C @ D @ H @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__max2_1) ).
thf(1276,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xevaln__max2__1__1 @ C @ A @ D @ B @ E @ F ) @ F )
| ~ ( c_Natural_Oevaln @ A @ B @ G @ F )
| ~ ( c_Natural_Oevaln @ C @ D @ H @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(490,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_6) ).
thf(1646,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(588,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(194,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(961,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ A @ C ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_1) ).
thf(1341,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ A @ C ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(232,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1062,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(536,plain,
! [A: $i] :
( ( v_ca
!= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(cnf,[status(esa)],[503]) ).
thf(537,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_b @ v_c )
!= v_ca )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(lifteq,[status(thm)],[536]) ).
thf(3501,plain,
! [A: $i] :
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
!= v_ca )
| ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ v_s0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_x ) @ v_G ) ) ),
inference(rewrite,[status(thm)],[537,531,522]) ).
thf(311,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(1244,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(32,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(568,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_c @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_b @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ D @ ( v_n @ D ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_17) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_c @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_b @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ D @ ( v_n @ D ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(667,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(399,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ D )
| ~ ( c_lessequals @ E @ C @ tc_nat )
| ~ ( c_Natural_Oevaln @ A @ B @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__nonstrict_0) ).
thf(1440,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ D )
| ~ ( c_lessequals @ E @ C @ tc_nat )
| ~ ( c_Natural_Oevaln @ A @ B @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(340,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ E @ A @ F @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).
thf(1308,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ E @ A @ F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(111,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).
thf(763,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
thf(1513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1886,plain,
( ( hBOOL @ v_x )
| ( v_s2 != v_s0 )
| ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
!= ( hAPP @ v_ba @ v_s2 ) ) ),
inference(paramod_ordered,[status(thm)],[1466,1714]) ).
thf(1893,plain,
( ( hBOOL @ v_x )
| ( v_s2 != v_s0 )
| ( ( c_Fun_Oid @ t_a )
!= v_ba )
| ( v_x != v_s2 ) ),
inference(simp,[status(thm)],[1886]) ).
thf(2510,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( v_s2 != v_s0 )
| ( ( hAPP @ ( c_COMBI @ A ) @ B )
!= ( hAPP @ v_ba @ v_s2 ) ) ),
inference(paramod_ordered,[status(thm)],[1552,1714]) ).
thf(2582,plain,
! [B: $i,A: $i] :
( ( hBOOL @ B )
| ( v_s2 != v_s0 )
| ( ( c_COMBI @ A )
!= v_ba )
| ( B != v_s2 ) ),
inference(simp,[status(thm)],[2510]) ).
thf(2623,plain,
! [A: $i] :
( ( hBOOL @ v_s2 )
| ( v_s2 != v_s0 )
| ( ( c_COMBI @ A )
!= v_ba ) ),
inference(simp,[status(thm)],[2582]) ).
thf(225,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Fun_Ofcomp @ A @ ( c_Fun_Ofcomp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
thf(1045,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Fun_Ofcomp @ A @ ( c_Fun_Ofcomp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(23,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(549,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(400,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1442,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCond @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCond @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(327,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_2) ).
thf(1280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(460,axiom,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1578,plain,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(140,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(833,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(480,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ A @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ G ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UN_4) ).
thf(1625,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ A @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ G ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
!= ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
!= ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(154,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(867,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Natural_Oevalc @ C @ B @ D )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ C @ E ) @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
thf(1480,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Natural_Oevalc @ C @ B @ D )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ C @ E ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(603,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(488,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_4) ).
thf(1642,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(752,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(834,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(polarity_switch,[status(thm)],[833]) ).
thf(835,plain,
! [A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[834]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ D @ A ) ) @ D ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ D @ C @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_0) ).
thf(1593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ D @ A ) ) @ D ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ D @ C @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(423,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1495,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(495,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OAss @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ B @ I ) @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I65_J_0) ).
thf(1657,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OAss @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ B @ I ) @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1287,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ A @ B ) ),
inference(polarity_switch,[status(thm)],[1286]) ).
thf(1288,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[1287]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(696,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I9_J_0) ).
thf(955,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ A @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ D @ A ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ D @ C @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_1) ).
thf(1610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ A @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ D @ A ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ D @ C @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(1313,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OWhile @ B @ C ) ),
inference(polarity_switch,[status(thm)],[1312]) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OWhile @ B @ C ) ),
inference(lifteq,[status(thm)],[1313]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OBODY @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).
thf(1172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OBODY @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(166,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
thf(897,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(193,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(960,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1473,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(885,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(polarity_switch,[status(thm)],[884]) ).
thf(886,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(lifteq,[status(thm)],[885]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(839,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
thf(728,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I24_J_0) ).
thf(987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(318,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OLocal @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ C @ I ) @ J ) @ K ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I3_J_0) ).
thf(1261,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OLocal @ I @ J @ K ) @ L )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ C @ I ) @ J ) @ K ) @ ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ K @ L ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__id_0) ).
thf(1152,plain,
! [B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(462,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1582,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(64,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(362,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OWhile @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ F @ I ) @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).
thf(1357,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OWhile @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ F @ I ) @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(172,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(908,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(336,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OAss @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ B @ I ) @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I2_J_0) ).
thf(1299,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_Ocom__rec @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OAss @ I @ J ) @ K )
= ( hAPP @ ( hAPP @ B @ I ) @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(3380,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= v_ba )
| ( B != v_s0 ) ),
inference(simp,[status(thm)],[2060]) ).
thf(3394,plain,
! [A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= v_ba ),
inference(simp,[status(thm)],[3380]) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(polarity_switch,[status(thm)],[869]) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(lifteq,[status(thm)],[870]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(2406,plain,
( ~ ( hBOOL @ ( hAPP @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
| ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
!= ( hAPP @ ( c_in @ t_a ) @ v_x ) ) ),
inference(paramod_ordered,[status(thm)],[1466,2096]) ).
thf(2420,plain,
( ~ ( hBOOL @ ( hAPP @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
| ( ( c_Fun_Oid @ t_a )
!= ( c_in @ t_a ) )
| ( v_x != v_x ) ),
inference(simp,[status(thm)],[2406]) ).
thf(2430,plain,
( ~ ( hBOOL @ ( hAPP @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
| ( ( c_Fun_Oid @ t_a )
!= ( c_in @ t_a ) ) ),
inference(simp,[status(thm)],[2420]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(371,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
| ~ ( c_Natural_Oevaln @ B @ D @ E @ F )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).
thf(1378,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
| ~ ( c_Natural_Oevaln @ B @ D @ E @ F )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(351,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1331,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1841,plain,
( ( hBOOL @ v_x )
| ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
!= ( hAPP @ v_ba @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[1466,501]) ).
thf(1848,plain,
( ( hBOOL @ v_x )
| ( ( c_Fun_Oid @ t_a )
!= v_ba )
| ( v_x != v_s0 ) ),
inference(simp,[status(thm)],[1841]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( c_Set_Oinsert @ ( hAPP @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( c_Set_Oinsert @ ( hAPP @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(639,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(236,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(1069,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_c @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_b @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ D @ ( v_n @ D ) @ t_a ) ),
inference(cnf,[status(esa)],[510]) ).
thf(2655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ B ) )
| ~ ( c_Natural_Oevaln @ v_ca @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ v_ba @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_P @ A ) @ C ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ D @ ( v_n @ D ) @ t_a ) ),
inference(rewrite,[status(thm)],[532,531,522]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_0) ).
thf(1653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ A @ B @ C @ D @ E ) @ C @ E )
| ( E = D )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ D @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_2) ).
thf(1367,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ ( c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 @ A @ B @ C @ D @ E ) @ C @ E )
| ( E = D )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ D @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(185,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).
thf(940,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(935,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ C @ D @ A )
| ~ ( c_Natural_Oevalc @ C @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(1009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ C @ D @ A )
| ~ ( c_Natural_Oevalc @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
= ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
= ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(2884,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ B @ v_s0 ) )
| ( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
!= ( hAPP @ v_P @ v_xb ) ) ),
inference(paramod_ordered,[status(thm)],[1554,502]) ).
thf(2909,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ B @ v_s0 ) )
| ( ( c_Fun_Oid @ A )
!= v_P )
| ( B != v_xb ) ),
inference(simp,[status(thm)],[2884]) ).
thf(2993,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ v_xb @ v_s0 ) )
| ( ( c_Fun_Oid @ A )
!= v_P ) ),
inference(simp,[status(thm)],[2909]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ A @ B @ t_a @ C @ D ) @ v_x )
= ( hAPP @ B @ ( hAPP @ A @ v_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__def_0) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ A @ B @ t_a @ C @ D ) @ v_x )
= ( hAPP @ B @ ( hAPP @ A @ v_x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1014,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ C )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).
thf(1417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ C )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(101788,plain,
$false,
inference(cvc4,[status(thm)],[892,1501,629,1454,1237,909,1315,777,1295,1549,1024,1469,1168,760,1554,1110,1855,977,1005,1406,683,730,1522,1618,994,1422,1591,511,1533,677,1437,1608,1655,1137,1310,550,797,715,1233,698,1640,945,1063,538,930,1078,1788,1426,1867,500,814,1327,747,913,829,1196,3629,1001,2972,1391,841,1359,1386,1475,565,1518,1265,1228,1623,1482,3263,570,1985,719,785,504,1323,1511,702,1059,1132,1545,638,1087,1147,1247,1319,1479,1347,1115,1568,2989,1398,881,1489,924,1465,756,1714,789,591,1040,514,1383,1581,905,766,1377,877,734,1072,774,1526,660,998,1433,1201,1600,507,1104,849,1651,1074,512,529,2646,1306,761,1338,2641,1067,1636,546,793,1047,798,1163,1274,1343,1021,1355,1255,862,1570,598,820,1487,630,1370,1560,1223,894,1042,952,561,1666,916,1365,879,1178,665,522,1159,1210,757,1128,1634,1291,1012,1106,2464,847,1032,1602,852,1555,1079,2327,1573,974,1402,1350,1143,650,1375,725,1096,1540,593,869,499,1397,742,578,1270,1259,980,1498,1587,783,1118,1567,1659,933,554,1182,1461,669,1424,1584,3032,1214,1446,1644,1419,2460,1683,884,1329,1028,1082,901,686,2419,1016,1207,1612,679,1324,1099,1297,1456,654,1552,1192,1050,569,1627,622,837,647,1263,515,1150,1451,738,984,911,1393,503,605,1333,1241,633,805,508,541,1054,1170,558,1663,1515,1086,938,1286,1035,1187,674,1278,1648,3660,965,513,824,856,3396,1631,618,2413,1301,1595,904,1916,1125,2981,1620,1535,958,1520,1124,1226,584,1154,1007,694,1615,1389,875,826,711,1503,1669,572,1312,1107,1239,1092,1090,919,704,947,1638,641,1428,611,787,713,498,1194,900,831,1408,1282,2415,1524,736,1492,1175,1589,990,996,509,649,1801,616,1122,811,1471,1080,1557,816,609,700,1325,895,1344,943,1293,932,1112,890,1667,626,915,983,768,636,1528,780,563,1435,1477,1250,1102,505,922,658,1562,1198,1396,2096,531,1467,663,1134,812,754,553,968,1413,1076,1081,749,1145,1018,836,1551,1547,557,855,1156,887,971,1605,1252,1267,1531,993,690,1598,1070,872,2060,1400,707,1230,1484,1716,791,717,502,1317,3623,1130,1218,1336,1538,808,544,907,1404,744,1543,1257,656,613,864,1140,1797,571,1372,1272,3398,859,1221,1284,1353,600,1052,1506,845,1421,1084,1459,1180,1553,671,1321,688,581,1216,1126,1575,771,2490,1189,1289,2643,1276,1646,588,961,963,1341,652,1629,1062,1508,3501,1244,568,510,667,1440,1308,1212,763,1513,1661,1893,2623,1045,549,1444,1442,1161,800,620,1280,1578,833,1625,818,1303,1148,867,1480,603,1642,752,950,835,1593,1380,1495,1657,506,1056,1288,1065,696,1165,955,1610,1363,1314,1172,897,1410,960,1473,886,928,839,728,987,1261,1152,1537,1582,644,1357,908,723,822,1431,1299,3394,871,1120,501,607,2430,575,596,1378,1331,803,1184,1848,1037,1416,639,1069,708,2655,1653,1367,940,935,1009,1463,1565,2993,1204,1449,1014,1417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV849-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 02:42:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.10 % [INFO] Parsing done (229ms).
% 1.71/1.11 % [INFO] Running in sequential loop mode.
% 2.30/1.32 % [INFO] eprover registered as external prover.
% 2.30/1.32 % [INFO] cvc4 registered as external prover.
% 2.30/1.32 % [INFO] Scanning for conjecture ...
% 2.52/1.45 % [INFO] Found a conjecture and 489 axioms. Running axiom selection ...
% 3.04/1.58 % [INFO] Axiom selection finished. Selected 479 axioms (removed 10 axioms).
% 3.41/1.69 % [INFO] Problem is propositional (TPTP CNF).
% 3.68/1.70 % [INFO] Type checking passed.
% 3.68/1.71 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 257.37/56.18 % External prover 'cvc4' found a proof!
% 257.37/56.18 % [INFO] Killing All external provers ...
% 257.37/56.19 % Time passed: 55680ms (effective reasoning time: 55071ms)
% 257.37/56.26 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 257.37/56.26 % Axioms used in derivation (479): cls_inf__sup__absorb_0, cls_inf__sup__aci_I2_J_0, cls_com_Osimps_I18_J_0, cls_evaln_OWhileFalse_0, cls_Diff__iff_2, cls_bot__fun__eq_0, cls_evaln__max2_1, cls_WTs__elim__cases_I6_J_0, cls_vimage__code_0, cls_com_Osimps_I1_J_0, cls_Int__Un__distrib_0, cls_com_Osimps_I55_J_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_sup__ge1_0, cls_insertE_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_Suc__inject_0, cls_com_Osimps_I5_J_0, cls_ball__conj__distrib_3, cls_insert__inter__insert_0, cls_com_Osimps_I32_J_0, cls_eq__imp__le_0, cls_COMBC__def_0, cls_Suc__n__not__n_0, cls_empty__is__image_1, cls_com_Osimps_I44_J_0, cls_com_Osimps_I14_J_0, cls_Un__empty__left_0, clsarity_nat__Lattices_Odistrib__lattice, cls_hoare__valids__def_2, cls_id__o_0, cls_sup__bot__right_0, cls_insert__code_1, cls_WT_OSemi_0, clsarity_bool__Lattices_Olower__semilattice, cls_distrib__sup__le_0, cls_le__SUPI_0, cls_inf__sup__aci_I6_J_0, cls_Un__commute_0, cls_ord_OgreaterThan__iff_0, cls_UnCI_1, cls_vimage__Diff_0, cls_WTs__elim__cases_I4_J_1, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_evaln__WHILE__case_0, cls_triple_Oinject_1, cls_evalc_OSemi_0, cls_empty__iff_0, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_o__eq__id__dest_0, cls_mem__def_1, cls_bexE_1, clsarity_nat__Orderings_Olinorder, cls_com_Osimps_I56_J_0, cls_WT_OSkip_0, cls_com_Osimps_I31_J_0, cls_Int__Un__distrib2_0, cls_inf1E_1, cls_com_Osimps_I7_J_1, cls_com_Osimps_I5_J_1, cls_Diff__triv_0, cls_evalc__WHILE__case_0, cls_COMBI__def__raw_0, cls_bex__UN_3, cls_inf__sup__distrib1_0, cls_triples__valid__Suc_1, cls_sup__inf__distrib2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_com_Osimps_I4_J_2, cls_le__sup__iff_0, cls_ballE_0, cls_com_Osimps_I66_J_0, cls_com_Osimps_I43_J_0, cls_insert__iff_1, cls_Diff__insert_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_pred__equals__eq_0, cls_ord_OatLeastAtMost__iff_2, cls_WTs__elim__cases_I5_J_0, cls_Un__left__commute_0, cls_com_Osimps_I54_J_0, cls_evaln_OSkip_0, cls_com_Orecs_I6_J_0, cls_inf__commute_0, cls_com_Osimps_I47_J_0, cls_vimage__compose_0, cls_evalc__elim__cases_I1_J_0, cls_Un__Int__distrib2_0, cls_Int__empty__right_0, cls_Suc__le__mono_0, cls_com_Osimps_I45_J_0, cls_vimage__insert_0, cls_inf__fun__eq_0, cls_UN__extend__simps_I1_J_0, cls_evaln__elim__cases_I5_J_1, cls_Un__empty_2, cls_le__iff__sup_1, cls_le__antisym_0, cls_le__supI_0, cls_empty__is__image_0, cls_ord_OatLeastLessThan__iff_0, cls_rev__image__eqI_0, cls_SUP1__I_0, cls_triple_Oinject_2, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_ball__conj__distrib_1, cls_com_Osimps_I26_J_0, cls_UN__iff_2, cls_le__iff__sup_0, cls_WTs__elim__cases_I4_J_0, cls_image__id_0, cls_vimageI_0, cls_triple__valid__Suc_0, cls_id__apply_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_com_Osimps_I61_J_0, cls_vimage__id_0, cls_com_Orecs_I7_J_0, cls_com_Osimps_I48_J_0, cls_sup__eq__bot__eq2_0, cls_com_Osimps_I37_J_0, cls_com_Osimps_I10_J_0, cls_Int__insert__right_1, cls_com_Osimps_I65_J_0, cls_UN__Un_0, cls_com_Osimps_I38_J_0, cls_vimage__ident_0, cls_com_Osimps_I60_J_0, cls_evalc_OWhileFalse_0, cls_com_Osimps_I6_J_0, cls_com_Orecs_I1_J_0, cls_UnCI_0, cls_com_Osimps_I23_J_0, cls_evaln__WHILE__case_1, cls_bexI_1, cls_singleton__iff_1, cls_com_Osimps_I20_J_0, cls_complete__lattice_OInf__empty_0, cls_insert__code_2, cls_bex__Un_6, cls_com_Osimps_I58_J_0, cls_evalc_OSkip_0, cls_Diff__idemp_0, cls_not__less__eq__eq_1, cls_com_Osimps_I40_J_0, cls_com_Osimps_I21_J_0, cls_WTs__elim__cases_I8_J_0, cls_insert__Diff__single_0, cls_com_Osimps_I57_J_0, cls_image__insert_0, cls_evalc__elim__cases_I5_J_0, cls_com_Osimps_I64_J_0, cls_vimage__Un_0, cls_com_Osimps_I51_J_0, cls_SUP1__iff_2, cls_inf__absorb2_0, cls_ball__conj__distrib_0, clsarity_bool__Lattices_Oupper__semilattice, cls_WT_OCall_0, cls_com_Osimps_I7_J_0, cls_bex__UN_4, cls_ord_OlessThan__iff_0, cls_doubleton__eq__iff_2, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_com_Osimps_I59_J_0, cls_vimage__singleton__eq_1, clsarity_nat__Orderings_Obot, cls_bex__Un_5, cls_com__det_0, cls_id__fcomp_0, cls_inf__sup__aci_I3_J_0, cls_Int__insert__left_1, cls_evaln__nonstrict_0, cls_Int__empty__left_0, cls_com_Osimps_I50_J_0, cls_le__inf__iff_0, clsarity_nat__Lattices_Olower__semilattice, cls_evaln_OSemi_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_evaln__WHILE__case_4, cls_com_Osimps_I69_J_0, cls_com_Osimps_I30_J_0, cls_evaln__elim__cases_I5_J_0, cls_com_Orecs_I5_J_0, cls_le__SucE_0, cls_Suc__le__mono_1, cls_linorder__linear_0, cls_Un__empty_0, cls_bex__Un_7, clsarity_fun__Lattices_Olattice, cls_Int__assoc_0, cls_evaln__max2_0, cls_bexE_0, cls_com_Osimps_I2_J_0, cls_ord_OatLeastAtMost__iff_1, cls_image__empty_0, cls_sup__Un__eq_0, cls_com_Osimps_I68_J_0, cls_evaln_OIfFalse_0, cls_com_Osimps_I3_J_1, cls_com_Osimps_I46_J_0, cls_insert__is__Un_0, cls_com_Osimps_I19_J_0, cls_order__trans_0, cls_com_Osimps_I27_J_0, cls_com_Osimps_I8_J_0, cls_inf__le2_0, cls_insertI1_0, cls_DiffI_0, cls_evaln_OWhileTrue_0, cls_com_Osimps_I29_J_0, cls_com_Osimps_I9_J_0, cls_le__supE_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_Diff__Int__distrib2_0, cls_com_Osimps_I67_J_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_Diff__insert2_0, cls_Int__commute_0, cls_sup__least_0, cls_WTs__elim__cases_I5_J_1, cls_com_Orecs_I8_J_0, cls_le__trans_0, cls_com_Osimps_I17_J_0, cls_com_Osimps_I70_J_0, cls_evaln__WHILE__case_2, cls_image__ident_0, cls_ord_OatLeastLessThan__iff_1, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_WTs__elim__cases_I3_J_0, cls_singletonE_0, clsarity_nat__Orderings_Opreorder, cls_com_Osimps_I25_J_0, clsarity_nat__Lattices_Olattice, cls_DiffE_0, cls_Int__Diff_0, cls_image__iff_2, cls_insertCI_0, cls_le__infE_0, cls_SUP2__iff_2, cls_complete__lattice_OSup__binary_0, cls_le__inf__iff_2, cls_Un__Diff__cancel_0, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_ord_OlessThan__iff_1, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_com_Osimps_I34_J_0, cls_vimage__Int_0, cls_le__infI1_0, cls_bot1E_0, cls_Int__absorb_0, cls_inf__assoc_0, cls_evalc_OWhileTrue_0, cls_eval__eq_1, cls_le__supI2_0, cls_Un__Diff__cancel2_0, cls_o__eq__dest_0, cls_Un__assoc_0, cls_bexI_0, cls_bex__empty_0, cls_UnE_0, cls_Int__left__absorb_0, cls_Diff__disjoint_0, cls_inf__sup__ord_I4_J_0, cls_fcomp__id_0, cls_com_Osimps_I28_J_0, cls_o__eq__dest__lhs_0, cls_complete__lattice_Odual__complete__lattice_0, cls_nat_Oinject_0, cls_com_Osimps_I2_J_1, cls_id__def_0, cls_doubleton__eq__iff_3, cls_Diff__Int__distrib_0, cls_com_Osimps_I42_J_0, cls_com_Osimps_I13_J_0, cls_Un__absorb_0, cls_ord_OatLeastAtMost__iff_0, cls_SUP2__I_0, clsarity_bool__Lattices_Olattice, cls_vimage__eq_1, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_hoare__valids__def_1, cls_com_Osimps_I49_J_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_evaln__Suc_0, cls_Un__Int__distrib_0, cls_com_Osimps_I12_J_0, cls_com_Osimps_I35_J_0, cls_le__supI1_0, cls_le__eqI_0, cls_WT_OIf_0, cls_sup__left__idem_0, cls_complete__lattice_OSup__insert_0, cls_o__id_0, cls_rev__bexI_0, cls_insert__not__empty_0, cls_inf__idem_0, clsarity_fun__Lattices_Obounded__lattice, cls_complete__lattice_OInf__lower_0, cls_vimageE_0, cls_inf__bot__left_0, cls_com_Osimps_I36_J_0, cls_inf1I_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_o__def_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_insert__absorb2_0, cls_sup__fun__eq_0, cls_UNION__empty__conv_I1_J_0, cls_inf__sup__aci_I4_J_0, cls_sup__inf__absorb_0, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_fun__diff__def_0, cls_inf__Int__eq_0, cls_vimage__singleton__eq_0, cls_com_Osimps_I52_J_0, cls_Int__iff_2, cls_vimage__code_1, cls_UN__I_0, cls_complete__lattice_OInf__singleton_0, cls_inf__greatest_0, cls_nat__le__linear_0, cls_le__Suc__eq_2, cls_com_Osimps_I1_J_1, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_Un__left__absorb_0, cls_IntI_0, cls_evaln__evalc_0, cls_evalc__elim__cases_I5_J_2, cls_inf__sup__ord_I3_J_0, cls_inf__sup__aci_I5_J_0, cls_Diff__Int_0, cls_evaln__WHILE__case_3, cls_ord_OatLeastLessThan__iff_2, cls_triple_Oinject_0, cls_Un__empty_1, cls_comp__cong_0, cls_le__iff__inf_0, cls_sup__idem_0, cls_evaln_OIfTrue_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_eq__eqI_1, cls_com_Osimps_I4_J_1, cls_evaln__elim__cases_I1_J_0, cls_Suc__n__not__le__n_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_singleton__inject_0, cls_bex__Un_4, cls_Suc__leD_0, cls_vimageI2_0, cls_sup__ge2_0, clsarity_fun__Orderings_Opreorder, cls_IntE_0, cls_sup1CI_0, cls_sup__left__commute_0, cls_n__not__Suc__n_0, cls_IntE_1, clsarity_bool__Lattices_Odistrib__lattice, cls_com_Osimps_I41_J_0, cls_le__infE_1, cls_com_Orecs_I2_J_0, cls_image__eqI_0, cls_fcomp__apply_0, cls_inf__le1_0, cls_insertCI_1, cls_inf__left__idem_0, cls_complete__lattice_OSup__upper_0, cls_com_Osimps_I22_J_0, cls_doubleton__eq__iff_4, cls_ord_OatMost__iff_0, cls_rev__bexI_1, cls_insert__code_0, cls_le__eqI_1, cls_Un__Diff__Int_0, cls_vimageD_0, cls_WT_OAssign_0, cls_fcomp__def_0, cls_DiffE_1, cls_complete__lattice_OSup__empty_0, cls_evalc_OIfFalse_0, cls_Diff__Int2_0, cls_Diff__insert__absorb_0, cls_evaln__elim__cases_I5_J_2, cls_disjoint__iff__not__equal_0, cls_ord_OatMost__iff_1, cls_com_Orecs_I3_J_0, cls_sup__inf__distrib1_0, cls_fcomp__assoc_0, cls_com_Osimps_I15_J_0, cls_vimage__empty_0, cls_COMBI__def_0, cls_insert__commute_0, cls_insert__iff_2, cls_le__infI2_0, cls_UNION__empty__conv_I2_J_0, cls_sup__bot__left_0, cls_ord_OgreaterThan__iff_1, cls_hoare__valids__def_0, cls_insert__image_0, cls_evalc__elim__cases_I5_J_1, cls_com_Osimps_I16_J_0, cls_image__compose_0, cls_image__is__empty_0, cls_com_Osimps_I2_J_2, cls_com_Osimps_I63_J_0, cls_com_Osimps_I11_J_0, clsarity_fun__Lattices_Odistrib__lattice, clsarity_fun__HOL_Ominus, cls_triple__valid__def2_0, cls_com_Osimps_I53_J_0, cls_com_Osimps_I39_J_0, cls_UN__insert_0, cls_com_Osimps_I33_J_0, cls_Un__insert__right_0, cls_ballE_1, cls_inf__sup__distrib2_0, cls_com_Osimps_I24_J_0, cls_imageI_0, cls_WT_OLocal_0, cls_com_Osimps_I4_J_0, cls_evalc_OIfTrue_0, cls_o__apply_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_le__SucI_0, cls_not__less__eq__eq_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_ball__conj__distrib_2, cls_com_Orecs_I4_J_0, cls_inf1E_0, cls_empty__Diff_0, cls_o__assoc_0, cls_com_Osimps_I71_J_0, cls_le__refl_0, cls_triples__valid__Suc_0, cls_com_Osimps_I62_J_0, cls_While_0, clsarity_nat__HOL_Ominus, cls_com_Osimps_I7_J_2
% 257.37/56.26 % No. of inferences in proof: 1159
% 257.37/56.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 55680 ms resp. 55071 ms w/o parsing
% 258.22/56.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 258.22/56.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------