%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV848-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:47 AM UTC 2026
% Result : Unsatisfiable 13.58s 4.41s
% Output : Refutation 14.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 434
% Syntax : Number of formulae : 869 ( 353 unt; 0 typ; 0 def)
% Number of atoms : 1617 ( 582 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 11176 ( 820 ~; 748 |; 0 &;9608 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 67 usr; 12 con; 0-10 aty)
% Number of variables : 3540 ( 0 ^;3540 !; 0 ?;3540 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(v_P_decl,type,
v_P: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_sa_decl,type,
v_sa: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_decl,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(v_na_decl,type,
v_na: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_in_decl,type,
c_in: $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_decl,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(v_nb_decl,type,
v_nb: $i > $i ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Com_Ocom_OLocal_decl,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(c_Com_Ocom_OAss_decl,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Com_Ocom_OCall_decl,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Set_Ovimage_decl,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_OCond_decl,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Com_OWT_decl,type,
c_Com_OWT: $i > $o ).
thf(c_Com_Ocom_OBODY_decl,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(c_Fun_Ofcomp_decl,type,
c_Fun_Ofcomp: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice_decl,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Natural_Oevalc_decl,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(c_Com_Ocom_Ocom__rec_decl,type,
c_Com_Ocom_Ocom__rec: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1_decl,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_decl,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: $i > $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevaln__max2__1__1_decl,type,
c_Natural_Osko__Natural__Xevaln__max2__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_Ocom__case_decl,type,
c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_decl,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_decl,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1_decl,type,
v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1_decl,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__valids_decl,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__2: $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_decl,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3_decl,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__1_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__1: $i > $i > $i ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(809,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1411,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E = D )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_2) ).
thf(1190,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E = D )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( C @ ( A @ ( D @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_3) ).
thf(1454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( C @ ( A @ ( D @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(23,axiom,
tc_nat @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(479,plain,
tc_nat @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(180,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(893,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(303,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( F @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).
thf(1179,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( F @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(354,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( B @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
thf(1295,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( B @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(273,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I2_J_0) ).
thf(1110,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(429,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_0) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(909,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(628,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(137,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(777,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(51,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Ovimage ) ) ) )
= ( C @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Ovimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__compose_0) ).
thf(555,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Ovimage ) ) ) )
= ( C @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Ovimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(311,axiom,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1200,plain,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(216,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(977,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(316,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(1211,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(400,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(1401,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(287,axiom,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1142,plain,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(4,negated_conjecture,
( ~ ( v_sa @ ( v_x @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL )
| ( v_sa @ ( v_b @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(440,plain,
( ~ ( v_sa @ ( v_x @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL )
| ( v_sa @ ( v_b @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).
thf(1437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(861,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).
thf(741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(256,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(1073,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(258,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(1078,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(373,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).
thf(1342,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(379,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(1354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(424,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_4) ).
thf(1458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(91,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(670,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(829,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(182,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
thf(898,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
thf(1243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(163,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I33_J_0) ).
thf(841,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_5) ).
thf(1359,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(432,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1475,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(1366,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(1,negated_conjecture,
( c_Com_Ocom_OSKIP
= ( v_c @ ( v_b @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(436,plain,
( c_Com_Ocom_OSKIP
= ( v_c @ ( v_b @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(178,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(885,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(246,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(1046,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(412,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1430,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(719,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(785,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(403,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_7) ).
thf(1409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).
thf(724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(587,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
thf(619,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(838,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(426,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_6) ).
thf(1462,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(250,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(1059,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).
thf(1479,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(213,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(770,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( D @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_0) ).
thf(1415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( D @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(28,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
thf(492,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(591,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(388,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1373,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(284,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I1_J_0) ).
thf(1136,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(155,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(821,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(357,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(1302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(235,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( D @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
thf(1020,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( D @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).
thf(634,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(998,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(312,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( B @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).
thf(1201,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( B @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(507,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(42,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(527,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(69,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(602,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(131,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
thf(766,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).
thf(877,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(277,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ ( A @ ( E @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).
thf(1119,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ ( A @ ( E @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(774,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(192,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(920,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(678,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(661,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(925,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(253,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I3_J_0) ).
thf(1067,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_1) ).
thf(1163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(452,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( v_G @ ( A @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(439,plain,
! [A: $i] :
( ~ ( v_G @ ( A @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).
thf(1223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(138,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(778,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(54,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
thf(561,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).
thf(1238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(788,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(386,axiom,
c_Com_Ocom_OSKIP @ c_Com_OWT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(1370,plain,
c_Com_Ocom_OSKIP @ c_Com_OWT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCall ) ) @ c_Com_OWT )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
thf(916,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCall ) ) @ c_Com_OWT )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(90,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
thf(665,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(13,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(461,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(309,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(396,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).
thf(1392,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(847,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(56,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
thf(566,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(5,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_G @ ( D @ v_nb @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( v_b @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ ( v_c @ c_Natural_Oevaln ) ) ) )
| ( B @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_G @ ( D @ v_nb @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( v_b @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ ( v_c @ c_Natural_Oevaln ) ) ) )
| ( B @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(259,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( A @ ( D @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( F @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( E @ ( B @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__def2_0) ).
thf(1079,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( A @ ( D @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( F @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( E @ ( B @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(1027,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(352,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1291,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(326,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).
thf(1234,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(1270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
thf(1328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(278,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).
thf(1121,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(323,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
thf(1227,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Ovimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__id_0) ).
thf(980,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Ovimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(1096,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(285,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).
thf(1138,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(398,axiom,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1397,plain,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(471,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Oimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(933,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Oimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(126,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(753,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(410,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(27,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I23_J_0) ).
thf(489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(317,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
thf(1214,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(243,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I28_J_0) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
thf(901,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(20,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(476,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
!= ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1114,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
!= ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(340,axiom,
( ( v_P @ ( t_a @ c_COMBI @ hAPP ) )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1263,plain,
( ( v_P @ ( t_a @ c_COMBI @ hAPP ) )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(1099,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I30_J_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(423,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(1456,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1231,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(11,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(457,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(220,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
thf(984,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(291,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1150,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(334,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( H @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( F @ ( G @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ( E @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__max2__1__1 ) ) ) ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__max2_0) ).
thf(1249,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( H @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( F @ ( G @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ( E @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__max2__1__1 ) ) ) ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(282,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1131,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I32_J_0) ).
thf(654,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
thf(1318,plain,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_Com_OWT )
| ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(921,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_Com_OWT )
| ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
thf(657,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(248,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
thf(1054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_4) ).
thf(1071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(134,axiom,
! [B: $i,A: $i] : ( B @ ( A @ c_Com_Ocom_OAss ) @ c_Com_OWT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).
thf(773,plain,
! [B: $i,A: $i] : ( B @ ( A @ c_Com_Ocom_OAss ) @ c_Com_OWT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(350,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1286,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( C @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_2) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( C @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(289,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( E @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).
thf(1146,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( E @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(319,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1219,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(975,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(694,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(395,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(1389,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(394,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(1388,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
thf(826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(958,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(337,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( tc_nat @ ( C @ ( E @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__nonstrict_0) ).
thf(1256,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( tc_nat @ ( C @ ( E @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(47,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I43_J_0) ).
thf(545,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(387,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).
thf(1371,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(361,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1312,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(1090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(148,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).
thf(804,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(338,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1258,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(427,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(1464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1356,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(315,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(1209,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).
thf(681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
thf(1117,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(119,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(736,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(376,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1349,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(288,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).
thf(1144,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(1376,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(177,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
thf(880,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(649,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(21,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(477,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(430,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I7_J_0) ).
thf(1471,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(78,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I27_J_0) ).
thf(631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(552,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(799,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(75,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(621,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(104,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(374,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I4_J_0) ).
thf(1344,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(274,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).
thf(1112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(189,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(915,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(132,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(769,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(425,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP2__iff_2) ).
thf(1460,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(780,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(1015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).
thf(1000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OWhile ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
thf(1477,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OWhile ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(383,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(1364,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(188,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(912,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(245,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP2__I_0) ).
thf(1044,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(418,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1445,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(505,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(2,negated_conjecture,
v_sa @ ( v_x @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(438,plain,
v_sa @ ( v_x @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(358,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(1304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(428,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).
thf(1467,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(408,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(1420,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(196,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(927,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(260,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(1081,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(1049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_1) ).
thf(1413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(257,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(1076,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(313,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
thf(1203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(663,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(136,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(776,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(690,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(174,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Ovimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Ovimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1368,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(110,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
thf(712,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(557,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(322,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1225,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(107,axiom,
tc_nat @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(707,plain,
tc_nat @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ~ ( t_a @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_1) ).
thf(1432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ~ ( t_a @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(59,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
thf(576,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
thf(643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(907,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(356,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( D @ ( B @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
thf(1300,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( D @ ( B @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
thf(1452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_0) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(401,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1404,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(1427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(115,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(727,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(230,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(1008,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(72,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(612,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(497,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(349,axiom,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(1284,plain,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1353,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(266,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I6_J_0) ).
thf(1094,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(978,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(286,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).
thf(1140,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
thf(571,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(329,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( L @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I5_J_0) ).
thf(1240,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( L @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(15,axiom,
tc_nat @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(465,plain,
tc_nat @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_0) ).
thf(1084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).
thf(1157,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(318,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1216,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(1126,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I24_J_0) ).
thf(844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(272,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( B @ ( E @ ( A @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).
thf(1108,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( B @ ( E @ ( A @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(903,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(345,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( F @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).
thf(1276,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( F @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1326,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(336,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
thf(1253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(251,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).
thf(1062,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(269,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( D @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).
thf(1101,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( D @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(117,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(731,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(181,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
thf(896,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
thf(748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(239,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(1030,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1440,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(308,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I8_J_0) ).
thf(1193,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] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(22,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(478,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
thf(832,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(360,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E = B )
| ( E @ ( B @ ( C @ ( A @ ( D @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_1) ).
thf(1309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E = B )
| ( E @ ( B @ ( C @ ( A @ ( D @ c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(417,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(1442,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(1133,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(347,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( F @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( B @ ( E @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).
thf(1280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( F @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( B @ ( E @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(161,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I26_J_0) ).
thf(835,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_While_0) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_Ocom_OBODY @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_Ocom_OBODY @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
thf(918,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(1172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).
thf(1056,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1165,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1346,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(6,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( D @ v_nb @ ( D @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( v_b @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ ( v_c @ c_Natural_Oevaln ) ) ) )
| ( B @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( D @ v_nb @ ( D @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( v_b @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ ( v_c @ c_Natural_Oevaln ) ) ) )
| ( B @ ( A @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I9_J_0) ).
thf(1288,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(209,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(960,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(431,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I65_J_0) ).
thf(1473,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(532,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(252,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(1065,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(728,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(987,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(281,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).
thf(1129,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__def_0) ).
thf(1268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(390,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1378,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(156,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(822,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(364,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1320,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(200,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(935,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(543,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(242,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1037,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(676,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(263,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( H @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ~ ( F @ ( G @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( F @ ( F @ ( E @ ( B @ ( D @ ( A @ ( C @ c_Natural_Osko__Natural__Xevaln__max2__1__1 ) ) ) ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__max2_1) ).
thf(1088,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( H @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ~ ( F @ ( G @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( F @ ( F @ ( E @ ( B @ ( D @ ( A @ ( C @ c_Natural_Osko__Natural__Xevaln__max2__1__1 ) ) ) ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1449,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(469,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(201,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I22_J_0) ).
thf(940,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(254,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(1069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1482,plain,
$false,
inference(e,[status(thm)],[809,1411,1190,1454,479,1237,893,962,1179,1295,1110,1024,1469,909,628,1315,518,777,555,1200,977,1211,523,1406,1401,1422,449,1142,440,1437,861,741,1073,1078,550,500,797,814,1342,945,1354,930,1458,670,1260,698,829,898,1243,782,841,1359,1475,1366,436,1265,885,1046,1430,719,785,1330,802,1409,724,587,1323,619,838,1462,1059,559,1247,870,1479,969,1013,770,1415,492,591,1373,646,1136,514,966,821,1302,756,1383,1020,574,905,480,1169,634,1394,1351,998,1201,1242,507,527,602,766,877,692,1447,956,1119,774,920,678,661,925,761,1338,1067,1163,1206,452,512,439,1223,746,778,1042,1123,598,561,1238,788,1370,916,665,583,461,1195,1392,1106,847,566,852,435,1079,1027,1291,710,1234,874,1270,948,1328,1121,1227,980,1096,1006,1138,593,610,989,1397,471,1160,1361,933,753,537,1424,637,489,1214,1039,1155,901,686,476,1114,1263,1099,1297,738,1456,1231,457,984,721,1150,1249,1131,654,1333,1434,1318,1086,921,657,1054,1071,773,1286,1035,1278,750,1251,1146,1103,1273,856,733,1219,824,819,975,694,1389,1388,826,958,1256,545,1371,1312,1090,804,1258,1464,1356,540,466,1092,764,1209,681,1282,1117,736,1349,996,1144,1376,1307,880,649,863,1175,890,477,811,1471,631,552,816,799,621,483,700,964,1344,1293,1177,462,1112,626,915,769,1460,943,1022,1198,780,1015,1000,1477,1364,912,521,1044,1245,1445,868,505,438,1304,1166,1467,795,1420,927,1081,1340,1018,1049,1413,473,1076,1203,589,663,548,617,516,458,1181,776,525,690,640,872,705,954,1368,993,712,557,1003,1225,1400,707,673,1432,585,717,502,576,951,643,907,1300,1452,1188,1186,1404,744,703,1427,727,1008,612,497,1221,1284,1353,600,1094,978,1140,446,571,1240,991,465,1084,671,1157,581,759,1216,1126,1010,844,1108,688,903,1276,1326,1253,1385,1062,1101,731,896,748,1030,510,1440,1193,478,832,1309,1442,1133,1280,835,1229,1380,854,1148,790,865,564,918,807,1172,1056,696,1165,1346,928,437,1335,1033,1288,960,1473,532,1065,728,987,1129,1268,1152,1378,822,982,607,486,1320,935,923,659,543,1037,676,1088,1449,708,469,940,454,1069,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV848-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n009.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 15:03:44 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.35 % [INFO] Parsing done (342ms).
% 1.89/1.36 % [INFO] Running in sequential loop mode.
% 3.13/1.78 % [INFO] eprover registered as external prover.
% 3.13/1.79 % [INFO] Scanning for conjecture ...
% 3.59/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 438 axioms. Running axiom selection ...
% 4.81/2.20 % [INFO] Axiom selection finished. Selected 428 axioms (removed 10 axioms).
% 5.52/2.42 % [INFO] Problem is propositional (TPTP CNF).
% 5.52/2.44 % [INFO] Type checking passed.
% 5.52/2.44 % [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 ...
% 13.58/4.40 % External prover 'e' found a proof!
% 13.58/4.40 % [INFO] Killing All external provers ...
% 13.58/4.40 % Time passed: 3835ms (effective reasoning time: 3031ms)
% 13.58/4.40 % Axioms used in derivation (428): cls_inf__sup__absorb_0, cls_inf__sup__aci_I2_J_0, cls_com_Osimps_I18_J_0, cls_evaln_OWhileFalse_0, 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_sup__ge1_0, cls_insertE_0, cls_com_Osimps_I3_J_0, cls_Suc__inject_0, cls_com_Osimps_I5_J_0, 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_WTs__elim__cases_I4_J_1, cls_inf__sup__aci_I6_J_0, cls_Un__commute_0, cls_UnCI_1, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_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, 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_evalc__WHILE__case_0, cls_COMBI__def__raw_0, 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_inf__left__commute_0, cls_com_Osimps_I66_J_0, cls_com_Osimps_I43_J_0, cls_insert__iff_1, 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_le__supE_1, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, 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_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_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_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, clsarity_bool__Lattices_Oupper__semilattice, cls_WT_OCall_0, cls_com_Osimps_I7_J_0, 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_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_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_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_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_complete__lattice_OInf__insert_0, cls_image__Un_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_bex__empty_0, cls_o__eq__dest_0, cls_Un__assoc_0, cls_UnE_0, cls_Int__left__absorb_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_com_Osimps_I42_J_0, cls_nat_Oinject_0, cls_com_Osimps_I2_J_1, cls_id__def_0, cls_doubleton__eq__iff_3, cls_com_Osimps_I13_J_0, cls_Un__absorb_0, cls_ord_OatLeastAtMost__iff_0, cls_SUP2__I_0, clsarity_bool__Lattices_Olattice, cls_bot__empty__eq_0, 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_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_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_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_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_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_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_doubleton__eq__iff_4, cls_complete__lattice_OSup__upper_0, cls_com_Osimps_I22_J_0, cls_rev__bexI_1, cls_insert__code_0, cls_vimageD_0, cls_evalc_OIfFalse_0, cls_WT_OAssign_0, cls_fcomp__def_0, cls_complete__lattice_OSup__empty_0, cls_sup__bot__left_0, cls_evaln__elim__cases_I5_J_2, cls_disjoint__iff__not__equal_0, 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_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_Un__insert__right_0, cls_com_Osimps_I2_J_2, cls_com_Osimps_I63_J_0, cls_com_Osimps_I11_J_0, clsarity_fun__Lattices_Odistrib__lattice, 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_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_com_Orecs_I4_J_0, cls_inf1E_0, cls_com_Osimps_I7_J_2, 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
% 13.58/4.40 % No. of inferences in proof: 869
% 13.58/4.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3835 ms resp. 3031 ms w/o parsing
% 14.79/4.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.79/4.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------