%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV277-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:58:41 AM UTC 2026
% Result : Unsatisfiable 83.88s 30.24s
% Output : Refutation 85.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 201
% Syntax : Number of formulae : 1208 ( 557 unt; 0 typ; 11 def)
% Number of atoms : 2505 (1201 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 12364 (1323 ~; 858 |; 0 &;10183 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 53 usr; 11 con; 0-3 aty)
% Number of variables : 2285 ( 0 ^;2263 !; 11 ?;2285 :)
% ( 0 !>; 0 ?*; 0 @-; 11 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_X_decl,type,
v_X: $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(v_H_decl,type,
v_H: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i > $i ).
thf(v_K_decl,type,
v_K: $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_Message_OkeysFor_decl,type,
c_Message_OkeysFor: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Message_Omsg_OAgent_decl,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(c_Message_OHPair_decl,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_Message_Omsg_OMPair_decl,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Message_Omsg_OHash_decl,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Message_Omsg_ONumber_decl,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(c_Message_Omsg_OCrypt_decl,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Set_Ocontents_decl,type,
c_Set_Ocontents: $i > $i > $i ).
thf(v_sko__uhi_decl,type,
v_sko__uhi: $i > $i > $i ).
thf(class_Wellfounded__Recursion_Owellorder_decl,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(class_Parity_Oeven__odd_decl,type,
class_Parity_Oeven__odd: $i > $o ).
thf(c_Event_Oknows_decl,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_decl,type,
c_Message_Oagent_OSpy: $i ).
thf(c_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_Main_Oall__not__in__conv__1_decl,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Divides_Odiv_decl,type,
class_Divides_Odiv: $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONonce @ A )
= B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONumber @ A )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_OinvKey @ A )
= B ) ) ) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(4,negated_conjecture,
tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(195,plain,
tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[324]) ).
thf(16249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,325]) ).
thf(16250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[16249]) ).
thf(16251,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[16250:[bind(A,$thf( v_K )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(16356,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) ),
inference(simp,[status(thm)],[16251]) ).
thf(5,negated_conjecture,
~ ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(191,plain,
~ ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(197,plain,
~ ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[191]) ).
thf(17714,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16356,197]) ).
thf(17715,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[17714]) ).
thf(17822,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[17715]) ).
thf(17875,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[17822]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) )
= ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) ) ),
inference(lifteq,[status(thm)],[346]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).
thf(553,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(554,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
inference(lifteq,[status(thm)],[553]) ).
thf(86,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(409,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(410,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[409]) ).
thf(764,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,410]) ).
thf(765,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[764]) ).
thf(769,plain,
! [B: $i,A: $i] :
( ( tc_nat != B )
| ( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= c_emptyset )
| ( v_K != A ) ),
inference(simp,[status(thm)],[765]) ).
thf(772,plain,
( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= c_emptyset ),
inference(simp,[status(thm)],[769]) ).
thf(1070,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz @ c_Message_OkeysFor )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[554,772]) ).
thf(1083,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= v_H )
| ( ( A @ c_Message_Oanalz @ c_Message_OkeysFor )
!= c_emptyset ) ),
inference(simp,[status(thm)],[1070]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[233]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(275,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONonce @ A )
= B ),
inference(detectInverse,[status(thm)],[274]) ).
thf(276,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk2 )
= A ),
inference(cnf,[status(esa)],[275]) ).
thf(941,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk2 )
= A ),
inference(lifteq,[status(thm)],[276]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[261]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[262]) ).
thf(1,negated_conjecture,
tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(192,plain,
tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(110,axiom,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(463,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(464,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[463]) ).
thf(88,axiom,
( ( c_emptyset @ c_Message_Oparts )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
thf(412,plain,
( ( c_emptyset @ c_Message_Oparts )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(413,plain,
( ( c_emptyset @ c_Message_Oparts )
= c_emptyset ),
inference(lifteq,[status(thm)],[412]) ).
thf(746,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(rewrite,[status(thm)],[464,413]) ).
thf(747,plain,
! [A: $i] :
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,746]) ).
thf(748,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[747]) ).
thf(753,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( v_H @ c_Message_Oanalz @ c_Message_Osynth )
!= c_emptyset )
| ( v_X != A ) ),
inference(simp,[status(thm)],[748]) ).
thf(756,plain,
( ( v_H @ c_Message_Oanalz @ c_Message_Osynth )
!= c_emptyset ),
inference(simp,[status(thm)],[753]) ).
thf(3415,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( B != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,756]) ).
thf(3416,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3415:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4877,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_in ) ) ),
inference(simp,[status(thm)],[3416]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2_0) ).
thf(350,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[350]) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[351]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_1) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(12784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,296]) ).
thf(12785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[12784]) ).
thf(12786,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12785:[bind(A,$thf( v_K )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(12863,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) ),
inference(simp,[status(thm)],[12786]) ).
thf(14091,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12863,410]) ).
thf(14092,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[14091]) ).
thf(14128,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != C )
| ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) )
!= c_emptyset )
| ( v_K != B ) ),
inference(simp,[status(thm)],[14092]) ).
thf(14171,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[14128]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4_0) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(627,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[626]) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[627]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(444,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(445,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) )
= ( A @ c_Message_Osynth @ c_Message_Oparts ) ),
inference(lifteq,[status(thm)],[444]) ).
thf(9529,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_union ) ) )
= ( A @ c_Message_Osynth @ c_Message_Oparts ) ) ),
inference(paramod_ordered,[status(thm)],[413,445]) ).
thf(9530,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_union ) ) )
= ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts ) ),
inference(pattern_uni,[status(thm)],[9529:[bind(A,$thf( c_emptyset ))]]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(433,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(434,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[433]) ).
thf(9731,plain,
( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
= ( c_emptyset @ c_Message_Osynth ) ),
inference(rewrite,[status(thm)],[9530,434]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
thf(473,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(474,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
inference(lifteq,[status(thm)],[473]) ).
thf(9811,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( ( A @ c_Message_Oparts )
= ( c_emptyset @ c_Message_Osynth @ c_Message_Oanalz ) ) ),
inference(paramod_ordered,[status(thm)],[9731,474]) ).
thf(9812,plain,
( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
= ( c_emptyset @ c_Message_Osynth @ c_Message_Oanalz ) ),
inference(pattern_uni,[status(thm)],[9811:[bind(A,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(10013,plain,
( ( c_emptyset @ c_Message_Osynth @ c_Message_Oanalz )
= ( c_emptyset @ c_Message_Osynth ) ),
inference(rewrite,[status(thm)],[9812,9731]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).
thf(486,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(487,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) )
= ( A @ c_Message_Osynth @ c_Message_Oanalz ) ),
inference(lifteq,[status(thm)],[486]) ).
thf(12064,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oanalz )
!= ( A @ c_Message_Oanalz ) )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_union ) ) )
= ( A @ c_Message_Osynth @ c_Message_Oanalz ) ) ),
inference(paramod_ordered,[status(thm)],[10013,487]) ).
thf(12065,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_union ) ) )
= ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz ) ),
inference(pattern_uni,[status(thm)],[12064:[bind(A,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(9773,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_union ) ) )
= ( A @ c_Message_Osynth @ c_Message_Oparts ) ) ),
inference(paramod_ordered,[status(thm)],[9731,445]) ).
thf(9774,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_union ) ) )
= ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts ) ),
inference(pattern_uni,[status(thm)],[9773:[bind(A,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(12119,plain,
( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
= ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz ) ),
inference(rewrite,[status(thm)],[12065,9774]) ).
thf(87,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(411,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__mono_0) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[302]) ).
thf(13069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oparts @ ( C @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[411,303]) ).
thf(13070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oparts @ ( C @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[13069]) ).
thf(13071,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[13070:[bind(A,$thf( A )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( c_emptyset )),bind(D,$thf( A ))]]) ).
thf(13631,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( c_emptyset @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[13071,413]) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[333]) ).
thf(19094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( c_emptyset @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Pow ) @ ( B @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13631,334]) ).
thf(19095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( c_emptyset @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Pow ) @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[19094]) ).
thf(19096,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) @ ( c_emptyset @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[19095:[bind(A,$thf( E )),bind(B,$thf( c_emptyset )),bind(C,$thf( E @ c_Message_Oparts )),bind(D,$thf( tc_Message_Omsg ))]]) ).
thf(19105,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[19096]) ).
thf(20432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19105,410]) ).
thf(20433,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[20432]) ).
thf(20458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= C )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) )
!= c_emptyset )
| ( c_emptyset != B ) ),
inference(simp,[status(thm)],[20433]) ).
thf(20509,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) )
!= c_emptyset ),
inference(simp,[status(thm)],[20458]) ).
thf(20543,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[12119,20509]) ).
thf(20544,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[20543:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth ))]]) ).
thf(73,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(376,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_1) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[247]) ).
thf(2385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[376,248]) ).
thf(2386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2385]) ).
thf(2387,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2386:[bind(A,$thf( E @ c_Message_Osynth )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( E @ c_Message_Osynth )),bind(D,$thf( E ))]]) ).
thf(2434,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(simp,[status(thm)],[2387]) ).
thf(2705,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2434,248]) ).
thf(2706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2705]) ).
thf(2707,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2706:[bind(A,$thf( E )),bind(B,$thf( E @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( E ))]]) ).
thf(2720,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(simp,[status(thm)],[2707]) ).
thf(2770,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2720,248]) ).
thf(2771,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2770]) ).
thf(2772,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2771:[bind(A,$thf( F )),bind(B,$thf( F @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( F ))]]) ).
thf(2787,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(simp,[status(thm)],[2772]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
thf(518,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(135,axiom,
( ( c_emptyset @ c_Message_OkeysFor )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
thf(514,plain,
( ( c_emptyset @ c_Message_OkeysFor )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(515,plain,
( ( c_emptyset @ c_Message_OkeysFor )
= c_emptyset ),
inference(lifteq,[status(thm)],[514]) ).
thf(774,plain,
( ( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( c_emptyset @ c_Message_OkeysFor ) )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[515,772]) ).
thf(775,plain,
( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( c_emptyset @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[774]) ).
thf(777,plain,
( ( v_H @ c_Message_Oanalz )
!= c_emptyset ),
inference(simp,[status(thm)],[775]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( C @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).
thf(555,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( C @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(521,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(lifteq,[status(thm)],[520]) ).
thf(3,negated_conjecture,
~ ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(194,plain,
~ ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(198,plain,
~ ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[194]) ).
thf(639,plain,
( ( ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,198]) ).
thf(640,plain,
( ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[639]) ).
thf(642,plain,
( ( tc_nat != tc_nat )
| ( ( v_H @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[640]) ).
thf(644,plain,
( ( v_H @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[642]) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[521,644]) ).
thf(2350,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[2339]) ).
thf(2363,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[2350]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
thf(522,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(lifteq,[status(thm)],[522]) ).
thf(2388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[411,248]) ).
thf(2389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2388]) ).
thf(2390,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2389:[bind(A,$thf( E @ c_Message_Osynth )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( c_emptyset )),bind(D,$thf( E ))]]) ).
thf(2438,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) ),
inference(simp,[status(thm)],[2390]) ).
thf(19088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Pow ) @ ( B @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2438,334]) ).
thf(19089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Pow ) @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[19088]) ).
thf(19090,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[19089:[bind(A,$thf( F )),bind(B,$thf( c_emptyset @ c_Message_Osynth )),bind(C,$thf( F @ c_Message_Osynth )),bind(D,$thf( tc_Message_Omsg ))]]) ).
thf(19103,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ),
inference(simp,[status(thm)],[19090]) ).
thf(720,plain,
( ( v_H @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ),
inference(simp,[status(thm)],[644]) ).
thf(9814,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(paramod_ordered,[status(thm)],[9731,720]) ).
thf(9831,plain,
( ( ( c_emptyset @ c_Message_Osynth )
!= v_H )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(simp,[status(thm)],[9814]) ).
thf(10270,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= v_H )
| ( ( c_emptyset @ c_Message_Osynth )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(paramod_ordered,[status(thm)],[10013,9831]) ).
thf(10271,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= v_H ) ),
inference(simp,[status(thm)],[10270]) ).
thf(10272,plain,
( ( ( c_emptyset @ c_Message_Osynth )
!= v_H )
| ( ( c_emptyset @ c_Message_Osynth )
!= v_H ) ),
inference(simp,[status(thm)],[10271]) ).
thf(10276,plain,
( ( c_emptyset @ c_Message_Osynth )
!= v_H ),
inference(simp,[status(thm)],[10272]) ).
thf(10290,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_emptyset @ c_Message_Osynth ) )
| ( B != v_H )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,10276]) ).
thf(10291,plain,
! [B: $i,A: $i] :
( ( A != v_H )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[10290:[bind(A,$thf( c_emptyset @ c_Message_Osynth )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(10298,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ),
inference(simp,[status(thm)],[10291]) ).
thf(39430,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19103,10298]) ).
thf(39431,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ) ),
inference(simp,[status(thm)],[39430]) ).
thf(39566,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= B )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) )
!= ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(simp,[status(thm)],[39431]) ).
thf(39594,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) )
!= ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_insert ) ) ) ),
inference(simp,[status(thm)],[39566]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1_0) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2438,248]) ).
thf(2456,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2455]) ).
thf(2457,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2456:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(13146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2457,303]) ).
thf(13147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[13146]) ).
thf(13148,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[13147:[bind(A,$thf( F )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( F @ c_Message_Osynth ))]]) ).
thf(13259,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) ),
inference(simp,[status(thm)],[13148]) ).
thf(15763,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[13259,12119]) ).
thf(15765,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Osynth @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9731,15763]) ).
thf(15766,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[15765:[bind(A,$thf( c_emptyset ))]]) ).
thf(15908,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15766,248]) ).
thf(15909,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15908]) ).
thf(15910,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[15909:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )),bind(B,$thf( c_emptyset ))]]) ).
thf(16047,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15910,303]) ).
thf(16048,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16047]) ).
thf(16049,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[16048:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(16602,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(rewrite,[status(thm)],[16049,9731]) ).
thf(16617,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16602,248]) ).
thf(16618,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16617]) ).
thf(16619,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ c_Message_Osynth @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[16618:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts )),bind(B,$thf( c_emptyset ))]]) ).
thf(3909,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( A != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,772]) ).
thf(3910,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3909:[bind(A,$thf( A )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )),bind(C,$thf( C ))]]) ).
thf(5173,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[3910]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6_0) ).
thf(377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[377]) ).
thf(379,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[378]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).
thf(440,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_union ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( C @ ( A @ c_Union ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_union ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( C @ ( A @ c_Union ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Union ) @ ( C @ ( A @ c_Union ) @ c_union ) ) )
= ( C @ ( C @ tc_set @ ( B @ ( A @ c_union ) ) @ c_Union ) ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(20311,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[9731,19105]) ).
thf(20312,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ),
inference(pattern_uni,[status(thm)],[20311:[bind(A,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(3421,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( A != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,756]) ).
thf(3422,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3421:[bind(A,$thf( A )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth )),bind(C,$thf( C ))]]) ).
thf(4883,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[3422]) ).
thf(20675,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20312,4883]) ).
thf(20676,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[20675]) ).
thf(20798,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[20676]) ).
thf(20830,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) ),
inference(simp,[status(thm)],[20798]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
= ( C @ ( A @ ( B @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
= ( C @ ( A @ ( B @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
= ( C @ ( A @ ( B @ c_union ) ) ) ),
inference(lifteq,[status(thm)],[288]) ).
thf(16164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,325]) ).
thf(16165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[16164]) ).
thf(16166,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[16165:[bind(A,$thf( v_X )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( D ))]]) ).
thf(16334,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) ),
inference(simp,[status(thm)],[16166]) ).
thf(17141,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16334,410]) ).
thf(17142,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[17141]) ).
thf(17162,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != C )
| ( ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) )
!= c_emptyset )
| ( v_X != B ) ),
inference(simp,[status(thm)],[17142]) ).
thf(17204,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[17162]) ).
thf(17395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
!= ( tc_Message_Omsg @ ( D @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) ) )
| ( ( C @ ( A @ ( B @ c_union ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[289,17204]) ).
thf(17396,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_union ) ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[17395:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth )),bind(B,$thf( G )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( G @ c_union ) ) ))]]) ).
thf(17469,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_union ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[17396]) ).
thf(17494,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_union ) ) ) )
| ( ( A @ c_Message_Osynth @ c_Message_Oanalz )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[487,17469]) ).
thf(17495,plain,
( ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oanalz )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[17494:[bind(A,$thf( v_H @ c_Message_Oanalz )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Oanalz ))]]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_1) ).
thf(385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(16021,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15910,248]) ).
thf(16022,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16021]) ).
thf(16023,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[16022:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth )),bind(B,$thf( c_emptyset ))]]) ).
thf(16513,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16023,303]) ).
thf(16514,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16513]) ).
thf(16515,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[16514:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(40970,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(rewrite,[status(thm)],[16515,9731]) ).
thf(4431,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( v_H @ c_Message_Oparts ) )
| ( A
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,720]) ).
thf(4432,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4431:[bind(A,$thf( A )),bind(B,$thf( v_H @ c_Message_Oparts )),bind(C,$thf( C ))]]) ).
thf(4870,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) ),
inference(simp,[status(thm)],[4432]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_1) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[235]) ).
thf(1916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[411,236]) ).
thf(1917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1916]) ).
thf(1918,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1917:[bind(A,$thf( E @ c_Message_Oanalz )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( c_emptyset )),bind(D,$thf( E ))]]) ).
thf(1974,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1918]) ).
thf(24,axiom,
( ( c_emptyset @ c_Message_Oanalz )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
thf(242,plain,
( ( c_emptyset @ c_Message_Oanalz )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(243,plain,
( ( c_emptyset @ c_Message_Oanalz )
= c_emptyset ),
inference(lifteq,[status(thm)],[242]) ).
thf(1975,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( c_emptyset @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[1974,243]) ).
thf(18987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( c_emptyset @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Pow ) @ ( B @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,334]) ).
thf(18988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( c_emptyset @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Pow ) @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[18987]) ).
thf(18989,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[18988:[bind(A,$thf( E )),bind(B,$thf( c_emptyset )),bind(C,$thf( E @ c_Message_Oanalz )),bind(D,$thf( tc_Message_Omsg ))]]) ).
thf(19110,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[18989]) ).
thf(10294,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( c_emptyset @ c_Message_Osynth ) )
| ( A != v_H )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,10276]) ).
thf(10295,plain,
! [B: $i,A: $i] :
( ( A != v_H )
| ~ ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[10294:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth )),bind(C,$thf( C ))]]) ).
thf(10300,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) @ ( v_H @ c_in ) ) ),
inference(simp,[status(thm)],[10295]) ).
thf(11934,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) @ ( v_H @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,10300]) ).
thf(11935,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) @ ( v_H @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[11934]) ).
thf(11983,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( v_H != v_X ) ),
inference(simp,[status(thm)],[11935]) ).
thf(11994,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( v_H != v_X ) ),
inference(simp,[status(thm)],[11983]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(2524,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2457,248]) ).
thf(2525,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2524]) ).
thf(2526,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2525:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(2554,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2526,248]) ).
thf(2555,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2554]) ).
thf(2556,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2555:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(2600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2556,248]) ).
thf(2601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2600]) ).
thf(2602,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2601:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(2740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2602,248]) ).
thf(2741,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2740]) ).
thf(2742,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2741:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(2807,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2742,248]) ).
thf(2808,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2807]) ).
thf(2809,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2808:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(2842,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2809,248]) ).
thf(2843,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2842]) ).
thf(2844,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2843:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16486,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16023,248]) ).
thf(16487,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16486]) ).
thf(16488,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[16487:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Osynth )),bind(B,$thf( c_emptyset ))]]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[319]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(455,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(456,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(lifteq,[status(thm)],[455]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
thf(583,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(584,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(lifteq,[status(thm)],[583]) ).
thf(173,axiom,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__parts_0) ).
thf(590,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1295,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Message_Oparts @ c_Message_Oparts )
!= ( B @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[584,590]) ).
thf(1296,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1295:[bind(A,$thf( C )),bind(B,$thf( C @ c_Message_Oparts ))]]) ).
thf(1301,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1296]) ).
thf(1338,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[1301,474]) ).
thf(1345,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( B @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[456,1338]) ).
thf(1346,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1345:[bind(A,$thf( C )),bind(B,$thf( C @ c_Message_Oanalz ))]]) ).
thf(1357,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1346]) ).
thf(1717,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[1357,456]) ).
thf(1737,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[413,1717]) ).
thf(1738,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[1737:[bind(A,$thf( c_emptyset ))]]) ).
thf(1786,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ),
inference(rewrite,[status(thm)],[1738,413]) ).
thf(19033,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1786,334]) ).
thf(19034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[19033]) ).
thf(19035,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ),
inference(pattern_uni,[status(thm)],[19034:[bind(A,$thf( c_emptyset )),bind(B,$thf( c_emptyset )),bind(C,$thf( tc_Message_Omsg ))]]) ).
thf(19169,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19035,4883]) ).
thf(19170,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[19169]) ).
thf(19276,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[19170]) ).
thf(19318,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) ),
inference(simp,[status(thm)],[19276]) ).
thf(14008,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12863,197]) ).
thf(14009,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[14008]) ).
thf(14147,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[14009]) ).
thf(14188,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[14147]) ).
thf(637,plain,
( ( ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,197]) ).
thf(638,plain,
( ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[637]) ).
thf(641,plain,
( ( tc_nat != tc_nat )
| ( ( v_G @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[638]) ).
thf(643,plain,
( ( v_G @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[641]) ).
thf(668,plain,
( ( v_G @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ),
inference(simp,[status(thm)],[643]) ).
thf(9778,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_G @ c_Message_Oparts ) )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(paramod_ordered,[status(thm)],[9731,668]) ).
thf(9850,plain,
( ( ( c_emptyset @ c_Message_Osynth )
!= v_G )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(simp,[status(thm)],[9778]) ).
thf(17754,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16356,198]) ).
thf(17755,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[17754]) ).
thf(17839,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[17755]) ).
thf(17888,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[17839]) ).
thf(2,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(193,plain,
~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(196,plain,
~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[193]) ).
thf(647,plain,
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,196]) ).
thf(648,plain,
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[647]) ).
thf(650,plain,
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( v_H @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(simp,[status(thm)],[648]) ).
thf(651,plain,
( ( ( v_H @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(simp,[status(thm)],[650]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
thf(570,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(4427,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,720]) ).
thf(4428,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4427:[bind(A,$thf( v_H @ c_Message_Oparts )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4866,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_in ) ) ),
inference(simp,[status(thm)],[4428]) ).
thf(3181,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( v_H @ c_Message_Oanalz ) )
| ( A != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,777]) ).
thf(3182,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3181:[bind(A,$thf( A )),bind(B,$thf( v_H @ c_Message_Oanalz )),bind(C,$thf( C ))]]) ).
thf(4645,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[3182]) ).
thf(5847,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4645]) ).
thf(5848,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[5847]) ).
thf(5902,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( c_emptyset != v_X ) ),
inference(simp,[status(thm)],[5848]) ).
thf(5910,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( c_emptyset != v_X ) ),
inference(simp,[status(thm)],[5902]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Oanalz @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Oanalz @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(587,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(polarity_switch,[status(thm)],[342]) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(lifteq,[status(thm)],[343]) ).
thf(3026,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2844,248]) ).
thf(3027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[3026]) ).
thf(3028,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[3027:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(6111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3028,248]) ).
thf(6112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6111]) ).
thf(6113,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[6112:[bind(A,$thf( A )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( A ))]]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(cnf,[status(esa)],[228]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(lifteq,[status(thm)],[229]) ).
thf(231,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ),
inference(detectInverse,[status(thm)],[230]) ).
thf(232,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk1 )
= A ),
inference(cnf,[status(esa)],[231]) ).
thf(934,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk1 )
= A ),
inference(lifteq,[status(thm)],[232]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[355]) ).
thf(357,plain,
! [B: $i,A: $i] :
( ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) )
| ( A = c_emptyset ) ),
inference(lifteq,[status(thm)],[356]) ).
thf(6624,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4866]) ).
thf(6625,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[6624]) ).
thf(6641,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oparts )
!= v_K ) ),
inference(simp,[status(thm)],[6625]) ).
thf(6662,plain,
( ( ( tc_nat @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oparts )
!= v_K ) ),
inference(simp,[status(thm)],[6641]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).
thf(559,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(215,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(216,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
= ( A @ ( c_emptyset @ c_Pow ) ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(158,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).
thf(561,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(1167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[561,410]) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != D )
| ( ( B @ c_Message_Osynth )
!= c_emptyset )
| ( ( A @ c_Message_Omsg_ONumber )
!= C ) ),
inference(simp,[status(thm)],[1168]) ).
thf(1182,plain,
! [A: $i] :
( ( A @ c_Message_Osynth )
!= c_emptyset ),
inference(simp,[status(thm)],[1174]) ).
thf(3763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( D @ c_Message_Osynth ) )
| ( B != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,1182]) ).
thf(3764,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( C @ c_Message_Osynth @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3763:[bind(A,$thf( E @ c_Message_Osynth )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(5100,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( B @ c_Message_Osynth @ c_in ) ) ),
inference(simp,[status(thm)],[3764]) ).
thf(8002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) )
| ~ ( B @ ( A @ ( c_emptyset @ c_Pow ) @ ( C @ c_Message_Osynth @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[216,5100]) ).
thf(8003,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( B @ ( c_emptyset @ c_Pow ) @ ( A @ c_Message_Osynth @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[8002:[bind(A,$thf( D )),bind(B,$thf( D @ tc_set ))]]) ).
thf(8054,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( B @ ( c_emptyset @ c_Pow ) @ ( A @ c_Message_Osynth @ c_in ) ) ),
inference(simp,[status(thm)],[8003]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
thf(576,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(577,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(lifteq,[status(thm)],[576]) ).
thf(6922,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[577,644]) ).
thf(6930,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[6922]) ).
thf(6951,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[6930]) ).
thf(270,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(polarity_switch,[status(thm)],[269]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(lifteq,[status(thm)],[270]) ).
thf(1475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( D @ ( C @ ( B @ c_insert ) ) ) )
| ( ( A @ ( c_emptyset @ c_Pow ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[216,271]) ).
thf(1476,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[1475:[bind(A,$thf( E )),bind(B,$thf( c_emptyset )),bind(C,$thf( c_emptyset )),bind(D,$thf( E @ tc_set ))]]) ).
thf(1479,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
!= c_emptyset ),
inference(simp,[status(thm)],[1476]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(cnf,[status(esa)],[314]) ).
thf(316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(lifteq,[status(thm)],[315]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_0) ).
thf(416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(12195,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_G @ c_Message_Oparts ) )
| ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[12119,643]) ).
thf(12229,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )
!= v_G )
| ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[12195]) ).
thf(3765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( D @ c_Message_Osynth ) )
| ( A != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,1182]) ).
thf(3766,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( C @ c_Message_Osynth @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3765:[bind(A,$thf( A )),bind(B,$thf( E @ c_Message_Osynth )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(5101,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( B @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[3766]) ).
thf(19148,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( B @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19035,5101]) ).
thf(19149,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( B @ c_Message_Osynth @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[19148]) ).
thf(19273,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( B @ c_Message_Osynth @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[19149]) ).
thf(19314,plain,
! [A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( A @ c_Message_Osynth @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) ),
inference(simp,[status(thm)],[19273]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(591,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(722,plain,
( ( ( c_emptyset @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( c_emptyset @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[413,644]) ).
thf(726,plain,
( ( c_emptyset != v_H )
| ( ( v_H @ c_Message_Oanalz )
!= c_emptyset ) ),
inference(simp,[status(thm)],[722]) ).
thf(731,plain,
( ( ( c_emptyset @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( c_emptyset != v_H )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[243,726]) ).
thf(732,plain,
( ( ( c_emptyset @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( c_emptyset != v_H ) ),
inference(simp,[status(thm)],[731]) ).
thf(733,plain,
( ( c_emptyset != v_H )
| ( c_emptyset != v_H ) ),
inference(simp,[status(thm)],[732]) ).
thf(734,plain,
c_emptyset != v_H,
inference(simp,[status(thm)],[733]) ).
thf(3555,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( B != v_H )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,734]) ).
thf(3556,plain,
! [B: $i,A: $i] :
( ( A != v_H )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3555:[bind(A,$thf( c_emptyset ))]]) ).
thf(4998,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[3556]) ).
thf(5290,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4998]) ).
thf(5291,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[5290]) ).
thf(5323,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( c_emptyset != v_X ) ),
inference(simp,[status(thm)],[5291]) ).
thf(5333,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( c_emptyset != v_X ) ),
inference(simp,[status(thm)],[5323]) ).
thf(9759,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9731,590]) ).
thf(9760,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[9759:[bind(A,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(10168,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ),
inference(rewrite,[status(thm)],[9760,10013]) ).
thf(19082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10168,334]) ).
thf(19083,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[19082]) ).
thf(19084,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ),
inference(pattern_uni,[status(thm)],[19083:[bind(A,$thf( c_emptyset @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth )),bind(C,$thf( tc_Message_Omsg ))]]) ).
thf(19548,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19084,410]) ).
thf(19549,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[19548]) ).
thf(19589,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= B )
| ( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) )
!= c_emptyset )
| ( ( c_emptyset @ c_Message_Osynth )
!= A ) ),
inference(simp,[status(thm)],[19549]) ).
thf(19598,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) )
!= c_emptyset ),
inference(simp,[status(thm)],[19589]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(353,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(4123,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( v_G @ c_Message_Oparts ) )
| ( A
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,668]) ).
thf(4124,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4123:[bind(A,$thf( A )),bind(B,$thf( v_G @ c_Message_Oparts )),bind(C,$thf( C ))]]) ).
thf(4565,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) ),
inference(simp,[status(thm)],[4124]) ).
thf(6490,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4565]) ).
thf(6491,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[6490]) ).
thf(6549,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_X ) ),
inference(simp,[status(thm)],[6491]) ).
thf(6562,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_X ) ),
inference(simp,[status(thm)],[6549]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(480,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_1) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(17488,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_union ) ) ) )
| ( ( A @ c_Message_Osynth @ c_Message_Oparts )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[445,17469]) ).
thf(17489,plain,
( ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[17488:[bind(A,$thf( v_H @ c_Message_Oanalz )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Oparts ))]]) ).
thf(26522,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts ) )
| ( c_emptyset != c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,17489]) ).
thf(26523,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts ) )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[26522]) ).
thf(26524,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[26523:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts )),bind(B,$thf( B ))]]) ).
thf(27923,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) ),
inference(simp,[status(thm)],[26524]) ).
thf(125,axiom,
tc_nat @ class_Wellfounded__Recursion_Owellorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
thf(492,plain,
tc_nat @ class_Wellfounded__Recursion_Owellorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_3) ).
thf(574,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(2936,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[523,643]) ).
thf(2951,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[2936]) ).
thf(2964,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[2951]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__HPair_0) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(2335,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[521,643]) ).
thf(2354,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[2335]) ).
thf(2367,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[2354]) ).
thf(3557,plain,
! [C: $i,B: $i,A: $i] :
( ( B != c_emptyset )
| ( A != v_H )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,734]) ).
thf(3558,plain,
! [B: $i,A: $i] :
( ( A != v_H )
| ~ ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3557:[bind(A,$thf( A )),bind(B,$thf( c_emptyset ))]]) ).
thf(4999,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_in ) ) ),
inference(simp,[status(thm)],[3558]) ).
thf(5357,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4999]) ).
thf(5358,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[5357]) ).
thf(5390,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( v_H != v_X ) ),
inference(simp,[status(thm)],[5358]) ).
thf(5401,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( v_H != v_X ) ),
inference(simp,[status(thm)],[5390]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
thf(612,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(613,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(lifteq,[status(thm)],[612]) ).
thf(7299,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[613,643]) ).
thf(7328,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[7299]) ).
thf(7336,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[7328]) ).
thf(1110,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(paramod_ordered,[status(thm)],[584,720]) ).
thf(1119,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts )
!= v_H )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[1110]) ).
thf(81,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(396,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(20704,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20312,4645]) ).
thf(20705,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[20704]) ).
thf(20792,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[20705]) ).
thf(20826,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) ),
inference(simp,[status(thm)],[20792]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(3177,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz ) )
| ( B != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,777]) ).
thf(3178,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3177:[bind(A,$thf( v_H @ c_Message_Oanalz )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4642,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) ),
inference(simp,[status(thm)],[3178]) ).
thf(5764,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) )
| ~ ( B @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[216,4642]) ).
thf(5765,plain,
! [A: $i] :
~ ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[5764:[bind(A,$thf( C )),bind(B,$thf( C @ tc_set ))]]) ).
thf(5824,plain,
! [A: $i] :
~ ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) ),
inference(simp,[status(thm)],[5765]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(206,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15933,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15766,303]) ).
thf(15934,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15933]) ).
thf(15935,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[15934:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )),bind(B,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(16357,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(rewrite,[status(thm)],[15935,9731,456]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_2) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
= ( B @ ( A @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).
thf(527,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5_0) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_0) ).
thf(290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(cnf,[status(esa)],[290]) ).
thf(292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(lifteq,[status(thm)],[291]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
thf(529,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(5313,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4998]) ).
thf(5314,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[5313]) ).
thf(5324,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( c_emptyset != v_K ) ),
inference(simp,[status(thm)],[5314]) ).
thf(5334,plain,
( ( ( tc_nat @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( c_emptyset != v_K ) ),
inference(simp,[status(thm)],[5324]) ).
thf(1030,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oparts )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[474,777]) ).
thf(1047,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts )
!= v_H )
| ( ( A @ c_Message_Oparts )
!= c_emptyset ) ),
inference(simp,[status(thm)],[1030]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
thf(452,plain,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(4449,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,644]) ).
thf(4450,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4449:[bind(A,$thf( A )),bind(B,$thf( v_H @ c_Message_Oparts @ c_Message_OkeysFor )),bind(C,$thf( C ))]]) ).
thf(4888,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_in ) ) ),
inference(simp,[status(thm)],[4450]) ).
thf(5807,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4642]) ).
thf(5808,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[5807]) ).
thf(5818,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_K ) ),
inference(simp,[status(thm)],[5808]) ).
thf(5839,plain,
( ( ( tc_nat @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_K ) ),
inference(simp,[status(thm)],[5818]) ).
thf(19135,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19035,5173]) ).
thf(19136,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[19135]) ).
thf(19289,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[19136]) ).
thf(19329,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) ),
inference(simp,[status(thm)],[19289]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_1) ).
thf(364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(cnf,[status(esa)],[364]) ).
thf(366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
thf(328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(cnf,[status(esa)],[328]) ).
thf(330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(lifteq,[status(thm)],[329]) ).
thf(331,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[330]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( A @ sk6 ) )
= B ),
inference(cnf,[status(esa)],[331]) ).
thf(18168,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( A @ sk6 ) )
= B ),
inference(lifteq,[status(thm)],[332]) ).
thf(1010,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ( ( A @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[456,644]) ).
thf(1021,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= v_H )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[1010]) ).
thf(178,axiom,
tc_nat @ class_Divides_Odiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).
thf(598,plain,
tc_nat @ class_Divides_Odiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(6534,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4565]) ).
thf(6535,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[6534]) ).
thf(6553,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_K ) ),
inference(simp,[status(thm)],[6535]) ).
thf(6565,plain,
( ( ( tc_nat @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_K ) ),
inference(simp,[status(thm)],[6553]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(polarity_switch,[status(thm)],[422]) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(lifteq,[status(thm)],[423]) ).
thf(5353,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) )
| ~ ( B @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[216,4999]) ).
thf(5354,plain,
! [A: $i] :
~ ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[5353:[bind(A,$thf( C )),bind(B,$thf( C @ tc_set ))]]) ).
thf(5396,plain,
! [A: $i] :
~ ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_in ) ) ),
inference(simp,[status(thm)],[5354]) ).
thf(19242,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19035,410]) ).
thf(19243,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[19242]) ).
thf(19281,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= B )
| ( ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) )
!= c_emptyset )
| ( c_emptyset != A ) ),
inference(simp,[status(thm)],[19243]) ).
thf(19322,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) )
!= c_emptyset ),
inference(simp,[status(thm)],[19281]) ).
thf(25361,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) )
| ( c_emptyset != c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,19322]) ).
thf(25362,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[25361]) ).
thf(25363,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[25362:[bind(A,$thf( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) )),bind(B,$thf( B ))]]) ).
thf(27454,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[25363]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[258]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(13209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2438,303]) ).
thf(13210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[13209]) ).
thf(13211,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[13210:[bind(A,$thf( E )),bind(B,$thf( c_emptyset @ c_Message_Osynth )),bind(C,$thf( E @ c_Message_Osynth ))]]) ).
thf(13235,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) ),
inference(simp,[status(thm)],[13211]) ).
thf(14375,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[13235,9731]) ).
thf(14404,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Osynth @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[12119,14375]) ).
thf(14405,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[14404:[bind(A,$thf( c_emptyset @ c_Message_Osynth ))]]) ).
thf(19004,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14405,334]) ).
thf(19005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[19004]) ).
thf(19006,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ),
inference(pattern_uni,[status(thm)],[19005:[bind(A,$thf( c_emptyset @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )),bind(C,$thf( tc_Message_Omsg ))]]) ).
thf(12198,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[12119,1717]) ).
thf(12199,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[12198:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth ))]]) ).
thf(12874,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ),
inference(rewrite,[status(thm)],[12199,12119]) ).
thf(14916,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12874,320]) ).
thf(14917,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14916]) ).
thf(14918,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[14917:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth ))]]) ).
thf(15102,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14918,303]) ).
thf(15103,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15102]) ).
thf(15104,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[15103:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz ))]]) ).
thf(15392,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ),
inference(rewrite,[status(thm)],[15104,12119,456]) ).
thf(15438,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15392,303]) ).
thf(15439,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15438]) ).
thf(15440,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[15439:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts ))]]) ).
thf(24165,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(rewrite,[status(thm)],[15440,456,584]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[340]) ).
thf(24274,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24165,341]) ).
thf(24275,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[24274]) ).
thf(24276,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[24275:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth ))]]) ).
thf(39713,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(rewrite,[status(thm)],[24276,12119,584]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_1) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1006,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( v_G @ c_Message_Oparts ) )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(paramod_ordered,[status(thm)],[456,668]) ).
thf(1012,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= v_G )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[1006]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_2) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(cnf,[status(esa)],[297]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(lifteq,[status(thm)],[298]) ).
thf(300,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ),
inference(detectInverse,[status(thm)],[299]) ).
thf(301,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk4 )
= A ),
inference(cnf,[status(esa)],[300]) ).
thf(948,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk4 )
= A ),
inference(lifteq,[status(thm)],[301]) ).
thf(78,axiom,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(388,plain,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_1) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1105,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts @ c_Message_Oparts )
!= ( v_G @ c_Message_Oparts ) )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(paramod_ordered,[status(thm)],[584,668]) ).
thf(1118,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts )
!= v_G )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[1105]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
thf(499,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(519,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(lifteq,[status(thm)],[518]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).
thf(578,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1061,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[554,777]) ).
thf(1082,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= v_H )
| ( ( A @ c_Message_Oanalz )
!= c_emptyset ) ),
inference(simp,[status(thm)],[1061]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_0) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[224]) ).
thf(19073,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15910,334]) ).
thf(19074,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[19073]) ).
thf(19075,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth @ c_in ) ),
inference(pattern_uni,[status(thm)],[19074:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth )),bind(C,$thf( tc_Message_Omsg ))]]) ).
thf(5885,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4645]) ).
thf(5886,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[5885]) ).
thf(5895,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( c_emptyset != v_K ) ),
inference(simp,[status(thm)],[5886]) ).
thf(5905,plain,
( ( ( tc_nat @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( c_emptyset != v_K ) ),
inference(simp,[status(thm)],[5895]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(547,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(17805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16356,410]) ).
thf(17806,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[17805]) ).
thf(17847,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != C )
| ( ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) )
!= c_emptyset )
| ( v_K != B ) ),
inference(simp,[status(thm)],[17806]) ).
thf(17895,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[17847]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(polarity_switch,[status(thm)],[535]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(lifteq,[status(thm)],[536]) ).
thf(9795,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_G @ c_Message_Oparts ) )
| ( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( c_emptyset @ c_Message_Osynth @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[9731,643]) ).
thf(9852,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_G @ c_Message_Oparts ) )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(simp,[status(thm)],[9795]) ).
thf(15339,plain,
( ( ( v_G @ c_Message_Oparts )
!= ( c_emptyset @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(rewrite,[status(thm)],[9852,9731]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(457,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(4277,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( B
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,643]) ).
thf(4278,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4277:[bind(A,$thf( v_G @ c_Message_Oparts @ c_Message_OkeysFor )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4717,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ c_in ) ) ),
inference(simp,[status(thm)],[4278]) ).
thf(25485,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ c_Message_Osynth ) )
| ( c_emptyset != c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,1182]) ).
thf(25486,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ c_Message_Osynth ) )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[25485]) ).
thf(25487,plain,
! [B: $i,A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( B @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[25486:[bind(A,$thf( D @ c_Message_Osynth )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(27499,plain,
! [B: $i,A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( B @ c_Message_Osynth @ c_lessequals ) ) ),
inference(simp,[status(thm)],[25487]) ).
thf(12214,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(paramod_ordered,[status(thm)],[12119,720]) ).
thf(12226,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )
!= v_H )
| ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )
!= v_H ) ),
inference(simp,[status(thm)],[12214]) ).
thf(12270,plain,
( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth )
!= v_H ),
inference(simp,[status(thm)],[12226]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
thf(605,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(7303,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[613,644]) ).
thf(7312,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[7303]) ).
thf(7333,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[7312]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(3903,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( B != c_emptyset )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,772]) ).
thf(3904,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3903:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(5170,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_in ) ) ),
inference(simp,[status(thm)],[3904]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3_0) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(polarity_switch,[status(thm)],[264]) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[203]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_2) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__HPair_0) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(311,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) )
= ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oanalz ) ),
inference(lifteq,[status(thm)],[310]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_1) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(19463,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19084,10298]) ).
thf(19464,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) ) ),
inference(simp,[status(thm)],[19463]) ).
thf(19567,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(simp,[status(thm)],[19464]) ).
thf(19627,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) ),
inference(simp,[status(thm)],[19567]) ).
thf(19197,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19035,4645]) ).
thf(19198,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[19197]) ).
thf(19274,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[19198]) ).
thf(19315,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) ),
inference(simp,[status(thm)],[19274]) ).
thf(1913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[376,236]) ).
thf(1914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1913]) ).
thf(1915,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1914:[bind(A,$thf( E @ c_Message_Oanalz )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( E @ c_Message_Oanalz )),bind(D,$thf( E ))]]) ).
thf(1971,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1915]) ).
thf(2001,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[1971,554]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_insert ) ) @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).
thf(618,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_insert ) ) @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(5380,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4999]) ).
thf(5381,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_in ) ) ) ),
inference(simp,[status(thm)],[5380]) ).
thf(5389,plain,
! [A: $i] :
( ( tc_nat != A )
| ( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( v_K != v_H ) ),
inference(simp,[status(thm)],[5381]) ).
thf(5400,plain,
( ( ( tc_nat @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( v_K != v_H ) ),
inference(simp,[status(thm)],[5389]) ).
thf(11891,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,10298]) ).
thf(11892,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[11891]) ).
thf(11899,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= v_K ) ),
inference(simp,[status(thm)],[11892]) ).
thf(11920,plain,
( ( ( tc_nat @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= v_K ) ),
inference(simp,[status(thm)],[11899]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(601,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(12137,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( ( A @ c_Message_Oparts )
!= v_H )
| ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[12119,1047]) ).
thf(12138,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= v_H )
| ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[12137:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth ))]]) ).
thf(28871,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )
!= v_H )
| ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[12138,12119]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
thf(277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(lifteq,[status(thm)],[278]) ).
thf(9853,plain,
( ( ( c_emptyset @ c_Message_Osynth )
!= v_G )
| ( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( c_emptyset @ c_Message_Osynth @ c_Message_OkeysFor ) ) ),
inference(simp,[status(thm)],[9795]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(21580,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[345,196]) ).
thf(21581,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[21580]) ).
thf(21699,plain,
! [C: $i,B: $i,A: $i] :
( ( C != tc_Message_Omsg )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( A
!= ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey ) ) ),
inference(simp,[status(thm)],[21581]) ).
thf(21707,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[21699]) ).
thf(2940,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[523,644]) ).
thf(2943,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[2940]) ).
thf(2970,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[2943]) ).
thf(367,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[366]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk8 ) )
= B ),
inference(cnf,[status(esa)],[367]) ).
thf(40529,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk8 ) )
= B ),
inference(lifteq,[status(thm)],[368]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14913,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oanalz @ ( B @ c_Message_Oanalz @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oanalz @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2001,320]) ).
thf(14914,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oanalz @ ( B @ c_Message_Oanalz @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Oanalz @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14913]) ).
thf(14915,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[14914:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(25827,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( c_emptyset != c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,772]) ).
thf(25828,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[25827]) ).
thf(25829,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[25828:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )),bind(B,$thf( B ))]]) ).
thf(27618,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(simp,[status(thm)],[25829]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).
thf(545,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(280,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[279]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( A @ sk3 ) )
= B ),
inference(cnf,[status(esa)],[280]) ).
thf(7815,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( A @ sk3 ) )
= B ),
inference(lifteq,[status(thm)],[281]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_0) ).
thf(402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(24855,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) )
| ( c_emptyset != c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,19598]) ).
thf(24856,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[24855]) ).
thf(24857,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[24856:[bind(A,$thf( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) )),bind(B,$thf( B ))]]) ).
thf(27210,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[24857]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(17034,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
!= ( tc_Message_Omsg @ ( D @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) ) )
| ( tc_Message_Omsg @ ( C @ ( A @ ( B @ c_union ) ) @ ( v_X @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,16334]) ).
thf(17035,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_union ) ) @ ( v_X @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[17034:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth )),bind(B,$thf( G )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( G @ c_union ) ) ))]]) ).
thf(17205,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_union ) ) @ ( v_X @ c_in ) ) ),
inference(simp,[status(thm)],[17035]) ).
thf(18349,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_union ) ) ) )
| ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Message_Oparts @ ( v_X @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[445,17205]) ).
thf(18350,plain,
tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oparts @ ( v_X @ c_in ) ),
inference(pattern_uni,[status(thm)],[18349:[bind(A,$thf( v_H @ c_Message_Oanalz )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Oparts ))]]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(9815,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( c_emptyset @ c_Message_Osynth @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[9731,644]) ).
thf(9841,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(simp,[status(thm)],[9815]) ).
thf(14807,plain,
( ( ( v_H @ c_Message_Oparts )
!= ( c_emptyset @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Osynth ) ) ),
inference(rewrite,[status(thm)],[9841,9731]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
thf(335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[312]) ).
thf(4119,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( v_G @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,668]) ).
thf(4120,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4119:[bind(A,$thf( v_G @ c_Message_Oparts )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4561,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_in ) ) ),
inference(simp,[status(thm)],[4120]) ).
thf(6400,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4561]) ).
thf(6401,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[6400]) ).
thf(6451,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_G @ c_Message_Oparts )
!= v_X ) ),
inference(simp,[status(thm)],[6401]) ).
thf(6478,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_G @ c_Message_Oparts )
!= v_X ) ),
inference(simp,[status(thm)],[6451]) ).
thf(6670,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4870]) ).
thf(6671,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[6670]) ).
thf(6734,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_X ) ),
inference(simp,[status(thm)],[6671]) ).
thf(6742,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_X ) ),
inference(simp,[status(thm)],[6734]) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[217]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(20376,plain,
! [A: $i] :
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )
!= ( A @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[12119,19105]) ).
thf(20377,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ),
inference(pattern_uni,[status(thm)],[20376:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth ))]]) ).
thf(21262,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20377,4998]) ).
thf(21263,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[21262]) ).
thf(21360,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[21263]) ).
thf(21410,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Pow ) ) ),
inference(simp,[status(thm)],[21360]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(18366,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_union ) ) ) )
| ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Message_Oanalz @ ( v_X @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[487,17205]) ).
thf(18367,plain,
tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oanalz @ ( v_X @ c_in ) ),
inference(pattern_uni,[status(thm)],[18366:[bind(A,$thf( v_H @ c_Message_Oanalz )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Oanalz ))]]) ).
thf(245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[244]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
thf(599,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(645,plain,
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,196]) ).
thf(646,plain,
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(649,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_K ) ),
inference(simp,[status(thm)],[646]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(616,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21628,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[345,198]) ).
thf(21629,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[21628]) ).
thf(21681,plain,
! [C: $i,B: $i,A: $i] :
( ( C != tc_nat )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( A != v_K ) ),
inference(simp,[status(thm)],[21629]) ).
thf(21731,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( v_K @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[21681]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
thf(621,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(469,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(470,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
inference(lifteq,[status(thm)],[469]) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
inference(cnf,[status(esa)],[621]) ).
thf(623,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
inference(lifteq,[status(thm)],[622]) ).
thf(624,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_OinvKey @ A )
= B ),
inference(detectInverse,[status(thm)],[623]) ).
thf(625,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ sk12 )
= A ),
inference(cnf,[status(esa)],[624]) ).
thf(1140,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ sk12 )
= A ),
inference(lifteq,[status(thm)],[625]) ).
thf(1145,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) )
| ( ( A @ sk12 )
= B ) ),
inference(paramod_ordered,[status(thm)],[470,1140]) ).
thf(1146,plain,
! [A: $i] :
( ( A @ sk12 )
= ( A @ c_Message_OinvKey ) ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( C )),bind(B,$thf( C @ c_Message_OinvKey ))]]) ).
thf(1149,plain,
! [A: $i] :
( ( A @ sk12 )
= ( A @ c_Message_OinvKey ) ),
inference(simp,[status(thm)],[1146]) ).
thf(12709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,296]) ).
thf(12710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[12709]) ).
thf(12711,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_insert ) ) @ ( v_X @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12710:[bind(A,$thf( v_X )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( D ))]]) ).
thf(12841,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_insert ) ) @ ( v_X @ c_in ) ) ),
inference(simp,[status(thm)],[12711]) ).
thf(13863,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_insert ) ) @ ( v_X @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12841,410]) ).
thf(13864,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_insert ) ) @ ( v_X @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[13863]) ).
thf(13885,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != C )
| ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_insert ) ) )
!= c_emptyset )
| ( v_X != B ) ),
inference(simp,[status(thm)],[13864]) ).
thf(13940,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[13885]) ).
thf(2889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2787,248]) ).
thf(2890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2889]) ).
thf(2891,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2890:[bind(A,$thf( G )),bind(B,$thf( G @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( G ))]]) ).
thf(2911,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(simp,[status(thm)],[2891]) ).
thf(117,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(477,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(24477,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oanalz ) )
| ( c_emptyset != c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,17495]) ).
thf(24478,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oanalz ) )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[24477]) ).
thf(24479,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[24478:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oanalz )),bind(B,$thf( B ))]]) ).
thf(27925,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[24479]) ).
thf(4443,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( B
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,644]) ).
thf(4444,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4443:[bind(A,$thf( v_H @ c_Message_Oparts @ c_Message_OkeysFor )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4882,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ c_in ) ) ),
inference(simp,[status(thm)],[4444]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(cnf,[status(esa)],[321]) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(lifteq,[status(thm)],[322]) ).
thf(7475,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) )
| ~ ( B @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[216,5170]) ).
thf(7476,plain,
! [A: $i] :
~ ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[7475:[bind(A,$thf( C )),bind(B,$thf( C @ tc_set ))]]) ).
thf(7566,plain,
! [A: $i] :
~ ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_in ) ) ),
inference(simp,[status(thm)],[7476]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(17693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
!= ( tc_nat @ ( D @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) ) )
| ( tc_nat @ ( C @ ( A @ ( B @ c_union ) ) @ ( v_K @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,16356]) ).
thf(17694,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) @ ( v_K @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[17693:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )),bind(B,$thf( G )),bind(C,$thf( tc_nat )),bind(D,$thf( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( G @ c_union ) ) ))]]) ).
thf(17874,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) @ ( v_K @ c_in ) ) ),
inference(simp,[status(thm)],[17694]) ).
thf(23989,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17874,198]) ).
thf(23990,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[23989]) ).
thf(24094,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[23990]) ).
thf(24132,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[24094]) ).
thf(633,plain,
( ( ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,198]) ).
thf(634,plain,
( ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[633]) ).
thf(636,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( v_H @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( v_K != v_X ) ),
inference(simp,[status(thm)],[634]) ).
thf(6714,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4870]) ).
thf(6715,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[6714]) ).
thf(6728,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_K ) ),
inference(simp,[status(thm)],[6715]) ).
thf(6738,plain,
( ( ( tc_nat @ ( c_emptyset @ ( v_H @ c_Message_Oparts @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_K ) ),
inference(simp,[status(thm)],[6728]) ).
thf(24362,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz ) )
| ( c_emptyset != c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,777]) ).
thf(24363,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz ) )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[24362]) ).
thf(24364,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[24363:[bind(A,$thf( v_H @ c_Message_Oanalz )),bind(B,$thf( B ))]]) ).
thf(27841,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[24364]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(lifteq,[status(thm)],[222]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21898,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19110,4998]) ).
thf(21899,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[21898]) ).
thf(21972,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= B )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) )
!= ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[21899]) ).
thf(22021,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) )
!= ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_insert ) ) ) ),
inference(simp,[status(thm)],[21972]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).
thf(304,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(polarity_switch,[status(thm)],[304]) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_union ) ) @ ( tc_Message_Omsg @ ( C @ ( A @ c_insert ) ) @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__subset__Un_0) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_union ) ) @ ( tc_Message_Omsg @ ( C @ ( A @ c_insert ) ) @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_0) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[326]) ).
thf(16758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_Message_Osynth @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[376,327]) ).
thf(16759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_Message_Osynth @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( D @ c_Message_Osynth @ ( C @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16758]) ).
thf(16760,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[16759:[bind(A,$thf( E @ c_Message_Osynth )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( E )),bind(D,$thf( E ))]]) ).
thf(16934,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[16760]) ).
thf(16975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16934,327]) ).
thf(16976,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16975]) ).
thf(16977,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[16976:[bind(A,$thf( E @ c_Message_Osynth )),bind(B,$thf( E )),bind(C,$thf( E @ c_Message_Osynth ))]]) ).
thf(17006,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[16977]) ).
thf(25066,plain,
! [B: $i,A: $i] :
( ( c_emptyset != c_emptyset )
| ( A != v_H )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[357,734]) ).
thf(25067,plain,
! [B: $i,A: $i] :
( ( A != v_H )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[25066:[]]) ).
thf(27345,plain,
! [A: $i] :
~ ( A @ tc_set @ ( c_emptyset @ ( v_H @ c_lessequals ) ) ),
inference(simp,[status(thm)],[25067]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(12120,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_union ) ) )
= ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz ) ),
inference(rewrite,[status(thm)],[9774,12119]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(172,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).
thf(589,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(144,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(531,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(21601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[345,197]) ).
thf(21602,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[21601]) ).
thf(21702,plain,
! [C: $i,B: $i,A: $i] :
( ( C != tc_nat )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( A != v_K ) ),
inference(simp,[status(thm)],[21602]) ).
thf(21711,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( v_K @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[21702]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
inference(lifteq,[status(thm)],[208]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
thf(525,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_1) ).
thf(557,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
= ( B @ ( A @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_2) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
= ( B @ ( A @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(20640,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20312,5173]) ).
thf(20641,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[20640]) ).
thf(20791,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[20641]) ).
thf(20824,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) ) ),
inference(simp,[status(thm)],[20791]) ).
thf(11971,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) @ ( v_H @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,10300]) ).
thf(11972,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) @ ( v_H @ c_in ) ) ) ),
inference(simp,[status(thm)],[11971]) ).
thf(11977,plain,
! [A: $i] :
( ( tc_nat != A )
| ( ( A @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( v_K != v_H ) ),
inference(simp,[status(thm)],[11972]) ).
thf(11988,plain,
( ( ( tc_nat @ ( c_emptyset @ ( c_emptyset @ c_Message_Osynth @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( v_K != v_H ) ),
inference(simp,[status(thm)],[11977]) ).
thf(21945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19110,410]) ).
thf(21946,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[21945]) ).
thf(21985,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= C )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) )
!= c_emptyset )
| ( c_emptyset != B ) ),
inference(simp,[status(thm)],[21946]) ).
thf(22033,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Oanalz @ c_Pow ) )
!= c_emptyset ),
inference(simp,[status(thm)],[21985]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19195,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19035,4998]) ).
thf(19196,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[19195]) ).
thf(19284,plain,
! [A: $i] :
( ( A
!= ( tc_Message_Omsg @ tc_set ) )
| ( ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[19196]) ).
thf(19325,plain,
( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Pow ) ) ),
inference(simp,[status(thm)],[19284]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_2) ).
thf(585,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[369]) ).
thf(14047,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12863,198]) ).
thf(14048,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[14047]) ).
thf(14137,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[14048]) ).
thf(14179,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[14137]) ).
thf(14514,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14405,303]) ).
thf(14515,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14514]) ).
thf(14516,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[14515:[bind(A,$thf( c_emptyset @ c_Message_Osynth )),bind(B,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz ))]]) ).
thf(14589,plain,
tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ ( c_emptyset @ c_Message_Osynth @ c_lessequals ) ),
inference(rewrite,[status(thm)],[14516,9731,456]) ).
thf(5577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2911,248]) ).
thf(5578,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_lessequals ) ) ) )
| ( tc_Message_Omsg @ tc_set @ ( C @ c_Message_Osynth @ ( B @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5577]) ).
thf(5579,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[5578:[bind(A,$thf( H )),bind(B,$thf( H @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth )),bind(C,$thf( H ))]]) ).
thf(5628,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Osynth @ c_lessequals ) ) ),
inference(simp,[status(thm)],[5579]) ).
thf(18990,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16357,334]) ).
thf(18991,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ c_Message_Osynth @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[18990]) ).
thf(18992,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts @ c_in ) ),
inference(pattern_uni,[status(thm)],[18991:[bind(A,$thf( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oparts )),bind(B,$thf( c_emptyset @ c_Message_Osynth )),bind(C,$thf( tc_Message_Omsg ))]]) ).
thf(19682,plain,
tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_Message_Osynth @ c_Message_Oanalz @ c_in ) ),
inference(rewrite,[status(thm)],[18992,12119]) ).
thf(176,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(595,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(2242,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[519,643]) ).
thf(2249,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[2242]) ).
thf(2266,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[2249]) ).
thf(11854,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,10298]) ).
thf(11855,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[11854]) ).
thf(11900,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= v_X ) ),
inference(simp,[status(thm)],[11855]) ).
thf(11921,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_H @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( c_emptyset @ c_Message_Osynth )
!= v_X ) ),
inference(simp,[status(thm)],[11900]) ).
thf(20383,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19105,4998]) ).
thf(20384,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[20383]) ).
thf(20469,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= B )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) )
!= ( B @ ( c_emptyset @ ( v_H @ c_insert ) ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[20384]) ).
thf(20519,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ c_Pow ) )
!= ( tc_Message_Omsg @ tc_set @ ( c_emptyset @ ( v_H @ c_insert ) ) ) ),
inference(simp,[status(thm)],[20469]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__mono_0) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(17929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
!= ( tc_nat @ ( D @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_union ) ) ) )
| ( ( C @ ( A @ ( B @ c_union ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[289,17895]) ).
thf(17930,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[17929:[bind(A,$thf( v_H @ c_Message_Oanalz @ c_Message_OkeysFor )),bind(B,$thf( G )),bind(C,$thf( tc_nat )),bind(D,$thf( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( G @ c_union ) ) ))]]) ).
thf(18002,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[17930]) ).
thf(9750,plain,
( ( ( c_emptyset @ c_Message_Osynth @ c_Message_Oparts )
!= ( v_G @ c_Message_Oparts ) )
| ~ ( tc_nat @ ( c_emptyset @ c_Message_Osynth @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[9731,197]) ).
thf(9834,plain,
( ( ( c_emptyset @ c_Message_Osynth )
!= v_G )
| ~ ( tc_nat @ ( c_emptyset @ c_Message_Osynth @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[9750]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(465,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(23951,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17874,197]) ).
thf(23952,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[23951]) ).
thf(24098,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[23952]) ).
thf(24135,plain,
! [A: $i] :
( ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_union ) ) )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[24098]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[362]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_0) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(140,axiom,
tc_nat @ class_Parity_Oeven__odd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).
thf(524,plain,
tc_nat @ class_Parity_Oeven__odd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(6918,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[577,643]) ).
thf(6936,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[6918]) ).
thf(6953,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) )
!= ( v_G @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[6936]) ).
thf(336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(cnf,[status(esa)],[335]) ).
thf(337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(lifteq,[status(thm)],[336]) ).
thf(338,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[337]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( B @ sk7 ) )
= A ),
inference(cnf,[status(esa)],[338]) ).
thf(20282,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( B @ sk7 ) )
= A ),
inference(lifteq,[status(thm)],[339]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(6444,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,4561]) ).
thf(6445,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_G @ c_Message_Oparts @ c_in ) ) )
!= ( tc_nat @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[6444]) ).
thf(6459,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_G @ c_Message_Oparts )
!= v_K ) ),
inference(simp,[status(thm)],[6445]) ).
thf(6484,plain,
( ( ( tc_nat @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ( ( v_G @ c_Message_Oparts )
!= v_K ) ),
inference(simp,[status(thm)],[6459]) ).
thf(207,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[206]) ).
thf(5769,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4642]) ).
thf(5770,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[5769]) ).
thf(5815,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_X ) ),
inference(simp,[status(thm)],[5770]) ).
thf(5837,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oanalz )
!= v_X ) ),
inference(simp,[status(thm)],[5815]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1039,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
!= ( v_H @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oparts @ c_Message_OkeysFor )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[474,772]) ).
thf(1045,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts )
!= v_H )
| ( ( A @ c_Message_Oparts @ c_Message_OkeysFor )
!= c_emptyset ) ),
inference(simp,[status(thm)],[1039]) ).
thf(26,axiom,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(246,plain,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[213]) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[286]) ).
thf(606,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(cnf,[status(esa)],[605]) ).
thf(607,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(lifteq,[status(thm)],[606]) ).
thf(608,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ),
inference(detectInverse,[status(thm)],[607]) ).
thf(609,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk11 )
= A ),
inference(cnf,[status(esa)],[608]) ).
thf(1133,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk11 )
= A ),
inference(lifteq,[status(thm)],[609]) ).
thf(317,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[316]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ sk5 ) )
= A ),
inference(cnf,[status(esa)],[317]) ).
thf(14350,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ sk5 ) )
= A ),
inference(lifteq,[status(thm)],[318]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).
thf(603,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_1) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ c_Union ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ c_Union ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(631,plain,
( ( ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,197]) ).
thf(632,plain,
( ( tc_nat @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[631]) ).
thf(635,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( v_G @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( v_K != v_X ) ),
inference(simp,[status(thm)],[632]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
thf(532,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(cnf,[status(esa)],[391]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(lifteq,[status(thm)],[392]) ).
thf(394,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONumber @ A )
= B ),
inference(detectInverse,[status(thm)],[393]) ).
thf(395,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk9 )
= A ),
inference(cnf,[status(esa)],[394]) ).
thf(955,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk9 )
= A ),
inference(lifteq,[status(thm)],[395]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[237]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) )
= ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) ) ),
inference(lifteq,[status(thm)],[293]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__HPair_0) ).
thf(506,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_union ) ) @ ( tc_Message_Omsg @ ( C @ ( A @ c_insert ) ) @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[267]) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[282]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(459,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(2246,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( ( B @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) ) ),
inference(paramod_ordered,[status(thm)],[519,644]) ).
thf(2262,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( B
!= ( v_H @ c_Message_Oanalz ) ) ),
inference(simp,[status(thm)],[2246]) ).
thf(2270,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) )
!= ( v_H @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[2262]) ).
thf(39537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19103,410]) ).
thf(39538,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) @ ( c_emptyset @ c_Message_Osynth @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[39537]) ).
thf(39557,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set )
!= C )
| ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) )
!= c_emptyset )
| ( ( c_emptyset @ c_Message_Osynth )
!= B ) ),
inference(simp,[status(thm)],[39538]) ).
thf(39588,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ c_Pow ) )
!= c_emptyset ),
inference(simp,[status(thm)],[39557]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[199]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).
thf(501,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(4283,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( v_G @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,643]) ).
thf(4284,plain,
! [B: $i,A: $i] :
( ( A
!= ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor ) )
| ~ ( B @ ( B @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4283:[bind(A,$thf( A )),bind(B,$thf( v_G @ c_Message_Oparts @ c_Message_OkeysFor )),bind(C,$thf( C ))]]) ).
thf(4723,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_G @ c_Message_Oparts @ c_Message_OkeysFor @ c_insert ) ) @ ( v_H @ c_Message_Oanalz @ c_Message_OkeysFor @ c_in ) ) ),
inference(simp,[status(thm)],[4284]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[307]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
thf(543,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) )
| ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).
thf(496,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) )
| ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(polarity_switch,[status(thm)],[252]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(6580,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,4866]) ).
thf(6581,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) @ ( v_H @ c_Message_Oparts @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[6580]) ).
thf(6642,plain,
! [A: $i] :
( ( A != tc_Message_Omsg )
| ( ( A @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oparts )
!= v_X ) ),
inference(simp,[status(thm)],[6581]) ).
thf(6663,plain,
( ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_H @ c_Message_Oanalz @ c_insert ) ) )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_H @ c_Message_Oparts )
!= v_X ) ),
inference(simp,[status(thm)],[6642]) ).
thf(44577,plain,
$false,
inference(e,[status(thm)],[629,17875,347,1083,234,941,4877,352,249,14171,333,628,9731,20544,2787,518,777,555,2363,523,39594,217,16619,5173,379,440,202,20830,17495,247,614,269,385,40970,4870,19110,20312,2434,11994,538,2844,340,288,16488,320,19318,14188,9850,17888,651,257,389,570,4866,5910,504,587,344,6113,196,934,357,6662,559,8054,6951,1479,284,325,228,289,448,316,261,416,12229,216,756,19314,591,321,376,5333,19598,514,353,6562,480,475,27923,492,15763,348,574,2964,397,2367,5401,7336,1119,396,20826,2809,411,243,428,5824,206,1975,16357,734,221,293,5101,527,312,307,292,248,380,512,529,201,15766,5334,4999,1047,233,452,4888,5839,16356,220,19329,366,18168,334,1021,302,598,561,6565,424,5396,27454,260,349,19006,39713,297,192,407,467,252,197,361,435,461,493,3028,551,456,324,1012,566,484,24165,19322,583,522,285,224,12863,948,388,10298,4883,593,610,1118,499,519,578,14405,1082,488,225,19075,554,1182,590,5905,547,16023,328,471,17895,193,537,515,15339,457,4717,27499,12270,605,7333,371,5170,237,244,266,360,205,508,311,541,19627,19315,412,2001,618,425,296,444,5400,11920,601,12874,430,28871,2556,264,12119,279,9853,21707,2602,584,2970,40529,772,286,14915,577,27618,545,7815,562,4998,191,402,27210,413,391,18350,1786,445,572,4645,14807,335,236,2457,17204,350,313,16334,6478,6742,219,274,21410,419,18367,377,230,245,599,649,434,616,303,271,208,21731,2742,535,213,621,1149,626,13940,668,198,330,2911,477,27925,345,4882,323,7566,520,19103,240,251,16602,521,399,24132,636,6738,27841,455,223,299,226,22021,306,267,17006,27345,438,241,17874,473,12120,490,589,531,20509,255,516,342,355,553,194,21711,209,487,525,557,295,282,414,327,19035,20824,2720,409,11988,263,310,12841,22033,4561,199,463,19325,643,585,370,470,576,14179,14589,5628,613,19682,16934,10300,1717,314,595,2266,11921,20519,446,17489,5100,612,18002,9834,465,450,24135,363,15910,482,203,524,581,319,304,6953,258,2526,20282,568,290,6484,207,5837,478,272,383,346,549,1045,235,246,433,510,214,287,1133,410,14375,422,14350,373,603,564,210,326,341,10168,358,195,474,635,532,720,955,239,242,294,4565,506,268,19105,283,596,644,459,277,442,2270,39588,200,10276,501,369,17469,486,337,17205,4723,309,543,215,2438,222,496,364,254,227,4642,469,6663,13631,10013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV277-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/11.03 % Computer : n002.cluster.edu
% 0.16/11.03 % Model : x86_64 x86_64
% 0.16/11.03 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/11.03 % Memory : 8046.5625MB
% 0.16/11.03 % OS : Linux 6.8.0-71-generic
% 0.16/11.04 % CPULimit : 300
% 0.16/11.04 % WCLimit : 300
% 0.16/11.04 % DateTime : Sat Sep 26 13:28:47 UTC 2026
% 0.16/11.04 % CPUTime :
% 0.16/11.04 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/11.61 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.57/12.15 % [INFO] Parsing done (532ms).
% 2.57/12.17 % [INFO] Running in sequential loop mode.
% 3.12/12.53 % [INFO] eprover registered as external prover.
% 3.12/12.54 % [INFO] Scanning for conjecture ...
% 4.24/12.84 % [INFO] Found a conjecture (or negated_conjecture) and 2894 axioms. Running axiom selection ...
% 5.15/13.04 % [INFO] Axiom selection finished. Selected 185 axioms (removed 2709 axioms).
% 5.64/13.16 % [INFO] Problem is propositional (TPTP CNF).
% 5.64/13.18 % [INFO] Type checking passed.
% 5.64/13.18 % [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 ...
% 83.88/30.23 % External prover 'e' found a proof!
% 83.88/30.24 % [INFO] Killing All external provers ...
% 83.88/30.24 % Time passed: 19052ms (effective reasoning time: 18063ms)
% 83.88/30.24 % Axioms used in derivation (185): cls_Message_Oanalz_OInj_0, cls_Message_Oanalz__synth__Un_0, cls_Set_OPow__iff_1, cls_Set_Osingleton__insert__inj__eq_0, cls_Message_OHPair__neqs__2_0, cls_Message_Oparts__insert__subset__Un_0, cls_Event_OkeysFor__synth_H_0, cls_Set_OsubsetI_1, cls_Message_Oparts__Un_0, cls_Message_Oanalz__analzD__dest_0, cls_Message_OCrypt__synth__eq_0, cls_Message_Oparts__insert__Crypt_0, cls_Message_Oanalz__synth_0, cls_Message_OkeysFor__Un_0, cls_Message_Oparts__empty_0, cls_Message_OKey__synth__eq_1, cls_Message_Oanalz__conj__parts_0, cls_Message_Oanalz__idem_0, cls_Message_OHPair__synth__analz_1, cls_Message_Oanalz__empty_0, cls_Message_Oparts__insert__MPair_0, cls_Set_Osingleton__inject__dest_0, cls_Message_Oanalz__insert__HPair_0, cls_Message_Oanalz__Crypt__if_0, cls_Message_Oparts__mono_0, cls_Set_OUn__subset__iff_2, cls_Message_Omsg_Oinject__1_0, cls_Message_Oparts__insert__Nonce_0, cls_Message_OHPair__neqs__5_0, cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0, cls_Event_OkeysFor__synth_H_3, cls_Set_OPow__iff_0, cls_Message_OMPair__synth__analz_2, clsarity_nat_47, cls_Message_OHash__synth_0, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Message_OHPair__eq_0, cls_Message_Oparts__insert__Agent_0, cls_Message_Osynth_OHash_0, cls_Message_Oparts__subset__iff_1, cls_Set_Osubset__refl_0, cls_Message_Oanalz__insert__Agent_0, cls_Message_Omsg_Oinject__6_0, cls_Message_Oanalz__insert__Nonce_0, cls_Message_Oparts_OInj_0, cls_Set_OUnion__insert_0, cls_Message_Oparts__synth_0, cls_Set_Osubset__empty_0, cls_Message_OkeysFor__empty_0, cls_Message_Omsg_Oinject__5_0, clsarity_nat_44, cls_Message_OCrypt__synth_1, cls_Set_OsubsetI_0, cls_Message_OHPair__neqs__6_0, cls_Message_Oparts__insert__Key_0, cls_Set_Oinsert__subset_2, cls_Message_OHPair__synth__analz_0, cls_Message_Osynth_OMPair_0, cls_Message_ONonce__synth__eq_1, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Set_OUn__iff_0, cls_Message_Oparts__insert__HPair_0, cls_Set_OUn__empty_1, cls_Message_Omsg_Oinject__2_0, cls_Message_Omsg_Oinject__7_1, cls_Set_Oinsert__iff_2, cls_Message_OFake__analz__eq_0, cls_Message_Oparts__subset__iff_0, cls_Set_OsingletonD__dest_0, cls_Set_Oinsert__not__empty_0, cls_Set_Oempty__subsetI_0, cls_Set_OUn__subset__iff_0, cls_Message_OkeysFor__insert__HPair_0, cls_Message_Omsg_Oinject__4_0, cls_Set_Oempty__iff_0, cls_Message_OAgent__synth_0, cls_Set_OUnion__empty__conv_0, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Message_OHPair__eq__MPair_0, cls_Message_Oparts__insert__Hash_0, cls_Message_Omsg_Oinject__6_1, cls_Set_Osubset__antisym_0, cls_Message_Osynth__subset__iff_1, cls_Message_ONumber__synth_0, cls_Set_OsubsetD_0, cls_Message_OkeysFor__insert__Agent_0, cls_Message_Oparts__insert__Number_0, cls_Message_Oanalz__insert__Key_0, cls_Message_Oanalz__insert__Hash_0, cls_Set_OUnion__Un__distrib_0, cls_Set_Oall__not__in__conv_0, cls_Set_Oinsert__iff_1, cls_Set_Osubset__empty_1, cls_Set_Osingleton__insert__inj__eq_1, cls_Message_OHash__synth__analz_1, cls_Set_Oempty__Union__conv_0, cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Event_OkeysFor__synth_H_2, cls_Message_Oin__parts__UnE_0, cls_Set_Oinsert__subset_1, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0, cls_Message_OMPair__eq__HPair_0, cls_Message_OMPair__analz_1, cls_Message_OkeysFor__insert__Nonce_0, cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0, cls_Message_OHPair__eq__MPair_1, cls_Message_Osynth__subset__iff_0, cls_Set_OUn__insert__left_0, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Set_OUn__insert__right_0, cls_Message_OkeysFor__insert__Crypt_0, cls_Message_OHPair__neqs__3_0, cls_Set_OUnion__iff_2, cls_Message_Osynth_OCrypt_0, cls_Message_OMPair__parts_1, cls_Message_ONonce__synth__eq_0, cls_Message_Osynth__synthD__dest_0, clsarity_nat_12, cls_Message_OkeysFor__insert__Hash_0, cls_Set_OUn__iff_1, cls_Message_OkeysFor__insert__Number_0, cls_Set_OUnion__empty_0, cls_Message_Oanalz__insert__MPair_0, cls_Set_Oempty__not__insert_0, cls_Message_OHPair__neqs__1_0, cls_Message_Oanalz__subset__parts_0, cls_Message_Oanalz__insert__Number_0, cls_Message_OinvKey__eq_0, cls_Message_OHash__synth__analz_0, cls_Message_OCrypt__synth__eq_1, cls_Set_OUn__empty__left_0, cls_Set_OUn__empty__right_0, cls_Message_Oanalz__parts_0, cls_Message_Oanalz__Crypt__if_1, cls_Message_OMPair__synth_1, cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0, cls_Set_Ocontents__eq_0, cls_Message_Osynth_OInj_0, cls_Message_OkeysFor__insert__MPair_0, cls_Message_Oanalz__subset__iff_1, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Message_Ostrange__Un__eq_0, cls_Message_OMPair__analz_0, clsarity_nat_8, cls_Message_OkeysFor__insert__Key_0, cls_Message_OMPair__eq__HPair_1, cls_Message_Oanalz__analz__Un_0, cls_Event_OkeysFor__synth_H_1, cls_Message_Oparts__cut__eq_0, cls_Message_OKey__synth__eq_0, clsarity_nat_24, cls_Message_Oanalz_ODecrypt__dest_0, cls_Message_OHPair__eq__MPair_2, cls_Message_OHPair__synth__analz_2, cls_Set_OUn__subset__iff_1, cls_Message_Omsg_Oinject__7_0, cls_Message_OMPair__parts_0, cls_Message_Omsg_Oinject__3_0, cls_Message_Oparts__analz_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__iff_0, cls_Set_Oinsert__absorb2_0, cls_Set_OUnion__Pow__eq_0, cls_Set_OUn__empty_2, cls_Message_Oparts__emptyE_0, cls_Set_OUn__iff_2, cls_Message_OkeysFor__mono_0, cls_Message_Oanalz__subset__iff_0, cls_Set_OPow__empty_0, cls_Set_Osingleton__insert__inj__eq_2, clsarity_set_4, cls_Message_Oparts__idem_0, cls_Message_OMPair__eq__HPair_2, cls_Message_OMPair__synth__analz_0, cls_Set_Oinsert__subset_0, cls_Message_OMPair__synth__analz_1, cls_Message_OMPair__synth_0, cls_Message_OHPair__neqs__4_0, cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0, cls_Message_OHPair__eq_1, cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0, cls_Set_OUn__absorb_0
% 83.88/30.24 % No. of inferences in proof: 1197
% 83.88/30.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19052 ms resp. 18063 ms w/o parsing
% 85.36/30.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 85.36/30.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------