TSTP Solution File: SWV249-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV249-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:14:30 EDT 2023
% Result : Unsatisfiable 215.23s 41.26s
% Output : Refutation 216.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 506
% Syntax : Number of formulae : 1997 ( 713 unt; 90 typ; 0 def)
% Number of atoms : 4071 (2103 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 19001 (2339 ~;1970 |; 0 &;14692 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 175 ( 175 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 90 usr; 12 con; 0-5 aty)
% Number of variables : 3898 ( 0 ^;3898 !; 0 ?;3898 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_X_type,type,
v_X: $i ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(v_G_type,type,
v_G: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(v_H_type,type,
v_H: $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Orderings_Omax_type,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Orderings_Omin_type,type,
c_Orderings_Omin: $i > $i > $i > $i ).
thf(c_Finite__Set_OMax_type,type,
c_Finite__Set_OMax: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_type,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(c_SetInterval_OgreaterThanLessThan_type,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Main_Oempty__Union__conv__1_type,type,
c_Main_Oempty__Union__conv__1: $i > $i > $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Main_OUnion__empty__conv__1_type,type,
c_Main_OUnion__empty__conv__1: $i > $i > $i ).
thf(class_Nat_Opower_type,type,
class_Nat_Opower: $i > $o ).
thf(c_Finite__Set_OMin_type,type,
c_Finite__Set_OMin: $i > $i > $i ).
thf(c_UNIV_type,type,
c_UNIV: $i ).
thf(c_Main_OUnionE__1_type,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanAtMost_type,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_type,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Message_Omsg_OHash_type,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_SetInterval_OatLeast_type,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(c_Inter_type,type,
c_Inter: $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
thf(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(c_Main_OInter__UNIV__conv__1__1_type,type,
c_Main_OInter__UNIV__conv__1__1: $i > $i > $i ).
thf(c_Main_OMax__le__iff__1_type,type,
c_Main_OMax__le__iff__1: $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThan_type,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Datatype__Universe_Ouprod_type,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_type,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Main_OuprodE__1_type,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_type,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(c_Main_Ofinite__Union__1_type,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OMax__less__iff__1_type,type,
c_Main_OMax__less__iff__1: $i > $i > $i > $i ).
thf(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Main_OMin__gr__iff__1_type,type,
c_Main_OMin__gr__iff__1: $i > $i > $i > $i ).
thf(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Main_OInter__UNIV__conv__2__1_type,type,
c_Main_OInter__UNIV__conv__2__1: $i > $i > $i ).
thf(c_Main_OUnion__iff__1_type,type,
c_Main_OUnion__iff__1: $i > $i > $i > $i ).
thf(c_Main_OInter__iff__1_type,type,
c_Main_OInter__iff__1: $i > $i > $i > $i ).
thf(c_Message_Omsg_ONumber_type,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(c_Main_OInterI__1_type,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_OMin__ge__iff__1_type,type,
c_Main_OMin__ge__iff__1: $i > $i > $i > $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_type,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Oall__not__in__conv__1_type,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_List_Olistset_type,type,
c_List_Olistset: $i > $i > $i ).
thf(c_List_Oset__Cons_type,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_type,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_Set_Ocontents_type,type,
c_Set_Ocontents: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i > $i > $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
thf(868,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
= c_emptyset ),
inference(lifteq,[status(thm)],[868]) ).
thf(1,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(405,plain,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
thf(547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[547]) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset )
| ~ ( c_in @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[548]) ).
thf(15652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset )
| ( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg )
!= ( c_in @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[405,549]) ).
thf(15653,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15652:[bind(A,$thf( v_X )),bind(B,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( D ))]]) ).
thf(15687,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[15653]) ).
thf(15725,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ v_X @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[869,15687]) ).
thf(15750,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ v_X @ C @ tc_Message_Omsg ) )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[15725]) ).
thf(15767,plain,
! [A: $i] :
( ( c_insert @ v_X @ A @ tc_Message_Omsg )
!= ( c_uminus @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(simp,[status(thm)],[15750]) ).
thf(273,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
thf(1035,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1036,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(lifteq,[status(thm)],[1035]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(808,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(809,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
inference(lifteq,[status(thm)],[808]) ).
thf(70,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(551,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(65,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
thf(542,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(543,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(polarity_switch,[status(thm)],[542]) ).
thf(5455,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[551,543]) ).
thf(5457,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[5455]) ).
thf(5469,plain,
! [B: $i,A: $i] :
( ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[5457]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
inference(cnf,[status(esa)],[628]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
thf(1190,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(cnf,[status(esa)],[757]) ).
thf(759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(lifteq,[status(thm)],[758]) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( sk9 @ A @ ( c_Message_Omsg_OCrypt @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_OCrypt),[sk9])]) ).
thf(143,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(733,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
thf(630,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(631,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) ) ),
inference(cnf,[status(esa)],[630]) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[631]) ).
thf(34774,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) )
| ( ( class_Orderings_Olinorder @ tc_nat )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[733,632]) ).
thf(34775,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
= ( c_SetInterval_OatMost @ A @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[34774:[bind(A,$thf( tc_nat ))]]) ).
thf(34886,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
= ( c_SetInterval_OatMost @ A @ tc_nat ) ),
inference(simp,[status(thm)],[34775]) ).
thf(34900,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ ( tc_set @ C ) )
= B )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[34886,809]) ).
thf(34901,plain,
! [A: $i] :
( ( c_SetInterval_OgreaterThan @ A @ tc_nat )
= ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) ),
inference(pattern_uni,[status(thm)],[34900:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OgreaterThan @ D @ tc_nat )),bind(C,$thf( tc_nat ))]]) ).
thf(35087,plain,
! [A: $i] :
( ( c_SetInterval_OgreaterThan @ A @ tc_nat )
= ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[34901]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
thf(846,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(54,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
thf(518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(228,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(940,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(941,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(polarity_switch,[status(thm)],[940]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(481,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
thf(645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeast @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
thf(892,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeast @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(24,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(455,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(413,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(414,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(cnf,[status(esa)],[413]) ).
thf(415,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( c_lessequals @ A @ c_0 @ tc_nat ) ),
inference(lifteq,[status(thm)],[414]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(412,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
!= ( c_in @ C @ c_emptyset @ D ) ),
inference(paramod_ordered,[status(thm)],[412,941]) ).
thf(2480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint )
!= C )
| ( c_emptyset != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_IntDef_Oint )
!= D ) ),
inference(simp,[status(thm)],[2467]) ).
thf(2482,plain,
c_emptyset != c_Finite__Set_OFinites,
inference(simp,[status(thm)],[2480]) ).
thf(2490,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_Finite__Set_OFinites != c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,2482]) ).
thf(2491,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(pattern_uni,[status(thm)],[2490:[bind(A,$thf( c_emptyset ))]]) ).
thf(2597,plain,
! [A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,2491]) ).
thf(2610,plain,
! [A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2597]) ).
thf(2612,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[2610]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
thf(657,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(658,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
inference(lifteq,[status(thm)],[657]) ).
thf(30,axiom,
( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
thf(466,plain,
( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(467,plain,
( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
= c_emptyset ),
inference(lifteq,[status(thm)],[466]) ).
thf(169,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(799,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(15634,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ B @ E @ D ) @ C @ D )
!= c_emptyset )
| ( ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[799,549]) ).
thf(15635,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15634:[bind(A,$thf( F )),bind(B,$thf( c_SetInterval_OlessThan @ F @ tc_nat )),bind(C,$thf( c_Finite__Set_OFinites )),bind(D,$thf( tc_set @ tc_nat )),bind(E,$thf( E ))]]) ).
thf(15679,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[15635]) ).
thf(20099,plain,
! [B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
!= ( c_SetInterval_OlessThan @ B @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[467,15679]) ).
thf(20100,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[20099:[bind(A,$thf( A )),bind(B,$thf( c_0 ))]]) ).
thf(20227,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[658,20100]) ).
thf(20254,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20227]) ).
thf(20273,plain,
! [A: $i] :
( ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[20254]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oempty__Union__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oempty__Union__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(233,axiom,
( ( c_Message_Oparts @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
thf(953,plain,
( ( c_Message_Oparts @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(954,plain,
( ( c_Message_Oparts @ c_emptyset )
= c_emptyset ),
inference(lifteq,[status(thm)],[953]) ).
thf(222,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
thf(925,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(926,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(lifteq,[status(thm)],[925]) ).
thf(250,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(990,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(991,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ A ) ) ),
inference(lifteq,[status(thm)],[990]) ).
thf(9065,plain,
! [B: $i,A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ B ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
!= ( c_Message_Oparts @ B ) ) ),
inference(paramod_ordered,[status(thm)],[926,991]) ).
thf(9066,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9065:[bind(A,$thf( C )),bind(B,$thf( c_Message_Oparts @ C ))]]) ).
thf(9105,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ),
inference(simp,[status(thm)],[9066]) ).
thf(12051,plain,
! [A: $i] :
( ( ( c_union @ c_emptyset @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) )
| ( ( c_Message_Oparts @ c_emptyset )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[954,9105]) ).
thf(12052,plain,
( ( c_union @ c_emptyset @ ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[12051:[bind(A,$thf( c_emptyset ))]]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(873,plain,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
inference(lifteq,[status(thm)],[873]) ).
thf(12374,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[12052,874,954]) ).
thf(12376,plain,
! [A: $i] :
( ( ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) )
= ( c_Message_Oparts @ A ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12374,1036]) ).
thf(12377,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[12376:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(12426,plain,
( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[12377,12374,954]) ).
thf(357,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).
thf(1215,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(12457,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
!= ( c_Message_Osynth @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12426,1215]) ).
thf(12458,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg ),
inference(pattern_uni,[status(thm)],[12457:[bind(A,$thf( A )),bind(B,$thf( c_Message_Oparts @ c_emptyset ))]]) ).
thf(9073,plain,
! [A: $i] :
( ( ( c_union @ c_emptyset @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Oparts @ c_emptyset )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[954,991]) ).
thf(9074,plain,
( ( c_union @ c_emptyset @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[9073:[bind(A,$thf( c_emptyset ))]]) ).
thf(9116,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(rewrite,[status(thm)],[9074,874]) ).
thf(9117,plain,
! [A: $i] :
( ( ( c_Message_Oparts @ A )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9116,1036]) ).
thf(9118,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[9117:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(9223,plain,
( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(rewrite,[status(thm)],[9118,9116]) ).
thf(13058,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ),
inference(rewrite,[status(thm)],[12458,9223]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_1) ).
thf(1031,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ E @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
thf(468,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ E @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
thf(777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(555,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
inference(cnf,[status(esa)],[554]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
thf(664,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(665,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) ) ),
inference(cnf,[status(esa)],[664]) ).
thf(666,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[665]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).
thf(1295,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
thf(408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(521,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(522,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(cnf,[status(esa)],[521]) ).
thf(523,plain,
! [A: $i] :
( ( A = c_0 )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(lifteq,[status(thm)],[522]) ).
thf(209,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(895,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(3761,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Orderings_Oorder @ c_0 )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,895]) ).
thf(3762,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( class_Orderings_Oorder @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3761:[bind(A,$thf( tc_nat ))]]) ).
thf(12468,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
!= ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[12426,9105]) ).
thf(12469,plain,
( ( c_union @ ( c_Message_Oparts @ c_emptyset ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[12468:[bind(A,$thf( c_emptyset ))]]) ).
thf(13182,plain,
( ( c_union @ c_emptyset @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[12469,9223,954]) ).
thf(13203,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= A )
| ( ( c_union @ c_emptyset @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= ( c_union @ c_emptyset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13182,874]) ).
thf(13204,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(pattern_uni,[status(thm)],[13203:[bind(A,$thf( c_Message_Osynth @ c_emptyset )),bind(B,$thf( tc_Message_Omsg ))]]) ).
thf(13332,plain,
( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(rewrite,[status(thm)],[13204,12374]) ).
thf(13340,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,13332]) ).
thf(13341,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[13340:[bind(A,$thf( c_emptyset ))]]) ).
thf(173,axiom,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
thf(806,plain,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(807,plain,
( ( c_insert @ c_0 @ c_emptyset @ tc_nat )
= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) ),
inference(lifteq,[status(thm)],[806]) ).
thf(390,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(1281,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(10672,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ B )
| ( ( c_insert @ c_0 @ c_emptyset @ tc_nat )
!= ( c_insert @ A @ c_emptyset @ B ) ) ),
inference(paramod_ordered,[status(thm)],[807,1281]) ).
thf(10673,plain,
c_in @ c_0 @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat,
inference(pattern_uni,[status(thm)],[10672:[bind(A,$thf( c_0 )),bind(B,$thf( tc_nat ))]]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(994,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(482,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
inference(cnf,[status(esa)],[481]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
thf(419,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(420,plain,
! [B: $i,A: $i] :
( ( c_minus @ B @ A @ tc_nat )
= ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(lifteq,[status(thm)],[419]) ).
thf(6851,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
inference(rewrite,[status(thm)],[482,420]) ).
thf(196,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(866,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(867,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(polarity_switch,[status(thm)],[866]) ).
thf(6899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( ( c_less @ B @ A @ tc_nat )
!= ( c_less @ C @ C @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[6851,867]) ).
thf(6900,plain,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ A @ tc_nat ) @ tc_nat ) @ tc_nat ),
inference(pattern_uni,[status(thm)],[6899:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(cnf,[status(esa)],[739]) ).
thf(741,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A ) ),
inference(lifteq,[status(thm)],[740]) ).
thf(89,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(592,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(cnf,[status(esa)],[593]) ).
thf(23423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[592,594]) ).
thf(23424,plain,
! [B: $i,A: $i] : ( c_in @ ( c_minus @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[23423:[bind(A,$thf( E )),bind(B,$thf( c_SetInterval_OatMost @ E @ tc_nat )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(23455,plain,
! [B: $i,A: $i] : ( c_in @ ( c_minus @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(simp,[status(thm)],[23424]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(1269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
thf(603,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(604,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
= c_emptyset ),
inference(lifteq,[status(thm)],[603]) ).
thf(15597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ B @ E @ D ) @ C @ D )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13058,549]) ).
thf(15598,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15597:[bind(A,$thf( F )),bind(B,$thf( c_Message_Omsg_ONumber @ F )),bind(C,$thf( c_Message_Osynth @ c_emptyset )),bind(D,$thf( tc_Message_Omsg )),bind(E,$thf( E ))]]) ).
thf(15692,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[15598]) ).
thf(16837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[604,15692]) ).
thf(16863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_Message_Osynth @ c_emptyset ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[16837]) ).
thf(16881,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) )
!= ( c_Message_Osynth @ c_emptyset ) ),
inference(simp,[status(thm)],[16863]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oparts @ ( c_insert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oparts @ ( c_insert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(397,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(1294,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(265,axiom,
( ( c_Message_Oanalz @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
thf(1020,plain,
( ( c_Message_Oanalz @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1021,plain,
( ( c_Message_Oanalz @ c_emptyset )
= c_emptyset ),
inference(lifteq,[status(thm)],[1020]) ).
thf(7,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(416,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(86,axiom,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(586,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(587,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
inference(polarity_switch,[status(thm)],[586]) ).
thf(1373,plain,
! [A: $i] :
~ ( c_in @ A @ c_emptyset @ tc_Message_Omsg ),
inference(rewrite,[status(thm)],[587,954]) ).
thf(1374,plain,
! [A: $i] :
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg )
!= ( c_in @ A @ c_emptyset @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[405,1373]) ).
thf(1376,plain,
! [A: $i] :
( ( v_X != A )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_emptyset )
| ( tc_Message_Omsg != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[1374]) ).
thf(1378,plain,
( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_emptyset ),
inference(simp,[status(thm)],[1376]) ).
thf(1449,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[415,1378]) ).
thf(1450,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[1449:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ))]]) ).
thf(1621,plain,
( ( c_emptyset != c_0 )
| ( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat )
!= ( c_lessequals @ c_0 @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[416,1450]) ).
thf(1639,plain,
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 )
| ( c_0 != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[1621]) ).
thf(1640,plain,
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 ) ),
inference(simp,[status(thm)],[1639]) ).
thf(1641,plain,
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[1021,1640]) ).
thf(1649,plain,
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[1641]) ).
thf(1745,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1649]) ).
thf(1746,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G ) ),
inference(pattern_uni,[status(thm)],[1745:[bind(A,$thf( c_emptyset ))]]) ).
thf(2343,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_emptyset != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1746]) ).
thf(2344,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_emptyset != v_G ) ),
inference(pattern_uni,[status(thm)],[2343:[bind(A,$thf( c_emptyset ))]]) ).
thf(2352,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[2344]) ).
thf(4948,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_0 != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,2352]) ).
thf(4949,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[4948:[bind(A,$thf( c_emptyset ))]]) ).
thf(4962,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_0 != v_G ) ),
inference(simp,[status(thm)],[4949]) ).
thf(10393,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_0 != v_G )
| ( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1294,4962]) ).
thf(10421,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_0 != v_G )
| ( c_emptyset != c_emptyset )
| ( A != c_0 )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[10393]) ).
thf(10431,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_0 != v_G )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[10421]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(682,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(683,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(cnf,[status(esa)],[682]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
thf(730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(389,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).
thf(1280,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(15656,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ C @ F @ E ) @ D @ E )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
!= ( c_in @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1280,549]) ).
thf(15657,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15656:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( c_Message_Omsg_OAgent @ G )),bind(D,$thf( c_Message_Osynth @ H )),bind(E,$thf( tc_Message_Omsg ))]]) ).
thf(15689,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[15657]) ).
thf(26840,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ E ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[869,15689]) ).
thf(26882,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) )
| ( A
!= ( c_Message_Osynth @ E ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[26840]) ).
thf(26890,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_Message_Osynth @ C ) @ ( tc_set @ tc_Message_Omsg ) )
!= ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) ),
inference(simp,[status(thm)],[26882]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(1205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(21,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(448,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(449,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(polarity_switch,[status(thm)],[448]) ).
thf(202,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(878,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(cnf,[status(esa)],[653]) ).
thf(655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(lifteq,[status(thm)],[654]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(206,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(888,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(6011,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[888,543]) ).
thf(6013,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[6011]) ).
thf(6031,plain,
! [B: $i,A: $i] :
( ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[6013]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(1305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1436,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg )
| ( A
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[415,405]) ).
thf(1437,plain,
( ~ ( c_lessequals @ ( c_Message_Oanalz @ v_G ) @ c_0 @ tc_nat )
| ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg ) ),
inference(pattern_uni,[status(thm)],[1436:[bind(A,$thf( c_Message_Oanalz @ v_G ))]]) ).
thf(9234,plain,
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) )
!= c_0 )
| ( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[9223,1640]) ).
thf(9268,plain,
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) )
!= c_0 )
| ( ( c_Message_Osynth @ c_emptyset )
!= v_G ) ),
inference(simp,[status(thm)],[9234]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
thf(1078,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(879,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[878]) ).
thf(880,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[879]) ).
thf(1432,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A != c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[415,880]) ).
thf(1433,plain,
( ~ ( c_lessequals @ c_UNIV @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[1432:[bind(A,$thf( c_UNIV ))]]) ).
thf(1604,plain,
( ( c_emptyset != c_0 )
| ( ( c_lessequals @ c_UNIV @ c_0 @ tc_nat )
!= ( c_lessequals @ c_0 @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[416,1433]) ).
thf(1606,plain,
( ( c_emptyset != c_0 )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[1604]) ).
thf(1608,plain,
( ( c_emptyset != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[1606]) ).
thf(12,axiom,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(425,plain,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(426,plain,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
inference(lifteq,[status(thm)],[425]) ).
thf(2035,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ A @ tc_nat ) @ tc_nat )
= c_0 ),
inference(rewrite,[status(thm)],[426,420]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(445,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(cnf,[status(esa)],[445]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(lifteq,[status(thm)],[446]) ).
thf(4228,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(rewrite,[status(thm)],[447,420]) ).
thf(4241,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ B @ C @ tc_nat )
| ( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ A @ tc_nat ) @ tc_nat )
!= ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ C @ B @ tc_nat ) @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[2035,4228]) ).
thf(4242,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(pattern_uni,[status(thm)],[4241:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(3233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
!= ( c_in @ C @ c_emptyset @ D ) ),
inference(paramod_ordered,[status(thm)],[1215,941]) ).
thf(3245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= C )
| ( ( c_Message_Osynth @ B )
!= c_emptyset )
| ( tc_Message_Omsg != D ) ),
inference(simp,[status(thm)],[3233]) ).
thf(3253,plain,
! [A: $i] :
( ( c_Message_Osynth @ A )
!= c_emptyset ),
inference(simp,[status(thm)],[3245]) ).
thf(12449,plain,
! [A: $i] :
( ( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
!= c_emptyset )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
!= ( c_Message_Osynth @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12426,3253]) ).
thf(12450,plain,
( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[12449:[bind(A,$thf( c_Message_Oparts @ c_emptyset ))]]) ).
thf(12631,plain,
( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset ),
inference(rewrite,[status(thm)],[12450,9223]) ).
thf(12637,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[415,12631]) ).
thf(12638,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ c_emptyset ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[12637:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(12660,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Osynth @ c_emptyset ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,12638]) ).
thf(12691,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[12660]) ).
thf(12701,plain,
( ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 ) ),
inference(simp,[status(thm)],[12691]) ).
thf(12713,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,12701]) ).
thf(12714,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[12713:[bind(A,$thf( c_emptyset ))]]) ).
thf(13301,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,12714]) ).
thf(13302,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[13301:[bind(A,$thf( c_emptyset ))]]) ).
thf(13330,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 ) ),
inference(simp,[status(thm)],[13302]) ).
thf(13694,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,13330]) ).
thf(13704,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( A != c_emptyset )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[13694]) ).
thf(13713,plain,
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[13704]) ).
thf(14346,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_Message_Osynth @ c_0 ) ) ),
inference(paramod_ordered,[status(thm)],[415,13713]) ).
thf(14347,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ c_0 ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[14346:[bind(A,$thf( c_Message_Osynth @ c_0 ))]]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(60,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
thf(530,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(531,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(cnf,[status(esa)],[530]) ).
thf(532,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(lifteq,[status(thm)],[531]) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ A @ B @ C @ ( c_Datatype__Universe_OScons @ D @ A @ B @ C ) )
= D ),
introduced(tautology,[new_symbols(inverse(c_Datatype__Universe_OScons),[sk2])]) ).
thf(69,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(550,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(45,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
thf(499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(500,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(cnf,[status(esa)],[499]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 ) ),
inference(cnf,[status(esa)],[470]) ).
thf(472,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(lifteq,[status(thm)],[471]) ).
thf(1326,plain,
( ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[405,543]) ).
thf(1327,plain,
( ( c_UNIV != v_X )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= tc_Message_Omsg ) ),
inference(simp,[status(thm)],[1326]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__2__1 @ A @ B )
!= c_UNIV )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__2__1 @ A @ B )
!= c_UNIV )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_union @ B @ A @ C ) @ C )
= ( c_union @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_union @ B @ A @ C ) @ C )
= ( c_union @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B ) ),
inference(cnf,[status(esa)],[536]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) ) ),
inference(lifteq,[status(thm)],[537]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ A @ C )
| ( c_emptyset
= ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
thf(670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ A @ C )
| ( c_emptyset
= ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(242,axiom,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(974,plain,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(975,plain,
! [A: $i] :
( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
= ( c_Pow @ c_emptyset @ A ) ),
inference(lifteq,[status(thm)],[974]) ).
thf(199,axiom,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(872,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
inference(cnf,[status(esa)],[600]) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset )
| ~ ( c_in @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[601]) ).
thf(24884,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ C @ ( c_insert @ B @ E @ D ) @ D )
!= c_emptyset )
| ( ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[872,602]) ).
thf(24885,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24884:[bind(A,$thf( F )),bind(B,$thf( c_emptyset )),bind(C,$thf( c_Finite__Set_OFinites )),bind(D,$thf( tc_set @ F ))]]) ).
thf(24943,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
!= c_emptyset ),
inference(simp,[status(thm)],[24885]) ).
thf(33563,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ c_Finite__Set_OFinites @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ C ) )
!= c_emptyset )
| ( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
!= ( c_insert @ c_emptyset @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[975,24943]) ).
thf(33564,plain,
! [A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ A ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[33563:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(3337,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[523,1640]) ).
thf(3338,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[3337:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ))]]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(15641,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ B @ E @ D ) @ C @ D )
!= c_emptyset )
| ( ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[872,549]) ).
thf(15642,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ c_emptyset @ A @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15641:[bind(A,$thf( F )),bind(B,$thf( c_emptyset )),bind(C,$thf( c_Finite__Set_OFinites )),bind(D,$thf( tc_set @ F ))]]) ).
thf(15682,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ c_emptyset @ A @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
!= c_emptyset ),
inference(simp,[status(thm)],[15642]) ).
thf(22936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ c_emptyset @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(paramod_ordered,[status(thm)],[658,15682]) ).
thf(22963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ c_emptyset @ C @ ( tc_set @ D ) )
!= c_emptyset )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ D ) ) ),
inference(simp,[status(thm)],[22936]) ).
thf(22989,plain,
! [B: $i,A: $i] :
( ( c_insert @ c_emptyset @ A @ ( tc_set @ B ) )
!= c_emptyset ),
inference(simp,[status(thm)],[22963]) ).
thf(1438,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_in @ v_X @ c_0 @ tc_Message_Omsg )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[415,405]) ).
thf(1439,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat )
| ( c_in @ v_X @ c_0 @ tc_Message_Omsg ) ),
inference(pattern_uni,[status(thm)],[1438:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ))]]) ).
thf(23897,plain,
! [A: $i] :
( ( c_in @ v_X @ c_0 @ tc_Message_Omsg )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,1439]) ).
thf(23914,plain,
! [A: $i] :
( ( c_in @ v_X @ c_0 @ tc_Message_Omsg )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[23897]) ).
thf(23929,plain,
( ( c_in @ v_X @ c_0 @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 ) ),
inference(simp,[status(thm)],[23914]) ).
thf(12527,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
!= ( c_Message_Osynth @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12426,1280]) ).
thf(12528,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg ),
inference(pattern_uni,[status(thm)],[12527:[bind(A,$thf( A )),bind(B,$thf( c_Message_Oparts @ c_emptyset ))]]) ).
thf(13119,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ),
inference(rewrite,[status(thm)],[12528,9223]) ).
thf(15647,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ B @ E @ D ) @ C @ D )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13119,549]) ).
thf(15648,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15647:[bind(A,$thf( F )),bind(B,$thf( c_Message_Omsg_OAgent @ F )),bind(C,$thf( c_Message_Osynth @ c_emptyset )),bind(D,$thf( tc_Message_Omsg )),bind(E,$thf( E ))]]) ).
thf(15685,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[15648]) ).
thf(16746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[604,15685]) ).
thf(16772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_Message_Osynth @ c_emptyset ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[16746]) ).
thf(16784,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) )
!= ( c_Message_Osynth @ c_emptyset ) ),
inference(simp,[status(thm)],[16772]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(943,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[942]) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[943]) ).
thf(945,plain,
! [A: $i] :
( ( sk14 @ ( c_Message_Omsg_OKey @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_OKey),[sk14])]) ).
thf(23365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[799,594]) ).
thf(23366,plain,
! [B: $i,A: $i] : ( c_in @ ( c_minus @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[23365:[bind(A,$thf( E )),bind(B,$thf( c_SetInterval_OlessThan @ E @ tc_nat )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(23501,plain,
! [B: $i,A: $i] : ( c_in @ ( c_minus @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(simp,[status(thm)],[23366]) ).
thf(24277,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_minus @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
| ( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
!= ( c_SetInterval_OlessThan @ B @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[467,23501]) ).
thf(24278,plain,
! [A: $i] : ( c_in @ ( c_minus @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[24277:[bind(A,$thf( A )),bind(B,$thf( c_0 ))]]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(605,plain,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(606,plain,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[605]) ).
thf(24551,plain,
c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ),
inference(rewrite,[status(thm)],[24278,606]) ).
thf(24559,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_in @ c_emptyset @ c_0 @ ( tc_set @ tc_nat ) )
| ( A != c_Finite__Set_OFinites ) ),
inference(paramod_ordered,[status(thm)],[523,24551]) ).
thf(24560,plain,
( ( c_less @ c_0 @ c_Finite__Set_OFinites @ tc_nat )
| ( c_in @ c_emptyset @ c_0 @ ( tc_set @ tc_nat ) ) ),
inference(pattern_uni,[status(thm)],[24559:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(285,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).
thf(1061,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1062,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) ) ),
inference(lifteq,[status(thm)],[1061]) ).
thf(9538,plain,
! [B: $i,A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ B ) ) )
| ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
!= ( c_Message_Oanalz @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1036,1062]) ).
thf(9539,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9538:[bind(A,$thf( C )),bind(B,$thf( c_Message_Oparts @ C ))]]) ).
thf(9594,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ),
inference(simp,[status(thm)],[9539]) ).
thf(82511,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ),
inference(rewrite,[status(thm)],[9594,9105]) ).
thf(82538,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ B ) ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) )
!= ( c_Message_Oparts @ B ) ) ),
inference(paramod_ordered,[status(thm)],[82511,82511]) ).
thf(82539,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[82538:[bind(A,$thf( D )),bind(B,$thf( c_Message_Osynth @ ( c_Message_Oparts @ D ) ))]]) ).
thf(82701,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[82539]) ).
thf(85192,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) ) ),
inference(rewrite,[status(thm)],[82701,82511]) ).
thf(85230,plain,
! [A: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ) ) )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
!= ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[13332,85192]) ).
thf(85231,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[85230:[bind(A,$thf( c_emptyset ))]]) ).
thf(256,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(1002,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1003,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(lifteq,[status(thm)],[1002]) ).
thf(9071,plain,
! [B: $i,A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ B ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
!= ( c_Message_Oparts @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1003,991]) ).
thf(9072,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9071:[bind(A,$thf( C )),bind(B,$thf( c_Message_Oanalz @ C ))]]) ).
thf(9106,plain,
! [A: $i] :
( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) ) ),
inference(simp,[status(thm)],[9072]) ).
thf(69993,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) ) )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1021,9106]) ).
thf(69994,plain,
( ( c_union @ ( c_Message_Oparts @ c_emptyset ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[69993:[bind(A,$thf( c_emptyset ))]]) ).
thf(12512,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
!= ( c_Message_Osynth @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12426,1062]) ).
thf(12513,plain,
( ( c_union @ ( c_Message_Oanalz @ ( c_Message_Oparts @ c_emptyset ) ) @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[12512:[bind(A,$thf( c_Message_Oparts @ c_emptyset ))]]) ).
thf(14723,plain,
( ( c_union @ ( c_Message_Oparts @ c_emptyset ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[12513,13332,9223,1036]) ).
thf(70227,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[69994,14723,1021]) ).
thf(70243,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70227,9105]) ).
thf(70244,plain,
( ( c_union @ ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ),
inference(pattern_uni,[status(thm)],[70243:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(70063,plain,
! [A: $i] :
( ( ( c_union @ c_emptyset @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) ) )
| ( ( c_Message_Oparts @ c_emptyset )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[954,9106]) ).
thf(70064,plain,
( ( c_union @ c_emptyset @ ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[70063:[bind(A,$thf( c_emptyset ))]]) ).
thf(70576,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[70064,874,1021]) ).
thf(70578,plain,
! [A: $i] :
( ( ( c_Message_Oparts @ A )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70576,1036]) ).
thf(70579,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[70578:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(70731,plain,
( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[70579,70576,1021]) ).
thf(70733,plain,
( ( c_union @ ( c_Message_Oparts @ c_emptyset ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[14723,70731]) ).
thf(71001,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(rewrite,[status(thm)],[70733,1021,991]) ).
thf(79424,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ),
inference(rewrite,[status(thm)],[70244,9106,71001]) ).
thf(85507,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ),
inference(rewrite,[status(thm)],[85231,79424,13332]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
!= c_emptyset )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
!= c_emptyset )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(163,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(782,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( B = c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( B = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(20208,plain,
! [B: $i,A: $i] :
( ( ( c_inter @ ( c_Pow @ c_emptyset @ A ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
!= ( c_insert @ c_emptyset @ B @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[975,20100]) ).
thf(20209,plain,
( ( c_inter @ ( c_Pow @ c_emptyset @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[20208:[bind(A,$thf( tc_nat )),bind(B,$thf( c_emptyset ))]]) ).
thf(20324,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_Pow @ c_emptyset @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[658,20209]) ).
thf(20350,plain,
! [B: $i,A: $i] :
( ( ( c_Pow @ c_emptyset @ tc_nat )
!= c_emptyset )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20324]) ).
thf(20368,plain,
( ( c_Pow @ c_emptyset @ tc_nat )
!= c_emptyset ),
inference(simp,[status(thm)],[20350]) ).
thf(20386,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Pow @ c_0 @ tc_nat )
!= c_emptyset )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,20368]) ).
thf(20387,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Pow @ c_0 @ tc_nat )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[20386:[bind(A,$thf( c_emptyset ))]]) ).
thf(43556,plain,
! [A: $i] :
( ( ( c_Pow @ c_0 @ tc_nat )
!= c_emptyset )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,20387]) ).
thf(43558,plain,
! [A: $i] :
( ( ( c_Pow @ c_0 @ tc_nat )
!= c_emptyset )
| ( A != c_emptyset )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[43556]) ).
thf(43578,plain,
( ( ( c_Pow @ c_0 @ tc_nat )
!= c_emptyset )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[43558]) ).
thf(43940,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_Pow @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[415,43578]) ).
thf(43941,plain,
( ~ ( c_lessequals @ ( c_Pow @ c_0 @ tc_nat ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[43940:[bind(A,$thf( c_Pow @ c_0 @ tc_nat ))]]) ).
thf(1600,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_UNIV @ c_0 @ tc_nat )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1433]) ).
thf(1601,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_UNIV @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[1600:[bind(A,$thf( c_emptyset ))]]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(371,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(417,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(973,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
inference(lifteq,[status(thm)],[972]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(883,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(polarity_switch,[status(thm)],[883]) ).
thf(885,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(lifteq,[status(thm)],[884]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
thf(436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3879,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg )
| ( A
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[523,405]) ).
thf(3880,plain,
( ( c_less @ c_0 @ ( c_Message_Oanalz @ v_G ) @ tc_nat )
| ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg ) ),
inference(pattern_uni,[status(thm)],[3879:[bind(A,$thf( c_Message_Oanalz @ v_G ))]]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
thf(1254,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_inter @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
thf(569,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_inter @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(570,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_inter @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(lifteq,[status(thm)],[569]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1298,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(lifteq,[status(thm)],[1297]) ).
thf(71003,plain,
! [A: $i] :
( ( ( c_Message_Oparts @ A )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71001,1036]) ).
thf(71004,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[71003:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(71222,plain,
( ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(rewrite,[status(thm)],[71004,71001,70731]) ).
thf(71365,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) )
!= ( c_Message_Osynth @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71222,991]) ).
thf(71366,plain,
( ( c_union @ ( c_Message_Oparts @ ( c_Message_Oanalz @ c_emptyset ) ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[71365:[bind(A,$thf( c_Message_Oanalz @ c_emptyset ))]]) ).
thf(71729,plain,
( ( c_union @ ( c_Message_Oparts @ c_emptyset ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[71366,71222,1003]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
thf(504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(22682,plain,
! [A: $i] :
( ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Oanalz @ v_G ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,1437]) ).
thf(22694,plain,
! [A: $i] :
( ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg )
| ( A
!= ( c_Message_Oanalz @ v_G ) )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[22682]) ).
thf(22710,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ v_G )
!= c_0 ) ),
inference(simp,[status(thm)],[22694]) ).
thf(101,axiom,
class_Nat_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(619,plain,
class_Nat_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[750]) ).
thf(24557,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,24551]) ).
thf(24558,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(pattern_uni,[status(thm)],[24557:[bind(A,$thf( c_emptyset ))]]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(9569,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Osynth @ c_emptyset ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oanalz @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9223,1062]) ).
thf(9570,plain,
( ( c_union @ ( c_Message_Osynth @ c_emptyset ) @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[9569:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(9135,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Osynth @ c_emptyset ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9116,991]) ).
thf(9136,plain,
( ( c_union @ ( c_Message_Osynth @ c_emptyset ) @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[9135:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(9620,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ),
inference(rewrite,[status(thm)],[9570,9136]) ).
thf(82553,plain,
! [A: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9620,82511]) ).
thf(82554,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[82553:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ))]]) ).
thf(82781,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ),
inference(rewrite,[status(thm)],[82554,9620]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(1286,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[1286]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
thf(802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(15603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset )
| ( ( c_in @ c_0 @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
!= ( c_in @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10673,549]) ).
thf(15604,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15603:[bind(A,$thf( c_0 )),bind(B,$thf( c_SetInterval_OatMost @ c_0 @ tc_nat )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(15699,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(simp,[status(thm)],[15604]) ).
thf(15823,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ c_0 @ C @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[604,15699]) ).
thf(15857,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ c_0 @ C @ tc_nat ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) )
| ( B != tc_nat ) ),
inference(simp,[status(thm)],[15823]) ).
thf(15881,plain,
! [A: $i] :
( ( c_uminus @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) ),
inference(simp,[status(thm)],[15857]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
thf(1059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1544,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
| ( A != c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[415,543]) ).
thf(1545,plain,
( ~ ( c_lessequals @ c_UNIV @ c_0 @ tc_nat )
| ~ ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(pattern_uni,[status(thm)],[1544:[bind(A,$thf( c_UNIV ))]]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(558,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[557]) ).
thf(559,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[558]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
thf(636,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(637,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[636]) ).
thf(638,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[637]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
thf(1147,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(20308,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_Pow @ c_emptyset @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[869,20209]) ).
thf(20346,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_Pow @ c_emptyset @ tc_nat ) )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20308]) ).
thf(20364,plain,
( ( c_Pow @ c_emptyset @ tc_nat )
!= ( c_uminus @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ tc_nat ) ) ) ),
inference(simp,[status(thm)],[20346]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(1100,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(83,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(580,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(5778,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[580,543]) ).
thf(5779,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[5778]) ).
thf(5792,plain,
! [B: $i,A: $i] :
( ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[5779]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ B @ C )
| ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
thf(817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ B @ C )
| ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(15611,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ C @ F @ E ) @ D @ E )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
!= ( c_in @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1215,549]) ).
thf(15612,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15611:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( c_Message_Omsg_ONumber @ G )),bind(D,$thf( c_Message_Osynth @ H )),bind(E,$thf( tc_Message_Omsg ))]]) ).
thf(15705,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[15612]) ).
thf(26935,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ E ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[604,15705]) ).
thf(26973,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_Message_Osynth @ E ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[26935]) ).
thf(26991,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) )
!= ( c_Message_Osynth @ C ) ),
inference(simp,[status(thm)],[26973]) ).
thf(10,axiom,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(421,plain,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(198,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(870,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(15664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ B @ E @ D ) @ C @ D )
!= c_emptyset )
| ( ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[592,549]) ).
thf(15665,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15664:[bind(A,$thf( F )),bind(B,$thf( c_SetInterval_OatMost @ F @ tc_nat )),bind(C,$thf( c_Finite__Set_OFinites )),bind(D,$thf( tc_set @ tc_nat )),bind(E,$thf( E ))]]) ).
thf(15695,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_insert @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[15665]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[768]) ).
thf(770,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[769]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
thf(881,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(10680,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1281,543]) ).
thf(10694,plain,
! [B: $i,A: $i] :
( ( A != c_UNIV )
| ( ( c_insert @ A @ c_emptyset @ B )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[10680]) ).
thf(10702,plain,
( ( c_insert @ c_UNIV @ c_emptyset @ ( tc_set @ tc_nat ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[10694]) ).
thf(15821,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ c_0 @ C @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[869,15699]) ).
thf(15854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ c_0 @ C @ tc_nat ) )
| ( A
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) )
| ( B != tc_nat ) ),
inference(simp,[status(thm)],[15821]) ).
thf(15878,plain,
! [A: $i] :
( ( c_insert @ c_0 @ A @ tc_nat )
!= ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[15854]) ).
thf(34,axiom,
! [A: $i] :
( ( c_Orderings_Omin @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
thf(474,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(475,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ c_0 @ tc_nat )
= c_0 ),
inference(lifteq,[status(thm)],[474]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(88,axiom,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(590,plain,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(591,plain,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
inference(lifteq,[status(thm)],[590]) ).
thf(1451,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( A
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[415,1378]) ).
thf(1452,plain,
( ~ ( c_lessequals @ ( c_Message_Oanalz @ v_G ) @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[1451:[bind(A,$thf( c_Message_Oanalz @ v_G ))]]) ).
thf(1753,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Oanalz @ v_G ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,1452]) ).
thf(1773,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( ( c_Message_Oanalz @ v_G )
!= c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[1753]) ).
thf(1774,plain,
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( ( c_Message_Oanalz @ v_G )
!= c_0 ) ),
inference(simp,[status(thm)],[1773]) ).
thf(1840,plain,
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_emptyset != c_0 )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[1021,1774]) ).
thf(1850,plain,
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[1840]) ).
thf(1861,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G )
| ( A
!= ( c_Message_Osynth @ c_0 ) ) ),
inference(paramod_ordered,[status(thm)],[415,1850]) ).
thf(1862,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ c_0 ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G ) ),
inference(pattern_uni,[status(thm)],[1861:[bind(A,$thf( c_Message_Osynth @ c_0 ))]]) ).
thf(2516,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( c_emptyset != v_G )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Osynth @ c_0 ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,1862]) ).
thf(2536,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( c_emptyset != v_G )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2516]) ).
thf(2538,plain,
( ( c_emptyset != c_0 )
| ( c_emptyset != v_G )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 ) ),
inference(simp,[status(thm)],[2536]) ).
thf(3669,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset != v_G )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,2538]) ).
thf(3670,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( c_emptyset != v_G )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[3669:[bind(A,$thf( c_emptyset ))]]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
thf(623,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(cnf,[status(esa)],[645]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(20384,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_Pow @ c_emptyset @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[415,20368]) ).
thf(20385,plain,
( ~ ( c_lessequals @ ( c_Pow @ c_emptyset @ tc_nat ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[20384:[bind(A,$thf( c_Pow @ c_emptyset @ tc_nat ))]]) ).
thf(38436,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ ( c_Pow @ c_emptyset @ tc_nat ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,20385]) ).
thf(38447,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A
!= ( c_Pow @ c_emptyset @ tc_nat ) )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[38436]) ).
thf(38466,plain,
( ( c_emptyset != c_0 )
| ( ( c_Pow @ c_emptyset @ tc_nat )
!= c_0 ) ),
inference(simp,[status(thm)],[38447]) ).
thf(43065,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Pow @ c_emptyset @ tc_nat )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,38466]) ).
thf(43066,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Pow @ c_emptyset @ tc_nat )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[43065:[bind(A,$thf( c_emptyset ))]]) ).
thf(238,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(966,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
thf(492,plain,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(634,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(polarity_switch,[status(thm)],[633]) ).
thf(635,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(lifteq,[status(thm)],[634]) ).
thf(4526,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
!= c_emptyset )
| ( ( c_insert @ c_0 @ c_emptyset @ tc_nat )
!= ( c_insert @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[807,635]) ).
thf(4527,plain,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[4526:[bind(A,$thf( c_0 )),bind(B,$thf( c_emptyset )),bind(C,$thf( tc_nat ))]]) ).
thf(4540,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[415,4527]) ).
thf(4541,plain,
( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[4540:[bind(A,$thf( c_SetInterval_OatMost @ c_0 @ tc_nat ))]]) ).
thf(5517,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,4541]) ).
thf(5520,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[5517]) ).
thf(5525,plain,
( ( c_emptyset != c_0 )
| ( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
!= c_0 ) ),
inference(simp,[status(thm)],[5520]) ).
thf(5540,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,5525]) ).
thf(5541,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[5540:[bind(A,$thf( c_emptyset ))]]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
thf(514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_union @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_inter @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_union @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_inter @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C )
= ( c_uminus @ ( c_union @ A @ B @ C ) @ ( tc_set @ C ) ) ),
inference(lifteq,[status(thm)],[573]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(1051,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(179,axiom,
! [A: $i] :
( ( c_Union @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
thf(820,plain,
! [A: $i] :
( ( c_Union @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(821,plain,
! [A: $i] :
( ( c_Union @ c_UNIV @ A )
= c_UNIV ),
inference(lifteq,[status(thm)],[820]) ).
thf(214,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(905,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[478]) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[479]) ).
thf(12677,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ ( c_Message_Osynth @ c_emptyset ) @ c_0 @ tc_nat )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,12638]) ).
thf(12678,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ ( c_Message_Osynth @ c_emptyset ) @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[12677:[bind(A,$thf( c_emptyset ))]]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(1072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
inference(lifteq,[status(thm)],[626]) ).
thf(33998,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(rewrite,[status(thm)],[627,420]) ).
thf(20101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_SetInterval_OlessThan @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[869,15679]) ).
thf(20145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ ( c_SetInterval_OlessThan @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20101]) ).
thf(20174,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ tc_nat ) ) ) ),
inference(simp,[status(thm)],[20145]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).
thf(998,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(71376,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) )
!= ( c_Message_Osynth @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71222,1062]) ).
thf(71377,plain,
( ( c_union @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ c_emptyset ) ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ c_emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[71376:[bind(A,$thf( c_Message_Oanalz @ c_emptyset ))]]) ).
thf(348,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).
thf(1194,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1195,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
inference(lifteq,[status(thm)],[1194]) ).
thf(72045,plain,
( ( c_union @ ( c_Message_Oanalz @ c_emptyset ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ),
inference(rewrite,[status(thm)],[71377,71222,1195]) ).
thf(1729,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_UNIV != c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1608]) ).
thf(1730,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( c_UNIV != c_0 ) ),
inference(pattern_uni,[status(thm)],[1729:[bind(A,$thf( c_emptyset ))]]) ).
thf(2908,plain,
! [B: $i,A: $i] :
( ( c_UNIV != c_0 )
| ( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1294,1730]) ).
thf(2940,plain,
! [B: $i,A: $i] :
( ( c_UNIV != c_0 )
| ( c_emptyset != c_emptyset )
| ( A != c_0 )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[2908]) ).
thf(2982,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[2940]) ).
thf(213,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(904,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(2439,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_UNIV @ B )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[904,543]) ).
thf(2442,plain,
! [B: $i,A: $i] :
( ( A != c_UNIV )
| ( c_UNIV != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[2439]) ).
thf(2447,plain,
c_UNIV != c_Finite__Set_OFinites,
inference(simp,[status(thm)],[2442]) ).
thf(2449,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_Finite__Set_OFinites != c_0 )
| ( A != c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[415,2447]) ).
thf(2450,plain,
( ~ ( c_lessequals @ c_UNIV @ c_0 @ tc_nat )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(pattern_uni,[status(thm)],[2449:[bind(A,$thf( c_UNIV ))]]) ).
thf(2493,plain,
! [A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ c_UNIV @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,2450]) ).
thf(2506,plain,
! [A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( c_UNIV != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2493]) ).
thf(2508,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[2506]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
= ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
= ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1542,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ c_0 )
| ( A
!= ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[415,543]) ).
thf(1543,plain,
( ~ ( c_lessequals @ ( tc_set @ tc_nat ) @ c_0 @ tc_nat )
| ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ c_0 ) ),
inference(pattern_uni,[status(thm)],[1542:[bind(A,$thf( tc_set @ tc_nat ))]]) ).
thf(6746,plain,
! [A: $i] :
( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ ( tc_set @ tc_nat ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,1543]) ).
thf(6795,plain,
! [A: $i] :
( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ c_0 )
| ( ( tc_set @ tc_nat )
!= c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[6746]) ).
thf(6809,plain,
( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ c_0 )
| ( ( tc_set @ tc_nat )
!= c_0 ) ),
inference(simp,[status(thm)],[6795]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ C )
= ( c_union @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(1169,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ C )
= ( c_union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(692,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(cnf,[status(esa)],[744]) ).
thf(80001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_inter @ B @ D @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[799,745]) ).
thf(80002,plain,
! [B: $i,A: $i] : ( c_in @ ( c_inter @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[80001:[bind(A,$thf( E )),bind(B,$thf( c_SetInterval_OlessThan @ E @ tc_nat )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(80256,plain,
! [B: $i,A: $i] : ( c_in @ ( c_inter @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(simp,[status(thm)],[80002]) ).
thf(234,axiom,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(955,plain,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(956,plain,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
inference(lifteq,[status(thm)],[955]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
thf(1119,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(15729,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ v_X @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[658,15687]) ).
thf(15760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ v_X @ C @ tc_Message_Omsg )
!= c_emptyset )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[15729]) ).
thf(15774,plain,
! [A: $i] :
( ( c_insert @ v_X @ A @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[15760]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
thf(1104,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(849,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1380,plain,
( ( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[1021,1378]) ).
thf(1381,plain,
( ( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[1380]) ).
thf(1521,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_emptyset != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1381]) ).
thf(1522,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_emptyset != v_G ) ),
inference(pattern_uni,[status(thm)],[1521:[bind(A,$thf( c_emptyset ))]]) ).
thf(2025,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_0 != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1522]) ).
thf(2026,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[2025:[bind(A,$thf( c_emptyset ))]]) ).
thf(2034,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_0 != v_G ) ),
inference(simp,[status(thm)],[2026]) ).
thf(2763,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_0 != v_G )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,2034]) ).
thf(2783,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_0 != v_G )
| ( c_emptyset != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2763]) ).
thf(2788,plain,
( ( ( c_Message_Osynth @ c_0 )
!= c_emptyset )
| ( c_0 != v_G )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[2783]) ).
thf(2789,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( A
!= ( c_Message_Osynth @ c_0 ) ) ),
inference(paramod_ordered,[status(thm)],[415,2788]) ).
thf(2790,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ c_0 ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[2789:[bind(A,$thf( c_Message_Osynth @ c_0 ))]]) ).
thf(5623,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Osynth @ c_0 ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,2790]) ).
thf(5626,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( A
!= ( c_Message_Osynth @ c_0 ) )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[5623]) ).
thf(5634,plain,
( ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 ) ),
inference(simp,[status(thm)],[5626]) ).
thf(5818,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( A
!= ( c_Message_Osynth @ c_0 ) ) ),
inference(paramod_ordered,[status(thm)],[523,5634]) ).
thf(5819,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_0 ) @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[5818:[bind(A,$thf( c_Message_Osynth @ c_0 ))]]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
thf(526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(cnf,[status(esa)],[526]) ).
thf(3491,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_SetInterval_OlessThan @ c_0 @ c_0 )
= c_emptyset )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,467]) ).
thf(3492,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( ( c_SetInterval_OlessThan @ c_0 @ c_0 )
= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[3491:[bind(A,$thf( tc_nat ))]]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_1) ).
thf(452,plain,
! [A: $i] :
( ~ ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(678,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(cnf,[status(esa)],[677]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
thf(659,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(660,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[659]) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[660]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
inference(cnf,[status(esa)],[545]) ).
thf(66,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(544,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(3851,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_HOL_Ominus @ c_0 )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,544]) ).
thf(3852,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( class_HOL_Ominus @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3851:[bind(A,$thf( tc_nat ))]]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(15626,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ C @ F @ E ) @ D @ E )
!= c_emptyset )
| ( ( c_in @ A @ c_UNIV @ B )
!= ( c_in @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[904,549]) ).
thf(15627,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ C @ B ) @ c_UNIV @ B )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[15626:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_UNIV )),bind(E,$thf( B ))]]) ).
thf(15675,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ C @ B ) @ c_UNIV @ B )
!= c_emptyset ),
inference(simp,[status(thm)],[15627]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_UNIV @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
thf(790,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_UNIV @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_UNIV @ B )
= A ),
inference(lifteq,[status(thm)],[790]) ).
thf(34549,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ C @ B )
!= c_emptyset ),
inference(rewrite,[status(thm)],[15675,791]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(cnf,[status(esa)],[712]) ).
thf(714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(lifteq,[status(thm)],[713]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
thf(1074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(24899,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ D @ ( c_insert @ C @ F @ E ) @ E )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
!= ( c_in @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1280,602]) ).
thf(24900,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ C ) @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24899:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( c_Message_Omsg_OAgent @ G )),bind(D,$thf( c_Message_Osynth @ H )),bind(E,$thf( tc_Message_Omsg ))]]) ).
thf(24950,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ C ) @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[24900]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(920,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(5389,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[550,543]) ).
thf(5394,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[5389]) ).
thf(5406,plain,
! [B: $i,A: $i] :
( ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[5394]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ B @ D @ A )
| ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ B @ D @ A )
| ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ B @ D @ A )
| ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(cnf,[status(esa)],[528]) ).
thf(6871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( ( c_less @ B @ A @ tc_nat )
!= ( c_less @ C @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[6851,449]) ).
thf(6872,plain,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ c_0 @ tc_nat ) @ tc_nat ) @ tc_nat ),
inference(pattern_uni,[status(thm)],[6871:[bind(A,$thf( c_0 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(6964,plain,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ c_0 @ tc_nat ) @ tc_nat ) @ tc_nat ),
inference(simp,[status(thm)],[6872]) ).
thf(422,plain,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
inference(lifteq,[status(thm)],[421]) ).
thf(1806,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ c_0 @ tc_nat ) @ tc_nat )
= c_0 ),
inference(rewrite,[status(thm)],[422,420]) ).
thf(6991,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(rewrite,[status(thm)],[6964,1806]) ).
thf(7021,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_less @ c_0 @ c_0 @ c_0 )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[415,6991]) ).
thf(7022,plain,
( ~ ( c_lessequals @ tc_nat @ c_0 @ tc_nat )
| ~ ( c_less @ c_0 @ c_0 @ c_0 ) ),
inference(pattern_uni,[status(thm)],[7021:[bind(A,$thf( tc_nat ))]]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
thf(761,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__right_0) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(46831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( ( c_less @ B @ C @ A )
!= ( c_less @ c_0 @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[678,6991]) ).
thf(46832,plain,
( ~ ( class_Orderings_Oord @ tc_nat )
| ~ ( c_in @ c_0 @ ( c_SetInterval_OlessThan @ c_0 @ tc_nat ) @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[46831:[bind(A,$thf( tc_nat )),bind(B,$thf( c_0 )),bind(C,$thf( c_0 ))]]) ).
thf(149,axiom,
class_Orderings_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(746,plain,
class_Orderings_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(58957,plain,
( ~ $true
| ~ ( c_in @ c_0 @ c_emptyset @ tc_nat ) ),
inference(rewrite,[status(thm)],[46832,467,746]) ).
thf(58958,plain,
~ ( c_in @ c_0 @ c_emptyset @ tc_nat ),
inference(simp,[status(thm)],[58957]) ).
thf(59035,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_in @ c_0 @ c_0 @ tc_nat )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,58958]) ).
thf(59036,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_in @ c_0 @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[59035:[bind(A,$thf( c_emptyset ))]]) ).
thf(69425,plain,
! [A: $i] :
( ~ ( c_in @ c_0 @ c_0 @ tc_nat )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,59036]) ).
thf(69567,plain,
! [A: $i] :
( ~ ( c_in @ c_0 @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[69425]) ).
thf(69599,plain,
( ~ ( c_in @ c_0 @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[69567]) ).
thf(22917,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_Pow @ c_emptyset @ A ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
!= c_emptyset )
| ( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
!= ( c_insert @ c_emptyset @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[975,15682]) ).
thf(22918,plain,
! [A: $i] :
( ( c_inter @ ( c_Pow @ c_emptyset @ A ) @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[22917:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(23533,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_Pow @ c_emptyset @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(paramod_ordered,[status(thm)],[869,22918]) ).
thf(23576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_Pow @ c_emptyset @ C ) )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ C ) ) ),
inference(simp,[status(thm)],[23533]) ).
thf(23594,plain,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
!= ( c_uminus @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ A ) ) ) ),
inference(simp,[status(thm)],[23576]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_minus @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) )
= ( c_minus @ D @ B @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(1067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_minus @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) )
= ( c_minus @ D @ B @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(16744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[869,15685]) ).
thf(16768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[16744]) ).
thf(16780,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg )
!= ( c_uminus @ ( c_Message_Osynth @ c_emptyset ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(simp,[status(thm)],[16768]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ( c_union @ c_UNIV @ A @ B )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( c_union @ c_UNIV @ A @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
thf(1057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(582,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(polarity_switch,[status(thm)],[581]) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ B @ A @ C )
!= A ),
inference(lifteq,[status(thm)],[582]) ).
thf(6608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_0 != B )
| ( A
!= ( c_List_Olist_OCons @ C @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[523,583]) ).
thf(6609,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_List_Olist_OCons @ A @ B @ C ) @ tc_nat )
| ( c_0 != B ) ),
inference(pattern_uni,[status(thm)],[6608:[bind(A,$thf( c_List_Olist_OCons @ E @ F @ G )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(6612,plain,
! [B: $i,A: $i] : ( c_less @ c_0 @ ( c_List_Olist_OCons @ A @ c_0 @ B ) @ tc_nat ),
inference(simp,[status(thm)],[6609]) ).
thf(6626,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_List_Olist_OCons @ A @ c_0 @ B ) @ tc_nat )
!= ( c_less @ C @ c_0 @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[6612,449]) ).
thf(6643,plain,
! [C: $i,B: $i,A: $i] :
( ( c_0 != C )
| ( ( c_List_Olist_OCons @ A @ c_0 @ B )
!= c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[6626]) ).
thf(6652,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ c_0 @ B )
!= c_0 ),
inference(simp,[status(thm)],[6643]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1350,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[1021,405]) ).
thf(1355,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[1350]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
thf(1123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(18,axiom,
class_Orderings_Olinorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(441,plain,
class_Orderings_Olinorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(44029,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) )
| ( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[441,666]) ).
thf(44030,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
= ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) ),
inference(pattern_uni,[status(thm)],[44029:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(44111,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
= ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) ),
inference(simp,[status(thm)],[44030]) ).
thf(44323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ B @ C )
= c_emptyset )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44111,869]) ).
thf(44324,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= c_emptyset ),
inference(pattern_uni,[status(thm)],[44323:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OatLeast @ D @ tc_IntDef_Oint )),bind(C,$thf( tc_IntDef_Oint ))]]) ).
thf(44431,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= c_emptyset ),
inference(simp,[status(thm)],[44324]) ).
thf(2911,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1294,2491]) ).
thf(2953,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_emptyset )
| ( A != c_0 )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[2911]) ).
thf(2969,plain,
! [A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[2953]) ).
thf(11,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
thf(423,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(424,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
inference(lifteq,[status(thm)],[423]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(141,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(728,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(729,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(cnf,[status(esa)],[728]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
thf(584,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
inference(lifteq,[status(thm)],[584]) ).
thf(24895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset )
| ( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg )
!= ( c_in @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[405,602]) ).
thf(24896,plain,
! [A: $i] :
( ( c_inter @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24895:[bind(A,$thf( v_X )),bind(B,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( D ))]]) ).
thf(24948,plain,
! [A: $i] :
( ( c_inter @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[24896]) ).
thf(25202,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( c_inter @ A @ A @ B )
!= ( c_inter @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_insert @ v_X @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
inference(paramod_ordered,[status(thm)],[585,24948]) ).
thf(25222,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_emptyset @ A )
!= ( c_inter @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_insert @ v_X @ B @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(simp,[status(thm)],[25202]) ).
thf(25245,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_emptyset @ A )
!= ( c_inter @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_insert @ v_X @ B @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(simp,[status(thm)],[25222]) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
inference(lifteq,[status(thm)],[810]) ).
thf(59163,plain,
! [A: $i] :
( ( c_inter @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(rewrite,[status(thm)],[25245,811]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
thf(1238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(5923,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 )
| ( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[472,543]) ).
thf(5924,plain,
( ( c_Finite__Set_Ocard @ c_UNIV @ tc_nat )
= c_0 ),
inference(pattern_uni,[status(thm)],[5923:[bind(A,$thf( c_UNIV )),bind(B,$thf( tc_nat ))]]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatMost @ B @ A )
!= ( c_SetInterval_OatMost @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatMost @ B @ A )
!= ( c_SetInterval_OatMost @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(5814,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_0 != v_G )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,5634]) ).
thf(5815,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( c_0 != v_G )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[5814:[bind(A,$thf( c_emptyset ))]]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
thf(561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(406,plain,
~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(407,plain,
~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
inference(polarity_switch,[status(thm)],[406]) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
inference(lifteq,[status(thm)],[692]) ).
thf(24817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset )
| ( ( c_in @ c_0 @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
!= ( c_in @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10673,602]) ).
thf(24818,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_insert @ c_0 @ A @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24817:[bind(A,$thf( c_0 )),bind(B,$thf( c_SetInterval_OatMost @ c_0 @ tc_nat )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(24964,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_insert @ c_0 @ A @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(simp,[status(thm)],[24818]) ).
thf(2605,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( A != c_Finite__Set_OFinites ) ),
inference(paramod_ordered,[status(thm)],[415,2491]) ).
thf(2606,plain,
( ~ ( c_lessequals @ c_Finite__Set_OFinites @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[2605:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(33,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(473,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(3813,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_HOL_Ominus @ c_0 )
| ( A != tc_IntDef_Oint ) ),
inference(paramod_ordered,[status(thm)],[523,473]) ).
thf(3814,plain,
( ( c_less @ c_0 @ tc_IntDef_Oint @ tc_nat )
| ( class_HOL_Ominus @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3813:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(10938,plain,
! [B: $i,A: $i] :
( ( ( c_Set_Ocontents @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ B )
= A )
| ( ( c_insert @ c_0 @ c_emptyset @ tc_nat )
!= ( c_insert @ A @ c_emptyset @ B ) ) ),
inference(paramod_ordered,[status(thm)],[807,1287]) ).
thf(10939,plain,
( ( c_Set_Ocontents @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
= c_0 ),
inference(pattern_uni,[status(thm)],[10938:[bind(A,$thf( c_0 )),bind(B,$thf( tc_nat ))]]) ).
thf(624,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(cnf,[status(esa)],[623]) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset )
| ~ ( c_in @ A @ B @ ( tc_set @ C ) ) ),
inference(lifteq,[status(thm)],[624]) ).
thf(55,axiom,
class_Nat_Opower @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(520,plain,
class_Nat_Opower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(3749,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Nat_Opower @ c_0 )
| ( A != tc_IntDef_Oint ) ),
inference(paramod_ordered,[status(thm)],[523,520]) ).
thf(3750,plain,
( ( c_less @ c_0 @ tc_IntDef_Oint @ tc_nat )
| ( class_Nat_Opower @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3749:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_emptyset
!= ( c_Union @ B @ C ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
thf(889,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_emptyset
!= ( c_Union @ B @ C ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
thf(459,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset ) ),
inference(cnf,[status(esa)],[459]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset )
| ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(lifteq,[status(thm)],[460]) ).
thf(1633,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1450]) ).
thf(1634,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[1633:[bind(A,$thf( c_emptyset ))]]) ).
thf(25,axiom,
class_Orderings_Oord @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(456,plain,
class_Orderings_Oord @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
thf(916,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
thf(564,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(565,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(cnf,[status(esa)],[564]) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) )
| ~ ( class_Orderings_Oorder @ A ) ),
inference(lifteq,[status(thm)],[565]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(484,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(15,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
thf(432,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(433,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(cnf,[status(esa)],[432]) ).
thf(434,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(lifteq,[status(thm)],[433]) ).
thf(435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ A @ B @ C @ ( c_Datatype__Universe_OScons @ A @ D @ B @ C ) )
= D ),
introduced(tautology,[new_symbols(inverse(c_Datatype__Universe_OScons),[sk1])]) ).
thf(2306,plain,
! [A: $i] :
( ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[799,543]) ).
thf(2309,plain,
! [A: $i] :
( ( ( c_SetInterval_OlessThan @ A @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[2306]) ).
thf(2313,plain,
! [A: $i] :
( ( c_SetInterval_OlessThan @ A @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[2309]) ).
thf(3444,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Oanalz @ c_0 )
= c_emptyset )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,1021]) ).
thf(3445,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Oanalz @ c_0 )
= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[3444:[bind(A,$thf( c_emptyset ))]]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(1012,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(725,plain,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[724]) ).
thf(726,plain,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[725]) ).
thf(727,plain,
! [A: $i] :
( ( sk8 @ ( c_Message_OinvKey @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Message_OinvKey),[sk8])]) ).
thf(2239,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ A )
= B )
| ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
!= ( c_Message_OinvKey @ B ) ) ),
inference(paramod_ordered,[status(thm)],[591,727]) ).
thf(2240,plain,
! [A: $i] :
( ( sk8 @ A )
= ( c_Message_OinvKey @ A ) ),
inference(pattern_uni,[status(thm)],[2239:[bind(A,$thf( C )),bind(B,$thf( c_Message_OinvKey @ C ))]]) ).
thf(2245,plain,
! [A: $i] :
( ( sk8 @ A )
= ( c_Message_OinvKey @ A ) ),
inference(simp,[status(thm)],[2240]) ).
thf(15791,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_insert @ v_X @ B @ tc_Message_Omsg ) ) ),
inference(paramod_ordered,[status(thm)],[415,15774]) ).
thf(15792,plain,
! [A: $i] :
( ~ ( c_lessequals @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[15791:[bind(A,$thf( c_insert @ v_X @ D @ tc_Message_Omsg )),bind(B,$thf( D ))]]) ).
thf(15797,plain,
! [A: $i] :
( ~ ( c_lessequals @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[15792]) ).
thf(47432,plain,
! [B: $i,A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ ( c_insert @ v_X @ B @ tc_Message_Omsg ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,15797]) ).
thf(47434,plain,
! [B: $i,A: $i] :
( ( c_emptyset != c_0 )
| ( A
!= ( c_insert @ v_X @ B @ tc_Message_Omsg ) )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[47432]) ).
thf(47454,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_insert @ v_X @ A @ tc_Message_Omsg )
!= c_0 ) ),
inference(simp,[status(thm)],[47434]) ).
thf(47591,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_insert @ v_X @ B @ tc_Message_Omsg )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,47454]) ).
thf(47592,plain,
! [A: $i] :
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_insert @ v_X @ A @ tc_Message_Omsg )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[47591:[bind(A,$thf( c_emptyset ))]]) ).
thf(47606,plain,
! [A: $i] :
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_insert @ v_X @ A @ tc_Message_Omsg )
!= c_0 ) ),
inference(simp,[status(thm)],[47592]) ).
thf(20119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_SetInterval_OlessThan @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[658,15679]) ).
thf(20152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ ( c_SetInterval_OlessThan @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20119]) ).
thf(20184,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[20152]) ).
thf(4544,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_SetInterval_OatMost @ c_0 @ c_0 )
!= c_emptyset )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[415,4527]) ).
thf(4545,plain,
( ~ ( c_lessequals @ tc_nat @ c_0 @ tc_nat )
| ( ( c_SetInterval_OatMost @ c_0 @ c_0 )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[4544:[bind(A,$thf( tc_nat ))]]) ).
thf(6123,plain,
! [A: $i] :
( ( ( c_SetInterval_OatMost @ c_0 @ c_0 )
!= c_emptyset )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ tc_nat @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,4545]) ).
thf(6147,plain,
! [A: $i] :
( ( ( c_SetInterval_OatMost @ c_0 @ c_0 )
!= c_emptyset )
| ( tc_nat != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[6123]) ).
thf(6153,plain,
( ( ( c_SetInterval_OatMost @ c_0 @ c_0 )
!= c_emptyset )
| ( tc_nat != c_0 ) ),
inference(simp,[status(thm)],[6147]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
inference(cnf,[status(esa)],[613]) ).
thf(615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset )
| ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(lifteq,[status(thm)],[614]) ).
thf(9119,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
= c_0 )
| ( A
!= ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[523,9116]) ).
thf(9120,plain,
( ( c_less @ c_0 @ ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
= c_0 ) ),
inference(pattern_uni,[status(thm)],[9119:[bind(A,$thf( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ))]]) ).
thf(13205,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) ) )
| ( ( c_union @ c_emptyset @ A @ B )
!= ( c_union @ c_emptyset @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ) ) ),
inference(paramod_ordered,[status(thm)],[874,13182]) ).
thf(13206,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(pattern_uni,[status(thm)],[13205:[bind(A,$thf( c_Message_Osynth @ c_emptyset )),bind(B,$thf( tc_Message_Omsg ))]]) ).
thf(19707,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_emptyset ) @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
= c_0 ) ),
inference(rewrite,[status(thm)],[9120,13206]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_1) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(20207,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[869,20100]) ).
thf(20257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) ) )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20207]) ).
thf(20277,plain,
! [A: $i] :
( ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ tc_nat ) ) ) ),
inference(simp,[status(thm)],[20257]) ).
thf(97,axiom,
! [A: $i] :
( ( c_Inter @ c_emptyset @ A )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
thf(609,plain,
! [A: $i] :
( ( c_Inter @ c_emptyset @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(610,plain,
! [A: $i] :
( ( c_Inter @ c_emptyset @ A )
= c_UNIV ),
inference(lifteq,[status(thm)],[609]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(519,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
inference(cnf,[status(esa)],[518]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(82,axiom,
! [A: $i] :
( ( c_Inter @ c_UNIV @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
thf(578,plain,
! [A: $i] :
( ( c_Inter @ c_UNIV @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
thf(694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[694]) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[695]) ).
thf(697,plain,
! [B: $i,A: $i] :
( ( sk7 @ A @ ( c_Message_Omsg_OCrypt @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_OCrypt),[sk7])]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1540,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ c_0 ) )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[415,543]) ).
thf(1541,plain,
( ~ ( c_lessequals @ tc_nat @ c_0 @ tc_nat )
| ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ c_0 ) ) ),
inference(pattern_uni,[status(thm)],[1540:[bind(A,$thf( tc_nat ))]]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(379,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(1259,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
thf(650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(231,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(948,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1642,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1640]) ).
thf(1643,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[1642:[bind(A,$thf( c_emptyset ))]]) ).
thf(2929,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 )
| ( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1294,1643]) ).
thf(2942,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 )
| ( c_emptyset != c_emptyset )
| ( A != c_0 )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[2929]) ).
thf(2984,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[2942]) ).
thf(3802,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( tc_set @ B )
!= tc_nat )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[523,2984]) ).
thf(3803,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_nat )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(pattern_uni,[status(thm)],[3802:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )),bind(B,$thf( B ))]]) ).
thf(4048,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_nat )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[3803]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(13395,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ ( c_Message_Oparts @ c_emptyset ) )
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[13332,405]) ).
thf(13445,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
| ( ( c_Message_Oparts @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(simp,[status(thm)],[13395]) ).
thf(21115,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ v_G )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[13445,954]) ).
thf(1138,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(lifteq,[status(thm)],[1137]) ).
thf(2723,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( A != c_Finite__Set_OFinites ) ),
inference(paramod_ordered,[status(thm)],[415,2612]) ).
thf(2724,plain,
( ~ ( c_lessequals @ c_Finite__Set_OFinites @ c_0 @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[2723:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(3631,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Orderings_Olinorder @ c_0 )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,733]) ).
thf(3632,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( class_Orderings_Olinorder @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3631:[bind(A,$thf( tc_nat ))]]) ).
thf(81016,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_inter @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[80256,543]) ).
thf(81022,plain,
! [B: $i,A: $i] :
( ( ( c_inter @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[81016]) ).
thf(81096,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[81022]) ).
thf(783,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(polarity_switch,[status(thm)],[782]) ).
thf(20103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ ( c_SetInterval_OlessThan @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[604,15679]) ).
thf(20146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ ( c_SetInterval_OlessThan @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20103]) ).
thf(20175,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_insert @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ ( tc_set @ tc_nat ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[20146]) ).
thf(19868,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_emptyset ) @ tc_nat )
| ( c_emptyset != c_0 )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[19707,1378]) ).
thf(19879,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_emptyset ) @ tc_nat )
| ( c_emptyset != c_0 )
| ( ( c_Message_Oanalz @ v_G )
!= c_emptyset ) ),
inference(simp,[status(thm)],[19868]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).
thf(1028,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(15825,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ c_0 @ C @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[658,15699]) ).
thf(15858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ c_0 @ C @ tc_nat )
!= c_emptyset )
| ( A
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) )
| ( B != tc_nat ) ),
inference(simp,[status(thm)],[15825]) ).
thf(15882,plain,
! [A: $i] :
( ( c_insert @ c_0 @ A @ tc_nat )
!= c_emptyset ),
inference(simp,[status(thm)],[15858]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
thf(1292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
inference(cnf,[status(esa)],[667]) ).
thf(669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
inference(lifteq,[status(thm)],[668]) ).
thf(3440,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Orderings_Oord @ c_0 )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,746]) ).
thf(3441,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( class_Orderings_Oord @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3440:[bind(A,$thf( tc_nat ))]]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(44284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ ( tc_set @ C ) )
= B )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44111,809]) ).
thf(44285,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
= ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) ),
inference(pattern_uni,[status(thm)],[44284:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OatLeast @ D @ tc_IntDef_Oint )),bind(C,$thf( tc_IntDef_Oint ))]]) ).
thf(44449,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
= ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) ),
inference(simp,[status(thm)],[44285]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
thf(486,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
inference(cnf,[status(esa)],[486]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Omax @ B @ B @ A )
= B )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[487]) ).
thf(1546,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_in @ c_UNIV @ c_0 @ ( tc_set @ tc_nat ) )
| ( A != c_Finite__Set_OFinites ) ),
inference(paramod_ordered,[status(thm)],[415,543]) ).
thf(1547,plain,
( ~ ( c_lessequals @ c_Finite__Set_OFinites @ c_0 @ tc_nat )
| ~ ( c_in @ c_UNIV @ c_0 @ ( tc_set @ tc_nat ) ) ),
inference(pattern_uni,[status(thm)],[1546:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(10102,plain,
! [A: $i] :
( ~ ( c_in @ c_UNIV @ c_0 @ ( tc_set @ tc_nat ) )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ c_Finite__Set_OFinites @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,1547]) ).
thf(10120,plain,
! [A: $i] :
( ~ ( c_in @ c_UNIV @ c_0 @ ( tc_set @ tc_nat ) )
| ( A != c_Finite__Set_OFinites )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[10102]) ).
thf(10135,plain,
( ~ ( c_in @ c_UNIV @ c_0 @ ( tc_set @ tc_nat ) )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[10120]) ).
thf(10671,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B )
!= ( c_in @ c_UNIV @ c_0 @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,10135]) ).
thf(10683,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_OFinites != c_0 )
| ( A != c_UNIV )
| ( ( c_insert @ A @ c_emptyset @ B )
!= c_0 )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[10671]) ).
thf(10708,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( ( c_insert @ c_UNIV @ c_emptyset @ ( tc_set @ tc_nat ) )
!= c_0 ) ),
inference(simp,[status(thm)],[10683]) ).
thf(24338,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_minus @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[23501,543]) ).
thf(24343,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[24338]) ).
thf(24370,plain,
! [B: $i,A: $i] :
( ( c_minus @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= c_UNIV ),
inference(simp,[status(thm)],[24343]) ).
thf(47294,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Pow @ c_0 @ tc_nat )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,43066]) ).
thf(47295,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Pow @ c_0 @ tc_nat )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[47294:[bind(A,$thf( c_emptyset ))]]) ).
thf(47331,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Pow @ c_0 @ tc_nat )
!= c_0 ) ),
inference(simp,[status(thm)],[47295]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
thf(752,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(753,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[752]) ).
thf(21673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ ( c_SetInterval_OatMost @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[604,15695]) ).
thf(21716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ ( c_SetInterval_OatMost @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[21673]) ).
thf(21737,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_insert @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ ( tc_set @ tc_nat ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[21716]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatMost @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OgreaterThan @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
thf(901,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatMost @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OgreaterThan @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
thf(686,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
thf(476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(22916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ c_emptyset @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(paramod_ordered,[status(thm)],[869,15682]) ).
thf(22957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ c_emptyset @ C @ ( tc_set @ D ) ) )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ D ) ) ),
inference(simp,[status(thm)],[22916]) ).
thf(22983,plain,
! [B: $i,A: $i] :
( ( c_insert @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_uminus @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(simp,[status(thm)],[22957]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
thf(442,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
inference(cnf,[status(esa)],[442]) ).
thf(444,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Omin @ B @ B @ A )
= B )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[443]) ).
thf(3190,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Omin @ B @ B @ A )
= B )
| ( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[441,444]) ).
thf(3191,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ A @ tc_IntDef_Oint )
= A ),
inference(pattern_uni,[status(thm)],[3190:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(3194,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ A @ tc_IntDef_Oint )
= A ),
inference(simp,[status(thm)],[3191]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__mono_0) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(20210,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[604,20100]) ).
thf(20252,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20210]) ).
thf(20271,plain,
! [A: $i] :
( ( c_uminus @ ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ ( tc_set @ tc_nat ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[20252]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(240,axiom,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
thf(970,plain,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(1155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
thf(736,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(737,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
inference(cnf,[status(esa)],[736]) ).
thf(738,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[737]) ).
thf(73529,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B )
| ( ( class_Orderings_Olinorder @ tc_nat )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[733,738]) ).
thf(73530,plain,
! [A: $i] :
( ( c_Finite__Set_OMin @ ( c_insert @ A @ c_emptyset @ tc_nat ) @ tc_nat )
= A ),
inference(pattern_uni,[status(thm)],[73529:[bind(A,$thf( tc_nat ))]]) ).
thf(73630,plain,
! [A: $i] :
( ( c_Finite__Set_OMin @ ( c_insert @ A @ c_emptyset @ tc_nat ) @ tc_nat )
= A ),
inference(simp,[status(thm)],[73530]) ).
thf(73885,plain,
! [A: $i] :
( ( ( c_Finite__Set_OMin @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
= A )
| ( ( c_insert @ c_0 @ c_emptyset @ tc_nat )
!= ( c_insert @ A @ c_emptyset @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[807,73630]) ).
thf(73886,plain,
( ( c_Finite__Set_OMin @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
= c_0 ),
inference(pattern_uni,[status(thm)],[73885:[bind(A,$thf( c_0 ))]]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(705,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[704]) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[705]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
thf(701,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(cnf,[status(esa)],[514]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
thf(1131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(3769,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[523,1643]) ).
thf(3770,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[3769:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ))]]) ).
thf(47,axiom,
class_Orderings_Oorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(503,plain,
class_Orderings_Oorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(552,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(553,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(cnf,[status(esa)],[552]) ).
thf(15998,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ B @ B @ A )
| ( ( class_Orderings_Oorder @ tc_IntDef_Oint )
!= ( class_Orderings_Oorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[503,553]) ).
thf(15999,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_IntDef_Oint ),
inference(pattern_uni,[status(thm)],[15998:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(16112,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_IntDef_Oint ),
inference(simp,[status(thm)],[15999]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(26,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
thf(457,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1689,plain,
! [A: $i] :
( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(paramod_ordered,[status(thm)],[455,407]) ).
thf(1708,plain,
! [A: $i] :
( ( ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) )
!= c_0 )
| ( A
!= ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ( ( tc_set @ tc_Message_Omsg )
!= tc_nat ) ),
inference(simp,[status(thm)],[1689]) ).
thf(1715,plain,
( ( ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) )
!= c_0 )
| ( ( tc_set @ tc_Message_Omsg )
!= tc_nat ) ),
inference(simp,[status(thm)],[1708]) ).
thf(24427,plain,
( ( c_in @ v_X @ c_0 @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[1021,23929]) ).
thf(24483,plain,
( ( c_in @ v_X @ c_0 @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[24427]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(cnf,[status(esa)],[620]) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A ) ),
inference(lifteq,[status(thm)],[621]) ).
thf(186,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(837,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(22735,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg )
| ( c_emptyset != c_0 )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[1021,22710]) ).
thf(22778,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ c_0 ) @ tc_Message_Omsg )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[22735]) ).
thf(117,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(663,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(6457,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat ) @ A @ tc_nat ),
inference(rewrite,[status(thm)],[663,420]) ).
thf(6610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_0 != B )
| ( A
!= ( c_List_Olist_OCons @ C @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[415,583]) ).
thf(6611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_List_Olist_OCons @ A @ B @ C ) @ c_0 @ tc_nat )
| ( c_0 != B ) ),
inference(pattern_uni,[status(thm)],[6610:[bind(A,$thf( c_List_Olist_OCons @ E @ F @ G )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(6613,plain,
! [B: $i,A: $i] :
~ ( c_lessequals @ ( c_List_Olist_OCons @ A @ c_0 @ B ) @ c_0 @ tc_nat ),
inference(simp,[status(thm)],[6611]) ).
thf(7070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
!= ( c_lessequals @ ( c_List_Olist_OCons @ C @ c_0 @ D ) @ c_0 @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[6457,6613]) ).
thf(7089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat )
!= ( c_List_Olist_OCons @ C @ c_0 @ D ) )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[7070]) ).
thf(7102,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ c_0 @ tc_nat ) @ tc_nat )
!= ( c_List_Olist_OCons @ B @ c_0 @ C ) ),
inference(simp,[status(thm)],[7089]) ).
thf(11432,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ c_0 @ B )
!= c_0 ),
inference(rewrite,[status(thm)],[7102,1806]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ ( c_insert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).
thf(1114,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ ( c_insert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(647,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(23776,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_minus @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[23455,543]) ).
thf(23788,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[23776]) ).
thf(23835,plain,
! [B: $i,A: $i] :
( ( c_minus @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= c_UNIV ),
inference(simp,[status(thm)],[23788]) ).
thf(35023,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ B @ ( tc_set @ tc_nat ) )
!= c_UNIV )
| ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= ( c_SetInterval_OatMost @ C @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[34886,23835]) ).
thf(35024,plain,
! [B: $i,A: $i] :
( ( c_minus @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ B @ ( tc_set @ tc_nat ) )
!= c_UNIV ),
inference(pattern_uni,[status(thm)],[35023:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(46970,plain,
! [B: $i,A: $i] :
( ( c_minus @ ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) @ B @ ( tc_set @ tc_nat ) )
!= c_UNIV ),
inference(rewrite,[status(thm)],[35024,35087]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(3335,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,1640]) ).
thf(3336,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[3335:[bind(A,$thf( c_emptyset ))]]) ).
thf(4147,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[523,3336]) ).
thf(4148,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_nat )
| ( c_less @ c_0 @ c_emptyset @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[4147:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ))]]) ).
thf(409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
inference(cnf,[status(esa)],[408]) ).
thf(1309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) )
!= ( c_lessequals @ ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ) ),
inference(paramod_ordered,[status(thm)],[409,407]) ).
thf(1318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( ( c_SetInterval_OatLeastLessThan @ E @ B @ A )
!= ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) )
| ( ( c_SetInterval_OatLeastLessThan @ D @ C @ A )
!= ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
| ( ( tc_set @ A )
!= ( tc_set @ tc_Message_Omsg ) ) ),
inference(simp,[status(thm)],[1309]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(1086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
thf(506,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(507,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(cnf,[status(esa)],[506]) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(lifteq,[status(thm)],[507]) ).
thf(13338,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
= ( c_Message_Osynth @ c_0 ) )
| ( A
!= ( c_Message_Oparts @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[523,13332]) ).
thf(13339,plain,
( ( c_less @ c_0 @ ( c_Message_Oparts @ c_emptyset ) @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
= ( c_Message_Osynth @ c_0 ) ) ),
inference(pattern_uni,[status(thm)],[13338:[bind(A,$thf( c_Message_Oparts @ c_emptyset ))]]) ).
thf(25681,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
= ( c_Message_Osynth @ c_0 ) ) ),
inference(rewrite,[status(thm)],[13339,954]) ).
thf(25824,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[25681,3336]) ).
thf(25874,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( ( c_Message_Oanalz @ v_G )
!= c_emptyset ) ),
inference(simp,[status(thm)],[25824]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(cnf,[status(esa)],[673]) ).
thf(13,axiom,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(427,plain,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(428,plain,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
inference(lifteq,[status(thm)],[427]) ).
thf(2189,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ c_0 @ A @ tc_nat ) @ tc_nat )
= A ),
inference(rewrite,[status(thm)],[428,420]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(1202,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
thf(792,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(3855,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[523,1649]) ).
thf(3856,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_emptyset ) @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G ) ),
inference(pattern_uni,[status(thm)],[3855:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(64,axiom,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(541,plain,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(3507,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Orderings_Oord @ c_0 )
| ( A != tc_IntDef_Oint ) ),
inference(paramod_ordered,[status(thm)],[523,456]) ).
thf(3508,plain,
( ( c_less @ c_0 @ tc_IntDef_Oint @ tc_nat )
| ( class_Orderings_Oord @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3507:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
thf(772,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(cnf,[status(esa)],[772]) ).
thf(662,plain,
! [A: $i] :
( ( sk6 @ ( c_Message_Omsg_OAgent @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_OAgent),[sk6])]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__1__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__1__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__1__1 @ A @ B )
!= c_UNIV )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
thf(616,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__1__1 @ A @ B )
!= c_UNIV )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(617,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__1__1 @ A @ B )
!= c_UNIV )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
inference(cnf,[status(esa)],[616]) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__1__1 @ A @ B )
!= c_UNIV )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
inference(lifteq,[status(thm)],[617]) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) ) ),
inference(cnf,[status(esa)],[511]) ).
thf(513,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[512]) ).
thf(7853,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Omax @ B @ B @ A )
= B )
| ( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[441,488]) ).
thf(7854,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ A @ tc_IntDef_Oint )
= A ),
inference(pattern_uni,[status(thm)],[7853:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(7866,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ A @ tc_IntDef_Oint )
= A ),
inference(simp,[status(thm)],[7854]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(9121,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Oparts @ c_0 )
= ( c_Message_Osynth @ c_emptyset ) )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[523,9116]) ).
thf(9122,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_emptyset ) @ tc_nat )
| ( ( c_Message_Oparts @ c_0 )
= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[9121:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1523,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset )
| ( c_0 != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1381]) ).
thf(1524,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[1523:[bind(A,$thf( c_emptyset ))]]) ).
thf(2132,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset )
| ( c_0 != v_G )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,1524]) ).
thf(2152,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset )
| ( c_0 != v_G )
| ( c_emptyset != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2132]) ).
thf(2155,plain,
( ( ( c_Message_Osynth @ c_emptyset )
!= c_emptyset )
| ( c_0 != v_G )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[2152]) ).
thf(2178,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[415,2155]) ).
thf(2179,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ c_emptyset ) @ c_0 @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[2178:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(4662,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ ( c_Message_Osynth @ c_emptyset ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,2179]) ).
thf(4685,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[4662]) ).
thf(4691,plain,
( ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 ) ),
inference(simp,[status(thm)],[4685]) ).
thf(4871,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[523,4691]) ).
thf(4872,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_emptyset ) @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[4871:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(80131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_inter @ B @ D @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[592,745]) ).
thf(80132,plain,
! [B: $i,A: $i] : ( c_in @ ( c_inter @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[80131:[bind(A,$thf( E )),bind(B,$thf( c_SetInterval_OatMost @ E @ tc_nat )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(80176,plain,
! [B: $i,A: $i] : ( c_in @ ( c_inter @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(simp,[status(thm)],[80132]) ).
thf(80505,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_inter @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[80176,543]) ).
thf(80525,plain,
! [B: $i,A: $i] :
( ( ( c_inter @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[80505]) ).
thf(80597,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[80525]) ).
thf(9230,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,9223]) ).
thf(9231,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[9230:[bind(A,$thf( c_emptyset ))]]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(34942,plain,
! [B: $i,A: $i] :
( ( ( c_inter @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( c_insert @ c_0 @ B @ tc_nat ) @ tc_nat )
!= c_emptyset )
| ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[34886,24964]) ).
thf(34943,plain,
! [A: $i] :
( ( c_inter @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( c_insert @ c_0 @ A @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[34942:[bind(A,$thf( c_0 ))]]) ).
thf(35115,plain,
! [A: $i] :
( ( c_inter @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( c_insert @ c_0 @ A @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(simp,[status(thm)],[34943]) ).
thf(43632,plain,
! [A: $i] :
( ( c_inter @ ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) @ ( c_insert @ c_0 @ A @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(rewrite,[status(thm)],[35115,35087]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
thf(689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
inference(cnf,[status(esa)],[730]) ).
thf(732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
inference(lifteq,[status(thm)],[731]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(20309,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_Pow @ c_emptyset @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[604,20209]) ).
thf(20353,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_Pow @ c_emptyset @ tc_nat ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20309]) ).
thf(20356,plain,
( ( c_uminus @ ( c_Pow @ c_emptyset @ tc_nat ) @ ( tc_set @ ( tc_set @ tc_nat ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[20353]) ).
thf(579,plain,
! [A: $i] :
( ( c_Inter @ c_UNIV @ A )
= c_emptyset ),
inference(lifteq,[status(thm)],[578]) ).
thf(8714,plain,
! [A: $i] :
( ~ ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
| ( ( c_lessequals @ A @ A @ tc_nat )
!= ( c_lessequals @ c_UNIV @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[4242,1545]) ).
thf(8717,plain,
! [A: $i] :
( ~ ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
| ( A != c_UNIV )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[8714]) ).
thf(8740,plain,
( ~ ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[8717]) ).
thf(3403,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,1450]) ).
thf(3404,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[3403:[bind(A,$thf( c_emptyset ))]]) ).
thf(743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
inference(cnf,[status(esa)],[742]) ).
thf(34930,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ ( c_insert @ c_0 @ B @ tc_nat ) @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[34886,15881]) ).
thf(35053,plain,
! [B: $i,A: $i] :
( ( A != c_0 )
| ( tc_nat != tc_nat )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ ( c_insert @ c_0 @ B @ tc_nat ) @ ( tc_set @ tc_nat ) ) ) ),
inference(simp,[status(thm)],[34930]) ).
thf(35103,plain,
! [A: $i] :
( ( c_uminus @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[35053]) ).
thf(43352,plain,
! [A: $i] :
( ( c_uminus @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) ),
inference(rewrite,[status(thm)],[35103,35087]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
thf(875,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ B @ C )
| ( c_emptyset
= ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).
thf(575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ B @ C )
| ( c_emptyset
= ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ B @ C )
| ( c_emptyset
= ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
inference(cnf,[status(esa)],[575]) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
= c_emptyset )
| ( c_in @ D @ B @ C ) ),
inference(lifteq,[status(thm)],[576]) ).
thf(2257,plain,
! [A: $i] :
( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ c_0 ) )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ tc_nat @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,1541]) ).
thf(2281,plain,
! [A: $i] :
( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ c_0 ) )
| ( tc_nat != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2257]) ).
thf(2288,plain,
( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ c_0 ) )
| ( tc_nat != c_0 ) ),
inference(simp,[status(thm)],[2281]) ).
thf(10663,plain,
! [B: $i,A: $i] :
( ( tc_nat != c_0 )
| ( ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ c_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,2288]) ).
thf(10693,plain,
! [B: $i,A: $i] :
( ( tc_nat != c_0 )
| ( A != c_UNIV )
| ( ( c_insert @ A @ c_emptyset @ B )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ c_0 ) ) ),
inference(simp,[status(thm)],[10663]) ).
thf(10700,plain,
( ( tc_nat != c_0 )
| ( ( c_insert @ c_UNIV @ c_emptyset @ ( tc_set @ c_0 ) )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[10693]) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( B = c_UNIV ) ),
inference(cnf,[status(esa)],[709]) ).
thf(711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( B = c_UNIV ) ),
inference(lifteq,[status(thm)],[710]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( ( c_minus @ B @ ( c_insert @ A @ D @ C ) @ ( tc_set @ C ) )
= ( c_minus @ B @ D @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
thf(1256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( ( c_minus @ B @ ( c_insert @ A @ D @ C ) @ ( tc_set @ C ) )
= ( c_minus @ B @ D @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(13684,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( A
!= ( c_Message_Osynth @ c_0 ) ) ),
inference(paramod_ordered,[status(thm)],[415,13330]) ).
thf(13685,plain,
( ~ ( c_lessequals @ ( c_Message_Osynth @ c_0 ) @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[13684:[bind(A,$thf( c_Message_Osynth @ c_0 ))]]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
thf(1226,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(24870,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ C @ ( c_insert @ B @ E @ D ) @ D )
!= c_emptyset )
| ( ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[799,602]) ).
thf(24871,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24870:[bind(A,$thf( F )),bind(B,$thf( c_SetInterval_OlessThan @ F @ tc_nat )),bind(C,$thf( c_Finite__Set_OFinites )),bind(D,$thf( tc_set @ tc_nat )),bind(E,$thf( E ))]]) ).
thf(24936,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[24871]) ).
thf(109,axiom,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(640,plain,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(641,plain,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
inference(lifteq,[status(thm)],[640]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
inference(cnf,[status(esa)],[571]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
thf(497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
inference(cnf,[status(esa)],[497]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1349,plain,
( ( c_UNIV != v_X )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= tc_Message_Omsg )
| ( ( c_Message_Oanalz @ c_emptyset )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[1021,1327]) ).
thf(1356,plain,
( ( c_UNIV != v_X )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= tc_Message_Omsg )
| ( c_emptyset != v_G ) ),
inference(simp,[status(thm)],[1349]) ).
thf(63,axiom,
! [A: $i] :
( ( c_Orderings_Omin @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
thf(539,plain,
! [A: $i] :
( ( c_Orderings_Omin @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(540,plain,
! [A: $i] :
( ( c_Orderings_Omin @ c_0 @ A @ tc_nat )
= c_0 ),
inference(lifteq,[status(thm)],[539]) ).
thf(671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ A @ C )
| ( c_emptyset
= ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
inference(cnf,[status(esa)],[670]) ).
thf(672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
= c_emptyset )
| ( c_in @ D @ A @ C ) ),
inference(lifteq,[status(thm)],[671]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
thf(1271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(8357,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ c_0 @ c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ tc_nat @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,7022]) ).
thf(8402,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ c_0 @ c_0 )
| ( tc_nat != c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[8357]) ).
thf(8432,plain,
( ~ ( c_less @ c_0 @ c_0 @ c_0 )
| ( tc_nat != c_0 ) ),
inference(simp,[status(thm)],[8402]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(23535,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_Pow @ c_emptyset @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(paramod_ordered,[status(thm)],[604,22918]) ).
thf(23575,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_Pow @ c_emptyset @ C ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ C ) ) ),
inference(simp,[status(thm)],[23535]) ).
thf(23593,plain,
! [A: $i] :
( ( c_uminus @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ ( tc_set @ A ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[23575]) ).
thf(917,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[916]) ).
thf(918,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[917]) ).
thf(919,plain,
! [A: $i] :
( ( sk13 @ ( c_Message_Omsg_ONumber @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_ONumber),[sk13])]) ).
thf(172,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(804,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(71223,plain,
( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
= ( c_Message_Osynth @ c_emptyset ) ),
inference(rewrite,[status(thm)],[70731,71222]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
thf(1224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(7851,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Omax @ B @ B @ A )
= B )
| ( ( class_Orderings_Olinorder @ tc_nat )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[733,488]) ).
thf(7852,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ A @ tc_nat )
= A ),
inference(pattern_uni,[status(thm)],[7851:[bind(A,$thf( tc_nat ))]]) ).
thf(7865,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ A @ tc_nat )
= A ),
inference(simp,[status(thm)],[7852]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_UNIV
!= ( c_Inter @ B @ C ) )
| ( A = c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_UNIV
!= ( c_Inter @ B @ C ) )
| ( A = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
thf(831,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(438,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(439,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
inference(cnf,[status(esa)],[438]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
= c_0 )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(lifteq,[status(thm)],[439]) ).
thf(2802,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ B @ A @ tc_nat ) @ tc_nat )
= c_0 )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(rewrite,[status(thm)],[440,420]) ).
thf(20229,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( c_inter @ A @ A @ B )
!= ( c_inter @ ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,20100]) ).
thf(20250,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_emptyset @ A )
!= ( c_inter @ ( c_insert @ c_emptyset @ B @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20229]) ).
thf(20269,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_emptyset @ A )
!= ( c_inter @ ( c_insert @ c_emptyset @ B @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[20250]) ).
thf(53717,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(rewrite,[status(thm)],[20269,811]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(156,axiom,
! [A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_2) ).
thf(764,plain,
! [A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(16839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[658,15692]) ).
thf(16866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg )
!= c_emptyset )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[16839]) ).
thf(16883,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[16866]) ).
thf(680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
inference(cnf,[status(esa)],[679]) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
inference(lifteq,[status(thm)],[680]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).
thf(1282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_less @ D @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
thf(784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_less @ D @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1048,plain,
! [B: $i,A: $i] :
( ( c_union @ c_UNIV @ A @ B )
= c_UNIV ),
inference(lifteq,[status(thm)],[1047]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(22,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
thf(450,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(451,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ tc_nat )
= A ),
inference(lifteq,[status(thm)],[450]) ).
thf(77,axiom,
( ( c_SetInterval_OatLeast @ c_0 @ tc_nat )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
thf(567,plain,
( ( c_SetInterval_OatLeast @ c_0 @ tc_nat )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(cnf,[status(esa)],[647]) ).
thf(649,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E )
= A )
| ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(lifteq,[status(thm)],[648]) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
inference(cnf,[status(esa)],[597]) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
inference(lifteq,[status(thm)],[598]) ).
thf(26931,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ E ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[869,15705]) ).
thf(26976,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) )
| ( A
!= ( c_Message_Osynth @ E ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[26931]) ).
thf(26994,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_Message_Osynth @ C ) @ ( tc_set @ tc_Message_Omsg ) )
!= ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) ),
inference(simp,[status(thm)],[26976]) ).
thf(21689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_SetInterval_OatMost @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[658,15695]) ).
thf(21722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ ( c_SetInterval_OatMost @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[21689]) ).
thf(21746,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[21722]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
| ( c_emptyset
= ( c_inter @ B @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
| ( c_emptyset
= ( c_inter @ B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(cnf,[status(esa)],[476]) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
inference(cnf,[status(esa)],[534]) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
inference(lifteq,[status(thm)],[815]) ).
thf(38,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(483,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(1022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
thf(1112,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(493,plain,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
inference(cnf,[status(esa)],[492]) ).
thf(494,plain,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(lifteq,[status(thm)],[493]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(9644,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9620,991]) ).
thf(9645,plain,
( ( c_union @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ),
inference(pattern_uni,[status(thm)],[9644:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ))]]) ).
thf(9987,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ),
inference(rewrite,[status(thm)],[9645,1062]) ).
thf(82622,plain,
! [A: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9987,82511]) ).
thf(82623,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[82622:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ))]]) ).
thf(84187,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[82623,9987]) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(cnf,[status(esa)],[698]) ).
thf(700,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[699]) ).
thf(9253,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) )
!= ( c_Message_Oanalz @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[9223,405]) ).
thf(9280,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ c_emptyset )
!= v_G ) ),
inference(simp,[status(thm)],[9253]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ A @ B )
= A ),
inference(lifteq,[status(thm)],[780]) ).
thf(81221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != c_UNIV )
| ( ( c_inter @ c_UNIV @ A @ B )
!= ( c_inter @ ( c_SetInterval_OlessThan @ D @ tc_nat ) @ C @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[781,81096]) ).
thf(81247,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
!= ( c_inter @ ( c_SetInterval_OlessThan @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(simp,[status(thm)],[81221]) ).
thf(81276,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
!= ( c_inter @ ( c_SetInterval_OlessThan @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(simp,[status(thm)],[81247]) ).
thf(82359,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_SetInterval_OlessThan @ B @ tc_nat ) @ A @ tc_nat )
!= c_UNIV ),
inference(rewrite,[status(thm)],[81276,781]) ).
thf(2592,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( c_UNIV != c_0 )
| ( A != c_Finite__Set_OFinites ) ),
inference(paramod_ordered,[status(thm)],[415,2508]) ).
thf(2593,plain,
( ~ ( c_lessequals @ c_Finite__Set_OFinites @ c_0 @ tc_nat )
| ( c_UNIV != c_0 ) ),
inference(pattern_uni,[status(thm)],[2592:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(48761,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ ( c_Pow @ c_0 @ tc_nat ) @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[455,43941]) ).
thf(48816,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( ( c_Pow @ c_0 @ tc_nat )
!= c_0 )
| ( A != c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[48761]) ).
thf(48840,plain,
( ( c_emptyset != c_0 )
| ( ( c_Pow @ c_0 @ tc_nat )
!= c_0 ) ),
inference(simp,[status(thm)],[48816]) ).
thf(15732,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( c_inter @ c_UNIV @ A @ B )
!= ( c_inter @ ( c_insert @ v_X @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg ) ) ),
inference(paramod_ordered,[status(thm)],[781,15687]) ).
thf(15753,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_emptyset @ A )
!= ( c_inter @ ( c_insert @ v_X @ B @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg ) ),
inference(simp,[status(thm)],[15732]) ).
thf(15769,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_emptyset @ A )
!= ( c_inter @ ( c_insert @ v_X @ B @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg ) ),
inference(simp,[status(thm)],[15753]) ).
thf(48535,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(rewrite,[status(thm)],[15769,811]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
thf(462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24555,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ c_0 )
| ( A
!= ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[523,24551]) ).
thf(24556,plain,
( ( c_less @ c_0 @ ( tc_set @ tc_nat ) @ tc_nat )
| ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ c_0 ) ),
inference(pattern_uni,[status(thm)],[24555:[bind(A,$thf( tc_set @ tc_nat ))]]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(607,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(608,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[607]) ).
thf(562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A )
| ( C = c_emptyset ) ),
inference(cnf,[status(esa)],[561]) ).
thf(563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A ) ),
inference(lifteq,[status(thm)],[562]) ).
thf(10657,plain,
! [B: $i,A: $i] :
( ( ( tc_set @ tc_nat )
!= c_0 )
| ( ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ c_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1281,6809]) ).
thf(10682,plain,
! [B: $i,A: $i] :
( ( ( tc_set @ tc_nat )
!= c_0 )
| ( A != c_UNIV )
| ( ( c_insert @ A @ c_emptyset @ B )
!= c_Finite__Set_OFinites )
| ( B != c_0 ) ),
inference(simp,[status(thm)],[10657]) ).
thf(10707,plain,
( ( ( tc_set @ tc_nat )
!= c_0 )
| ( ( c_insert @ c_UNIV @ c_emptyset @ c_0 )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[10682]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B ) ),
inference(cnf,[status(esa)],[429]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) ) ),
inference(lifteq,[status(thm)],[430]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_inter @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
thf(912,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_inter @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
thf(684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ D @ C @ A ) @ A ) ),
inference(cnf,[status(esa)],[684]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_1) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(3837,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Oparts @ c_0 )
= c_emptyset )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,954]) ).
thf(3838,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Oparts @ c_0 )
= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[3837:[bind(A,$thf( c_emptyset ))]]) ).
thf(372,axiom,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(1245,plain,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(3673,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G )
| ( A
!= ( c_Message_Osynth @ c_0 ) ) ),
inference(paramod_ordered,[status(thm)],[523,2538]) ).
thf(3674,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_0 ) @ tc_nat )
| ( c_emptyset != c_0 )
| ( c_emptyset != v_G ) ),
inference(pattern_uni,[status(thm)],[3673:[bind(A,$thf( c_Message_Osynth @ c_0 ))]]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(986,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
thf(1000,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(cnf,[status(esa)],[504]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
thf(922,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(4937,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_emptyset != v_G )
| ( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1294,2352]) ).
thf(4958,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_emptyset != v_G )
| ( c_emptyset != c_emptyset )
| ( A != c_0 )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[4937]) ).
thf(4965,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_0 )
!= c_0 )
| ( c_emptyset != v_G )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[4958]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
= ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(588,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
= ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(589,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
= ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
inference(lifteq,[status(thm)],[588]) ).
thf(4867,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_0 != v_G )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,4691]) ).
thf(4868,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( c_0 != v_G )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[4867:[bind(A,$thf( c_emptyset ))]]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
thf(1133,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(lifteq,[status(thm)],[1133]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__2__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__2__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
thf(516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
| ( c_emptyset
= ( c_inter @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
| ( c_emptyset
= ( c_inter @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(35015,plain,
! [A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[34886,4527]) ).
thf(35016,plain,
( ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[35015:[bind(A,$thf( c_0 ))]]) ).
thf(35147,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
!= ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[809,35016]) ).
thf(35209,plain,
! [A: $i] :
( ( c_uminus @ ( c_uminus @ c_emptyset @ ( tc_set @ A ) ) @ ( tc_set @ A ) )
!= ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[35147]) ).
thf(35214,plain,
! [A: $i] :
( ( c_uminus @ ( c_uminus @ c_emptyset @ ( tc_set @ A ) ) @ ( tc_set @ A ) )
!= ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[35209]) ).
thf(64420,plain,
( ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(rewrite,[status(thm)],[35214,809,35087]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(795,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__2__1 @ A @ B )
!= c_UNIV )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
inference(cnf,[status(esa)],[747]) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__2__1 @ A @ B )
!= c_UNIV )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
inference(lifteq,[status(thm)],[748]) ).
thf(134,axiom,
( ( c_Message_OkeysFor @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
thf(707,plain,
( ( c_Message_OkeysFor @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(708,plain,
( ( c_Message_OkeysFor @ c_emptyset )
= c_emptyset ),
inference(lifteq,[status(thm)],[707]) ).
thf(3974,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_OkeysFor @ c_0 )
= c_emptyset )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,708]) ).
thf(3975,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_OkeysFor @ c_0 )
= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[3974:[bind(A,$thf( c_emptyset ))]]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(44011,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) )
| ( ( class_Orderings_Olinorder @ tc_nat )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[733,666]) ).
thf(44012,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
= ( c_SetInterval_OlessThan @ A @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[44011:[bind(A,$thf( tc_nat ))]]) ).
thf(44106,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
= ( c_SetInterval_OlessThan @ A @ tc_nat ) ),
inference(simp,[status(thm)],[44012]) ).
thf(44113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ ( tc_set @ C ) )
= B )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44106,809]) ).
thf(44114,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
= ( c_SetInterval_OatLeast @ A @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[44113:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OatLeast @ D @ tc_nat )),bind(C,$thf( tc_nat ))]]) ).
thf(44268,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
= ( c_SetInterval_OatLeast @ A @ tc_nat ) ),
inference(simp,[status(thm)],[44114]) ).
thf(24911,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ C @ ( c_insert @ B @ E @ D ) @ D )
!= c_emptyset )
| ( ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[592,602]) ).
thf(24912,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24911:[bind(A,$thf( F )),bind(B,$thf( c_SetInterval_OatMost @ F @ tc_nat )),bind(C,$thf( c_Finite__Set_OFinites )),bind(D,$thf( tc_set @ tc_nat )),bind(E,$thf( E ))]]) ).
thf(24956,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[24912]) ).
thf(458,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ),
inference(lifteq,[status(thm)],[457]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(823,plain,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[822]) ).
thf(971,plain,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[970]) ).
thf(44170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ B @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ C )
= c_emptyset )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44106,604]) ).
thf(44171,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ tc_nat )
= c_emptyset ),
inference(pattern_uni,[status(thm)],[44170:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OatLeast @ D @ tc_nat )),bind(C,$thf( tc_nat ))]]) ).
thf(44248,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ tc_nat )
= c_emptyset ),
inference(simp,[status(thm)],[44171]) ).
thf(2168,plain,
! [A: $i] :
( ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[592,543]) ).
thf(2169,plain,
! [A: $i] :
( ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[2168]) ).
thf(2175,plain,
! [A: $i] :
( ( c_SetInterval_OatMost @ A @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[2169]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
thf(1267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(82824,plain,
! [A: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ A ) ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82781,82511]) ).
thf(82825,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[82824:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ))]]) ).
thf(84803,plain,
( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ) )
= ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[82825,82781]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(cnf,[status(esa)],[524]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ A @ c_emptyset @ C ) @ ( tc_set @ C ) ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ A @ c_emptyset @ C ) @ ( tc_set @ C ) ) @ C )
= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(73553,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B )
| ( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[441,738]) ).
thf(73554,plain,
! [A: $i] :
( ( c_Finite__Set_OMin @ ( c_insert @ A @ c_emptyset @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= A ),
inference(pattern_uni,[status(thm)],[73553:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(73606,plain,
! [A: $i] :
( ( c_Finite__Set_OMin @ ( c_insert @ A @ c_emptyset @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= A ),
inference(simp,[status(thm)],[73554]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ c_UNIV @ B )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_UNIV @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(44152,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ B @ C )
= c_emptyset )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44106,869]) ).
thf(44153,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ tc_nat )
= c_emptyset ),
inference(pattern_uni,[status(thm)],[44152:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OatLeast @ D @ tc_nat )),bind(C,$thf( tc_nat ))]]) ).
thf(44280,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ ( c_SetInterval_OatLeast @ A @ tc_nat ) @ tc_nat )
= c_emptyset ),
inference(simp,[status(thm)],[44153]) ).
thf(568,plain,
( ( c_SetInterval_OatLeast @ c_0 @ tc_nat )
= c_UNIV ),
inference(lifteq,[status(thm)],[567]) ).
thf(3871,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_SetInterval_OatLeast @ c_0 @ c_0 )
= c_UNIV )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,568]) ).
thf(3872,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( ( c_SetInterval_OatLeast @ c_0 @ c_0 )
= c_UNIV ) ),
inference(pattern_uni,[status(thm)],[3871:[bind(A,$thf( tc_nat ))]]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(10936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Ocontents @ ( c_Pow @ c_emptyset @ A ) @ C )
= B )
| ( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
!= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(paramod_ordered,[status(thm)],[975,1287]) ).
thf(10937,plain,
! [A: $i] :
( ( c_Set_Ocontents @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ A ) )
= c_emptyset ),
inference(pattern_uni,[status(thm)],[10936:[bind(A,$thf( D )),bind(B,$thf( c_emptyset )),bind(C,$thf( tc_set @ D ))]]) ).
thf(10952,plain,
! [A: $i] :
( ( c_Set_Ocontents @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ A ) )
= c_emptyset ),
inference(simp,[status(thm)],[10937]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(cnf,[status(esa)],[715]) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset )
| ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A ) ),
inference(lifteq,[status(thm)],[716]) ).
thf(3442,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset = c_0 )
| ( A
!= ( c_Message_Oanalz @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[523,1021]) ).
thf(3443,plain,
( ( c_less @ c_0 @ ( c_Message_Oanalz @ c_emptyset ) @ tc_nat )
| ( c_emptyset = c_0 ) ),
inference(pattern_uni,[status(thm)],[3442:[bind(A,$thf( c_Message_Oanalz @ c_emptyset ))]]) ).
thf(7538,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( c_emptyset = c_0 ) ),
inference(rewrite,[status(thm)],[3443,1021]) ).
thf(47597,plain,
! [A: $i] :
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_insert @ v_X @ A @ tc_Message_Omsg )
!= c_0 )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[7538,47454]) ).
thf(47598,plain,
! [A: $i] :
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_insert @ v_X @ A @ tc_Message_Omsg )
!= c_0 ) ),
inference(pattern_uni,[status(thm)],[47597:[]]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
thf(501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(cnf,[status(esa)],[501]) ).
thf(463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(cnf,[status(esa)],[462]) ).
thf(44341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ B @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ C )
= c_emptyset )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44111,604]) ).
thf(44342,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= c_emptyset ),
inference(pattern_uni,[status(thm)],[44341:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OatLeast @ D @ tc_IntDef_Oint )),bind(C,$thf( tc_IntDef_Oint ))]]) ).
thf(44435,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OatLeast @ A @ tc_IntDef_Oint ) @ ( c_SetInterval_OlessThan @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= c_emptyset ),
inference(simp,[status(thm)],[44342]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(lifteq,[status(thm)],[1129]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
thf(1220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(34983,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ B @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= ( c_SetInterval_OatMost @ C @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[34886,21746]) ).
thf(34984,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ B @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[34983:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(46551,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) @ B @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(rewrite,[status(thm)],[34984,35087]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(1188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(1186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(3163,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( ( tc_set @ B )
!= tc_nat )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[415,2984]) ).
thf(3164,plain,
! [A: $i] :
( ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(pattern_uni,[status(thm)],[3163:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) )),bind(B,$thf( B ))]]) ).
thf(3174,plain,
! [A: $i] :
( ~ ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ c_0 @ tc_nat )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[3164]) ).
thf(71232,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,71222]) ).
thf(71233,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[71232:[bind(A,$thf( c_emptyset ))]]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_1) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(15826,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( c_inter @ A @ c_UNIV @ B )
!= ( c_inter @ ( c_insert @ c_0 @ C @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[791,15699]) ).
thf(15852,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_UNIV @ A )
!= ( c_inter @ ( c_insert @ c_0 @ B @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat ) ),
inference(simp,[status(thm)],[15826]) ).
thf(15876,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_UNIV @ A )
!= ( c_inter @ ( c_insert @ c_0 @ B @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat ) ),
inference(simp,[status(thm)],[15852]) ).
thf(53526,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(rewrite,[status(thm)],[15876,658]) ).
thf(35017,plain,
! [B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ c_0 @ B @ tc_nat ) @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ tc_nat )
!= c_emptyset )
| ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[34886,15699]) ).
thf(35018,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ tc_nat )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[35017:[bind(A,$thf( c_0 ))]]) ).
thf(35086,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( c_uminus @ ( c_SetInterval_OgreaterThan @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ tc_nat )
!= c_emptyset ),
inference(simp,[status(thm)],[35018]) ).
thf(42749,plain,
! [A: $i] :
( ( c_inter @ ( c_insert @ c_0 @ A @ tc_nat ) @ ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) @ tc_nat )
!= c_emptyset ),
inference(rewrite,[status(thm)],[35086,35087]) ).
thf(702,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(cnf,[status(esa)],[701]) ).
thf(703,plain,
! [B: $i,A: $i] :
( ( B = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[702]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_0) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( sk5 @ A @ ( c_Message_Omsg_OMPair @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_OMPair),[sk5])]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
= ( c_Pow @ ( c_inter @ A @ B @ C ) @ C ) ),
inference(lifteq,[status(thm)],[611]) ).
thf(16581,plain,
! [A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) )
| ( ( c_insert @ c_0 @ c_emptyset @ tc_nat )
!= ( c_insert @ c_0 @ A @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[807,15878]) ).
thf(16582,plain,
( ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= ( c_SetInterval_OatMost @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[16581:[bind(A,$thf( c_emptyset ))]]) ).
thf(24842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset )
| ( ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[24551,602]) ).
thf(24843,plain,
! [A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24842:[bind(A,$thf( c_emptyset )),bind(B,$thf( c_Finite__Set_OFinites )),bind(C,$thf( tc_set @ tc_nat )),bind(D,$thf( D ))]]) ).
thf(24923,plain,
! [A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(simp,[status(thm)],[24843]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(1008,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
thf(595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(24836,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ D @ ( c_insert @ C @ F @ E ) @ E )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
!= ( c_in @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1215,602]) ).
thf(24837,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ C ) @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24836:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( c_Message_Omsg_ONumber @ G )),bind(D,$thf( c_Message_Osynth @ H )),bind(E,$thf( tc_Message_Omsg ))]]) ).
thf(24920,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ C ) @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[24837]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(10660,plain,
! [B: $i,A: $i] :
( ( c_UNIV != c_0 )
| ( ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B )
!= ( c_in @ c_0 @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,8740]) ).
thf(10686,plain,
! [B: $i,A: $i] :
( ( c_UNIV != c_0 )
| ( A != c_0 )
| ( ( c_insert @ A @ c_emptyset @ B )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[10660]) ).
thf(10712,plain,
( ( c_UNIV != c_0 )
| ( ( c_insert @ c_0 @ c_emptyset @ ( tc_set @ tc_nat ) )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[10686]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(1180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(73,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(556,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(2910,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G )
| ( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1294,1746]) ).
thf(2944,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G )
| ( c_emptyset != c_emptyset )
| ( A != c_0 )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[2910]) ).
thf(2960,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[2944]) ).
thf(330,axiom,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(1157,plain,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(43,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
thf(495,plain,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(1216,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(771,plain,
! [B: $i,A: $i] :
( ( sk10 @ A @ ( c_Message_Omsg_OMPair @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_OMPair),[sk10])]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(6272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pow @ c_emptyset @ A )
!= c_emptyset )
| ( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
!= ( c_insert @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[975,635]) ).
thf(6273,plain,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[6272:[bind(A,$thf( E )),bind(B,$thf( c_emptyset )),bind(C,$thf( c_emptyset )),bind(D,$thf( tc_set @ E ))]]) ).
thf(6286,plain,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
!= c_emptyset ),
inference(simp,[status(thm)],[6273]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
thf(464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(cnf,[status(esa)],[464]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(cnf,[status(esa)],[686]) ).
thf(688,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A ) ),
inference(lifteq,[status(thm)],[687]) ).
thf(485,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(cnf,[status(esa)],[484]) ).
thf(7271,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(rewrite,[status(thm)],[485,420]) ).
thf(10651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B )
!= ( c_in @ C @ c_emptyset @ D ) ),
inference(paramod_ordered,[status(thm)],[1281,941]) ).
thf(10690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( c_insert @ A @ c_emptyset @ B )
!= c_emptyset )
| ( B != D ) ),
inference(simp,[status(thm)],[10651]) ).
thf(10697,plain,
! [B: $i,A: $i] :
( ( c_insert @ A @ c_emptyset @ B )
!= c_emptyset ),
inference(simp,[status(thm)],[10690]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(896,plain,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
thf(946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(24813,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ C @ ( c_insert @ B @ E @ D ) @ D )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13058,602]) ).
thf(24814,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ c_emptyset ) @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24813:[bind(A,$thf( F )),bind(B,$thf( c_Message_Omsg_ONumber @ F )),bind(C,$thf( c_Message_Osynth @ c_emptyset )),bind(D,$thf( tc_Message_Omsg )),bind(E,$thf( E ))]]) ).
thf(24962,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ c_emptyset ) @ ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[24814]) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(lifteq,[status(thm)],[1243]) ).
thf(1253,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_UNIV @ B )
= c_UNIV ),
inference(lifteq,[status(thm)],[1252]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ A @ C )
| ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
thf(963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ A @ C )
| ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(cnf,[status(esa)],[516]) ).
thf(651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(cnf,[status(esa)],[650]) ).
thf(652,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A ) ),
inference(lifteq,[status(thm)],[651]) ).
thf(25607,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( c_inter @ c_UNIV @ A @ B )
!= ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_insert @ c_0 @ C @ tc_nat ) @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[781,24964]) ).
thf(25634,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_emptyset @ A )
!= ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_insert @ c_0 @ B @ tc_nat ) @ tc_nat ) ),
inference(simp,[status(thm)],[25607]) ).
thf(25657,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_emptyset @ A )
!= ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_insert @ c_0 @ B @ tc_nat ) @ tc_nat ) ),
inference(simp,[status(thm)],[25634]) ).
thf(64200,plain,
! [A: $i] :
( ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_insert @ c_0 @ A @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(rewrite,[status(thm)],[25657,811]) ).
thf(270,axiom,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(1030,plain,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(cnf,[status(esa)],[509]) ).
thf(26844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ E ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[604,15689]) ).
thf(26878,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_Message_Osynth @ E ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[26844]) ).
thf(26912,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) )
!= ( c_Message_Osynth @ C ) ),
inference(simp,[status(thm)],[26878]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(22921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ c_emptyset @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(paramod_ordered,[status(thm)],[604,15682]) ).
thf(22962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ c_emptyset @ C @ ( tc_set @ D ) ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ D ) ) ),
inference(simp,[status(thm)],[22921]) ).
thf(22988,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_insert @ c_emptyset @ A @ ( tc_set @ B ) ) @ ( tc_set @ ( tc_set @ B ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[22962]) ).
thf(21671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_SetInterval_OatMost @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[869,15695]) ).
thf(21721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ ( c_SetInterval_OatMost @ D @ tc_nat ) @ C @ ( tc_set @ tc_nat ) ) )
| ( A != c_Finite__Set_OFinites )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[21671]) ).
thf(21745,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ ( tc_set @ tc_nat ) )
!= ( c_uminus @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ tc_nat ) ) ) ),
inference(simp,[status(thm)],[21721]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
thf(929,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(3867,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_UNIV = c_0 )
| ( A
!= ( c_SetInterval_OatLeast @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[523,568]) ).
thf(3868,plain,
( ( c_less @ c_0 @ ( c_SetInterval_OatLeast @ c_0 @ tc_nat ) @ tc_nat )
| ( c_UNIV = c_0 ) ),
inference(pattern_uni,[status(thm)],[3867:[bind(A,$thf( c_SetInterval_OatLeast @ c_0 @ tc_nat ))]]) ).
thf(13716,plain,
( ( c_less @ c_0 @ c_UNIV @ tc_nat )
| ( c_UNIV = c_0 ) ),
inference(rewrite,[status(thm)],[3868,568]) ).
thf(16835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[869,15692]) ).
thf(16867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_insert @ ( c_Message_Omsg_ONumber @ D ) @ C @ tc_Message_Omsg ) )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[16835]) ).
thf(16884,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_Message_Omsg_ONumber @ B ) @ A @ tc_Message_Omsg )
!= ( c_uminus @ ( c_Message_Osynth @ c_emptyset ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(simp,[status(thm)],[16867]) ).
thf(355,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(1212,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(762,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(cnf,[status(esa)],[761]) ).
thf(763,plain,
! [B: $i,A: $i] :
( ( ( c_Union @ A @ B )
= c_emptyset )
| ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) ) ),
inference(lifteq,[status(thm)],[762]) ).
thf(24889,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ C @ ( c_insert @ B @ E @ D ) @ D )
!= c_emptyset )
| ( ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg )
!= ( c_in @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13119,602]) ).
thf(24890,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ c_emptyset ) @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24889:[bind(A,$thf( F )),bind(B,$thf( c_Message_Omsg_OAgent @ F )),bind(C,$thf( c_Message_Osynth @ c_emptyset )),bind(D,$thf( tc_Message_Omsg )),bind(E,$thf( E ))]]) ).
thf(24945,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_Message_Osynth @ c_emptyset ) @ ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg ) @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[24890]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(1161,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(170,axiom,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(800,plain,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(42889,plain,
! [A: $i] :
( ( ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) @ tc_nat )
!= c_emptyset )
| ( ( c_insert @ c_0 @ c_emptyset @ tc_nat )
!= ( c_insert @ c_0 @ A @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[807,42749]) ).
thf(42890,plain,
( ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_uminus @ ( c_uminus @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) @ tc_nat )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[42889:[bind(A,$thf( c_emptyset ))]]) ).
thf(43217,plain,
( ( c_inter @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ ( c_SetInterval_OatMost @ c_0 @ tc_nat ) @ tc_nat )
!= c_emptyset ),
inference(rewrite,[status(thm)],[42890,809]) ).
thf(735,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(cnf,[status(esa)],[734]) ).
thf(10661,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ B @ ( c_Pow @ c_emptyset @ A ) @ C )
| ( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
!= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(paramod_ordered,[status(thm)],[975,1281]) ).
thf(10662,plain,
! [A: $i] : ( c_in @ c_emptyset @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ A ) ),
inference(pattern_uni,[status(thm)],[10661:[bind(A,$thf( D )),bind(B,$thf( c_emptyset )),bind(C,$thf( tc_set @ D ))]]) ).
thf(10701,plain,
! [A: $i] : ( c_in @ c_emptyset @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ A ) ),
inference(simp,[status(thm)],[10662]) ).
thf(9228,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Oanalz @ c_0 )
= ( c_Message_Osynth @ c_emptyset ) )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[523,9223]) ).
thf(9229,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ c_emptyset ) @ tc_nat )
| ( ( c_Message_Oanalz @ c_0 )
= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[9228:[bind(A,$thf( c_Message_Osynth @ c_emptyset ))]]) ).
thf(4,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(410,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
thf(950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Inter @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Inter @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(3881,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_in @ v_X @ c_0 @ tc_Message_Omsg )
| ( A
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ) ),
inference(paramod_ordered,[status(thm)],[523,405]) ).
thf(3882,plain,
( ( c_less @ c_0 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_nat )
| ( c_in @ v_X @ c_0 @ tc_Message_Omsg ) ),
inference(pattern_uni,[status(thm)],[3881:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ))]]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(25011,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( c_inter @ A @ c_UNIV @ B )
!= ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ C @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[791,24923]) ).
thf(25035,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_UNIV @ A )
!= ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ B @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[25011]) ).
thf(25052,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ c_UNIV @ A )
!= ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ B @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[25035]) ).
thf(58728,plain,
! [A: $i] :
( ( c_inter @ c_Finite__Set_OFinites @ ( c_insert @ c_emptyset @ A @ ( tc_set @ tc_nat ) ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(rewrite,[status(thm)],[25052,658]) ).
thf(801,plain,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[800]) ).
thf(16748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
!= ( c_inter @ ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ c_emptyset ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[658,15685]) ).
thf(16777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ ( c_Message_Omsg_OAgent @ D ) @ C @ tc_Message_Omsg )
!= c_emptyset )
| ( A
!= ( c_Message_Osynth @ c_emptyset ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[16748]) ).
thf(16788,plain,
! [B: $i,A: $i] :
( ( c_insert @ ( c_Message_Omsg_OAgent @ B ) @ A @ tc_Message_Omsg )
!= c_emptyset ),
inference(simp,[status(thm)],[16777]) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
inference(cnf,[status(esa)],[436]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_minus @ ( c_SetInterval_OatLeastLessThan @ B @ D @ A ) @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_minus @ ( c_SetInterval_OatLeastLessThan @ B @ D @ A ) @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(719,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset ) ),
inference(cnf,[status(esa)],[718]) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset )
| ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(lifteq,[status(thm)],[719]) ).
thf(15727,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
!= ( c_inter @ ( c_insert @ v_X @ C @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[604,15687]) ).
thf(15759,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_insert @ v_X @ C @ tc_Message_Omsg ) )
| ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) )
| ( B != tc_Message_Omsg ) ),
inference(simp,[status(thm)],[15727]) ).
thf(15773,plain,
! [A: $i] :
( ( c_uminus @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) )
!= ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) ),
inference(simp,[status(thm)],[15759]) ).
thf(79548,plain,
! [A: $i] :
( ( ( c_union @ ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ A ) ) )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) )
!= ( c_Message_Oparts @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79424,991]) ).
thf(79549,plain,
( ( c_union @ ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[79548:[bind(A,$thf( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Message_Osynth @ c_emptyset ) ) ))]]) ).
thf(81742,plain,
( ( c_union @ ( c_Message_Oanalz @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) @ tc_Message_Omsg )
= ( c_Message_Oparts @ ( c_Message_Osynth @ ( c_Message_Osynth @ ( c_Message_Osynth @ c_emptyset ) ) ) ) ),
inference(rewrite,[status(thm)],[79549,9620,71223]) ).
thf(3849,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Orderings_Olinorder @ c_0 )
| ( A != tc_IntDef_Oint ) ),
inference(paramod_ordered,[status(thm)],[523,441]) ).
thf(3850,plain,
( ( c_less @ c_0 @ tc_IntDef_Oint @ tc_nat )
| ( class_Orderings_Olinorder @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3849:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(80708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != c_UNIV )
| ( ( c_inter @ c_UNIV @ A @ B )
!= ( c_inter @ ( c_SetInterval_OatMost @ D @ tc_nat ) @ C @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[781,80597]) ).
thf(80731,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
!= ( c_inter @ ( c_SetInterval_OatMost @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(simp,[status(thm)],[80708]) ).
thf(80760,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
!= ( c_inter @ ( c_SetInterval_OatMost @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(simp,[status(thm)],[80731]) ).
thf(82214,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_SetInterval_OatMost @ B @ tc_nat ) @ A @ tc_nat )
!= c_UNIV ),
inference(rewrite,[status(thm)],[80760,781]) ).
thf(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
= ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
inference(lifteq,[status(thm)],[766]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(1288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(3180,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Omin @ B @ B @ A )
= B )
| ( ( class_Orderings_Olinorder @ tc_nat )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[733,444]) ).
thf(3181,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ A @ tc_nat )
= A ),
inference(pattern_uni,[status(thm)],[3180:[bind(A,$thf( tc_nat ))]]) ).
thf(3196,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ A @ tc_nat )
= A ),
inference(simp,[status(thm)],[3181]) ).
thf(2345,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_0 != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[415,1746]) ).
thf(2346,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_0 != v_G ) ),
inference(pattern_uni,[status(thm)],[2345:[bind(A,$thf( c_emptyset ))]]) ).
thf(2353,plain,
( ~ ( c_lessequals @ c_emptyset @ c_0 @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_0 != v_G ) ),
inference(simp,[status(thm)],[2346]) ).
thf(5221,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_0 != v_G )
| ( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ c_emptyset @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1294,2353]) ).
thf(5243,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_0 != v_G )
| ( c_emptyset != c_emptyset )
| ( A != c_0 )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[5221]) ).
thf(5251,plain,
! [A: $i] :
( ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_0 != v_G )
| ( ( tc_set @ A )
!= tc_nat ) ),
inference(simp,[status(thm)],[5243]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
thf(1261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[642]) ).
thf(644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[643]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(992,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(400,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
thf(1299,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A )
| ( C = c_emptyset ) ),
inference(cnf,[status(esa)],[689]) ).
thf(691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
inference(lifteq,[status(thm)],[690]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(1236,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(2501,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_UNIV @ c_0 @ tc_nat )
| ( A != c_Finite__Set_OFinites ) ),
inference(paramod_ordered,[status(thm)],[415,2450]) ).
thf(2502,plain,
( ~ ( c_lessequals @ c_Finite__Set_OFinites @ c_0 @ tc_nat )
| ~ ( c_lessequals @ c_UNIV @ c_0 @ tc_nat ) ),
inference(pattern_uni,[status(thm)],[2501:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(5944,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Finite__Set_Ocard @ c_UNIV @ c_0 )
= c_0 )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,5924]) ).
thf(5945,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( ( c_Finite__Set_Ocard @ c_UNIV @ c_0 )
= c_0 ) ),
inference(pattern_uni,[status(thm)],[5944:[bind(A,$thf( tc_nat ))]]) ).
thf(34799,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) )
| ( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
!= ( class_Orderings_Olinorder @ A ) ) ),
inference(paramod_ordered,[status(thm)],[441,632]) ).
thf(34800,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
= ( c_SetInterval_OatMost @ A @ tc_IntDef_Oint ) ),
inference(pattern_uni,[status(thm)],[34799:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(34895,plain,
! [A: $i] :
( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
= ( c_SetInterval_OatMost @ A @ tc_IntDef_Oint ) ),
inference(simp,[status(thm)],[34800]) ).
thf(36593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_IntDef_Oint ) @ ( tc_set @ C ) )
= B )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) )
!= ( c_uminus @ B @ ( tc_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[34895,809]) ).
thf(36594,plain,
! [A: $i] :
( ( c_SetInterval_OgreaterThan @ A @ tc_IntDef_Oint )
= ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) ) ),
inference(pattern_uni,[status(thm)],[36593:[bind(A,$thf( D )),bind(B,$thf( c_SetInterval_OgreaterThan @ D @ tc_IntDef_Oint )),bind(C,$thf( tc_IntDef_Oint ))]]) ).
thf(36837,plain,
! [A: $i] :
( ( c_SetInterval_OgreaterThan @ A @ tc_IntDef_Oint )
= ( c_uminus @ ( c_SetInterval_OatMost @ A @ tc_IntDef_Oint ) @ ( tc_set @ tc_IntDef_Oint ) ) ),
inference(simp,[status(thm)],[36594]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(860,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
inference(cnf,[status(esa)],[595]) ).
thf(3258,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Nat_Opower @ c_0 )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[523,619]) ).
thf(3259,plain,
( ( c_less @ c_0 @ tc_nat @ tc_nat )
| ( class_Nat_Opower @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3258:[bind(A,$thf( tc_nat ))]]) ).
thf(9123,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,9116]) ).
thf(9124,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Oparts @ ( c_Message_Osynth @ c_0 ) )
= ( c_Message_Osynth @ c_emptyset ) ) ),
inference(pattern_uni,[status(thm)],[9123:[bind(A,$thf( c_emptyset ))]]) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(cnf,[status(esa)],[721]) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(lifteq,[status(thm)],[722]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).
thf(982,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(5942,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Finite__Set_Ocard @ c_0 @ tc_nat )
= c_0 )
| ( A != c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[523,5924]) ).
thf(5943,plain,
( ( c_less @ c_0 @ c_UNIV @ tc_nat )
| ( ( c_Finite__Set_Ocard @ c_0 @ tc_nat )
= c_0 ) ),
inference(pattern_uni,[status(thm)],[5942:[bind(A,$thf( c_UNIV ))]]) ).
thf(24990,plain,
! [B: $i,A: $i] :
( ( ( c_inter @ c_Finite__Set_OFinites @ ( c_Pow @ c_emptyset @ A ) @ ( tc_set @ tc_nat ) )
!= c_emptyset )
| ( ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) )
!= ( c_insert @ c_emptyset @ B @ ( tc_set @ tc_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[975,24923]) ).
thf(24991,plain,
( ( c_inter @ c_Finite__Set_OFinites @ ( c_Pow @ c_emptyset @ tc_nat ) @ ( tc_set @ tc_nat ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[24990:[bind(A,$thf( tc_nat )),bind(B,$thf( c_emptyset ))]]) ).
thf(3853,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[523,1649]) ).
thf(3854,plain,
( ( c_less @ c_0 @ c_emptyset @ tc_nat )
| ( ( c_Message_Osynth @ c_emptyset )
!= c_0 )
| ( c_emptyset != v_G ) ),
inference(pattern_uni,[status(thm)],[3853:[bind(A,$thf( c_emptyset ))]]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(639,plain,
! [A: $i] :
( ( sk4 @ ( c_Message_Omsg_ONonce @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_ONonce),[sk4])]) ).
thf(676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
inference(cnf,[status(esa)],[675]) ).
thf(469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ E @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(cnf,[status(esa)],[468]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_1) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(560,plain,
! [A: $i] :
( ( sk3 @ ( c_Message_Omsg_OHash @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Message_Omsg_OHash),[sk3])]) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
inference(cnf,[status(esa)],[489]) ).
thf(491,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) )
| ~ ( class_Orderings_Olinorder @ A ) ),
inference(lifteq,[status(thm)],[490]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(1088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(15785,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_emptyset != c_0 )
| ( A
!= ( c_insert @ v_X @ B @ tc_Message_Omsg ) ) ),
inference(paramod_ordered,[status(thm)],[523,15774]) ).
thf(15786,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(pattern_uni,[status(thm)],[15785:[bind(A,$thf( c_insert @ v_X @ D @ tc_Message_Omsg )),bind(B,$thf( D ))]]) ).
thf(15800,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_insert @ v_X @ A @ tc_Message_Omsg ) @ tc_nat )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[15786]) ).
thf(496,plain,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
inference(lifteq,[status(thm)],[495]) ).
thf(3574,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( class_Orderings_Oorder @ c_0 )
| ( A != tc_IntDef_Oint ) ),
inference(paramod_ordered,[status(thm)],[523,503]) ).
thf(3575,plain,
( ( c_less @ c_0 @ tc_IntDef_Oint @ tc_nat )
| ( class_Orderings_Oorder @ c_0 ) ),
inference(pattern_uni,[status(thm)],[3574:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(104848,plain,
$false,
inference(e,[status(thm)],[15767,1036,809,5469,629,1190,760,35087,846,518,941,1110,481,645,892,2612,1024,20273,909,13058,628,1031,1083,468,777,555,666,1295,408,3762,13341,10673,994,6900,741,23455,1269,1173,523,16881,1158,10431,683,730,1290,26890,873,1205,449,878,655,511,6031,677,1305,597,1437,9268,1078,1608,14347,1137,533,550,500,1164,472,6851,1327,698,747,1063,538,670,12714,2035,33564,715,3338,1275,22989,23929,3253,1640,16784,945,24560,1222,85507,1095,1196,898,782,709,43941,1601,1265,20209,1127,2491,1243,841,417,973,885,436,3880,1228,1254,570,1298,71729,504,22710,619,751,24558,934,542,1055,724,82781,1287,802,15881,71001,1059,1545,559,638,1147,20364,606,13332,1100,1232,5792,817,26991,421,870,15695,770,881,416,10702,448,15878,475,1302,1450,591,3670,623,646,834,43066,806,966,24943,492,5541,514,1151,937,1020,574,1051,821,905,480,12678,1215,734,866,1072,33998,20174,998,988,1433,72045,2982,602,2508,766,6809,1169,82511,12638,692,80256,20368,956,1119,15774,774,1104,849,5819,527,3492,452,942,678,661,546,925,3852,1199,34549,534,714,1074,24950,920,5406,529,7022,1153,761,810,15682,69599,23594,1067,16780,1047,1730,1057,6652,746,1021,1042,1355,1123,44431,2969,424,429,729,59163,1238,5924,15687,957,820,5815,561,15692,407,693,630,24964,2606,3814,815,10939,625,3750,1178,24551,583,889,461,757,1281,1634,456,974,1106,916,467,566,484,852,435,682,1195,2313,551,3445,1012,2245,47606,20184,6153,615,19707,1121,1006,20277,593,869,610,499,857,519,742,578,697,1234,1541,874,1143,58958,1259,650,948,4048,20387,980,21115,1138,2724,59036,3632,81096,783,420,20175,19879,1028,15882,1292,669,3441,526,489,44449,488,10708,24370,47331,554,753,21737,1182,901,686,476,4545,642,22983,3194,1016,1207,590,20271,679,1039,970,1155,547,73886,706,701,515,1297,738,1131,3770,16112,1192,457,984,721,1002,1715,24483,622,837,22778,11432,1114,647,1263,2450,46970,73630,569,2482,1246,503,605,4148,1318,1086,633,508,657,25874,674,2189,530,953,926,1202,792,3856,541,1286,1035,1026,3508,1167,773,586,662,718,888,906,750,618,425,513,7866,824,9122,745,573,444,733,1135,412,4872,80597,9231,1273,43632,5525,689,584,423,694,732,1125,772,20356,579,8740,3404,904,975,743,43352,875,826,577,10700,711,1256,13685,1226,545,24936,413,641,1139,24948,445,572,498,6991,466,1090,1356,540,672,1271,8432,611,787,23593,919,804,71223,704,1224,7865,1194,1209,831,2802,616,53717,1307,764,604,406,16883,4228,681,6613,1282,784,1117,1806,419,1048,736,990,996,451,567,509,880,649,434,599,26994,21746,1439,863,1175,477,811,4541,535,816,609,594,483,626,1022,1177,1112,494,1080,84187,552,799,726,700,520,9280,82359,2593,895,1149,12631,48840,48535,462,1061,24556,868,608,563,10707,1250,1102,431,653,2984,658,912,685,521,1171,1213,768,20100,3838,636,1245,780,1643,455,883,15689,3674,986,2288,9106,1000,13330,505,438,922,4965,675,589,4868,663,927,1277,1134,812,516,12701,754,1049,64420,473,1076,795,47454,749,3975,15797,1145,1018,553,44268,24956,458,823,1547,640,25681,707,971,44248,739,2175,1267,13713,84803,525,712,557,1003,580,855,1070,73606,872,954,1252,44280,3872,409,1230,673,10952,1300,791,441,585,717,47598,502,463,44435,470,808,1130,1220,544,46551,1053,1188,1186,3174,71233,1218,53526,6457,42749,744,1543,703,1141,656,1284,600,20385,978,571,612,16582,613,24923,1008,595,13119,497,24920,1240,991,10712,450,1180,556,2960,1157,495,1216,1010,844,771,1108,6286,465,931,539,976,688,524,581,7271,759,10697,896,1062,946,3336,24962,632,1244,781,4527,588,10135,1253,963,15685,517,652,64200,2447,1030,71222,914,510,478,15699,26912,684,549,536,1045,568,22988,667,21745,1294,929,13716,16884,1212,763,24945,1161,800,43217,1133,80176,620,752,15679,15705,405,23835,867,603,735,10701,1280,9229,432,410,967,950,1097,3882,43578,1248,790,58728,801,506,807,16788,437,664,828,696,720,955,9987,15773,564,81742,23501,3850,82214,474,767,1033,1288,3196,5251,960,635,6612,532,1065,886,44106,415,1093,728,1129,1261,427,528,644,992,822,1299,691,442,501,607,1236,2502,5945,7538,464,85192,575,44111,4242,36837,860,596,1378,459,22918,3259,9124,723,982,1004,486,5943,24991,3854,1184,659,543,639,676,592,469,940,1037,560,491,1088,15800,496,708,38466,3575,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV249-1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:31:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.17/1.19 % [INFO] Parsing done (338ms).
% 2.30/1.20 % [INFO] Running in sequential loop mode.
% 2.62/1.44 % [INFO] eprover registered as external prover.
% 2.62/1.45 % [INFO] cvc4 registered as external prover.
% 2.62/1.45 % [INFO] Scanning for conjecture ...
% 3.38/1.61 % [INFO] Found a conjecture and 2828 axioms. Running axiom selection ...
% 4.32/1.82 % [INFO] Axiom selection finished. Selected 402 axioms (removed 2426 axioms).
% 4.71/1.94 % [INFO] Problem is propositional (TPTP CNF).
% 4.71/1.95 % [INFO] Type checking passed.
% 4.71/1.96 % [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 ...
% 215.23/41.25 % External prover 'e' found a proof!
% 215.23/41.25 % [INFO] Killing All external provers ...
% 215.23/41.25 % Time passed: 40734ms (effective reasoning time: 40051ms)
% 215.23/41.25 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 215.23/41.26 % Axioms used in derivation (402): cls_Message_Oanalz__synth__Un_0, cls_Nat_Onot__less0_0, cls_Set_OPow__UNIV_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_Set_OPow__iff_1, cls_Set_Oempty__Union__conv_1, cls_SetInterval_OgreaterThanLessThan__iff_0, cls_Set_Oinsert__disjoint__1_1, cls_Datatype__Universe_OuprodI_0, cls_Nat_Onot__gr0_0, cls_Message_Oanalz_OInj_0, cls_Finite__Set_Ofinite__Union_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Finite__Set_OMin__gr__iff_2, cls_SetInterval_OgreaterThanAtMost__iff_2, cls_Set_Osingleton__insert__inj__eq_0, cls_SetInterval_OatMost__0_0, cls_Finite__Set_OMin__insert_0, cls_Set_OInt__iff_2, cls_Set_OUNIV__not__empty_0, cls_Set_OsubsetI_1, cls_Message_Oparts__Un_0, cls_Message_Oanalz__analzD__dest_0, cls_Message_OCrypt__synth__eq_0, cls_Message_Oanalz__synth_0, cls_Message_OkeysFor__Un_0, cls_Message_Oparts__empty_0, clsarity_nat_7, cls_Nat_Odiff__is__0__eq_0, cls_Set_ODiff__cancel_0, cls_Message_Oparts__insert__Crypt_0, cls_Set_Osubset__UNIV_0, cls_Finite__Set_OMin__singleton_0, cls_Finite__Set_Ocard__infinite_0, cls_Set_Oinsert__Diff1_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2, cls_Message_OKey__synth__eq_1, cls_Finite__Set_OMax__less__iff_2, cls_Set_OInt__UNIV__left_0, cls_Message_Oanalz__idem_0, cls_Message_Osynth__mono_0, cls_Datatype__Universe_OScons__Scons__eq_1, clsrel_Orderings_Olinorder_4, cls_SetInterval_OCompl__atLeast_0, cls_SetInterval_OgreaterThan__subset__iff_1, cls_Orderings_Oorder__less__irrefl_0, cls_SetInterval_OatLeast__iff_1, cls_Set_Oinsert__disjoint__2_2, cls_Finite__Set_OFinites_OemptyI_0, cls_Message_Oanalz__empty_0, cls_Message_Oparts__insert__MPair_0, cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0, cls_Set_Osingleton__inject__dest_0, cls_Nat_Odiff__0__eq__0_0, cls_Message_Oanalz__Crypt__if_0, cls_Set_OInt__subset__iff_0, cls_Set_OUnionE_1, cls_Set_OCompl__iff_1, cls_List_Olist_Oinject_1, cls_Finite__Set_OFinites_OinsertI_0, cls_Set_OUn__subset__iff_2, cls_Message_Oparts__insert__Nonce_0, clsarity_set_2, clsarity_nat_3, cls_Nat_Oless__irrefl_0, cls_Message_Omsg_Oinject__1_0, cls_Set_OInt__UNIV_2, cls_Set_OUn__UNIV__left_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_SetInterval_OlessThan__subset__iff_1, cls_Set_OPow__iff_0, cls_SetInterval_OatMost__iff_1, cls_Nat_Ozero__less__diff_1, cls_Set_Odisjoint__insert__2_1, cls_Finite__Set_Ofinite__Int_0, cls_Message_OHash__synth_0, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Finite__Set_Ocard__0__eq_1, cls_Set_OInter__UNIV_0, cls_Set_ODiff__UNIV_0, cls_Message_Osynth_OHash_0, cls_Set_OInter__iff_0, cls_Set_Osubset__refl_0, cls_SetInterval_Oivl__subset_1, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Set_OCompl__eq__Compl__iff_0, clsarity_IntDef__Oint_0, cls_Message_Oparts__insert__Agent_0, cls_Finite__Set_Ofinite__Un_2, cls_Message_Oparts__subset__iff_1, cls_Set_OpsubsetI_0, cls_Set_ODiff__iff_2, cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0, cls_Set_OInterI_1, cls_Message_Oanalz__insert__Agent_0, cls_Message_Omsg_Oinject__6_0, cls_Finite__Set_Ofinite__Diff__insert_1, cls_SetInterval_OatLeastLessThan__iff_2, cls_Finite__Set_Ofinite__Un_0, cls_Message_Oanalz__insert__Nonce_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, cls_Message_Oparts_OInj_0, cls_Set_OUnion__insert_0, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, cls_Set_OUn__Diff__cancel2_0, cls_Set_Odisjoint__insert__1_1, cls_Orderings_Omax__less__iff__conj_0, cls_Set_Osubset__empty_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_SetInterval_OatLeastAtMost__empty_0, cls_Message_OkeysFor__empty_0, cls_Message_Omsg_Oinject__5_0, cls_SetInterval_OatLeastAtMost__iff_2, cls_Message_Oparts__synth_0, cls_Message_OCrypt__synth_1, cls_Set_ODiff__insert0_0, cls_Set_OsubsetI_0, cls_Set_OUNIV__I_0, cls_SetInterval_OatLeastAtMost__singleton_0, cls_Finite__Set_OMin__ge__iff_2, cls_Infinite__Set_Onat__infinite_0, cls_SetInterval_Ocard__greaterThanAtMost_0, cls_Finite__Set_OMax__le__iff_2, cls_Set_Oinsert__subset_2, cls_Set_OUn__UNIV__right_0, cls_Set_OUnion__empty__conv_1, 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_Set_OUnion__iff_1, cls_Message_Oparts__insert__Key_0, cls_SetInterval_OgreaterThan__subset__iff_0, cls_Set_OUn__empty_1, cls_Set_OInter__UNIV__conv__1_0, cls_Message_Omsg_Oinject__2_0, cls_Set_Oinsert__disjoint__2_1, cls_Finite__Set_OMin__gr__iff_1, cls_SetInterval_OatLeast__subset__iff_0, cls_Finite__Set_Ofinite__insert_0, cls_Message_Omsg_Oinject__7_1, cls_Set_Oinsert__iff_2, cls_SetInterval_OlessThan__subset__iff_0, cls_Set_OCompl__Un_0, cls_Set_OCompl__subset__Compl__iff_0, cls_Orderings_Omin__less__iff__conj_2, cls_SetInterval_Ocard__lessThan_0, cls_Message_Oparts__subset__iff_0, clsarity_set_3, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_Nat_Ole__0__eq_0, cls_SetInterval_Osingle__Diff__lessThan_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_Oinsert__not__empty_0, cls_NatArith_Odiff__less_0, cls_SetInterval_OgreaterThan__iff_0, cls_Set_OsingletonD__dest_0, cls_Finite__Set_OMax__less__iff_1, cls_SetInterval_OlessThan__iff_0, cls_SetInterval_OCompl__greaterThan_0, cls_Nat_Ozero__less__diff_0, cls_Set_OInter__UNIV__conv__2_2, cls_Finite__Set_Ofinite__Int_1, clsarity_IntDef__Oint_31, cls_Message_Omsg_Oinject__4_0, cls_SetInterval_OCompl__lessThan_0, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olist_Oinject_0, cls_Set_Oempty__iff_0, cls_Set_Oempty__subsetI_0, cls_Set_OInt__UNIV__right_0, cls_Set_OUnion__iff_0, cls_Set_OUn__subset__iff_0, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Finite__Set_OMin__le_0, cls_Set_OUnion__empty__conv_2, cls_Set_Oempty__Diff_0, cls_Message_OAgent__synth_0, cls_SetInterval_OatLeastLessThan__iff_1, cls_Nat_Odiff__self__eq__0_0, cls_Set_Odisjoint__insert__2_2, cls_Set_OUnion__empty__conv_0, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_SetInterval_OCompl__atMost_0, cls_Set_OCompl__empty__eq_0, cls_Set_ODiff__iff_1, cls_Finite__Set_OMax__ge_0, cls_Message_Oparts__insert__Hash_0, cls_Message_Omsg_Oinject__6_1, cls_Set_Osubset__antisym_0, cls_Set_OInt__empty__left_0, cls_SetInterval_OatLeastLessThan__iff_0, cls_Message_Osynth__subset__iff_1, cls_Message_ONumber__synth_0, cls_Set_OsubsetD_0, cls_Finite__Set_Ofinite__Diff__insert_0, cls_SetInterval_OatMost__iff_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_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Set_OUnion__Un__distrib_0, cls_Set_OCompl__iff_0, cls_Datatype__Universe_OuprodE_2, clsrel_Orderings_Oorder_0, cls_Set_Oall__not__in__conv_0, cls_Finite__Set_Ofinite__Un_1, cls_Set_Osubset__empty_1, cls_Set_Osingleton__insert__inj__eq_1, cls_Datatype__Universe_OuprodE_0, cls_Set_OCompl__Diff__eq_0, cls_Nat_Omin__0R_0, cls_Set_Oinsert__iff_1, cls_Finite__Set_OMax__singleton_0, cls_SetInterval_OgreaterThanLessThan__iff_2, cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0, cls_Finite__Set_Ofinite__Pow__iff_0, cls_Set_Oinsert__disjoint__1_0, cls_Set_Oempty__Union__conv_0, cls_SetInterval_Oivl__subset_0, cls_Set_Odisjoint__insert__1_2, cls_Infinite__Set_Oatmost__one__unique_0, cls_SetInterval_OatLeastAtMost__iff_1, cls_Message_Oin__parts__UnE_0, cls_Finite__Set_OMin__ge__iff_1, cls_SetInterval_OatLeastLessThan__empty_0, cls_Set_Oinsert__Diff__single_0, cls_Message_OMPair__analz_1, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0, clsarity_set_1, cls_Message_Oanalz__mono_0, cls_Set_Oinsert__subset_1, cls_SetInterval_OgreaterThanAtMost__iff_0, cls_Set_OInt__UNIV_0, cls_Set_Oinsert__disjoint__2_0, cls_Message_Osynth__subset__iff_0, cls_Set_OCompl__UNIV__eq_0, cls_Set_OInter__UNIV__conv__1_1, cls_Finite__Set_Ofinite__Union_1, cls_Nat_Odiff__is__0__eq_H_0, cls_Set_OUn__insert__left_0, cls_Set_OInt__empty__right_0, cls_Finite__Set_OMin__ge__iff_0, cls_SetInterval_OatLeast__eq__iff_0, cls_Message_OkeysFor__insert__Nonce_0, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Set_OUn__insert__right_0, cls_Message_OkeysFor__insert__Crypt_0, cls_SetInterval_OatLeast__subset__iff_1, cls_NatArith_Odiff__diff__cancel_0, cls_Set_OInter__iff_2, cls_Nat_Oop_A_N_Odiff__0_0, cls_Orderings_Omax__less__iff__conj_1, cls_Set_OCompl__Int_0, cls_Finite__Set_OMax__less__iff_0, cls_Set_OUnion__iff_2, cls_Message_Osynth_OCrypt_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_SetInterval_Oivl__diff_0, cls_Finite__Set_OMax__le__iff_0, cls_Message_OMPair__parts_1, cls_Set_OInter__UNIV__conv__2_1, cls_Message_ONonce__synth__eq_0, cls_Message_Osynth__synthD__dest_0, cls_Finite__Set_OMin__gr__iff_0, clsarity_nat_12, cls_Message_OkeysFor__insert__Hash_0, cls_List_Onot__Cons__self_0, clsarity_IntDef__Oint_62, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0, cls_Set_OUn__iff_1, cls_Finite__Set_OMax__le__iff_1, clsarity_IntDef__Oint_5, cls_Message_OkeysFor__insert__Number_0, cls_SetInterval_OlessThan__iff_1, cls_Set_OUnion__empty_0, cls_Set_ODiff__Compl_0, cls_SetInterval_Oivl__subset_3, cls_Message_Oanalz__insert__MPair_0, cls_Datatype__Universe_OuprodE_1, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0, cls_Set_ODiff__eq__empty__iff_0, cls_Set_Oempty__not__insert_0, cls_Set_OpsubsetE_0, cls_Nat_Onot__gr0_1, cls_SetInterval_OgreaterThan__iff_1, cls_Orderings_Omin__less__iff__conj_0, cls_Set_ODiff__eq__empty__iff_1, cls_Set_OInt__subset__iff_2, cls_Set_OInt__iff_0, cls_Set_ODiff__empty_0, cls_SetInterval_OatMost__eq__iff_0, cls_Message_Oanalz__insert__Number_0, cls_Finite__Set_OMax__in_0, cls_Message_OinvKey__eq_0, clsarity_nat_9, cls_Set_OInt__iff_1, cls_Set_Oempty__Union__conv_2, cls_Message_OCrypt__synth__eq_1, cls_Set_Oinsert__disjoint__1_2, cls_Set_OInter__UNIV__conv__1_2, cls_SetInterval_OatLeast__iff_0, cls_Set_OUn__empty__right_0, cls_Message_Oanalz__parts_0, cls_Message_Oanalz__Crypt__if_1, cls_SetInterval_OgreaterThanLessThan__iff_1, cls_Message_OMPair__synth_1, cls_Nat_Omax__0L_0, cls_Set_OInt__UNIV_1, cls_Set_OUn__empty__left_0, cls_Set_OInterI_0, cls_Set_OUn__Diff__cancel_0, cls_Set_Ocontents__eq_0, cls_Message_Osynth_OInj_0, cls_Set_OPow__Int__eq_0, cls_SetInterval_OgreaterThanAtMost__iff_1, cls_Message_OkeysFor__insert__MPair_0, cls_Set_OInter__insert_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Finite__Set_OMin__in_0, cls_Message_Oanalz__subset__iff_1, cls_Set_ODiff__disjoint_0, clsrel_Orderings_Olinorder_3, cls_Finite__Set_Ofinite__Diff_0, cls_Message_OMPair__analz_0, cls_SetInterval_OatMost__subset__iff_0, cls_Message_OkeysFor__insert__Key_0, cls_Set_ODiff__iff_0, cls_Message_Ostrange__Un__eq_0, cls_Finite__Set_Ocard__empty_0, cls_SetInterval_OlessThan__0_0, cls_SetInterval_OgreaterThan__eq__iff_0, cls_Set_OUnionE_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0, cls_Message_Oanalz__analz__Un_0, cls_Set_OCompl__disjoint_0, cls_Message_Oparts__cut__eq_0, cls_SetInterval_Ocard__atLeastLessThan_0, cls_Message_OKey__synth__eq_0, cls_Set_OInter__empty_0, cls_Message_Oanalz_ODecrypt__dest_0, clsarity_set_0, cls_Nat_Ole0_0, cls_Message_Omsg_Oinject__7_0, cls_Message_OMPair__parts_0, cls_Message_Omsg_Oinject__3_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__iff_0, cls_List_Olistset_Osimps__2_0, cls_Set_Oinsert__absorb2_0, cls_Nat_Omin__0L_0, cls_SetInterval_OlessThan__eq__iff_0, cls_Set_OUn__subset__iff_1, cls_Set_OInt__absorb_0, cls_Message_Oparts__analz_0, cls_Set_OUnion__Pow__eq_0, cls_Set_Onot__psubset__empty_0, cls_SetInterval_OgreaterThanAtMost__empty_0, cls_Nat_Ole__0__eq_1, cls_Set_Odisjoint__insert__2_0, cls_Set_OUn__empty_2, cls_Finite__Set_OMax__insert_0, clsarity_nat_2, cls_Message_Oparts__emptyE_0, cls_Set_OUn__iff_2, cls_Set_OpsubsetE_1, cls_Message_Oanalz__subset__iff_0, cls_Orderings_Omax__less__iff__conj_2, cls_Set_OPow__empty_0, cls_Set_Osingleton__insert__inj__eq_2, cls_Set_Oinsert__inter__insert_0, cls_SetInterval_OatMost__subset__iff_1, cls_SetInterval_Ofinite__atMost_0, cls_Set_OInter__UNIV__conv__2_0, cls_Finite__Set_Ocard__0__eq_0, cls_SetInterval_Oivl__subset_2, clsarity_set_4, cls_Message_Oparts__idem_0, cls_Set_Odisjoint__insert__1_0, cls_Set_OUnion__UNIV_0, cls_Set_OInter__iff_1, cls_SetInterval_OatLeastAtMost__iff_0, cls_Set_Odouble__complement_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1, cls_Datatype__Universe_OScons__Scons__eq_0, cls_Set_Oinsert__subset_0, cls_Set_OUn__absorb_0, cls_Nat_Omax__0R_0, cls_Message_OMPair__synth_0, cls_SetInterval_OatLeast__0_0, cls_Set_OInt__subset__iff_1, cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0, cls_Set_OCompl__disjoint2_0, cls_Orderings_Omin__less__iff__conj_1, cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0
% 215.23/41.26 % No. of inferences in proof: 1907
% 215.23/41.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 40734 ms resp. 40051 ms w/o parsing
% 216.15/41.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 216.15/41.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------