TSTP Solution File: SWV259-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV259-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 12:14:35 EDT 2023
% Result : Unsatisfiable 10.78s 3.23s
% Output : Refutation 10.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 394
% Syntax : Number of formulae : 717 ( 209 unt; 72 typ; 0 def)
% Number of atoms : 1385 ( 424 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 6940 ( 684 ~; 740 |; 0 &;5516 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 148 ( 148 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 72 usr; 9 con; 0-5 aty)
% Number of variables : 1788 ( 0 ^;1788 !; 0 ?;1788 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_X_type,type,
v_X: $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(v_H_type,type,
v_H: $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(tc_set_type,type,
tc_set: $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $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_Orderings_Omax_type,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $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(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(class_Nat_Opower_type,type,
class_Nat_Opower: $i > $o ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: $i > $i > $i ).
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(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_union_type,type,
c_union: $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_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_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_SetInterval_OatLeast_type,type,
c_SetInterval_OatLeast: $i > $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(314,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(1036,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)],[314]) ).
thf(25,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(365,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)],[25]) ).
thf(15,axiom,
class_Orderings_Oord @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(347,plain,
class_Orderings_Oord @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(268,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(941,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)],[268]) ).
thf(107,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(555,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)],[107]) ).
thf(141,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(645,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)],[141]) ).
thf(245,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(892,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)],[245]) ).
thf(253,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(909,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)],[253]) ).
thf(311,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(1031,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)],[311]) ).
thf(79,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(481,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(18,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(352,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)],[18]) ).
thf(95,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(523,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)],[95]) ).
thf(293,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(994,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)],[293]) ).
thf(129,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(614,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)],[129]) ).
thf(122,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(597,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)],[122]) ).
thf(230,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(861,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)],[230]) ).
thf(45,axiom,
class_Orderings_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(408,plain,
class_Orderings_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(285,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(977,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)],[285]) ).
thf(236,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(873,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)],[236]) ).
thf(65,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(449,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)],[65]) ).
thf(239,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(878,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)],[239]) ).
thf(145,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(655,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)],[145]) ).
thf(34,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(384,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)],[34]) ).
thf(98,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(533,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)],[98]) ).
thf(75,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(472,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)],[75]) ).
thf(163,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(698,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)],[163]) ).
thf(270,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(945,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)],[270]) ).
thf(215,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(829,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)],[215]) ).
thf(296,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(1001,plain,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(167,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(709,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)],[167]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
thf(841,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(319,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(1046,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)],[319]) ).
thf(111,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(565,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)],[111]) ).
thf(143,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(651,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(36,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(389,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)],[36]) ).
thf(172,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(724,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)],[172]) ).
thf(88,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(504,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)],[88]) ).
thf(131,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(619,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(21,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(357,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)],[21]) ).
thf(101,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(542,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)],[101]) ).
thf(205,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(802,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(13,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(344,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(210,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(817,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)],[210]) ).
thf(226,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(853,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)],[226]) ).
thf(52,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(421,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)],[52]) ).
thf(282,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(969,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)],[282]) ).
thf(240,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(881,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)],[240]) ).
thf(302,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(1013,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)],[302]) ).
thf(191,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(770,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)],[191]) ).
thf(199,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(789,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)],[199]) ).
thf(29,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(376,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)],[29]) ).
thf(133,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(623,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)],[133]) ).
thf(81,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(485,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)],[81]) ).
thf(266,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(937,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)],[266]) ).
thf(16,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(348,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)],[16]) ).
thf(212,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(821,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)],[212]) ).
thf(251,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(905,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)],[251]) ).
thf(158,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(687,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)],[158]) ).
thf(275,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(956,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(39,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(396,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)],[39]) ).
thf(55,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(428,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)],[55]) ).
thf(224,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(849,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)],[224]) ).
thf(96,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(527,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(124,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(602,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)],[124]) ).
thf(189,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(766,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)],[189]) ).
thf(238,axiom,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(877,plain,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(160,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(692,plain,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(47,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(411,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(290,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(988,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)],[290]) ).
thf(31,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(380,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)],[31]) ).
thf(61,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(439,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)],[61]) ).
thf(154,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(678,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(97,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(529,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)],[97]) ).
thf(147,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(661,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_UNIV @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(103,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(546,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)],[103]) ).
thf(260,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(925,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)],[260]) ).
thf(187,axiom,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(761,plain,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(203,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(798,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)],[203]) ).
thf(276,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(957,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)],[276]) ).
thf(306,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(1021,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)],[306]) ).
thf(317,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(1042,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)],[317]) ).
thf(135,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(630,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)],[135]) ).
thf(56,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(429,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)],[56]) ).
thf(174,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(729,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)],[174]) ).
thf(256,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(916,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)],[256]) ).
thf(223,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(847,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)],[223]) ).
thf(23,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(361,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)],[23]) ).
thf(60,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(435,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)],[60]) ).
thf(5,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(329,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)],[5]) ).
thf(149,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(665,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)],[149]) ).
thf(117,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(583,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)],[117]) ).
thf(70,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(461,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)],[70]) ).
thf(84,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(493,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)],[84]) ).
thf(156,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(682,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)],[156]) ).
thf(105,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(551,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)],[105]) ).
thf(68,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(456,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(324,plain,
~ ( c_lessequals @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(284,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(974,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)],[284]) ).
thf(272,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(948,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)],[272]) ).
thf(304,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(1017,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)],[304]) ).
thf(299,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(1006,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(35,axiom,
class_Orderings_Oorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(388,plain,
class_Orderings_Oorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(234,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(869,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)],[234]) ).
thf(127,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(610,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)],[127]) ).
thf(197,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(783,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)],[197]) ).
thf(228,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(857,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)],[228]) ).
thf(180,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(742,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)],[180]) ).
thf(115,axiom,
( ( c_Message_OkeysFor @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
thf(578,plain,
( ( c_Message_OkeysFor @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(286,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(980,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)],[286]) ).
thf(43,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(403,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)],[43]) ).
thf(241,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(884,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)],[241]) ).
thf(309,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(1028,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(9,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(339,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)],[9]) ).
thf(264,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(933,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)],[264]) ).
thf(184,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(753,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)],[184]) ).
thf(138,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(637,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)],[138]) ).
thf(316,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(1039,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)],[316]) ).
thf(166,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(706,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)],[166]) ).
thf(249,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(901,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)],[249]) ).
thf(77,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(476,plain,
! [B: $i,A: $i] :
( ( c_union @ c_UNIV @ A @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(164,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(701,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)],[164]) ).
thf(92,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(515,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)],[92]) ).
thf(321,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(1050,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)],[321]) ).
thf(288,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(984,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)],[288]) ).
thf(171,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(721,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)],[171]) ).
thf(297,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(1002,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)],[297]) ).
thf(112,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(569,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)],[112]) ).
thf(195,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(779,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)],[195]) ).
thf(27,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(371,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)],[27]) ).
thf(12,axiom,
class_Nat_Opower @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(343,plain,
class_Nat_Opower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(206,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(805,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)],[206]) ).
thf(89,axiom,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(508,plain,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(258,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(921,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)],[258]) ).
thf(152,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(674,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)],[152]) ).
thf(136,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(633,plain,
! [A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(22,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(360,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)],[22]) ).
thf(193,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(773,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)],[193]) ).
thf(201,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(794,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)],[201]) ).
thf(118,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(586,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)],[118]) ).
thf(170,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(718,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)],[170]) ).
thf(243,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(888,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)],[243]) ).
thf(54,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(425,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)],[54]) ).
thf(213,axiom,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(824,plain,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(181,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(745,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(280,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(965,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)],[280]) ).
thf(183,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(750,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(91,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(513,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)],[91]) ).
thf(57,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(430,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(211,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(819,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(161,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(694,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)],[161]) ).
thf(42,axiom,
class_Nat_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(402,plain,
class_Nat_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(175,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(732,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)],[175]) ).
thf(221,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(843,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)],[221]) ).
thf(48,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(413,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)],[48]) ).
thf(237,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(875,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(214,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(826,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)],[214]) ).
thf(139,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(641,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)],[139]) ).
thf(37,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(391,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)],[37]) ).
thf(63,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(445,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)],[63]) ).
thf(32,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(382,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)],[32]) ).
thf(113,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(572,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)],[113]) ).
thf(198,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(787,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)],[198]) ).
thf(73,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(466,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)],[73]) ).
thf(8,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(335,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)],[8]) ).
thf(257,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(919,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)],[257]) ).
thf(165,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(704,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)],[165]) ).
thf(271,axiom,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(947,plain,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(17,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(350,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)],[17]) ).
thf(151,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(672,plain,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(168,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(713,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)],[168]) ).
thf(86,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(498,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)],[86]) ).
thf(125,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(604,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)],[125]) ).
thf(320,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(1048,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)],[320]) ).
thf(177,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(737,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)],[177]) ).
thf(59,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(434,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)],[59]) ).
thf(231,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(863,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)],[231]) ).
thf(301,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(1011,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(51,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(419,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(291,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(990,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)],[291]) ).
thf(294,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(996,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)],[294]) ).
thf(24,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(362,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(66,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(451,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)],[66]) ).
thf(244,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(890,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)],[244]) ).
thf(208,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(811,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(186,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(758,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)],[186]) ).
thf(14,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(345,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)],[14]) ).
thf(1,negated_conjecture,
c_in @ v_X @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(323,plain,
c_in @ v_X @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(132,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(621,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)],[132]) ).
thf(80,axiom,
! [A: $i] :
( ( c_Inter @ c_emptyset @ A )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
thf(483,plain,
! [A: $i] :
( ( c_Inter @ c_emptyset @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(94,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(520,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)],[94]) ).
thf(134,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(626,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)],[134]) ).
thf(190,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(769,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(269,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(943,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)],[269]) ).
thf(150,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(668,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)],[150]) ).
thf(71,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(462,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)],[71]) ).
thf(310,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(1029,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(246,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(895,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)],[246]) ).
thf(287,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(983,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(40,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(399,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)],[40]) ).
thf(277,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(959,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)],[277]) ).
thf(318,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(1044,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)],[318]) ).
thf(303,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(1015,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)],[303]) ).
thf(110,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(563,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(225,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(851,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)],[225]) ).
thf(144,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(653,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(146,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(658,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)],[146]) ).
thf(254,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(912,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)],[254]) ).
thf(157,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(685,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(38,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(394,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)],[38]) ).
thf(289,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(986,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)],[289]) ).
thf(313,axiom,
( ( c_Message_Oparts @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
thf(1034,plain,
( ( c_Message_Oparts @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(83,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(490,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)],[83]) ).
thf(119,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(589,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)],[119]) ).
thf(155,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(680,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(261,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(927,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)],[261]) ).
thf(130,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(617,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)],[130]) ).
thf(267,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(939,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)],[267]) ).
thf(11,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(342,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,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(355,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)],[20]) ).
thf(106,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(553,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)],[106]) ).
thf(218,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(836,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)],[218]) ).
thf(148,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(663,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)],[148]) ).
thf(104,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(548,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)],[104]) ).
thf(142,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(648,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)],[142]) ).
thf(82,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(487,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)],[82]) ).
thf(194,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(776,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)],[194]) ).
thf(108,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(557,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)],[108]) ).
thf(159,axiom,
! [A: $i] :
( ( c_Union @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
thf(690,plain,
! [A: $i] :
( ( c_Union @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(308,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(1025,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)],[308]) ).
thf(283,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(971,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(4,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(327,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)],[4]) ).
thf(274,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(954,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)],[274]) ).
thf(178,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(739,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(46,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(409,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)],[46]) ).
thf(116,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(580,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)],[116]) ).
thf(227,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(855,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)],[227]) ).
thf(200,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(791,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)],[200]) ).
thf(6,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(331,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)],[6]) ).
thf(315,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(1038,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(140,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(643,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)],[140]) ).
thf(273,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(951,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)],[273]) ).
thf(207,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(808,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)],[207]) ).
thf(102,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(544,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)],[102]) ).
thf(252,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(907,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)],[252]) ).
thf(307,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(1023,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)],[307]) ).
thf(123,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(600,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)],[123]) ).
thf(322,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(1052,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)],[322]) ).
thf(173,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(727,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)],[173]) ).
thf(300,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(1008,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)],[300]) ).
thf(121,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(595,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(128,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(612,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)],[128]) ).
thf(229,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(859,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)],[229]) ).
thf(222,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(845,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)],[222]) ).
thf(250,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(903,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)],[250]) ).
thf(26,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(368,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)],[26]) ).
thf(192,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(771,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_UNIV @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(263,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(931,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)],[263]) ).
thf(100,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(539,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)],[100]) ).
thf(182,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(748,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)],[182]) ).
thf(41,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(401,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)],[41]) ).
thf(50,axiom,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(418,plain,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(196,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(781,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)],[196]) ).
thf(278,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(961,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)],[278]) ).
thf(209,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(813,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)],[209]) ).
thf(279,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(963,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)],[279]) ).
thf(93,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(517,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)],[93]) ).
thf(90,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(510,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)],[90]) ).
thf(262,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(929,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)],[262]) ).
thf(78,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(478,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)],[78]) ).
thf(188,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(763,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)],[188]) ).
thf(33,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(383,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(248,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(899,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)],[248]) ).
thf(216,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(832,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)],[216]) ).
thf(99,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(536,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)],[99]) ).
thf(255,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(914,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)],[255]) ).
thf(30,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(378,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)],[30]) ).
thf(169,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(716,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)],[169]) ).
thf(204,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(800,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(295,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(999,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)],[295]) ).
thf(64,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(447,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)],[64]) ).
thf(58,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(432,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)],[58]) ).
thf(281,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(967,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)],[281]) ).
thf(217,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(835,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(44,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(405,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(233,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(867,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)],[233]) ).
thf(232,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(865,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)],[232]) ).
thf(28,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(373,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)],[28]) ).
thf(176,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(735,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)],[176]) ).
thf(3,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(326,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
class_Orderings_Olinorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(341,plain,
class_Orderings_Olinorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(312,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(1033,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(137,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(635,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)],[137]) ).
thf(162,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(696,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)],[162]) ).
thf(202,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(796,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)],[202]) ).
thf(247,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(897,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)],[247]) ).
thf(76,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(474,plain,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(242,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(886,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)],[242]) ).
thf(49,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(415,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)],[49]) ).
thf(219,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(839,plain,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(179,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(740,plain,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(72,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(464,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)],[72]) ).
thf(7,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(332,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)],[7]) ).
thf(114,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(575,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)],[114]) ).
thf(305,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(1019,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)],[305]) ).
thf(69,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(459,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)],[69]) ).
thf(292,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(992,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)],[292]) ).
thf(298,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(1004,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)],[298]) ).
thf(62,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(442,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)],[62]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ 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_Oparts_OBody__dest_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ 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)],[235]) ).
thf(87,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(501,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(126,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(607,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)],[126]) ).
thf(74,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(469,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)],[74]) ).
thf(19,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(354,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(265,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(935,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)],[265]) ).
thf(259,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(923,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)],[259]) ).
thf(109,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(560,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)],[109]) ).
thf(120,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(592,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)],[120]) ).
thf(185,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(755,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)],[185]) ).
thf(153,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(676,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)],[153]) ).
thf(85,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(496,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)],[85]) ).
thf(67,axiom,
! [A: $i] :
( ( c_Inter @ c_UNIV @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
thf(454,plain,
! [A: $i] :
( ( c_Inter @ c_UNIV @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1162,plain,
$false,
inference(cvc4,[status(thm)],[1036,365,347,941,555,645,892,909,1031,481,352,523,994,614,597,861,408,977,873,449,878,655,384,533,472,698,945,829,1001,709,841,1046,565,651,389,724,504,619,357,542,802,344,817,853,421,969,881,1013,770,789,376,623,485,937,348,821,905,687,956,396,428,849,527,602,766,877,692,411,988,380,439,678,529,661,546,925,761,798,957,1021,1042,630,429,729,916,847,361,435,329,665,583,461,493,682,551,456,324,974,948,1017,1006,388,869,610,783,857,742,578,980,403,884,1028,339,933,753,637,1039,706,901,476,701,515,1050,984,721,1002,569,779,371,343,805,508,921,674,633,360,773,794,586,718,888,425,824,745,965,750,513,430,819,423,694,402,732,843,413,875,826,641,391,445,382,572,787,466,335,919,704,947,350,672,713,498,604,1048,737,434,863,1011,419,990,996,362,451,890,811,758,345,323,621,483,520,626,769,943,668,462,1029,895,983,399,959,1044,1015,563,851,653,658,912,685,394,986,1034,490,589,680,927,617,939,342,355,553,836,663,548,648,487,776,557,690,1025,971,327,954,739,409,580,855,791,331,1038,643,951,808,544,907,1023,600,1052,727,1008,595,612,859,845,903,368,771,931,539,748,401,418,781,961,813,963,517,510,929,478,763,383,899,832,536,914,378,716,800,999,447,432,967,835,405,867,865,373,735,326,341,1033,635,696,796,897,474,886,415,839,740,464,332,575,1019,459,992,1004,442,871,501,607,469,354,935,923,560,592,755,676,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV259-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 02:29:19 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.80/1.14 % [INFO] Parsing done (287ms).
% 1.80/1.15 % [INFO] Running in sequential loop mode.
% 2.45/1.34 % [INFO] eprover registered as external prover.
% 2.45/1.34 % [INFO] cvc4 registered as external prover.
% 2.45/1.34 % [INFO] Scanning for conjecture ...
% 2.96/1.49 % [INFO] Found a conjecture and 2777 axioms. Running axiom selection ...
% 3.67/1.65 % [INFO] Axiom selection finished. Selected 320 axioms (removed 2457 axioms).
% 3.93/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 3.93/1.76 % [INFO] Type checking passed.
% 3.93/1.76 % [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 ...
% 10.78/3.22 % External prover 'cvc4' found a proof!
% 10.78/3.22 % [INFO] Killing All external provers ...
% 10.78/3.22 % Time passed: 2689ms (effective reasoning time: 2065ms)
% 10.78/3.22 % 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)>
% 10.78/3.22 % Axioms used in derivation (320): 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_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_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_Set_ODiff__cancel_0, cls_Message_OkeysFor__Un_0, cls_Message_Oparts__empty_0, clsarity_nat_7, cls_Set_Osubset__UNIV_0, cls_Finite__Set_OMin__singleton_0, cls_Set_Oinsert__Diff1_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2, cls_Finite__Set_OFinites_OemptyI_0, cls_Finite__Set_OMax__less__iff_2, cls_Set_OInt__UNIV__left_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_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0, cls_Set_Osingleton__inject__dest_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, 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_Set_Osingleton__insert__inj__eq_H_0, cls_Set_Odisjoint__insert__2_1, cls_Finite__Set_Ofinite__Int_0, cls_Set_OInter__UNIV_0, cls_Set_ODiff__UNIV_0, clsarity_IntDef__Oint_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, 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_Omsg_Oinject__6_0, cls_Finite__Set_Ofinite__Diff__insert_1, cls_SetInterval_OatLeastLessThan__iff_2, cls_Finite__Set_Ofinite__Un_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_SetInterval_OatLeastAtMost__iff_2, 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_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_Finite__Set_OMax__le__iff_2, cls_SetInterval_OgreaterThan__subset__iff_0, cls_Set_Oinsert__subset_2, cls_Set_OUn__UNIV__right_0, cls_Set_OUnion__empty__conv_1, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Set_OUn__iff_0, cls_Set_OUnion__iff_1, 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_Orderings_Omin__less__iff__conj_2, 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_Message_Oparts__subset__iff_0, clsarity_set_3, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_SetInterval_Osingle__Diff__lessThan_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_Oinsert__not__empty_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_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_OsubsetD_0, cls_Set_OUnion__empty__conv_2, cls_Set_Oempty__Diff_0, cls_SetInterval_OatLeastLessThan__iff_1, 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_Omsg_Oinject__6_1, cls_Set_Osubset__antisym_0, cls_Set_OInt__empty__left_0, cls_SetInterval_OatLeastLessThan__iff_0, cls_Finite__Set_Ofinite__Diff__insert_0, cls_SetInterval_OatMost__iff_0, cls_Message_OkeysFor__insert__Agent_0, cls_Message_Oparts_OBody__dest_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_Set_Oinsert__iff_1, 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_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_Set_Oinsert__subset_1, cls_Finite__Set_OMin__ge__iff_1, cls_SetInterval_OatLeastLessThan__empty_0, cls_Set_Oinsert__Diff__single_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0, clsarity_set_1, cls_SetInterval_OgreaterThanAtMost__iff_0, cls_Set_OInt__UNIV_0, cls_Set_Oinsert__disjoint__2_0, cls_Set_OCompl__UNIV__eq_0, cls_Set_OInter__UNIV__conv__1_1, cls_Finite__Set_Ofinite__Union_1, 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_Orderings_Omax__less__iff__conj_1, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Set_OUn__insert__right_0, cls_SetInterval_OatLeast__subset__iff_1, cls_NatArith_Odiff__diff__cancel_0, cls_Set_OInter__iff_2, cls_Set_OCompl__Int_0, cls_Finite__Set_OMax__less__iff_0, cls_Set_OUnion__iff_2, 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_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_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_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_Finite__Set_OMax__in_0, clsarity_nat_9, cls_Set_OInt__iff_1, cls_Set_Oempty__Union__conv_2, 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_SetInterval_OgreaterThanLessThan__iff_1, 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_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_Set_ODiff__disjoint_0, clsrel_Orderings_Olinorder_3, cls_Finite__Set_Ofinite__Diff_0, cls_SetInterval_OatMost__subset__iff_0, cls_Message_OkeysFor__insert__Key_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0, cls_Set_ODiff__iff_0, cls_Message_Ostrange__Un__eq_0, cls_SetInterval_OgreaterThan__eq__iff_0, cls_Set_OUnionE_0, cls_Set_OCompl__disjoint_0, cls_Set_OInter__empty_0, clsarity_set_0, cls_Message_Omsg_Oinject__7_0, cls_Message_OMPair__parts_0, cls_Message_Omsg_Oinject__3_0, cls_Set_OInt__absorb_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__iff_0, cls_List_Olistset_Osimps__2_0, cls_Set_Oinsert__absorb2_0, cls_SetInterval_OlessThan__eq__iff_0, cls_Set_OUn__subset__iff_1, cls_Set_OUnion__Pow__eq_0, cls_Set_Onot__psubset__empty_0, cls_SetInterval_OgreaterThanAtMost__empty_0, 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_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_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_Orderings_Omin__less__iff__conj_1, cls_Set_OInt__subset__iff_1, cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0, cls_Set_OCompl__disjoint2_0
% 10.78/3.22 % No. of inferences in proof: 645
% 10.78/3.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2689 ms resp. 2065 ms w/o parsing
% 10.78/3.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.78/3.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------