%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ063-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:21:16 AM UTC 2026
% Result : Unsatisfiable 10.06s 4.02s
% Output : Refutation 11.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 221
% Syntax : Number of formulae : 443 ( 195 unt; 0 typ; 0 def)
% Number of atoms : 751 ( 332 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 4140 ( 304 ~; 308 |; 0 &;3528 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 55 usr; 9 con; 0-5 aty)
% Number of variables : 1180 ( 0 ^;1180 !; 0 ?;1180 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_u_decl,type,
v_u: $i ).
thf(c_Mutil_Otiling_decl,type,
c_Mutil_Otiling: $i > $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_decl,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_Main_OInter__UNIV__conv__1__1_decl,type,
c_Main_OInter__UNIV__conv__1__1: $i > $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Main_OuprodE__1_decl,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_decl,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OInter__UNIV__conv__2__1_decl,type,
c_Main_OInter__UNIV__conv__2__1: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odprod_decl,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_Main_Oempty__Union__conv__1_decl,type,
c_Main_Oempty__Union__conv__1: $i > $i > $i ).
thf(c_Main_OUnion__iff__1_decl,type,
c_Main_OUnion__iff__1: $i > $i > $i > $i ).
thf(c_Main_OInter__iff__1_decl,type,
c_Main_OInter__iff__1: $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_decl,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OInterI__1_decl,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_OUnion__empty__conv__1_decl,type,
c_Main_OUnion__empty__conv__1: $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Equiv__Relations_Oquotient_decl,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_Main_Oall__not__in__conv__1_decl,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_List_Olistset_decl,type,
c_List_Olistset: $i > $i > $i ).
thf(c_List_Oset__Cons_decl,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(c_List_Olexn_decl,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_Set_Ocontents_decl,type,
c_Set_Ocontents: $i > $i > $i ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(8,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(234,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
= ( C @ ( B @ ( A @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
= ( C @ ( B @ ( A @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(203,axiom,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(683,plain,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(13,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(247,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
thf(597,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(523,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
thf(655,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olistset ) )
= ( C @ ( C @ ( B @ c_List_Olistset ) @ ( A @ c_List_Oset__Cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olistset ) )
= ( C @ ( C @ ( B @ c_List_Olistset ) @ ( A @ c_List_Oset__Cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
thf(715,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ c_Inter ) )
!= c_UNIV )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ c_Inter ) )
!= c_UNIV )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(92,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
thf(436,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(257,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(389,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(702,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(344,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_insert ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_insert ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(167,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(606,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(5,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(228,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
thf(316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Finite__Set_Ocard ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
thf(261,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Finite__Set_Ocard ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_uminus ) )
= ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_uminus ) )
= ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(514,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) ) )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) ) )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__assoc_0) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
thf(660,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
thf(507,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
thf(527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Inter ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
thf(307,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Inter ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(69,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(381,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Union ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
thf(366,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Union ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(7,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(233,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(452,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(24,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(270,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
thf(529,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(349,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_union ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( C @ ( A @ c_Union ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_union ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( C @ ( A @ c_Union ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(467,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(15,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(252,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_inter ) ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
thf(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_inter ) ) @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
thf(665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(130,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(522,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( c_emptyset
= ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
thf(551,plain,
! [B: $i,A: $i] :
( c_emptyset
= ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,negated_conjecture,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( c_emptyset @ c_union ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(224,plain,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( c_emptyset @ c_union ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
thf(697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(356,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
thf(499,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
thf(637,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(115,axiom,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(489,plain,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
thf(679,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(215,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(706,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(175,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(622,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
thf(569,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(66,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(633,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_inter ) ) )
= c_emptyset )
| ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
thf(541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_inter ) ) )
= c_emptyset )
| ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( D @ ( B @ c_inter ) ) ) )
| ( c_emptyset
!= ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( D @ ( B @ c_inter ) ) ) )
| ( c_emptyset
!= ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
thf(558,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ c_Union ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ c_Union ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_1) ).
thf(662,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(237,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(618,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(27,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
thf(279,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(584,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_0) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Inter ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
thf(291,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Inter ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) )
= c_emptyset )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) )
= c_emptyset )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(611,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= c_0 )
| ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= c_0 )
| ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(9,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(236,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(214,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(704,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(672,plain,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Inter ) )
= ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Inter ) )
= ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_emptyset @ ( A @ c_Relation_OImage ) ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_emptyset @ ( A @ c_Relation_OImage ) ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(6,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(230,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
thf(616,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
thf(362,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
thf(567,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(72,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(387,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(169,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(609,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
thf(700,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
thf(520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(2,negated_conjecture,
( ( t_a @ ( v_u @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(223,plain,
( ( t_a @ ( v_u @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(394,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_inter ) ) @ c_Pow ) )
= ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( C @ ( A @ c_Pow ) @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
thf(505,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_inter ) ) @ c_Pow ) )
= ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( C @ ( A @ c_Pow ) @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(431,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(17,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(255,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
thf(516,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) )
= c_emptyset )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) )
= c_emptyset )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
thf(707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_Odprod ) ) ) @ c_Relation_ODomain ) ) )
= ( D @ ( C @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( A @ c_Relation_ODomain ) ) @ c_Datatype__Universe_Ouprod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
thf(331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_Odprod ) ) ) @ c_Relation_ODomain ) ) )
= ( D @ ( C @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( A @ c_Relation_ODomain ) ) @ c_Datatype__Universe_Ouprod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(463,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( B @ c_inter ) ) )
= c_emptyset )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
thf(576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( B @ c_inter ) ) )
= c_emptyset )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(140,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_UNIV @ c_inter ) ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_2) ).
thf(600,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_UNIV @ c_inter ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
thf(571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(465,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(197,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ c_Mutil_Otiling ) @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling_Oempty_0) ).
thf(671,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ c_Mutil_Otiling ) @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(19,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(258,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(588,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(211,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(699,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( c_UNIV
!= ( C @ ( B @ c_Inter ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
thf(652,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( c_UNIV
!= ( C @ ( B @ c_Inter ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
thf(433,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(667,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_union ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_union ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(25,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
thf(272,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(79,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(405,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
thf(564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
!= c_0 )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
!= c_0 )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
thf(239,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(341,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_inter ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_inter ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(193,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(664,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__right_0) ).
thf(635,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
thf(720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) )
= ( C @ tc_set @ ( D @ ( B @ c_minus ) ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
thf(415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) )
= ( C @ tc_set @ ( D @ ( B @ c_minus ) ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(624,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
thf(644,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
thf(442,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
thf(501,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
thf(607,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_OImage ) ) ) )
= ( B @ ( C @ ( A @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_OImage ) ) ) )
= ( B @ ( C @ ( A @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(207,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(691,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(4,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(227,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
thf(469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1,negated_conjecture,
t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(222,plain,
t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( D @ ( C @ ( A @ c_inter ) ) ) )
| ( c_emptyset
!= ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
thf(592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( D @ ( C @ ( A @ c_inter ) ) ) )
| ( c_emptyset
!= ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(100,axiom,
! [A: $i] :
( ( ( A @ ( c_emptyset @ c_Finite__Set_Ocard ) )
= c_0 )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_1) ).
thf(454,plain,
! [A: $i] :
( ( ( A @ ( c_emptyset @ c_Finite__Set_Ocard ) )
= c_0 )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(723,plain,
$false,
inference(e,[status(thm)],[629,518,234,333,249,408,683,247,597,523,582,655,511,614,677,384,533,715,472,538,436,257,389,702,344,460,421,606,228,289,316,261,321,376,253,485,514,353,480,602,293,660,265,507,397,687,527,312,307,439,546,381,366,233,452,270,529,302,349,392,693,429,467,252,329,665,522,493,551,710,324,285,224,697,356,499,669,476,637,489,590,679,706,622,647,457,569,371,503,244,633,541,657,558,674,586,662,343,237,298,412,618,279,573,689,444,584,562,423,402,281,579,291,641,382,611,335,236,704,672,604,406,681,230,318,616,362,567,509,649,387,631,609,483,626,700,520,399,695,223,394,267,505,431,490,426,531,255,487,516,553,525,712,295,707,263,331,717,463,338,576,359,544,600,314,571,595,465,450,556,671,368,258,418,588,699,652,351,378,433,667,478,272,684,549,536,287,300,620,447,410,405,564,305,326,239,341,437,474,664,635,720,283,415,624,644,442,501,607,277,691,227,469,309,560,639,222,592,364,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ063-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n005.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 05:10:18 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.56/1.50 % [INFO] Parsing done (496ms).
% 2.56/1.52 % [INFO] Running in sequential loop mode.
% 3.14/1.89 % [INFO] eprover registered as external prover.
% 3.30/1.90 % [INFO] Scanning for conjecture ...
% 4.06/2.19 % [INFO] Found a conjecture (or negated_conjecture) and 2732 axioms. Running axiom selection ...
% 5.26/2.46 % [INFO] Axiom selection finished. Selected 218 axioms (removed 2514 axioms).
% 5.60/2.59 % [INFO] Problem is propositional (TPTP CNF).
% 5.86/2.60 % [INFO] Type checking passed.
% 5.86/2.61 % [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 ...
% 10.06/4.01 % External prover 'e' found a proof!
% 10.06/4.01 % [INFO] Killing All external provers ...
% 10.06/4.01 % Time passed: 3456ms (effective reasoning time: 2484ms)
% 10.06/4.02 % Axioms used in derivation (218): cls_Nat_Onot__gr0_0, cls_Nat_Onot__less0_0, cls_Set_OPow__UNIV_0, cls_Relation_ODomain__empty_0, cls_Set_OPow__iff_1, cls_Set_Oempty__Union__conv_1, cls_Transitive__Closure_Otrancl__range_0, cls_Set_Oinsert__disjoint__1_1, cls_Finite__Set_Ofinite__Union_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Equiv__Relations_Oquotient__is__empty2_0, cls_Datatype__Universe_OuprodI_0, cls_Set_Osingleton__insert__inj__eq_0, cls_Set_OInt__iff_2, cls_Relation_ODomain__diag_0, cls_Set_OUNIV__not__empty_0, cls_Relation_ORange__diag_0, cls_Set_OsubsetI_1, cls_Set_ODiff__cancel_0, cls_Nat_Odiff__is__0__eq_0, cls_Set_Osubset__UNIV_0, cls_Finite__Set_Ocard__infinite_0, cls_Set_Oinsert__Diff1_0, cls_Set_Oinsert__disjoint__2_2, cls_Finite__Set_OFinites_OemptyI_0, cls_Set_Osingleton__inject__dest_0, cls_Set_OInt__UNIV__left_0, cls_Datatype__Universe_OScons__Scons__eq_1, cls_Nat_Odiff__0__eq__0_0, cls_Set_OInt__subset__iff_0, cls_Set_OUnionE_1, cls_Set_OCompl__iff_1, cls_List_Olist_Oinject_1, cls_Finite__Set_OFinites_OinsertI_0, cls_Set_OUn__subset__iff_2, cls_Nat_Oless__irrefl_0, cls_Set_OInt__UNIV_2, cls_Set_OUn__UNIV__left_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_Set_OPow__iff_0, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Nat_Ozero__less__diff_1, cls_Set_Odisjoint__insert__2_1, cls_Finite__Set_Ofinite__Int_0, cls_Finite__Set_Ocard__0__eq_1, cls_Set_OInter__UNIV_0, cls_Set_ODiff__UNIV_0, cls_Set_OInter__iff_0, cls_Set_Osubset__refl_0, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Set_OCompl__eq__Compl__iff_0, cls_Finite__Set_Ofinite__Un_2, cls_Set_OpsubsetI_0, cls_Set_ODiff__iff_2, cls_Set_OInterI_1, cls_Finite__Set_Ofinite__Diff__insert_1, cls_Finite__Set_Ofinite__Un_0, cls_Set_OUnion__insert_0, cls_Set_OUn__Diff__cancel2_0, cls_Set_Odisjoint__insert__1_1, cls_Set_Osubset__empty_0, cls_Set_OUNIV__I_0, cls_Set_ODiff__insert0_0, cls_Set_OsubsetI_0, cls_Infinite__Set_Onat__infinite_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_Set_Oinsert__disjoint__2_1, cls_Finite__Set_Ofinite__insert_0, cls_Set_Oinsert__iff_2, cls_Set_OCompl__Un_0, cls_Set_OCompl__subset__Compl__iff_0, cls_Set_OsingletonD__dest_0, clsarity_set_3, cls_Nat_Ole__0__eq_0, cls_Set_Oinsert__not__empty_0, cls_NatArith_Odiff__less_0, cls_Transitive__Closure_Otrancl__empty_0, cls_Nat_Ozero__less__diff_0, cls_Set_OInter__UNIV__conv__2_2, cls_Finite__Set_Ofinite__Int_1, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_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_Set_OsubsetD_0, cls_Set_OUnion__empty__conv_2, cls_Set_Oempty__Diff_0, cls_Nat_Odiff__self__eq__0_0, cls_Set_Odisjoint__insert__2_2, cls_Set_OUnion__empty__conv_0, cls_Set_OsingletonI_0, cls_Set_OCompl__empty__eq_0, cls_Set_ODiff__iff_1, cls_Relation_ORange__empty_0, cls_Set_Osubset__antisym_0, cls_Set_OInt__empty__left_0, cls_Finite__Set_Ofinite__Diff__insert_0, cls_Relation_OImage__empty_0, cls_Datatype__Universe_OuprodE_2, cls_Set_OUnion__Un__distrib_0, cls_Set_OCompl__iff_0, cls_Set_Oall__not__in__conv_0, cls_Set_Oinsert__iff_1, cls_Finite__Set_Ofinite__Un_1, cls_Equiv__Relations_Oquotient__is__empty_0, cls_Set_Osubset__empty_1, cls_Set_Osingleton__insert__inj__eq_1, cls_Finite__Set_Ofinite__Pow__iff_0, cls_Datatype__Universe_OuprodE_0, cls_Set_OCompl__Diff__eq_0, cls_Set_Oinsert__disjoint__1_0, cls_Set_Oempty__Union__conv_0, cls_Set_Odisjoint__insert__1_2, cls_Infinite__Set_Oatmost__one__unique_0, cls_Set_Oinsert__subset_1, cls_Set_Oinsert__Diff__single_0, cls_Set_OInt__UNIV_0, cls_Set_Oinsert__disjoint__2_0, cls_Mutil_Otiling_Oempty_0, cls_Set_OCompl__UNIV__eq_0, cls_Set_OInter__UNIV__conv__1_1, cls_Finite__Set_Ofinite__Union_1, cls_Nat_Odiff__is__0__eq_H_0, cls_Set_OUn__insert__left_0, cls_Set_OInt__empty__right_0, cls_Nat_Oop_A_N_Odiff__0_0, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Set_OUn__insert__right_0, cls_NatArith_Odiff__diff__cancel_0, cls_Set_OInter__iff_2, cls_Set_OCompl__Int_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Set_OUnion__iff_2, cls_Set_OInter__UNIV__conv__2_1, cls_List_Onot__Cons__self_0, cls_Set_OUn__iff_1, cls_Set_OUnion__empty_0, cls_Set_ODiff__Compl_0, clsarity_nat_12, cls_Equiv__Relations_Oquotient__is__empty2_1, cls_Datatype__Universe_OuprodE_1, cls_Set_ODiff__eq__empty__iff_0, cls_Set_Oempty__not__insert_0, cls_Set_OpsubsetE_0, cls_Nat_Onot__gr0_1, cls_Set_ODiff__eq__empty__iff_1, cls_Set_OInt__subset__iff_2, cls_Set_OInt__iff_0, cls_Transitive__Closure_Otrancl__domain_0, cls_Set_ODiff__empty_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_Relation_Odiag__empty_0, cls_Set_OUn__empty__right_0, cls_Set_OInt__UNIV_1, cls_Set_OUn__empty__left_0, cls_Datatype__Universe_ODomain__dprod_0, cls_Set_OUn__assoc_0, cls_Set_OInterI_0, cls_Set_OUn__Diff__cancel_0, cls_Set_Ocontents__eq_0, cls_Set_OPow__Int__eq_0, cls_Set_ODiff__disjoint_0, cls_Set_OInter__insert_0, cls_Set_ODiff__iff_0, cls_Finite__Set_Ofinite__Diff_0, cls_Finite__Set_Ocard__empty_0, cls_Set_OUnionE_0, cls_Equiv__Relations_Oquotient__is__empty_1, cls_Mutil_Otiling_OUn_0, cls_Set_OCompl__disjoint_0, cls_Set_OInter__empty_0, cls_List_Olexn_Osimps__1_0, clsarity_set_0, cls_Nat_Ole0_0, cls_Set_OUn__subset__iff_1, 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_Set_OUnion__Pow__eq_0, cls_Set_Onot__psubset__empty_0, cls_Nat_Ole__0__eq_1, cls_Set_OPow__empty_0, cls_Set_Odisjoint__insert__2_0, cls_Set_OUn__empty_2, cls_Set_OUn__iff_2, cls_Set_OpsubsetE_1, cls_Set_Osingleton__insert__inj__eq_2, cls_Set_Oinsert__inter__insert_0, cls_Set_OInter__UNIV__conv__2_0, cls_Set_Odouble__complement_0, cls_Finite__Set_Ocard__0__eq_0, clsarity_set_4, cls_Datatype__Universe_OScons__Scons__eq_0, cls_Set_Odisjoint__insert__1_0, cls_Set_OUnion__UNIV_0, cls_Set_OInter__iff_1, cls_Set_Oinsert__subset_0, cls_Set_OUn__absorb_0, cls_Relation_OImage__diag_0, cls_Set_OInt__subset__iff_1, cls_Set_OCompl__disjoint2_0
% 10.06/4.02 % No. of inferences in proof: 443
% 10.06/4.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3456 ms resp. 2484 ms w/o parsing
% 11.19/4.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.19/4.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------