%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL440-1 : 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 : n016.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 07:51:50 AM UTC 2026
% Result : Unsatisfiable 5.35s 26.93s
% Output : Refutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 196
% Syntax : Number of formulae : 393 ( 85 unt; 0 typ; 0 def)
% Number of atoms : 757 ( 236 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 5836 ( 380 ~; 364 |; 0 &;5092 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 85 usr; 9 con; 0-6 aty)
% Number of variables : 1404 ( 0 ^;1404 !; 0 ?;1404 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_PropLog_Opl_Oop_A_N_62_decl,type,
c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).
thf(c_PropLog_Opl_Ofalse_decl,type,
c_PropLog_Opl_Ofalse: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_PropLog_Othms_decl,type,
c_PropLog_Othms: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(tc_PropLog_Opl_decl,type,
tc_PropLog_Opl: $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__1_decl,type,
c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__2_decl,type,
c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__1_decl,type,
c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__2_decl,type,
c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).
thf(c_append_decl,type,
c_append: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_Datatype__Universe_Odprod_decl,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_decl,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_decl,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_decl,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_decl,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn0_decl,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn1_decl,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Olex__prod_decl,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odsum_decl,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(c_Sum__Type_OInr_decl,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_decl,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_PropLog_Opl_Ovar_decl,type,
c_PropLog_Opl_Ovar: $i > $i > $i ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Main_OPlusE__1_decl,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_decl,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_List_Olenlex_decl,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Main_OImageE__1_decl,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_decl,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_decl,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $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_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_decl,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_decl,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oquotient_decl,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_Main_Oin__listsI__1_decl,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_Main_OInterI__1_decl,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_decl,type,
c_Datatype_Oo2s: $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_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_decl,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_decl,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_decl,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OdiagE__1_decl,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_decl,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OIdE__1_decl,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_ODomainE__1_decl,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_PropLog_Opl_Ovar ) )
!= ( B @ ( C @ c_PropLog_Opl_Ovar ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Oinject__1__iff1_0) ).
thf(365,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_PropLog_Opl_Ovar ) )
!= ( B @ ( C @ c_PropLog_Opl_Ovar ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(110,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(479,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)],[110]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(468,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(13,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__iff1_1) ).
thf(234,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)],[13]) ).
thf(192,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(666,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(111,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(481,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)],[111]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( c_PropLog_Opl_Ofalse @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( c_PropLog_Opl_Ofalse @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oimp__false_0) ).
thf(628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( c_PropLog_Opl_Ofalse @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( c_PropLog_Opl_Ofalse @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,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__iff1_0) ).
thf(308,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)],[39]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(188,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_OUnCI_1) ).
thf(655,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)],[188]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(202,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(78,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__iff1_1) ).
thf(404,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)],[78]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(565,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( D @ ( B @ c_union ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__Un1_0) ).
thf(504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( D @ ( B @ c_union ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(157,axiom,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(587,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(61,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__iff1_1) ).
thf(357,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)],[61]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(46,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__iff2_0) ).
thf(325,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)],[46]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(289,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(96,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(448,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(108,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__iff2_0) ).
thf(475,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)],[108]) ).
thf(159,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(591,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(44,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(321,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(113,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_ODiffI_0) ).
thf(485,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)],[113]) ).
thf(125,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(514,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)],[125]) ).
thf(59,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(132,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(529,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)],[132]) ).
thf(70,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(381,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( A @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__right_0) ).
thf(512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( A @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(93,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__iff1_1) ).
thf(439,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)],[93]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(90,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(429,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(21,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(57,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(349,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( C @ ( D @ c_PropLog_Opl_Ovar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__6__iff1_0) ).
thf(630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( C @ ( D @ c_PropLog_Opl_Ovar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(252,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( c_emptyset @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( c_PropLog_Opl_Ofalse @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(197,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( c_emptyset @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( c_PropLog_Opl_Ofalse @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(175,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__iff1_0) ).
thf(625,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)],[175]) ).
thf(48,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__iff1_0) ).
thf(329,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)],[48]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(102,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__iff2_0) ).
thf(461,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)],[102]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_union ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__Un2_0) ).
thf(519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_union ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(42,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(317,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)],[42]) ).
thf(186,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(650,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)],[186]) ).
thf(169,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_ODiffE_0) ).
thf(615,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)],[169]) ).
thf(77,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(403,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(118,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__iff1_0) ).
thf(499,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)],[118]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( c_PropLog_Opl_Ofalse
!= ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__3__iff1_0) ).
thf(554,plain,
! [C: $i,B: $i,A: $i] :
( c_PropLog_Opl_Ofalse
!= ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(135,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(537,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)],[135]) ).
thf(180,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(637,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)],[180]) ).
thf(115,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_OUnCI_0) ).
thf(489,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)],[115]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(212,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(173,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_OinsertCI_0) ).
thf(622,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)],[173]) ).
thf(73,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(393,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(185,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__iff1_0) ).
thf(647,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)],[185]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(178,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_OUnionI_0) ).
thf(633,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)],[178]) ).
thf(4,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__iff1_0) ).
thf(205,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)],[4]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(195,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(674,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)],[195]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(171,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_OInterD_0) ).
thf(618,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)],[171]) ).
thf(88,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(425,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)],[88]) ).
thf(150,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__iff2_0) ).
thf(573,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(163,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_OIntI_0) ).
thf(601,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)],[163]) ).
thf(145,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(562,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(152,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_OIntE_0) ).
thf(577,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)],[152]) ).
thf(138,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(545,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)],[138]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_PropLog_Opl @ ( B @ ( C @ c_PropLog_Othms ) @ ( B @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( B @ tc_PropLog_Opl @ ( B @ ( C @ c_PropLog_Othms ) @ ( B @ ( c_PropLog_Opl_Ofalse @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Ofalse__imp_0) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_PropLog_Opl @ ( B @ ( C @ c_PropLog_Othms ) @ ( B @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( B @ tc_PropLog_Opl @ ( B @ ( C @ c_PropLog_Othms ) @ ( B @ ( c_PropLog_Opl_Ofalse @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(466,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(335,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(58,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__iff1_1) ).
thf(350,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)],[58]) ).
thf(136,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(540,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(604,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(451,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(25,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(162,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( C @ ( E @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Oinject__2__iff1_1) ).
thf(494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( C @ ( E @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(609,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(45,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(323,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(112,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(483,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)],[112]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_PropLog_Opl_Ovar ) )
!= c_PropLog_Opl_Ofalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__2__iff1_0) ).
thf(668,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_PropLog_Opl_Ovar ) )
!= c_PropLog_Opl_Ofalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(55,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(345,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)],[55]) ).
thf(141,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(552,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)],[141]) ).
thf(128,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__iff1_0) ).
thf(521,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)],[128]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(91,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__iff2_0) ).
thf(431,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)],[91]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(394,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(38,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(306,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)],[38]) ).
thf(158,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__iff2_0) ).
thf(589,plain,
! [B: $i,A: $i] :
( c_emptyset
= ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(170,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(617,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(60,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__iff1_0) ).
thf(355,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)],[60]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_PropLog_Opl_Ovar ) )
!= ( B @ ( D @ ( C @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__5__iff1_0) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_PropLog_Opl_Ovar ) )
!= ( B @ ( D @ ( C @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(82,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(414,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)],[82]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(331,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(119,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_ODiffE_1) ).
thf(502,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)],[119]) ).
thf(103,axiom,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(463,plain,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(52,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(338,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(183,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(643,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(71,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(386,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(168,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(612,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)],[168]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(194,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__iff1_0) ).
thf(671,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)],[194]) ).
thf(129,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(524,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(154,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(581,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(126,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(517,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)],[126]) ).
thf(43,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__iff2_0) ).
thf(319,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)],[43]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(652,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(84,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__iff1_0) ).
thf(418,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)],[84]) ).
thf(148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(568,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(69,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(378,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)],[69]) ).
thf(123,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_OUnE_0) ).
thf(510,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)],[123]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= c_PropLog_Opl_Ofalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__4__iff1_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= c_PropLog_Opl_Ofalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(287,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(172,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(41,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__iff1_0) ).
thf(315,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)],[41]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(22,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(67,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__iff2_0) ).
thf(373,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)],[67]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] : ( B @ tc_PropLog_Opl @ ( B @ ( C @ c_PropLog_Othms ) @ ( B @ ( A @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms__I_0) ).
thf(603,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_PropLog_Opl @ ( B @ ( C @ c_PropLog_Othms ) @ ( B @ ( A @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(146,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_OinsertCI_1) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(239,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(191,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(664,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)],[191]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
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_OIntE_1) ).
thf(532,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(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(506,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(174,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(624,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(104,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(464,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(427,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(161,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(596,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(131,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(528,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(184,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_OinsertE_0) ).
thf(644,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)],[184]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(607,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(190,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( C @ ( E @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Oinject__2__iff1_0) ).
thf(659,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( C @ ( E @ ( D @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(137,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(560,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(639,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( c_PropLog_Opl_Ofalse
!= ( B @ ( A @ c_PropLog_Opl_Ovar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__1__iff1_0) ).
thf(676,plain,
! [B: $i,A: $i] :
( c_PropLog_Opl_Ofalse
!= ( B @ ( A @ c_PropLog_Opl_Ovar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
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__iff1_1) ).
thf(491,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(679,plain,
$false,
inference(e,[status(thm)],[340,365,479,347,468,234,666,481,333,628,217,308,449,247,655,202,404,565,257,570,504,587,357,421,284,416,325,289,448,475,591,321,376,485,514,353,280,453,396,265,529,381,220,534,512,439,302,429,275,260,349,407,630,252,197,361,625,329,583,461,519,317,650,615,403,593,420,499,554,537,637,489,547,212,622,393,647,244,633,205,508,657,398,674,412,618,425,573,444,601,562,423,577,545,579,291,641,391,313,466,335,350,540,604,451,434,271,599,477,494,609,323,483,668,345,552,521,455,223,299,226,431,241,394,306,589,487,617,342,355,458,525,557,282,414,327,199,331,502,463,338,470,359,643,585,370,386,446,612,231,363,671,524,581,517,319,304,652,418,568,378,510,549,214,287,620,315,410,262,273,373,603,564,210,239,294,664,635,532,506,268,624,464,575,427,596,528,644,607,254,659,543,560,639,676,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL440-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % 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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.05/25.26 % CPULimit : 300
% 0.05/25.26 % WCLimit : 300
% 0.05/25.26 % DateTime : Fri Sep 25 22:33:34 UTC 2026
% 0.05/25.27 % CPUTime :
% 0.05/25.27 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/25.54 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/25.74 % [INFO] Parsing done (203ms).
% 1.08/25.75 % [INFO] Running in sequential loop mode.
% 1.69/25.94 % [INFO] eprover registered as external prover.
% 1.69/25.94 % [INFO] Scanning for conjecture ...
% 2.00/26.03 % [INFO] Found a conjecture (or negated_conjecture) and 1373 axioms. Running axiom selection ...
% 2.38/26.12 % [INFO] Axiom selection finished. Selected 195 axioms (removed 1178 axioms).
% 2.79/26.21 % [INFO] Problem is propositional (TPTP CNF).
% 2.79/26.22 % [INFO] Type checking passed.
% 2.79/26.22 % [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 ...
% 5.35/26.93 % External prover 'e' found a proof!
% 5.35/26.93 % [INFO] Killing All external provers ...
% 5.35/26.93 % Time passed: 1591ms (effective reasoning time: 1174ms)
% 5.35/26.93 % Axioms used in derivation (195): cls_Equiv__Relations_Oquotient__is__empty__iff1_0, cls_List_Olistrel__Cons1_0, cls_Finite__Set_Ofinite__converse__iff1_0, cls_List_Ofinite__set_0, cls_Finite__Set_Ofinite__Union_0, cls_PropLog_Opl_Odistinct__5__iff1_0, cls_List_Oset__empty2__iff2_0, cls_Datatype__Universe_OuprodI_0, cls_PropLog_Oweaken__left__Un2_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_List_Oappend__in__lists__conv__iff2_0, cls_Datatype__Universe_Odsum__In0I_0, cls_List_Oset__empty2__iff1_0, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_Set_OsubsetI_1, cls_PropLog_Opl_Odistinct__3__iff1_0, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_List_ONil__is__append__conv__iff2_0, cls_Sum__Type_OInr__eq__iff1_0, cls_Set_OemptyE_0, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_PropLog_Opl_Oinject__1__iff1_0, cls_Finite__Set_OFinites_OemptyI_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, cls_Set_OUnionE_1, cls_List_Olistrel__Nil1_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Relation_OconverseE_1, cls_Sum__Type_OPlusE_0, cls_Finite__Set_Ofinite__Int_0, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, cls_Infinite__Set_Onat__not__finite_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_PropLog_Oweaken__right_0, cls_PropLog_Opl_Oinject__2__iff1_1, cls_Relation_ORangeE_0, cls_Set_OInterI_1, cls_List_Oset__empty__iff2_0, cls_Set_OUnCI_1, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Set_OPow__iff__iff2_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_Relation_OdiagI_0, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_PropLog_Opl_Odistinct__1__iff1_0, cls_Set_OsubsetI_0, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_Sum__Type_OPlusE_3, cls_PropLog_Oweaken__left__Un1_0, cls_List_Oself__append__conv__iff2_0, cls_List_Olistrel__Cons2_0, cls_Relation_ODomainI_0, cls_Set_OinsertE_0, cls_Set_OUnE_0, cls_List_Owf__lex_0, cls_Set_OUn__empty__iff1_1, cls_Relation_Orel__compE_2, cls_PropLog_Opl_Oinject__2__iff1_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_List_Oappend__is__Nil__conv__iff2_0, cls_Relation_OIdI_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_List_Oin__listsI_1, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_Datatype_Oelem__o2s__iff1_0, cls_PropLog_Opl_Odistinct__2__iff1_0, cls_Datatype__Universe_OuprodE_2, cls_PropLog_Opl_Odistinct__6__iff1_0, cls_Relation_Oconverse__iff__iff1_0, cls_Relation_OconverseE_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_List_Olist_Oinject__iff1_1, cls_Datatype__Universe_OuprodE_0, cls_Equiv__Relations_Oquotient__is__empty__iff2_0, cls_Set_ODiffE_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Datatype__Universe_OdprodE_2, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Set_OIntI_0, cls_Finite__Set_Ofinite__Union_1, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_Datatype__Universe_OdprodI_0, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, cls_List_Oappend__self__conv__iff2_0, cls_Set_OUn__empty__iff2_0, cls_List_Oappend__same__eq__iff1_0, cls_Equiv__Relations_Oquotient__is__empty2__iff1_0, cls_Set_ODiffI_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OUnionI_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_List_Olistrel__Nil2_0, cls_Relation_Orel__compI_0, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Datatype__Universe_OIn0__eq__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, cls_Relation_OdiagE_1, cls_Relation_OImage__singleton__iff__iff1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_List_Olist_Odistinct__1__iff1_0, cls_List_Olistrel__Cons1_1, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, cls_PropLog_Othms__I_0, cls_Relation_ODomainE_0, cls_List_Oin__listsI_0, cls_PropLog_Ofalse__imp_0, cls_PropLog_Othms_OH_0, cls_Sum__Type_OPlusE_1, cls_PropLog_Oimp__false_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Set_OUnionE_0, cls_List_Oappend1__eq__conv__iff1_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, cls_Sum__Type_OInl__eq__iff1_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, cls_Relation_OImage__singleton__iff__iff2_0, cls_List_Owf__lenlex_0, cls_Relation_OIdE_0, cls_PropLog_Opl_Odistinct__4__iff1_0, cls_Equiv__Relations_Oquotient__is__empty2__iff2_0, cls_Set_OIntE_0, cls_Relation_Orel__compE_1, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0
% 5.35/26.93 % No. of inferences in proof: 393
% 5.35/26.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1591 ms resp. 1174 ms w/o parsing
% 5.88/27.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.88/27.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------