%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET853-1 : 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 08:31:10 AM UTC 2026
% Result : Unsatisfiable 148.82s 64.46s
% Output : Refutation 141.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 309
% Syntax : Number of formulae : 1820 ( 527 unt; 0 typ; 8 def)
% Number of atoms : 4341 (1827 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 20529 (2559 ~;1937 |; 0 &;16033 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 122 ( 119 usr; 17 con; 0-6 aty)
% Number of variables : 3867 ( 0 ^;3851 !; 8 ?;3867 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_Zorn_OTFin_decl,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(v_S_decl,type,
v_S: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(v_xa_decl,type,
v_xa: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Zorn_Osucc_decl,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_decl,type,
c_append: $i > $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $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_Divides_Oop_Advd_decl,type,
c_Divides_Oop_Advd: $i > $i > $i > $o ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_plus_decl,type,
c_plus: $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_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(c_SetInterval_OlessThan_decl,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(tc_Datatype_Ooption_decl,type,
tc_Datatype_Ooption: $i > $i ).
thf(c_SetInterval_OgreaterThan_decl,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OIn1_decl,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odsum_decl,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(c_Datatype__Universe_Odprod_decl,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn0_decl,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $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(tc_sum_decl,type,
tc_sum: $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_UNIV_decl,type,
c_UNIV: $i ).
thf(c_IntDef_Oint_decl,type,
c_IntDef_Oint: $i > $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Main_OImageE__1_decl,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $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_Ooption_OSome_decl,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $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_Datatype__Universe_Ousum_decl,type,
c_Datatype__Universe_Ousum: $i > $i > $i > $i > $i ).
thf(c_Main_OusumE__2_decl,type,
c_Main_OusumE__2: $i > $i > $i > $i > $i ).
thf(c_Main_OusumE__1_decl,type,
c_Main_OusumE__1: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_SetInterval_OgreaterThanAtMost_decl,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_decl,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Zorn_OTFin__linear__lemma1__1_decl,type,
c_Zorn_OTFin__linear__lemma1__1: $i > $i > $i > $i ).
thf(c_Zorn_OUnion__lemma0__1_decl,type,
c_Zorn_OUnion__lemma0__1: $i > $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $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_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Pow_decl,type,
c_Pow: $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_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $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_inter_decl,type,
c_inter: $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_OdprodE__1_decl,type,
c_Main_OdprodE__1: $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_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_OdprodE__2_decl,type,
c_Main_OdprodE__2: $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_Main_Orel__compE__2_decl,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_decl,type,
c_SetInterval_OgreaterThanLessThan: $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(sk1_decl,type,
sk1: $i > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
= B ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_IntDef_Oint @ A )
= B ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
= B ) ) ) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(73,axiom,
tc_bool @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
thf(476,plain,
tc_bool @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
thf(480,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(481,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[480]) ).
thf(39420,plain,
! [A: $i] :
( ( ( tc_bool @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[476,481]) ).
thf(39421,plain,
! [A: $i] :
( ( ( tc_bool @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[39420]) ).
thf(39422,plain,
tc_bool @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[39421:[bind(A,$thf( tc_bool ))]]) ).
thf(39453,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[39422,481]) ).
thf(39454,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[39453]) ).
thf(39455,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[39454:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(39565,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[39455,481]) ).
thf(39566,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[39565]) ).
thf(39567,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[39566:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(39817,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[39567,481]) ).
thf(39818,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[39817]) ).
thf(39819,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[39818:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(40293,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[39819,481]) ).
thf(40294,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[40293]) ).
thf(40295,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[40294:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(40519,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[40295,481]) ).
thf(40520,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[40519]) ).
thf(40521,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[40520:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(41289,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[40521,481]) ).
thf(41290,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[41289]) ).
thf(41291,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[41290:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(41591,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[41291,481]) ).
thf(41592,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[41591]) ).
thf(41593,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[41592:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(42975,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[41593,481]) ).
thf(42976,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[42975]) ).
thf(42977,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[42976:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(43353,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[42977,481]) ).
thf(43354,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[43353]) ).
thf(43355,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[43354:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(53655,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[43355,481]) ).
thf(53656,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[53655]) ).
thf(53657,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[53656:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(55774,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[53657,481]) ).
thf(55775,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[55774]) ).
thf(55776,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[55775:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(27,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(364,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(365,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[364]) ).
thf(366,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(39588,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39455]) ).
thf(39589,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39588:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(204,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(760,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)],[204]) ).
thf(75,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(479,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(244,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(846,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(14,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(331,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)],[14]) ).
thf(332,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(cnf,[status(esa)],[331]) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[332]) ).
thf(69,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
thf(467,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(468,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[467]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[554]) ).
thf(195,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(743,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(199,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(750,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(751,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[750]) ).
thf(2251,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[743,751]) ).
thf(2252,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2251]) ).
thf(2267,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2252]) ).
thf(2280,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ),
inference(simp,[status(thm)],[2267]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(645,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(267,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(892,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)],[267]) ).
thf(29,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(369,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(370,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[369]) ).
thf(371,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[370]) ).
thf(2,negated_conjecture,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(305,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(299,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(956,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(957,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[956]) ).
thf(1544,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[305,957]) ).
thf(1545,plain,
! [B: $i,A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1544]) ).
thf(1548,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set )
!= B )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_emptyset )
| ( v_xa != A ) ),
inference(simp,[status(thm)],[1545]) ).
thf(1551,plain,
( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_emptyset ),
inference(simp,[status(thm)],[1548]) ).
thf(8768,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_emptyset != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,1551]) ).
thf(8769,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8768:[bind(A,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) ))]]) ).
thf(17,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(336,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(337,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[336]) ).
thf(9802,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_0 ) ),
inference(paramod_ordered,[status(thm)],[8769,337]) ).
thf(9803,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9802]) ).
thf(9804,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( c_0 != A )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9803]) ).
thf(9813,plain,
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9804]) ).
thf(9980,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,9813]) ).
thf(9981,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9980]) ).
thf(9982,plain,
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9981:[bind(A,$thf( c_emptyset ))]]) ).
thf(56796,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[55776,481]) ).
thf(56797,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[56796]) ).
thf(56798,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[56797:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
thf(431,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(432,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[431]) ).
thf(433,plain,
! [A: $i] :
( ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[432]) ).
thf(3,negated_conjecture,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(306,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,negated_conjecture,
~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(302,plain,
~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(310,plain,
~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[302]) ).
thf(968,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[306,310]) ).
thf(969,plain,
( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[968]) ).
thf(970,plain,
( ( ( t_a @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_xa ) ),
inference(simp,[status(thm)],[969]) ).
thf(971,plain,
( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_xa ),
inference(simp,[status(thm)],[970]) ).
thf(8796,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,971]) ).
thf(8797,plain,
( ( c_0 != v_xa )
| ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8796:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(133,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(609,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(610,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[609]) ).
thf(14122,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_xa ) ),
inference(paramod_ordered,[status(thm)],[8797,610]) ).
thf(14123,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 != v_xa ) ),
inference(simp,[status(thm)],[14122]) ).
thf(14164,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= A )
| ( c_0 != A )
| ( c_0 != v_xa ) ),
inference(simp,[status(thm)],[14123]) ).
thf(14176,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_0 != v_xa ) ),
inference(simp,[status(thm)],[14164]) ).
thf(25053,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,14176]) ).
thf(25054,plain,
! [A: $i] :
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[25053:[]]) ).
thf(25531,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_IntDef_Oint @ ( v_xa @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[25054]) ).
thf(276,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(910,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(2220,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[910,751]) ).
thf(2221,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2220]) ).
thf(2227,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_UNIV )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[2221]) ).
thf(2231,plain,
c_Finite__Set_OFinites != c_UNIV,
inference(simp,[status(thm)],[2227]) ).
thf(9926,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,2231]) ).
thf(9927,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9926:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(11502,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,9927]) ).
thf(11503,plain,
! [A: $i] :
( ( A != c_UNIV )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[11502]) ).
thf(11504,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[11503:[bind(A,$thf( c_UNIV ))]]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(552,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(553,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[552]) ).
thf(72238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[553,610]) ).
thf(72239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[72238]) ).
thf(72240,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[72239:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(72446,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[72240]) ).
thf(291,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(941,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)],[291]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
thf(352,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,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(329,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[329]) ).
thf(26,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(359,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)],[26]) ).
thf(360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[359]) ).
thf(361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(lifteq,[status(thm)],[360]) ).
thf(362,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( A @ sk2 ) ) )
= B ),
inference(cnf,[status(esa)],[362]) ).
thf(7589,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( A @ sk2 ) ) )
= B ),
inference(lifteq,[status(thm)],[363]) ).
thf(7600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( C @ sk2 ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[330,7589]) ).
thf(7601,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ sk2 ) ) )
= c_List_Olist_ONil ),
inference(pattern_uni,[status(thm)],[7600:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_List_Olist_ONil )),bind(E,$thf( B ))]]) ).
thf(33,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(382,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(166,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(691,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(6858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[691,468]) ).
thf(6859,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[6858]) ).
thf(6877,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= C )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) ) ),
inference(simp,[status(thm)],[6859]) ).
thf(6900,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc )
!= B ),
inference(simp,[status(thm)],[6877]) ).
thf(8178,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) )
| ( ( c_0 @ c_Suc )
!= C )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,6900]) ).
thf(8179,plain,
! [B: $i,A: $i] :
( ( ( c_0 @ c_Suc )
!= B )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8178:[bind(A,$thf( tc_nat @ ( E @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(9451,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[8179]) ).
thf(9470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9451,468]) ).
thf(9471,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9470]) ).
thf(9529,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9471]) ).
thf(9557,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9529]) ).
thf(14533,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,9557]) ).
thf(14534,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14533]) ).
thf(14535,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[14534:[bind(A,$thf( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(14577,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[14535]) ).
thf(20372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,14577]) ).
thf(20373,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[20372]) ).
thf(20413,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[20373]) ).
thf(20440,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[20413]) ).
thf(23418,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,20440]) ).
thf(23419,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23418]) ).
thf(23420,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[23419:[bind(A,$thf( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( G ))]]) ).
thf(25737,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[23420]) ).
thf(163,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(683,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)],[163]) ).
thf(292,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(943,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(2593,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,310]) ).
thf(2594,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2593]) ).
thf(2602,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[2594]) ).
thf(2607,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[2602]) ).
thf(2730,plain,
! [A: $i] :
( ( A
!= ( t_a @ tc_set ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[2607]) ).
thf(2764,plain,
( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[2730]) ).
thf(8917,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_emptyset != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,2764]) ).
thf(8918,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8917:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(15061,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_0 ) ),
inference(paramod_ordered,[status(thm)],[8918,610]) ).
thf(15062,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[15061]) ).
thf(15104,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= A )
| ( c_0 != A )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[15062]) ).
thf(15109,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[15104]) ).
thf(15141,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,15109]) ).
thf(15142,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[15141]) ).
thf(15143,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[15142:[bind(A,$thf( c_emptyset ))]]) ).
thf(194,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(741,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)],[194]) ).
thf(258,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(873,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)],[258]) ).
thf(122,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).
thf(580,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(9,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(318,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(319,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[318]) ).
thf(1266,plain,
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[580,319]) ).
thf(1267,plain,
( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1266]) ).
thf(1268,plain,
( ( tc_nat != tc_nat )
| ( ( c_0 @ c_Suc )
!= c_0 )
| ( c_0 != c_0 ) ),
inference(simp,[status(thm)],[1267]) ).
thf(1269,plain,
( ( c_0 @ c_Suc )
!= c_0 ),
inference(simp,[status(thm)],[1268]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
thf(597,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(176,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(709,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(4292,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[709,751]) ).
thf(4293,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4292]) ).
thf(4320,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4293]) ).
thf(4322,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4320]) ).
thf(4747,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4322]) ).
thf(56,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
thf(434,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(435,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[434]) ).
thf(436,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[435]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[320]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[321]) ).
thf(7228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) ) )
| ( ( c_List_Olist_ONil @ c_Suc )
!= D )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,6900]) ).
thf(7229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ c_Suc )
!= C )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7228:[bind(A,$thf( tc_nat @ ( F @ ( E @ c_plus ) ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(7244,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[7229]) ).
thf(15333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7244,610]) ).
thf(15334,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[15333]) ).
thf(15395,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) )
!= C )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[15334]) ).
thf(15417,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[15395]) ).
thf(15496,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,15417]) ).
thf(15497,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15496]) ).
thf(15498,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[15497:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( F @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( F ))]]) ).
thf(15543,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[15498]) ).
thf(22217,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,15543]) ).
thf(22218,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[22217]) ).
thf(22263,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[22218]) ).
thf(22316,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[22263]) ).
thf(27132,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,22316]) ).
thf(27133,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[27132]) ).
thf(27134,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[27133:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( F @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( F )),bind(C,$thf( J ))]]) ).
thf(29289,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[27134]) ).
thf(97,axiom,
tc_nat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(523,plain,
tc_nat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(205,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(762,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)],[205]) ).
thf(115,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(558,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1709,plain,
! [B: $i,A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,558]) ).
thf(1710,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_Product__Type_Ounit @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1709:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(1924,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_Product__Type_Ounit @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1710]) ).
thf(83,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
thf(491,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(492,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[491]) ).
thf(7728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[691,492]) ).
thf(7729,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[7728]) ).
thf(7741,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) ) ),
inference(simp,[status(thm)],[7729]) ).
thf(7786,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc )
!= A ),
inference(simp,[status(thm)],[7741]) ).
thf(13826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) ) )
| ( ( c_List_Olist_ONil @ c_Suc )
!= C )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,7786]) ).
thf(13827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ c_Suc )
!= B )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[13826:[bind(A,$thf( tc_nat @ ( F @ ( E @ c_plus ) ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(13834,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[13827]) ).
thf(187,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(730,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)],[187]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( A @ c_lessequals ) ) )
| ( A = v_x )
| ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(304,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( A @ c_lessequals ) ) )
| ( A = v_x )
| ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(311,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( A @ c_lessequals ) ) )
| ( A = v_x )
| ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[304]) ).
thf(312,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( A = v_x ) ),
inference(lifteq,[status(thm)],[311]) ).
thf(1131,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( A = v_x ) ),
inference(paramod_ordered,[status(thm)],[305,312]) ).
thf(1132,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( A = v_x ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1133,plain,
( ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( v_xa @ c_lessequals ) ) )
| ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( v_xa = v_x ) ),
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( v_xa ))]]) ).
thf(1478,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( v_xa @ c_lessequals ) ) )
| ( v_xa = v_x ) ),
inference(paramod_ordered,[status(thm)],[1133,310]) ).
thf(1479,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( v_xa @ c_lessequals ) ) )
| ( v_xa = v_x ) ),
inference(simp,[status(thm)],[1478]) ).
thf(1488,plain,
( ( ( t_a @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( v_xa @ c_lessequals ) ) )
| ( v_xa = v_x ) ),
inference(simp,[status(thm)],[1479]) ).
thf(1493,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( v_xa @ c_lessequals ) ) )
| ( v_xa = v_x ) ),
inference(simp,[status(thm)],[1488]) ).
thf(3702,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( v_xa @ c_lessequals ) ) ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ~ $true
| ( v_xa = v_x ) ),
inference(paramod_ordered,[status(thm)],[306,1493]) ).
thf(3703,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( v_xa @ c_lessequals ) ) ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ( v_xa = v_x ) ),
inference(simp,[status(thm)],[3702]) ).
thf(3763,plain,
( ( ( t_a @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ( v_xa != v_xa )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ( v_xa = v_x ) ),
inference(simp,[status(thm)],[3703]) ).
thf(3772,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ( v_xa = v_x ) ),
inference(simp,[status(thm)],[3763]) ).
thf(256,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(870,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(3803,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[870,310]) ).
thf(3804,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[3803]) ).
thf(3811,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) ) ),
inference(simp,[status(thm)],[3804]) ).
thf(3816,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) ) ),
inference(simp,[status(thm)],[3811]) ).
thf(3949,plain,
! [A: $i] :
( ( A
!= ( t_a @ tc_set ) )
| ( t_a != t_a )
| ( v_xa != v_x )
| ( v_S != v_S ) ),
inference(simp,[status(thm)],[3816]) ).
thf(4002,plain,
v_xa != v_x,
inference(simp,[status(thm)],[3949]) ).
thf(4075,plain,
( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x ),
inference(simplifyReflect,[status(thm)],[3772,4002]) ).
thf(28503,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,2764]) ).
thf(28504,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[28503:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(11537,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,9927]) ).
thf(11538,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[11537]) ).
thf(11560,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[11538]) ).
thf(11571,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[11560]) ).
thf(3544,plain,
! [B: $i,A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_emptyset != c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2764]) ).
thf(3545,plain,
! [A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3544:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )),bind(B,$thf( B ))]]) ).
thf(3549,plain,
! [A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[3545]) ).
thf(1747,plain,
! [B: $i,A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_emptyset != c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1551]) ).
thf(1748,plain,
! [A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1747:[bind(A,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) )),bind(B,$thf( B ))]]) ).
thf(1939,plain,
! [A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1748]) ).
thf(59,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(440,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)],[59]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[509]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) ) ),
inference(lifteq,[status(thm)],[510]) ).
thf(28304,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,971]) ).
thf(28305,plain,
( ( c_0 != v_xa )
| ~ ( tc_nat @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[28304:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(39425,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[558,481]) ).
thf(39426,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[39425]) ).
thf(39427,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[39426:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(39508,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[39427,481]) ).
thf(39509,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[39508]) ).
thf(39510,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[39509:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(160,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(677,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)],[160]) ).
thf(441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[440]) ).
thf(442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(lifteq,[status(thm)],[441]) ).
thf(443,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[442]) ).
thf(444,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( B @ sk4 ) ) )
= A ),
inference(cnf,[status(esa)],[443]) ).
thf(30375,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( B @ sk4 ) ) )
= A ),
inference(lifteq,[status(thm)],[444]) ).
thf(43,axiom,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(406,plain,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(99,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(527,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)],[99]) ).
thf(64874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[527,957]) ).
thf(64875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[64874]) ).
thf(64956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ tc_prod ) )
!= D )
| ( c_Relation_OId != c_emptyset )
| ( ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) )
!= C ) ),
inference(simp,[status(thm)],[64875]) ).
thf(64988,plain,
c_Relation_OId != c_emptyset,
inference(simp,[status(thm)],[64956]) ).
thf(65013,plain,
! [A: $i] :
( ( A != c_Relation_OId )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,64988]) ).
thf(65014,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_Relation_OId @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[65013:[bind(A,$thf( c_Relation_OId ))]]) ).
thf(65599,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_nat @ ( c_Relation_OId @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,65014]) ).
thf(65600,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_nat @ ( c_Relation_OId @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[65599]) ).
thf(65648,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_Relation_OId != c_0 )
| ( A != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[65600]) ).
thf(65670,plain,
( ( c_Relation_OId != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[65648]) ).
thf(65691,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,65670]) ).
thf(65692,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[65691]) ).
thf(65693,plain,
( ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[65692:[bind(A,$thf( c_emptyset ))]]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(102,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(532,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)],[102]) ).
thf(533,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(cnf,[status(esa)],[532]) ).
thf(2560,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[691,610]) ).
thf(2561,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2560]) ).
thf(2570,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[2561]) ).
thf(2575,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(simp,[status(thm)],[2570]) ).
thf(2582,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ c_Suc ) )
| ( c_List_Olist_ONil != C )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2575]) ).
thf(2583,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil != B )
| ( tc_nat @ ( A @ tc_List_Olist @ ( B @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[2582:[bind(A,$thf( D @ c_Suc )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2585,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[2583]) ).
thf(7706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2585,492]) ).
thf(7707,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[7706]) ).
thf(7742,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[7707]) ).
thf(7787,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[7742]) ).
thf(28709,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,7787]) ).
thf(28710,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28709]) ).
thf(28711,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[28710:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( E ))]]) ).
thf(29059,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[28711]) ).
thf(86,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(498,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)],[86]) ).
thf(499,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[498]) ).
thf(500,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[499]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( A @ ( C @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
thf(814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( A @ ( C @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(278,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(913,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)],[278]) ).
thf(19,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(340,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)],[19]) ).
thf(105,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(537,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)],[105]) ).
thf(538,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(cnf,[status(esa)],[537]) ).
thf(110,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(548,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)],[110]) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(polarity_switch,[status(thm)],[548]) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(lifteq,[status(thm)],[549]) ).
thf(11,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(323,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(46,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(413,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)],[46]) ).
thf(414,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(cnf,[status(esa)],[413]) ).
thf(19167,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[323,414]) ).
thf(19168,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[19167]) ).
thf(19169,plain,
tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ),
inference(pattern_uni,[status(thm)],[19168:[bind(A,$thf( c_Wellfounded__Relations_Oless__than )),bind(B,$thf( tc_nat ))]]) ).
thf(19234,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,414]) ).
thf(19235,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[19234]) ).
thf(19236,plain,
tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ),
inference(pattern_uni,[status(thm)],[19235:[bind(A,$thf( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) )),bind(B,$thf( tc_nat @ tc_List_Olist ))]]) ).
thf(88,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(503,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)],[88]) ).
thf(504,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(cnf,[status(esa)],[503]) ).
thf(74205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( F @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[504,72446]) ).
thf(74206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( F @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[74205]) ).
thf(74207,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[74206:[bind(A,$thf( A )),bind(B,$thf( c_Wellfounded__Relations_Oless__than )),bind(C,$thf( A )),bind(D,$thf( tc_nat )),bind(E,$thf( tc_nat )),bind(F,$thf( A ))]]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(567,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(cnf,[status(esa)],[566]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(lifteq,[status(thm)],[567]) ).
thf(569,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ),
inference(detectInverse,[status(thm)],[568]) ).
thf(570,plain,
! [A: $i] :
( ( A @ c_Suc @ sk7 )
= A ),
inference(cnf,[status(esa)],[569]) ).
thf(2434,plain,
! [A: $i] :
( ( A @ c_Suc @ sk7 )
= A ),
inference(lifteq,[status(thm)],[570]) ).
thf(4,negated_conjecture,
( v_xa
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(307,plain,
( v_xa
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(308,plain,
( v_xa
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) ),
inference(polarity_switch,[status(thm)],[307]) ).
thf(309,plain,
( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_xa ),
inference(lifteq,[status(thm)],[308]) ).
thf(1835,plain,
! [B: $i,A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_List_Olist_ONil != v_xa )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,309]) ).
thf(1836,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_xa )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1835:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )),bind(B,$thf( B ))]]) ).
thf(1872,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_xa )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(71,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(472,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)],[71]) ).
thf(26812,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,9813]) ).
thf(26813,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[26812]) ).
thf(26814,plain,
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[26813:[bind(A,$thf( c_emptyset ))]]) ).
thf(236,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(829,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)],[236]) ).
thf(23143,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_x )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,4075]) ).
thf(23144,plain,
( ( c_0 != v_x )
| ~ ( tc_IntDef_Oint @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23143:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(9088,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,309]) ).
thf(9089,plain,
( ( c_0 != v_xa )
| ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9088:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(15820,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_xa ) ),
inference(paramod_ordered,[status(thm)],[9089,610]) ).
thf(15821,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 != v_xa ) ),
inference(simp,[status(thm)],[15820]) ).
thf(15862,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= A )
| ( c_0 != A )
| ( c_0 != v_xa ) ),
inference(simp,[status(thm)],[15821]) ).
thf(15876,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_0 != v_xa ) ),
inference(simp,[status(thm)],[15862]) ).
thf(15907,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,15876]) ).
thf(15908,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[15907:[]]) ).
thf(15931,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( tc_nat @ ( v_xa @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[15908]) ).
thf(82,axiom,
tc_IntDef_Oint @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(490,plain,
tc_IntDef_Oint @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1737,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,490]) ).
thf(1738,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1737:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1935,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1738]) ).
thf(77,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(482,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(7716,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[482,492]) ).
thf(7717,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[7716]) ).
thf(7745,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[7717]) ).
thf(7761,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[7745]) ).
thf(297,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(953,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(462,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(cnf,[status(esa)],[462]) ).
thf(34668,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[953,463]) ).
thf(34669,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[34668]) ).
thf(34670,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[34669:[bind(A,$thf( D )),bind(B,$thf( D @ tc_set ))]]) ).
thf(34857,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[34670]) ).
thf(48,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(417,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
thf(474,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[474]) ).
thf(38103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[417,475]) ).
thf(38104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[38103]) ).
thf(38105,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[38104:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_0 ))]]) ).
thf(38363,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38105,475]) ).
thf(38364,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[38363]) ).
thf(38365,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[38364:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( tc_IntDef_Oint @ ( c_0 @ c_uminus ) ))]]) ).
thf(38447,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ~ $true
| ( B = c_0 ) ),
inference(paramod_ordered,[status(thm)],[38105,433]) ).
thf(38448,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ( B = c_0 ) ),
inference(simp,[status(thm)],[38447]) ).
thf(38449,plain,
( ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) )
= c_0 ),
inference(pattern_uni,[status(thm)],[38448:[bind(A,$thf( c_0 )),bind(B,$thf( tc_IntDef_Oint @ ( c_0 @ c_uminus ) ))]]) ).
thf(38648,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(rewrite,[status(thm)],[38365,38449]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( B @ ( D @ ( C @ c_Union ) @ c_lessequals ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Union ) @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_OUnion__lemma0__1 ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
thf(898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( B @ ( D @ ( C @ c_Union ) @ c_lessequals ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Union ) @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_OUnion__lemma0__1 ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(242,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(841,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)],[242]) ).
thf(190,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(735,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(4647,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[735,751]) ).
thf(4648,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4647]) ).
thf(4673,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4648]) ).
thf(4679,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4673]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( A @ ( D @ ( C @ c_Union ) @ c_lessequals ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Union ) @ ( B @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Zorn_OUnion__lemma0__1 ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
thf(724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( A @ ( D @ ( C @ c_Union ) @ c_lessequals ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Union ) @ ( B @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Zorn_OUnion__lemma0__1 ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(10088,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ~ ( tc_nat @ tc_set @ ( c_0 @ ( c_UNIV @ c_in ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,751]) ).
thf(10089,plain,
( ~ ( tc_nat @ tc_set @ ( c_0 @ ( c_UNIV @ c_in ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10088:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(17806,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13834,337]) ).
thf(17807,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[17806]) ).
thf(17810,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[17807]) ).
thf(17824,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[17810]) ).
thf(30,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(372,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)],[30]) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,479]) ).
thf(1664,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( tc_nat ))]]) ).
thf(1907,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1664]) ).
thf(139,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(619,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)],[139]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(39639,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[39510,481]) ).
thf(39640,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[39639]) ).
thf(39641,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[39640:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(40198,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[39641,481]) ).
thf(40199,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[40198]) ).
thf(40200,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[40199:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(40405,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[40200,481]) ).
thf(40406,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[40405]) ).
thf(40407,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[40406:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(41156,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[40407,481]) ).
thf(41157,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[41156]) ).
thf(41158,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[41157:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(41439,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[41158,481]) ).
thf(41440,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[41439]) ).
thf(41441,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[41440:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(42804,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[41441,481]) ).
thf(42805,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[42804]) ).
thf(42806,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[42805:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(43163,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[42806,481]) ).
thf(43164,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[43163]) ).
thf(43165,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[43164:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(23285,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,9813]) ).
thf(23286,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23285]) ).
thf(23287,plain,
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23286:[bind(A,$thf( c_emptyset ))]]) ).
thf(295,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(949,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)],[295]) ).
thf(147,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(642,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(643,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[642]) ).
thf(2624,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2585,643]) ).
thf(2625,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2624]) ).
thf(2644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= c_emptyset )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[2625]) ).
thf(2654,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[2644]) ).
thf(36,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(387,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)],[36]) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(cnf,[status(esa)],[387]) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(lifteq,[status(thm)],[388]) ).
thf(280,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(917,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)],[280]) ).
thf(107,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(542,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
thf(460,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(272,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(902,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)],[272]) ).
thf(116,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(559,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)],[116]) ).
thf(248,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(853,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)],[248]) ).
thf(7230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_Suc ) )
| ( c_List_Olist_ONil != D )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,6900]) ).
thf(7231,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil != C )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7230:[bind(A,$thf( tc_nat @ ( G @ ( F @ c_plus ) ) @ c_Suc )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G ))]]) ).
thf(7245,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[7231]) ).
thf(16344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7245,337]) ).
thf(16345,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[16344]) ).
thf(16351,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[16345]) ).
thf(16393,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[16351]) ).
thf(16454,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,16393]) ).
thf(16455,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16454]) ).
thf(16456,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[16455:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( G @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(16495,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[16456]) ).
thf(209,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(770,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)],[209]) ).
thf(266,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(891,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(2183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[891,957]) ).
thf(2184,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2193,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= C )
| ( c_Finite__Set_OFinites != c_emptyset )
| ( c_emptyset != B ) ),
inference(simp,[status(thm)],[2184]) ).
thf(2197,plain,
c_Finite__Set_OFinites != c_emptyset,
inference(simp,[status(thm)],[2193]) ).
thf(10503,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,2197]) ).
thf(10504,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10503:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(12765,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,10504]) ).
thf(12766,plain,
! [A: $i] :
( ( A != c_emptyset )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[12765]) ).
thf(12767,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[12766:[bind(A,$thf( c_emptyset ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(316,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4432,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != v_xa ) ),
inference(paramod_ordered,[status(thm)],[1872,610]) ).
thf(4433,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4432]) ).
thf(4454,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= B )
| ( c_0 != B )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4433]) ).
thf(4471,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4454]) ).
thf(14238,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,7787]) ).
thf(14239,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[14238]) ).
thf(14240,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[14239:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( E ))]]) ).
thf(14316,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[14240]) ).
thf(39844,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39567]) ).
thf(39845,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39844:[bind(A,$thf( tc_bool ))]]) ).
thf(50,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(421,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
thf(881,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).
thf(415,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[415]) ).
thf(6848,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[482,468]) ).
thf(6849,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[6848]) ).
thf(6879,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[6849]) ).
thf(6903,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[6879]) ).
thf(10764,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,6903]) ).
thf(10765,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10764]) ).
thf(10766,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[10765:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(11139,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[10766]) ).
thf(174,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(706,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(4214,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[706,751]) ).
thf(4215,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4214]) ).
thf(4240,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4215]) ).
thf(4253,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[4240]) ).
thf(202,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(756,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)],[202]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
thf(789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(150,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(647,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(74246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,72446]) ).
thf(74247,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[74246]) ).
thf(74389,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[74247]) ).
thf(74400,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than ),
inference(simp,[status(thm)],[74389]) ).
thf(3948,plain,
! [A: $i] :
( ( A
!= ( t_a @ tc_set ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) ) ),
inference(simp,[status(thm)],[3816]) ).
thf(4001,plain,
( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) ),
inference(simp,[status(thm)],[3948]) ).
thf(141,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(623,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)],[141]) ).
thf(79,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(485,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)],[79]) ).
thf(10084,plain,
! [A: $i] :
( ( A
!= ( tc_nat @ tc_set ) )
| ~ ( c_0 @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,751]) ).
thf(10085,plain,
( ~ ( c_0 @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
| ~ ( tc_nat @ ( c_0 @ ( tc_nat @ tc_set @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10084:[bind(A,$thf( tc_nat @ tc_set ))]]) ).
thf(106,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(539,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(540,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[539]) ).
thf(541,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[540]) ).
thf(10334,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,541]) ).
thf(10335,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10334:[bind(A,$thf( c_UNIV ))]]) ).
thf(12207,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,10335]) ).
thf(12208,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[12207]) ).
thf(12232,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[12208]) ).
thf(12237,plain,
( ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[12232]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(514,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(21,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(346,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)],[21]) ).
thf(347,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[346]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( A @ ( B @ c_append ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[347]) ).
thf(963,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[305,751]) ).
thf(964,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_xa @ c_in ) ) ) ),
inference(simp,[status(thm)],[963]) ).
thf(966,plain,
( ( ( t_a @ tc_set @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_Finite__Set_OFinites )
| ( c_UNIV != v_xa ) ),
inference(simp,[status(thm)],[964]) ).
thf(8141,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_x )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,4075]) ).
thf(8142,plain,
( ( c_0 != v_x )
| ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8141:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(13483,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_x ) ),
inference(paramod_ordered,[status(thm)],[8142,610]) ).
thf(13484,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 != v_x ) ),
inference(simp,[status(thm)],[13483]) ).
thf(13522,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= A )
| ( c_0 != A )
| ( c_0 != v_x ) ),
inference(simp,[status(thm)],[13484]) ).
thf(13533,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_0 != v_x ) ),
inference(simp,[status(thm)],[13522]) ).
thf(25061,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,16393]) ).
thf(25062,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[25061]) ).
thf(25063,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[25062:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( G @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(25535,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[25063]) ).
thf(23288,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,9813]) ).
thf(23289,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23288]) ).
thf(23290,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23289:[bind(A,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) ))]]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
thf(924,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(10949,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,309]) ).
thf(10950,plain,
( ( c_0 != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10949:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(6840,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2585,468]) ).
thf(6841,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[6840]) ).
thf(6875,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[6841]) ).
thf(6897,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[6875]) ).
thf(8417,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,6897]) ).
thf(8418,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8417]) ).
thf(8419,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[8418:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( D ))]]) ).
thf(9190,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[8419]) ).
thf(16923,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9190,337]) ).
thf(16924,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[16923]) ).
thf(16926,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[16924]) ).
thf(16944,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[16926]) ).
thf(126,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(591,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)],[126]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(53386,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[43165,481]) ).
thf(53387,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[53386]) ).
thf(53388,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[53387:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(53947,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[53388,481]) ).
thf(53948,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[53947]) ).
thf(53949,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[53948:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(56477,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[53949,481]) ).
thf(56478,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[56477]) ).
thf(56479,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[56478:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(57138,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[56479,481]) ).
thf(57139,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[57138]) ).
thf(57140,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[57139:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ ( D @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ ( D @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(13828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_Suc ) )
| ( c_List_Olist_ONil != C )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,7786]) ).
thf(13829,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil != B )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[13828:[bind(A,$thf( tc_nat @ ( G @ ( F @ c_plus ) ) @ c_Suc )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G ))]]) ).
thf(13836,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[13829]) ).
thf(18046,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13836,610]) ).
thf(18047,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[18046]) ).
thf(18111,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= C )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[18047]) ).
thf(18142,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[18111]) ).
thf(25201,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,18142]) ).
thf(25202,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[25201]) ).
thf(25203,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[25202:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( H @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( H ))]]) ).
thf(25603,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[25203]) ).
thf(72396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[553,337]) ).
thf(72397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[72396]) ).
thf(72398,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[72397:[bind(A,$thf( A )),bind(B,$thf( c_0 )),bind(C,$thf( A ))]]) ).
thf(72559,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[504,72398]) ).
thf(72560,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[72559]) ).
thf(72561,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[72560:[bind(A,$thf( c_0 )),bind(B,$thf( c_Wellfounded__Relations_Oless__than )),bind(C,$thf( C )),bind(D,$thf( tc_nat )),bind(E,$thf( tc_nat )),bind(F,$thf( C ))]]) ).
thf(72796,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ),
inference(simp,[status(thm)],[72561]) ).
thf(73230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[910,72796]) ).
thf(73231,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[73230]) ).
thf(73386,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= c_UNIV )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[73231]) ).
thf(73471,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[73386]) ).
thf(167,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(692,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)],[167]) ).
thf(64,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(453,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)],[64]) ).
thf(39,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(396,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)],[39]) ).
thf(18547,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14316,610]) ).
thf(18548,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[18547]) ).
thf(18613,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )
!= C )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[18548]) ).
thf(18639,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[18613]) ).
thf(155,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(660,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)],[155]) ).
thf(40223,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39641]) ).
thf(40224,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[40223:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
thf(428,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(89,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(505,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)],[89]) ).
thf(506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(polarity_switch,[status(thm)],[505]) ).
thf(507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(lifteq,[status(thm)],[506]) ).
thf(8741,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,490]) ).
thf(8742,plain,
( ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8741:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(246,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(850,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(2354,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[850,751]) ).
thf(2355,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2354]) ).
thf(2368,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2355]) ).
thf(2371,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ),
inference(simp,[status(thm)],[2368]) ).
thf(8924,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,6903]) ).
thf(8925,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8924]) ).
thf(8926,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[8925:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(9354,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[8926]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
thf(425,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(426,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[425]) ).
thf(21122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9354,426]) ).
thf(21123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[21122]) ).
thf(21124,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[21123:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( H @ c_Suc @ ( E @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(21238,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[21124]) ).
thf(72047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21238,337]) ).
thf(72048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) ),
inference(simp,[status(thm)],[72047]) ).
thf(72056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
!= c_0 )
| ( c_0 != D ) ),
inference(simp,[status(thm)],[72048]) ).
thf(72138,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[72056]) ).
thf(2622,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2585,610]) ).
thf(2623,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2622]) ).
thf(2642,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= B )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[2623]) ).
thf(2651,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[2642]) ).
thf(25243,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,2651]) ).
thf(25244,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[25243]) ).
thf(25245,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[25244:[bind(A,$thf( F @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( F ))]]) ).
thf(25623,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[25245]) ).
thf(26950,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,20440]) ).
thf(26951,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[26950]) ).
thf(26952,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[26951:[bind(A,$thf( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( G ))]]) ).
thf(29226,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[26952]) ).
thf(20826,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(paramod_ordered,[status(thm)],[15143,643]) ).
thf(20827,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[20826]) ).
thf(20855,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != c_emptyset )
| ( c_0 != A )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[20827]) ).
thf(20871,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[20855]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
thf(451,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(cnf,[status(esa)],[451]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
thf(920,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(32,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(380,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)],[32]) ).
thf(109,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(546,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)],[109]) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_HOL_Ominus )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,542]) ).
thf(1681,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_HOL_Ominus )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1680:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1915,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_HOL_Ominus )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1681]) ).
thf(103,axiom,
tc_IntDef_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(534,plain,
tc_IntDef_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(317,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[316]) ).
thf(2103,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(paramod_ordered,[status(thm)],[1939,337]) ).
thf(2104,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2103]) ).
thf(2105,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != B )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2104]) ).
thf(2119,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2105]) ).
thf(2137,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(paramod_ordered,[status(thm)],[317,2119]) ).
thf(2138,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Nat_Osize ) ) )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2137]) ).
thf(2150,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist )
!= ( B @ tc_List_Olist ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2138]) ).
thf(2281,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2150]) ).
thf(2311,plain,
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2281]) ).
thf(2417,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil )
| ( c_List_Olist_ONil != c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2311]) ).
thf(2418,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[2417]) ).
thf(2419,plain,
! [A: $i] :
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[2418:[bind(A,$thf( c_emptyset ))]]) ).
thf(2425,plain,
! [A: $i] :
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[2419]) ).
thf(2482,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ~ $true
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil ) ),
inference(paramod_ordered,[status(thm)],[2425,337]) ).
thf(2483,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2482]) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != B )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2483]) ).
thf(2496,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) )
!= c_0 )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2484]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
thf(714,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(9472,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9451,492]) ).
thf(9473,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9472]) ).
thf(9533,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9473]) ).
thf(9563,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9533]) ).
thf(24586,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,9563]) ).
thf(24587,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[24586]) ).
thf(24588,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[24587:[bind(A,$thf( tc_nat @ ( E @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(25448,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[24588]) ).
thf(221,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(798,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)],[221]) ).
thf(92,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(512,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)],[92]) ).
thf(58,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(439,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(65019,plain,
! [A: $i] :
( ( A != c_Relation_OId )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,64988]) ).
thf(65020,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Relation_OId @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[65019:[bind(A,$thf( c_Relation_OId ))]]) ).
thf(100,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(528,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)],[100]) ).
thf(529,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(cnf,[status(esa)],[528]) ).
thf(8396,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,534]) ).
thf(8397,plain,
( ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8396:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(cnf,[status(esa)],[380]) ).
thf(39525,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39427]) ).
thf(39526,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39525:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(15,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).
thf(334,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8251,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,7761]) ).
thf(8252,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8251]) ).
thf(8253,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[8252:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(9134,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[8253]) ).
thf(12465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9134,492]) ).
thf(12466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[12465]) ).
thf(12519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[12466]) ).
thf(12542,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[12519]) ).
thf(22,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(349,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)],[22]) ).
thf(232,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(820,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)],[232]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(51,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(423,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[423]) ).
thf(39660,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39510]) ).
thf(39661,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39660:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(72607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,72398]) ).
thf(72608,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[72607]) ).
thf(72753,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[72608]) ).
thf(72779,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than ),
inference(simp,[status(thm)],[72753]) ).
thf(353,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(polarity_switch,[status(thm)],[352]) ).
thf(354,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(lifteq,[status(thm)],[353]) ).
thf(29003,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,354]) ).
thf(29004,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[29003]) ).
thf(29005,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[29004:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).
thf(29230,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[29005]) ).
thf(268,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(894,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)],[268]) ).
thf(6486,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(paramod_ordered,[status(thm)],[3549,610]) ).
thf(6487,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[6486]) ).
thf(6523,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= B )
| ( c_0 != B )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[6487]) ).
thf(6550,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[6523]) ).
thf(213,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(778,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)],[213]) ).
thf(40225,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39641]) ).
thf(40226,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[40225:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(cnf,[status(esa)],[390]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[391]) ).
thf(44,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(407,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)],[44]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
thf(630,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(cnf,[status(esa)],[561]) ).
thf(563,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(lifteq,[status(thm)],[562]) ).
thf(564,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_IntDef_Oint @ A )
= B ),
inference(detectInverse,[status(thm)],[563]) ).
thf(565,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ sk6 )
= A ),
inference(cnf,[status(esa)],[564]) ).
thf(2396,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ sk6 )
= A ),
inference(lifteq,[status(thm)],[565]) ).
thf(57482,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[56798,481]) ).
thf(57483,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[57482]) ).
thf(57484,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[57483:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(67926,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[57484,481]) ).
thf(67927,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[67926]) ).
thf(67928,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[67927:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(65675,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,65670]) ).
thf(65676,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[65675]) ).
thf(65677,plain,
( ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[65676:[bind(A,$thf( c_emptyset ))]]) ).
thf(72601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[910,72398]) ).
thf(72602,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[72601]) ).
thf(72762,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( c_UNIV != c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[72602]) ).
thf(72780,plain,
c_UNIV != c_Wellfounded__Relations_Oless__than,
inference(simp,[status(thm)],[72762]) ).
thf(72856,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,72780]) ).
thf(72857,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[72856:[bind(A,$thf( c_UNIV ))]]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( A @ ( D @ ( C @ c_Union ) @ c_lessequals ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Union ) @ ( B @ c_lessequals ) ) )
| ( D @ tc_set @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Zorn_OUnion__lemma0__1 ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
thf(879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( A @ ( D @ ( C @ c_Union ) @ c_lessequals ) ) )
| ( D @ tc_set @ ( D @ ( C @ c_Union ) @ ( B @ c_lessequals ) ) )
| ( D @ tc_set @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Zorn_OUnion__lemma0__1 ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(265,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(889,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)],[265]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[460]) ).
thf(84,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(493,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)],[84]) ).
thf(28838,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,2651]) ).
thf(28839,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28838]) ).
thf(28840,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[28839:[bind(A,$thf( F @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( F ))]]) ).
thf(29141,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[28840]) ).
thf(1401,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,310]) ).
thf(1402,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1401]) ).
thf(1403,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set )
!= tc_nat )
| ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[1402]) ).
thf(1407,plain,
( ( ( t_a @ tc_set @ tc_set )
!= tc_nat )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[1403]) ).
thf(111,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(551,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(23351,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,7761]) ).
thf(23352,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23351]) ).
thf(23353,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[23352:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(25709,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[23353]) ).
thf(177,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(710,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)],[177]) ).
thf(27202,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,13533]) ).
thf(27203,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[27202:[]]) ).
thf(29298,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( v_x @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[27203]) ).
thf(80,axiom,
tc_IntDef_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(487,plain,
tc_IntDef_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1745,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_Orderings_Olinorder )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,487]) ).
thf(1746,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1745:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1938,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1746]) ).
thf(245,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(847,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)],[245]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
thf(483,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(cnf,[status(esa)],[483]) ).
thf(156,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(665,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(16,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(335,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(19164,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[335,414]) ).
thf(19165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[19164]) ).
thf(19166,plain,
! [A: $i] : ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ),
inference(pattern_uni,[status(thm)],[19165:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(19434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19166,414]) ).
thf(19435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[19434]) ).
thf(19436,plain,
! [A: $i] : ( A @ tc_List_Olist @ tc_List_Olist @ ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ),
inference(pattern_uni,[status(thm)],[19435:[bind(A,$thf( F )),bind(B,$thf( F @ ( c_emptyset @ c_List_Olex ) )),bind(C,$thf( F @ tc_List_Olist ))]]) ).
thf(19454,plain,
! [A: $i] : ( A @ tc_List_Olist @ tc_List_Olist @ ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ),
inference(simp,[status(thm)],[19436]) ).
thf(124,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(583,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)],[124]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[520]) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) ) ),
inference(lifteq,[status(thm)],[521]) ).
thf(12,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(324,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)],[12]) ).
thf(72850,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,72780]) ).
thf(72851,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[72850:[bind(A,$thf( c_UNIV ))]]) ).
thf(76342,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,72851]) ).
thf(76343,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[76342]) ).
thf(76390,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_UNIV != c_0 )
| ( A != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[76343]) ).
thf(76410,plain,
( ( c_UNIV != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[76390]) ).
thf(8296,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,542]) ).
thf(8297,plain,
( ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8296:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(136,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(615,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)],[136]) ).
thf(65027,plain,
! [A: $i] :
( ( A != c_Relation_OId )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,64988]) ).
thf(65028,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_Relation_OId @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[65027:[bind(A,$thf( c_Relation_OId ))]]) ).
thf(127,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(593,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)],[127]) ).
thf(28796,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,18142]) ).
thf(28797,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28796]) ).
thf(28798,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[28797:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( H @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( H ))]]) ).
thf(29113,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[28798]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[401]) ).
thf(16117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9134,402]) ).
thf(16118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[16117]) ).
thf(16119,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[16118:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( F @ ( H @ c_Suc @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(16218,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[16119]) ).
thf(71602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16218,337]) ).
thf(71603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) ),
inference(simp,[status(thm)],[71602]) ).
thf(71604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != D ) ),
inference(simp,[status(thm)],[71603]) ).
thf(71660,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[71604]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
thf(578,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(8693,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,323]) ).
thf(8694,plain,
( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8693:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(95,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(517,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)],[95]) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(polarity_switch,[status(thm)],[517]) ).
thf(519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(lifteq,[status(thm)],[518]) ).
thf(12512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9134,337]) ).
thf(12513,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[12512]) ).
thf(12515,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[12513]) ).
thf(12538,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[12515]) ).
thf(72580,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[529,72398]) ).
thf(72581,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[72580]) ).
thf(72582,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[72581:[bind(A,$thf( c_0 )),bind(B,$thf( B )),bind(C,$thf( tc_nat )),bind(D,$thf( tc_nat )),bind(E,$thf( c_Wellfounded__Relations_Oless__than )),bind(F,$thf( B ))]]) ).
thf(72805,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[72582]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
thf(650,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(142,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(626,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(34693,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[626,463]) ).
thf(34694,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[34693]) ).
thf(34695,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[34694:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(34798,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[34695]) ).
thf(17916,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,17824]) ).
thf(17917,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[17916]) ).
thf(17918,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[17917:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( G @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(17990,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[17918]) ).
thf(39848,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39567]) ).
thf(39849,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39848:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(42,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(403,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)],[42]) ).
thf(25,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(356,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)],[25]) ).
thf(70,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(469,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)],[70]) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[469]) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[470]) ).
thf(263,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(884,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)],[263]) ).
thf(146,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(637,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)],[146]) ).
thf(81,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(488,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)],[81]) ).
thf(489,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(cnf,[status(esa)],[488]) ).
thf(25114,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,7787]) ).
thf(25115,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[25114]) ).
thf(25116,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[25115:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( E ))]]) ).
thf(25544,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[25116]) ).
thf(1611,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,534]) ).
thf(1612,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1611:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1889,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1612]) ).
thf(161,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(679,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)],[161]) ).
thf(25408,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,354]) ).
thf(25409,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[25408]) ).
thf(25410,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[25409:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).
thf(25716,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[25410]) ).
thf(288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
thf(933,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(68769,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,751]) ).
thf(68770,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[68769]) ).
thf(68861,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[68770]) ).
thf(68911,plain,
( ( tc_nat @ tc_set @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[68861]) ).
thf(164,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(686,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)],[164]) ).
thf(325,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(cnf,[status(esa)],[324]) ).
thf(326,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(lifteq,[status(thm)],[325]) ).
thf(327,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[326]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(cnf,[status(esa)],[327]) ).
thf(2317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(lifteq,[status(thm)],[328]) ).
thf(547,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(cnf,[status(esa)],[546]) ).
thf(38,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
thf(393,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(515,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[514]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(25036,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,15109]) ).
thf(25037,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[25036]) ).
thf(25038,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[25037:[bind(A,$thf( c_emptyset ))]]) ).
thf(65,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(455,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)],[65]) ).
thf(456,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(cnf,[status(esa)],[455]) ).
thf(457,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(lifteq,[status(thm)],[456]) ).
thf(277,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(911,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)],[277]) ).
thf(13578,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,13533]) ).
thf(13579,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[13578:[]]) ).
thf(13594,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_x @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[13579]) ).
thf(94,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(516,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(8774,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,516]) ).
thf(8775,plain,
( ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8774:[bind(A,$thf( tc_nat ))]]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
thf(837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(23574,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,22316]) ).
thf(23575,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23574]) ).
thf(23576,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[23575:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( F @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( F )),bind(C,$thf( J ))]]) ).
thf(25794,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[23576]) ).
thf(20,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(343,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)],[20]) ).
thf(218,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(792,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)],[218]) ).
thf(290,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(938,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)],[290]) ).
thf(90,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(508,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)],[90]) ).
thf(58497,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[57140,481]) ).
thf(58498,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[58497]) ).
thf(58499,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[58498:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(40,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(398,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)],[40]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(926,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(101,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(530,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(301,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(960,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(6258,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[960,751]) ).
thf(6259,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[6258]) ).
thf(6296,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[6259]) ).
thf(6311,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[6296]) ).
thf(219,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(794,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)],[219]) ).
thf(125,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(586,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)],[125]) ).
thf(9983,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,9813]) ).
thf(9984,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9983]) ).
thf(9985,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9984:[bind(A,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) ))]]) ).
thf(181,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(718,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)],[181]) ).
thf(274,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(906,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)],[274]) ).
thf(45,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(410,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)],[45]) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(cnf,[status(esa)],[410]) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[411]) ).
thf(234,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(824,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)],[234]) ).
thf(40229,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39641]) ).
thf(40230,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[40229:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
thf(856,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(120,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(573,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)],[120]) ).
thf(1,negated_conjecture,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_x @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(303,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_x @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(961,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[303,751]) ).
thf(962,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[961]) ).
thf(965,plain,
( ( ( t_a @ tc_set @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_Finite__Set_OFinites )
| ( c_UNIV != v_x ) ),
inference(simp,[status(thm)],[962]) ).
thf(138,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(618,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)],[138]) ).
thf(24963,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,6903]) ).
thf(24964,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[24963]) ).
thf(24965,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[24964:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(25515,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[24965]) ).
thf(513,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(cnf,[status(esa)],[512]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(cnf,[status(esa)],[428]) ).
thf(430,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[429]) ).
thf(7598,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( C @ sk2 ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[424,7589]) ).
thf(7599,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_List_Olist_ONil @ sk2 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[7598:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_List_Olist_ONil )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(197,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
thf(745,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(12637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9354,492]) ).
thf(12638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[12637]) ).
thf(12687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[12638]) ).
thf(12704,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[12687]) ).
thf(28631,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,15109]) ).
thf(28632,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28631]) ).
thf(28633,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[28632:[bind(A,$thf( c_emptyset ))]]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
thf(689,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(8717,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,626]) ).
thf(8718,plain,
( ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8717:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(31,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(375,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)],[31]) ).
thf(189,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(733,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)],[189]) ).
thf(30398,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( D @ sk4 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[330,30375]) ).
thf(30399,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_List_Olist_ONil @ sk4 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[30398:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_List_Olist_ONil )),bind(E,$thf( B ))]]) ).
thf(168,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(694,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)],[168]) ).
thf(188,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(732,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(16058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9354,402]) ).
thf(16059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[16058]) ).
thf(16060,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[16059:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( H @ c_Suc @ ( E @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(16180,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[16060]) ).
thf(70861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( D @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16180,610]) ).
thf(70862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( D @ c_less ) ) ) ),
inference(simp,[status(thm)],[70861]) ).
thf(70977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
!= D )
| ( c_0 != D ) ),
inference(simp,[status(thm)],[70862]) ).
thf(71036,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[70977]) ).
thf(21199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9134,426]) ).
thf(21200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[21199]) ).
thf(21201,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[21200:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( F @ ( H @ c_Suc @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(21289,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[21201]) ).
thf(12463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9134,468]) ).
thf(12464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[12463]) ).
thf(12518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= D )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[12464]) ).
thf(12541,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( C @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[12518]) ).
thf(27095,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,16944]) ).
thf(27096,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[27095]) ).
thf(27097,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[27096:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( J ))]]) ).
thf(29272,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[27097]) ).
thf(300,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(958,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)],[300]) ).
thf(4569,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[732,751]) ).
thf(4570,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4569]) ).
thf(4597,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4570]) ).
thf(4612,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[4597]) ).
thf(108,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(543,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)],[108]) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(cnf,[status(esa)],[543]) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(lifteq,[status(thm)],[544]) ).
thf(26675,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,2231]) ).
thf(26676,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[26675:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(39470,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39422]) ).
thf(39471,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39470:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(60,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(445,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)],[60]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12800,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,10504]) ).
thf(12801,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[12800]) ).
thf(12826,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[12801]) ).
thf(12836,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[12826]) ).
thf(24927,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,12836]) ).
thf(24928,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[24927]) ).
thf(24929,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[24928:[bind(A,$thf( c_emptyset ))]]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(465,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[464]) ).
thf(466,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) ) ),
inference(lifteq,[status(thm)],[465]) ).
thf(294,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(947,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)],[294]) ).
thf(18419,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,18142]) ).
thf(18420,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[18419]) ).
thf(18421,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18420:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( H @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( H ))]]) ).
thf(18487,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[18421]) ).
thf(158,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
thf(672,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(24339,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,2197]) ).
thf(24340,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[24339:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(134,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(611,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)],[134]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(cnf,[status(esa)],[637]) ).
thf(639,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(lifteq,[status(thm)],[638]) ).
thf(640,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[639]) ).
thf(641,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk12 ) )
= A ),
inference(cnf,[status(esa)],[640]) ).
thf(68694,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk12 ) )
= A ),
inference(lifteq,[status(thm)],[641]) ).
thf(281,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(919,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(224,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(804,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)],[224]) ).
thf(162,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(681,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)],[162]) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ( A != tc_bool )
| ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,476]) ).
thf(1626,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_bool @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1625:[bind(A,$thf( tc_bool ))]]) ).
thf(1894,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_bool @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1626]) ).
thf(215,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(784,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)],[215]) ).
thf(191,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(736,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)],[191]) ).
thf(39842,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39567]) ).
thf(39843,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39842:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(130,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(599,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)],[130]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(863,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(206,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(764,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)],[206]) ).
thf(131,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(604,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)],[131]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(237,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(831,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)],[237]) ).
thf(8087,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,479]) ).
thf(8088,plain,
( ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8087:[bind(A,$thf( tc_nat ))]]) ).
thf(376,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(cnf,[status(esa)],[375]) ).
thf(377,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(lifteq,[status(thm)],[376]) ).
thf(28656,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,16393]) ).
thf(28657,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28656]) ).
thf(28658,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[28657:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( G @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(29683,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[28658]) ).
thf(10229,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,6897]) ).
thf(10230,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10229]) ).
thf(10231,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[10230:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( D ))]]) ).
thf(11338,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[10231]) ).
thf(14252,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,7787]) ).
thf(14253,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14252]) ).
thf(14254,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[14253:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( E ))]]) ).
thf(14322,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[14254]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(12661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9354,610]) ).
thf(12662,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[12661]) ).
thf(12690,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= C )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[12662]) ).
thf(12707,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[12690]) ).
thf(28841,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,12707]) ).
thf(28842,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28841]) ).
thf(28843,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[28842:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( G ))]]) ).
thf(29142,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[28843]) ).
thf(203,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(758,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)],[203]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).
thf(535,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(621,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(74513,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( F @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[504,72805]) ).
thf(74514,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( F @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[74513]) ).
thf(74515,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[74514:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) )),bind(C,$thf( c_0 )),bind(D,$thf( tc_nat )),bind(E,$thf( tc_nat )),bind(F,$thf( A ))]]) ).
thf(76981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[910,74515]) ).
thf(76982,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[76981]) ).
thf(77185,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) )
!= c_UNIV )
| ( A != C ) ),
inference(simp,[status(thm)],[76982]) ).
thf(77286,plain,
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[77185]) ).
thf(75608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,74207]) ).
thf(75609,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[75608]) ).
thf(75759,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[75609]) ).
thf(75866,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) ) ),
inference(simp,[status(thm)],[75759]) ).
thf(26749,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,11571]) ).
thf(26750,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[26749]) ).
thf(26751,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[26750:[bind(A,$thf( c_UNIV ))]]) ).
thf(228,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(811,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)],[228]) ).
thf(344,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(cnf,[status(esa)],[343]) ).
thf(345,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(lifteq,[status(thm)],[344]) ).
thf(251,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(858,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)],[251]) ).
thf(28,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
thf(367,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13568,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,13533]) ).
thf(13569,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[13568:[]]) ).
thf(13592,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( tc_nat @ ( v_x @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[13569]) ).
thf(230,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(816,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)],[230]) ).
thf(1761,plain,
! [B: $i,A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_List_Olist_ONil != v_xa )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,971]) ).
thf(1762,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_xa )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1761:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )),bind(B,$thf( B ))]]) ).
thf(1944,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_xa )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1762]) ).
thf(4874,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != v_xa ) ),
inference(paramod_ordered,[status(thm)],[1944,610]) ).
thf(4875,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4874]) ).
thf(4896,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= B )
| ( c_0 != B )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4875]) ).
thf(4911,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4896]) ).
thf(27175,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,12237]) ).
thf(27176,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[27175]) ).
thf(27177,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[27176:[bind(A,$thf( c_emptyset ))]]) ).
thf(1667,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,523]) ).
thf(1668,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1667:[bind(A,$thf( tc_nat ))]]) ).
thf(1909,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1668]) ).
thf(185,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(726,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)],[185]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
thf(700,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(279,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(915,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)],[279]) ).
thf(4951,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ( c_List_Olist_ONil != v_xa ) ),
inference(paramod_ordered,[status(thm)],[317,4911]) ).
thf(4952,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) ) )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4951]) ).
thf(4966,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist )
!= ( B @ tc_List_Olist ) )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4952]) ).
thf(7958,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4966]) ).
thf(8032,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[7958]) ).
thf(12725,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,12237]) ).
thf(12726,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[12725]) ).
thf(12727,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[12726:[bind(A,$thf( c_emptyset ))]]) ).
thf(34095,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,17990]) ).
thf(34096,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34095]) ).
thf(34163,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[34096]) ).
thf(34225,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[34163]) ).
thf(10871,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,2651]) ).
thf(10872,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10871]) ).
thf(10873,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[10872:[bind(A,$thf( F @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( F ))]]) ).
thf(11173,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[10873]) ).
thf(14425,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,14176]) ).
thf(14426,plain,
! [A: $i] :
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[14425:[]]) ).
thf(14453,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( tc_nat @ ( v_xa @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[14426]) ).
thf(26939,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,17824]) ).
thf(26940,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[26939]) ).
thf(26941,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[26940:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( G @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(29217,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[26941]) ).
thf(14751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[508,957]) ).
thf(14752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[14751]) ).
thf(14778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_List_Olist )
!= D )
| ( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset )
| ( c_List_Olist_ONil != C ) ),
inference(simp,[status(thm)],[14752]) ).
thf(14800,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset ),
inference(simp,[status(thm)],[14778]) ).
thf(18873,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ tc_set @ c_lessequals ) ) ) )
| ~ ( c_0 @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,10085]) ).
thf(18874,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ tc_set @ c_lessequals ) ) ) )
| ~ ( c_0 @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[18873]) ).
thf(18927,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( tc_nat @ tc_set )
!= c_0 )
| ~ ( c_0 @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[18874]) ).
thf(18962,plain,
( ( ( tc_nat @ tc_set )
!= c_0 )
| ~ ( c_0 @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[18927]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(153,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(653,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)],[153]) ).
thf(6754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( D @ tc_set @ ( c_emptyset @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[551,643]) ).
thf(6755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( D @ tc_set @ ( c_emptyset @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[6754]) ).
thf(6784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_set )
!= tc_IntDef_Oint )
| ( ( B @ c_IntDef_Oint )
!= c_emptyset )
| ( ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) )
!= C ) ),
inference(simp,[status(thm)],[6755]) ).
thf(6785,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_IntDef_Oint )
| ( ( A @ c_IntDef_Oint )
!= c_emptyset ) ),
inference(simp,[status(thm)],[6784]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(208,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
thf(768,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(235,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(827,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)],[235]) ).
thf(9837,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,9813]) ).
thf(9838,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9837]) ).
thf(9839,plain,
( ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9838:[bind(A,$thf( c_emptyset ))]]) ).
thf(11693,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 ) ),
inference(paramod_ordered,[status(thm)],[9839,643]) ).
thf(11694,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 ) ),
inference(simp,[status(thm)],[11693]) ).
thf(11716,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != c_emptyset )
| ( c_0 != A )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 ) ),
inference(simp,[status(thm)],[11694]) ).
thf(11721,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_0 ) ),
inference(simp,[status(thm)],[11716]) ).
thf(15917,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,15876]) ).
thf(15918,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[15917:[]]) ).
thf(15933,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_xa @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15918]) ).
thf(262,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(883,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)],[262]) ).
thf(39846,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39567]) ).
thf(39847,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39846:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(10033,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,7761]) ).
thf(10034,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10033]) ).
thf(10035,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[10034:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(11272,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[10035]) ).
thf(283,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(922,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(23644,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,13533]) ).
thf(23645,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_x )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23644:[]]) ).
thf(25803,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_IntDef_Oint @ ( v_x @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23645]) ).
thf(4511,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ( c_List_Olist_ONil != v_xa ) ),
inference(paramod_ordered,[status(thm)],[317,4471]) ).
thf(4512,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) ) )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4511]) ).
thf(4526,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist )
!= ( B @ tc_List_Olist ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4512]) ).
thf(7507,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[4526]) ).
thf(7571,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_xa ) ),
inference(simp,[status(thm)],[7507]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(polarity_switch,[status(thm)],[372]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[373]) ).
thf(9775,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_0 )
| ( tc_nat @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,8769]) ).
thf(9776,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( tc_nat @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9775]) ).
thf(9777,plain,
( ( tc_nat @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9776:[bind(A,$thf( c_emptyset ))]]) ).
thf(23529,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) )
| ( ( c_0 @ c_Suc )
!= B )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,7786]) ).
thf(23530,plain,
! [B: $i,A: $i] :
( ( ( c_0 @ c_Suc )
!= A )
| ~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23529:[bind(A,$thf( tc_nat @ ( E @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(25773,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[23530]) ).
thf(30109,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[417,25773]) ).
thf(30110,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[30109]) ).
thf(30216,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_IntDef_Oint )
| ( ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) )
!= c_0 )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[30110]) ).
thf(30223,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[30216]) ).
thf(15150,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,15109]) ).
thf(15151,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15150]) ).
thf(15152,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[15151:[bind(A,$thf( c_emptyset ))]]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[340]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(24,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(355,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(23537,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,16944]) ).
thf(23538,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23537]) ).
thf(23539,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[23538:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( J ))]]) ).
thf(25777,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[23539]) ).
thf(473,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(cnf,[status(esa)],[472]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(27920,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,2197]) ).
thf(27921,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[27920:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(23617,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,12237]) ).
thf(23618,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23617]) ).
thf(23619,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23618:[bind(A,$thf( c_emptyset ))]]) ).
thf(159,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(675,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)],[159]) ).
thf(39586,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39455]) ).
thf(39587,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39586:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(531,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[530]) ).
thf(293,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(944,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)],[293]) ).
thf(151,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(648,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)],[151]) ).
thf(137,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(617,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(68325,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[58499,481]) ).
thf(68326,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[68325]) ).
thf(68327,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[68326:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(201,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(754,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)],[201]) ).
thf(76987,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,74515]) ).
thf(76988,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[76987]) ).
thf(77186,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[76988]) ).
thf(77290,plain,
! [A: $i] :
( ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) ) ),
inference(simp,[status(thm)],[77186]) ).
thf(62,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(450,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(8862,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,450]) ).
thf(8863,plain,
( ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8862:[bind(A,$thf( tc_nat ))]]) ).
thf(39662,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39510]) ).
thf(39663,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39662:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(30392,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( D @ sk4 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[424,30375]) ).
thf(30393,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ sk4 ) ) )
= c_List_Olist_ONil ),
inference(pattern_uni,[status(thm)],[30392:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_List_Olist_ONil )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(212,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(776,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)],[212]) ).
thf(23148,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,2231]) ).
thf(23149,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23148:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(173,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(705,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(707,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(264,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(887,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)],[264]) ).
thf(368,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(lifteq,[status(thm)],[367]) ).
thf(8889,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( c_0 @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,368]) ).
thf(8890,plain,
( ( ( c_0 @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8889:[bind(A,$thf( tc_nat ))]]) ).
thf(28648,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,14176]) ).
thf(28649,plain,
! [A: $i] :
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[28648:[]]) ).
thf(29675,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( v_xa @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28649]) ).
thf(298,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(954,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)],[298]) ).
thf(8127,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,523]) ).
thf(8128,plain,
( ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8127:[bind(A,$thf( tc_nat ))]]) ).
thf(73236,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,72796]) ).
thf(73237,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[73236]) ).
thf(73402,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) ) )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[73237]) ).
thf(73474,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
inference(simp,[status(thm)],[73402]) ).
thf(33542,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,16495]) ).
thf(33543,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[33542]) ).
thf(33605,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[33543]) ).
thf(33649,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[33605]) ).
thf(178,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(712,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)],[178]) ).
thf(114,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(556,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)],[114]) ).
thf(557,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(cnf,[status(esa)],[556]) ).
thf(249,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(855,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(12172,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,10335]) ).
thf(12173,plain,
! [A: $i] :
( ( A != c_emptyset )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[12172]) ).
thf(12174,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[12173:[bind(A,$thf( c_emptyset ))]]) ).
thf(8497,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,476]) ).
thf(8498,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8497:[bind(A,$thf( tc_bool ))]]) ).
thf(26670,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_x )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,4075]) ).
thf(26671,plain,
( ( c_0 != v_x )
| ~ ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[26670:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(23407,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,17824]) ).
thf(23408,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23407]) ).
thf(23409,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[23408:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( G @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(25732,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[23409]) ).
thf(87,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(501,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(502,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[501]) ).
thf(378,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[377]) ).
thf(379,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( A @ sk3 ) ) )
= B ),
inference(cnf,[status(esa)],[378]) ).
thf(12405,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( A @ sk3 ) ) )
= B ),
inference(lifteq,[status(thm)],[379]) ).
thf(39590,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39455]) ).
thf(39591,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39590:[bind(A,$thf( tc_bool ))]]) ).
thf(10086,plain,
! [A: $i] :
( ( A != c_UNIV )
| ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_0 @ c_in ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,751]) ).
thf(10087,plain,
( ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_0 @ c_in ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10086:[bind(A,$thf( c_UNIV ))]]) ).
thf(20658,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_0 @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,10087]) ).
thf(20659,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[20658]) ).
thf(20729,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[20659]) ).
thf(20760,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[20729]) ).
thf(4092,plain,
! [B: $i,A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_List_Olist_ONil != v_x )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,4075]) ).
thf(4093,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_x )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4092:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )),bind(B,$thf( B ))]]) ).
thf(4098,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_x )
| ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4093]) ).
thf(7128,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != v_x ) ),
inference(paramod_ordered,[status(thm)],[4098,337]) ).
thf(7129,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ( c_List_Olist_ONil != v_x ) ),
inference(simp,[status(thm)],[7128]) ).
thf(7130,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != B )
| ( c_List_Olist_ONil != v_x ) ),
inference(simp,[status(thm)],[7129]) ).
thf(7149,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_List_Olist_ONil != v_x ) ),
inference(simp,[status(thm)],[7130]) ).
thf(8527,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,558]) ).
thf(8528,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8527:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(18,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(338,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(226,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(808,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(13402,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( c_0 @ ( tc_bool @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,8498]) ).
thf(13403,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( c_0 @ ( tc_bool @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[13402:[bind(A,$thf( tc_nat ))]]) ).
thf(8756,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,487]) ).
thf(8757,plain,
( ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8756:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1735,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_Orderings_Oorder )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,626]) ).
thf(1736,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1735:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1934,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1736]) ).
thf(74573,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,72805]) ).
thf(74574,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[74573]) ).
thf(74760,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) ) )
| ( A
!= ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[74574]) ).
thf(74776,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Pair ) ) ) @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) ) ),
inference(simp,[status(thm)],[74760]) ).
thf(135,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(613,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)],[135]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[385]) ).
thf(24922,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,2764]) ).
thf(24923,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[24922:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(128,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(595,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)],[128]) ).
thf(23222,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,11571]) ).
thf(23223,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23222]) ).
thf(23224,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23223:[bind(A,$thf( c_UNIV ))]]) ).
thf(28508,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,12836]) ).
thf(28509,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28508]) ).
thf(28510,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[28509:[bind(A,$thf( c_emptyset ))]]) ).
thf(8695,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,323]) ).
thf(8696,plain,
( ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8695:[bind(A,$thf( tc_nat ))]]) ).
thf(196,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(744,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(172,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(703,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)],[172]) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(cnf,[status(esa)],[445]) ).
thf(119,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(571,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)],[119]) ).
thf(85,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(496,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)],[85]) ).
thf(497,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(cnf,[status(esa)],[496]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
thf(876,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(143,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(627,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)],[143]) ).
thf(27737,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != c_0 )
| ( c_0 != v_xa )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,15876]) ).
thf(27738,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[27737]) ).
thf(27739,plain,
( ( c_0 != v_xa )
| ~ ( tc_nat @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[27738:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(24163,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,15876]) ).
thf(24164,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[24163:[]]) ).
thf(25959,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_IntDef_Oint @ ( v_xa @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[24164]) ).
thf(494,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(cnf,[status(esa)],[493]) ).
thf(495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[494]) ).
thf(39527,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39427]) ).
thf(39528,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39527:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(10636,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,971]) ).
thf(10637,plain,
( ( c_0 != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10636:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(210,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(771,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)],[210]) ).
thf(38600,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( ( c_0 @ ( c_0 @ c_uminus ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,38449]) ).
thf(38601,plain,
( ( ( c_0 @ ( c_0 @ c_uminus ) )
= c_0 )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[38600:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(287,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(931,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)],[287]) ).
thf(98,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(524,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)],[98]) ).
thf(123,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(581,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(35582,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,18487]) ).
thf(35583,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[35582]) ).
thf(35647,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[35583]) ).
thf(35690,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[35647]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(350,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(cnf,[status(esa)],[349]) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[350]) ).
thf(39664,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39510]) ).
thf(39665,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39664:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(145,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(632,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)],[145]) ).
thf(23620,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,12237]) ).
thf(23621,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23620]) ).
thf(23622,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23621:[bind(A,$thf( c_UNIV ))]]) ).
thf(214,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(781,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)],[214]) ).
thf(19344,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19236,414]) ).
thf(19345,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[19344]) ).
thf(19346,plain,
tc_nat @ tc_List_Olist @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ),
inference(pattern_uni,[status(thm)],[19345:[bind(A,$thf( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) )),bind(B,$thf( tc_nat @ tc_List_Olist @ tc_List_Olist ))]]) ).
thf(170,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(699,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(23016,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( v_xa @ c_lessequals ) ) ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[306,15933]) ).
thf(23017,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( v_xa @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( v_xa @ c_lessequals ) ) ) )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[23016]) ).
thf(23040,plain,
( ( ( t_a @ tc_set @ tc_set )
!= tc_nat )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( v_xa != v_xa )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[23017]) ).
thf(23044,plain,
( ( ( t_a @ tc_set @ tc_set )
!= tc_nat )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[23040]) ).
thf(198,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(748,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)],[198]) ).
thf(65709,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,65670]) ).
thf(65710,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[65709]) ).
thf(65711,plain,
( ( c_Relation_OId != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[65710:[bind(A,$thf( c_emptyset ))]]) ).
thf(68787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[647,957]) ).
thf(68788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[68787]) ).
thf(68869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset )
| ( A != C ) ),
inference(simp,[status(thm)],[68788]) ).
thf(68876,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[68869]) ).
thf(49,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(418,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)],[49]) ).
thf(27743,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,15876]) ).
thf(27744,plain,
! [A: $i] :
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[27743:[]]) ).
thf(29463,plain,
( ( ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( v_xa @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[27744]) ).
thf(286,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(929,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)],[286]) ).
thf(536,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[535]) ).
thf(157,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(667,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)],[157]) ).
thf(26815,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,9813]) ).
thf(26816,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_S @ c_Zorn_OTFin ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[26815]) ).
thf(26817,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[26816:[bind(A,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) ))]]) ).
thf(478,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
inference(cnf,[status(esa)],[477]) ).
thf(14635,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,9563]) ).
thf(14636,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[14635]) ).
thf(14637,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[14636:[bind(A,$thf( tc_nat @ ( E @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(14717,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[14637]) ).
thf(21558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14717,610]) ).
thf(21559,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[21558]) ).
thf(21628,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
!= C )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[21559]) ).
thf(21680,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[21628]) ).
thf(28875,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,21680]) ).
thf(28876,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[28875]) ).
thf(28877,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[28876:[bind(A,$thf( tc_nat @ ( E @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( E )),bind(C,$thf( G ))]]) ).
thf(29158,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[28877]) ).
thf(10946,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,354]) ).
thf(10947,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10946]) ).
thf(10948,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[10947:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).
thf(11227,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(simp,[status(thm)],[10948]) ).
thf(34,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(383,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)],[34]) ).
thf(2022,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[482,643]) ).
thf(2023,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2022]) ).
thf(2030,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( ( A @ c_Suc )
!= c_emptyset )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[2023]) ).
thf(2036,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( ( A @ c_Suc )
!= c_emptyset ) ),
inference(simp,[status(thm)],[2030]) ).
thf(180,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
thf(716,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(222,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(800,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)],[222]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
thf(752,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(cnf,[status(esa)],[313]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[314]) ).
thf(12635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9354,468]) ).
thf(12636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[12635]) ).
thf(12686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= D )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[12636]) ).
thf(12702,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( C @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[12686]) ).
thf(9921,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_x )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,4075]) ).
thf(9922,plain,
( ( c_0 != v_x )
| ~ ( tc_nat @ ( c_0 @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9921:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(239,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(835,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)],[239]) ).
thf(39472,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39422]) ).
thf(39473,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[39472:[bind(A,$thf( tc_bool ))]]) ).
thf(231,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(818,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)],[231]) ).
thf(255,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(867,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)],[255]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(24157,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != c_0 )
| ( c_0 != v_xa )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,15876]) ).
thf(24158,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[24157]) ).
thf(24159,plain,
( ( c_0 != v_xa )
| ~ ( tc_IntDef_Oint @ ( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[24158:[bind(A,$thf( t_a @ ( v_x @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(61,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(447,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)],[61]) ).
thf(74567,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[910,72805]) ).
thf(74568,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[74567]) ).
thf(74753,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) )
!= c_UNIV )
| ( A
!= ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[74568]) ).
thf(74770,plain,
( ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[74753]) ).
thf(238,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(833,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)],[238]) ).
thf(967,plain,
( ( ( t_a @ tc_set )
!= tc_nat )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_Finite__Set_OFinites )
| ( c_UNIV != v_x ) ),
inference(simp,[status(thm)],[965]) ).
thf(34906,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[551,34798]) ).
thf(34907,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[34906]) ).
thf(34991,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_IntDef_Oint )
| ( ( B @ c_IntDef_Oint )
!= C )
| ( ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) )
!= C ) ),
inference(simp,[status(thm)],[34907]) ).
thf(35053,plain,
! [B: $i,A: $i] :
( ( B @ c_IntDef_Oint )
!= ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) ) ),
inference(simp,[status(thm)],[34991]) ).
thf(14650,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,9563]) ).
thf(14651,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14650]) ).
thf(14652,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[14651:[bind(A,$thf( tc_nat @ ( E @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(14723,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[14652]) ).
thf(24723,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_0 != v_xa )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[433,971]) ).
thf(24724,plain,
( ( c_0 != v_xa )
| ~ ( tc_IntDef_Oint @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[24723:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(357,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(cnf,[status(esa)],[356]) ).
thf(358,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(lifteq,[status(thm)],[357]) ).
thf(57,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(437,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[398]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[399]) ).
thf(182,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(720,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)],[182]) ).
thf(220,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(796,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)],[220]) ).
thf(169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
thf(696,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(27178,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,12237]) ).
thf(27179,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[27178]) ).
thf(27180,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[27179:[bind(A,$thf( c_UNIV ))]]) ).
thf(252,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(860,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)],[252]) ).
thf(3830,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[705,751]) ).
thf(3831,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[3830]) ).
thf(3856,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[3831]) ).
thf(3869,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[3856]) ).
thf(148,axiom,
! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_1) ).
thf(644,plain,
! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(233,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(822,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)],[233]) ).
thf(8772,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,617]) ).
thf(8773,plain,
( ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8772:[bind(A,$thf( tc_nat ))]]) ).
thf(13260,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,12836]) ).
thf(13261,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[13260]) ).
thf(13262,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[13261:[bind(A,$thf( c_emptyset ))]]) ).
thf(241,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(839,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)],[241]) ).
thf(186,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(728,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)],[186]) ).
thf(193,axiom,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(740,plain,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(12132,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,11571]) ).
thf(12133,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[12132]) ).
thf(12134,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[12133:[bind(A,$thf( c_UNIV ))]]) ).
thf(53,axiom,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
thf(427,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(275,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(908,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)],[275]) ).
thf(40227,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,39641]) ).
thf(40228,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[40227:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(26878,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[436,7761]) ).
thf(26879,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[26878]) ).
thf(26880,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[26879:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(29186,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[26880]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(10757,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,2764]) ).
thf(10758,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10757:[bind(A,$thf( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) ))]]) ).
thf(132,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(607,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)],[132]) ).
thf(9502,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9451,610]) ).
thf(9503,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[9502]) ).
thf(9530,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= B )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[9503]) ).
thf(9558,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9530]) ).
thf(486,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(cnf,[status(esa)],[485]) ).
thf(289,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(935,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)],[289]) ).
thf(14032,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( c_0 @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,8528]) ).
thf(14033,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( c_0 @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[14032:[bind(A,$thf( tc_nat ))]]) ).
thf(560,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(cnf,[status(esa)],[559]) ).
thf(6780,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[551,337]) ).
thf(6781,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[6780]) ).
thf(6782,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( B @ c_IntDef_Oint )
!= c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) )
!= C ) ),
inference(simp,[status(thm)],[6781]) ).
thf(6810,plain,
! [A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( A @ c_IntDef_Oint )
!= c_0 ) ),
inference(simp,[status(thm)],[6782]) ).
thf(14435,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[371,14176]) ).
thf(14436,plain,
! [A: $i] :
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ( A != v_xa )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[14435:[]]) ).
thf(14450,plain,
( ( ( t_a @ ( v_xa @ ( v_S @ c_Zorn_Osucc ) ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_xa @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14436]) ).
thf(458,plain,
? [A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
= B ),
inference(detectInverse,[status(thm)],[457]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk5 ) ) ) )
= A ),
inference(cnf,[status(esa)],[458]) ).
thf(33401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk5 ) ) ) )
= A ),
inference(lifteq,[status(thm)],[459]) ).
thf(972,plain,
( ( ( t_a @ tc_set )
!= tc_nat )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= c_Finite__Set_OFinites )
| ( c_UNIV != v_xa ) ),
inference(simp,[status(thm)],[966]) ).
thf(454,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(cnf,[status(esa)],[453]) ).
thf(112817,plain,
$false,
inference(e,[status(thm)],[809,55776,39589,760,479,846,333,468,555,2280,645,892,9982,56798,25531,11504,72446,941,481,352,7601,25737,683,2231,15143,741,873,1269,597,4747,29289,523,762,1924,13834,730,4075,28504,8797,11571,3549,6900,1939,440,511,28305,39510,677,30375,65693,385,533,29059,500,9813,814,913,340,538,550,19236,74207,2434,1872,472,2575,26814,829,23144,40521,15931,709,1935,320,7761,34857,38648,898,841,417,4679,4322,436,724,10089,17824,372,1907,619,802,43165,23287,949,2654,389,504,20440,917,751,542,460,902,559,853,16495,770,12767,316,4471,14316,39845,421,870,881,416,11139,4253,7786,756,789,74400,7245,22316,4001,623,9557,485,10085,12237,514,348,966,13533,25535,23290,475,924,492,10950,16944,591,806,57140,905,480,766,25603,73471,692,956,453,396,18639,660,40224,428,507,8742,774,2371,527,72138,312,307,25623,29226,20871,452,920,380,546,64988,72796,1915,534,2496,714,39427,25448,798,512,439,65020,529,8397,381,39526,366,334,12542,910,6897,349,820,561,424,39661,72779,29230,957,894,6550,778,21238,302,40226,392,407,630,2396,7244,72398,67928,65677,467,72857,361,879,329,889,461,493,29141,1407,551,25709,15417,710,29298,1938,847,566,484,9190,41593,665,19454,583,522,324,76410,8297,615,10335,65028,593,610,29113,71660,578,8694,519,12538,72805,317,650,34798,17990,39849,403,39422,356,471,884,554,537,642,637,489,25544,1889,679,706,25716,488,933,68911,686,476,2317,547,393,647,515,738,25038,457,911,13594,19166,8775,40407,8142,371,503,837,25794,343,792,938,508,58499,541,53949,398,558,953,926,530,6311,794,586,9985,718,906,412,425,2585,824,40230,856,573,965,750,618,25515,513,430,7599,745,12704,28633,689,8718,375,733,30399,423,694,732,71036,21289,12541,743,65014,29272,958,4612,545,402,26676,413,39471,445,382,313,498,24929,466,2425,947,9354,18487,672,24340,15876,38449,611,787,335,68694,919,804,9089,41291,2311,2119,681,1894,784,736,451,303,13836,39843,599,2197,863,764,604,900,406,831,8088,377,29683,11338,318,509,14322,434,477,29142,758,535,621,483,77286,75866,943,26751,330,811,387,345,858,367,552,72780,13592,816,4911,15543,609,27177,323,39567,1909,726,700,520,626,915,8032,12727,462,34225,65670,11173,14453,306,563,29217,14800,18962,851,653,6785,658,768,827,11721,15933,455,883,505,39847,14577,431,11272,922,426,25803,7571,9563,548,374,9777,30223,15152,342,355,1551,25777,473,722,27921,23619,490,675,39587,531,944,648,487,42806,617,516,68327,754,77290,553,8863,39663,30393,776,23149,705,707,887,8890,29675,954,8128,73474,310,33649,712,557,580,855,414,39819,12174,971,42977,8498,10504,26671,331,25732,502,12405,643,39591,56479,39641,20760,7149,463,8528,338,43355,951,808,13403,359,8757,1934,336,74776,613,19169,386,24923,595,23224,28510,8696,744,40200,703,446,571,497,876,57484,39455,627,450,27739,556,482,25959,7589,495,891,39528,10637,771,38601,931,539,524,581,35690,368,844,517,304,351,39665,632,2764,23622,781,19346,6903,699,896,23044,748,390,65711,68876,401,418,12836,29463,53657,433,16180,929,74515,536,9839,667,26817,478,29158,11227,10087,383,346,2036,72851,4098,716,800,15109,14176,752,16393,315,12702,9922,835,39473,818,7787,867,865,24159,447,74770,833,410,967,8769,35053,735,14723,305,326,24724,16218,53388,358,9134,437,474,400,18142,532,720,2651,796,12707,960,696,41158,9927,27180,415,21680,464,860,3869,528,644,41441,822,850,8773,691,501,13262,839,728,740,12134,427,908,40228,442,29186,871,10758,8918,369,607,9558,322,486,337,354,935,543,14033,560,6810,14450,491,33401,364,4002,972,469,1944,309,40295,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET853-1 : 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
% 0.06/20.59 % CPULimit : 300
% 0.06/20.59 % WCLimit : 300
% 0.06/20.59 % DateTime : Sat Sep 26 08:21:58 UTC 2026
% 0.06/20.59 % CPUTime :
% 0.06/20.59 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
% 0.88/21.08 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/21.44 % [INFO] Parsing done (357ms).
% 1.95/21.45 % [INFO] Running in sequential loop mode.
% 2.83/21.78 % [INFO] eprover registered as external prover.
% 2.83/21.79 % [INFO] Scanning for conjecture ...
% 3.34/21.97 % [INFO] Found a conjecture (or negated_conjecture) and 1366 axioms. Running axiom selection ...
% 4.24/22.17 % [INFO] Axiom selection finished. Selected 295 axioms (removed 1071 axioms).
% 5.04/22.34 % [INFO] Problem is propositional (TPTP CNF).
% 5.04/22.36 % [INFO] Type checking passed.
% 5.04/22.36 % [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 ...
% 148.82/64.45 % External prover 'e' found a proof!
% 148.82/64.45 % [INFO] Killing All external provers ...
% 148.82/64.45 % Time passed: 43733ms (effective reasoning time: 42991ms)
% 148.82/64.45 % Axioms used in derivation (295): cls_Finite__Set_Ofinite__converse__iff1_0, cls_IntDiv_Ozdvd__0__right_0, cls_Finite__Set_Ofinite__Union_0, cls_Datatype__Universe_Ousum__In1I_0, cls_Datatype__Universe_OuprodI_0, cls_Nat_Ole__0__eq__iff1_0, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, cls_List_Ofinite__set_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_SetInterval_OlessThan__iff__iff2_0, cls_List_Oset__empty2__iff2_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_SetInterval_OatLeast__subset__iff__iff2_0, cls_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, clsarity_prod_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_List_ONil__is__append__conv__iff2_0, cls_SetInterval_OgreaterThan__iff__iff2_0, clsarity_nat_7, 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_Finite__Set_OFinites_OemptyI_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Datatype__Universe_Ousum__In0I_0, cls_IntDiv_Ozdvd__0__left__iff2_0, clsrel_Orderings_Olinorder_4, cls_Nat_Oless__Suc0__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_Datatype__Universe_OusumE_2, 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_Nat_Oadd__is__0__iff1_1, clsarity_sum_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, cls_Zorn_OTFin__linear__lemma1_0, clsarity_set_2, cls_Nat_Onot__less0__iff1_0, cls_List_Olistrel__Nil1_0, clsarity_nat_3, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Set_OComplI_0, cls_Relation_OconverseE_1, cls_Finite__Set_Ofinite__Int_0, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_Nat_Oadd__is__0__iff2_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, clsarity_IntDef__Oint_0, cls_Infinite__Set_Onat__not__finite_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Relation_ORangeE_0, cls_SetInterval_OlessThan__iff__iff1_0, cls_Set_OInterI_1, cls_Nat_OSuc__Suc__eq__iff1_0, cls_List_Oset__empty__iff2_0, cls_Set_OUnCI_1, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Set_OPow__iff__iff2_0, cls_Zorn_Osucc__trans_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_Zorn_OUnion__lemma0_2, cls_SetInterval_OatMost__iff__iff2_0, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, cls_Nat_Ole__0__eq__iff2_0, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Relation_OdiagI_0, cls_Set_OCompl__subset__Compl__iff__iff2_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Set_OCompl__eq__Compl__iff__iff1_0, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_List_Olength__0__conv__iff2_0, cls_Divides_Odvd__0__left__iff__iff2_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_SetInterval_OatMost__eq__iff__iff1_0, cls_Relation_ODomainI_0, cls_Set_OinsertE_0, cls_Zorn_OTFin__linear__lemma1_3, cls_Set_Onot__psubset__empty__iff1_0, cls_Set_OUnE_0, cls_SetInterval_OlessThan__subset__iff__iff2_0, cls_List_Owf__lex_0, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, cls_Datatype__Universe_OusumE_1, cls_Set_OComplD__dest_0, cls_Set_OUn__empty__iff1_1, cls_Relation_Orel__compE_2, cls_Nat_OZero__not__Suc__iff1_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, clsarity_set_3, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_SetInterval_OatMost__subset__iff__iff2_0, cls_SetInterval_OatLeast__subset__iff__iff1_0, cls_SetInterval_Ofinite__atLeastLessThan_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_Relation_OIdI_0, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsarity_IntDef__Oint_31, cls_List_Oappend__is__Nil__conv__iff2_0, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Nat_OSuc__less__eq__iff2_0, cls_Divides_Odvd__0__left__iff__iff1_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_Nat_Oadd__gr__0__iff2_1, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Nat_Oless__Suc0__iff2_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_SetInterval_OatLeast__iff__iff2_0, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, cls_SetInterval_OatMost__subset__iff__iff1_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Relation_OconverseE_0, cls_List_Olength__greater__0__conv__iff2_0, cls_Datatype__Universe_OuprodE_2, clsrel_Orderings_Oorder_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_Oconverse__iff__iff1_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_List_Olist_Oinject__iff1_1, cls_Datatype__Universe_OuprodE_0, cls_Set_ODiffE_0, cls_Datatype__Universe_OusumE_0, cls_SetInterval_OatMost__iff__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, clsarity_set_1, 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_Nat_OSuc__le__mono__iff1_0, cls_Zorn_OTFin__linear__lemma1_2, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Nat_Onot__add__less1__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_IntDiv_Ozdvd__0__left__iff1_0, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, cls_Nat_Oadd__gr__0__iff1_0, cls_Divides_Odvd__0__right_0, cls_IntDef_Oint__int__eq__iff1_0, cls_IntDiv_Odvd__zminus__iff__iff1_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_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_SetInterval_Ofinite__greaterThanLessThan_0, clsarity_fun_1, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, clsarity_nat_12, cls_Nat_OSuc__le__mono__iff2_0, cls_IntDiv_Odvd__zminus__iff__iff2_0, cls_List_Oappend__self__conv__iff2_0, cls_SetInterval_OgreaterThan__iff__iff1_0, cls_List_Oappend__same__eq__iff1_0, clsarity_IntDef__Oint_5, cls_Set_OCompl__subset__Compl__iff__iff1_0, cls_Set_ODiffI_0, cls_Orderings_Oorder__less__irrefl__iff1_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, clsarity_IntDef__Oint_62, cls_Set_OUn__empty__iff2_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OpsubsetE_0, cls_Set_OUnionI_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_Zorn_OUnion__lemma0_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_Nat_OSuc__less__eq__iff1_0, cls_Relation_OdiagE_1, clsarity_nat_9, cls_Relation_OImage__singleton__iff__iff1_0, cls_Zorn_OAbrial__axiom1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Nat_Oneq0__conv__iff1_0, cls_Set_OInterI_0, cls_List_Olist_Odistinct__1__iff1_0, clsarity_bool_0, cls_Zorn_OUnion__lemma0_0, cls_Nat_Oadd__is__0__iff1_0, cls_SetInterval_OatLeast__eq__iff__iff1_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsarity_Product____Type__Ounit_0, cls_IntDef_Onegative__zle_0, cls_Sum__Type_OPlusE_1, cls_Set_OUnionE_0, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_List_Oin__listsI_0, cls_Divides_Odvd__1__left_0, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_List_Oappend1__eq__conv__iff1_0, clsarity_set_0, clsarity_Datatype__Ooption_0, cls_Nat_OSuc__not__Zero__iff1_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Nat_Ole0_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_Datatype__Universe_OusumE_3, cls_List_Olength__0__conv__iff1_0, clsarity_fun_0, cls_Relation_OIdE_0, clsarity_nat_2, cls_Set_OpsubsetE_1, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OIntE_0, cls_Relation_Orel__compE_1, clsarity_set_4, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, cls_Nat_Onot__add__less2__iff1_0, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_Zorn_OTFin__linear__lemma1_1, cls_IntDef_Onegative__zless_0, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_IntDiv_Ozminus__dvd__iff__iff2_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_SetInterval_OlessThan__subset__iff__iff1_0
% 148.82/64.45 % No. of inferences in proof: 1812
% 148.82/64.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 43733 ms resp. 42991 ms w/o parsing
% 141.57/64.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 141.57/64.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------