TSTP Solution File: SET858-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET858-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:54:40 EDT 2023
% Result : Unsatisfiable 275.16s 53.82s
% Output : Refutation 275.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 413
% Syntax : Number of formulae : 847 ( 229 unt; 113 typ; 0 def)
% Number of atoms : 1468 ( 481 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 8482 ( 763 ~; 688 |; 0 &;7031 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 281 ( 281 >; 0 *; 0 +; 0 <<)
% Number of symbols : 115 ( 113 usr; 16 con; 0-6 aty)
% Number of variables : 1900 ( 0 ^;1900 !; 0 ?;1900 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_m_type,type,
v_m: $i ).
thf(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(v_S_type,type,
v_S: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(v_n_type,type,
v_n: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_0_type,type,
c_0: $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_Wellfounded__Recursion_Owf_type,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Oless__than_type,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_type,type,
c_append: $i > $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Divides_Oop_Advd_type,type,
c_Divides_Oop_Advd: $i > $i > $i > $o ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_type,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_List_Olex_type,type,
c_List_Olex: $i > $i > $i ).
thf(class_Finite__Set_Ofinite_type,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_type,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OatLeast_type,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(class_Nat_Opower_type,type,
class_Nat_Opower: $i > $o ).
thf(tc_Datatype_Ooption_type,type,
tc_Datatype_Ooption: $i > $i ).
thf(c_SetInterval_OgreaterThan_type,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_type,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OIn1_type,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odsum_type,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i ).
thf(c_Datatype__Universe_Odprod_type,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn0_type,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Sum__Type_OInr_type,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_type,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(tc_sum_type,type,
tc_sum: $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_UNIV_type,type,
c_UNIV: $i ).
thf(c_IntDef_Oint_type,type,
c_IntDef_Oint: $i > $i ).
thf(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
thf(c_Main_OImageE__1_type,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OPlus_type,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__1_type,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_type,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_type,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_type,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_type,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_type,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Ousum_type,type,
c_Datatype__Universe_Ousum: $i > $i > $i > $i > $i ).
thf(c_Main_OusumE__2_type,type,
c_Main_OusumE__2: $i > $i > $i > $i > $i ).
thf(c_Main_OusumE__1_type,type,
c_Main_OusumE__1: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(c_SetInterval_OgreaterThanAtMost_type,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_type,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Zorn_OTFin__linear__lemma1__1_type,type,
c_Zorn_OTFin__linear__lemma1__1: $i > $i > $i > $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_type,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_type,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(c_Main_Oin__listsI__1_type,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_type,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_type,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__1_type,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_type,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_type,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_type,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_type,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_type,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_type,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_type,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OdiagE__1_type,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_type,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_type,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_type,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_type,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Main_OIdE__1_type,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Inter_type,type,
c_Inter: $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_OInterI__1_type,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_ODomainE__1_type,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(sk1_type,type,
sk1: $i > $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatMost @ B @ A )
!= ( c_SetInterval_OatMost @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatMost @ B @ A )
!= ( c_SetInterval_OatMost @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( A = c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[311]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
inference(lifteq,[status(thm)],[312]) ).
thf(164,axiom,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(667,plain,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(131,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(590,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(591,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(polarity_switch,[status(thm)],[590]) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( c_less @ A @ ( c_Suc @ A ) @ tc_nat )
!= ( c_less @ B @ B @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[667,591]) ).
thf(2245,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( c_Suc @ A )
!= B )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2236]) ).
thf(2249,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(simp,[status(thm)],[2245]) ).
thf(2332,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( c_List_Olist_ONil != C )
| ( A
!= ( c_Suc @ C ) ) ),
inference(paramod_ordered,[status(thm)],[313,2249]) ).
thf(2333,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( c_Suc @ B ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( c_List_Olist_ONil != B ) ),
inference(pattern_uni,[status(thm)],[2332:[bind(A,$thf( c_Suc @ D )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2336,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Osize @ ( c_Suc @ c_List_Olist_ONil ) @ ( tc_List_Olist @ A ) ) @ tc_nat ),
inference(simp,[status(thm)],[2333]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(254,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(846,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(278,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(893,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(75,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(468,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(555,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(6,axiom,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(307,plain,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(308,plain,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
inference(lifteq,[status(thm)],[307]) ).
thf(204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_Ousum @ E @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
thf(741,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_Ousum @ E @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(873,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C )
!= A )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
thf(762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C )
!= A )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(37,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(384,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(95,axiom,
class_Orderings_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(509,plain,
class_Orderings_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1048,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( class_Orderings_Oord @ c_List_Olist_ONil )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[313,509]) ).
thf(1049,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ tc_nat @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( class_Orderings_Oord @ c_List_Olist_ONil ) ),
inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( tc_nat ))]]) ).
thf(1137,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ tc_nat @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( class_Orderings_Oord @ c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[1049]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
thf(547,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(548,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[547]) ).
thf(549,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[548]) ).
thf(550,plain,
! [A: $i] :
( ( sk6 @ ( c_IntDef_Oint @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_IntDef_Oint),[sk6])]) ).
thf(91,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(500,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(814,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
thf(829,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(186,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(709,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(4,negated_conjecture,
~ ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(301,plain,
~ ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
inference(lifteq,[status(thm)],[319]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
thf(389,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
thf(838,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(26,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
thf(356,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(357,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(lifteq,[status(thm)],[356]) ).
thf(120,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).
thf(563,plain,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(15,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(326,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(327,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(polarity_switch,[status(thm)],[326]) ).
thf(947,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat )
!= ( c_less @ A @ c_0 @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[563,327]) ).
thf(948,plain,
! [A: $i] :
( ( c_0 != A )
| ( ( c_Suc @ c_0 )
!= c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[947]) ).
thf(949,plain,
( ( c_Suc @ c_0 )
!= c_0 ),
inference(simp,[status(thm)],[948]) ).
thf(232,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(802,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(21,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
thf(342,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(343,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(polarity_switch,[status(thm)],[342]) ).
thf(344,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(lifteq,[status(thm)],[343]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
thf(460,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(2397,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( c_Suc @ c_List_Olist_ONil ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
!= ( c_less @ B @ c_0 @ tc_nat ) ),
inference(paramod_ordered,[status(thm)],[2336,327]) ).
thf(2401,plain,
! [B: $i,A: $i] :
( ( c_0 != B )
| ( ( c_Nat_Osize @ ( c_Suc @ c_List_Olist_ONil ) @ ( tc_List_Olist @ A ) )
!= c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2397]) ).
thf(2403,plain,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Suc @ c_List_Olist_ONil ) @ ( tc_List_Olist @ A ) )
!= c_0 ),
inference(simp,[status(thm)],[2401]) ).
thf(14,axiom,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(325,plain,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(448,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(172,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(684,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(197,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(727,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(728,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(polarity_switch,[status(thm)],[727]) ).
thf(2814,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[684,728]) ).
thf(2815,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[2814]) ).
thf(2829,plain,
! [B: $i,A: $i] :
( ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[2815]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(817,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(271,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(881,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
thf(416,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(292,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(924,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(226,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(146,axiom,
! [B: $i,A: $i] : ( class_Nat_Opower @ ( tc_fun @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).
thf(623,plain,
! [B: $i,A: $i] : ( class_Nat_Opower @ ( tc_fun @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(135,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(598,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( class_Orderings_Oorder @ c_List_Olist_ONil )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[313,598]) ).
thf(1047,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ tc_nat @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( class_Orderings_Oorder @ c_List_Olist_ONil ) ),
inference(pattern_uni,[status(thm)],[1046:[bind(A,$thf( tc_nat ))]]) ).
thf(1136,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ tc_nat @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( class_Orderings_Oorder @ c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[1047]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(2,negated_conjecture,
c_in @ v_n @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(299,plain,
c_in @ v_n @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(936,plain,
( ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ v_n @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[299,728]) ).
thf(937,plain,
( ( c_UNIV != v_n )
| ( ( c_Zorn_OTFin @ v_S @ t_a )
!= c_Finite__Set_OFinites )
| ( ( tc_set @ ( tc_set @ t_a ) )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[936]) ).
thf(1,negated_conjecture,
c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(298,plain,
c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(294,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(927,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(928,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(polarity_switch,[status(thm)],[927]) ).
thf(1463,plain,
! [B: $i,A: $i] :
( ( c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
!= ( c_in @ A @ c_emptyset @ B ) ),
inference(paramod_ordered,[status(thm)],[298,928]) ).
thf(1466,plain,
! [B: $i,A: $i] :
( ( v_m != A )
| ( ( c_Zorn_OTFin @ v_S @ t_a )
!= c_emptyset )
| ( ( tc_set @ ( tc_set @ t_a ) )
!= B ) ),
inference(simp,[status(thm)],[1463]) ).
thf(1470,plain,
( ( c_Zorn_OTFin @ v_S @ t_a )
!= c_emptyset ),
inference(simp,[status(thm)],[1466]) ).
thf(1494,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( c_emptyset != c_List_Olist_ONil )
| ( A
!= ( c_Zorn_OTFin @ v_S @ t_a ) ) ),
inference(paramod_ordered,[status(thm)],[313,1470]) ).
thf(1495,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(pattern_uni,[status(thm)],[1494:[bind(A,$thf( c_Zorn_OTFin @ v_S @ t_a )),bind(B,$thf( B ))]]) ).
thf(1498,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[1495]) ).
thf(2282,plain,
! [B: $i,A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( ( c_less @ c_0 @ ( c_Nat_Osize @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
!= ( c_less @ B @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1498,327]) ).
thf(2283,plain,
! [B: $i,A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != B )
| ( ( c_Nat_Osize @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_List_Olist @ A ) )
!= c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2282]) ).
thf(2291,plain,
! [A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( ( c_Nat_Osize @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_List_Olist @ A ) )
!= c_0 ) ),
inference(simp,[status(thm)],[2283]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(25,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(353,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(138,axiom,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(602,plain,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(877,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(67,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
thf(453,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
thf(849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(104,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(525,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(526,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[525]) ).
thf(527,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[526]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(169,axiom,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(678,plain,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(925,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
thf(810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(36,axiom,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
thf(381,plain,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(3,negated_conjecture,
~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(300,plain,
~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(302,plain,
~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(polarity_switch,[status(thm)],[300]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
thf(561,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
thf(729,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ A @ ( tc_set @ C ) )
| ( c_lessequals @ D @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
thf(852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ A @ ( tc_set @ C ) )
| ( c_lessequals @ D @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
thf(665,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(211,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(757,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(13,axiom,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).
thf(324,plain,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(566,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(287,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(914,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(303,plain,
~ ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(polarity_switch,[status(thm)],[301]) ).
thf(2344,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[914,303]) ).
thf(2352,plain,
! [B: $i,A: $i] :
( ( c_emptyset != v_m )
| ( A != v_n )
| ( ( tc_set @ B )
!= ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[2344]) ).
thf(2358,plain,
! [A: $i] :
( ( c_emptyset != v_m )
| ( ( tc_set @ A )
!= ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[2352]) ).
thf(2445,plain,
! [A: $i] :
( ( c_emptyset != v_m )
| ( A
!= ( tc_set @ t_a ) ) ),
inference(simp,[status(thm)],[2358]) ).
thf(2470,plain,
c_emptyset != v_m,
inference(simp,[status(thm)],[2445]) ).
thf(2510,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( c_List_Olist_ONil != v_m )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[313,2470]) ).
thf(2511,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ c_emptyset @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( c_List_Olist_ONil != v_m ) ),
inference(pattern_uni,[status(thm)],[2510:[bind(A,$thf( c_emptyset ))]]) ).
thf(2515,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ c_emptyset @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( c_List_Olist_ONil != v_m ) ),
inference(simp,[status(thm)],[2511]) ).
thf(2637,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil != v_m )
| ( ( c_less @ c_0 @ ( c_Nat_Osize @ c_emptyset @ ( tc_List_Olist @ A ) ) @ tc_nat )
!= ( c_less @ B @ B @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[2515,591]) ).
thf(2654,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil != v_m )
| ( c_0 != B )
| ( ( c_Nat_Osize @ c_emptyset @ ( tc_List_Olist @ A ) )
!= B )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[2637]) ).
thf(2670,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_m )
| ( ( c_Nat_Osize @ c_emptyset @ ( tc_List_Olist @ A ) )
!= c_0 ) ),
inference(simp,[status(thm)],[2654]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(316,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(cnf,[status(esa)],[315]) ).
thf(317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(lifteq,[status(thm)],[316]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(145,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(621,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(622,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(polarity_switch,[status(thm)],[621]) ).
thf(1524,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat )
!= ( c_less @ B @ c_emptyset @ ( tc_set @ C ) ) ),
inference(paramod_ordered,[status(thm)],[468,622]) ).
thf(1534,plain,
! [C: $i,B: $i,A: $i] :
( ( c_0 != B )
| ( ( c_Suc @ A )
!= c_emptyset )
| ( ( tc_set @ C )
!= tc_nat ) ),
inference(simp,[status(thm)],[1524]) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= c_emptyset )
| ( ( tc_set @ B )
!= tc_nat ) ),
inference(simp,[status(thm)],[1534]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(2342,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[914,302]) ).
thf(2356,plain,
! [B: $i,A: $i] :
( ( c_emptyset != v_n )
| ( A != v_m )
| ( ( tc_set @ B )
!= ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[2342]) ).
thf(2363,plain,
! [A: $i] :
( ( c_emptyset != v_n )
| ( ( tc_set @ A )
!= ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[2356]) ).
thf(2516,plain,
! [A: $i] :
( ( c_emptyset != v_n )
| ( A
!= ( tc_set @ t_a ) ) ),
inference(simp,[status(thm)],[2363]) ).
thf(2537,plain,
c_emptyset != v_n,
inference(simp,[status(thm)],[2516]) ).
thf(193,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(720,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1484,plain,
! [A: $i] :
( ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[720,728]) ).
thf(1486,plain,
! [A: $i] :
( ( ( c_SetInterval_OatMost @ A @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[1484]) ).
thf(1493,plain,
! [A: $i] :
( ( c_SetInterval_OatMost @ A @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[1486]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(85,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(487,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(488,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(lifteq,[status(thm)],[487]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(339,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(297,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(933,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(552,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[551]) ).
thf(553,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[552]) ).
thf(554,plain,
! [A: $i] :
( ( sk7 @ ( c_Suc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_Suc),[sk7])]) ).
thf(109,axiom,
! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(537,plain,
! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(154,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(642,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(86,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(328,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(686,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(80,axiom,
class_Nat_Opower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(476,plain,
class_Nat_Opower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(31,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(370,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ~ ( c_lessequals @ v_n @ v_m @ c_List_Olist_ONil )
| ( A
!= ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[313,302]) ).
thf(1043,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ~ ( c_lessequals @ v_n @ v_m @ c_List_Olist_ONil ) ),
inference(pattern_uni,[status(thm)],[1042:[bind(A,$thf( tc_set @ ( tc_set @ t_a ) )),bind(B,$thf( B ))]]) ).
thf(1135,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ~ ( c_lessequals @ v_n @ v_m @ c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[1043]) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ v_n @ v_m @ c_List_Olist_ONil )
| ( ( c_less @ c_0 @ ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
!= ( c_less @ B @ B @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1135,591]) ).
thf(1408,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ v_n @ v_m @ c_List_Olist_ONil )
| ( c_0 != B )
| ( ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ A ) )
!= B )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[1403]) ).
thf(1410,plain,
! [A: $i] :
( ~ ( c_lessequals @ v_n @ v_m @ c_List_Olist_ONil )
| ( ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ A ) )
!= c_0 ) ),
inference(simp,[status(thm)],[1408]) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ v_n @ v_m @ c_List_Olist_ONil ) ) ),
inference(paramod_ordered,[status(thm)],[370,1410]) ).
thf(1587,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( c_0 != v_n )
| ( A != v_m )
| ( tc_nat != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[1585]) ).
thf(1588,plain,
! [A: $i] :
( ( ( c_Nat_Osize @ ( tc_set @ ( tc_set @ t_a ) ) @ ( tc_List_Olist @ A ) )
!= c_0 )
| ( c_0 != v_n )
| ( tc_nat != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[1587]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(194,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(721,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(123,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(569,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(779,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(32,axiom,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(371,plain,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(934,plain,
( ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[298,728]) ).
thf(935,plain,
( ( c_UNIV != v_m )
| ( ( c_Zorn_OTFin @ v_S @ t_a )
!= c_Finite__Set_OFinites )
| ( ( tc_set @ ( tc_set @ t_a ) )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[934]) ).
thf(938,plain,
( ( c_UNIV != v_m )
| ( ( c_Zorn_OTFin @ v_S @ t_a )
!= c_Finite__Set_OFinites )
| ( ( tc_set @ t_a )
!= tc_nat ) ),
inference(simp,[status(thm)],[935]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(657,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(214,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(765,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(2181,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_UNIV @ B )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[881,728]) ).
thf(2184,plain,
! [B: $i,A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_UNIV )
| ( B
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[2181]) ).
thf(2189,plain,
c_Finite__Set_OFinites != c_UNIV,
inference(simp,[status(thm)],[2184]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(773,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1039,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ c_List_Olist_ONil ) )
| ( A
!= ( tc_set @ t_a ) ) ),
inference(paramod_ordered,[status(thm)],[313,302]) ).
thf(1040,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ c_List_Olist_ONil ) ) ),
inference(pattern_uni,[status(thm)],[1039:[bind(A,$thf( tc_set @ t_a )),bind(B,$thf( B ))]]) ).
thf(1134,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ c_List_Olist_ONil ) ) ),
inference(simp,[status(thm)],[1040]) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ c_List_Olist_ONil ) )
| ( ( c_less @ c_0 @ ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ A ) ) @ tc_nat )
!= ( c_less @ B @ c_0 @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1134,327]) ).
thf(1256,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ c_List_Olist_ONil ) )
| ( c_0 != B )
| ( ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ A ) )
!= c_0 )
| ( tc_nat != tc_nat ) ),
inference(simp,[status(thm)],[1254]) ).
thf(1262,plain,
! [A: $i] :
( ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ c_List_Olist_ONil ) )
| ( ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ A ) )
!= c_0 ) ),
inference(simp,[status(thm)],[1256]) ).
thf(1283,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ v_n @ v_m @ ( tc_set @ c_List_Olist_ONil ) ) ) ),
inference(paramod_ordered,[status(thm)],[370,1262]) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( c_0 != v_n )
| ( A != v_m )
| ( ( tc_set @ c_List_Olist_ONil )
!= tc_nat ) ),
inference(simp,[status(thm)],[1283]) ).
thf(1286,plain,
! [A: $i] :
( ( ( c_Nat_Osize @ ( tc_set @ t_a ) @ ( tc_List_Olist @ A ) )
!= c_0 )
| ( c_0 != v_n )
| ( ( tc_set @ c_List_Olist_ONil )
!= tc_nat ) ),
inference(simp,[status(thm)],[1284]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(888,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(425,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(97,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(513,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(258,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(856,plain,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
inference(lifteq,[status(thm)],[411]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(240,axiom,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(819,plain,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_Ousum @ B @ E @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
thf(904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_Ousum @ B @ E @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(252,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(843,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(205,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(743,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
thf(579,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(114,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(545,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
thf(413,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(244,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(391,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(74,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
thf(466,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
inference(lifteq,[status(thm)],[334]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(804,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
thf(540,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
thf(672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ B @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ B @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(713,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(90,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(498,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(784,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(53,axiom,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
thf(419,plain,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(281,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(900,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( sk1 @ A @ B @ ( c_List_Olist_OCons @ C @ A @ B ) )
= C ),
introduced(tautology,[new_symbols(inverse(c_List_Olist_OCons),[sk1])]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(434,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(276,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(890,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(81,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
thf(477,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(88,axiom,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(494,plain,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(22,axiom,
! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(345,plain,
! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[321]) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ) ),
inference(lifteq,[status(thm)],[322]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(101,axiom,
class_Orderings_Oord @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(520,plain,
class_Orderings_Oord @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(769,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(71,axiom,
class_Finite__Set_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
thf(462,plain,
class_Finite__Set_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(148,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(626,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1208,plain,
! [A: $i] :
( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[370,303]) ).
thf(1210,plain,
! [A: $i] :
( ( c_0 != v_m )
| ( A != v_n )
| ( ( tc_set @ ( tc_set @ t_a ) )
!= tc_nat ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1213,plain,
( ( c_0 != v_m )
| ( ( tc_set @ ( tc_set @ t_a ) )
!= tc_nat ) ),
inference(simp,[status(thm)],[1210]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(158,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(653,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(912,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(173,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(685,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_sum @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
thf(521,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_sum @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
thf(695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(41,axiom,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(394,plain,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(78,axiom,
class_Orderings_Olinorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(473,plain,
class_Orderings_Olinorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(195,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
thf(722,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
thf(675,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ousum @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(795,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(237,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(812,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(156,axiom,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
thf(648,plain,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(617,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(99,axiom,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(516,plain,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(262,axiom,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(864,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1465,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
!= ( c_in @ B @ c_emptyset @ C ) ),
inference(paramod_ordered,[status(thm)],[864,928]) ).
thf(1468,plain,
! [C: $i,B: $i,A: $i] :
( ( c_emptyset != B )
| ( c_Finite__Set_OFinites != c_emptyset )
| ( ( tc_set @ A )
!= C ) ),
inference(simp,[status(thm)],[1465]) ).
thf(1472,plain,
c_Finite__Set_OFinites != c_emptyset,
inference(simp,[status(thm)],[1468]) ).
thf(69,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(458,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(242,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(823,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(2772,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[843,303]) ).
thf(2780,plain,
! [B: $i,A: $i] :
( ( A != v_m )
| ( A != v_n )
| ( ( tc_set @ B )
!= ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[2772]) ).
thf(2788,plain,
! [A: $i] :
( ( v_n != v_m )
| ( ( tc_set @ A )
!= ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[2780]) ).
thf(2842,plain,
! [A: $i] :
( ( v_n != v_m )
| ( A
!= ( tc_set @ t_a ) ) ),
inference(simp,[status(thm)],[2788]) ).
thf(2863,plain,
v_n != v_m,
inference(simp,[status(thm)],[2842]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1559,plain,
! [A: $i] :
( ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
!= ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[823,728]) ).
thf(1561,plain,
! [A: $i] :
( ( ( c_SetInterval_OlessThan @ A @ tc_nat )
!= c_UNIV )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_set @ tc_nat )
!= ( tc_set @ tc_nat ) ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1566,plain,
! [A: $i] :
( ( c_SetInterval_OlessThan @ A @ tc_nat )
!= c_UNIV ),
inference(simp,[status(thm)],[1561]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(48,axiom,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(409,plain,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(188,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(712,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(118,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(557,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(191,axiom,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(717,plain,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(92,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(502,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
thf(463,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(336,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[336]) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ B @ A @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[337]) ).
thf(235,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(808,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(113,axiom,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(544,plain,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(129,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(744,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(9,axiom,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(314,plain,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_prod @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_prod @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(73,axiom,
class_Nat_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(465,plain,
class_Nat_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(149,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(627,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
inference(polarity_switch,[status(thm)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[362]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(83,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(482,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(175,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(688,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
thf(495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(217,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(368,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(517,plain,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
inference(lifteq,[status(thm)],[516]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(401,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(731,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(781,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1207,plain,
! [A: $i] :
( ( c_lessequals @ c_0 @ A @ tc_nat )
!= ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[370,302]) ).
thf(1209,plain,
! [A: $i] :
( ( c_0 != v_n )
| ( A != v_m )
| ( ( tc_set @ ( tc_set @ t_a ) )
!= tc_nat ) ),
inference(simp,[status(thm)],[1207]) ).
thf(1212,plain,
( ( c_0 != v_n )
| ( ( tc_set @ ( tc_set @ t_a ) )
!= tc_nat ) ),
inference(simp,[status(thm)],[1209]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(346,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
thf(378,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(432,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(833,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(46,axiom,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(405,plain,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
thf(854,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
thf(422,plain,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
thf(373,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(121,axiom,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(564,plain,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
thf(506,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(358,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(60,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(437,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(245,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(828,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(79,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(474,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(215,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(767,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(51,axiom,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
thf(415,plain,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(56,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(427,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(260,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(860,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(105,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(528,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(155,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(644,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(63,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(442,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(140,axiom,
class_Orderings_Oorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(607,plain,
class_Orderings_Oorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(624,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[330]) ).
thf(332,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[331]) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( class_Nat_Opower @ c_List_Olist_ONil )
| ( A != tc_nat ) ),
inference(paramod_ordered,[status(thm)],[313,465]) ).
thf(1027,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ tc_nat @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( class_Nat_Opower @ c_List_Olist_ONil ) ),
inference(pattern_uni,[status(thm)],[1026:[bind(A,$thf( tc_nat ))]]) ).
thf(1129,plain,
! [A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ tc_nat @ ( tc_List_Olist @ A ) ) @ tc_nat )
| ( class_Nat_Opower @ c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[1027]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
thf(775,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(272,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(882,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(940,plain,
( ( c_UNIV != v_n )
| ( ( c_Zorn_OTFin @ v_S @ t_a )
!= c_Finite__Set_OFinites )
| ( ( tc_set @ t_a )
!= tc_nat ) ),
inference(simp,[status(thm)],[937]) ).
thf(7,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(309,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(659,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(592,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(99240,plain,
$false,
inference(cvc4,[status(thm)],[629,760,2336,479,846,893,518,468,909,333,777,555,308,741,873,523,762,440,655,384,1137,550,500,797,715,814,747,538,670,829,782,709,301,320,651,389,838,751,357,949,802,344,542,460,638,2403,325,448,2829,817,902,881,416,924,789,591,321,623,1136,514,937,2291,806,353,602,877,453,411,428,849,527,307,920,678,529,793,925,810,381,1470,534,2249,302,598,820,561,693,729,862,349,879,852,665,757,682,551,710,324,566,484,361,2670,697,2515,317,725,1540,869,857,403,1498,356,2537,1493,884,488,339,933,554,537,642,489,590,679,547,328,471,686,476,622,1588,701,721,569,779,371,503,938,311,657,765,2189,773,1286,398,662,718,888,906,298,425,513,824,856,573,689,1135,412,375,733,819,904,843,743,579,545,413,826,577,391,313,466,335,804,540,672,611,787,713,498,604,831,784,419,303,599,900,406,737,318,509,434,890,477,494,345,323,594,621,520,895,769,668,330,462,626,915,1213,455,608,563,299,438,653,922,912,685,521,636,695,394,306,473,722,675,795,927,812,749,754,836,1134,648,487,617,516,342,1472,458,823,525,2863,705,707,1566,327,739,409,712,557,791,717,502,840,1262,463,338,808,544,585,370,744,336,703,613,600,864,727,386,314,446,876,465,627,450,363,931,482,688,581,495,891,771,368,844,517,319,304,632,401,731,781,588,699,510,667,929,1212,684,346,800,914,378,300,315,432,833,405,854,422,867,865,373,735,564,326,918,506,358,437,828,532,720,897,474,1410,767,886,928,415,728,575,427,860,596,528,644,691,442,871,607,395,624,332,1129,935,775,491,364,882,469,940,309,659,592,2470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET858-1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n007.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 18:42:23 EDT 2023
% 0.16/0.36 % CPUTime :
% 1.02/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.16 % [INFO] Parsing done (264ms).
% 1.61/1.17 % [INFO] Running in sequential loop mode.
% 2.40/1.37 % [INFO] eprover registered as external prover.
% 2.40/1.37 % [INFO] cvc4 registered as external prover.
% 2.40/1.37 % [INFO] Scanning for conjecture ...
% 2.88/1.48 % [INFO] Found a conjecture and 1364 axioms. Running axiom selection ...
% 3.08/1.60 % [INFO] Axiom selection finished. Selected 293 axioms (removed 1071 axioms).
% 3.76/1.71 % [INFO] Problem is propositional (TPTP CNF).
% 3.76/1.72 % [INFO] Type checking passed.
% 3.76/1.73 % [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 ...
% 275.16/53.81 % External prover 'cvc4' found a proof!
% 275.16/53.81 % [INFO] Killing All external provers ...
% 275.16/53.81 % Time passed: 53299ms (effective reasoning time: 52642ms)
% 275.16/53.81 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 275.16/53.82 % Axioms used in derivation (293): 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_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, 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_Set_Osubset__trans_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_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_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_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_Zorn_OTFin__linear__lemma2_0, cls_Set_OUnionE_0, 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
% 275.16/53.82 % No. of inferences in proof: 734
% 275.16/53.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 53299 ms resp. 52642 ms w/o parsing
% 275.63/53.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 275.63/53.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------