TSTP Solution File: LAT276-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT276-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:27:16 EDT 2023
% Result : Unsatisfiable 13.85s 3.92s
% Output : Refutation 14.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 690
% Syntax : Number of formulae : 1236 ( 397 unt; 145 typ; 0 def)
% Number of atoms : 2159 ( 680 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 14526 (1004 ~;1068 |; 0 &;12454 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 364 ( 364 >; 0 *; 0 +; 0 <<)
% Number of symbols : 147 ( 145 usr; 21 con; 0-6 aty)
% Number of variables : 3086 ( 0 ^;3086 !; 0 ?;3086 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_S_type,type,
v_S: $i ).
thf(v_A_type,type,
v_A: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_L_type,type,
v_L: $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_xa_type,type,
v_xa: $i ).
thf(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(v_cl_type,type,
v_cl: $i ).
thf(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Tarski_Olub_type,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(v_r_type,type,
v_r: $i ).
thf(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(v_x_type,type,
v_x: $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__1_type,type,
c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__2_type,type,
c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__1_type,type,
c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__2_type,type,
c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_Orderings_Omin_type,type,
c_Orderings_Omin: $i > $i > $i > $i ).
thf(c_List_Olex_type,type,
c_List_Olex: $i > $i > $i ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_Orderings_Omax_type,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i > $i > $i ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_type,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Finite__Set_OMax_type,type,
c_Finite__Set_OMax: $i > $i > $i ).
thf(class_Nat_Opower_type,type,
class_Nat_Opower: $i > $o ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_type,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(c_Main_Oempty__Union__conv__1_type,type,
c_Main_Oempty__Union__conv__1: $i > $i > $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_type,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_List_Ozip_type,type,
c_List_Ozip: $i > $i > $i > $i > $i ).
thf(c_UNIV_type,type,
c_UNIV: $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Finite__Set_OMin_type,type,
c_Finite__Set_OMin: $i > $i > $i ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(c_Main_OUnion__empty__conv__1_type,type,
c_Main_OUnion__empty__conv__1: $i > $i > $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_type,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Main_OUnionE__1_type,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Tarski_Opotype_Opotype__ext_type,type,
c_Tarski_Opotype_Opotype__ext: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanAtMost_type,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_SetInterval_OatLeast_type,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_Inter_type,type,
c_Inter: $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i ).
thf(c_Wellfounded__Relations_Oless__than_type,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OMax__le__iff__1_type,type,
c_Main_OMax__le__iff__1: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Main_OInter__UNIV__conv__1__1_type,type,
c_Main_OInter__UNIV__conv__1__1: $i > $i > $i ).
thf(c_SetInterval_OgreaterThan_type,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_List_Olexord_type,type,
c_List_Olexord: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_type,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_type,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
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_Ousum_type,type,
c_Datatype__Universe_Ousum: $i > $i > $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_IntDef_Ointrel_type,type,
c_IntDef_Ointrel: $i ).
thf(c_Main_Ofinite__Union__1_type,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OMax__less__iff__1_type,type,
c_Main_OMax__less__iff__1: $i > $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odsum_type,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_Main_OdsumE__3_type,type,
c_Main_OdsumE__3: $i > $i > $i > $i > $i ).
thf(c_Main_OdsumE__4_type,type,
c_Main_OdsumE__4: $i > $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn0_type,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Main_OdsumE__1_type,type,
c_Main_OdsumE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OdsumE__2_type,type,
c_Main_OdsumE__2: $i > $i > $i > $i > $i ).
thf(c_Main_OMin__gr__iff__1_type,type,
c_Main_OMin__gr__iff__1: $i > $i > $i > $i ).
thf(c_Main_OInter__UNIV__conv__2__1_type,type,
c_Main_OInter__UNIV__conv__2__1: $i > $i > $i ).
thf(c_Main_OImageE__1_type,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Datatype__Universe_Odprod_type,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(c_Main_OUnion__iff__1_type,type,
c_Main_OUnion__iff__1: $i > $i > $i > $i ).
thf(c_fst_type,type,
c_fst: $i > $i > $i > $i ).
thf(c_snd_type,type,
c_snd: $i > $i > $i > $i ).
thf(c_Main_OInter__iff__1_type,type,
c_Main_OInter__iff__1: $i > $i > $i > $i ).
thf(c_List_Olenlex_type,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_Main_OInterI__1_type,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_OMin__ge__iff__1_type,type,
c_Main_OMin__ge__iff__1: $i > $i > $i > $i ).
thf(c_Set_Ocontents_type,type,
c_Set_Ocontents: $i > $i > $i ).
thf(c_List_Olistset_type,type,
c_List_Olistset: $i > $i > $i ).
thf(c_IntDef_OInteg_type,type,
c_IntDef_OInteg: $i ).
thf(c_Main_ORangeE__1_type,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_type,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_Wellfounded__Relations_Olex__prod_type,type,
c_Wellfounded__Relations_Olex__prod: $i > $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(v_sko__4mP_type,type,
v_sko__4mP: $i > $i > $i > $i ).
thf(c_Main_Olexord__Nil__left__1_type,type,
c_Main_Olexord__Nil__left__1: $i > $i > $i ).
thf(c_Main_Olexord__Nil__left__2_type,type,
c_Main_Olexord__Nil__left__2: $i > $i > $i ).
thf(c_Tarski_OCompleteLattice_type,type,
c_Tarski_OCompleteLattice: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
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_Relation_Orefl_type,type,
c_Relation_Orefl: $i > $i > $i > $o ).
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_Osurj__pair__1_type,type,
c_Main_Osurj__pair__1: $i > $i > $i > $i ).
thf(c_Main_Osurj__pair__2_type,type,
c_Main_Osurj__pair__2: $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_Main_Oall__not__in__conv__1_type,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_List_Oset__Cons_type,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(c_Main_OIdE__1_type,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_IntDef_OAbs__Integ_type,type,
c_IntDef_OAbs__Integ: $i > $i ).
thf(c_IntDef_ORep__Integ_type,type,
c_IntDef_ORep__Integ: $i > $i ).
thf(c_Main_ODomainE__1_type,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__1__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
thf(1369,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__1__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Datatype__Universe_Odsum @ A @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
= ( c_Datatype__Universe_Ousum @ ( c_Relation_ODomain @ A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Relation_ODomain @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Datatype__Universe_Odsum @ A @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
= ( c_Datatype__Universe_Ousum @ ( c_Relation_ODomain @ A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Relation_ODomain @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(400,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_0) ).
thf(1454,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(253,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(1105,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)],[253]) ).
thf(310,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_1) ).
thf(1237,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)],[310]) ).
thf(164,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ c_emptyset @ A )
= c_Relation_OId ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
thf(893,plain,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ c_emptyset @ A )
= c_Relation_OId ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(341,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(1315,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(8,negated_conjecture,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(555,plain,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(462,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_0) ).
thf(1586,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)],[462]) ).
thf(423,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(1501,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)],[423]) ).
thf(41,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
thf(628,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(58,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(666,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
| ( c_emptyset
= ( c_inter @ B @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
thf(1295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
| ( c_emptyset
= ( c_inter @ B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(18,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( A = D )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
thf(582,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( A = D )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ c_Relation_OId @ B @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
thf(1005,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ c_Relation_OId @ B @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(378,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_0) ).
thf(1401,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)],[378]) ).
thf(444,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(1544,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)],[444]) ).
thf(530,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(1728,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)],[530]) ).
thf(439,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olexord__Nil__left__1 @ A @ B ) @ ( c_Main_Olexord__Nil__left__2 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
thf(1533,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olexord__Nil__left__1 @ A @ B ) @ ( c_Main_Olexord__Nil__left__2 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(64,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
thf(677,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(336,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(1305,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(393,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(1437,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
thf(1173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(466,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(1596,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)],[466]) ).
thf(380,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(1406,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)],[380]) ).
thf(269,axiom,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(1142,plain,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(322,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(1269,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)],[322]) ).
thf(421,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(1497,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)],[421]) ).
thf(389,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(502,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_1) ).
thf(1671,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)],[502]) ).
thf(544,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_0) ).
thf(1756,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)],[544]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_L @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_x @ A ) @ v_S @ t_a )
| ~ ( c_in @ A @ v_A @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(550,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_L @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_x @ A ) @ v_S @ t_a )
| ~ ( c_in @ A @ v_A @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(533,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__1_0) ).
thf(1735,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(308,axiom,
! [A: $i] :
( ( c_Union @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
thf(1233,plain,
! [A: $i] :
( ( c_Union @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(126,axiom,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(814,plain,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(73,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(698,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(249,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_0) ).
thf(1095,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)],[249]) ).
thf(210,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(1001,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(457,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(1576,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)],[457]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( c_Pair @ ( c_Main_Osurj__pair__1 @ A @ B @ C ) @ ( c_Main_Osurj__pair__2 @ A @ B @ C ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( c_Pair @ ( c_Main_Osurj__pair__1 @ A @ B @ C ) @ ( c_Main_Osurj__pair__2 @ A @ B @ C ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(490,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_1) ).
thf(1645,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)],[490]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
thf(1529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(539,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
thf(1746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(167,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_1) ).
thf(898,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)],[167]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( c_inter @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
thf(782,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
thf(1441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(528,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_0) ).
thf(1724,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)],[528]) ).
thf(410,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(1475,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)],[410]) ).
thf(432,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
thf(1518,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(518,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(1703,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)],[518]) ).
thf(306,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_OUn__iff_0) ).
thf(1228,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)],[306]) ).
thf(479,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(1623,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)],[479]) ).
thf(85,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_1) ).
thf(724,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)],[85]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OIn0 @ ( c_Main_OdsumE__1 @ B @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ B @ A @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ C @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ C @ A @ 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_OdsumE_0) ).
thf(1298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OIn0 @ ( c_Main_OdsumE__1 @ B @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ B @ A @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ C @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ C @ A @ 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)],[333]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(719,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
thf(587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
thf(1323,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
thf(1462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(265,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(1132,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)],[265]) ).
thf(45,axiom,
class_Orderings_Olinorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(638,plain,
class_Orderings_Olinorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_inter @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_inter @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
thf(870,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
| ( c_emptyset
= ( c_inter @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
thf(1115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
| ( c_emptyset
= ( c_inter @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(454,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(1568,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)],[454]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
thf(1641,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(430,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_OCompl__iff_1) ).
thf(1514,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)],[430]) ).
thf(412,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_0) ).
thf(1479,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)],[412]) ).
thf(472,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_0) ).
thf(1609,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)],[472]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(456,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_0) ).
thf(1572,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)],[456]) ).
thf(536,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(1741,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
= ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(881,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
= ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(924,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(405,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
thf(1465,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(484,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
thf(1632,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_Suc @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
thf(646,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_Suc @ B ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Datatype__Universe_Odprod @ A @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
= ( c_Datatype__Universe_Ouprod @ ( c_Relation_ODomain @ A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Relation_ODomain @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Datatype__Universe_Odprod @ A @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
= ( c_Datatype__Universe_Ouprod @ ( c_Relation_ODomain @ A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Relation_ODomain @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(505,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_ODiff__iff_1) ).
thf(1677,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)],[505]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ c_0 @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ c_0 @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(196,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_1) ).
thf(966,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)],[196]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ A @ B ) @ C @ B @ B )
= ( c_inter @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ A @ B ) @ C @ B @ B )
= ( c_inter @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(417,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(1489,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)],[417]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(1415,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
thf(1418,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(38,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_0) ).
thf(623,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)],[38]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
= ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
thf(1136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
= ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
thf(834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(370,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(1383,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)],[370]) ).
thf(15,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(574,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
thf(687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(157,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
!= ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
| ( A = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_0) ).
thf(877,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
!= ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
| ( A = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(89,axiom,
! [A: $i] :
( ( c_SetInterval_OatLeastLessThan @ A @ ( c_Suc @ A ) @ tc_nat )
= ( c_insert @ A @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
thf(734,plain,
! [A: $i] :
( ( c_SetInterval_OatLeastLessThan @ A @ ( c_Suc @ A ) @ tc_nat )
= ( c_insert @ A @ c_emptyset @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_union @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_union @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( ( c_minus @ B @ ( c_insert @ A @ D @ C ) @ ( tc_set @ C ) )
= ( c_minus @ B @ D @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
thf(1394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( ( c_minus @ B @ ( c_insert @ A @ D @ C ) @ ( tc_set @ C ) )
= ( c_minus @ B @ D @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(209,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(998,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)],[209]) ).
thf(354,axiom,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(1345,plain,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(468,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(1600,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)],[468]) ).
thf(515,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ~ ( c_in @ B @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_IntDef_OAbs__Integ @ B )
!= ( c_IntDef_OAbs__Integ @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
thf(1697,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ~ ( c_in @ B @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_IntDef_OAbs__Integ @ B )
!= ( c_IntDef_OAbs__Integ @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(433,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_2) ).
thf(1521,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)],[433]) ).
thf(28,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_1) ).
thf(602,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)],[28]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= ( c_Relation_Odiag @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
thf(981,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= ( c_Relation_Odiag @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(1651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(240,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(1074,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(297,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(1206,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(185,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_0) ).
thf(942,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)],[185]) ).
thf(512,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_0) ).
thf(1691,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)],[512]) ).
thf(56,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
thf(661,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(5,negated_conjecture,
( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(546,plain,
( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
thf(1199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(124,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(810,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(520,axiom,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(1708,plain,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(339,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(1311,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(1636,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
thf(761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(531,axiom,
! [A: $i] :
( ~ ( c_in @ A @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_IntDef_ORep__Integ @ ( c_IntDef_OAbs__Integ @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
thf(1730,plain,
! [A: $i] :
( ~ ( c_in @ A @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_IntDef_ORep__Integ @ ( c_IntDef_OAbs__Integ @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
thf(798,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(278,axiom,
! [A: $i] :
( ( c_Relation_ODomain @ c_Relation_OId @ A @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
thf(1163,plain,
! [A: $i] :
( ( c_Relation_ODomain @ c_Relation_OId @ A @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ c_List_Olist_ONil @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ c_List_Olist_ONil @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ B @ D @ A )
| ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
thf(746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ B @ D @ A )
| ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(132,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(825,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(459,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
thf(1580,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(129,axiom,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(820,plain,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(500,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
= ( c_List_Olist_OCons @ ( c_Pair @ A @ D @ C @ F ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
thf(1666,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
= ( c_List_Olist_OCons @ ( c_Pair @ A @ D @ C @ F ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(416,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OdsumE__1 @ B @ A @ D @ E ) @ ( c_Main_OdsumE__2 @ B @ A @ 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 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ C @ A @ D @ E ) @ ( c_Main_OdsumE__4 @ C @ A @ 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_OdsumE_3) ).
thf(1487,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OdsumE__1 @ B @ A @ D @ E ) @ ( c_Main_OdsumE__2 @ B @ A @ 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 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ C @ A @ D @ E ) @ ( c_Main_OdsumE__4 @ C @ A @ 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)],[416]) ).
thf(477,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_1) ).
thf(1619,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)],[477]) ).
thf(87,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_0) ).
thf(729,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)],[87]) ).
thf(372,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
thf(910,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(218,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_OInt__iff_2) ).
thf(1021,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)],[218]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(261,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_OUn__iff_1) ).
thf(1123,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)],[261]) ).
thf(150,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(862,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)],[150]) ).
thf(455,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_1) ).
thf(1570,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)],[455]) ).
thf(504,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(1676,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(71,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ E @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
thf(693,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ E @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
thf(630,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(388,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_0) ).
thf(1423,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)],[388]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(916,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ c_UNIV @ B )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_UNIV @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( c_Orderings_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omax @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
thf(625,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omax @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(449,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(1555,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)],[449]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ C )
= ( c_union @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ C )
= ( c_union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_fst @ ( c_Pair @ A @ B @ C @ D ) @ C @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
thf(1687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_fst @ ( c_Pair @ A @ B @ C @ D ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_UNIV @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
thf(1210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(2,negated_conjecture,
c_in @ v_L @ v_A @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(551,plain,
c_in @ v_L @ v_A @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(140,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(842,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)],[140]) ).
thf(199,axiom,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(974,plain,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(143,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(847,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)],[143]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(566,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ c_Relation_OId @ A @ B @ B @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ c_Relation_OId @ A @ B @ B @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(66,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
thf(682,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(485,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_0) ).
thf(1634,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)],[485]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(464,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ A @ B @ v_r ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
thf(1592,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ A @ B @ v_r ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(34,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(615,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Pair @ ( c_fst @ A @ B @ C ) @ ( c_snd @ A @ B @ C ) @ B @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Pair @ ( c_fst @ A @ B @ C ) @ ( c_snd @ A @ B @ C ) @ B @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(260,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_0) ).
thf(1121,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)],[260]) ).
thf(256,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_1) ).
thf(1111,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)],[256]) ).
thf(442,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(259,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_0) ).
thf(1118,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)],[259]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_minus @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) )
= ( c_minus @ D @ B @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_minus @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) )
= ( c_minus @ D @ B @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(359,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_2) ).
thf(1360,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)],[359]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
!= c_emptyset )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(1350,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
!= c_emptyset )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(270,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_0) ).
thf(1143,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)],[270]) ).
thf(52,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(650,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
thf(948,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatMost @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(268,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
!= ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
| ( B = G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_1) ).
thf(1138,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
!= ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
| ( B = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(526,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(1719,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)],[526]) ).
thf(419,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_1) ).
thf(1493,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)],[419]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
thf(884,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(497,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_1) ).
thf(1659,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)],[497]) ).
thf(331,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_0) ).
thf(1292,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)],[331]) ).
thf(286,axiom,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(1182,plain,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
thf(1739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(60,axiom,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(669,plain,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(168,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_1) ).
thf(901,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)],[168]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
thf(1584,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInter__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(516,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ C @ D )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
thf(1700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ C @ D )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(397,axiom,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(1446,plain,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(77,axiom,
! [A: $i] :
( ( c_Orderings_Omin @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
thf(706,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(11,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(554,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_plus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_plus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ A @ C )
| ( c_emptyset
= ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ A @ C )
| ( c_emptyset
= ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(22,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_0) ).
thf(590,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
thf(679,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
thf(1039,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(197,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_0) ).
thf(970,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)],[197]) ).
thf(10,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_L @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ ( v_x @ A ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_A @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(547,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_L @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ ( v_x @ A ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_A @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(538,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(1744,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)],[538]) ).
thf(137,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(837,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)],[137]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ A @ C )
| ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
thf(1456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ A @ C )
| ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(501,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(1668,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)],[501]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ c_List_Olist_ONil @ A @ B @ C )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ c_List_Olist_ONil @ A @ B @ C )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
thf(1060,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
thf(721,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
thf(1002,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OlessThan @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( D
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(569,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( D
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(524,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(1715,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
thf(605,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
thf(1451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(91,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(738,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(481,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_1) ).
thf(1627,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)],[481]) ).
thf(435,axiom,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(1525,plain,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(116,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_0) ).
thf(792,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)],[116]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
thf(633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(514,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_1) ).
thf(1695,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)],[514]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(281,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_Oinsert__iff_0) ).
thf(1170,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)],[281]) ).
thf(329,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_0) ).
thf(1286,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)],[329]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
thf(1466,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(499,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(178,axiom,
! [A: $i] :
( ( c_Inter @ c_emptyset @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
thf(926,plain,
! [A: $i] :
( ( c_Inter @ c_emptyset @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(107,axiom,
class_Orderings_Oorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(773,plain,
class_Orderings_Oorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(117,axiom,
! [A: $i] :
( ( c_Orderings_Omin @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
thf(794,plain,
! [A: $i] :
( ( c_Orderings_Omin @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(82,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(718,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)],[82]) ).
thf(162,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_0) ).
thf(888,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)],[162]) ).
thf(428,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_0) ).
thf(1510,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)],[428]) ).
thf(543,axiom,
! [F: $i,E: $i,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 @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
thf(1754,plain,
! [F: $i,E: $i,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 @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(507,axiom,
c_in @ v_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
thf(1680,plain,
c_in @ v_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(252,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_OInt__iff_1) ).
thf(1103,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)],[252]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__right_0) ).
thf(1219,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
thf(1483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(1548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_inter @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
thf(856,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_inter @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( c_Orderings_Omin @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omin @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
thf(689,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Omin @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omin @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ A @ ( c_plus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ A @ ( c_plus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(483,axiom,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(1631,plain,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(315,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_OUn__iff_2) ).
thf(1251,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)],[315]) ).
thf(36,axiom,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(618,plain,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(169,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(904,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)],[169]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(475,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_1) ).
thf(1615,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)],[475]) ).
thf(542,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(1752,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)],[542]) ).
thf(93,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_0) ).
thf(743,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_List_Olistrel @ A @ B ) @ ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
thf(958,plain,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_List_Olistrel @ A @ B ) @ ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(141,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(843,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(262,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_0) ).
thf(1125,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)],[262]) ).
thf(133,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(826,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)],[133]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(711,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
thf(1226,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(424,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(1503,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)],[424]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(14,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
thf(572,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
thf(1312,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(80,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_0) ).
thf(713,plain,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(532,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_1) ).
thf(1733,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)],[532]) ).
thf(254,axiom,
class_Orderings_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(1107,plain,
class_Orderings_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ C @ tc_nat )
= ( c_minus @ ( c_Suc @ B ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
thf(1332,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ C @ tc_nat )
= ( c_minus @ ( c_Suc @ B ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(247,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(1092,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(246,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_1) ).
thf(1090,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)],[246]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(1224,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(358,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_0) ).
thf(1356,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)],[358]) ).
thf(47,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_1) ).
thf(641,plain,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(390,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_0) ).
thf(1428,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)],[390]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
thf(611,plain,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(291,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(1194,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)],[291]) ).
thf(381,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(1408,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)],[381]) ).
thf(327,axiom,
! [A: $i] :
( ( c_Relation_Odiag @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
thf(1282,plain,
! [A: $i] :
( ( c_Relation_Odiag @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(113,axiom,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(784,plain,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(90,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ tc_nat )
= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
thf(736,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ tc_nat )
= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(469,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_1) ).
thf(1603,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)],[469]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(1542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(527,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_OUnion__iff_2) ).
thf(1722,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)],[527]) ).
thf(35,axiom,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(616,plain,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
thf(1307,plain,
! [B: $i,A: $i] :
( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_union @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_inter @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
thf(863,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_union @ A @ B @ C ) @ ( tc_set @ C ) )
= ( c_inter @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(103,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(764,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(201,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_OInt__iff_0) ).
thf(979,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)],[201]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ D @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_plus @ A @ D @ tc_nat )
= ( c_plus @ C @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
thf(1589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ D @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_plus @ A @ D @ tc_nat )
= ( c_plus @ C @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(208,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_Oinsert__iff_2) ).
thf(996,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)],[208]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oempty__Union__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oempty__Union__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(394,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(1439,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(408,axiom,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
thf(1471,plain,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(31,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
thf(609,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
thf(848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(1325,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(353,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(1344,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(369,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(1381,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)],[369]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__1__1 @ A @ B )
!= c_UNIV )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__1__1 @ A @ B )
!= c_UNIV )
| ( ( c_Inter @ A @ B )
= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(148,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_1) ).
thf(858,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)],[148]) ).
thf(7,negated_conjecture,
( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(552,plain,
( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(165,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(895,plain,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(195,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_0) ).
thf(964,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)],[195]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ozip @ A @ B @ C @ D ) @ ( tc_List_Olist @ ( tc_prod @ C @ D ) ) )
= ( c_Orderings_Omin @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
thf(769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ozip @ A @ B @ C @ D ) @ ( tc_List_Olist @ ( tc_prod @ C @ D ) ) )
= ( c_Orderings_Omin @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(403,axiom,
! [A: $i] :
( ( c_List_Olistset @ c_List_Olist_ONil @ A )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
thf(1460,plain,
! [A: $i] :
( ( c_List_Olistset @ c_List_Olist_ONil @ A )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(203,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(983,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)],[203]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Arefl_A_Ipset_Acl1_J_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(1594,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ ( c_plus @ B @ C @ tc_nat ) @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ ( c_plus @ B @ C @ tc_nat ) @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(159,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(883,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)],[159]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_UNIV @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_UNIV @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
thf(986,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
thf(1435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(411,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_0) ).
thf(1477,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)],[411]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
thf(851,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
thf(653,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
thf(685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
thf(1044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
thf(695,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_minus @ ( c_SetInterval_OatLeastLessThan @ B @ D @ A ) @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
thf(1245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_minus @ ( c_SetInterval_OatLeastLessThan @ B @ D @ A ) @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( B = c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
thf(1066,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_UNIV )
| ( B = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(153,axiom,
! [A: $i] :
( ( c_Inter @ c_UNIV @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
thf(868,plain,
! [A: $i] :
( ( c_Inter @ c_UNIV @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(111,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_1) ).
thf(780,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)],[111]) ).
thf(489,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_2) ).
thf(1643,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)],[489]) ).
thf(529,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(1726,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)],[529]) ).
thf(361,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(1364,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)],[361]) ).
thf(224,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_1) ).
thf(1034,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)],[224]) ).
thf(545,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(1758,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)],[545]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ tc_nat )
= ( c_minus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(325,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_0) ).
thf(1277,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(184,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
| ~ ( c_less @ A @ ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Ozip @ D @ B @ E @ C ) @ A @ ( tc_prod @ E @ C ) )
= ( c_Pair @ ( c_List_Onth @ D @ A @ E ) @ ( c_List_Onth @ B @ A @ C ) @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
| ~ ( c_less @ A @ ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Ozip @ D @ B @ E @ C ) @ A @ ( tc_prod @ E @ C ) )
= ( c_Pair @ ( c_List_Onth @ D @ A @ E ) @ ( c_List_Onth @ B @ A @ C ) @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(271,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_0) ).
thf(1145,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)],[271]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).
thf(553,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(131,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
thf(823,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(230,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OdsumE__3 @ C @ A @ D @ E ) @ ( c_Main_OdsumE__4 @ C @ A @ 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 ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ B @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ B @ A @ 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_OdsumE_1) ).
thf(1049,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OdsumE__3 @ C @ A @ D @ E ) @ ( c_Main_OdsumE__4 @ C @ A @ 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 ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ B @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ B @ A @ 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)],[230]) ).
thf(384,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
thf(1413,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(1076,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(298,axiom,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
thf(1208,plain,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(21,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(589,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)],[21]) ).
thf(57,axiom,
! [A: $i] :
( ~ ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_1) ).
thf(663,plain,
! [A: $i] :
( ~ ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1,negated_conjecture,
c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(548,plain,
c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(266,axiom,
! [A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_2) ).
thf(1134,plain,
! [A: $i] :
( ( c_inter @ c_UNIV @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(51,axiom,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(648,plain,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(220,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(1025,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)],[220]) ).
thf(155,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_1) ).
thf(872,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)],[155]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
thf(1605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(491,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_1) ).
thf(1647,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)],[491]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( c_union @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
thf(1267,plain,
! [B: $i,A: $i] :
( ( c_union @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(438,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_ODiff__iff_0) ).
thf(1531,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)],[438]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ B @ C )
| ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
thf(1230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ B @ C )
| ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ B @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(776,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ B @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(540,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
thf(1748,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(431,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_0) ).
thf(1516,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)],[431]) ).
thf(467,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_OInter__iff_0) ).
thf(1598,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)],[467]) ).
thf(473,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(1611,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)],[473]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(391,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
thf(1432,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(289,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_0) ).
thf(1188,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)],[289]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
thf(585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
thf(840,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(16,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_0) ).
thf(576,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(506,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_Opair__in__Id__conv_1) ).
thf(1679,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)],[506]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(522,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(1711,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)],[522]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(1499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
thf(1262,plain,
! [C: $i,B: $i,A: $i] :
( ( c_uminus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( tc_set @ C ) )
= ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(309,axiom,
! [A: $i] :
( ( c_Relation_Oconverse @ c_Relation_OId @ A @ A )
= c_Relation_OId ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
thf(1235,plain,
! [A: $i] :
( ( c_Relation_Oconverse @ c_Relation_OId @ A @ A )
= c_Relation_OId ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(1538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(189,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(951,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)],[189]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
thf(808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_emptyset
!= ( c_Union @ B @ C ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_emptyset
!= ( c_Union @ B @ C ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(48,axiom,
class_Nat_Opower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(643,plain,
class_Nat_Opower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(76,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
thf(703,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(440,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__2_0) ).
thf(1536,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(517,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(1702,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)],[517]) ).
thf(33,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(613,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(541,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ D @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
thf(1749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ D @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(525,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_0) ).
thf(1717,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)],[525]) ).
thf(323,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OdsumE__1 @ B @ A @ D @ E ) @ ( c_Main_OdsumE__2 @ B @ A @ 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 ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ C @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ C @ A @ 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_OdsumE_2) ).
thf(1272,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odsum @ 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_OdsumE__1 @ B @ A @ D @ E ) @ ( c_Main_OdsumE__2 @ B @ A @ 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 ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ C @ A @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ C @ A @ 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)],[323]) ).
thf(476,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(1617,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)],[476]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(219,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_0) ).
thf(1023,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)],[219]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__2__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OInter__UNIV__conv__2__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ A @ c_emptyset @ C ) @ ( tc_set @ C ) ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ A @ c_emptyset @ C ) @ ( tc_set @ C ) ) @ C )
= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatMost @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OgreaterThan @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
thf(1353,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OatMost @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OgreaterThan @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(600,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_union @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_union @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(426,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(1506,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)],[426]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
thf(1372,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(24,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(595,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ c_Relation_OId @ A @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
thf(1421,plain,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ c_Relation_OId @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(40,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(627,plain,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(402,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(1459,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(285,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(1180,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)],[285]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(556,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(509,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(1685,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)],[509]) ).
thf(448,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(1553,plain,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(61,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) )
!= ( c_Nat_Osize @ F @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
thf(671,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) )
!= ( c_Nat_Osize @ F @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(200,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_0) ).
thf(976,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)],[200]) ).
thf(100,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(759,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)],[100]) ).
thf(398,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_0) ).
thf(1448,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)],[398]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(1289,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(106,axiom,
! [A: $i] :
( ( c_List_Olists @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
thf(771,plain,
! [A: $i] :
( ( c_List_Olists @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__2__1 @ A @ B )
!= c_UNIV )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OInter__UNIV__conv__2__1 @ A @ B )
!= c_UNIV )
| ( c_UNIV
= ( c_Inter @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(492,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(1649,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)],[492]) ).
thf(244,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_0) ).
thf(1084,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)],[244]) ).
thf(495,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(1654,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)],[495]) ).
thf(383,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(1412,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ B @ tc_nat ) @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
thf(1216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ B @ tc_nat ) @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
thf(891,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ A @ c_List_Olist_ONil @ B @ C )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ A @ c_List_Olist_ONil @ B @ C )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(487,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(1639,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(413,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_1) ).
thf(1481,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)],[413]) ).
thf(187,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_1) ).
thf(946,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)],[187]) ).
thf(482,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(1629,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)],[482]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ A @ B @ v_r ) @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(1523,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ A @ B @ v_r ) @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
thf(731,plain,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(450,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(1558,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)],[450]) ).
thf(316,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_2) ).
thf(1253,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)],[316]) ).
thf(74,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_1) ).
thf(699,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)],[74]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
thf(961,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(371,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_1) ).
thf(1385,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)],[371]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeast @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_uminus @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_SetInterval_OatLeast @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ C @ A @ B )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
thf(748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ C @ A @ B )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(235,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_0) ).
thf(1062,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)],[235]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(418,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(1491,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)],[418]) ).
thf(511,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_ODiff__iff_2) ).
thf(1689,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)],[511]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( c_union @ c_UNIV @ A @ B )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( c_union @ c_UNIV @ A @ B )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_minus @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
thf(667,plain,
! [B: $i,A: $i] :
( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_minus @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
thf(1706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(498,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(1661,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)],[498]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(338,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(1309,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)],[338]) ).
thf(471,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(1607,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)],[471]) ).
thf(102,axiom,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(763,plain,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(6,negated_conjecture,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(549,plain,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ v_xa @ v_S @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(396,axiom,
! [A: $i] :
( ( c_Relation_ORange @ c_Relation_OId @ A @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
thf(1444,plain,
! [A: $i] :
( ( c_Relation_ORange @ c_Relation_OId @ A @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(277,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_0) ).
thf(1161,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(37,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_1) ).
thf(620,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(429,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(1512,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)],[429]) ).
thf(458,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(1578,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)],[458]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
thf(1546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(480,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(1625,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)],[480]) ).
thf(128,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(818,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)],[128]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ B @ C )
| ( c_emptyset
= ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ B @ C )
| ( c_emptyset
= ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(146,axiom,
( ( c_SetInterval_OatLeast @ c_0 @ tc_nat )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
thf(854,plain,
( ( c_SetInterval_OatLeast @ c_0 @ tc_nat )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(335,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(1303,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)],[335]) ).
thf(436,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_0) ).
thf(1527,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)],[436]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_UNIV
!= ( c_Inter @ B @ C ) )
| ( A = c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
thf(1673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_UNIV
!= ( c_Inter @ B @ C ) )
| ( A = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_minus @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
thf(790,plain,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_minus @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(360,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1363,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(420,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
thf(1495,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(496,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(1657,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)],[496]) ).
thf(451,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_0) ).
thf(1561,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)],[451]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(134,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
!= ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
| ( C = H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_2) ).
thf(828,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
!= ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
| ( C = H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(236,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(1065,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)],[236]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_less @ D @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
thf(1165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_less @ D @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(349,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(1335,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)],[349]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_snd @ ( c_Pair @ A @ B @ C @ D ) @ C @ D )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
thf(1693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_snd @ ( c_Pair @ A @ B @ C @ D ) @ C @ D )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(382,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_0) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
thf(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(193,axiom,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(960,plain,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(635,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
thf(1473,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(537,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(92,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_0) ).
thf(740,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)],[92]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(149,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
thf(860,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(25,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_2) ).
thf(596,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)],[25]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
thf(992,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(523,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Tarski_Olub @ A @ v_cl @ t_a ) @ v_A @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0) ).
thf(1713,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Tarski_Olub @ A @ v_cl @ t_a ) @ v_A @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(70,axiom,
( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
thf(691,plain,
( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(30,axiom,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(607,plain,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(248,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_0) ).
thf(1093,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)],[248]) ).
thf(138,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(839,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)],[138]) ).
thf(460,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_OCompl__iff_0) ).
thf(1582,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)],[460]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
thf(1019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olists @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_List_Olists @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
thf(644,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olists @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_List_Olists @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(447,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(1550,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)],[447]) ).
thf(425,axiom,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(1505,plain,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(377,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_2) ).
thf(1399,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)],[377]) ).
thf(478,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(1621,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)],[478]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ A @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ A @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(182,axiom,
class_Nat_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(935,plain,
class_Nat_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(534,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_0) ).
thf(1737,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)],[534]) ).
thf(46,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_0) ).
thf(639,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)],[46]) ).
thf(407,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_1) ).
thf(1468,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)],[407]) ).
thf(238,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_0) ).
thf(1069,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)],[238]) ).
thf(78,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_0) ).
thf(708,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)],[78]) ).
thf(198,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(972,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)],[198]) ).
thf(494,axiom,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(1653,plain,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ c_emptyset @ B @ C )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
thf(1367,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ c_emptyset @ B @ C )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(508,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_1) ).
thf(1681,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)],[508]) ).
thf(287,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_Oinsert__iff_1) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(55,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(659,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Inter @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Inter @ B @ C )
!= c_UNIV )
| ( A = c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(98,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
thf(755,plain,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(63,axiom,
class_Orderings_Oord @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(676,plain,
class_Orderings_Oord @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1828,plain,
$false,
inference(cvc4,[status(thm)],[1036,1369,1168,1454,1105,1237,893,1315,555,1586,1501,628,1031,666,1295,582,1005,994,1401,1544,1728,1533,677,1305,1437,1173,1596,1406,1142,1269,1497,1426,1671,1756,550,1735,1275,1233,814,698,930,1095,1001,1576,1613,1645,1529,1746,898,1243,1127,782,1441,1724,1475,1518,1703,1228,1623,724,1709,1298,719,751,1279,1330,1264,587,1323,1462,1132,638,1379,870,1013,1115,1568,1641,1100,1087,1514,1479,1609,1347,1572,1741,881,924,1465,1632,646,1151,1677,806,966,821,1489,1415,1418,623,1136,834,1383,574,687,877,734,1072,774,1394,998,1345,1201,1600,1697,1521,602,981,1651,1074,1206,942,1691,661,546,1199,810,1708,1311,1636,1153,761,1047,1730,798,1057,1163,957,746,825,1042,1580,598,820,1666,1487,1619,729,1387,910,1021,778,1123,862,1570,1676,693,630,1423,916,1365,625,1555,1178,1687,1159,1210,757,551,842,974,847,566,1079,1027,682,1195,1634,1392,1592,1259,615,1328,1121,1111,1540,593,1118,989,1397,1360,1350,874,1143,650,948,1138,1719,1493,884,1659,1292,1182,1739,669,901,1584,1700,1446,706,554,753,1016,590,679,1039,970,547,1744,837,701,1456,1668,1192,1060,721,1002,569,1715,605,1451,738,1627,1525,1318,792,1241,633,1695,1563,1054,1170,1286,1466,674,1663,1185,926,773,794,718,888,1510,1754,1680,1103,1219,1483,1548,856,1301,689,1374,1631,1251,618,904,1007,1615,1752,743,958,843,1125,826,711,1256,1226,1503,936,572,1312,713,1733,1107,1332,1092,1090,919,1224,1356,641,1428,611,787,1194,1408,1282,784,736,1603,1542,1722,616,1307,863,764,979,1589,996,1376,1439,1471,1339,816,609,726,848,1325,1344,1381,932,858,552,1029,895,1149,964,769,1460,983,1594,1213,883,1176,986,1113,1435,1477,851,653,922,912,685,1044,695,1245,1066,868,780,1643,1726,1364,1034,1758,944,1277,812,1081,939,1145,553,823,1049,1413,1076,1203,1208,589,663,548,1134,648,580,1025,872,1605,1647,954,1267,1531,1230,776,1748,1516,1598,1611,1156,1432,1188,585,840,576,1679,907,1711,1499,1262,1235,1538,951,808,1336,643,1404,703,1536,1702,613,1749,1717,1272,1617,656,1023,1221,1284,1353,600,1485,1052,1506,1372,595,845,1421,627,1459,1180,556,1685,1553,671,976,759,1448,1289,771,1108,1649,1084,1654,1412,1216,891,1010,1390,1639,1481,946,1629,1523,731,1558,1253,699,961,1385,1341,896,748,1062,1508,1491,1689,914,667,1706,1661,832,1309,1607,763,549,1444,716,1161,620,1512,1578,1097,1546,1625,818,865,854,1303,1527,1673,1248,790,801,1363,1495,1657,1561,1197,828,1065,1165,796,1335,1693,1410,767,960,635,1473,886,1742,928,740,1129,860,596,992,1713,691,607,1093,839,1582,1019,644,1550,1505,1399,1621,803,1320,935,1737,639,1468,1069,708,972,1653,1367,1681,1184,659,1565,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT276-1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 14:38:41 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.86/1.15 % [INFO] Parsing done (302ms).
% 1.86/1.16 % [INFO] Running in sequential loop mode.
% 2.56/1.37 % [INFO] eprover registered as external prover.
% 2.56/1.37 % [INFO] cvc4 registered as external prover.
% 2.56/1.37 % [INFO] Scanning for conjecture ...
% 3.28/1.55 % [INFO] Found a conjecture and 2746 axioms. Running axiom selection ...
% 4.42/1.80 % [INFO] Axiom selection finished. Selected 534 axioms (removed 2212 axioms).
% 4.78/1.94 % [INFO] Problem is propositional (TPTP CNF).
% 4.78/1.95 % [INFO] Type checking passed.
% 4.78/1.95 % [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 ...
% 13.85/3.91 % External prover 'cvc4' found a proof!
% 13.85/3.91 % [INFO] Killing All external provers ...
% 13.85/3.91 % Time passed: 3395ms (effective reasoning time: 2754ms)
% 13.85/3.92 % 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)>
% 13.85/3.92 % Axioms used in derivation (534): cls_List_Olistrel__Cons1_0, cls_Nat_Onot__gr0_0, cls_Nat_Onot__less0_0, cls_Set_OPow__UNIV_0, cls_Relation_ODomain__empty_0, cls_Set_OPow__iff_1, cls_Set_Oempty__Union__conv_1, cls_Set_Oinsert__disjoint__1_1, cls_Datatype__Universe_Ousum__In1I_0, cls_Datatype__Universe_OuprodI_0, cls_Tarski_Opotype_Oselect__convs__2_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_Datatype__Universe_OdprodE_0, cls_Finite__Set_Ofinite__Union_0, cls_Set_OCompl__subset__Compl__iff_1, cls_NatArith_Oadd__diff__assoc2_0, cls_SetInterval_OgreaterThanLessThan__iff_0, cls_Transitive__Closure_Otrancl__range_0, cls_Finite__Set_OMin__gr__iff_2, cls_SetInterval_OgreaterThanAtMost__iff_2, cls_Nat_Onat__add__left__cancel__less_1, cls_Set_Osingleton__insert__inj__eq_0, cls_Datatype__Universe_Odsum__In0I_0, cls_Tarski_Opotype_Oext__inject_1, cls_List_Olists_ONil_0, cls_SetInterval_OatMost__0_0, cls_Finite__Set_OMin__insert_0, cls_List_Onth__zip_0, cls_Relation_OImageI_0, cls_Relation_ODomain__Id_0, cls_Set_OInt__iff_2, cls_List_Olistrel__Cons2_1, cls_Relation_ODomain__diag_0, cls_List_Olexord__cons__cons_2, cls_Nat_Onat__add__right__cancel_0, clsarity_prod_0, cls_List_OCons__in__lex_1, cls_Set_OUNIV__not__empty_0, cls_Relation_ORange__diag_0, cls_Set_OsubsetI_1, cls_Set_ODiff__cancel_0, cls_Wellfounded__Recursion_Owf__insert_0, cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0, clsarity_nat_7, cls_Nat_Odiff__is__0__eq_0, cls_Set_Osubset__UNIV_0, cls_Finite__Set_OMin__singleton_0, cls_Finite__Set_Ocard__infinite_0, cls_Set_Oinsert__Diff1_0, cls_SetInterval_Ocard__atLeastAtMost_0, cls_Product__Type_Ofst__conv_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2, cls_Finite__Set_OFinites_OemptyI_0, cls_Finite__Set_OMax__less__iff_2, cls_Datatype__Universe_OScons__Scons__eq_1, cls_Datatype__Universe_Ousum__In0I_0, clsrel_Orderings_Olinorder_4, cls_SetInterval_OCompl__atLeast_0, cls_SetInterval_OgreaterThan__subset__iff_1, cls_Transitive__Closure_Ortrancl__reflcl_0, cls_Orderings_Oorder__less__irrefl_0, cls_SetInterval_OatLeast__iff_1, cls_Set_Oinsert__disjoint__2_2, cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0, cls_Set_Osingleton__inject__dest_0, cls_Set_OInt__UNIV__left_0, cls_Relation_OImageE_0, cls_Nat_OSuc__Suc__eq_0, cls_Nat_Odiff__0__eq__0_0, cls_Set_OInt__subset__iff_0, cls_List_Olength__0__conv_1, cls_Set_OUnionE_1, cls_Set_OUn__subset__iff_2, cls_Nat_Oless__irrefl_0, cls_Set_OCompl__iff_1, cls_List_Olexord__Nil__left_0, cls_Transitive__Closure_Ortrancl__idemp_0, cls_List_Olist_Oinject_1, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Set_OInt__UNIV_2, cls_Set_OUn__UNIV__left_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, clsarity_set_2, cls_List_Olistrel__Nil1_0, clsarity_nat_3, cls_Datatype__Universe_OdsumE_1, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_SetInterval_OlessThan__subset__iff_1, cls_Set_OPow__iff_0, cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0, cls_SetInterval_OatMost__iff_1, cls_Nat_Ozero__less__diff_1, cls_Set_Odisjoint__insert__2_1, cls_Relation_Oconverse__converse_0, cls_Finite__Set_Ofinite__Int_0, cls_Relation_OconverseE_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_List_Olist_Osize__2_0, cls_Set_ODiff__UNIV_0, cls_Nat_Onat__add__left__cancel__le_0, clsarity_IntDef__Oint_0, cls_Set_OInter__iff_0, cls_Set_Osubset__refl_0, cls_SetInterval_Oivl__subset_1, cls_Product__Type_Osurj__pair_0, cls_Finite__Set_Ocard__0__eq_1, cls_NatArith_Odiff__diff__right_0, cls_Set_OInter__UNIV_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Set_OCompl__eq__Compl__iff_0, cls_Finite__Set_Ofinite__Un_2, cls_Set_OpsubsetI_0, cls_Relation_Opair__in__Id__conv_0, cls_Set_OInterI_1, cls_IntDef_OInteg_OAbs__Integ__inject_0, cls_Nat_Oadd__gr__0_2, cls_Nat_Onat__add__left__cancel__less_0, cls_Finite__Set_Ofinite__Diff__insert_1, cls_List_OCons__in__lex_5, cls_SetInterval_OatLeastLessThan__iff_2, cls_Finite__Set_Ofinite__Un_0, cls_List_Olength__zip_0, cls_Set_ODiff__iff_2, cls_Finite__Set_Ocard__insert__disjoint_0, cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0, cls_Relation_ORangeE_0, cls_List_OCons__in__lex_0, cls_Datatype__Universe_OIn1__not__In0_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, cls_IntDef_OInteg_OAbs__Integ__inverse_0, cls_Set_OUnion__insert_0, cls_Nat_Odiff__Suc__Suc_0, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, cls_Wellfounded__Recursion_Oacyclic__converse_1, cls_Set_OUn__Diff__cancel2_0, cls_Set_Odisjoint__insert__1_1, cls_Orderings_Omax__less__iff__conj_0, cls_Datatype__Universe_ODomain__dsum_0, cls_Set_Osubset__empty_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_SetInterval_OatLeastAtMost__empty_0, cls_Relation_OdiagI_0, cls_SetInterval_OatLeastAtMost__iff_2, cls_Datatype__Universe_OdprodE_1, cls_Nat_Ole__add__diff__inverse2_0, cls_Set_ODiff__insert0_0, cls_Set_OsubsetI_0, cls_List_OlistsE_0, cls_Finite__Set_Ofinite__converse_1, cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0, cls_IntDef_Ointrel__iff_1, cls_Set_OUNIV__I_0, cls_SetInterval_OatLeastAtMost__singleton_0, cls_Finite__Set_OMin__ge__iff_2, cls_Transitive__Closure_Ortrancl__empty_0, cls_SetInterval_Ocard__greaterThanAtMost_0, cls_Finite__Set_OMax__le__iff_2, cls_Set_Oinsert__subset_2, cls_Set_OUn__UNIV__right_0, cls_Nat_Oadd__is__0_1, cls_Set_OUnion__empty__conv_1, cls_List_Olexord__cons__cons_1, cls_Tarski_Opotype_Oext__inject_2, cls_Set_OUn__iff_0, cls_List_Owf__lex_0, cls_Set_OUnion__iff_1, cls_List_Olistrel__Cons2_0, cls_Infinite__Set_Onat__infinite_0, cls_SetInterval_OgreaterThan__subset__iff_0, cls_Relation_ODomainI_0, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OUn__empty_1, cls_Relation_OImage__Id_0, cls_Set_OInter__UNIV__conv__1_0, cls_Wellfounded__Recursion_Oacyclic__insert_1, cls_Set_Oinsert__disjoint__2_1, cls_Finite__Set_OMin__gr__iff_1, cls_SetInterval_OatLeast__subset__iff_0, cls_Finite__Set_Ofinite__insert_0, cls_SetInterval_OlessThan__subset__iff_0, cls_Set_OCompl__Un_0, cls_Set_OCompl__subset__Compl__iff_0, cls_Orderings_Omin__less__iff__conj_2, cls_SetInterval_Ocard__lessThan_0, cls_Relation_Orel__compE_2, cls_Set_Oinsert__iff_2, cls_Transitive__Closure_ODomain__rtrancl_0, cls_List_ONil2__notin__lex_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, clsarity_set_3, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_Nat_Ole__0__eq_0, cls_SetInterval_Osingle__Diff__lessThan_0, cls_Set_Oinsert__not__empty_0, cls_NatArith_Odiff__less_0, cls_SetInterval_OgreaterThan__iff_0, cls_Set_OsingletonD__dest_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Relation_OImage__singleton__iff_1, cls_Finite__Set_OMax__less__iff_1, cls_SetInterval_OlessThan__iff_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Nat_Ozero__less__diff_0, cls_List_OCons__in__lex_4, cls_Wellfounded__Recursion_Owf__not__refl_0, cls_Finite__Set_Ofinite__Int_1, clsarity_IntDef__Oint_31, cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0, cls_List_ONil__notin__lex_0, cls_SetInterval_OCompl__lessThan_0, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_Nat_OSuc__le__mono_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olist_Oinject_0, cls_Nat_OSuc__less__eq_1, cls_Set_Oempty__iff_0, cls_Transitive__Closure_Otrancl__empty_0, cls_SetInterval_OCompl__greaterThan_0, cls_Set_Oempty__subsetI_0, cls_Set_OInt__UNIV__right_0, cls_Relation_Oconverse__iff_1, cls_Set_OInter__UNIV__conv__2_2, cls_Set_OUnion__iff_0, cls_Set_OUn__subset__iff_0, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Finite__Set_OMin__le_0, cls_Set_OsubsetD_0, cls_Set_OUnion__empty__conv_2, cls_Set_Oempty__Diff_0, cls_SetInterval_OatLeastLessThan__iff_1, cls_Set_Odisjoint__insert__2_2, cls_Set_OUnion__empty__conv_0, cls_Set_OsingletonI_0, cls_Set_OCompl__empty__eq_0, cls_Set_ODiff__iff_1, cls_Finite__Set_OMax__ge_0, cls_Relation_ORange__empty_0, cls_Set_Osubset__antisym_0, cls_Set_OInt__empty__left_0, cls_SetInterval_OatLeastLessThan__iff_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, cls_SetInterval_OCompl__atMost_0, cls_Relation_ORange__Id_0, cls_Finite__Set_Ofinite__Diff__insert_0, cls_SetInterval_OatMost__iff_0, cls_Nat_Omin__Suc__Suc_0, cls_List_Olength__greater__0__conv_1, cls_Datatype__Universe_OdsumE_2, cls_List_Ozip_Osimps__1_0, cls_Relation_OImage__empty_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_OconverseE_0, cls_Set_OUnion__Un__distrib_0, cls_Set_OCompl__iff_0, cls_Datatype__Universe_OuprodE_2, clsrel_Orderings_Oorder_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1, cls_List_Olists__Int__eq_0, cls_Finite__Set_Ofinite__Un_1, cls_Set_Osingleton__insert__inj__eq_1, cls_Datatype__Universe_OuprodE_0, cls_Datatype__Universe_OIn0__eq_0, cls_Set_OCompl__Diff__eq_0, cls_Set_Oall__not__in__conv_0, cls_Nat_OSuc__diff__diff_0, cls_Nat_Omin__0R_0, cls_Set_Oinsert__iff_1, cls_Finite__Set_OMax__singleton_0, cls_SetInterval_OgreaterThanLessThan__iff_2, cls_Set_Osubset__empty_1, cls_Finite__Set_Ofinite__converse_0, cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0, cls_Finite__Set_Ofinite__Pow__iff_0, cls_NatArith_Odiff__Suc__diff__eq2_0, cls_Set_Oinsert__disjoint__1_0, cls_SetInterval_Oivl__subset_0, cls_Set_Odisjoint__insert__1_2, cls_SetInterval_OatLeastAtMost__iff_1, cls_Datatype__Universe_OdprodE_2, cls_List_Olength__0__conv_0, cls_Set_Oinsert__subset_1, cls_Relation_ORangeI_0, cls_SetInterval_OatLeastLessThan__empty_0, cls_Set_Oinsert__Diff__single_0, cls_Nat_OSuc__le__mono_1, cls_Set_Oempty__Union__conv_0, cls_Relation_OId__O__R_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Relation_Opair__in__Id__conv_1, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0, clsarity_set_1, cls_Relation_Oconverse__diag_0, cls_Finite__Set_OMin__ge__iff_1, cls_Wellfounded__Relations_Otrans__less__than_0, cls_IntDef_Ointrel__iff_0, cls_SetInterval_OgreaterThanAtMost__iff_0, cls_Set_OInt__UNIV_0, cls_Set_Oinsert__disjoint__2_0, cls_SetInterval_OatLeast__eq__iff_0, cls_List_Olength__greater__0__conv_0, cls_Nat_Oadd__gr__0_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0, cls_Transitive__Closure_ORange__rtrancl_0, cls_Set_OCompl__UNIV__eq_0, cls_Set_OInter__UNIV__conv__1_1, cls_Finite__Set_Ofinite__Union_1, cls_Nat_Odiff__is__0__eq_H_0, cls_Set_OUn__insert__left_0, cls_Finite__Set_OMin__ge__iff_0, cls_Set_OInt__empty__right_0, cls_Wellfounded__Recursion_Oacyclic__converse_0, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Wellfounded__Recursion_Owf__insert_2, cls_Nat_Oless__Suc0_0, cls_Set_OUn__insert__right_0, cls_Nat_Onot__add__less1_0, cls_Relation_OR__O__Id_0, cls_SetInterval_OatLeast__subset__iff_1, cls_NatArith_Odiff__diff__cancel_0, cls_List_Olist_Odistinct__2_0, cls_List_Olistrel__Nil_0, cls_IntDef_Oequiv__intrel__iff_0, cls_Product__Type_OPair__eq_1, cls_Nat_Oop_A_N_Odiff__0_0, cls_Orderings_Omax__less__iff__conj_1, cls_Set_OInter__iff_2, cls_Nat_Oadd__is__0_2, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_SetInterval_OatLeastLessThan__singleton_0, cls_Set_OCompl__Int_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_Finite__Set_OMax__less__iff_0, cls_Datatype__Universe_OdprodI_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_List_OCons__in__lex_3, cls_SetInterval_Oivl__diff_0, cls_Relation_Oconverse__iff_0, cls_Finite__Set_OMax__le__iff_0, cls_Set_OInter__UNIV__conv__2_1, cls_Set_OUnion__iff_2, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0, cls_List_Olistrel__Cons1_2, clsarity_nat_12, cls_Relation_OImage__singleton__iff_0, cls_List_Onot__Cons__self_0, clsarity_IntDef__Oint_62, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0, cls_Set_OUn__iff_1, cls_Finite__Set_OMax__le__iff_1, clsarity_IntDef__Oint_5, cls_SetInterval_OlessThan__iff_1, cls_Nat_Omax__Suc__Suc_0, cls_Set_OUnion__empty_0, cls_Nat_Odiff__Suc__less_0, cls_Wellfounded__Recursion_Oacyclic__insert_2, cls_Datatype__Universe_Odsum__In1I_0, cls_List_OlistsE_1, cls_Finite__Set_OMin__gr__iff_0, cls_Nat_Oadd__0__right_0, cls_Nat_Ole__add__diff__inverse_0, cls_Set_ODiff__Compl_0, cls_SetInterval_Oivl__subset_3, cls_Datatype__Universe_OdsumE_3, cls_Datatype__Universe_OuprodE_1, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0, cls_List_Olist_Odistinct__1_0, cls_Set_Oempty__not__insert_0, cls_Set_OpsubsetE_0, cls_Wellfounded__Relations_Oless__than__iff_1, cls_Nat_Oadd__Suc__right_0, cls_Nat_Onot__gr0_1, cls_SetInterval_OgreaterThan__iff_1, cls_Orderings_Omin__less__iff__conj_0, cls_Set_ODiff__eq__empty__iff_1, cls_Set_OInt__subset__iff_2, cls_Nat_Onot__add__less2_0, cls_List_Olistrel__Nil2_0, cls_Relation_Orel__compI_0, cls_List_Onth__Cons__0_0, cls_Set_ODiff__eq__empty__iff_0, cls_Set_OInt__iff_0, cls_Transitive__Closure_Otrancl__domain_0, cls_List_Olexord__Nil__right_0, cls_Set_ODiff__empty_0, cls_SetInterval_OatMost__eq__iff_0, cls_Finite__Set_OMax__in_0, cls_Relation_OdiagE_1, clsarity_nat_9, cls_Wellfounded__Relations_Otrans__lex__prod_0, cls_NatArith_Odiff__Suc__diff__eq1_0, cls_Set_OInt__iff_1, cls_SetInterval_Ocard__greaterThanLessThan_0, cls_Set_Oempty__Union__conv_2, cls_Set_Oinsert__disjoint__1_2, cls_Relation_Odiag__empty_0, cls_SetInterval_OatLeast__iff_0, cls_NatArith_Oadd__diff__assoc_0, cls_Set_OUn__empty__right_0, cls_Transitive__Closure_Otrancl__reflcl_0, cls_Datatype__Universe_ODomain__dprod_0, cls_Nat_Omax__0L_0, cls_Set_OInter__UNIV__conv__1_2, cls_Nat_Odiff__diff__left_0, cls_Set_OInt__UNIV_1, cls_Set_OUn__empty__left_0, cls_SetInterval_OgreaterThanLessThan__iff_1, cls_Wellfounded__Recursion_Owf__insert_1, cls_Set_OUn__Diff__cancel_0, cls_Set_OPow__Int__eq_0, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Arefl_A_Ipset_Acl1_J_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_SetInterval_OgreaterThanAtMost__iff_1, cls_List_Olistrel__Cons1_1, cls_Set_OInter__insert_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Nat_Oless__Suc0_1, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, cls_Set_Ocontents__eq_0, cls_List_Ozip__Nil_0, cls_Nat_OSuc__not__Zero_0, cls_Finite__Set_OMin__in_0, cls_Set_ODiff__disjoint_0, cls_Finite__Set_Ofinite__Diff_0, cls_List_Olists__UNIV_0, cls_SetInterval_Ocard__atMost_0, cls_Nat_Onat__add__left__cancel_0, cls_Set_ODiff__iff_0, clsarity_Product____Type__Ounit_0, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_List_Olexord__cons__cons_3, cls_SetInterval_OatMost__subset__iff_0, cls_Finite__Set_Ocard__empty_0, cls_SetInterval_OlessThan__0_0, cls_SetInterval_OgreaterThan__eq__iff_0, cls_Set_OUnionE_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0, cls_IntDef_Oequiv__intrel__iff_1, cls_List_Olistset_Osimps__1_0, cls_Set_OCompl__disjoint_0, cls_Set_OInter__empty_0, clsarity_set_0, cls_List_Olexord__Nil__left_1, cls_Transitive__Closure_Oreflcl__trancl_0, cls_Datatype_Oprod_Osize_0, cls_SetInterval_Ocard__atLeastLessThan_0, cls_Product__Type_OPair__eq_0, cls_Nat_OSuc__less__eq_0, cls_List_Olexord__cons__cons_0, cls_List_OCons__in__lex_2, cls_Transitive__Closure_Ortrancl__idemp__self__comp_0, cls_Product__Type_Osnd__conv_0, cls_Set_OInt__absorb_0, cls_Datatype__Universe_OdsumE_0, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_Set_OUn__empty_0, cls_List_Olistset_Osimps__2_0, cls_Nat_Ole0_0, cls_List_Ozip__Cons__Cons_0, cls_SetInterval_OlessThan__eq__iff_0, cls_Set_OUn__subset__iff_1, cls_Set_Oinsert__iff_0, cls_Wellfounded__Recursion_Oacyclic__insert_0, cls_Set_Oinsert__absorb2_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Nat_Oadd__gr__0_1, cls_Set_OUnion__Pow__eq_0, cls_Set_Onot__psubset__empty_0, cls_Nat_Omin__0L_0, cls_List_Onth__Cons__Suc_0, cls_SetInterval_OgreaterThanAtMost__empty_0, cls_Nat_Ole__0__eq_1, cls_Set_Odisjoint__insert__2_0, cls_Set_OUn__empty_2, cls_Relation_OIdE_0, clsarity_nat_2, cls_Set_OUn__iff_2, cls_Set_OpsubsetE_1, cls_Datatype__Universe_OIn0__not__In1_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0, cls_Orderings_Omax__less__iff__conj_2, cls_Set_OPow__empty_0, cls_Finite__Set_OMax__insert_0, cls_List_Owf__lenlex_0, cls_Nat_Oop_A_L_Oadd__Suc_0, cls_Tarski_Opotype_Oselect__convs__1_0, cls_Set_Osingleton__insert__inj__eq_2, cls_Nat_OZero__not__Suc_0, cls_Set_Oinsert__inter__insert_0, cls_SetInterval_OatMost__subset__iff_1, cls_Nat_OlessI_0, cls_Datatype__Universe_OIn1__eq_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OInter__UNIV__conv__2_0, cls_Finite__Set_Ocard__0__eq_0, cls_SetInterval_Oivl__subset_2, clsarity_set_4, cls_Product__Type_Opair__collapse_0, cls_Set_Odisjoint__insert__1_0, cls_Set_OUnion__UNIV_0, cls_Set_OInter__iff_1, cls_SetInterval_OatLeastAtMost__iff_0, cls_Set_Odouble__complement_0, cls_Relation_Orel__compE_1, cls_Nat_OSuc__pred_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1, cls_Datatype__Universe_OScons__Scons__eq_0, cls_Wellfounded__Relations_Oless__than__iff_0, cls_Set_Oinsert__subset_0, cls_Set_OUn__absorb_0, cls_List_Olists_OCons_0, cls_Nat_Omax__0R_0, cls_Relation_OImage__diag_0, cls_SetInterval_OatLeast__0_0, cls_Tarski_Opotype_Oext__inject_0, cls_Orderings_Omin__less__iff__conj_1, cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0, cls_Relation_Oconverse__Id_0, cls_Set_OCompl__disjoint2_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1, cls_Set_OInt__subset__iff_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0
% 13.85/3.92 % No. of inferences in proof: 1091
% 13.85/3.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3395 ms resp. 2754 ms w/o parsing
% 14.49/4.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.49/4.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------