TSTP Solution File: LAT277-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT277-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:27:17 EDT 2023
% Result : Unsatisfiable 6.94s 2.57s
% Output : Refutation 7.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 237
% Syntax : Number of formulae : 401 ( 137 unt; 74 typ; 0 def)
% Number of atoms : 563 ( 186 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 4908 ( 250 ~; 236 |; 0 &;4422 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 181 ( 181 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 74 usr; 15 con; 0-6 aty)
% Number of variables : 1054 ( 0 ^;1054 !; 0 ?;1054 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_x_type,type,
v_x: $i ).
thf(v_A_type,type,
v_A: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_r_type,type,
v_r: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $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(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_List_Olex_type,type,
c_List_Olex: $i > $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_type,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_Wellfounded__Recursion_Owf_type,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $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(tc_nat_type,type,
tc_nat: $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Tarski_OPartialOrder_type,type,
c_Tarski_OPartialOrder: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i > $i > $i ).
thf(c_List_Ozip_type,type,
c_List_Ozip: $i > $i > $i > $i > $i ).
thf(c_Relation_Orefl_type,type,
c_Relation_Orefl: $i > $i > $i > $o ).
thf(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(c_List_Olexord_type,type,
c_List_Olexord: $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_type,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Odiag_type,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_IntDef_Ointrel_type,type,
c_IntDef_Ointrel: $i ).
thf(c_Main_OImageE__1_type,type,
c_Main_OImageE__1: $i > $i > $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_List_Olenlex_type,type,
c_List_Olenlex: $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_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_cl_type,type,
v_cl: $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_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_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_OdiagE__1_type,type,
c_Main_OdiagE__1: $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_Main_OIdE__1_type,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Main_ODomainE__1_type,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(102,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(385,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(188,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)],[11]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
thf(336,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)],[79]) ).
thf(92,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(365,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(518,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)],[162]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(468,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)],[138]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(308,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)],[67]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(449,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)],[129]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
thf(269,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)],[49]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(202,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)],[17]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(408,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)],[113]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(170,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)],[4]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
thf(404,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)],[111]) ).
thf(117,axiom,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(417,plain,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
thf(301,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)],[64]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(257,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)],[43]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(184,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)],[9]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(504,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)],[155]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
thf(357,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)],[88]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
thf(284,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)],[56]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(325,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)],[75]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
thf(228,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)],[30]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
thf(289,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)],[58]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(216,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)],[24]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
thf(475,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)],[141]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
thf(179,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)],[7]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
| ~ ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
| ~ ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
| ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_3) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
| ~ ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
| ~ ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
| ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(34,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ c_emptyset @ A )
= c_Relation_OId ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
thf(238,plain,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ c_emptyset @ A )
= c_Relation_OId ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(348,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)],[84]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(492,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)],[149]) ).
thf(1,negated_conjecture,
c_in @ v_x @ v_A @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(164,plain,
c_in @ v_x @ v_A @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(453,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)],[131]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
thf(396,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( 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)],[107]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).
thf(243,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( 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)],[37]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
thf(265,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)],[46]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(206,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)],[19]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(292,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)],[60]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
thf(248,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)],[39]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
thf(380,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)],[99]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
thf(439,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)],[125]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(220,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)],[26]) ).
thf(93,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
thf(366,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
thf(334,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(105,axiom,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(392,plain,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
thf(297,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)],[62]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(275,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)],[52]) ).
thf(2,negated_conjecture,
~ ( c_in @ ( c_Pair @ v_x @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(165,plain,
~ ( c_in @ ( c_Pair @ v_x @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_fst @ ( c_Pair @ A @ B @ C @ D ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
thf(484,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)],[145]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(197,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)],[15]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ A @ c_List_Olist_ONil @ B @ C )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
thf(361,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)],[90]) ).
thf(74,axiom,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(324,plain,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
thf(224,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)],[28]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
thf(488,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)],[147]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(212,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)],[22]) ).
thf(76,axiom,
! [A: $i] :
( ( c_Relation_Oconverse @ c_Relation_OId @ A @ A )
= c_Relation_OId ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
thf(328,plain,
! [A: $i] :
( ( c_Relation_Oconverse @ c_Relation_OId @ A @ A )
= c_Relation_OId ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(471,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)],[139]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(393,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)],[106]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(515,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)],[160]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
thf(457,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)],[133]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(173,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)],[5]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ c_Relation_OId @ A @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ c_Relation_OId @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(82,axiom,
! [A: $i] :
( ( c_Relation_Odiag @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
thf(343,plain,
! [A: $i] :
( ( c_Relation_Odiag @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
thf(266,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)],[47]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(508,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)],[157]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(398,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)],[108]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
thf(412,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)],[115]) ).
thf(120,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(425,plain,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
thf(375,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)],[97]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(513,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)],[159]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(430,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)],[122]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
thf(176,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)],[6]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
thf(402,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)],[110]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
thf(286,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)],[57]) ).
thf(59,axiom,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(291,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)],[59]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(259,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)],[44]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
thf(445,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)],[127]) ).
thf(100,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/sandbox2/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(382,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)],[100]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(313,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)],[69]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
thf(498,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)],[152]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
thf(466,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)],[137]) ).
thf(85,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(350,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(406,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)],[112]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
thf(419,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)],[118]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(451,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)],[130]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(245,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)],[38]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
thf(303,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)],[65]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= ( c_Relation_Odiag @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
thf(271,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)],[50]) ).
thf(20,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(208,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(142,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
thf(477,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)],[142]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
thf(387,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)],[103]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
thf(494,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)],[150]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(345,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)],[83]) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(520,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)],[163]) ).
thf(35,axiom,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(240,plain,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(330,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)],[77]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Orefl @ A @ B @ C )
| ~ ( c_in @ D @ A @ C )
| ( c_in @ ( c_Pair @ D @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OreflD_0) ).
thf(462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Orefl @ A @ B @ C )
| ~ ( c_in @ D @ A @ C )
| ( c_in @ ( c_Pair @ D @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ c_Relation_OId @ B @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
thf(278,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)],[53]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
thf(455,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)],[132]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
thf(306,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)],[66]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
thf(299,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)],[63]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
thf(226,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)],[29]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
thf(241,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)],[36]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(167,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)],[3]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
thf(473,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)],[140]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
thf(490,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)],[148]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
thf(255,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)],[42]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(516,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)],[161]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
thf(355,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)],[87]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
thf(194,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)],[14]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ c_Relation_OId @ A @ B @ B @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
thf(295,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)],[61]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).
thf(282,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( 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)],[55]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(310,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)],[68]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(199,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)],[16]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(182,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)],[8]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
thf(502,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)],[154]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(338,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)],[80]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ c_emptyset @ B @ C )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
thf(359,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)],[89]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
thf(250,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)],[40]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(363,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)],[91]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(482,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)],[144]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(218,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)],[25]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(368,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ c_List_Olist_ONil @ A @ B @ C )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
thf(319,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)],[71]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
thf(390,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)],[104]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(186,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)],[10]) ).
thf(98,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(378,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
thf(235,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)],[33]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
thf(478,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)],[143]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(123,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
thf(433,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(510,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)],[158]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(447,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)],[128]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
thf(410,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)],[114]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(12,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(190,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
| ~ ( class_Finite__Set_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(422,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)],[119]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(273,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)],[51]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(21,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(210,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(81,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(341,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
thf(437,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)],[124]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
thf(400,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)],[109]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
thf(415,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)],[116]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
thf(506,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)],[156]) ).
thf(48,axiom,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(268,plain,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
thf(464,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)],[136]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(427,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)],[121]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(459,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)],[134]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
thf(442,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)],[126]) ).
thf(153,axiom,
c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
thf(501,plain,
c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(322,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)],[73]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_snd @ ( c_Pair @ A @ B @ C @ D ) @ C @ D )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
thf(486,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)],[146]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(222,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)],[27]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
thf(496,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)],[151]) ).
thf(522,plain,
$false,
inference(e,[status(thm)],[385,188,336,365,518,468,352,308,449,269,202,408,170,404,417,301,257,184,504,357,284,325,228,289,216,475,179,321,253,238,348,492,164,280,453,396,243,265,206,292,233,248,380,439,220,366,334,392,297,192,275,165,484,197,361,324,224,488,212,328,471,393,515,457,173,371,343,266,508,398,412,425,375,513,430,176,402,286,291,204,259,445,382,313,498,466,350,406,419,230,451,245,303,271,208,477,387,494,345,520,240,330,462,278,455,306,299,226,241,167,473,490,255,516,355,194,295,282,310,199,182,502,338,359,250,363,482,218,368,319,390,186,378,235,478,383,214,433,510,447,315,410,262,190,422,273,373,210,341,437,400,415,506,268,464,427,459,442,501,322,486,222,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT277-1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n015.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 14:25:53 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.14 % [INFO] Parsing done (288ms).
% 1.81/1.15 % [INFO] Running in sequential loop mode.
% 2.47/1.34 % [INFO] eprover registered as external prover.
% 2.47/1.34 % [INFO] cvc4 registered as external prover.
% 2.47/1.34 % [INFO] Scanning for conjecture ...
% 2.96/1.49 % [INFO] Found a conjecture and 2744 axioms. Running axiom selection ...
% 3.66/1.64 % [INFO] Axiom selection finished. Selected 161 axioms (removed 2583 axioms).
% 3.92/1.72 % [INFO] Problem is propositional (TPTP CNF).
% 3.92/1.73 % [INFO] Type checking passed.
% 3.92/1.73 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.94/2.56 % External prover 'e' found a proof!
% 6.94/2.56 % [INFO] Killing All external provers ...
% 6.94/2.56 % Time passed: 2034ms (effective reasoning time: 1411ms)
% 6.94/2.56 % 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)>
% 6.94/2.57 % Axioms used in derivation (161): cls_List_Olistrel__Cons1_0, cls_Relation_ODomain__empty_0, cls_Transitive__Closure_Otrancl__range_0, cls_Nat_Onat__add__left__cancel__less_1, cls_Set_Osingleton__insert__inj__eq_0, cls_List_Olists_ONil_0, cls_List_Onth__zip_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_Relation_ODomain__diag_0, cls_List_OCons__in__lex_1, cls_Relation_ORange__diag_0, cls_List_Olexord__cons__cons_2, cls_Nat_Onat__add__right__cancel_0, clsarity_prod_0, cls_Wellfounded__Recursion_Owf__insert_0, cls_Product__Type_Ofst__conv_0, cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Set_Osingleton__inject__dest_0, cls_Relation_OImageE_0, cls_Transitive__Closure_Ortrancl__reflcl_0, cls_List_Olexord__Nil__left_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Nat_Oless__irrefl_0, cls_List_Olistrel__Nil1_0, cls_Transitive__Closure_Ortrancl__idemp_0, cls_List_Olist_Oinject_1, cls_Relation_Oconverse__converse_0, cls_Relation_OconverseE_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Product__Type_Osurj__pair_0, cls_Relation_Orel__compE_0, cls_Relation_Opair__in__Id__conv_0, cls_Relation_ORangeE_0, cls_List_OCons__in__lex_0, cls_Nat_Onat__add__left__cancel__less_0, cls_List_OCons__in__lex_5, cls_Wellfounded__Recursion_Oacyclic__converse_1, cls_Relation_OdiagI_0, cls_IntDef_Ointrel__iff_1, cls_Transitive__Closure_Ortrancl__empty_0, cls_List_OlistsE_0, cls_Tarski_OPartialOrder__iff_0, cls_List_Olistrel__Cons2_0, cls_Relation_ODomainI_0, cls_List_Olexord__cons__cons_1, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OUn__iff_0, cls_List_Owf__lex_0, cls_Set_OUn__empty_1, cls_Relation_OImage__Id_0, cls_Wellfounded__Recursion_Oacyclic__insert_1, cls_Relation_Orel__compE_2, cls_Set_Oinsert__iff_2, cls_List_ONil2__notin__lex_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, cls_Relation_OreflD_0, clsarity_set_3, cls_Relation_OImage__singleton__iff_1, cls_Set_Oinsert__not__empty_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Transitive__Closure_Otrancl__empty_0, cls_List_OCons__in__lex_4, cls_Relation_Oconverse__iff_1, cls_List_ONil__notin__lex_0, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_List_Olist_Oinject_0, cls_Set_Oempty__iff_0, cls_Wellfounded__Recursion_Owf__not__refl_0, cls_Tarski_Ocl_A_58_APartialOrder_0, cls_Set_OsingletonI_0, cls_Relation_ORange__empty_0, cls_List_Ozip_Osimps__1_0, cls_Relation_OImage__empty_0, cls_Relation_OconverseE_0, cls_Set_Oall__not__in__conv_0, cls_Set_Oinsert__iff_1, cls_Relation_Oconverse__diag_0, cls_Relation_ORangeI_0, cls_Relation_OId__O__R_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Relation_Opair__in__Id__conv_1, cls_Wellfounded__Relations_Otrans__less__than_0, cls_IntDef_Ointrel__iff_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0, cls_Set_OUn__insert__left_0, cls_Wellfounded__Recursion_Oacyclic__converse_0, cls_Wellfounded__Recursion_Owf__insert_2, cls_Set_OUn__insert__right_0, cls_Nat_Onot__add__less1_0, cls_Relation_OR__O__Id_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_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_List_OCons__in__lex_3, cls_Relation_Oconverse__iff_0, cls_Tarski_OPartialOrder__iff_2, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_Relation_OImage__singleton__iff_0, cls_List_Onot__Cons__self_0, cls_Set_OUn__iff_1, cls_Wellfounded__Recursion_Oacyclic__insert_2, cls_Tarski_OPartialOrder__iff_1, cls_Relation_Orel__compI_0, cls_List_Olist_Odistinct__1_0, cls_Set_Oempty__not__insert_0, cls_Wellfounded__Relations_Oless__than__iff_1, cls_Nat_Onot__add__less2_0, cls_List_Olistrel__Nil2_0, cls_Transitive__Closure_Otrancl__domain_0, cls_List_Olexord__Nil__right_0, cls_Relation_OdiagE_1, cls_Wellfounded__Relations_Otrans__lex__prod_0, cls_Relation_Odiag__empty_0, cls_Set_OUn__empty__left_0, cls_Set_OUn__empty__right_0, cls_Transitive__Closure_Otrancl__reflcl_0, cls_Wellfounded__Recursion_Owf__insert_1, cls_List_Olistrel__Cons2_2, cls_List_Olistrel__Cons1_1, cls_Set_Ocontents__eq_0, cls_List_Ozip__Nil_0, cls_Relation_ODomainE_0, cls_List_Olexord__cons__cons_3, cls_IntDef_Oequiv__intrel__iff_1, cls_Nat_Onat__add__left__cancel_0, clsarity_Product____Type__Ounit_0, cls_List_Olistset_Osimps__1_0, cls_Product__Type_OPair__eq_0, cls_List_Olexord__Nil__left_1, cls_Transitive__Closure_Oreflcl__trancl_0, cls_List_Ozip__Cons__Cons_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_OUn__empty_0, cls_Set_Oinsert__absorb2_0, cls_Set_Onot__psubset__empty_0, cls_Set_Oinsert__iff_0, cls_Wellfounded__Recursion_Oacyclic__insert_0, cls_Set_OUn__empty_2, cls_List_Owf__lenlex_0, cls_Relation_OIdE_0, cls_Set_OUn__iff_2, cls_Relation_Orel__compE_1, cls_Product__Type_Opair__collapse_0, cls_Wellfounded__Relations_Oless__than__iff_0, cls_Set_OUn__absorb_0, cls_List_Olists_OCons_0, cls_Tarski_OPartialOrder__iff_3, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_Relation_Oconverse__Id_0
% 6.94/2.57 % No. of inferences in proof: 327
% 6.94/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2034 ms resp. 1411 ms w/o parsing
% 7.30/2.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.30/2.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------