%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV245-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:58:31 AM UTC 2026
% Result : Unsatisfiable 34.67s 8.10s
% Output : Refutation 32.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 206
% Syntax : Number of formulae : 413 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 821 ( 232 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 5816 ( 402 ~; 408 |; 0 &;5006 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 90 ( 88 usr; 12 con; 0-6 aty)
% Number of variables : 1384 ( 0 ^;1384 !; 0 ?;1384 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Message_Omsg_OMPair_decl,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(v_Y_decl,type,
v_Y: $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(v_H_decl,type,
v_H: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_decl,type,
c_append: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Datatype__Universe_OIn0_decl,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn1_decl,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(c_Datatype__Universe_Odprod_decl,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_decl,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_decl,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_decl,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_decl,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Message_Omsg_OCrypt_decl,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Message_Omsg_ONumber_decl,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_Message_Omsg_OHash_decl,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Datatype__Universe_Odsum_decl,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OInr_decl,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_decl,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Message_Omsg_OAgent_decl,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(c_Main_OImageE__1_decl,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Main_OPlusE__1_decl,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_decl,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Datatype_Ooption_OSome_decl,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_decl,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_decl,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_decl,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_decl,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_Main_Oin__listsI__1_decl,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_Main_OInterI__1_decl,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_decl,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Main_OuprodE__1_decl,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_decl,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_decl,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_decl,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdiagE__1_decl,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_decl,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OIdE__1_decl,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_decl,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i > $i ).
thf(c_Main_ODomainE__1_decl,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(117,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(518,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(628,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(16,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(249,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(655,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).
thf(511,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(677,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(97,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(472,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).
thf(709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(40,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(320,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(141,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OAgent_0) ).
thf(570,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(111,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(504,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(163,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).
thf(606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(284,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).
thf(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(151,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(591,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(376,plain,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(165,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(623,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(105,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(485,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(221,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(68,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(439,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(529,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(183,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(661,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(66,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(392,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(429,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(166,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(625,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(185,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(92,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(461,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(566,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(104,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(484,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(45,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(339,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(669,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(686,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(99,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(476,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(647,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(135,axiom,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(558,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(662,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(53,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(360,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(33,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(573,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(86,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(444,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(286,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__least_0) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(146,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(579,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(641,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(73,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(406,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).
thf(377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(88,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(451,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth_0) ).
thf(649,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(83,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(434,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(2,negated_conjecture,
tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_G @ c_Message_Osynth @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) @ ( v_Y @ ( v_X @ c_Message_Omsg_OMPair ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(208,plain,
tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_G @ c_Message_Osynth @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) @ ( v_Y @ ( v_X @ c_Message_Omsg_OMPair ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(477,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(152,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(594,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(56,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(367,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(59,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(675,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(3,negated_conjecture,
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_G @ c_Message_Osynth @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) @ ( v_X @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(209,plain,
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_G @ c_Message_Osynth @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) @ ( v_X @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(617,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(147,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(705,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(673,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(502,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(703,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(613,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
thf(600,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(94,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(465,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(167,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_ONumber_0) ).
thf(627,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(539,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(671,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(688,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(108,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(495,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(390,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(201,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(699,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1,negated_conjecture,
tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz @ ( v_Y @ ( v_X @ c_Message_Omsg_OMPair ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(207,plain,
tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz @ ( v_Y @ ( v_X @ c_Message_Omsg_OMPair ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(603,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(46,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(341,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(70,axiom,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(400,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(171,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(427,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(153,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(175,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(337,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(543,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).
thf(639,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(222,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(227,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(2552,plain,
$false,
inference(e,[status(thm)],[479,518,468,352,628,249,276,449,655,511,269,677,385,533,500,472,404,709,417,288,301,320,651,257,570,504,619,357,606,284,325,216,591,376,623,211,485,348,480,602,221,396,507,527,439,529,661,233,452,260,598,392,693,429,625,665,461,551,456,224,566,484,583,522,697,615,388,420,339,537,669,637,679,547,686,476,393,647,701,371,343,244,266,311,541,657,398,558,662,633,360,298,412,279,573,296,444,562,402,286,577,281,545,579,291,641,382,313,611,335,236,350,406,681,377,230,318,362,451,509,649,434,271,208,477,631,535,594,621,520,251,330,462,345,367,695,306,505,431,241,653,531,374,553,490,675,209,487,617,516,580,705,707,414,409,263,673,441,585,502,470,703,613,600,571,465,627,556,539,482,671,688,495,218,390,588,699,568,207,667,684,549,422,603,564,341,474,400,635,575,427,596,644,691,369,337,543,560,639,222,454,364,254,227,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV245-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/0.53 % Computer : n007.cluster.edu
% 0.16/0.53 % Model : x86_64 x86_64
% 0.16/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.53 % Memory : 8046.5625MB
% 0.16/0.53 % OS : Linux 6.8.0-71-generic
% 0.16/0.53 % CPULimit : 300
% 0.16/0.53 % WCLimit : 300
% 0.16/0.53 % DateTime : Sat Sep 26 13:19:54 UTC 2026
% 0.16/0.53 % CPUTime :
% 0.16/0.53 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.91/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.34/1.53 % [INFO] Parsing done (416ms).
% 2.34/1.54 % [INFO] Running in sequential loop mode.
% 3.35/1.93 % [INFO] eprover registered as external prover.
% 3.35/1.94 % [INFO] Scanning for conjecture ...
% 4.05/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 1400 axioms. Running axiom selection ...
% 4.78/2.33 % [INFO] Axiom selection finished. Selected 203 axioms (removed 1197 axioms).
% 5.24/2.49 % [INFO] Problem is propositional (TPTP CNF).
% 5.70/2.51 % [INFO] Type checking passed.
% 5.70/2.51 % [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 ...
% 34.67/8.09 % External prover 'e' found a proof!
% 34.67/8.09 % [INFO] Killing All external provers ...
% 34.67/8.10 % Time passed: 7420ms (effective reasoning time: 6546ms)
% 34.67/8.10 % Axioms used in derivation (203): cls_Message_Omsg_Oinject__6__iff1_0, cls_Message_Omsg_Oinject__7__iff1_0, cls_List_Ofinite__set_0, cls_Finite__Set_Ofinite__Union_0, cls_List_Oset__empty2__iff2_0, cls_Datatype__Universe_OuprodI_0, cls_Finite__Set_Ofinite__converse__iff1_0, cls_Message_Oanalz_OInj_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_List_Oappend__in__lists__conv__iff2_0, cls_Datatype__Universe_Odsum__In0I_0, cls_List_Oset__empty2__iff1_0, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, cls_Message_Oanalz__analzD__dest_0, cls_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_List_ONil__is__append__conv__iff2_0, cls_Message_Osynth_OAgent_0, cls_Sum__Type_OInr__eq__iff1_0, cls_Set_OemptyE_0, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Finite__Set_OFinites_OemptyI_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, cls_Set_OUnionE_1, cls_Finite__Set_OFinites_OinsertI_0, cls_List_Olistrel__Nil1_0, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Sum__Type_OPlusE_0, cls_Finite__Set_Ofinite__Int_0, cls_Message_OHash__synth_0, cls_Relation_OconverseE_1, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, cls_Infinite__Set_Onat__not__finite_0, cls_Message_Osynth_OHash_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Relation_ORangeE_0, cls_Message_Osynth_ONumber_0, cls_Set_OInterI_1, cls_Message_Omsg_Oinject__7__iff1_1, cls_List_Oset__empty__iff2_0, cls_Set_OUnCI_1, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Message_Oparts_OInj_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_Relation_OdiagI_0, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Set_OUn__least_0, cls_Set_OPow__iff__iff2_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Message_OCrypt__synth_1, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_Relation_ODomainI_0, cls_Message_Osynth_OMPair_0, cls_Set_OUnE_0, cls_List_Owf__lex_0, cls_Message_Omsg_Oinject__4__iff1_0, cls_Set_OinsertE_0, cls_Set_OUn__empty__iff1_1, cls_Relation_Orel__compE_2, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, cls_Message_Omsg_Oinject__3__iff1_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_List_Oappend__is__Nil__conv__iff2_0, cls_Relation_OIdI_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_List_Oin__listsI_1, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Datatype__Universe_OuprodE_2, cls_Relation_Oconverse__iff__iff1_0, cls_Relation_OconverseE_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_List_Olist_Oinject__iff1_1, cls_Message_Omsg_Oinject__5__iff1_0, cls_Datatype__Universe_OuprodE_0, cls_Set_ODiffE_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Datatype__Universe_OdprodE_2, cls_Message_Oin__parts__UnE_0, cls_Message_Oanalz__mono_0, cls_Relation_ORangeI_0, cls_Message_OCrypt__synth_0, cls_List_Oset__empty__iff1_0, cls_Message_Omsg_Oinject__1__iff1_0, cls_Message_OMPair__analz_1, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Set_OIntI_0, cls_Finite__Set_Ofinite__Union_1, cls_Message_Omsg_Oinject__2__iff1_0, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_Message_OMPair__parts_1, cls_Message_Osynth_OCrypt_0, cls_Datatype__Universe_OdprodI_0, cls_Message_Osynth__synthD__dest_0, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, cls_List_Oappend__self__conv__iff2_0, cls_Set_OUn__empty__iff2_0, cls_List_Oappend__same__eq__iff1_0, cls_Set_ODiffI_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, cls_Message_ONonce__synth_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OUnionI_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_List_Olistrel__Nil2_0, cls_Relation_Orel__compI_0, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Datatype__Universe_OIn0__eq__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, cls_Relation_OdiagE_1, cls_Relation_OImage__singleton__iff__iff1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Message_OMPair__synth_1, cls_Set_OInterI_0, cls_List_Olist_Odistinct__1__iff1_0, cls_Message_Osynth_OInj_0, cls_Relation_ODomainE_0, cls_List_Oin__listsI_0, cls_Message_OMPair__analz_0, cls_Sum__Type_OPlusE_1, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Set_OUnionE_0, cls_Message_Omsg_Oinject__6__iff1_1, cls_List_Oappend1__eq__conv__iff1_0, cls_Message_OKey__synth_0, cls_Message_Oanalz_ODecrypt__dest_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, cls_Sum__Type_OInl__eq__iff1_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, cls_Message_OMPair__parts_0, cls_Relation_OImage__singleton__iff__iff2_0, cls_Relation_OIdE_0, cls_Message_Oparts__emptyE_0, cls_Set_OIntE_0, cls_Relation_Orel__compE_1, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, cls_Message_OMPair__synth_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0
% 34.67/8.10 % No. of inferences in proof: 413
% 34.67/8.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7420 ms resp. 6546 ms w/o parsing
% 32.21/8.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.21/8.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------