TSTP Solution File: SWV274-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV274-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:14:42 EDT 2023
% Result : Unsatisfiable 7.50s 2.69s
% Output : Refutation 8.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 297
% Syntax : Number of formulae : 506 ( 77 unt; 89 typ; 0 def)
% Number of atoms : 831 ( 232 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 5824 ( 408 ~; 414 |; 0 &;5002 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 231 ( 231 >; 0 *; 0 +; 0 <<)
% Number of symbols : 91 ( 89 usr; 11 con; 0-6 aty)
% Number of variables : 1396 ( 0 ^;1396 !; 0 ?;1396 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_Y_type,type,
v_Y: $i ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(v_X_type,type,
v_X: $i ).
thf(v_H_type,type,
v_H: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_type,type,
c_append: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i ).
thf(c_Datatype__Universe_OIn0_type,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn1_type,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Datatype__Universe_Odprod_type,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(tc_Datatype__Universe_Onode_type,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_type,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_type,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_type,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_type,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_type,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Wellfounded__Recursion_Owf_type,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Olex__prod_type,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Message_Omsg_ONumber_type,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_UNIV_type,type,
c_UNIV: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Message_Omsg_OHash_type,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Datatype__Universe_Odsum_type,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i ).
thf(c_Wellfounded__Recursion_Oacyclic_type,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Sum__Type_OInr_type,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_type,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(c_List_Olex_type,type,
c_List_Olex: $i > $i > $i ).
thf(c_Sum__Type_OPlus_type,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tc_sum_type,type,
tc_sum: $i > $i > $i ).
thf(c_Main_OPlusE__1_type,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_type,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_type,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_type,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_List_Olenlex_type,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Main_OImageE__1_type,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_type,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_type,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_type,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_type,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_type,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(c_Main_Oin__listsI__1_type,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_Inter_type,type,
c_Inter: $i > $i > $i ).
thf(c_Main_OInterI__1_type,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_type,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Main_OuprodE__1_type,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_type,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_type,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_type,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_type,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdiagE__1_type,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_type,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OIdE__1_type,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_type,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
thf(c_Main_ODomainE__1_type,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(183,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(645,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(629,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(105,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(479,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(51,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(347,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(141,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OAgent_0) ).
thf(555,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(194,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(666,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(153,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(582,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(92,axiom,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(449,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(440,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(340,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(79,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(417,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(146,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(565,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(86,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(436,plain,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(587,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(98,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(460,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(80,axiom,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(421,plain,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(111,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(492,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(173,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(623,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(3,negated_conjecture,
~ ( c_in @ v_Y @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(211,plain,
~ ( c_in @ v_Y @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(163,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(602,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(687,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).
thf(396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).
thf(366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(131,axiom,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(534,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(52,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(349,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(161,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(598,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(83,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(429,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(25,axiom,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(275,plain,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(329,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(224,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(147,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(566,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(186,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(55,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(356,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(102,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(471,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(47,axiom,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(339,plain,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(71,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(393,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(654,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(165,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(605,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(244,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(558,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(530,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(586,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(192,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(662,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).
thf(618,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(205,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(689,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(62,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(584,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(81,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(423,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(151,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(577,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(445,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(672,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(164,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_ONumber_0) ).
thf(604,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(219,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(63,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(377,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(185,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(649,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(104,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(68,axiom,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(387,plain,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONonce__synth_0) ).
thf(631,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(520,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(240,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(203,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(685,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(608,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(306,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(658,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
c_in @ v_Y @ ( c_Message_Osynth @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(209,plain,
c_in @ v_Y @ ( c_Message_Osynth @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ B @ ( c_Message_Osynth @ C ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__trans_0) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ B @ ( c_Message_Osynth @ C ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(458,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(152,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(327,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(44,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(331,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(643,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(656,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(162,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(612,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(465,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(351,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(383,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(620,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(91,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(447,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(273,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(2,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(210,plain,
c_in @ v_X @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(506,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(56,axiom,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(358,plain,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(528,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(158,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(592,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(496,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(711,plain,
$false,
inference(cvc4,[status(thm)],[645,629,479,347,518,555,666,333,249,408,582,683,217,449,440,614,677,385,340,538,670,417,565,436,389,504,587,344,542,460,421,284,261,475,492,443,623,211,514,574,353,480,602,687,280,221,453,396,660,312,512,270,546,381,366,534,233,452,302,349,598,693,429,275,467,252,329,522,551,456,324,224,566,484,650,356,610,471,339,526,637,590,679,393,647,654,569,605,237,244,633,508,558,674,530,586,662,298,618,430,264,689,375,584,562,423,402,577,291,641,391,445,498,335,540,672,604,681,219,377,230,318,649,616,477,387,494,631,594,213,520,240,626,462,685,608,306,267,658,490,548,255,209,516,342,553,458,580,295,414,327,310,331,370,502,359,643,544,656,600,314,571,612,465,450,482,524,363,556,258,652,351,378,246,510,667,383,536,287,300,620,447,432,410,405,273,373,210,506,358,437,664,400,635,532,696,427,596,528,277,691,227,322,486,560,639,592,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV274-1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:13:07 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.10 % [INFO] Parsing done (250ms).
% 1.82/1.11 % [INFO] Running in sequential loop mode.
% 2.41/1.31 % [INFO] eprover registered as external prover.
% 2.41/1.31 % [INFO] cvc4 registered as external prover.
% 2.41/1.31 % [INFO] Scanning for conjecture ...
% 2.57/1.42 % [INFO] Found a conjecture and 1400 axioms. Running axiom selection ...
% 3.08/1.52 % [INFO] Axiom selection finished. Selected 205 axioms (removed 1195 axioms).
% 3.32/1.62 % [INFO] Problem is propositional (TPTP CNF).
% 3.62/1.63 % [INFO] Type checking passed.
% 3.62/1.63 % [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 ...
% 7.50/2.69 % External prover 'cvc4' found a proof!
% 7.50/2.69 % [INFO] Killing All external provers ...
% 7.50/2.69 % Time passed: 2167ms (effective reasoning time: 1579ms)
% 7.50/2.69 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.50/2.69 % Axioms used in derivation (205): 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_List_Olistrel__Nil1_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_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_Set_OPow__iff__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_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_Message_Oparts_OBody__dest_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_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_Message_Osynth__trans_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_List_Owf__lenlex_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
% 7.50/2.69 % No. of inferences in proof: 417
% 7.50/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2167 ms resp. 1579 ms w/o parsing
% 8.30/2.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.30/2.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------