%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT255^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.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 : Wed Feb 25 08:45:19 AM UTC 2026
% Result : Theorem 15.37s 3.51s
% Output : Refutation 15.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT255^1 : TPTP v9.2.1. Released v7.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Feb 24 06:13:04 EST 2026
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : DAT255^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.44 % Domain : Data Structures
% 0.16/0.44 % Problem : Data structure for translators from streams to streams 65
% 0.16/0.44 % Version : [Bla16] axioms : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.16/0.44 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.44 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.44 % Source : [Bla16]
% 0.16/0.44 % Names : stream_processor__65.p [Bla16]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.67 v7.2.0, 0.75 v7.1.0
% 0.16/0.44 % Syntax : Number of formulae : 339 ( 132 unt; 64 typ; 0 def)
% 0.16/0.44 % Number of atoms : 666 ( 256 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 9 ( 2 avg)
% 0.16/0.44 % Number of connectives : 5395 ( 54 ~; 3 |; 36 &;4970 @)
% 0.16/0.44 % ( 0 <=>; 332 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 28 ( 10 avg)
% 0.16/0.44 % Number of types : 6 ( 5 usr)
% 0.16/0.44 % Number of type conns : 446 ( 446 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 62 ( 59 usr; 4 con; 0-9 aty)
% 0.16/0.44 % Number of variables : 1527 ( 43 ^;1343 !; 33 ?;1527 :)
% 0.16/0.44 % ( 108 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.44 % SPC : TH1_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.44 % 2016-07-13 14:39:16.277
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 %----Could-be-implicit typings (11)
% 0.16/0.44 thf(ty_t_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060nu_062,type,
% 0.16/0.44 stream1273403375_sp_nu: $tType > $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream901396144_sp_mu: $tType > $tType > $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_Product__Type_Oprod,type,
% 0.16/0.44 product_prod: $tType > $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_Stream_Ostream,type,
% 0.16/0.44 stream: $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_Set_Oset,type,
% 0.16/0.44 set: $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_Nat_Onat,type,
% 0.16/0.44 nat: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_itself,type,
% 0.16/0.44 itself: $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_tf_d,type,
% 0.16/0.44 d: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_tf_c,type,
% 0.16/0.44 c: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_tf_b,type,
% 0.16/0.44 b: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_tf_a,type,
% 0.16/0.44 a: $tType ).
% 0.16/0.44
% 0.16/0.44 %----Explicit typings (53)
% 0.16/0.44 thf(sy_cl_HOL_Otype,type,
% 0.16/0.44 type:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Oord,type,
% 0.16/0.44 ord:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Otop,type,
% 0.16/0.44 top:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Oorder__top,type,
% 0.16/0.44 order_top:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Complete__Lattices_OSup,type,
% 0.16/0.44 complete_Sup:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.16/0.44 comple187826305attice:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain,type,
% 0.16/0.44 bNF_Ca1785829860lChain:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( A > B ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_BNF__Def_OfstOp,type,
% 0.16/0.44 bNF_fstOp:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > ( product_prod @ A @ C ) > ( product_prod @ A @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_BNF__Def_Opick__middlep,type,
% 0.16/0.44 bNF_pick_middlep:
% 0.16/0.44 !>[B: $tType,A: $tType,C: $tType] : ( ( B > A > $o ) > ( A > C > $o ) > B > C > A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_BNF__Def_OsndOp,type,
% 0.16/0.44 bNF_sndOp:
% 0.16/0.44 !>[C: $tType,A: $tType,B: $tType] : ( ( C > A > $o ) > ( A > B > $o ) > ( product_prod @ C @ B ) > ( product_prod @ A @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Complete__Lattices_OSup__class_OSup,type,
% 0.16/0.44 complete_Sup_Sup:
% 0.16/0.44 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Fun_Oinj__on,type,
% 0.16/0.44 inj_on:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Fun_Othe__inv__into,type,
% 0.16/0.44 the_inv_into:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > B > A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.16/0.44 uminus_uminus:
% 0.16/0.44 !>[A: $tType] : ( A > A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.16/0.44 ord_less_eq:
% 0.16/0.44 !>[A: $tType] : ( A > A > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.16/0.44 top_top:
% 0.16/0.44 !>[A: $tType] : A ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair,type,
% 0.16/0.44 product_Pair:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oapfst,type,
% 0.16/0.44 product_apfst:
% 0.16/0.44 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( product_prod @ A @ B ) > ( product_prod @ C @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oapsnd,type,
% 0.16/0.44 product_apsnd:
% 0.16/0.44 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( product_prod @ A @ B ) > ( product_prod @ A @ C ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Ocurry,type,
% 0.16/0.44 product_curry:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.16/0.44 produc2004651681e_prod:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Omap__prod,type,
% 0.16/0.44 product_map_prod:
% 0.16/0.44 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C ) > ( B > D ) > ( product_prod @ A @ B ) > ( product_prod @ C @ D ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 0.16/0.44 product_rec_bool:
% 0.16/0.44 !>[T: $tType] : ( T > T > $o > T ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.16/0.44 product_rec_prod:
% 0.16/0.44 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 0.16/0.44 product_case_prod:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 0.16/0.44 product_fst:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 0.16/0.44 product_snd:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 0.16/0.44 product_swap:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Pure_Otype,type,
% 0.16/0.44 type2:
% 0.16/0.44 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Set_OCollect,type,
% 0.16/0.44 collect:
% 0.16/0.44 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Set_Obind,type,
% 0.16/0.44 bind:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > ( set @ B ) ) > ( set @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Set_Oimage,type,
% 0.16/0.44 image:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Set_Ovimage,type,
% 0.16/0.44 vimage:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Orun_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream5064451run_mu:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( stream901396144_sp_mu @ A @ B @ C ) > ( stream @ A ) > ( product_prod @ ( product_prod @ B @ C ) @ ( stream @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_OGet,type,
% 0.16/0.44 stream1294929701mu_Get:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > ( stream901396144_sp_mu @ A @ B @ C ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_OPut,type,
% 0.16/0.44 stream1370332830mu_Put:
% 0.16/0.44 !>[B: $tType,C: $tType,A: $tType] : ( B > C > ( stream901396144_sp_mu @ A @ B @ C ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Ocase__sp_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream160000856_sp_mu:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > D ) > ( B > C > D ) > ( stream901396144_sp_mu @ A @ B @ C ) > D ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Opred__sp_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream123009735_sp_mu:
% 0.16/0.44 !>[A: $tType,B: $tType,E: $tType] : ( ( A > $o ) > ( B > $o ) > ( stream901396144_sp_mu @ E @ A @ B ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Orec__sp_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream674629690_sp_mu:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType,G: $tType] : ( ( ( A > ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ G ) ) > G ) > ( B > C > G ) > ( stream901396144_sp_mu @ A @ B @ C ) > G ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Orel__sp_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream1924447089_sp_mu:
% 0.16/0.44 !>[A: $tType,C: $tType,B: $tType,D: $tType,E: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( stream901396144_sp_mu @ E @ A @ B ) > ( stream901396144_sp_mu @ E @ C @ D ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Oset1__sp_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream2074884121_sp_mu:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( stream901396144_sp_mu @ A @ B @ C ) > ( set @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Oset2__sp_092_060_094sub_062_092_060mu_062,type,
% 0.16/0.44 stream1259315544_sp_mu:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( ( stream901396144_sp_mu @ A @ B @ C ) > ( set @ C ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osub,type,
% 0.16/0.44 stream152839592le_sub:
% 0.16/0.44 !>[A: $tType,B: $tType,C: $tType] : ( set @ ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream901396144_sp_mu @ A @ B @ C ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Wellfounded_Olex__prod,type,
% 0.16/0.44 lex_prod:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Wellfounded_Omeasure,type,
% 0.16/0.44 measure:
% 0.16/0.44 !>[A: $tType] : ( ( A > nat ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Wellfounded_Owf,type,
% 0.16/0.44 wf:
% 0.16/0.44 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Wfrec_Osame__fst,type,
% 0.16/0.44 same_fst:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Zorn_OChains,type,
% 0.16/0.44 chains:
% 0.16/0.44 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Zorn_Ochain__subset,type,
% 0.16/0.44 chain_subset:
% 0.16/0.44 !>[A: $tType] : ( ( set @ ( set @ A ) ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Zorn_Ochains,type,
% 0.16/0.44 chains2:
% 0.16/0.44 !>[A: $tType] : ( ( set @ ( set @ A ) ) > ( set @ ( set @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_member,type,
% 0.16/0.44 member:
% 0.16/0.44 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_P,type,
% 0.16/0.44 p: $o ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_x,type,
% 0.16/0.44 x: product_prod @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) ).
% 0.16/0.44
% 0.16/0.44 %----Relevant facts (256)
% 0.16/0.44 thf(fact_0_sp_092_060_094sub_062_092_060mu_062_Oinject_I1_J,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C ),Y1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( ( ( stream1294929701mu_Get @ A @ B @ C @ X1 )
% 0.16/0.44 = ( stream1294929701mu_Get @ A @ B @ C @ Y1 ) )
% 0.16/0.44 = ( X1 = Y1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.inject(1)
% 0.16/0.44 thf(fact_1_sp_092_060_094sub_062_092_060mu_062_Oinject_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,X21: B,X22: C,Y21: B,Y22: C] :
% 0.16/0.44 ( ( ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 )
% 0.16/0.44 = ( stream1370332830mu_Put @ B @ C @ A @ Y21 @ Y22 ) )
% 0.16/0.44 = ( ( X21 = Y21 )
% 0.16/0.44 & ( X22 = Y22 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.inject(2)
% 0.16/0.44 thf(fact_2_sp_092_060_094sub_062_092_060mu_062_Odistinct_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C ),X21: B,X22: C] :
% 0.16/0.44 ( ( stream1294929701mu_Get @ A @ B @ C @ X1 )
% 0.16/0.44 != ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.distinct(1)
% 0.16/0.44 thf(fact_3_sp_092_060_094sub_062_092_060mu_062_Oexhaust,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,Y: stream901396144_sp_mu @ A @ B @ C] :
% 0.16/0.44 ( ! [X12: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( stream1294929701mu_Get @ A @ B @ C @ X12 ) )
% 0.16/0.44 => ~ ! [X212: B,X222: C] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( stream1370332830mu_Put @ B @ C @ A @ X212 @ X222 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.exhaust
% 0.16/0.44 thf(fact_4_subI,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,F: A > ( stream901396144_sp_mu @ A @ B @ C ),A2: A] : ( member @ ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream901396144_sp_mu @ A @ B @ C ) ) @ ( product_Pair @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( F @ A2 ) @ ( stream1294929701mu_Get @ A @ B @ C @ F ) ) @ ( stream152839592le_sub @ A @ B @ C ) ) ).
% 0.16/0.44
% 0.16/0.44 % subI
% 0.16/0.44 thf(fact_5_prod_Oinject,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.16/0.44 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.16/0.44 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.16/0.44 = ( ( X1 = Y1 )
% 0.16/0.44 & ( X2 = Y2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inject
% 0.16/0.44 thf(fact_6_old_Oprod_Oinject,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.16/0.44 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.16/0.44 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.16/0.44 = ( ( A2 = A3 )
% 0.16/0.44 & ( B2 = B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inject
% 0.16/0.44 thf(fact_7_run_092_060_094sub_062_092_060mu_062_Osimps_I2_J,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,B2: B,Sp: C,S: stream @ A] :
% 0.16/0.44 ( ( stream5064451run_mu @ A @ B @ C @ ( stream1370332830mu_Put @ B @ C @ A @ B2 @ Sp ) @ S )
% 0.16/0.44 = ( product_Pair @ ( product_prod @ B @ C ) @ ( stream @ A ) @ ( product_Pair @ B @ C @ B2 @ Sp ) @ S ) ) ).
% 0.16/0.44
% 0.16/0.44 % run\<^sub>\<mu>.simps(2)
% 0.16/0.44 thf(fact_8_surj__pair,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 0.16/0.44 ? [X: A,Y3: B] :
% 0.16/0.44 ( P
% 0.16/0.44 = ( product_Pair @ A @ B @ X @ Y3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_pair
% 0.16/0.44 thf(fact_9_prod__cases,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 0.16/0.44 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.16/0.44 => ( P2 @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases
% 0.16/0.44 thf(fact_10_Pair__inject,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.16/0.44 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.16/0.44 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.16/0.44 => ~ ( ( A2 = A3 )
% 0.16/0.44 => ( B2 != B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Pair_inject
% 0.16/0.44 thf(fact_11_prod__cases3,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.44 ~ ! [A4: A,B4: B,C2: C] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases3
% 0.16/0.44 thf(fact_12_prod__cases4,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.16/0.44 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases4
% 0.16/0.44 thf(fact_13_prod__cases5,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.16/0.44 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases5
% 0.16/0.44 thf(fact_14_prod__cases6,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.16/0.44 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases6
% 0.16/0.44 thf(fact_15_prod__cases7,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 0.16/0.44 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2,G2: G] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases7
% 0.16/0.44 thf(fact_16_old_Oprod_Oinducts,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.16/0.44 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.16/0.44 => ( P2 @ Prod ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inducts
% 0.16/0.44 thf(fact_17_old_Oprod_Oexhaust,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.16/0.44 ~ ! [A4: A,B4: B] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.exhaust
% 0.16/0.44 thf(fact_18_prod__induct7,axiom,
% 0.16/0.44 ! [G: $tType,F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 0.16/0.44 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) )
% 0.16/0.44 => ( P2 @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_induct7
% 0.16/0.44 thf(fact_19_prod__induct6,axiom,
% 0.16/0.44 ! [F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.16/0.44 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 0.16/0.44 => ( P2 @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_induct6
% 0.16/0.44 thf(fact_20_prod__induct5,axiom,
% 0.16/0.44 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.16/0.44 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.16/0.44 => ( P2 @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_induct5
% 0.16/0.44 thf(fact_21_prod__induct4,axiom,
% 0.16/0.44 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.16/0.44 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.16/0.44 => ( P2 @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_induct4
% 0.16/0.44 thf(fact_22_prod__induct3,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.44 ( ! [A4: A,B4: B,C2: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 0.16/0.44 => ( P2 @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_induct3
% 0.16/0.44 thf(fact_23_old_Oprod_Orec,axiom,
% 0.16/0.44 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.16/0.44 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.16/0.44 = ( F1 @ A2 @ B2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.rec
% 0.16/0.44 thf(fact_24_internal__case__prod__conv,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.16/0.44 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.16/0.44 = ( C3 @ A2 @ B2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % internal_case_prod_conv
% 0.16/0.44 thf(fact_25_ssubst__Pair__rhs,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,R: A,S: B,R2: set @ ( product_prod @ A @ B ),S2: B] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S ) @ R2 )
% 0.16/0.44 => ( ( S2 = S )
% 0.16/0.44 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ssubst_Pair_rhs
% 0.16/0.44 thf(fact_26_curry__conv,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,B: $tType] :
% 0.16/0.44 ( ( product_curry @ B @ C @ A )
% 0.16/0.44 = ( ^ [F4: ( product_prod @ B @ C ) > A,A5: B,B5: C] : ( F4 @ ( product_Pair @ B @ C @ A5 @ B5 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % curry_conv
% 0.16/0.44 thf(fact_27_sp_092_060_094sub_062_092_060mu_062_Osimps_I6_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,D: $tType,C: $tType,F1: ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > D,F22: B > C > D,X21: B,X22: C] :
% 0.16/0.44 ( ( stream160000856_sp_mu @ A @ B @ C @ D @ F1 @ F22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) )
% 0.16/0.44 = ( F22 @ X21 @ X22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.simps(6)
% 0.16/0.44 thf(fact_28_sp_092_060_094sub_062_092_060mu_062_Osimps_I5_J,axiom,
% 0.16/0.44 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > D,F22: B > C > D,X1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( ( stream160000856_sp_mu @ A @ B @ C @ D @ F1 @ F22 @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) )
% 0.16/0.44 = ( F1 @ X1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.simps(5)
% 0.16/0.44 thf(fact_29_curryI,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.16/0.44 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.16/0.44 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % curryI
% 0.16/0.44 thf(fact_30_sp_092_060_094sub_062_092_060mu_062_Osimps_I8_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,G: $tType,C: $tType,F1: ( A > ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ G ) ) > G,F22: B > C > G,X21: B,X22: C] :
% 0.16/0.44 ( ( stream674629690_sp_mu @ A @ B @ C @ G @ F1 @ F22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) )
% 0.16/0.44 = ( F22 @ X21 @ X22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.simps(8)
% 0.16/0.44 thf(fact_31_sp_092_060_094sub_062_092_060mu_062_Opred__inject_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,P1: B > $o,P22: C > $o,A2: B,Aa: C] :
% 0.16/0.44 ( ( stream123009735_sp_mu @ B @ C @ A @ P1 @ P22 @ ( stream1370332830mu_Put @ B @ C @ A @ A2 @ Aa ) )
% 0.16/0.44 = ( ( P1 @ A2 )
% 0.16/0.44 & ( P22 @ Aa ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.pred_inject(2)
% 0.16/0.44 thf(fact_32_swap__simp,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X3: B,Y: A] :
% 0.16/0.44 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) )
% 0.16/0.44 = ( product_Pair @ A @ B @ Y @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % swap_simp
% 0.16/0.44 thf(fact_33_swap__swap,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P: product_prod @ A @ B] :
% 0.16/0.44 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P ) )
% 0.16/0.44 = P ) ).
% 0.16/0.44
% 0.16/0.44 % swap_swap
% 0.16/0.44 thf(fact_34_curryD,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.16/0.44 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.16/0.44 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % curryD
% 0.16/0.44 thf(fact_35_curryE,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.16/0.44 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.16/0.44 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % curryE
% 0.16/0.44 thf(fact_36_pair__in__swap__image,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Y: A,X3: B,A6: set @ ( product_prod @ B @ A )] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y @ X3 ) @ ( image @ ( product_prod @ B @ A ) @ ( product_prod @ A @ B ) @ ( product_swap @ B @ A ) @ A6 ) )
% 0.16/0.44 = ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ X3 @ Y ) @ A6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pair_in_swap_image
% 0.16/0.44 thf(fact_37_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I2_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,D: $tType,C: $tType,G: $tType,R1: A > C > $o,R22: B > D > $o,Y21: A,Y22: B,X1: G > ( stream901396144_sp_mu @ G @ C @ D )] :
% 0.16/0.44 ~ ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 @ ( stream1370332830mu_Put @ A @ B @ G @ Y21 @ Y22 ) @ ( stream1294929701mu_Get @ G @ C @ D @ X1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_distinct(2)
% 0.16/0.44 thf(fact_38_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,E: $tType,A: $tType,F2: $tType,R1: B > E > $o,R22: C > F2 > $o,X1: A > ( stream901396144_sp_mu @ A @ B @ C ),Y21: E,Y22: F2] :
% 0.16/0.44 ~ ( stream1924447089_sp_mu @ B @ E @ C @ F2 @ A @ R1 @ R22 @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) @ ( stream1370332830mu_Put @ E @ F2 @ A @ Y21 @ Y22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_distinct(1)
% 0.16/0.44 thf(fact_39_internal__case__prod__def,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType] :
% 0.16/0.44 ( ( produc2004651681e_prod @ A @ B @ C )
% 0.16/0.44 = ( product_case_prod @ A @ B @ C ) ) ).
% 0.16/0.44
% 0.16/0.44 % internal_case_prod_def
% 0.16/0.44 thf(fact_40_wf__sub,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType] : ( wf @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream152839592le_sub @ A @ B @ C ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_sub
% 0.16/0.44 thf(fact_41_apsnd__conv,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,F: C > B,X3: A,Y: C] :
% 0.16/0.44 ( ( product_apsnd @ C @ B @ A @ F @ ( product_Pair @ A @ C @ X3 @ Y ) )
% 0.16/0.44 = ( product_Pair @ A @ B @ X3 @ ( F @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % apsnd_conv
% 0.16/0.44 thf(fact_42_old_Obool_Osimps_I5_J,axiom,
% 0.16/0.44 ! [T: $tType,F1: T,F22: T] :
% 0.16/0.44 ( ( product_rec_bool @ T @ F1 @ F22 @ $true )
% 0.16/0.44 = F1 ) ).
% 0.16/0.44
% 0.16/0.44 % old.bool.simps(5)
% 0.16/0.44 thf(fact_43_old_Obool_Osimps_I6_J,axiom,
% 0.16/0.44 ! [T: $tType,F1: T,F22: T] :
% 0.16/0.44 ( ( product_rec_bool @ T @ F1 @ F22 @ $false )
% 0.16/0.44 = F22 ) ).
% 0.16/0.44
% 0.16/0.44 % old.bool.simps(6)
% 0.16/0.44 thf(fact_44_apfst__conv,axiom,
% 0.16/0.44 ! [C: $tType,A: $tType,B: $tType,F: C > A,X3: C,Y: B] :
% 0.16/0.44 ( ( product_apfst @ C @ A @ B @ F @ ( product_Pair @ C @ B @ X3 @ Y ) )
% 0.16/0.44 = ( product_Pair @ A @ B @ ( F @ X3 ) @ Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % apfst_conv
% 0.16/0.44 thf(fact_45_mem__Collect__eq,axiom,
% 0.16/0.44 ! [A: $tType,A2: A,P2: A > $o] :
% 0.16/0.44 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.16/0.44 = ( P2 @ A2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % mem_Collect_eq
% 0.16/0.44 thf(fact_46_Collect__mem__eq,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A] :
% 0.16/0.44 ( ( collect @ A
% 0.16/0.44 @ ^ [X4: A] : ( member @ A @ X4 @ A6 ) )
% 0.16/0.44 = A6 ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_mem_eq
% 0.16/0.44 thf(fact_47_Collect__cong,axiom,
% 0.16/0.44 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( P2 @ X )
% 0.16/0.44 = ( Q @ X ) )
% 0.16/0.44 => ( ( collect @ A @ P2 )
% 0.16/0.44 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_cong
% 0.16/0.44 thf(fact_48_ext,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,G3: A > B] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( F @ X )
% 0.16/0.44 = ( G3 @ X ) )
% 0.16/0.44 => ( F = G3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % ext
% 0.16/0.44 thf(fact_49_curry__case__prod,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,F: A > B > C] :
% 0.16/0.44 ( ( product_curry @ A @ B @ C @ ( product_case_prod @ A @ B @ C @ F ) )
% 0.16/0.44 = F ) ).
% 0.16/0.44
% 0.16/0.44 % curry_case_prod
% 0.16/0.44 thf(fact_50_case__prod__curry,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,F: ( product_prod @ A @ B ) > C] :
% 0.16/0.44 ( ( product_case_prod @ A @ B @ C @ ( product_curry @ A @ B @ C @ F ) )
% 0.16/0.44 = F ) ).
% 0.16/0.44
% 0.16/0.44 % case_prod_curry
% 0.16/0.44 thf(fact_51_sp_092_060_094sub_062_092_060mu_062_Orel__eq,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,G: $tType] :
% 0.16/0.44 ( ( stream1924447089_sp_mu @ A @ A @ B @ B @ G
% 0.16/0.44 @ ^ [Y4: A,Z: A] : ( Y4 = Z )
% 0.16/0.44 @ ^ [Y4: B,Z: B] : ( Y4 = Z ) )
% 0.16/0.44 = ( ^ [Y4: stream901396144_sp_mu @ G @ A @ B,Z: stream901396144_sp_mu @ G @ A @ B] : ( Y4 = Z ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_eq
% 0.16/0.44 thf(fact_52_sp_092_060_094sub_062_092_060mu_062_Orel__refl,axiom,
% 0.16/0.44 ! [D: $tType,C: $tType,G: $tType,R1a: C > C > $o,R2a: D > D > $o,X3: stream901396144_sp_mu @ G @ C @ D] :
% 0.16/0.44 ( ! [X: C] : ( R1a @ X @ X )
% 0.16/0.44 => ( ! [X: D] : ( R2a @ X @ X )
% 0.16/0.44 => ( stream1924447089_sp_mu @ C @ C @ D @ D @ G @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_refl
% 0.16/0.44 thf(fact_53_apsnd__apfst__commute,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,D: $tType,F: C > B,G3: D > A,P: product_prod @ D @ C] :
% 0.16/0.44 ( ( product_apsnd @ C @ B @ A @ F @ ( product_apfst @ D @ A @ C @ G3 @ P ) )
% 0.16/0.44 = ( product_apfst @ D @ A @ B @ G3 @ ( product_apsnd @ C @ B @ D @ F @ P ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % apsnd_apfst_commute
% 0.16/0.44 thf(fact_54_mem__case__prodE,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,Z2: A,C3: B > C > ( set @ A ),P: product_prod @ B @ C] :
% 0.16/0.44 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C3 @ P ) )
% 0.16/0.44 => ~ ! [X: B,Y3: C] :
% 0.16/0.44 ( ( P
% 0.16/0.44 = ( product_Pair @ B @ C @ X @ Y3 ) )
% 0.16/0.44 => ~ ( member @ A @ Z2 @ ( C3 @ X @ Y3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % mem_case_prodE
% 0.16/0.44 thf(fact_55_old_Oprod_Ocase,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,B: $tType,F: A > B > C,X1: A,X2: B] :
% 0.16/0.44 ( ( product_case_prod @ A @ B @ C @ F @ ( product_Pair @ A @ B @ X1 @ X2 ) )
% 0.16/0.44 = ( F @ X1 @ X2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.case
% 0.16/0.44 thf(fact_56_sp_092_060_094sub_062_092_060mu_062_Orel__intros_I2_J,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,E: $tType,A: $tType,F2: $tType,R1: B > E > $o,X21: B,Y21: E,R22: C > F2 > $o,X22: C,Y22: F2] :
% 0.16/0.44 ( ( R1 @ X21 @ Y21 )
% 0.16/0.44 => ( ( R22 @ X22 @ Y22 )
% 0.16/0.44 => ( stream1924447089_sp_mu @ B @ E @ C @ F2 @ A @ R1 @ R22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) @ ( stream1370332830mu_Put @ E @ F2 @ A @ Y21 @ Y22 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_intros(2)
% 0.16/0.44 thf(fact_57_sp_092_060_094sub_062_092_060mu_062_Orel__inject_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,E: $tType,B: $tType,C: $tType,F2: $tType,R1: B > E > $o,R22: C > F2 > $o,X21: B,X22: C,Y21: E,Y22: F2] :
% 0.16/0.44 ( ( stream1924447089_sp_mu @ B @ E @ C @ F2 @ A @ R1 @ R22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) @ ( stream1370332830mu_Put @ E @ F2 @ A @ Y21 @ Y22 ) )
% 0.16/0.44 = ( ( R1 @ X21 @ Y21 )
% 0.16/0.44 & ( R22 @ X22 @ Y22 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_inject(2)
% 0.16/0.44 thf(fact_58_image__eqI,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,B2: A,F: B > A,X3: B,A6: set @ B] :
% 0.16/0.44 ( ( B2
% 0.16/0.44 = ( F @ X3 ) )
% 0.16/0.44 => ( ( member @ B @ X3 @ A6 )
% 0.16/0.44 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_eqI
% 0.16/0.44 thf(fact_59_wf__def,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( wf @ A )
% 0.16/0.44 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ! [P3: A > $o] :
% 0.16/0.44 ( ! [X4: A] :
% 0.16/0.44 ( ! [Y5: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X4 ) @ R3 )
% 0.16/0.44 => ( P3 @ Y5 ) )
% 0.16/0.44 => ( P3 @ X4 ) )
% 0.16/0.44 => ( ^ [P4: A > $o] :
% 0.16/0.44 ! [X5: A] : ( P4 @ X5 )
% 0.16/0.44 @ P3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_def
% 0.16/0.44 thf(fact_60_wfE__min,axiom,
% 0.16/0.44 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),X3: A,Q: set @ A] :
% 0.16/0.44 ( ( wf @ A @ R2 )
% 0.16/0.44 => ( ( member @ A @ X3 @ Q )
% 0.16/0.44 => ~ ! [Z3: A] :
% 0.16/0.44 ( ( member @ A @ Z3 @ Q )
% 0.16/0.44 => ~ ! [Y6: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ Z3 ) @ R2 )
% 0.16/0.44 => ~ ( member @ A @ Y6 @ Q ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wfE_min
% 0.16/0.44 thf(fact_61_wfI__min,axiom,
% 0.16/0.44 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ( ! [X: A,Q2: set @ A] :
% 0.16/0.44 ( ( member @ A @ X @ Q2 )
% 0.16/0.44 => ? [Xa: A] :
% 0.16/0.44 ( ( member @ A @ Xa @ Q2 )
% 0.16/0.44 & ! [Y3: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ Xa ) @ R2 )
% 0.16/0.44 => ~ ( member @ A @ Y3 @ Q2 ) ) ) )
% 0.16/0.44 => ( wf @ A @ R2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % wfI_min
% 0.16/0.44 thf(fact_62_wfUNIVI,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ( ! [P5: A > $o,X: A] :
% 0.16/0.44 ( ! [Xa: A] :
% 0.16/0.44 ( ! [Y3: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ Xa ) @ R )
% 0.16/0.44 => ( P5 @ Y3 ) )
% 0.16/0.44 => ( P5 @ Xa ) )
% 0.16/0.44 => ( P5 @ X ) )
% 0.16/0.44 => ( wf @ A @ R ) ) ).
% 0.16/0.44
% 0.16/0.44 % wfUNIVI
% 0.16/0.44 thf(fact_63_wf__asym,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A,X3: A] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ X3 ) @ R )
% 0.16/0.44 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ A2 ) @ R ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_asym
% 0.16/0.44 thf(fact_64_wf__induct,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),P2: A > $o,A2: A] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ( ! [X: A] :
% 0.16/0.44 ( ! [Y6: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X ) @ R )
% 0.16/0.44 => ( P2 @ Y6 ) )
% 0.16/0.44 => ( P2 @ X ) )
% 0.16/0.44 => ( P2 @ A2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_induct
% 0.16/0.44 thf(fact_65_wf__irrefl,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ R ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_irrefl
% 0.16/0.44 thf(fact_66_rev__image__eqI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X3: A,A6: set @ A,B2: B,F: A > B] :
% 0.16/0.44 ( ( member @ A @ X3 @ A6 )
% 0.16/0.44 => ( ( B2
% 0.16/0.44 = ( F @ X3 ) )
% 0.16/0.44 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rev_image_eqI
% 0.16/0.44 thf(fact_67_ball__imageD,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: B > A,A6: set @ B,P2: A > $o] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( member @ A @ X @ ( image @ B @ A @ F @ A6 ) )
% 0.16/0.44 => ( P2 @ X ) )
% 0.16/0.44 => ! [X6: B] :
% 0.16/0.44 ( ( member @ B @ X6 @ A6 )
% 0.16/0.44 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ball_imageD
% 0.16/0.44 thf(fact_68_image__cong,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,M: set @ A,N: set @ A,F: A > B,G3: A > B] :
% 0.16/0.44 ( ( M = N )
% 0.16/0.44 => ( ! [X: A] :
% 0.16/0.44 ( ( member @ A @ X @ N )
% 0.16/0.44 => ( ( F @ X )
% 0.16/0.44 = ( G3 @ X ) ) )
% 0.16/0.44 => ( ( image @ A @ B @ F @ M )
% 0.16/0.44 = ( image @ A @ B @ G3 @ N ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_cong
% 0.16/0.44 thf(fact_69_bex__imageD,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: B > A,A6: set @ B,P2: A > $o] :
% 0.16/0.44 ( ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( image @ B @ A @ F @ A6 ) )
% 0.16/0.44 & ( P2 @ X6 ) )
% 0.16/0.44 => ? [X: B] :
% 0.16/0.44 ( ( member @ B @ X @ A6 )
% 0.16/0.44 & ( P2 @ ( F @ X ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bex_imageD
% 0.16/0.44 thf(fact_70_image__iff,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Z2: A,F: B > A,A6: set @ B] :
% 0.16/0.44 ( ( member @ A @ Z2 @ ( image @ B @ A @ F @ A6 ) )
% 0.16/0.44 = ( ? [X4: B] :
% 0.16/0.44 ( ( member @ B @ X4 @ A6 )
% 0.16/0.44 & ( Z2
% 0.16/0.44 = ( F @ X4 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_iff
% 0.16/0.44 thf(fact_71_imageI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X3: A,A6: set @ A,F: A > B] :
% 0.16/0.44 ( ( member @ A @ X3 @ A6 )
% 0.16/0.44 => ( member @ B @ ( F @ X3 ) @ ( image @ A @ B @ F @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % imageI
% 0.16/0.44 thf(fact_72_wf__induct__rule,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),P2: A > $o,A2: A] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ( ! [X: A] :
% 0.16/0.44 ( ! [Y6: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X ) @ R )
% 0.16/0.44 => ( P2 @ Y6 ) )
% 0.16/0.44 => ( P2 @ X ) )
% 0.16/0.44 => ( P2 @ A2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_induct_rule
% 0.16/0.44 thf(fact_73_wf__eq__minimal,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( wf @ A )
% 0.16/0.44 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ! [Q3: set @ A] :
% 0.16/0.44 ( ? [X4: A] : ( member @ A @ X4 @ Q3 )
% 0.16/0.44 => ? [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ Q3 )
% 0.16/0.44 & ! [Y5: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X4 ) @ R3 )
% 0.16/0.44 => ~ ( member @ A @ Y5 @ Q3 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_eq_minimal
% 0.16/0.44 thf(fact_74_wf__not__refl,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ R ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_not_refl
% 0.16/0.44 thf(fact_75_wf__not__sym,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A,X3: A] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ X3 ) @ R )
% 0.16/0.44 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ A2 ) @ R ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_not_sym
% 0.16/0.44 thf(fact_76_wf__measure,axiom,
% 0.16/0.44 ! [A: $tType,F: A > nat] : ( wf @ A @ ( measure @ A @ F ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_measure
% 0.16/0.44 thf(fact_77_dependent__wf__choice,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ A ),P2: ( A > B ) > A > B > $o] :
% 0.16/0.44 ( ( wf @ A @ R2 )
% 0.16/0.44 => ( ! [F3: A > B,G2: A > B,X: A,R4: B] :
% 0.16/0.44 ( ! [Z4: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z4 @ X ) @ R2 )
% 0.16/0.44 => ( ( F3 @ Z4 )
% 0.16/0.44 = ( G2 @ Z4 ) ) )
% 0.16/0.44 => ( ( P2 @ F3 @ X @ R4 )
% 0.16/0.44 = ( P2 @ G2 @ X @ R4 ) ) )
% 0.16/0.44 => ( ! [X: A,F3: A > B] :
% 0.16/0.44 ( ! [Y6: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X ) @ R2 )
% 0.16/0.44 => ( P2 @ F3 @ Y6 @ ( F3 @ Y6 ) ) )
% 0.16/0.44 => ? [X13: B] : ( P2 @ F3 @ X @ X13 ) )
% 0.16/0.44 => ? [F3: A > B] :
% 0.16/0.44 ! [X6: A] : ( P2 @ F3 @ X6 @ ( F3 @ X6 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % dependent_wf_choice
% 0.16/0.44 thf(fact_78_split__cong,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,Q4: product_prod @ A @ B,F: A > B > C,G3: A > B > C,P: product_prod @ A @ B] :
% 0.16/0.44 ( ! [X: A,Y3: B] :
% 0.16/0.44 ( ( ( product_Pair @ A @ B @ X @ Y3 )
% 0.16/0.44 = Q4 )
% 0.16/0.44 => ( ( F @ X @ Y3 )
% 0.16/0.44 = ( G3 @ X @ Y3 ) ) )
% 0.16/0.44 => ( ( P = Q4 )
% 0.16/0.44 => ( ( product_case_prod @ A @ B @ C @ F @ P )
% 0.16/0.44 = ( product_case_prod @ A @ B @ C @ G3 @ Q4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_cong
% 0.16/0.44 thf(fact_79_wf__lex__prod,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Ra: set @ ( product_prod @ A @ A ),Rb: set @ ( product_prod @ B @ B )] :
% 0.16/0.44 ( ( wf @ A @ Ra )
% 0.16/0.44 => ( ( wf @ B @ Rb )
% 0.16/0.44 => ( wf @ ( product_prod @ A @ B ) @ ( lex_prod @ A @ B @ Ra @ Rb ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_lex_prod
% 0.16/0.44 thf(fact_80_in__lex__prod,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B,R: set @ ( product_prod @ A @ A ),S: set @ ( product_prod @ B @ B )] :
% 0.16/0.44 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ ( lex_prod @ A @ B @ R @ S ) )
% 0.16/0.44 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A3 ) @ R )
% 0.16/0.44 | ( ( A2 = A3 )
% 0.16/0.44 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B3 ) @ S ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % in_lex_prod
% 0.16/0.44 thf(fact_81_surj__swap,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( image @ ( product_prod @ B @ A ) @ ( product_prod @ A @ B ) @ ( product_swap @ B @ A ) @ ( top_top @ ( set @ ( product_prod @ B @ A ) ) ) )
% 0.16/0.44 = ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_swap
% 0.16/0.44 thf(fact_82_Sup_OSUP__cong,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A6: set @ B,B6: set @ B,C4: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 0.16/0.44 ( ( A6 = B6 )
% 0.16/0.44 => ( ! [X: B] :
% 0.16/0.44 ( ( member @ B @ X @ B6 )
% 0.16/0.44 => ( ( C4 @ X )
% 0.16/0.44 = ( D3 @ X ) ) )
% 0.16/0.44 => ( ( Sup @ ( image @ B @ A @ C4 @ A6 ) )
% 0.16/0.44 = ( Sup @ ( image @ B @ A @ D3 @ B6 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup.SUP_cong
% 0.16/0.44 thf(fact_83_UNIV__I,axiom,
% 0.16/0.44 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UNIV_I
% 0.16/0.44 thf(fact_84_UNIV__witness,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ? [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UNIV_witness
% 0.16/0.44 thf(fact_85_UNIV__eq__I,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A] :
% 0.16/0.44 ( ! [X: A] : ( member @ A @ X @ A6 )
% 0.16/0.44 => ( ( top_top @ ( set @ A ) )
% 0.16/0.44 = A6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % UNIV_eq_I
% 0.16/0.44 thf(fact_86_range__eqI,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,B2: A,F: B > A,X3: B] :
% 0.16/0.44 ( ( B2
% 0.16/0.44 = ( F @ X3 ) )
% 0.16/0.44 => ( member @ A @ B2 @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % range_eqI
% 0.16/0.44 thf(fact_87_rangeI,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: B > A,X3: B] : ( member @ A @ ( F @ X3 ) @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rangeI
% 0.16/0.44 thf(fact_88_sp_092_060_094sub_062_092_060mu_062_Oinduct,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,P2: ( stream901396144_sp_mu @ A @ B @ C ) > $o,Sp_mu: stream901396144_sp_mu @ A @ B @ C] :
% 0.16/0.44 ( ! [X: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( ! [Xa: stream901396144_sp_mu @ A @ B @ C] :
% 0.16/0.44 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ Xa @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ X @ ( top_top @ ( set @ A ) ) ) )
% 0.16/0.44 => ( P2 @ Xa ) )
% 0.16/0.44 => ( P2 @ ( stream1294929701mu_Get @ A @ B @ C @ X ) ) )
% 0.16/0.44 => ( ! [X1a: B,X23: C] : ( P2 @ ( stream1370332830mu_Put @ B @ C @ A @ X1a @ X23 ) )
% 0.16/0.44 => ( P2 @ Sp_mu ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.induct
% 0.16/0.44 thf(fact_89_Inf_OINF__cong,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A6: set @ B,B6: set @ B,C4: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 0.16/0.44 ( ( A6 = B6 )
% 0.16/0.44 => ( ! [X: B] :
% 0.16/0.44 ( ( member @ B @ X @ B6 )
% 0.16/0.44 => ( ( C4 @ X )
% 0.16/0.44 = ( D3 @ X ) ) )
% 0.16/0.44 => ( ( Inf @ ( image @ B @ A @ C4 @ A6 ) )
% 0.16/0.44 = ( Inf @ ( image @ B @ A @ D3 @ B6 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Inf.INF_cong
% 0.16/0.44 thf(fact_90_iso__tuple__UNIV__I,axiom,
% 0.16/0.44 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % iso_tuple_UNIV_I
% 0.16/0.44 thf(fact_91_top__apply,axiom,
% 0.16/0.44 ! [C: $tType,D: $tType] :
% 0.16/0.44 ( ( top @ C @ ( type2 @ C ) )
% 0.16/0.44 => ( ( top_top @ ( D > C ) )
% 0.16/0.44 = ( ^ [X4: D] : ( top_top @ C ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % top_apply
% 0.16/0.44 thf(fact_92_surjD,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.16/0.44 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ? [X: B] :
% 0.16/0.44 ( Y
% 0.16/0.44 = ( F @ X ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % surjD
% 0.16/0.44 thf(fact_93_surjE,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.16/0.44 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ~ ! [X: B] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( F @ X ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % surjE
% 0.16/0.44 thf(fact_94_surjI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,G3: B > A,F: A > B] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( G3 @ ( F @ X ) )
% 0.16/0.44 = X )
% 0.16/0.44 => ( ( image @ B @ A @ G3 @ ( top_top @ ( set @ B ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % surjI
% 0.16/0.44 thf(fact_95_surj__def,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: B > A] :
% 0.16/0.44 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) )
% 0.16/0.44 = ( ! [Y5: A] :
% 0.16/0.44 ? [X4: B] :
% 0.16/0.44 ( Y5
% 0.16/0.44 = ( F @ X4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_def
% 0.16/0.44 thf(fact_96_top__set__def,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( top_top @ ( set @ A ) )
% 0.16/0.44 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % top_set_def
% 0.16/0.44 thf(fact_97_sp_092_060_094sub_062_092_060mu_062_Oset__cases_I2_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,E3: C,A2: stream901396144_sp_mu @ A @ B @ C] :
% 0.16/0.44 ( ( member @ C @ E3 @ ( stream1259315544_sp_mu @ A @ B @ C @ A2 ) )
% 0.16/0.44 => ( ! [Z3: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( ( A2
% 0.16/0.44 = ( stream1294929701mu_Get @ A @ B @ C @ Z3 ) )
% 0.16/0.44 => ! [X: stream901396144_sp_mu @ A @ B @ C] :
% 0.16/0.44 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ X @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ Z3 @ ( top_top @ ( set @ A ) ) ) )
% 0.16/0.44 => ~ ( member @ C @ E3 @ ( stream1259315544_sp_mu @ A @ B @ C @ X ) ) ) )
% 0.16/0.44 => ~ ! [Z1: B] :
% 0.16/0.44 ( A2
% 0.16/0.44 != ( stream1370332830mu_Put @ B @ C @ A @ Z1 @ E3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.set_cases(2)
% 0.16/0.44 thf(fact_98_sp_092_060_094sub_062_092_060mu_062_Oset__cases_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,E3: B,A2: stream901396144_sp_mu @ A @ B @ C] :
% 0.16/0.44 ( ( member @ B @ E3 @ ( stream2074884121_sp_mu @ A @ B @ C @ A2 ) )
% 0.16/0.44 => ( ! [Z3: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( ( A2
% 0.16/0.44 = ( stream1294929701mu_Get @ A @ B @ C @ Z3 ) )
% 0.16/0.44 => ! [X: stream901396144_sp_mu @ A @ B @ C] :
% 0.16/0.44 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ X @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ Z3 @ ( top_top @ ( set @ A ) ) ) )
% 0.16/0.44 => ~ ( member @ B @ E3 @ ( stream2074884121_sp_mu @ A @ B @ C @ X ) ) ) )
% 0.16/0.44 => ~ ! [Z22: C] :
% 0.16/0.44 ( A2
% 0.16/0.44 != ( stream1370332830mu_Put @ B @ C @ A @ E3 @ Z22 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.set_cases(1)
% 0.16/0.44 thf(fact_99_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I3_J,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,Xc: stream901396144_sp_mu @ A @ B @ C,Aa: A > ( stream901396144_sp_mu @ A @ B @ C ),Xe: C] :
% 0.16/0.44 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ Xc @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ Aa @ ( top_top @ ( set @ A ) ) ) )
% 0.16/0.44 => ( ( member @ C @ Xe @ ( stream1259315544_sp_mu @ A @ B @ C @ Xc ) )
% 0.16/0.44 => ( member @ C @ Xe @ ( stream1259315544_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ Aa ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.set_intros(3)
% 0.16/0.44 thf(fact_100_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I1_J,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,X3: stream901396144_sp_mu @ A @ B @ C,A2: A > ( stream901396144_sp_mu @ A @ B @ C ),Xa2: B] :
% 0.16/0.44 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ X3 @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ A2 @ ( top_top @ ( set @ A ) ) ) )
% 0.16/0.44 => ( ( member @ B @ Xa2 @ ( stream2074884121_sp_mu @ A @ B @ C @ X3 ) )
% 0.16/0.44 => ( member @ B @ Xa2 @ ( stream2074884121_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ A2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.set_intros(1)
% 0.16/0.44 thf(fact_101_map__prod__surj,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,D: $tType,B: $tType,F: A > B,G3: C > D] :
% 0.16/0.44 ( ( ( image @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 = ( top_top @ ( set @ B ) ) )
% 0.16/0.44 => ( ( ( image @ C @ D @ G3 @ ( top_top @ ( set @ C ) ) )
% 0.16/0.44 = ( top_top @ ( set @ D ) ) )
% 0.16/0.44 => ( ( image @ ( product_prod @ A @ C ) @ ( product_prod @ B @ D ) @ ( product_map_prod @ A @ B @ C @ D @ F @ G3 ) @ ( top_top @ ( set @ ( product_prod @ A @ C ) ) ) )
% 0.16/0.44 = ( top_top @ ( set @ ( product_prod @ B @ D ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_prod_surj
% 0.16/0.44 thf(fact_102_top1I,axiom,
% 0.16/0.44 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 0.16/0.44
% 0.16/0.44 % top1I
% 0.16/0.44 thf(fact_103_map__prod__simp,axiom,
% 0.16/0.44 ! [C: $tType,A: $tType,B: $tType,D: $tType,F: C > A,G3: D > B,A2: C,B2: D] :
% 0.16/0.44 ( ( product_map_prod @ C @ A @ D @ B @ F @ G3 @ ( product_Pair @ C @ D @ A2 @ B2 ) )
% 0.16/0.44 = ( product_Pair @ A @ B @ ( F @ A2 ) @ ( G3 @ B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_prod_simp
% 0.16/0.44 thf(fact_104_map__prod__imageI,axiom,
% 0.16/0.44 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: A,B2: B,R2: set @ ( product_prod @ A @ B ),F: A > C,G3: B > D] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R2 )
% 0.16/0.44 => ( member @ ( product_prod @ C @ D ) @ ( product_Pair @ C @ D @ ( F @ A2 ) @ ( G3 @ B2 ) ) @ ( image @ ( product_prod @ A @ B ) @ ( product_prod @ C @ D ) @ ( product_map_prod @ A @ C @ B @ D @ F @ G3 ) @ R2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_prod_imageI
% 0.16/0.44 thf(fact_105_sp_092_060_094sub_062_092_060mu_062_Orel__refl__strong,axiom,
% 0.16/0.44 ! [C: $tType,A: $tType,B: $tType,X3: stream901396144_sp_mu @ B @ A @ C,R1a: A > A > $o,R2a: C > C > $o] :
% 0.16/0.44 ( ! [Z1: A] :
% 0.16/0.44 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ B @ A @ C @ X3 ) )
% 0.16/0.44 => ( R1a @ Z1 @ Z1 ) )
% 0.16/0.44 => ( ! [Z22: C] :
% 0.16/0.44 ( ( member @ C @ Z22 @ ( stream1259315544_sp_mu @ B @ A @ C @ X3 ) )
% 0.16/0.44 => ( R2a @ Z22 @ Z22 ) )
% 0.16/0.44 => ( stream1924447089_sp_mu @ A @ A @ C @ C @ B @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_refl_strong
% 0.16/0.44 thf(fact_106_sp_092_060_094sub_062_092_060mu_062_Orel__mono__strong,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,D: $tType,C: $tType,G: $tType,R1: A > C > $o,R22: B > D > $o,X3: stream901396144_sp_mu @ G @ A @ B,Y: stream901396144_sp_mu @ G @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 0.16/0.44 ( ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 @ X3 @ Y )
% 0.16/0.44 => ( ! [Z1: A,Y12: C] :
% 0.16/0.44 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ X3 ) )
% 0.16/0.44 => ( ( member @ C @ Y12 @ ( stream2074884121_sp_mu @ G @ C @ D @ Y ) )
% 0.16/0.44 => ( ( R1 @ Z1 @ Y12 )
% 0.16/0.44 => ( R1a @ Z1 @ Y12 ) ) ) )
% 0.16/0.44 => ( ! [Z22: B,Y23: D] :
% 0.16/0.44 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ X3 ) )
% 0.16/0.44 => ( ( member @ D @ Y23 @ ( stream1259315544_sp_mu @ G @ C @ D @ Y ) )
% 0.16/0.44 => ( ( R22 @ Z22 @ Y23 )
% 0.16/0.44 => ( R2a @ Z22 @ Y23 ) ) ) )
% 0.16/0.44 => ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1a @ R2a @ X3 @ Y ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_mono_strong
% 0.16/0.44 thf(fact_107_sp_092_060_094sub_062_092_060mu_062_Orel__cong,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,D: $tType,C: $tType,G: $tType,X3: stream901396144_sp_mu @ G @ A @ B,Ya: stream901396144_sp_mu @ G @ A @ B,Y: stream901396144_sp_mu @ G @ C @ D,Xa2: stream901396144_sp_mu @ G @ C @ D,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 0.16/0.44 ( ( X3 = Ya )
% 0.16/0.44 => ( ( Y = Xa2 )
% 0.16/0.44 => ( ! [Z1: A,Y12: C] :
% 0.16/0.44 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ Ya ) )
% 0.16/0.44 => ( ( member @ C @ Y12 @ ( stream2074884121_sp_mu @ G @ C @ D @ Xa2 ) )
% 0.16/0.44 => ( ( R1 @ Z1 @ Y12 )
% 0.16/0.44 = ( R1a @ Z1 @ Y12 ) ) ) )
% 0.16/0.44 => ( ! [Z22: B,Y23: D] :
% 0.16/0.44 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ Ya ) )
% 0.16/0.44 => ( ( member @ D @ Y23 @ ( stream1259315544_sp_mu @ G @ C @ D @ Xa2 ) )
% 0.16/0.44 => ( ( R22 @ Z22 @ Y23 )
% 0.16/0.44 = ( R2a @ Z22 @ Y23 ) ) ) )
% 0.16/0.44 => ( ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 @ X3 @ Y )
% 0.16/0.44 = ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1a @ R2a @ Ya @ Xa2 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_cong
% 0.16/0.44 thf(fact_108_sp_092_060_094sub_062_092_060mu_062_Opred__mono__strong,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,G: $tType,P1: A > $o,P22: B > $o,X3: stream901396144_sp_mu @ G @ A @ B,P1a: A > $o,P2a: B > $o] :
% 0.16/0.44 ( ( stream123009735_sp_mu @ A @ B @ G @ P1 @ P22 @ X3 )
% 0.16/0.44 => ( ! [Z1: A] :
% 0.16/0.44 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ X3 ) )
% 0.16/0.44 => ( ( P1 @ Z1 )
% 0.16/0.44 => ( P1a @ Z1 ) ) )
% 0.16/0.44 => ( ! [Z22: B] :
% 0.16/0.44 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ X3 ) )
% 0.16/0.44 => ( ( P22 @ Z22 )
% 0.16/0.44 => ( P2a @ Z22 ) ) )
% 0.16/0.44 => ( stream123009735_sp_mu @ A @ B @ G @ P1a @ P2a @ X3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.pred_mono_strong
% 0.16/0.44 thf(fact_109_sp_092_060_094sub_062_092_060mu_062_Opred__cong,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,G: $tType,X3: stream901396144_sp_mu @ G @ A @ B,Ya: stream901396144_sp_mu @ G @ A @ B,P1: A > $o,P1a: A > $o,P22: B > $o,P2a: B > $o] :
% 0.16/0.44 ( ( X3 = Ya )
% 0.16/0.44 => ( ! [Z1: A] :
% 0.16/0.44 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ Ya ) )
% 0.16/0.44 => ( ( P1 @ Z1 )
% 0.16/0.44 = ( P1a @ Z1 ) ) )
% 0.16/0.44 => ( ! [Z22: B] :
% 0.16/0.44 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ Ya ) )
% 0.16/0.44 => ( ( P22 @ Z22 )
% 0.16/0.44 = ( P2a @ Z22 ) ) )
% 0.16/0.44 => ( ( stream123009735_sp_mu @ A @ B @ G @ P1 @ P22 @ X3 )
% 0.16/0.44 = ( stream123009735_sp_mu @ A @ B @ G @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.pred_cong
% 0.16/0.44 thf(fact_110_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I2_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,A1: B,A22: C] : ( member @ B @ A1 @ ( stream2074884121_sp_mu @ A @ B @ C @ ( stream1370332830mu_Put @ B @ C @ A @ A1 @ A22 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.set_intros(2)
% 0.16/0.44 thf(fact_111_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I4_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,A2a: C,A1a: B] : ( member @ C @ A2a @ ( stream1259315544_sp_mu @ A @ B @ C @ ( stream1370332830mu_Put @ B @ C @ A @ A1a @ A2a ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.set_intros(4)
% 0.16/0.44 thf(fact_112_prod__fun__imageE,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,D: $tType,C: $tType,C3: product_prod @ A @ B,F: C > A,G3: D > B,R2: set @ ( product_prod @ C @ D )] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ B ) @ C3 @ ( image @ ( product_prod @ C @ D ) @ ( product_prod @ A @ B ) @ ( product_map_prod @ C @ A @ D @ B @ F @ G3 ) @ R2 ) )
% 0.16/0.44 => ~ ! [X: C,Y3: D] :
% 0.16/0.44 ( ( C3
% 0.16/0.44 = ( product_Pair @ A @ B @ ( F @ X ) @ ( G3 @ Y3 ) ) )
% 0.16/0.44 => ~ ( member @ ( product_prod @ C @ D ) @ ( product_Pair @ C @ D @ X @ Y3 ) @ R2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_fun_imageE
% 0.16/0.44 thf(fact_113_top__empty__eq,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( top_top @ ( A > $o ) )
% 0.16/0.44 = ( ^ [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % top_empty_eq
% 0.16/0.44 thf(fact_114_top__conj_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,P2: $o,X3: A] :
% 0.16/0.44 ( ( P2
% 0.16/0.44 & ( top_top @ ( A > $o ) @ X3 ) )
% 0.16/0.44 = P2 ) ).
% 0.16/0.44
% 0.16/0.44 % top_conj(2)
% 0.16/0.44 thf(fact_115_top__conj_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,X3: A,P2: $o] :
% 0.16/0.44 ( ( ( top_top @ ( A > $o ) @ X3 )
% 0.16/0.44 & P2 )
% 0.16/0.44 = P2 ) ).
% 0.16/0.44
% 0.16/0.44 % top_conj(1)
% 0.16/0.44 thf(fact_116_sp_092_060_094sub_062_092_060mu_062_Osimps_I15_J,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,A: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( ( stream2074884121_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) )
% 0.16/0.44 = ( complete_Sup_Sup @ ( set @ B ) @ ( image @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( set @ B ) @ ( stream2074884121_sp_mu @ A @ B @ C ) @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ X1 @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.simps(15)
% 0.16/0.44 thf(fact_117_sp_092_060_094sub_062_092_060mu_062_Osimps_I17_J,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,A: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 0.16/0.44 ( ( stream1259315544_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) )
% 0.16/0.44 = ( complete_Sup_Sup @ ( set @ C ) @ ( image @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( set @ C ) @ ( stream1259315544_sp_mu @ A @ B @ C ) @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ X1 @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.simps(17)
% 0.16/0.44 thf(fact_118_UN__ball__bex__simps_I3_J,axiom,
% 0.16/0.44 ! [D: $tType,A6: set @ ( set @ D ),P2: D > $o] :
% 0.16/0.44 ( ( ? [X4: D] :
% 0.16/0.44 ( ( member @ D @ X4 @ ( complete_Sup_Sup @ ( set @ D ) @ A6 ) )
% 0.16/0.44 & ( P2 @ X4 ) ) )
% 0.16/0.44 = ( ? [X4: set @ D] :
% 0.16/0.44 ( ( member @ ( set @ D ) @ X4 @ A6 )
% 0.16/0.44 & ? [Y5: D] :
% 0.16/0.44 ( ( member @ D @ Y5 @ X4 )
% 0.16/0.44 & ( P2 @ Y5 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UN_ball_bex_simps(3)
% 0.16/0.44 thf(fact_119_UN__ball__bex__simps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ ( set @ A ),P2: A > $o] :
% 0.16/0.44 ( ( ! [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) )
% 0.16/0.44 => ( P2 @ X4 ) ) )
% 0.16/0.44 = ( ! [X4: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ X4 @ A6 )
% 0.16/0.44 => ! [Y5: A] :
% 0.16/0.44 ( ( member @ A @ Y5 @ X4 )
% 0.16/0.44 => ( P2 @ Y5 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UN_ball_bex_simps(1)
% 0.16/0.44 thf(fact_120_UnionI,axiom,
% 0.16/0.44 ! [A: $tType,X7: set @ A,C4: set @ ( set @ A ),A6: A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ X7 @ C4 )
% 0.16/0.44 => ( ( member @ A @ A6 @ X7 )
% 0.16/0.44 => ( member @ A @ A6 @ ( complete_Sup_Sup @ ( set @ A ) @ C4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UnionI
% 0.16/0.44 thf(fact_121_Union__iff,axiom,
% 0.16/0.44 ! [A: $tType,A6: A,C4: set @ ( set @ A )] :
% 0.16/0.44 ( ( member @ A @ A6 @ ( complete_Sup_Sup @ ( set @ A ) @ C4 ) )
% 0.16/0.44 = ( ? [X4: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ X4 @ C4 )
% 0.16/0.44 & ( member @ A @ A6 @ X4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Union_iff
% 0.16/0.44 thf(fact_122_ball__UN,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,B6: B > ( set @ A ),A6: set @ B,P2: A > $o] :
% 0.16/0.44 ( ( ! [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B6 @ A6 ) ) )
% 0.16/0.44 => ( P2 @ X4 ) ) )
% 0.16/0.44 = ( ! [X4: B] :
% 0.16/0.44 ( ( member @ B @ X4 @ A6 )
% 0.16/0.44 => ! [Y5: A] :
% 0.16/0.44 ( ( member @ A @ Y5 @ ( B6 @ X4 ) )
% 0.16/0.44 => ( P2 @ Y5 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ball_UN
% 0.16/0.44 thf(fact_123_bex__UN,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,B6: B > ( set @ A ),A6: set @ B,P2: A > $o] :
% 0.16/0.44 ( ( ? [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B6 @ A6 ) ) )
% 0.16/0.44 & ( P2 @ X4 ) ) )
% 0.16/0.44 = ( ? [X4: B] :
% 0.16/0.44 ( ( member @ B @ X4 @ A6 )
% 0.16/0.44 & ? [Y5: A] :
% 0.16/0.44 ( ( member @ A @ Y5 @ ( B6 @ X4 ) )
% 0.16/0.44 & ( P2 @ Y5 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bex_UN
% 0.16/0.44 thf(fact_124_UN__ball__bex__simps_I2_J,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,B6: B > ( set @ C ),A6: set @ B,P2: C > $o] :
% 0.16/0.44 ( ( ! [X4: C] :
% 0.16/0.44 ( ( member @ C @ X4 @ ( complete_Sup_Sup @ ( set @ C ) @ ( image @ B @ ( set @ C ) @ B6 @ A6 ) ) )
% 0.16/0.44 => ( P2 @ X4 ) ) )
% 0.16/0.44 = ( ! [X4: B] :
% 0.16/0.44 ( ( member @ B @ X4 @ A6 )
% 0.16/0.44 => ! [Y5: C] :
% 0.16/0.44 ( ( member @ C @ Y5 @ ( B6 @ X4 ) )
% 0.16/0.44 => ( P2 @ Y5 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UN_ball_bex_simps(2)
% 0.16/0.44 thf(fact_125_UN__ball__bex__simps_I4_J,axiom,
% 0.16/0.44 ! [F2: $tType,E: $tType,B6: E > ( set @ F2 ),A6: set @ E,P2: F2 > $o] :
% 0.16/0.44 ( ( ? [X4: F2] :
% 0.16/0.44 ( ( member @ F2 @ X4 @ ( complete_Sup_Sup @ ( set @ F2 ) @ ( image @ E @ ( set @ F2 ) @ B6 @ A6 ) ) )
% 0.16/0.44 & ( P2 @ X4 ) ) )
% 0.16/0.44 = ( ? [X4: E] :
% 0.16/0.44 ( ( member @ E @ X4 @ A6 )
% 0.16/0.44 & ? [Y5: F2] :
% 0.16/0.44 ( ( member @ F2 @ Y5 @ ( B6 @ X4 ) )
% 0.16/0.44 & ( P2 @ Y5 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UN_ball_bex_simps(4)
% 0.16/0.44 thf(fact_126_Sup__UNIV,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ( ( complete_Sup_Sup @ A @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 = ( top_top @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_UNIV
% 0.16/0.44 thf(fact_127_Union__UNIV,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( complete_Sup_Sup @ ( set @ A ) @ ( top_top @ ( set @ ( set @ A ) ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Union_UNIV
% 0.16/0.44 thf(fact_128_UnionE,axiom,
% 0.16/0.44 ! [A: $tType,A6: A,C4: set @ ( set @ A )] :
% 0.16/0.44 ( ( member @ A @ A6 @ ( complete_Sup_Sup @ ( set @ A ) @ C4 ) )
% 0.16/0.44 => ~ ! [X8: set @ A] :
% 0.16/0.44 ( ( member @ A @ A6 @ X8 )
% 0.16/0.44 => ~ ( member @ ( set @ A ) @ X8 @ C4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UnionE
% 0.16/0.44 thf(fact_129_SUP__cong,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType] :
% 0.16/0.44 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A6: set @ B,B6: set @ B,C4: B > A,D3: B > A] :
% 0.16/0.44 ( ( A6 = B6 )
% 0.16/0.44 => ( ! [X: B] :
% 0.16/0.44 ( ( member @ B @ X @ B6 )
% 0.16/0.44 => ( ( C4 @ X )
% 0.16/0.44 = ( D3 @ X ) ) )
% 0.16/0.44 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ C4 @ A6 ) )
% 0.16/0.44 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ D3 @ B6 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % SUP_cong
% 0.16/0.44 thf(fact_130_same__fstI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P2: A > $o,X3: A,Y7: B,Y: B,R2: A > ( set @ ( product_prod @ B @ B ) )] :
% 0.16/0.44 ( ( P2 @ X3 )
% 0.16/0.44 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y7 @ Y ) @ ( R2 @ X3 ) )
% 0.16/0.44 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y7 ) @ ( product_Pair @ A @ B @ X3 @ Y ) ) @ ( same_fst @ A @ B @ P2 @ R2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % same_fstI
% 0.16/0.44 thf(fact_131_wf__same__fst,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P2: A > $o,R2: A > ( set @ ( product_prod @ B @ B ) )] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( P2 @ X )
% 0.16/0.44 => ( wf @ B @ ( R2 @ X ) ) )
% 0.16/0.44 => ( wf @ ( product_prod @ A @ B ) @ ( same_fst @ A @ B @ P2 @ R2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_same_fst
% 0.16/0.44 thf(fact_132_wf__map__prod__image,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F: A > B] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( wf @ B @ ( image @ ( product_prod @ A @ A ) @ ( product_prod @ B @ B ) @ ( product_map_prod @ A @ B @ A @ B @ F @ F ) @ R ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_map_prod_image
% 0.16/0.44 thf(fact_133_member__bind,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X3: A,P2: set @ B,F: B > ( set @ A )] :
% 0.16/0.44 ( ( member @ A @ X3 @ ( bind @ B @ A @ P2 @ F ) )
% 0.16/0.44 = ( member @ A @ X3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ P2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % member_bind
% 0.16/0.44 thf(fact_134_inj__apfst,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,A: $tType,F: A > C] :
% 0.16/0.44 ( ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ C @ B ) @ ( product_apfst @ A @ C @ B @ F ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 0.16/0.44 = ( inj_on @ A @ C @ F @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_apfst
% 0.16/0.44 thf(fact_135_inj__apsnd,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,B: $tType,F: B > C] :
% 0.16/0.44 ( ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ A @ C ) @ ( product_apsnd @ B @ C @ A @ F ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 0.16/0.44 = ( inj_on @ B @ C @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_apsnd
% 0.16/0.44 thf(fact_136_inj__on__image__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,A6: set @ A,G3: A > B,F: A > A] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( member @ A @ X @ A6 )
% 0.16/0.44 => ! [Xa3: A] :
% 0.16/0.44 ( ( member @ A @ Xa3 @ A6 )
% 0.16/0.44 => ( ( ( G3 @ ( F @ X ) )
% 0.16/0.44 = ( G3 @ ( F @ Xa3 ) ) )
% 0.16/0.44 = ( ( G3 @ X )
% 0.16/0.44 = ( G3 @ Xa3 ) ) ) ) )
% 0.16/0.44 => ( ( inj_on @ A @ A @ F @ A6 )
% 0.16/0.44 => ( ( inj_on @ A @ B @ G3 @ ( image @ A @ A @ F @ A6 ) )
% 0.16/0.44 = ( inj_on @ A @ B @ G3 @ A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_on_image_iff
% 0.16/0.44 thf(fact_137_inj__on__image,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A6: set @ ( set @ A )] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) )
% 0.16/0.44 => ( inj_on @ ( set @ A ) @ ( set @ B ) @ ( image @ A @ B @ F ) @ A6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_on_image
% 0.16/0.44 thf(fact_138_inj__swap,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,A6: set @ ( product_prod @ A @ B )] : ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ B @ A ) @ ( product_swap @ A @ B ) @ A6 ) ).
% 0.16/0.44
% 0.16/0.44 % inj_swap
% 0.16/0.44 thf(fact_139_inj__eq,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,X3: A,Y: A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( ( F @ X3 )
% 0.16/0.44 = ( F @ Y ) )
% 0.16/0.44 = ( X3 = Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_eq
% 0.16/0.44 thf(fact_140_injI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B] :
% 0.16/0.44 ( ! [X: A,Y3: A] :
% 0.16/0.44 ( ( ( F @ X )
% 0.16/0.44 = ( F @ Y3 ) )
% 0.16/0.44 => ( X = Y3 ) )
% 0.16/0.44 => ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % injI
% 0.16/0.44 thf(fact_141_injD,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,X3: A,Y: A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( ( F @ X3 )
% 0.16/0.44 = ( F @ Y ) )
% 0.16/0.44 => ( X3 = Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % injD
% 0.16/0.44 thf(fact_142_range__ex1__eq,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,B2: B] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( member @ B @ B2 @ ( image @ A @ B @ F @ ( top_top @ ( set @ A ) ) ) )
% 0.16/0.44 = ( ? [X4: A] :
% 0.16/0.44 ( ( B2
% 0.16/0.44 = ( F @ X4 ) )
% 0.16/0.44 & ! [Y5: A] :
% 0.16/0.44 ( ( B2
% 0.16/0.44 = ( F @ Y5 ) )
% 0.16/0.44 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % range_ex1_eq
% 0.16/0.44 thf(fact_143_inj__image__eq__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( ( image @ A @ B @ F @ A6 )
% 0.16/0.44 = ( image @ A @ B @ F @ B6 ) )
% 0.16/0.44 = ( A6 = B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_image_eq_iff
% 0.16/0.44 thf(fact_144_inj__image__mem__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A2: A,A6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A6 ) )
% 0.16/0.44 = ( member @ A @ A2 @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_image_mem_iff
% 0.16/0.44 thf(fact_145_bind__UNION,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType] :
% 0.16/0.44 ( ( bind @ B @ A )
% 0.16/0.44 = ( ^ [A7: set @ B,F4: B > ( set @ A )] : ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F4 @ A7 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bind_UNION
% 0.16/0.44 thf(fact_146_prod_Oinj__map,axiom,
% 0.16/0.44 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F22: B > D] :
% 0.16/0.44 ( ( inj_on @ A @ C @ F1 @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( inj_on @ B @ D @ F22 @ ( top_top @ ( set @ B ) ) )
% 0.16/0.44 => ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ C @ D ) @ ( product_map_prod @ A @ C @ B @ D @ F1 @ F22 ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inj_map
% 0.16/0.44 thf(fact_147_the__inv__into__onto,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ A6 )
% 0.16/0.44 => ( ( image @ B @ A @ ( the_inv_into @ A @ B @ A6 @ F ) @ ( image @ A @ B @ F @ A6 ) )
% 0.16/0.44 = A6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % the_inv_into_onto
% 0.16/0.44 thf(fact_148_range__fst,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( image @ ( product_prod @ A @ B ) @ A @ ( product_fst @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % range_fst
% 0.16/0.44 thf(fact_149_range__snd,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( image @ ( product_prod @ B @ A ) @ A @ ( product_snd @ B @ A ) @ ( top_top @ ( set @ ( product_prod @ B @ A ) ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % range_snd
% 0.16/0.44 thf(fact_150_fst__map__prod,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: C > A,G3: D > B,X3: product_prod @ C @ D] :
% 0.16/0.44 ( ( product_fst @ A @ B @ ( product_map_prod @ C @ A @ D @ B @ F @ G3 @ X3 ) )
% 0.16/0.44 = ( F @ ( product_fst @ C @ D @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fst_map_prod
% 0.16/0.44 thf(fact_151_snd__map__prod,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: C > B,G3: D > A,X3: product_prod @ C @ D] :
% 0.16/0.44 ( ( product_snd @ B @ A @ ( product_map_prod @ C @ B @ D @ A @ F @ G3 @ X3 ) )
% 0.16/0.44 = ( G3 @ ( product_snd @ C @ D @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % snd_map_prod
% 0.16/0.44 thf(fact_152_fst__apfst,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,F: C > A,X3: product_prod @ C @ B] :
% 0.16/0.44 ( ( product_fst @ A @ B @ ( product_apfst @ C @ A @ B @ F @ X3 ) )
% 0.16/0.44 = ( F @ ( product_fst @ C @ B @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fst_apfst
% 0.16/0.44 thf(fact_153_apfst__eq__conv,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,F: C > A,X3: product_prod @ C @ B,G3: C > A] :
% 0.16/0.44 ( ( ( product_apfst @ C @ A @ B @ F @ X3 )
% 0.16/0.44 = ( product_apfst @ C @ A @ B @ G3 @ X3 ) )
% 0.16/0.44 = ( ( F @ ( product_fst @ C @ B @ X3 ) )
% 0.16/0.44 = ( G3 @ ( product_fst @ C @ B @ X3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % apfst_eq_conv
% 0.16/0.44 thf(fact_154_snd__apfst,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,F: C > B,X3: product_prod @ C @ A] :
% 0.16/0.44 ( ( product_snd @ B @ A @ ( product_apfst @ C @ B @ A @ F @ X3 ) )
% 0.16/0.44 = ( product_snd @ C @ A @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % snd_apfst
% 0.16/0.44 thf(fact_155_fst__apsnd,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,A: $tType,F: C > B,X3: product_prod @ A @ C] :
% 0.16/0.44 ( ( product_fst @ A @ B @ ( product_apsnd @ C @ B @ A @ F @ X3 ) )
% 0.16/0.44 = ( product_fst @ A @ C @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % fst_apsnd
% 0.16/0.44 thf(fact_156_snd__apsnd,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,B: $tType,F: C > A,X3: product_prod @ B @ C] :
% 0.16/0.44 ( ( product_snd @ B @ A @ ( product_apsnd @ C @ A @ B @ F @ X3 ) )
% 0.16/0.44 = ( F @ ( product_snd @ B @ C @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % snd_apsnd
% 0.16/0.44 thf(fact_157_apsnd__eq__conv,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,A: $tType,F: C > B,X3: product_prod @ A @ C,G3: C > B] :
% 0.16/0.44 ( ( ( product_apsnd @ C @ B @ A @ F @ X3 )
% 0.16/0.44 = ( product_apsnd @ C @ B @ A @ G3 @ X3 ) )
% 0.16/0.44 = ( ( F @ ( product_snd @ A @ C @ X3 ) )
% 0.16/0.44 = ( G3 @ ( product_snd @ A @ C @ X3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % apsnd_eq_conv
% 0.16/0.44 thf(fact_158_prod_Ocollapse,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.16/0.44 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 0.16/0.44 = Prod ) ).
% 0.16/0.44
% 0.16/0.44 % prod.collapse
% 0.16/0.44 thf(fact_159_snd__swap,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X3: product_prod @ A @ B] :
% 0.16/0.44 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X3 ) )
% 0.16/0.44 = ( product_fst @ A @ B @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % snd_swap
% 0.16/0.44 thf(fact_160_fst__swap,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X3: product_prod @ B @ A] :
% 0.16/0.44 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X3 ) )
% 0.16/0.44 = ( product_snd @ B @ A @ X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % fst_swap
% 0.16/0.44 thf(fact_161_apfst__apsnd,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,D: $tType,C: $tType,F: C > A,G3: D > B,X3: product_prod @ C @ D] :
% 0.16/0.44 ( ( product_apfst @ C @ A @ B @ F @ ( product_apsnd @ D @ B @ C @ G3 @ X3 ) )
% 0.16/0.44 = ( product_Pair @ A @ B @ ( F @ ( product_fst @ C @ D @ X3 ) ) @ ( G3 @ ( product_snd @ C @ D @ X3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % apfst_apsnd
% 0.16/0.44 thf(fact_162_apsnd__apfst,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,D: $tType,F: C > B,G3: D > A,X3: product_prod @ D @ C] :
% 0.16/0.44 ( ( product_apsnd @ C @ B @ A @ F @ ( product_apfst @ D @ A @ C @ G3 @ X3 ) )
% 0.16/0.44 = ( product_Pair @ A @ B @ ( G3 @ ( product_fst @ D @ C @ X3 ) ) @ ( F @ ( product_snd @ D @ C @ X3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % apsnd_apfst
% 0.16/0.44 thf(fact_163_surjective__pairing,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,T2: product_prod @ A @ B] :
% 0.16/0.44 ( T2
% 0.16/0.44 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T2 ) @ ( product_snd @ A @ B @ T2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % surjective_pairing
% 0.16/0.44 thf(fact_164_prod_Oexhaust__sel,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.16/0.44 ( Prod
% 0.16/0.44 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.exhaust_sel
% 0.16/0.44 thf(fact_165_prod_Osplit__sel__asm,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,P2: C > $o,F: A > B > C,Prod: product_prod @ A @ B] :
% 0.16/0.44 ( ( P2 @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 0.16/0.44 = ( ~ ( ( Prod
% 0.16/0.44 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) )
% 0.16/0.44 & ~ ( P2 @ ( F @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.split_sel_asm
% 0.16/0.44 thf(fact_166_prod_Osplit__sel,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,P2: C > $o,F: A > B > C,Prod: product_prod @ A @ B] :
% 0.16/0.44 ( ( P2 @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 0.16/0.44 = ( ( Prod
% 0.16/0.44 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) )
% 0.16/0.44 => ( P2 @ ( F @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.split_sel
% 0.16/0.44 thf(fact_167_prod__eqI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P: product_prod @ A @ B,Q4: product_prod @ A @ B] :
% 0.16/0.44 ( ( ( product_fst @ A @ B @ P )
% 0.16/0.44 = ( product_fst @ A @ B @ Q4 ) )
% 0.16/0.44 => ( ( ( product_snd @ A @ B @ P )
% 0.16/0.44 = ( product_snd @ A @ B @ Q4 ) )
% 0.16/0.44 => ( P = Q4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_eqI
% 0.16/0.44 thf(fact_168_prod_Oexpand,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 0.16/0.44 ( ( ( ( product_fst @ A @ B @ Prod )
% 0.16/0.44 = ( product_fst @ A @ B @ Prod2 ) )
% 0.16/0.44 & ( ( product_snd @ A @ B @ Prod )
% 0.16/0.44 = ( product_snd @ A @ B @ Prod2 ) ) )
% 0.16/0.44 => ( Prod = Prod2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.expand
% 0.16/0.44 thf(fact_169_prod__eq__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( ^ [Y4: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y4 = Z ) )
% 0.16/0.44 = ( ^ [S3: product_prod @ A @ B,T3: product_prod @ A @ B] :
% 0.16/0.44 ( ( ( product_fst @ A @ B @ S3 )
% 0.16/0.44 = ( product_fst @ A @ B @ T3 ) )
% 0.16/0.44 & ( ( product_snd @ A @ B @ S3 )
% 0.16/0.44 = ( product_snd @ A @ B @ T3 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_eq_iff
% 0.16/0.44 thf(fact_170_case__prod__beta,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,B: $tType] :
% 0.16/0.44 ( ( product_case_prod @ B @ C @ A )
% 0.16/0.44 = ( ^ [F4: B > C > A,P6: product_prod @ B @ C] : ( F4 @ ( product_fst @ B @ C @ P6 ) @ ( product_snd @ B @ C @ P6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % case_prod_beta
% 0.16/0.44 thf(fact_171_prod_Ocase__eq__if,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType] :
% 0.16/0.44 ( ( product_case_prod @ A @ B @ C )
% 0.16/0.44 = ( ^ [F4: A > B > C,Prod3: product_prod @ A @ B] : ( F4 @ ( product_fst @ A @ B @ Prod3 ) @ ( product_snd @ A @ B @ Prod3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.case_eq_if
% 0.16/0.44 thf(fact_172_Product__Type_OCollect__case__prodD,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X3: product_prod @ A @ B,A6: A > B > $o] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ B ) @ X3 @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ A6 ) ) )
% 0.16/0.44 => ( A6 @ ( product_fst @ A @ B @ X3 ) @ ( product_snd @ A @ B @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Product_Type.Collect_case_prodD
% 0.16/0.44 thf(fact_173_fst__conv,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X1: A,X2: B] :
% 0.16/0.44 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X2 ) )
% 0.16/0.44 = X1 ) ).
% 0.16/0.44
% 0.16/0.44 % fst_conv
% 0.16/0.44 thf(fact_174_fst__eqD,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X3: A,Y: B,A2: A] :
% 0.16/0.44 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.16/0.44 = A2 )
% 0.16/0.44 => ( X3 = A2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % fst_eqD
% 0.16/0.44 thf(fact_175_snd__conv,axiom,
% 0.16/0.44 ! [Aa2: $tType,A: $tType,X1: Aa2,X2: A] :
% 0.16/0.44 ( ( product_snd @ Aa2 @ A @ ( product_Pair @ Aa2 @ A @ X1 @ X2 ) )
% 0.16/0.44 = X2 ) ).
% 0.16/0.44
% 0.16/0.44 % snd_conv
% 0.16/0.44 thf(fact_176_snd__eqD,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X3: B,Y: A,A2: A] :
% 0.16/0.44 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) )
% 0.16/0.44 = A2 )
% 0.16/0.44 => ( Y = A2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % snd_eqD
% 0.16/0.44 thf(fact_177_prod_Oswap__def,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( product_swap @ A @ B )
% 0.16/0.44 = ( ^ [P6: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P6 ) @ ( product_fst @ A @ B @ P6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.swap_def
% 0.16/0.44 thf(fact_178_inj__on__the__inv__into,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ A6 )
% 0.16/0.44 => ( inj_on @ B @ A @ ( the_inv_into @ A @ B @ A6 @ F ) @ ( image @ A @ B @ F @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_on_the_inv_into
% 0.16/0.44 thf(fact_179_f__the__inv__into__f,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: A > B,A6: set @ A,Y: B] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ A6 )
% 0.16/0.44 => ( ( member @ B @ Y @ ( image @ A @ B @ F @ A6 ) )
% 0.16/0.44 => ( ( F @ ( the_inv_into @ A @ B @ A6 @ F @ Y ) )
% 0.16/0.44 = Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % f_the_inv_into_f
% 0.16/0.44 thf(fact_180_the__inv__f__f,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,X3: A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( the_inv_into @ A @ B @ ( top_top @ ( set @ A ) ) @ F @ ( F @ X3 ) )
% 0.16/0.44 = X3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % the_inv_f_f
% 0.16/0.44 thf(fact_181_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P2: A > B > $o,X3: A,Y: B,A2: product_prod @ A @ B] :
% 0.16/0.44 ( ( P2 @ X3 @ Y )
% 0.16/0.44 => ( ( A2
% 0.16/0.44 = ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.16/0.44 => ( P2 @ ( product_fst @ A @ B @ A2 ) @ ( product_snd @ A @ B @ A2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % BNF_Greatest_Fixpoint.subst_Pair
% 0.16/0.44 thf(fact_182_conjI__realizer,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,P2: A > $o,P: A,Q: B > $o,Q4: B] :
% 0.16/0.44 ( ( P2 @ P )
% 0.16/0.44 => ( ( Q @ Q4 )
% 0.16/0.44 => ( ( P2 @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P @ Q4 ) ) )
% 0.16/0.44 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P @ Q4 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % conjI_realizer
% 0.16/0.44 thf(fact_183_exI__realizer,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,P2: A > B > $o,Y: A,X3: B] :
% 0.16/0.44 ( ( P2 @ Y @ X3 )
% 0.16/0.44 => ( P2 @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % exI_realizer
% 0.16/0.44 thf(fact_184_eq__snd__iff,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,B2: A,P: product_prod @ B @ A] :
% 0.16/0.44 ( ( B2
% 0.16/0.44 = ( product_snd @ B @ A @ P ) )
% 0.16/0.44 = ( ? [A5: B] :
% 0.16/0.44 ( P
% 0.16/0.44 = ( product_Pair @ B @ A @ A5 @ B2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % eq_snd_iff
% 0.16/0.44 thf(fact_185_sndI,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X3: product_prod @ A @ B,Y: A,Z2: B] :
% 0.16/0.44 ( ( X3
% 0.16/0.44 = ( product_Pair @ A @ B @ Y @ Z2 ) )
% 0.16/0.44 => ( ( product_snd @ A @ B @ X3 )
% 0.16/0.44 = Z2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sndI
% 0.16/0.44 thf(fact_186_eq__fst__iff,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A2: A,P: product_prod @ A @ B] :
% 0.16/0.44 ( ( A2
% 0.16/0.44 = ( product_fst @ A @ B @ P ) )
% 0.16/0.44 = ( ? [B5: B] :
% 0.16/0.44 ( P
% 0.16/0.44 = ( product_Pair @ A @ B @ A2 @ B5 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % eq_fst_iff
% 0.16/0.44 thf(fact_187_fstI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X3: product_prod @ A @ B,Y: A,Z2: B] :
% 0.16/0.44 ( ( X3
% 0.16/0.44 = ( product_Pair @ A @ B @ Y @ Z2 ) )
% 0.16/0.44 => ( ( product_fst @ A @ B @ X3 )
% 0.16/0.44 = Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % fstI
% 0.16/0.44 thf(fact_188_Collect__split__mono__strong,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,X7: set @ A,A6: set @ ( product_prod @ A @ B ),Y8: set @ B,P2: A > B > $o,Q: A > B > $o] :
% 0.16/0.44 ( ( X7
% 0.16/0.44 = ( image @ ( product_prod @ A @ B ) @ A @ ( product_fst @ A @ B ) @ A6 ) )
% 0.16/0.44 => ( ( Y8
% 0.16/0.44 = ( image @ ( product_prod @ A @ B ) @ B @ ( product_snd @ A @ B ) @ A6 ) )
% 0.16/0.44 => ( ! [X: A] :
% 0.16/0.44 ( ( member @ A @ X @ X7 )
% 0.16/0.44 => ! [Xa3: B] :
% 0.16/0.44 ( ( member @ B @ Xa3 @ Y8 )
% 0.16/0.44 => ( ( P2 @ X @ Xa3 )
% 0.16/0.44 => ( Q @ X @ Xa3 ) ) ) )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ A6 @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ P2 ) ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ A6 @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ Q ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_split_mono_strong
% 0.16/0.44 thf(fact_189_sndOp__def,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType] :
% 0.16/0.44 ( ( bNF_sndOp @ C @ A @ B )
% 0.16/0.44 = ( ^ [P3: C > A > $o,Q3: A > B > $o,Ac: product_prod @ C @ B] : ( product_Pair @ A @ B @ ( bNF_pick_middlep @ C @ A @ B @ P3 @ Q3 @ ( product_fst @ C @ B @ Ac ) @ ( product_snd @ C @ B @ Ac ) ) @ ( product_snd @ C @ B @ Ac ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sndOp_def
% 0.16/0.44 thf(fact_190_fstOp__def,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType] :
% 0.16/0.44 ( ( bNF_fstOp @ A @ B @ C )
% 0.16/0.44 = ( ^ [P3: A > B > $o,Q3: B > C > $o,Ac: product_prod @ A @ C] : ( product_Pair @ A @ B @ ( product_fst @ A @ C @ Ac ) @ ( bNF_pick_middlep @ A @ B @ C @ P3 @ Q3 @ ( product_fst @ A @ C @ Ac ) @ ( product_snd @ A @ C @ Ac ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fstOp_def
% 0.16/0.44 thf(fact_191_subset__antisym,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ A6 )
% 0.16/0.44 => ( A6 = B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_antisym
% 0.16/0.44 thf(fact_192_subsetI,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( member @ A @ X @ A6 )
% 0.16/0.44 => ( member @ A @ X @ B6 ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ A6 @ B6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % subsetI
% 0.16/0.44 thf(fact_193_inj__on__image__mem__iff__alt,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,B6: set @ A,A6: set @ A,A2: A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ B6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A6 ) )
% 0.16/0.44 => ( ( member @ A @ A2 @ B6 )
% 0.16/0.44 => ( member @ A @ A2 @ A6 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_on_image_mem_iff_alt
% 0.16/0.44 thf(fact_194_inj__on__image__mem__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,B6: set @ A,A2: A,A6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ B6 )
% 0.16/0.44 => ( ( member @ A @ A2 @ B6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A6 ) )
% 0.16/0.44 = ( member @ A @ A2 @ A6 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_on_image_mem_iff
% 0.16/0.44 thf(fact_195_inj__on__image__eq__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,C4: set @ A,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ C4 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ C4 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 0.16/0.44 => ( ( ( image @ A @ B @ F @ A6 )
% 0.16/0.44 = ( image @ A @ B @ F @ B6 ) )
% 0.16/0.44 = ( A6 = B6 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_on_image_eq_iff
% 0.16/0.44 thf(fact_196_image__mono,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,A6: set @ A,B6: set @ A,F: A > B] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) @ ( image @ A @ B @ F @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_mono
% 0.16/0.44 thf(fact_197_image__subsetI,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A6: set @ A,F: A > B,B6: set @ B] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( member @ A @ X @ A6 )
% 0.16/0.44 => ( member @ B @ ( F @ X ) @ B6 ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) @ B6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_subsetI
% 0.16/0.44 thf(fact_198_subset__imageE,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,B6: set @ A,F: B > A,A6: set @ B] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ B6 @ ( image @ B @ A @ F @ A6 ) )
% 0.16/0.44 => ~ ! [C5: set @ B] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ B ) @ C5 @ A6 )
% 0.16/0.44 => ( B6
% 0.16/0.44 != ( image @ B @ A @ F @ C5 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_imageE
% 0.16/0.44 thf(fact_199_image__subset__iff,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: B > A,A6: set @ B,B6: set @ A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ F @ A6 ) @ B6 )
% 0.16/0.44 = ( ! [X4: B] :
% 0.16/0.44 ( ( member @ B @ X4 @ A6 )
% 0.16/0.44 => ( member @ A @ ( F @ X4 ) @ B6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_subset_iff
% 0.16/0.44 thf(fact_200_subset__image__iff,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,B6: set @ A,F: B > A,A6: set @ B] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ B6 @ ( image @ B @ A @ F @ A6 ) )
% 0.16/0.44 = ( ? [AA: set @ B] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ B ) @ AA @ A6 )
% 0.16/0.44 & ( B6
% 0.16/0.44 = ( image @ B @ A @ F @ AA ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_image_iff
% 0.16/0.44 thf(fact_201_subrelI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.16/0.44 ( ! [X: A,Y3: B] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y3 ) @ R )
% 0.16/0.44 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y3 ) @ S ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 0.16/0.44
% 0.16/0.44 % subrelI
% 0.16/0.44 thf(fact_202_wf__subset,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),P: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ( ( wf @ A @ R )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ P @ R )
% 0.16/0.44 => ( wf @ A @ P ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % wf_subset
% 0.16/0.44 thf(fact_203_Collect__mono__iff,axiom,
% 0.16/0.44 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 0.16/0.44 = ( ! [X4: A] :
% 0.16/0.44 ( ( P2 @ X4 )
% 0.16/0.44 => ( Q @ X4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_mono_iff
% 0.16/0.44 thf(fact_204_contra__subsetD,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A,C3: A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ~ ( member @ A @ C3 @ B6 )
% 0.16/0.44 => ~ ( member @ A @ C3 @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % contra_subsetD
% 0.16/0.44 thf(fact_205_set__eq__subset,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 0.16/0.44 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.16/0.44 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % set_eq_subset
% 0.16/0.44 thf(fact_206_subset__trans,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A,C4: set @ A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ A6 @ C4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_trans
% 0.16/0.44 thf(fact_207_Collect__mono,axiom,
% 0.16/0.44 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( P2 @ X )
% 0.16/0.44 => ( Q @ X ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_mono
% 0.16/0.44 thf(fact_208_subset__refl,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A] : ( ord_less_eq @ ( set @ A ) @ A6 @ A6 ) ).
% 0.16/0.44
% 0.16/0.44 % subset_refl
% 0.16/0.44 thf(fact_209_rev__subsetD,axiom,
% 0.16/0.44 ! [A: $tType,C3: A,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( member @ A @ C3 @ A6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( member @ A @ C3 @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rev_subsetD
% 0.16/0.44 thf(fact_210_subset__iff,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.16/0.44 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.16/0.44 ! [T3: A] :
% 0.16/0.44 ( ( member @ A @ T3 @ A7 )
% 0.16/0.44 => ( member @ A @ T3 @ B7 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_iff
% 0.16/0.44 thf(fact_211_set__rev__mp,axiom,
% 0.16/0.44 ! [A: $tType,X3: A,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( member @ A @ X3 @ A6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( member @ A @ X3 @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % set_rev_mp
% 0.16/0.44 thf(fact_212_equalityD2,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( A6 = B6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % equalityD2
% 0.16/0.44 thf(fact_213_equalityD1,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( A6 = B6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ A6 @ B6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % equalityD1
% 0.16/0.44 thf(fact_214_subset__eq,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.16/0.44 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.16/0.44 ! [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ A7 )
% 0.16/0.44 => ( member @ A @ X4 @ B7 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_eq
% 0.16/0.44 thf(fact_215_equalityE,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( A6 = B6 )
% 0.16/0.44 => ~ ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % equalityE
% 0.16/0.44 thf(fact_216_subsetCE,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A,C3: A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( member @ A @ C3 @ A6 )
% 0.16/0.44 => ( member @ A @ C3 @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subsetCE
% 0.16/0.44 thf(fact_217_subsetD,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A,C3: A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( member @ A @ C3 @ A6 )
% 0.16/0.44 => ( member @ A @ C3 @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subsetD
% 0.16/0.44 thf(fact_218_in__mono,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A,X3: A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( member @ A @ X3 @ A6 )
% 0.16/0.44 => ( member @ A @ X3 @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % in_mono
% 0.16/0.44 thf(fact_219_set__mp,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A,X3: A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ( member @ A @ X3 @ A6 )
% 0.16/0.44 => ( member @ A @ X3 @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % set_mp
% 0.16/0.44 thf(fact_220_subset__UNIV,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A] : ( ord_less_eq @ ( set @ A ) @ A6 @ ( top_top @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_UNIV
% 0.16/0.44 thf(fact_221_top_Oextremum__uniqueI,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order_top @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A2: A] :
% 0.16/0.44 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 0.16/0.44 => ( A2
% 0.16/0.44 = ( top_top @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % top.extremum_uniqueI
% 0.16/0.44 thf(fact_222_top_Oextremum__unique,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order_top @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A2: A] :
% 0.16/0.44 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 0.16/0.44 = ( A2
% 0.16/0.44 = ( top_top @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % top.extremum_unique
% 0.16/0.44 thf(fact_223_top__greatest,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order_top @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( top_top @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % top_greatest
% 0.16/0.44 thf(fact_224_Sup__subset__mono,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ ( complete_Sup_Sup @ A @ B6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_subset_mono
% 0.16/0.44 thf(fact_225_Sup__upper2,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [U: A,A6: set @ A,V: A] :
% 0.16/0.44 ( ( member @ A @ U @ A6 )
% 0.16/0.44 => ( ( ord_less_eq @ A @ V @ U )
% 0.16/0.44 => ( ord_less_eq @ A @ V @ ( complete_Sup_Sup @ A @ A6 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_upper2
% 0.16/0.44 thf(fact_226_Sup__le__iff,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A6: set @ A,B2: A] :
% 0.16/0.44 ( ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ B2 )
% 0.16/0.44 = ( ! [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ A6 )
% 0.16/0.44 => ( ord_less_eq @ A @ X4 @ B2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_le_iff
% 0.16/0.44 thf(fact_227_Sup__upper,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X3: A,A6: set @ A] :
% 0.16/0.44 ( ( member @ A @ X3 @ A6 )
% 0.16/0.44 => ( ord_less_eq @ A @ X3 @ ( complete_Sup_Sup @ A @ A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_upper
% 0.16/0.44 thf(fact_228_Sup__least,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A6: set @ A,Z2: A] :
% 0.16/0.44 ( ! [X: A] :
% 0.16/0.44 ( ( member @ A @ X @ A6 )
% 0.16/0.44 => ( ord_less_eq @ A @ X @ Z2 ) )
% 0.16/0.44 => ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ Z2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_least
% 0.16/0.44 thf(fact_229_Sup__mono,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ! [A4: A] :
% 0.16/0.44 ( ( member @ A @ A4 @ A6 )
% 0.16/0.44 => ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ B6 )
% 0.16/0.44 & ( ord_less_eq @ A @ A4 @ X6 ) ) )
% 0.16/0.44 => ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ ( complete_Sup_Sup @ A @ B6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_mono
% 0.16/0.44 thf(fact_230_Sup__eqI,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A6: set @ A,X3: A] :
% 0.16/0.44 ( ! [Y3: A] :
% 0.16/0.44 ( ( member @ A @ Y3 @ A6 )
% 0.16/0.44 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.16/0.44 => ( ! [Y3: A] :
% 0.16/0.44 ( ! [Z4: A] :
% 0.16/0.44 ( ( member @ A @ Z4 @ A6 )
% 0.16/0.44 => ( ord_less_eq @ A @ Z4 @ Y3 ) )
% 0.16/0.44 => ( ord_less_eq @ A @ X3 @ Y3 ) )
% 0.16/0.44 => ( ( complete_Sup_Sup @ A @ A6 )
% 0.16/0.44 = X3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup_eqI
% 0.16/0.44 thf(fact_231_Union__upper,axiom,
% 0.16/0.44 ! [A: $tType,B6: set @ A,A6: set @ ( set @ A )] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ B6 @ A6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ B6 @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Union_upper
% 0.16/0.44 thf(fact_232_Union__least,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ ( set @ A ),C4: set @ A] :
% 0.16/0.44 ( ! [X8: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ X8 @ A6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ X8 @ C4 ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) @ C4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % Union_least
% 0.16/0.44 thf(fact_233_Union__mono,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ ( set @ A ),B6: set @ ( set @ A )] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ ( set @ A ) ) @ A6 @ B6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) @ ( complete_Sup_Sup @ ( set @ A ) @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Union_mono
% 0.16/0.44 thf(fact_234_SUP__eq,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A6: set @ B,B6: set @ C,F: B > A,G3: C > A] :
% 0.16/0.44 ( ! [I: B] :
% 0.16/0.44 ( ( member @ B @ I @ A6 )
% 0.16/0.44 => ? [X6: C] :
% 0.16/0.44 ( ( member @ C @ X6 @ B6 )
% 0.16/0.44 & ( ord_less_eq @ A @ ( F @ I ) @ ( G3 @ X6 ) ) ) )
% 0.16/0.44 => ( ! [J: C] :
% 0.16/0.44 ( ( member @ C @ J @ B6 )
% 0.16/0.44 => ? [X6: B] :
% 0.16/0.44 ( ( member @ B @ X6 @ A6 )
% 0.16/0.44 & ( ord_less_eq @ A @ ( G3 @ J ) @ ( F @ X6 ) ) ) )
% 0.16/0.44 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ A6 ) )
% 0.16/0.44 = ( complete_Sup_Sup @ A @ ( image @ C @ A @ G3 @ B6 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % SUP_eq
% 0.16/0.44 thf(fact_235_inj__image__subset__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) @ ( image @ A @ B @ F @ B6 ) )
% 0.16/0.44 = ( ord_less_eq @ ( set @ A ) @ A6 @ B6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_image_subset_iff
% 0.16/0.44 thf(fact_236_the__inv__into__into,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,X3: B,B6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ A6 )
% 0.16/0.44 => ( ( member @ B @ X3 @ ( image @ A @ B @ F @ A6 ) )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( member @ A @ ( the_inv_into @ A @ B @ A6 @ F @ X3 ) @ B6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % the_inv_into_into
% 0.16/0.44 thf(fact_237_Zorn__Lemma,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ ( set @ A )] :
% 0.16/0.44 ( ! [X: set @ ( set @ A )] :
% 0.16/0.44 ( ( member @ ( set @ ( set @ A ) ) @ X @ ( chains2 @ A @ A6 ) )
% 0.16/0.44 => ( member @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ X ) @ A6 ) )
% 0.16/0.44 => ? [X: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ X @ A6 )
% 0.16/0.44 & ! [Xa: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ Xa @ A6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ X @ Xa )
% 0.16/0.44 => ( Xa = X ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Zorn_Lemma
% 0.16/0.44 thf(fact_238_inj__image__Compl__subset,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ ( uminus_uminus @ ( set @ A ) @ A6 ) ) @ ( uminus_uminus @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_image_Compl_subset
% 0.16/0.44 thf(fact_239_ComplI,axiom,
% 0.16/0.44 ! [A: $tType,C3: A,A6: set @ A] :
% 0.16/0.44 ( ~ ( member @ A @ C3 @ A6 )
% 0.16/0.44 => ( member @ A @ C3 @ ( uminus_uminus @ ( set @ A ) @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ComplI
% 0.16/0.44 thf(fact_240_Compl__iff,axiom,
% 0.16/0.44 ! [A: $tType,C3: A,A6: set @ A] :
% 0.16/0.44 ( ( member @ A @ C3 @ ( uminus_uminus @ ( set @ A ) @ A6 ) )
% 0.16/0.44 = ( ~ ( member @ A @ C3 @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Compl_iff
% 0.16/0.44 thf(fact_241_Compl__eq__Compl__iff,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( ( uminus_uminus @ ( set @ A ) @ A6 )
% 0.16/0.44 = ( uminus_uminus @ ( set @ A ) @ B6 ) )
% 0.16/0.44 = ( A6 = B6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % Compl_eq_Compl_iff
% 0.16/0.44 thf(fact_242_Compl__subset__Compl__iff,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A6 ) @ ( uminus_uminus @ ( set @ A ) @ B6 ) )
% 0.16/0.44 = ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % Compl_subset_Compl_iff
% 0.16/0.44 thf(fact_243_Compl__anti__mono,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B6 ) @ ( uminus_uminus @ ( set @ A ) @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Compl_anti_mono
% 0.16/0.44 thf(fact_244_sp_092_060_094sub_062_092_060mu_062_Orel__mono,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,G: $tType,D: $tType,B: $tType,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 0.16/0.44 ( ( ord_less_eq @ ( A > C > $o ) @ R1 @ R1a )
% 0.16/0.44 => ( ( ord_less_eq @ ( B > D > $o ) @ R22 @ R2a )
% 0.16/0.44 => ( ord_less_eq @ ( ( stream901396144_sp_mu @ G @ A @ B ) > ( stream901396144_sp_mu @ G @ C @ D ) > $o ) @ ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 ) @ ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1a @ R2a ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sp\<^sub>\<mu>.rel_mono
% 0.16/0.44 thf(fact_245_chainsD2,axiom,
% 0.16/0.44 ! [A: $tType,C3: set @ ( set @ A ),S4: set @ ( set @ A )] :
% 0.16/0.44 ( ( member @ ( set @ ( set @ A ) ) @ C3 @ ( chains2 @ A @ S4 ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ C3 @ S4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % chainsD2
% 0.16/0.44 thf(fact_246_Collect__case__prod__mono,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,A6: A > B > $o,B6: A > B > $o] :
% 0.16/0.44 ( ( ord_less_eq @ ( A > B > $o ) @ A6 @ B6 )
% 0.16/0.44 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ A6 ) ) @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ B6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_case_prod_mono
% 0.16/0.44 thf(fact_247_ComplD,axiom,
% 0.16/0.44 ! [A: $tType,C3: A,A6: set @ A] :
% 0.16/0.44 ( ( member @ A @ C3 @ ( uminus_uminus @ ( set @ A ) @ A6 ) )
% 0.16/0.44 => ~ ( member @ A @ C3 @ A6 ) ) ).
% 0.16/0.44
% 0.16/0.44 % ComplD
% 0.16/0.44 thf(fact_248_double__complement,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ A] :
% 0.16/0.44 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A6 ) )
% 0.16/0.44 = A6 ) ).
% 0.16/0.44
% 0.16/0.44 % double_complement
% 0.16/0.44 thf(fact_249_chainsD,axiom,
% 0.16/0.44 ! [A: $tType,C3: set @ ( set @ A ),S4: set @ ( set @ A ),X3: set @ A,Y: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ ( set @ A ) ) @ C3 @ ( chains2 @ A @ S4 ) )
% 0.16/0.44 => ( ( member @ ( set @ A ) @ X3 @ C3 )
% 0.16/0.44 => ( ( member @ ( set @ A ) @ Y @ C3 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ X3 @ Y )
% 0.16/0.44 | ( ord_less_eq @ ( set @ A ) @ Y @ X3 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % chainsD
% 0.16/0.44 thf(fact_250_Zorn__Lemma2,axiom,
% 0.16/0.44 ! [A: $tType,A6: set @ ( set @ A )] :
% 0.16/0.44 ( ! [X: set @ ( set @ A )] :
% 0.16/0.44 ( ( member @ ( set @ ( set @ A ) ) @ X @ ( chains2 @ A @ A6 ) )
% 0.16/0.44 => ? [Xa: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ Xa @ A6 )
% 0.16/0.44 & ! [Xb: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ Xb @ X )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ Xb @ Xa ) ) ) )
% 0.16/0.44 => ? [X: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ X @ A6 )
% 0.16/0.44 & ! [Xa: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ Xa @ A6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ X @ Xa )
% 0.16/0.44 => ( Xa = X ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Zorn_Lemma2
% 0.16/0.44 thf(fact_251_surj__Compl__image__subset,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F: B > A,A6: set @ B] :
% 0.16/0.44 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.16/0.44 = ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ ( image @ B @ A @ F @ A6 ) ) @ ( image @ B @ A @ F @ ( uminus_uminus @ ( set @ B ) @ A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_Compl_image_subset
% 0.16/0.44 thf(fact_252_mono__Chains,axiom,
% 0.16/0.44 ! [A: $tType,R: set @ ( product_prod @ A @ A ),S: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ S )
% 0.16/0.44 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( chains @ A @ R ) @ ( chains @ A @ S ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % mono_Chains
% 0.16/0.44 thf(fact_253_relChain__def,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.44 => ( ( bNF_Ca1785829860lChain @ A @ B )
% 0.16/0.44 = ( ^ [R3: set @ ( product_prod @ A @ A ),As: A > B] :
% 0.16/0.44 ! [I2: A,J2: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ I2 @ J2 ) @ R3 )
% 0.16/0.44 => ( ord_less_eq @ B @ ( As @ I2 ) @ ( As @ J2 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % relChain_def
% 0.16/0.44 thf(fact_254_chain__subset__def,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( chain_subset @ A )
% 0.16/0.44 = ( ^ [C6: set @ ( set @ A )] :
% 0.16/0.44 ! [X4: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ X4 @ C6 )
% 0.16/0.44 => ! [Y5: set @ A] :
% 0.16/0.44 ( ( member @ ( set @ A ) @ Y5 @ C6 )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ A ) @ X4 @ Y5 )
% 0.16/0.44 | ( ord_less_eq @ ( set @ A ) @ Y5 @ X4 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % chain_subset_def
% 0.16/0.44 thf(fact_255_vimage__subsetI,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: A > B,B6: set @ B,A6: set @ A] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.16/0.44 => ( ( ord_less_eq @ ( set @ B ) @ B6 @ ( image @ A @ B @ F @ A6 ) )
% 0.16/0.44 => ( ord_less_eq @ ( set @ A ) @ ( vimage @ A @ B @ F @ B6 ) @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % vimage_subsetI
% 0.16/0.44
% 0.16/0.44 %----Type constructors (15)
% 0.16/0.44 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.16/0.44 ! [A8: $tType,A9: $tType] :
% 0.16/0.44 ( ( comple187826305attice @ A9 @ ( type2 @ A9 ) )
% 0.16/0.44 => ( comple187826305attice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 0.16/0.44 ! [A8: $tType,A9: $tType] :
% 0.16/0.44 ( ( complete_Sup @ A9 @ ( type2 @ A9 ) )
% 0.16/0.44 => ( complete_Sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.16/0.44 ! [A8: $tType,A9: $tType] :
% 0.16/0.44 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 0.16/0.44 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_fun___Orderings_Otop,axiom,
% 0.16/0.44 ! [A8: $tType,A9: $tType] :
% 0.16/0.44 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.16/0.44 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_fun___Orderings_Oord,axiom,
% 0.16/0.44 ! [A8: $tType,A9: $tType] :
% 0.16/0.44 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.16/0.44 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 0.16/0.44 ! [A8: $tType] : ( comple187826305attice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Set_Oset___Complete__Lattices_OSup_2,axiom,
% 0.16/0.44 ! [A8: $tType] : ( complete_Sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Set_Oset___Orderings_Oorder__top_3,axiom,
% 0.16/0.44 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 0.16/0.44 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 0.16/0.44 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_6,axiom,
% 0.16/0.44 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Complete__Lattices_OSup_7,axiom,
% 0.16/0.44 complete_Sup @ $o @ ( type2 @ $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Orderings_Oorder__top_8,axiom,
% 0.16/0.44 order_top @ $o @ ( type2 @ $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Orderings_Otop_9,axiom,
% 0.16/0.44 top @ $o @ ( type2 @ $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.16/0.44 ord @ $o @ ( type2 @ $o ) ).
% 0.16/0.44
% 0.16/0.44 %----Conjectures (4)
% 0.16/0.44 thf(conj_0,hypothesis,
% 0.16/0.44 ! [B8: b,Sp2: c,Fsp: stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a )] :
% 0.16/0.44 ( ( x
% 0.16/0.44 = ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1370332830mu_Put @ b @ c @ a @ B8 @ Sp2 ) @ Fsp ) )
% 0.16/0.44 => p ) ).
% 0.16/0.44
% 0.16/0.44 thf(conj_1,hypothesis,
% 0.16/0.44 ! [F5: a > ( stream901396144_sp_mu @ a @ b @ c ),B8: a,Sp2: stream1273403375_sp_nu @ d @ a] :
% 0.16/0.44 ( ( x
% 0.16/0.44 = ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ F5 ) @ ( stream1370332830mu_Put @ a @ ( stream1273403375_sp_nu @ d @ a ) @ d @ B8 @ Sp2 ) ) )
% 0.16/0.44 => p ) ).
% 0.16/0.44
% 0.16/0.44 thf(conj_2,hypothesis,
% 0.16/0.44 ! [F5: a > ( stream901396144_sp_mu @ a @ b @ c ),G4: d > ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) )] :
% 0.16/0.44 ( ( x
% 0.16/0.44 = ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ F5 ) @ ( stream1294929701mu_Get @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) @ G4 ) ) )
% 0.16/0.44 => p ) ).
% 0.16/0.44
% 0.16/0.44 thf(conj_3,conjecture,
% 0.16/0.44 p ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 2.70/1.48 ---- Embedded in THF ---
% 2.70/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.70/1.48 %%% Generated on Tue Feb 24 06:13:05 EST 2026
% 2.70/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.70/1.48 %%% Logic specification used:
% 2.70/1.48 %%% thf(spec, logic, $$dhol).
% 2.70/1.48
% 2.70/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2DTF27294.p
% 2.70/1.48 thf(ty_t_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060nu_062, type, stream1273403375_sp_nu: ($tType > ($tType > $tType))).
% 2.70/1.48 thf(ty_t_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062, type, stream901396144_sp_mu: ($tType > ($tType > ($tType > $tType)))).
% 2.70/1.48 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.70/1.48 thf(ty_t_Stream_Ostream, type, stream: ($tType > $tType)).
% 2.70/1.48 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.70/1.48 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.70/1.48 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.70/1.48 thf(ty_tf_d, type, d: $tType).
% 2.70/1.48 thf(ty_tf_c, type, c: $tType).
% 2.70/1.48 thf(ty_tf_b, type, b: $tType).
% 2.70/1.48 thf(ty_tf_a, type, a: $tType).
% 2.70/1.48 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.70/1.48 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.70/1.48 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.70/1.48 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.70/1.48 thf(sy_cl_Complete__Lattices_OSup, type, complete_Sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.70/1.48 thf(sy_cl_Complete__Lattices_Ocomplete__lattice, type, comple187826305attice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.70/1.48 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain, type, bNF_Ca1785829860lChain: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((A > B) > $o))))).
% 2.70/1.48 thf(sy_c_BNF__Def_OfstOp, type, bNF_fstOp: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > $o)) > ((B > (C > $o)) > (((product_prod @ A) @ C) > ((product_prod @ A) @ B))))))).
% 2.70/1.48 thf(sy_c_BNF__Def_Opick__middlep, type, bNF_pick_middlep: (!> [B:$tType,A:$tType,C:$tType]: (((B > (A > $o)) > ((A > (C > $o)) > (B > (C > A))))))).
% 2.70/1.48 thf(sy_c_BNF__Def_OsndOp, type, bNF_sndOp: (!> [C:$tType,A:$tType,B:$tType]: (((C > (A > $o)) > ((A > (B > $o)) > (((product_prod @ C) @ B) > ((product_prod @ A) @ B))))))).
% 2.70/1.48 thf(sy_c_Complete__Lattices_OSup__class_OSup, type, complete_Sup_Sup: (!> [A:$tType]: (((set @ A) > A)))).
% 2.70/1.48 thf(sy_c_Fun_Oinj__on, type, inj_on: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > $o))))).
% 2.70/1.48 thf(sy_c_Fun_Othe__inv__into, type, the_inv_into: (!> [A:$tType,B:$tType]: (((set @ A) > ((A > B) > (B > A)))))).
% 2.70/1.48 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.70/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.70/1.48 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.70/1.48 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.70/1.48 thf(sy_c_Product__Type_Oapfst, type, product_apfst: (!> [A:$tType,C:$tType,B:$tType]: (((A > C) > (((product_prod @ A) @ B) > ((product_prod @ C) @ B)))))).
% 2.70/1.48 thf(sy_c_Product__Type_Oapsnd, type, product_apsnd: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > (((product_prod @ A) @ B) > ((product_prod @ A) @ C)))))).
% 2.70/1.48 thf(sy_c_Product__Type_Ocurry, type, product_curry: (!> [A:$tType,B:$tType,C:$tType]: (((((product_prod @ A) @ B) > C) > (A > (B > C)))))).
% 2.70/1.48 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.70/1.48 thf(sy_c_Product__Type_Omap__prod, type, product_map_prod: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > C) > ((B > D) > (((product_prod @ A) @ B) > ((product_prod @ C) @ D))))))).
% 2.70/1.48 thf(sy_c_Product__Type_Oold_Obool_Orec__bool, type, product_rec_bool: (!> [T:$tType]: ((T > (T > ($o > T)))))).
% 2.70/1.48 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.70/1.48 thf(sy_c_Product__Type_Oprod_Ocase__prod, type, product_case_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.70/1.48 thf(sy_c_Product__Type_Oprod_Ofst, type, product_fst: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > A)))).
% 2.70/1.48 thf(sy_c_Product__Type_Oprod_Osnd, type, product_snd: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > B)))).
% 2.70/1.48 thf(sy_c_Product__Type_Oprod_Oswap, type, product_swap: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > ((product_prod @ B) @ A))))).
% 2.70/1.48 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.70/1.48 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.70/1.48 thf(sy_c_Set_Obind, type, bind: (!> [A:$tType,B:$tType]: (((set @ A) > ((A > (set @ B)) > (set @ B)))))).
% 2.70/1.48 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 2.70/1.48 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Orun_092_060_094sub_062_092_060mu_062, type, stream5064451run_mu: (!> [A:$tType,B:$tType,C:$tType]: (((((stream901396144_sp_mu @ A) @ B) @ C) > ((stream @ A) > ((product_prod @ ((product_prod @ B) @ C)) @ (stream @ A))))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_OGet, type, stream1294929701mu_Get: (!> [A:$tType,B:$tType,C:$tType]: (((A > (((stream901396144_sp_mu @ A) @ B) @ C)) > (((stream901396144_sp_mu @ A) @ B) @ C))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_OPut, type, stream1370332830mu_Put: (!> [B:$tType,C:$tType,A:$tType]: ((B > (C > (((stream901396144_sp_mu @ A) @ B) @ C)))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Ocase__sp_092_060_094sub_062_092_060mu_062, type, stream160000856_sp_mu: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: ((((A > (((stream901396144_sp_mu @ A) @ B) @ C)) > D) > ((B > (C > D)) > ((((stream901396144_sp_mu @ A) @ B) @ C) > D)))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Opred__sp_092_060_094sub_062_092_060mu_062, type, stream123009735_sp_mu: (!> [A:$tType,B:$tType,E:$tType]: (((A > $o) > ((B > $o) > ((((stream901396144_sp_mu @ E) @ A) @ B) > $o)))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Orec__sp_092_060_094sub_062_092_060mu_062, type, stream674629690_sp_mu: (!> [A:$tType,B:$tType,C:$tType,G:$tType]: ((((A > ((product_prod @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ G)) > G) > ((B > (C > G)) > ((((stream901396144_sp_mu @ A) @ B) @ C) > G)))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Orel__sp_092_060_094sub_062_092_060mu_062, type, stream1924447089_sp_mu: (!> [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > ((((stream901396144_sp_mu @ E) @ A) @ B) > ((((stream901396144_sp_mu @ E) @ C) @ D) > $o))))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Oset1__sp_092_060_094sub_062_092_060mu_062, type, stream2074884121_sp_mu: (!> [A:$tType,B:$tType,C:$tType]: (((((stream901396144_sp_mu @ A) @ B) @ C) > (set @ B))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Oset2__sp_092_060_094sub_062_092_060mu_062, type, stream1259315544_sp_mu: (!> [A:$tType,B:$tType,C:$tType]: (((((stream901396144_sp_mu @ A) @ B) @ C) > (set @ C))))).
% 2.70/1.48 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osub, type, stream152839592le_sub: (!> [A:$tType,B:$tType,C:$tType]: ((set @ ((product_prod @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ (((stream901396144_sp_mu @ A) @ B) @ C)))))).
% 2.70/1.48 thf(sy_c_Wellfounded_Olex__prod, type, lex_prod: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((set @ ((product_prod @ B) @ B)) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 2.70/1.48 thf(sy_c_Wellfounded_Omeasure, type, measure: (!> [A:$tType]: (((A > nat) > (set @ ((product_prod @ A) @ A)))))).
% 2.70/1.48 thf(sy_c_Wellfounded_Owf, type, wf: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.70/1.48 thf(sy_c_Wfrec_Osame__fst, type, same_fst: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > (set @ ((product_prod @ B) @ B))) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 2.70/1.48 thf(sy_c_Zorn_OChains, type, chains: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ (set @ A)))))).
% 2.70/1.48 thf(sy_c_Zorn_Ochain__subset, type, chain_subset: (!> [A:$tType]: (((set @ (set @ A)) > $o)))).
% 2.70/1.48 thf(sy_c_Zorn_Ochains, type, chains2: (!> [A:$tType]: (((set @ (set @ A)) > (set @ (set @ (set @ A))))))).
% 2.70/1.48 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.70/1.48 thf(sy_v_P, type, p: $o).
% 2.70/1.48 thf(sy_v_x, type, x: ((product_prod @ (((stream901396144_sp_mu @ a) @ b) @ c)) @ (((stream901396144_sp_mu @ d) @ a) @ ((stream1273403375_sp_nu @ d) @ a)))).
% 2.70/1.48 thf(fact_0_sp_092_060_094sub_062_092_060mu_062_Oinject_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,X1:(A > (((stream901396144_sp_mu @ A) @ B) @ C)),Y1:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: (((((((stream1294929701mu_Get @ A) @ B) @ C) @ X1) = ((((stream1294929701mu_Get @ A) @ B) @ C) @ Y1)) = (X1 = Y1))))).
% 2.70/1.48 thf(fact_1_sp_092_060_094sub_062_092_060mu_062_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,X21:B,X22:C,Y21:B,Y22:C]: ((((((((stream1370332830mu_Put @ B) @ C) @ A) @ X21) @ X22) = (((((stream1370332830mu_Put @ B) @ C) @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.70/1.48 thf(fact_2_sp_092_060_094sub_062_092_060mu_062_Odistinct_I1_J, axiom, (! [B:$tType,A:$tType,C:$tType,X1:(A > (((stream901396144_sp_mu @ A) @ B) @ C)),X21:B,X22:C]: ((((((stream1294929701mu_Get @ A) @ B) @ C) @ X1) != (((((stream1370332830mu_Put @ B) @ C) @ A) @ X21) @ X22))))).
% 2.70/1.48 thf(fact_3_sp_092_060_094sub_062_092_060mu_062_Oexhaust, axiom, (! [B:$tType,A:$tType,C:$tType,Y:(((stream901396144_sp_mu @ A) @ B) @ C)]: (((! [X12:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: ((Y != ((((stream1294929701mu_Get @ A) @ B) @ C) @ X12)))) => (~ ((! [X212:B,X222:C]: ((Y != (((((stream1370332830mu_Put @ B) @ C) @ A) @ X212) @ X222)))))))))).
% 2.70/1.48 thf(fact_4_subI, axiom, (! [C:$tType,B:$tType,A:$tType,F:(A > (((stream901396144_sp_mu @ A) @ B) @ C)),A2:A]: ((((member @ ((product_prod @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ (((stream901396144_sp_mu @ A) @ B) @ C))) @ ((((product_Pair @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ (F @ A2)) @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ F))) @ (((stream152839592le_sub @ A) @ B) @ C))))).
% 2.70/1.48 thf(fact_5_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 2.70/1.48 thf(fact_6_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 2.70/1.48 thf(fact_7_run_092_060_094sub_062_092_060mu_062_Osimps_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,B2:B,Sp:C,S:(stream @ A)]: (((((((stream5064451run_mu @ A) @ B) @ C) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ B2) @ Sp)) @ S) = ((((product_Pair @ ((product_prod @ B) @ C)) @ (stream @ A)) @ ((((product_Pair @ B) @ C) @ B2) @ Sp)) @ S))))).
% 2.70/1.48 thf(fact_8_surj__pair, axiom, (! [A:$tType,B:$tType,P:((product_prod @ A) @ B)]: ((? [X:A,Y3:B]: ((P = ((((product_Pair @ A) @ B) @ X) @ Y3))))))).
% 2.70/1.48 thf(fact_9_prod__cases, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),P:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ P))))).
% 2.70/1.48 thf(fact_10_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 2.70/1.48 thf(fact_11_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A4:A,B4:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2)))))))))).
% 2.70/1.48 thf(fact_12_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 2.70/1.48 thf(fact_13_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.70/1.48 thf(fact_14_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E,F3:F2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F3))))))))))))).
% 2.70/1.48 thf(fact_15_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F2:$tType,G:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E,F3:F2,G2:G]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G)) @ E2) @ ((((product_Pair @ F2) @ G) @ F3) @ G2)))))))))))))).
% 2.70/1.48 thf(fact_16_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ Prod))))).
% 2.70/1.48 thf(fact_17_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 2.70/1.48 thf(fact_18_prod__induct7, axiom, (! [G:$tType,F2:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E,F3:F2,G2:G]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G)) @ E2) @ ((((product_Pair @ F2) @ G) @ F3) @ G2))))))))) => (P2 @ X3))))).
% 2.70/1.48 thf(fact_19_prod__induct6, axiom, (! [F2:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E,F3:F2]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F3)))))))) => (P2 @ X3))))).
% 2.70/1.48 thf(fact_20_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P2 @ X3))))).
% 2.70/1.48 thf(fact_21_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A4:A,B4:B,C2:C,D2:D]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P2 @ X3))))).
% 2.70/1.48 thf(fact_22_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A4:A,B4:B,C2:C]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2))))) => (P2 @ X3))))).
% 2.70/1.48 thf(fact_23_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.70/1.48 thf(fact_24_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 2.70/1.48 thf(fact_25_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R:A,S:B,R2:(set @ ((product_prod @ A) @ B)),S2:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S)) @ R2) => ((S2 = S) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S2)) @ R2)))))).
% 2.70/1.48 thf(fact_26_curry__conv, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((product_curry @ B) @ C) @ A) = (^ [F4:(((product_prod @ B) @ C) > A),A5:B,B5:C]: ((F4 @ ((((product_Pair @ B) @ C) @ A5) @ B5)))))))).
% 2.70/1.48 thf(fact_27_sp_092_060_094sub_062_092_060mu_062_Osimps_I6_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,F1:((A > (((stream901396144_sp_mu @ A) @ B) @ C)) > D),F22:(B > (C > D)),X21:B,X22:C]: (((((((((stream160000856_sp_mu @ A) @ B) @ C) @ D) @ F1) @ F22) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ X21) @ X22)) = ((F22 @ X21) @ X22))))).
% 2.70/1.48 thf(fact_28_sp_092_060_094sub_062_092_060mu_062_Osimps_I5_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,F1:((A > (((stream901396144_sp_mu @ A) @ B) @ C)) > D),F22:(B > (C > D)),X1:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: (((((((((stream160000856_sp_mu @ A) @ B) @ C) @ D) @ F1) @ F22) @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ X1)) = (F1 @ X1))))).
% 2.70/1.48 thf(fact_29_curryI, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: (((F @ ((((product_Pair @ A) @ B) @ A2) @ B2)) => ((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2))))).
% 2.70/1.48 thf(fact_30_sp_092_060_094sub_062_092_060mu_062_Osimps_I8_J, axiom, (! [A:$tType,B:$tType,G:$tType,C:$tType,F1:((A > ((product_prod @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ G)) > G),F22:(B > (C > G)),X21:B,X22:C]: (((((((((stream674629690_sp_mu @ A) @ B) @ C) @ G) @ F1) @ F22) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ X21) @ X22)) = ((F22 @ X21) @ X22))))).
% 2.70/1.48 thf(fact_31_sp_092_060_094sub_062_092_060mu_062_Opred__inject_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,P1:(B > $o),P22:(C > $o),A2:B,Aa:C]: ((((((((stream123009735_sp_mu @ B) @ C) @ A) @ P1) @ P22) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ A2) @ Aa)) = ((P1 @ A2) & (P22 @ Aa)))))).
% 2.70/1.48 thf(fact_32_swap__simp, axiom, (! [A:$tType,B:$tType,X3:B,Y:A]: (((((product_swap @ B) @ A) @ ((((product_Pair @ B) @ A) @ X3) @ Y)) = ((((product_Pair @ A) @ B) @ Y) @ X3))))).
% 2.70/1.48 thf(fact_33_swap__swap, axiom, (! [B:$tType,A:$tType,P:((product_prod @ A) @ B)]: (((((product_swap @ B) @ A) @ (((product_swap @ A) @ B) @ P)) = P)))).
% 2.70/1.48 thf(fact_34_curryD, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.70/1.48 thf(fact_35_curryE, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.70/1.48 thf(fact_36_pair__in__swap__image, axiom, (! [A:$tType,B:$tType,Y:A,X3:B,A6:(set @ ((product_prod @ B) @ A))]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Y) @ X3)) @ ((((image @ ((product_prod @ B) @ A)) @ ((product_prod @ A) @ B)) @ ((product_swap @ B) @ A)) @ A6)) = (((member @ ((product_prod @ B) @ A)) @ ((((product_Pair @ B) @ A) @ X3) @ Y)) @ A6))))).
% 2.70/1.48 thf(fact_37_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I2_J, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,G:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y21:A,Y22:B,X1:(G > (((stream901396144_sp_mu @ G) @ C) @ D))]: ((~ ((((((((((stream1924447089_sp_mu @ A) @ C) @ B) @ D) @ G) @ R1) @ R22) @ (((((stream1370332830mu_Put @ A) @ B) @ G) @ Y21) @ Y22)) @ ((((stream1294929701mu_Get @ G) @ C) @ D) @ X1))))))).
% 2.70/1.48 thf(fact_38_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I1_J, axiom, (! [B:$tType,C:$tType,E:$tType,A:$tType,F2:$tType,R1:(B > (E > $o)),R22:(C > (F2 > $o)),X1:(A > (((stream901396144_sp_mu @ A) @ B) @ C)),Y21:E,Y22:F2]: ((~ ((((((((((stream1924447089_sp_mu @ B) @ E) @ C) @ F2) @ A) @ R1) @ R22) @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ X1)) @ (((((stream1370332830mu_Put @ E) @ F2) @ A) @ Y21) @ Y22))))))).
% 2.70/1.48 thf(fact_39_internal__case__prod__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((produc2004651681e_prod @ A) @ B) @ C) = (((product_case_prod @ A) @ B) @ C))))).
% 2.70/1.48 thf(fact_40_wf__sub, axiom, (! [C:$tType,B:$tType,A:$tType]: (((wf @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ (((stream152839592le_sub @ A) @ B) @ C))))).
% 2.70/1.48 thf(fact_41_apsnd__conv, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > B),X3:A,Y:C]: (((((((product_apsnd @ C) @ B) @ A) @ F) @ ((((product_Pair @ A) @ C) @ X3) @ Y)) = ((((product_Pair @ A) @ B) @ X3) @ (F @ Y)))))).
% 2.70/1.48 thf(fact_42_old_Obool_Osimps_I5_J, axiom, (! [T:$tType,F1:T,F22:T]: ((((((product_rec_bool @ T) @ F1) @ F22) @ $true) = F1)))).
% 2.70/1.48 thf(fact_43_old_Obool_Osimps_I6_J, axiom, (! [T:$tType,F1:T,F22:T]: ((((((product_rec_bool @ T) @ F1) @ F22) @ $false) = F22)))).
% 2.70/1.48 thf(fact_44_apfst__conv, axiom, (! [C:$tType,A:$tType,B:$tType,F:(C > A),X3:C,Y:B]: (((((((product_apfst @ C) @ A) @ B) @ F) @ ((((product_Pair @ C) @ B) @ X3) @ Y)) = ((((product_Pair @ A) @ B) @ (F @ X3)) @ Y))))).
% 2.70/1.48 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.70/1.48 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A6:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A6)))) = A6)))).
% 2.70/1.48 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P2 @ X) = (Q @ X)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.70/1.48 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G3:(A > B)]: (((! [X:A]: (((F @ X) = (G3 @ X)))) => (F = G3))))).
% 2.70/1.48 thf(fact_49_curry__case__prod, axiom, (! [C:$tType,B:$tType,A:$tType,F:(A > (B > C))]: ((((((product_curry @ A) @ B) @ C) @ ((((product_case_prod @ A) @ B) @ C) @ F)) = F)))).
% 2.70/1.48 thf(fact_50_case__prod__curry, axiom, (! [C:$tType,B:$tType,A:$tType,F:(((product_prod @ A) @ B) > C)]: ((((((product_case_prod @ A) @ B) @ C) @ ((((product_curry @ A) @ B) @ C) @ F)) = F)))).
% 2.70/1.48 thf(fact_51_sp_092_060_094sub_062_092_060mu_062_Orel__eq, axiom, (! [B:$tType,A:$tType,G:$tType]: (((((((((stream1924447089_sp_mu @ A) @ A) @ B) @ B) @ G) @ (^ [Y4:A,Z:A]: ((Y4 = Z)))) @ (^ [Y4:B,Z:B]: ((Y4 = Z)))) = (^ [Y4:(((stream901396144_sp_mu @ G) @ A) @ B),Z:(((stream901396144_sp_mu @ G) @ A) @ B)]: ((Y4 = Z))))))).
% 2.70/1.48 thf(fact_52_sp_092_060_094sub_062_092_060mu_062_Orel__refl, axiom, (! [D:$tType,C:$tType,G:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X3:(((stream901396144_sp_mu @ G) @ C) @ D)]: (((! [X:C]: (((R1a @ X) @ X))) => ((! [X:D]: (((R2a @ X) @ X))) => (((((((((stream1924447089_sp_mu @ C) @ C) @ D) @ D) @ G) @ R1a) @ R2a) @ X3) @ X3)))))).
% 2.70/1.48 thf(fact_53_apsnd__apfst__commute, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,F:(C > B),G3:(D > A),P:((product_prod @ D) @ C)]: (((((((product_apsnd @ C) @ B) @ A) @ F) @ (((((product_apfst @ D) @ A) @ C) @ G3) @ P)) = (((((product_apfst @ D) @ A) @ B) @ G3) @ (((((product_apsnd @ C) @ B) @ D) @ F) @ P)))))).
% 2.70/1.48 thf(fact_54_mem__case__prodE, axiom, (! [B:$tType,A:$tType,C:$tType,Z2:A,C3:(B > (C > (set @ A))),P:((product_prod @ B) @ C)]: (((((member @ A) @ Z2) @ (((((product_case_prod @ B) @ C) @ (set @ A)) @ C3) @ P)) => (~ ((! [X:B,Y3:C]: (((P = ((((product_Pair @ B) @ C) @ X) @ Y3)) => (~ ((((member @ A) @ Z2) @ ((C3 @ X) @ Y3))))))))))))).
% 2.70/1.48 thf(fact_55_old_Oprod_Ocase, axiom, (! [A:$tType,C:$tType,B:$tType,F:(A > (B > C)),X1:A,X2:B]: (((((((product_case_prod @ A) @ B) @ C) @ F) @ ((((product_Pair @ A) @ B) @ X1) @ X2)) = ((F @ X1) @ X2))))).
% 2.70/1.48 thf(fact_56_sp_092_060_094sub_062_092_060mu_062_Orel__intros_I2_J, axiom, (! [C:$tType,B:$tType,E:$tType,A:$tType,F2:$tType,R1:(B > (E > $o)),X21:B,Y21:E,R22:(C > (F2 > $o)),X22:C,Y22:F2]: ((((R1 @ X21) @ Y21) => (((R22 @ X22) @ Y22) => (((((((((stream1924447089_sp_mu @ B) @ E) @ C) @ F2) @ A) @ R1) @ R22) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ X21) @ X22)) @ (((((stream1370332830mu_Put @ E) @ F2) @ A) @ Y21) @ Y22))))))).
% 2.70/1.48 thf(fact_57_sp_092_060_094sub_062_092_060mu_062_Orel__inject_I2_J, axiom, (! [A:$tType,E:$tType,B:$tType,C:$tType,F2:$tType,R1:(B > (E > $o)),R22:(C > (F2 > $o)),X21:B,X22:C,Y21:E,Y22:F2]: (((((((((((stream1924447089_sp_mu @ B) @ E) @ C) @ F2) @ A) @ R1) @ R22) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ X21) @ X22)) @ (((((stream1370332830mu_Put @ E) @ F2) @ A) @ Y21) @ Y22)) = (((R1 @ X21) @ Y21) & ((R22 @ X22) @ Y22)))))).
% 2.70/1.48 thf(fact_58_image__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X3:B,A6:(set @ B)]: (((B2 = (F @ X3)) => ((((member @ B) @ X3) @ A6) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ A6))))))).
% 2.70/1.48 thf(fact_59_wf__def, axiom, (! [A:$tType]: (((wf @ A) = (^ [R3:(set @ ((product_prod @ A) @ A))]: ((! [P3:(A > $o)]: (((! [X4:A]: (((! [Y5:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y5) @ X4)) @ R3) => (P3 @ Y5)))) => (P3 @ X4)))) => ((^ [P4:(A > $o)]: ((! [X5:A]: ((P4 @ X5))))) @ P3)))))))))).
% 2.70/1.48 thf(fact_60_wfE__min, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A)),X3:A,Q:(set @ A)]: ((((wf @ A) @ R2) => ((((member @ A) @ X3) @ Q) => (~ ((! [Z3:A]: (((((member @ A) @ Z3) @ Q) => (~ ((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ Z3)) @ R2) => (~ ((((member @ A) @ Y6) @ Q)))))))))))))))))).
% 2.70/1.48 thf(fact_61_wfI__min, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: (((! [X:A,Q2:(set @ A)]: (((((member @ A) @ X) @ Q2) => (? [Xa:A]: (((((member @ A) @ Xa) @ Q2) & (! [Y3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ Xa)) @ R2) => (~ ((((member @ A) @ Y3) @ Q2)))))))))))) => ((wf @ A) @ R2))))).
% 2.70/1.48 thf(fact_62_wfUNIVI, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: (((! [P5:(A > $o),X:A]: (((! [Xa:A]: (((! [Y3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ Xa)) @ R) => (P5 @ Y3)))) => (P5 @ Xa)))) => (P5 @ X)))) => ((wf @ A) @ R))))).
% 2.70/1.48 thf(fact_63_wf__asym, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),A2:A,X3:A]: ((((wf @ A) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ X3)) @ R) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ A2)) @ R)))))))).
% 2.70/1.48 thf(fact_64_wf__induct, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),P2:(A > $o),A2:A]: ((((wf @ A) @ R) => ((! [X:A]: (((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ X)) @ R) => (P2 @ Y6)))) => (P2 @ X)))) => (P2 @ A2)))))).
% 2.70/1.48 thf(fact_65_wf__irrefl, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),A2:A]: ((((wf @ A) @ R) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ R))))))).
% 2.70/1.48 thf(fact_66_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X3:A,A6:(set @ A),B2:B,F:(A > B)]: (((((member @ A) @ X3) @ A6) => ((B2 = (F @ X3)) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ A6))))))).
% 2.70/1.48 thf(fact_67_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A6:(set @ B),P2:(A > $o)]: (((! [X:A]: (((((member @ A) @ X) @ ((((image @ B) @ A) @ F) @ A6)) => (P2 @ X)))) => (! [X6:B]: (((((member @ B) @ X6) @ A6) => (P2 @ (F @ X6))))))))).
% 2.70/1.48 thf(fact_68_image__cong, axiom, (! [B:$tType,A:$tType,M:(set @ A),N:(set @ A),F:(A > B),G3:(A > B)]: (((M = N) => ((! [X:A]: (((((member @ A) @ X) @ N) => ((F @ X) = (G3 @ X))))) => (((((image @ A) @ B) @ F) @ M) = ((((image @ A) @ B) @ G3) @ N))))))).
% 2.70/1.48 thf(fact_69_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A6:(set @ B),P2:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ ((((image @ B) @ A) @ F) @ A6)) & (P2 @ X6)))) => (? [X:B]: (((((member @ B) @ X) @ A6) & (P2 @ (F @ X))))))))).
% 2.70/1.48 thf(fact_70_image__iff, axiom, (! [A:$tType,B:$tType,Z2:A,F:(B > A),A6:(set @ B)]: (((((member @ A) @ Z2) @ ((((image @ B) @ A) @ F) @ A6)) = (? [X4:B]: (((((member @ B) @ X4) @ A6) & (Z2 = (F @ X4))))))))).
% 2.70/1.48 thf(fact_71_imageI, axiom, (! [B:$tType,A:$tType,X3:A,A6:(set @ A),F:(A > B)]: (((((member @ A) @ X3) @ A6) => (((member @ B) @ (F @ X3)) @ ((((image @ A) @ B) @ F) @ A6)))))).
% 2.70/1.48 thf(fact_72_wf__induct__rule, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),P2:(A > $o),A2:A]: ((((wf @ A) @ R) => ((! [X:A]: (((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ X)) @ R) => (P2 @ Y6)))) => (P2 @ X)))) => (P2 @ A2)))))).
% 2.70/1.48 thf(fact_73_wf__eq__minimal, axiom, (! [A:$tType]: (((wf @ A) = (^ [R3:(set @ ((product_prod @ A) @ A))]: ((! [Q3:(set @ A)]: (((? [X4:A]: ((((member @ A) @ X4) @ Q3))) => (? [X4:A]: (((((member @ A) @ X4) @ Q3) & (! [Y5:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y5) @ X4)) @ R3) => (~ ((((member @ A) @ Y5) @ Q3)))))))))))))))))).
% 2.70/1.48 thf(fact_74_wf__not__refl, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),A2:A]: ((((wf @ A) @ R) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ R))))))).
% 2.70/1.48 thf(fact_75_wf__not__sym, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),A2:A,X3:A]: ((((wf @ A) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ X3)) @ R) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ A2)) @ R)))))))).
% 2.70/1.48 thf(fact_76_wf__measure, axiom, (! [A:$tType,F:(A > nat)]: (((wf @ A) @ ((measure @ A) @ F))))).
% 2.70/1.48 thf(fact_77_dependent__wf__choice, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ A) @ A)),P2:((A > B) > (A > (B > $o)))]: ((((wf @ A) @ R2) => ((! [F3:(A > B),G2:(A > B),X:A,R4:B]: (((! [Z4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z4) @ X)) @ R2) => ((F3 @ Z4) = (G2 @ Z4))))) => ((((P2 @ F3) @ X) @ R4) = (((P2 @ G2) @ X) @ R4))))) => ((! [X:A,F3:(A > B)]: (((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ X)) @ R2) => (((P2 @ F3) @ Y6) @ (F3 @ Y6))))) => (? [X13:B]: ((((P2 @ F3) @ X) @ X13)))))) => (? [F3:(A > B)]: ((! [X6:A]: ((((P2 @ F3) @ X6) @ (F3 @ X6)))))))))))).
% 2.70/1.48 thf(fact_78_split__cong, axiom, (! [C:$tType,B:$tType,A:$tType,Q4:((product_prod @ A) @ B),F:(A > (B > C)),G3:(A > (B > C)),P:((product_prod @ A) @ B)]: (((! [X:A,Y3:B]: (((((((product_Pair @ A) @ B) @ X) @ Y3) = Q4) => (((F @ X) @ Y3) = ((G3 @ X) @ Y3))))) => ((P = Q4) => ((((((product_case_prod @ A) @ B) @ C) @ F) @ P) = (((((product_case_prod @ A) @ B) @ C) @ G3) @ Q4))))))).
% 2.70/1.48 thf(fact_79_wf__lex__prod, axiom, (! [A:$tType,B:$tType,Ra:(set @ ((product_prod @ A) @ A)),Rb:(set @ ((product_prod @ B) @ B))]: ((((wf @ A) @ Ra) => (((wf @ B) @ Rb) => ((wf @ ((product_prod @ A) @ B)) @ ((((lex_prod @ A) @ B) @ Ra) @ Rb))))))).
% 2.70/1.48 thf(fact_80_in__lex__prod, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B,R:(set @ ((product_prod @ A) @ A)),S:(set @ ((product_prod @ B) @ B))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ ((((product_Pair @ A) @ B) @ A3) @ B3))) @ ((((lex_prod @ A) @ B) @ R) @ S)) = ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A3)) @ R) | ((A2 = A3) & (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ B2) @ B3)) @ S))))))).
% 2.70/1.48 thf(fact_81_surj__swap, axiom, (! [B:$tType,A:$tType]: ((((((image @ ((product_prod @ B) @ A)) @ ((product_prod @ A) @ B)) @ ((product_swap @ B) @ A)) @ (top_top @ (set @ ((product_prod @ B) @ A)))) = (top_top @ (set @ ((product_prod @ A) @ B))))))).
% 2.70/1.48 thf(fact_82_Sup_OSUP__cong, axiom, (! [A:$tType,B:$tType,A6:(set @ B),B6:(set @ B),C4:(B > A),D3:(B > A),Sup:((set @ A) > A)]: (((A6 = B6) => ((! [X:B]: (((((member @ B) @ X) @ B6) => ((C4 @ X) = (D3 @ X))))) => ((Sup @ ((((image @ B) @ A) @ C4) @ A6)) = (Sup @ ((((image @ B) @ A) @ D3) @ B6)))))))).
% 2.70/1.48 thf(fact_83_UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.70/1.48 thf(fact_84_UNIV__witness, axiom, (! [A:$tType]: ((? [X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))))).
% 2.70/1.48 thf(fact_85_UNIV__eq__I, axiom, (! [A:$tType,A6:(set @ A)]: (((! [X:A]: ((((member @ A) @ X) @ A6))) => ((top_top @ (set @ A)) = A6))))).
% 2.70/1.48 thf(fact_86_range__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X3:B]: (((B2 = (F @ X3)) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ (top_top @ (set @ B)))))))).
% 2.70/1.48 thf(fact_87_rangeI, axiom, (! [A:$tType,B:$tType,F:(B > A),X3:B]: ((((member @ A) @ (F @ X3)) @ ((((image @ B) @ A) @ F) @ (top_top @ (set @ B))))))).
% 2.70/1.48 thf(fact_88_sp_092_060_094sub_062_092_060mu_062_Oinduct, axiom, (! [C:$tType,B:$tType,A:$tType,P2:((((stream901396144_sp_mu @ A) @ B) @ C) > $o),Sp_mu:(((stream901396144_sp_mu @ A) @ B) @ C)]: (((! [X:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: (((! [Xa:(((stream901396144_sp_mu @ A) @ B) @ C)]: (((((member @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ Xa) @ ((((image @ A) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ X) @ (top_top @ (set @ A)))) => (P2 @ Xa)))) => (P2 @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ X))))) => ((! [X1a:B,X23:C]: ((P2 @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ X1a) @ X23)))) => (P2 @ Sp_mu)))))).
% 2.70/1.48 thf(fact_89_Inf_OINF__cong, axiom, (! [A:$tType,B:$tType,A6:(set @ B),B6:(set @ B),C4:(B > A),D3:(B > A),Inf:((set @ A) > A)]: (((A6 = B6) => ((! [X:B]: (((((member @ B) @ X) @ B6) => ((C4 @ X) = (D3 @ X))))) => ((Inf @ ((((image @ B) @ A) @ C4) @ A6)) = (Inf @ ((((image @ B) @ A) @ D3) @ B6)))))))).
% 2.70/1.48 thf(fact_90_iso__tuple__UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.70/1.48 thf(fact_91_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X4:D]: ((top_top @ C)))))))).
% 2.70/1.48 thf(fact_92_surjD, axiom, (! [A:$tType,B:$tType,F:(B > A),Y:A]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (? [X:B]: ((Y = (F @ X)))))))).
% 2.70/1.48 thf(fact_93_surjE, axiom, (! [A:$tType,B:$tType,F:(B > A),Y:A]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (~ ((! [X:B]: ((Y != (F @ X)))))))))).
% 2.70/1.48 thf(fact_94_surjI, axiom, (! [B:$tType,A:$tType,G3:(B > A),F:(A > B)]: (((! [X:A]: (((G3 @ (F @ X)) = X))) => (((((image @ B) @ A) @ G3) @ (top_top @ (set @ B))) = (top_top @ (set @ A))))))).
% 2.70/1.48 thf(fact_95_surj__def, axiom, (! [B:$tType,A:$tType,F:(B > A)]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) = (! [Y5:A]: ((? [X4:B]: ((Y5 = (F @ X4)))))))))).
% 2.70/1.48 thf(fact_96_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.70/1.48 thf(fact_97_sp_092_060_094sub_062_092_060mu_062_Oset__cases_I2_J, axiom, (! [B:$tType,A:$tType,C:$tType,E3:C,A2:(((stream901396144_sp_mu @ A) @ B) @ C)]: (((((member @ C) @ E3) @ ((((stream1259315544_sp_mu @ A) @ B) @ C) @ A2)) => ((! [Z3:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: (((A2 = ((((stream1294929701mu_Get @ A) @ B) @ C) @ Z3)) => (! [X:(((stream901396144_sp_mu @ A) @ B) @ C)]: (((((member @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ X) @ ((((image @ A) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ Z3) @ (top_top @ (set @ A)))) => (~ ((((member @ C) @ E3) @ ((((stream1259315544_sp_mu @ A) @ B) @ C) @ X)))))))))) => (~ ((! [Z1:B]: ((A2 != (((((stream1370332830mu_Put @ B) @ C) @ A) @ Z1) @ E3))))))))))).
% 2.70/1.48 thf(fact_98_sp_092_060_094sub_062_092_060mu_062_Oset__cases_I1_J, axiom, (! [B:$tType,A:$tType,C:$tType,E3:B,A2:(((stream901396144_sp_mu @ A) @ B) @ C)]: (((((member @ B) @ E3) @ ((((stream2074884121_sp_mu @ A) @ B) @ C) @ A2)) => ((! [Z3:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: (((A2 = ((((stream1294929701mu_Get @ A) @ B) @ C) @ Z3)) => (! [X:(((stream901396144_sp_mu @ A) @ B) @ C)]: (((((member @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ X) @ ((((image @ A) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ Z3) @ (top_top @ (set @ A)))) => (~ ((((member @ B) @ E3) @ ((((stream2074884121_sp_mu @ A) @ B) @ C) @ X)))))))))) => (~ ((! [Z22:C]: ((A2 != (((((stream1370332830mu_Put @ B) @ C) @ A) @ E3) @ Z22))))))))))).
% 2.70/1.48 thf(fact_99_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I3_J, axiom, (! [C:$tType,B:$tType,A:$tType,Xc:(((stream901396144_sp_mu @ A) @ B) @ C),Aa:(A > (((stream901396144_sp_mu @ A) @ B) @ C)),Xe:C]: (((((member @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ Xc) @ ((((image @ A) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ Aa) @ (top_top @ (set @ A)))) => ((((member @ C) @ Xe) @ ((((stream1259315544_sp_mu @ A) @ B) @ C) @ Xc)) => (((member @ C) @ Xe) @ ((((stream1259315544_sp_mu @ A) @ B) @ C) @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ Aa)))))))).
% 2.70/1.48 thf(fact_100_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,X3:(((stream901396144_sp_mu @ A) @ B) @ C),A2:(A > (((stream901396144_sp_mu @ A) @ B) @ C)),Xa2:B]: (((((member @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ X3) @ ((((image @ A) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ A2) @ (top_top @ (set @ A)))) => ((((member @ B) @ Xa2) @ ((((stream2074884121_sp_mu @ A) @ B) @ C) @ X3)) => (((member @ B) @ Xa2) @ ((((stream2074884121_sp_mu @ A) @ B) @ C) @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ A2)))))))).
% 2.70/1.48 thf(fact_101_map__prod__surj, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F:(A > B),G3:(C > D)]: (((((((image @ A) @ B) @ F) @ (top_top @ (set @ A))) = (top_top @ (set @ B))) => ((((((image @ C) @ D) @ G3) @ (top_top @ (set @ C))) = (top_top @ (set @ D))) => (((((image @ ((product_prod @ A) @ C)) @ ((product_prod @ B) @ D)) @ ((((((product_map_prod @ A) @ B) @ C) @ D) @ F) @ G3)) @ (top_top @ (set @ ((product_prod @ A) @ C)))) = (top_top @ (set @ ((product_prod @ B) @ D))))))))).
% 2.70/1.48 thf(fact_102_top1I, axiom, (! [A:$tType,X3:A]: (((top_top @ (A > $o)) @ X3)))).
% 2.70/1.48 thf(fact_103_map__prod__simp, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,F:(C > A),G3:(D > B),A2:C,B2:D]: (((((((((product_map_prod @ C) @ A) @ D) @ B) @ F) @ G3) @ ((((product_Pair @ C) @ D) @ A2) @ B2)) = ((((product_Pair @ A) @ B) @ (F @ A2)) @ (G3 @ B2)))))).
% 2.70/1.48 thf(fact_104_map__prod__imageI, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,A2:A,B2:B,R2:(set @ ((product_prod @ A) @ B)),F:(A > C),G3:(B > D)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ R2) => (((member @ ((product_prod @ C) @ D)) @ ((((product_Pair @ C) @ D) @ (F @ A2)) @ (G3 @ B2))) @ ((((image @ ((product_prod @ A) @ B)) @ ((product_prod @ C) @ D)) @ ((((((product_map_prod @ A) @ C) @ B) @ D) @ F) @ G3)) @ R2)))))).
% 2.70/1.48 thf(fact_105_sp_092_060_094sub_062_092_060mu_062_Orel__refl__strong, axiom, (! [C:$tType,A:$tType,B:$tType,X3:(((stream901396144_sp_mu @ B) @ A) @ C),R1a:(A > (A > $o)),R2a:(C > (C > $o))]: (((! [Z1:A]: (((((member @ A) @ Z1) @ ((((stream2074884121_sp_mu @ B) @ A) @ C) @ X3)) => ((R1a @ Z1) @ Z1)))) => ((! [Z22:C]: (((((member @ C) @ Z22) @ ((((stream1259315544_sp_mu @ B) @ A) @ C) @ X3)) => ((R2a @ Z22) @ Z22)))) => (((((((((stream1924447089_sp_mu @ A) @ A) @ C) @ C) @ B) @ R1a) @ R2a) @ X3) @ X3)))))).
% 2.70/1.48 thf(fact_106_sp_092_060_094sub_062_092_060mu_062_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,G:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),X3:(((stream901396144_sp_mu @ G) @ A) @ B),Y:(((stream901396144_sp_mu @ G) @ C) @ D),R1a:(A > (C > $o)),R2a:(B > (D > $o))]: (((((((((((stream1924447089_sp_mu @ A) @ C) @ B) @ D) @ G) @ R1) @ R22) @ X3) @ Y) => ((! [Z1:A,Y12:C]: (((((member @ A) @ Z1) @ ((((stream2074884121_sp_mu @ G) @ A) @ B) @ X3)) => ((((member @ C) @ Y12) @ ((((stream2074884121_sp_mu @ G) @ C) @ D) @ Y)) => (((R1 @ Z1) @ Y12) => ((R1a @ Z1) @ Y12)))))) => ((! [Z22:B,Y23:D]: (((((member @ B) @ Z22) @ ((((stream1259315544_sp_mu @ G) @ A) @ B) @ X3)) => ((((member @ D) @ Y23) @ ((((stream1259315544_sp_mu @ G) @ C) @ D) @ Y)) => (((R22 @ Z22) @ Y23) => ((R2a @ Z22) @ Y23)))))) => (((((((((stream1924447089_sp_mu @ A) @ C) @ B) @ D) @ G) @ R1a) @ R2a) @ X3) @ Y))))))).
% 2.70/1.48 thf(fact_107_sp_092_060_094sub_062_092_060mu_062_Orel__cong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,G:$tType,X3:(((stream901396144_sp_mu @ G) @ A) @ B),Ya:(((stream901396144_sp_mu @ G) @ A) @ B),Y:(((stream901396144_sp_mu @ G) @ C) @ D),Xa2:(((stream901396144_sp_mu @ G) @ C) @ D),R1:(A > (C > $o)),R1a:(A > (C > $o)),R22:(B > (D > $o)),R2a:(B > (D > $o))]: (((X3 = Ya) => ((Y = Xa2) => ((! [Z1:A,Y12:C]: (((((member @ A) @ Z1) @ ((((stream2074884121_sp_mu @ G) @ A) @ B) @ Ya)) => ((((member @ C) @ Y12) @ ((((stream2074884121_sp_mu @ G) @ C) @ D) @ Xa2)) => (((R1 @ Z1) @ Y12) = ((R1a @ Z1) @ Y12)))))) => ((! [Z22:B,Y23:D]: (((((member @ B) @ Z22) @ ((((stream1259315544_sp_mu @ G) @ A) @ B) @ Ya)) => ((((member @ D) @ Y23) @ ((((stream1259315544_sp_mu @ G) @ C) @ D) @ Xa2)) => (((R22 @ Z22) @ Y23) = ((R2a @ Z22) @ Y23)))))) => ((((((((((stream1924447089_sp_mu @ A) @ C) @ B) @ D) @ G) @ R1) @ R22) @ X3) @ Y) = (((((((((stream1924447089_sp_mu @ A) @ C) @ B) @ D) @ G) @ R1a) @ R2a) @ Ya) @ Xa2))))))))).
% 2.70/1.48 thf(fact_108_sp_092_060_094sub_062_092_060mu_062_Opred__mono__strong, axiom, (! [B:$tType,A:$tType,G:$tType,P1:(A > $o),P22:(B > $o),X3:(((stream901396144_sp_mu @ G) @ A) @ B),P1a:(A > $o),P2a:(B > $o)]: ((((((((stream123009735_sp_mu @ A) @ B) @ G) @ P1) @ P22) @ X3) => ((! [Z1:A]: (((((member @ A) @ Z1) @ ((((stream2074884121_sp_mu @ G) @ A) @ B) @ X3)) => ((P1 @ Z1) => (P1a @ Z1))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ ((((stream1259315544_sp_mu @ G) @ A) @ B) @ X3)) => ((P22 @ Z22) => (P2a @ Z22))))) => ((((((stream123009735_sp_mu @ A) @ B) @ G) @ P1a) @ P2a) @ X3))))))).
% 2.70/1.48 thf(fact_109_sp_092_060_094sub_062_092_060mu_062_Opred__cong, axiom, (! [B:$tType,A:$tType,G:$tType,X3:(((stream901396144_sp_mu @ G) @ A) @ B),Ya:(((stream901396144_sp_mu @ G) @ A) @ B),P1:(A > $o),P1a:(A > $o),P22:(B > $o),P2a:(B > $o)]: (((X3 = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ ((((stream2074884121_sp_mu @ G) @ A) @ B) @ Ya)) => ((P1 @ Z1) = (P1a @ Z1))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ ((((stream1259315544_sp_mu @ G) @ A) @ B) @ Ya)) => ((P22 @ Z22) = (P2a @ Z22))))) => (((((((stream123009735_sp_mu @ A) @ B) @ G) @ P1) @ P22) @ X3) = ((((((stream123009735_sp_mu @ A) @ B) @ G) @ P1a) @ P2a) @ Ya)))))))).
% 2.70/1.48 thf(fact_110_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I2_J, axiom, (! [B:$tType,A:$tType,C:$tType,A1:B,A22:C]: ((((member @ B) @ A1) @ ((((stream2074884121_sp_mu @ A) @ B) @ C) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ A1) @ A22)))))).
% 2.70/1.48 thf(fact_111_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I4_J, axiom, (! [B:$tType,A:$tType,C:$tType,A2a:C,A1a:B]: ((((member @ C) @ A2a) @ ((((stream1259315544_sp_mu @ A) @ B) @ C) @ (((((stream1370332830mu_Put @ B) @ C) @ A) @ A1a) @ A2a)))))).
% 2.70/1.48 thf(fact_112_prod__fun__imageE, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,C3:((product_prod @ A) @ B),F:(C > A),G3:(D > B),R2:(set @ ((product_prod @ C) @ D))]: (((((member @ ((product_prod @ A) @ B)) @ C3) @ ((((image @ ((product_prod @ C) @ D)) @ ((product_prod @ A) @ B)) @ ((((((product_map_prod @ C) @ A) @ D) @ B) @ F) @ G3)) @ R2)) => (~ ((! [X:C,Y3:D]: (((C3 = ((((product_Pair @ A) @ B) @ (F @ X)) @ (G3 @ Y3))) => (~ ((((member @ ((product_prod @ C) @ D)) @ ((((product_Pair @ C) @ D) @ X) @ Y3)) @ R2)))))))))))).
% 2.70/1.48 thf(fact_113_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (top_top @ (set @ A))))))))).
% 2.70/1.48 thf(fact_114_top__conj_I2_J, axiom, (! [A:$tType,P2:$o,X3:A]: (((P2 & ((top_top @ (A > $o)) @ X3)) = P2)))).
% 2.70/1.48 thf(fact_115_top__conj_I1_J, axiom, (! [A:$tType,X3:A,P2:$o]: (((((top_top @ (A > $o)) @ X3) & P2) = P2)))).
% 2.70/1.48 thf(fact_116_sp_092_060_094sub_062_092_060mu_062_Osimps_I15_J, axiom, (! [B:$tType,C:$tType,A:$tType,X1:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: ((((((stream2074884121_sp_mu @ A) @ B) @ C) @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ X1)) = ((complete_Sup_Sup @ (set @ B)) @ ((((image @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ (set @ B)) @ (((stream2074884121_sp_mu @ A) @ B) @ C)) @ ((((image @ A) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ X1) @ (top_top @ (set @ A))))))))).
% 2.70/1.48 thf(fact_117_sp_092_060_094sub_062_092_060mu_062_Osimps_I17_J, axiom, (! [B:$tType,C:$tType,A:$tType,X1:(A > (((stream901396144_sp_mu @ A) @ B) @ C))]: ((((((stream1259315544_sp_mu @ A) @ B) @ C) @ ((((stream1294929701mu_Get @ A) @ B) @ C) @ X1)) = ((complete_Sup_Sup @ (set @ C)) @ ((((image @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ (set @ C)) @ (((stream1259315544_sp_mu @ A) @ B) @ C)) @ ((((image @ A) @ (((stream901396144_sp_mu @ A) @ B) @ C)) @ X1) @ (top_top @ (set @ A))))))))).
% 2.70/1.48 thf(fact_118_UN__ball__bex__simps_I3_J, axiom, (! [D:$tType,A6:(set @ (set @ D)),P2:(D > $o)]: (((? [X4:D]: (((((member @ D) @ X4) @ ((complete_Sup_Sup @ (set @ D)) @ A6)) & (P2 @ X4)))) = (? [X4:(set @ D)]: (((((member @ (set @ D)) @ X4) @ A6) & (? [Y5:D]: (((((member @ D) @ Y5) @ X4) & (P2 @ Y5))))))))))).
% 2.70/1.48 thf(fact_119_UN__ball__bex__simps_I1_J, axiom, (! [A:$tType,A6:(set @ (set @ A)),P2:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ ((complete_Sup_Sup @ (set @ A)) @ A6)) => (P2 @ X4)))) = (! [X4:(set @ A)]: (((((member @ (set @ A)) @ X4) @ A6) => (! [Y5:A]: (((((member @ A) @ Y5) @ X4) => (P2 @ Y5))))))))))).
% 2.70/1.48 thf(fact_120_UnionI, axiom, (! [A:$tType,X7:(set @ A),C4:(set @ (set @ A)),A6:A]: (((((member @ (set @ A)) @ X7) @ C4) => ((((member @ A) @ A6) @ X7) => (((member @ A) @ A6) @ ((complete_Sup_Sup @ (set @ A)) @ C4))))))).
% 2.70/1.48 thf(fact_121_Union__iff, axiom, (! [A:$tType,A6:A,C4:(set @ (set @ A))]: (((((member @ A) @ A6) @ ((complete_Sup_Sup @ (set @ A)) @ C4)) = (? [X4:(set @ A)]: (((((member @ (set @ A)) @ X4) @ C4) & (((member @ A) @ A6) @ X4)))))))).
% 2.70/1.48 thf(fact_122_ball__UN, axiom, (! [A:$tType,B:$tType,B6:(B > (set @ A)),A6:(set @ B),P2:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B6) @ A6))) => (P2 @ X4)))) = (! [X4:B]: (((((member @ B) @ X4) @ A6) => (! [Y5:A]: (((((member @ A) @ Y5) @ (B6 @ X4)) => (P2 @ Y5))))))))))).
% 2.70/1.48 thf(fact_123_bex__UN, axiom, (! [A:$tType,B:$tType,B6:(B > (set @ A)),A6:(set @ B),P2:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B6) @ A6))) & (P2 @ X4)))) = (? [X4:B]: (((((member @ B) @ X4) @ A6) & (? [Y5:A]: (((((member @ A) @ Y5) @ (B6 @ X4)) & (P2 @ Y5))))))))))).
% 2.70/1.48 thf(fact_124_UN__ball__bex__simps_I2_J, axiom, (! [C:$tType,B:$tType,B6:(B > (set @ C)),A6:(set @ B),P2:(C > $o)]: (((! [X4:C]: (((((member @ C) @ X4) @ ((complete_Sup_Sup @ (set @ C)) @ ((((image @ B) @ (set @ C)) @ B6) @ A6))) => (P2 @ X4)))) = (! [X4:B]: (((((member @ B) @ X4) @ A6) => (! [Y5:C]: (((((member @ C) @ Y5) @ (B6 @ X4)) => (P2 @ Y5))))))))))).
% 2.70/1.48 thf(fact_125_UN__ball__bex__simps_I4_J, axiom, (! [F2:$tType,E:$tType,B6:(E > (set @ F2)),A6:(set @ E),P2:(F2 > $o)]: (((? [X4:F2]: (((((member @ F2) @ X4) @ ((complete_Sup_Sup @ (set @ F2)) @ ((((image @ E) @ (set @ F2)) @ B6) @ A6))) & (P2 @ X4)))) = (? [X4:E]: (((((member @ E) @ X4) @ A6) & (? [Y5:F2]: (((((member @ F2) @ Y5) @ (B6 @ X4)) & (P2 @ Y5))))))))))).
% 2.70/1.48 thf(fact_126_Sup__UNIV, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (((complete_Sup_Sup @ A) @ (top_top @ (set @ A))) = (top_top @ A)))))).
% 2.70/1.48 thf(fact_127_Union__UNIV, axiom, (! [A:$tType]: ((((complete_Sup_Sup @ (set @ A)) @ (top_top @ (set @ (set @ A)))) = (top_top @ (set @ A)))))).
% 2.70/1.48 thf(fact_128_UnionE, axiom, (! [A:$tType,A6:A,C4:(set @ (set @ A))]: (((((member @ A) @ A6) @ ((complete_Sup_Sup @ (set @ A)) @ C4)) => (~ ((! [X8:(set @ A)]: (((((member @ A) @ A6) @ X8) => (~ ((((member @ (set @ A)) @ X8) @ C4)))))))))))).
% 2.70/1.48 thf(fact_129_SUP__cong, axiom, (! [A:$tType,B:$tType]: ((((complete_Sup @ A) @ (type2 @ A)) => (! [A6:(set @ B),B6:(set @ B),C4:(B > A),D3:(B > A)]: (((A6 = B6) => ((! [X:B]: (((((member @ B) @ X) @ B6) => ((C4 @ X) = (D3 @ X))))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ C4) @ A6)) = ((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ D3) @ B6))))))))))).
% 2.70/1.48 thf(fact_130_same__fstI, axiom, (! [B:$tType,A:$tType,P2:(A > $o),X3:A,Y7:B,Y:B,R2:(A > (set @ ((product_prod @ B) @ B)))]: (((P2 @ X3) => ((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ Y7) @ Y)) @ (R2 @ X3)) => (((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y7)) @ ((((product_Pair @ A) @ B) @ X3) @ Y))) @ ((((same_fst @ A) @ B) @ P2) @ R2))))))).
% 2.70/1.48 thf(fact_131_wf__same__fst, axiom, (! [B:$tType,A:$tType,P2:(A > $o),R2:(A > (set @ ((product_prod @ B) @ B)))]: (((! [X:A]: (((P2 @ X) => ((wf @ B) @ (R2 @ X))))) => ((wf @ ((product_prod @ A) @ B)) @ ((((same_fst @ A) @ B) @ P2) @ R2)))))).
% 2.70/1.48 thf(fact_132_wf__map__prod__image, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ A)),F:(A > B)]: ((((wf @ A) @ R) => (((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((wf @ B) @ ((((image @ ((product_prod @ A) @ A)) @ ((product_prod @ B) @ B)) @ ((((((product_map_prod @ A) @ B) @ A) @ B) @ F) @ F)) @ R))))))).
% 2.70/1.48 thf(fact_133_member__bind, axiom, (! [A:$tType,B:$tType,X3:A,P2:(set @ B),F:(B > (set @ A))]: (((((member @ A) @ X3) @ ((((bind @ B) @ A) @ P2) @ F)) = (((member @ A) @ X3) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ F) @ P2))))))).
% 2.70/1.48 thf(fact_134_inj__apfst, axiom, (! [B:$tType,C:$tType,A:$tType,F:(A > C)]: ((((((inj_on @ ((product_prod @ A) @ B)) @ ((product_prod @ C) @ B)) @ ((((product_apfst @ A) @ C) @ B) @ F)) @ (top_top @ (set @ ((product_prod @ A) @ B)))) = ((((inj_on @ A) @ C) @ F) @ (top_top @ (set @ A))))))).
% 2.70/1.48 thf(fact_135_inj__apsnd, axiom, (! [A:$tType,C:$tType,B:$tType,F:(B > C)]: ((((((inj_on @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ C)) @ ((((product_apsnd @ B) @ C) @ A) @ F)) @ (top_top @ (set @ ((product_prod @ A) @ B)))) = ((((inj_on @ B) @ C) @ F) @ (top_top @ (set @ B))))))).
% 2.70/1.48 thf(fact_136_inj__on__image__iff, axiom, (! [B:$tType,A:$tType,A6:(set @ A),G3:(A > B),F:(A > A)]: (((! [X:A]: (((((member @ A) @ X) @ A6) => (! [Xa3:A]: (((((member @ A) @ Xa3) @ A6) => (((G3 @ (F @ X)) = (G3 @ (F @ Xa3))) = ((G3 @ X) = (G3 @ Xa3))))))))) => (((((inj_on @ A) @ A) @ F) @ A6) => (((((inj_on @ A) @ B) @ G3) @ ((((image @ A) @ A) @ F) @ A6)) = ((((inj_on @ A) @ B) @ G3) @ A6))))))).
% 2.70/1.48 thf(fact_137_inj__on__image, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ (set @ A))]: ((((((inj_on @ A) @ B) @ F) @ ((complete_Sup_Sup @ (set @ A)) @ A6)) => ((((inj_on @ (set @ A)) @ (set @ B)) @ (((image @ A) @ B) @ F)) @ A6))))).
% 2.70/1.48 thf(fact_138_inj__swap, axiom, (! [B:$tType,A:$tType,A6:(set @ ((product_prod @ A) @ B))]: (((((inj_on @ ((product_prod @ A) @ B)) @ ((product_prod @ B) @ A)) @ ((product_swap @ A) @ B)) @ A6)))).
% 2.70/1.48 thf(fact_139_inj__eq, axiom, (! [B:$tType,A:$tType,F:(A > B),X3:A,Y:A]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => (((F @ X3) = (F @ Y)) = (X3 = Y)))))).
% 2.70/1.48 thf(fact_140_injI, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((! [X:A,Y3:A]: ((((F @ X) = (F @ Y3)) => (X = Y3)))) => ((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))))))).
% 2.70/1.48 thf(fact_141_injD, axiom, (! [B:$tType,A:$tType,F:(A > B),X3:A,Y:A]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => (((F @ X3) = (F @ Y)) => (X3 = Y)))))).
% 2.70/1.48 thf(fact_142_range__ex1__eq, axiom, (! [B:$tType,A:$tType,F:(A > B),B2:B]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ (top_top @ (set @ A)))) = (? [X4:A]: (((B2 = (F @ X4)) & (! [Y5:A]: (((B2 = (F @ Y5)) => (Y5 = X4)))))))))))).
% 2.70/1.48 thf(fact_143_inj__image__eq__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A),B6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((((image @ A) @ B) @ F) @ A6) = ((((image @ A) @ B) @ F) @ B6)) = (A6 = B6)))))).
% 2.70/1.48 thf(fact_144_inj__image__mem__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:A,A6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((member @ B) @ (F @ A2)) @ ((((image @ A) @ B) @ F) @ A6)) = (((member @ A) @ A2) @ A6)))))).
% 2.70/1.48 thf(fact_145_bind__UNION, axiom, (! [A:$tType,B:$tType]: ((((bind @ B) @ A) = (^ [A7:(set @ B),F4:(B > (set @ A))]: (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ F4) @ A7)))))))).
% 2.70/1.48 thf(fact_146_prod_Oinj__map, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,F1:(A > C),F22:(B > D)]: ((((((inj_on @ A) @ C) @ F1) @ (top_top @ (set @ A))) => (((((inj_on @ B) @ D) @ F22) @ (top_top @ (set @ B))) => ((((inj_on @ ((product_prod @ A) @ B)) @ ((product_prod @ C) @ D)) @ ((((((product_map_prod @ A) @ C) @ B) @ D) @ F1) @ F22)) @ (top_top @ (set @ ((product_prod @ A) @ B))))))))).
% 2.70/1.48 thf(fact_147_the__inv__into__onto, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A6) => (((((image @ B) @ A) @ ((((the_inv_into @ A) @ B) @ A6) @ F)) @ ((((image @ A) @ B) @ F) @ A6)) = A6))))).
% 2.70/1.48 thf(fact_148_range__fst, axiom, (! [B:$tType,A:$tType]: ((((((image @ ((product_prod @ A) @ B)) @ A) @ ((product_fst @ A) @ B)) @ (top_top @ (set @ ((product_prod @ A) @ B)))) = (top_top @ (set @ A)))))).
% 2.70/1.48 thf(fact_149_range__snd, axiom, (! [B:$tType,A:$tType]: ((((((image @ ((product_prod @ B) @ A)) @ A) @ ((product_snd @ B) @ A)) @ (top_top @ (set @ ((product_prod @ B) @ A)))) = (top_top @ (set @ A)))))).
% 2.70/1.48 thf(fact_150_fst__map__prod, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,F:(C > A),G3:(D > B),X3:((product_prod @ C) @ D)]: (((((product_fst @ A) @ B) @ (((((((product_map_prod @ C) @ A) @ D) @ B) @ F) @ G3) @ X3)) = (F @ (((product_fst @ C) @ D) @ X3)))))).
% 2.70/1.48 thf(fact_151_snd__map__prod, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,F:(C > B),G3:(D > A),X3:((product_prod @ C) @ D)]: (((((product_snd @ B) @ A) @ (((((((product_map_prod @ C) @ B) @ D) @ A) @ F) @ G3) @ X3)) = (G3 @ (((product_snd @ C) @ D) @ X3)))))).
% 2.70/1.48 thf(fact_152_fst__apfst, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > A),X3:((product_prod @ C) @ B)]: (((((product_fst @ A) @ B) @ (((((product_apfst @ C) @ A) @ B) @ F) @ X3)) = (F @ (((product_fst @ C) @ B) @ X3)))))).
% 2.70/1.48 thf(fact_153_apfst__eq__conv, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > A),X3:((product_prod @ C) @ B),G3:(C > A)]: ((((((((product_apfst @ C) @ A) @ B) @ F) @ X3) = (((((product_apfst @ C) @ A) @ B) @ G3) @ X3)) = ((F @ (((product_fst @ C) @ B) @ X3)) = (G3 @ (((product_fst @ C) @ B) @ X3))))))).
% 2.70/1.48 thf(fact_154_snd__apfst, axiom, (! [B:$tType,A:$tType,C:$tType,F:(C > B),X3:((product_prod @ C) @ A)]: (((((product_snd @ B) @ A) @ (((((product_apfst @ C) @ B) @ A) @ F) @ X3)) = (((product_snd @ C) @ A) @ X3))))).
% 2.70/1.48 thf(fact_155_fst__apsnd, axiom, (! [B:$tType,C:$tType,A:$tType,F:(C > B),X3:((product_prod @ A) @ C)]: (((((product_fst @ A) @ B) @ (((((product_apsnd @ C) @ B) @ A) @ F) @ X3)) = (((product_fst @ A) @ C) @ X3))))).
% 2.70/1.48 thf(fact_156_snd__apsnd, axiom, (! [A:$tType,C:$tType,B:$tType,F:(C > A),X3:((product_prod @ B) @ C)]: (((((product_snd @ B) @ A) @ (((((product_apsnd @ C) @ A) @ B) @ F) @ X3)) = (F @ (((product_snd @ B) @ C) @ X3)))))).
% 2.70/1.48 thf(fact_157_apsnd__eq__conv, axiom, (! [B:$tType,C:$tType,A:$tType,F:(C > B),X3:((product_prod @ A) @ C),G3:(C > B)]: ((((((((product_apsnd @ C) @ B) @ A) @ F) @ X3) = (((((product_apsnd @ C) @ B) @ A) @ G3) @ X3)) = ((F @ (((product_snd @ A) @ C) @ X3)) = (G3 @ (((product_snd @ A) @ C) @ X3))))))).
% 2.70/1.48 thf(fact_158_prod_Ocollapse, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)) = Prod)))).
% 2.70/1.48 thf(fact_159_snd__swap, axiom, (! [B:$tType,A:$tType,X3:((product_prod @ A) @ B)]: (((((product_snd @ B) @ A) @ (((product_swap @ A) @ B) @ X3)) = (((product_fst @ A) @ B) @ X3))))).
% 2.70/1.48 thf(fact_160_fst__swap, axiom, (! [A:$tType,B:$tType,X3:((product_prod @ B) @ A)]: (((((product_fst @ A) @ B) @ (((product_swap @ B) @ A) @ X3)) = (((product_snd @ B) @ A) @ X3))))).
% 2.70/1.48 thf(fact_161_apfst__apsnd, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,F:(C > A),G3:(D > B),X3:((product_prod @ C) @ D)]: (((((((product_apfst @ C) @ A) @ B) @ F) @ (((((product_apsnd @ D) @ B) @ C) @ G3) @ X3)) = ((((product_Pair @ A) @ B) @ (F @ (((product_fst @ C) @ D) @ X3))) @ (G3 @ (((product_snd @ C) @ D) @ X3))))))).
% 2.70/1.48 thf(fact_162_apsnd__apfst, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,F:(C > B),G3:(D > A),X3:((product_prod @ D) @ C)]: (((((((product_apsnd @ C) @ B) @ A) @ F) @ (((((product_apfst @ D) @ A) @ C) @ G3) @ X3)) = ((((product_Pair @ A) @ B) @ (G3 @ (((product_fst @ D) @ C) @ X3))) @ (F @ (((product_snd @ D) @ C) @ X3))))))).
% 2.70/1.48 thf(fact_163_surjective__pairing, axiom, (! [B:$tType,A:$tType,T2:((product_prod @ A) @ B)]: ((T2 = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ T2)) @ (((product_snd @ A) @ B) @ T2)))))).
% 2.70/1.48 thf(fact_164_prod_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))).
% 2.70/1.48 thf(fact_165_prod_Osplit__sel__asm, axiom, (! [C:$tType,B:$tType,A:$tType,P2:(C > $o),F:(A > (B > C)),Prod:((product_prod @ A) @ B)]: (((P2 @ (((((product_case_prod @ A) @ B) @ C) @ F) @ Prod)) = (~ (((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod))) & (~ ((P2 @ ((F @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))))))))).
% 2.70/1.48 thf(fact_166_prod_Osplit__sel, axiom, (! [C:$tType,B:$tType,A:$tType,P2:(C > $o),F:(A > (B > C)),Prod:((product_prod @ A) @ B)]: (((P2 @ (((((product_case_prod @ A) @ B) @ C) @ F) @ Prod)) = ((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod))) => (P2 @ ((F @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))))).
% 2.70/1.48 thf(fact_167_prod__eqI, axiom, (! [B:$tType,A:$tType,P:((product_prod @ A) @ B),Q4:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ P) = (((product_fst @ A) @ B) @ Q4)) => (((((product_snd @ A) @ B) @ P) = (((product_snd @ A) @ B) @ Q4)) => (P = Q4)))))).
% 2.70/1.48 thf(fact_168_prod_Oexpand, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B),Prod2:((product_prod @ A) @ B)]: (((((((product_fst @ A) @ B) @ Prod) = (((product_fst @ A) @ B) @ Prod2)) & ((((product_snd @ A) @ B) @ Prod) = (((product_snd @ A) @ B) @ Prod2))) => (Prod = Prod2))))).
% 2.70/1.48 thf(fact_169_prod__eq__iff, axiom, (! [B:$tType,A:$tType]: (((^ [Y4:((product_prod @ A) @ B),Z:((product_prod @ A) @ B)]: ((Y4 = Z))) = (^ [S3:((product_prod @ A) @ B),T3:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ S3) = (((product_fst @ A) @ B) @ T3)) & ((((product_snd @ A) @ B) @ S3) = (((product_snd @ A) @ B) @ T3))))))))).
% 2.70/1.48 thf(fact_170_case__prod__beta, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((product_case_prod @ B) @ C) @ A) = (^ [F4:(B > (C > A)),P6:((product_prod @ B) @ C)]: (((F4 @ (((product_fst @ B) @ C) @ P6)) @ (((product_snd @ B) @ C) @ P6)))))))).
% 2.70/1.48 thf(fact_171_prod_Ocase__eq__if, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((product_case_prod @ A) @ B) @ C) = (^ [F4:(A > (B > C)),Prod3:((product_prod @ A) @ B)]: (((F4 @ (((product_fst @ A) @ B) @ Prod3)) @ (((product_snd @ A) @ B) @ Prod3)))))))).
% 2.70/1.48 thf(fact_172_Product__Type_OCollect__case__prodD, axiom, (! [B:$tType,A:$tType,X3:((product_prod @ A) @ B),A6:(A > (B > $o))]: (((((member @ ((product_prod @ A) @ B)) @ X3) @ ((collect @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ A6))) => ((A6 @ (((product_fst @ A) @ B) @ X3)) @ (((product_snd @ A) @ B) @ X3)))))).
% 2.70/1.48 thf(fact_173_fst__conv, axiom, (! [B:$tType,A:$tType,X1:A,X2:B]: (((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X1) @ X2)) = X1)))).
% 2.70/1.48 thf(fact_174_fst__eqD, axiom, (! [B:$tType,A:$tType,X3:A,Y:B,A2:A]: ((((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) = A2) => (X3 = A2))))).
% 2.70/1.48 thf(fact_175_snd__conv, axiom, (! [Aa2:$tType,A:$tType,X1:Aa2,X2:A]: (((((product_snd @ Aa2) @ A) @ ((((product_Pair @ Aa2) @ A) @ X1) @ X2)) = X2)))).
% 2.70/1.48 thf(fact_176_snd__eqD, axiom, (! [B:$tType,A:$tType,X3:B,Y:A,A2:A]: ((((((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X3) @ Y)) = A2) => (Y = A2))))).
% 2.70/1.48 thf(fact_177_prod_Oswap__def, axiom, (! [B:$tType,A:$tType]: ((((product_swap @ A) @ B) = (^ [P6:((product_prod @ A) @ B)]: (((((product_Pair @ B) @ A) @ (((product_snd @ A) @ B) @ P6)) @ (((product_fst @ A) @ B) @ P6)))))))).
% 2.70/1.48 thf(fact_178_inj__on__the__inv__into, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A6) => ((((inj_on @ B) @ A) @ ((((the_inv_into @ A) @ B) @ A6) @ F)) @ ((((image @ A) @ B) @ F) @ A6)))))).
% 2.70/1.48 thf(fact_179_f__the__inv__into__f, axiom, (! [A:$tType,B:$tType,F:(A > B),A6:(set @ A),Y:B]: ((((((inj_on @ A) @ B) @ F) @ A6) => ((((member @ B) @ Y) @ ((((image @ A) @ B) @ F) @ A6)) => ((F @ (((((the_inv_into @ A) @ B) @ A6) @ F) @ Y)) = Y)))))).
% 2.70/1.48 thf(fact_180_the__inv__f__f, axiom, (! [B:$tType,A:$tType,F:(A > B),X3:A]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((((the_inv_into @ A) @ B) @ (top_top @ (set @ A))) @ F) @ (F @ X3)) = X3))))).
% 2.70/1.48 thf(fact_181_BNF__Greatest__Fixpoint_Osubst__Pair, axiom, (! [B:$tType,A:$tType,P2:(A > (B > $o)),X3:A,Y:B,A2:((product_prod @ A) @ B)]: ((((P2 @ X3) @ Y) => ((A2 = ((((product_Pair @ A) @ B) @ X3) @ Y)) => ((P2 @ (((product_fst @ A) @ B) @ A2)) @ (((product_snd @ A) @ B) @ A2))))))).
% 2.70/1.48 thf(fact_182_conjI__realizer, axiom, (! [A:$tType,B:$tType,P2:(A > $o),P:A,Q:(B > $o),Q4:B]: (((P2 @ P) => ((Q @ Q4) => ((P2 @ (((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ P) @ Q4))) & (Q @ (((product_snd @ A) @ B) @ ((((product_Pair @ A) @ B) @ P) @ Q4))))))))).
% 2.70/1.48 thf(fact_183_exI__realizer, axiom, (! [B:$tType,A:$tType,P2:(A > (B > $o)),Y:A,X3:B]: ((((P2 @ Y) @ X3) => ((P2 @ (((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X3) @ Y))) @ (((product_fst @ B) @ A) @ ((((product_Pair @ B) @ A) @ X3) @ Y))))))).
% 2.70/1.48 thf(fact_184_eq__snd__iff, axiom, (! [A:$tType,B:$tType,B2:A,P:((product_prod @ B) @ A)]: (((B2 = (((product_snd @ B) @ A) @ P)) = (? [A5:B]: ((P = ((((product_Pair @ B) @ A) @ A5) @ B2)))))))).
% 2.70/1.48 thf(fact_185_sndI, axiom, (! [A:$tType,B:$tType,X3:((product_prod @ A) @ B),Y:A,Z2:B]: (((X3 = ((((product_Pair @ A) @ B) @ Y) @ Z2)) => ((((product_snd @ A) @ B) @ X3) = Z2))))).
% 2.70/1.48 thf(fact_186_eq__fst__iff, axiom, (! [A:$tType,B:$tType,A2:A,P:((product_prod @ A) @ B)]: (((A2 = (((product_fst @ A) @ B) @ P)) = (? [B5:B]: ((P = ((((product_Pair @ A) @ B) @ A2) @ B5)))))))).
% 2.70/1.48 thf(fact_187_fstI, axiom, (! [B:$tType,A:$tType,X3:((product_prod @ A) @ B),Y:A,Z2:B]: (((X3 = ((((product_Pair @ A) @ B) @ Y) @ Z2)) => ((((product_fst @ A) @ B) @ X3) = Y))))).
% 2.70/1.48 thf(fact_188_Collect__split__mono__strong, axiom, (! [B:$tType,A:$tType,X7:(set @ A),A6:(set @ ((product_prod @ A) @ B)),Y8:(set @ B),P2:(A > (B > $o)),Q:(A > (B > $o))]: (((X7 = ((((image @ ((product_prod @ A) @ B)) @ A) @ ((product_fst @ A) @ B)) @ A6)) => ((Y8 = ((((image @ ((product_prod @ A) @ B)) @ B) @ ((product_snd @ A) @ B)) @ A6)) => ((! [X:A]: (((((member @ A) @ X) @ X7) => (! [Xa3:B]: (((((member @ B) @ Xa3) @ Y8) => (((P2 @ X) @ Xa3) => ((Q @ X) @ Xa3)))))))) => ((((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ A6) @ ((collect @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ P2))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ A6) @ ((collect @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ Q)))))))))).
% 2.70/1.48 thf(fact_189_sndOp__def, axiom, (! [B:$tType,A:$tType,C:$tType]: (((((bNF_sndOp @ C) @ A) @ B) = (^ [P3:(C > (A > $o)),Q3:(A > (B > $o)),Ac:((product_prod @ C) @ B)]: (((((product_Pair @ A) @ B) @ (((((((bNF_pick_middlep @ C) @ A) @ B) @ P3) @ Q3) @ (((product_fst @ C) @ B) @ Ac)) @ (((product_snd @ C) @ B) @ Ac))) @ (((product_snd @ C) @ B) @ Ac)))))))).
% 2.70/1.48 thf(fact_190_fstOp__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((bNF_fstOp @ A) @ B) @ C) = (^ [P3:(A > (B > $o)),Q3:(B > (C > $o)),Ac:((product_prod @ A) @ C)]: (((((product_Pair @ A) @ B) @ (((product_fst @ A) @ C) @ Ac)) @ (((((((bNF_pick_middlep @ A) @ B) @ C) @ P3) @ Q3) @ (((product_fst @ A) @ C) @ Ac)) @ (((product_snd @ A) @ C) @ Ac))))))))).
% 2.70/1.48 thf(fact_191_subset__antisym, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((ord_less_eq @ (set @ A)) @ B6) @ A6) => (A6 = B6)))))).
% 2.70/1.48 thf(fact_192_subsetI, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((! [X:A]: (((((member @ A) @ X) @ A6) => (((member @ A) @ X) @ B6)))) => (((ord_less_eq @ (set @ A)) @ A6) @ B6))))).
% 2.70/1.48 thf(fact_193_inj__on__image__mem__iff__alt, axiom, (! [B:$tType,A:$tType,F:(A > B),B6:(set @ A),A6:(set @ A),A2:A]: ((((((inj_on @ A) @ B) @ F) @ B6) => ((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((member @ B) @ (F @ A2)) @ ((((image @ A) @ B) @ F) @ A6)) => ((((member @ A) @ A2) @ B6) => (((member @ A) @ A2) @ A6)))))))).
% 2.70/1.48 thf(fact_194_inj__on__image__mem__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),B6:(set @ A),A2:A,A6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ B6) => ((((member @ A) @ A2) @ B6) => ((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((member @ B) @ (F @ A2)) @ ((((image @ A) @ B) @ F) @ A6)) = (((member @ A) @ A2) @ A6)))))))).
% 2.70/1.48 thf(fact_195_inj__on__image__eq__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),C4:(set @ A),A6:(set @ A),B6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ C4) => ((((ord_less_eq @ (set @ A)) @ A6) @ C4) => ((((ord_less_eq @ (set @ A)) @ B6) @ C4) => ((((((image @ A) @ B) @ F) @ A6) = ((((image @ A) @ B) @ F) @ B6)) = (A6 = B6)))))))).
% 2.70/1.48 thf(fact_196_image__mono, axiom, (! [B:$tType,A:$tType,A6:(set @ A),B6:(set @ A),F:(A > B)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => (((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A6)) @ ((((image @ A) @ B) @ F) @ B6)))))).
% 2.70/1.48 thf(fact_197_image__subsetI, axiom, (! [A:$tType,B:$tType,A6:(set @ A),F:(A > B),B6:(set @ B)]: (((! [X:A]: (((((member @ A) @ X) @ A6) => (((member @ B) @ (F @ X)) @ B6)))) => (((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A6)) @ B6))))).
% 2.70/1.48 thf(fact_198_subset__imageE, axiom, (! [A:$tType,B:$tType,B6:(set @ A),F:(B > A),A6:(set @ B)]: (((((ord_less_eq @ (set @ A)) @ B6) @ ((((image @ B) @ A) @ F) @ A6)) => (~ ((! [C5:(set @ B)]: (((((ord_less_eq @ (set @ B)) @ C5) @ A6) => (B6 != ((((image @ B) @ A) @ F) @ C5))))))))))).
% 2.70/1.48 thf(fact_199_image__subset__iff, axiom, (! [A:$tType,B:$tType,F:(B > A),A6:(set @ B),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((((image @ B) @ A) @ F) @ A6)) @ B6) = (! [X4:B]: (((((member @ B) @ X4) @ A6) => (((member @ A) @ (F @ X4)) @ B6)))))))).
% 2.70/1.48 thf(fact_200_subset__image__iff, axiom, (! [A:$tType,B:$tType,B6:(set @ A),F:(B > A),A6:(set @ B)]: (((((ord_less_eq @ (set @ A)) @ B6) @ ((((image @ B) @ A) @ F) @ A6)) = (? [AA:(set @ B)]: (((((ord_less_eq @ (set @ B)) @ AA) @ A6) & (B6 = ((((image @ B) @ A) @ F) @ AA))))))))).
% 2.70/1.48 thf(fact_201_subrelI, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((! [X:A,Y3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y3)) @ R) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y3)) @ S)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S))))).
% 2.70/1.48 thf(fact_202_wf__subset, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),P:(set @ ((product_prod @ A) @ A))]: ((((wf @ A) @ R) => ((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ P) @ R) => ((wf @ A) @ P)))))).
% 2.70/1.48 thf(fact_203_Collect__mono__iff, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)) = (! [X4:A]: (((P2 @ X4) => (Q @ X4)))))))).
% 2.70/1.48 thf(fact_204_contra__subsetD, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((~ ((((member @ A) @ C3) @ B6))) => (~ ((((member @ A) @ C3) @ A6)))))))).
% 2.70/1.48 thf(fact_205_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z:(set @ A)]: ((Y4 = Z))) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A7)))))))).
% 2.70/1.48 thf(fact_206_subset__trans, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((ord_less_eq @ (set @ A)) @ B6) @ C4) => (((ord_less_eq @ (set @ A)) @ A6) @ C4)))))).
% 2.70/1.48 thf(fact_207_Collect__mono, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P2 @ X) => (Q @ X)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)))))).
% 2.70/1.48 thf(fact_208_subset__refl, axiom, (! [A:$tType,A6:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A6) @ A6)))).
% 2.70/1.48 thf(fact_209_rev__subsetD, axiom, (! [A:$tType,C3:A,A6:(set @ A),B6:(set @ A)]: (((((member @ A) @ C3) @ A6) => ((((ord_less_eq @ (set @ A)) @ A6) @ B6) => (((member @ A) @ C3) @ B6)))))).
% 2.70/1.48 thf(fact_210_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A7) => (((member @ A) @ T3) @ B7)))))))))).
% 2.70/1.48 thf(fact_211_set__rev__mp, axiom, (! [A:$tType,X3:A,A6:(set @ A),B6:(set @ A)]: (((((member @ A) @ X3) @ A6) => ((((ord_less_eq @ (set @ A)) @ A6) @ B6) => (((member @ A) @ X3) @ B6)))))).
% 2.70/1.48 thf(fact_212_equalityD2, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((A6 = B6) => (((ord_less_eq @ (set @ A)) @ B6) @ A6))))).
% 2.70/1.48 thf(fact_213_equalityD1, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((A6 = B6) => (((ord_less_eq @ (set @ A)) @ A6) @ B6))))).
% 2.70/1.48 thf(fact_214_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ A7) => (((member @ A) @ X4) @ B7)))))))))).
% 2.70/1.48 thf(fact_215_equalityE, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((A6 = B6) => (~ (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => (~ ((((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))))).
% 2.70/1.48 thf(fact_216_subsetCE, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((member @ A) @ C3) @ A6) => (((member @ A) @ C3) @ B6)))))).
% 2.70/1.48 thf(fact_217_subsetD, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((member @ A) @ C3) @ A6) => (((member @ A) @ C3) @ B6)))))).
% 2.70/1.48 thf(fact_218_in__mono, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((member @ A) @ X3) @ A6) => (((member @ A) @ X3) @ B6)))))).
% 2.70/1.48 thf(fact_219_set__mp, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => ((((member @ A) @ X3) @ A6) => (((member @ A) @ X3) @ B6)))))).
% 2.70/1.48 thf(fact_220_subset__UNIV, axiom, (! [A:$tType,A6:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A6) @ (top_top @ (set @ A)))))).
% 2.70/1.48 thf(fact_221_top_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A2) => (A2 = (top_top @ A))))))))).
% 2.70/1.48 thf(fact_222_top_Oextremum__unique, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A2) = (A2 = (top_top @ A))))))))).
% 2.70/1.48 thf(fact_223_top__greatest, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ (top_top @ A)))))))).
% 2.70/1.48 thf(fact_224_Sup__subset__mono, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => (((ord_less_eq @ A) @ ((complete_Sup_Sup @ A) @ A6)) @ ((complete_Sup_Sup @ A) @ B6))))))))).
% 2.70/1.48 thf(fact_225_Sup__upper2, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [U:A,A6:(set @ A),V:A]: (((((member @ A) @ U) @ A6) => ((((ord_less_eq @ A) @ V) @ U) => (((ord_less_eq @ A) @ V) @ ((complete_Sup_Sup @ A) @ A6)))))))))).
% 2.70/1.48 thf(fact_226_Sup__le__iff, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A6:(set @ A),B2:A]: (((((ord_less_eq @ A) @ ((complete_Sup_Sup @ A) @ A6)) @ B2) = (! [X4:A]: (((((member @ A) @ X4) @ A6) => (((ord_less_eq @ A) @ X4) @ B2))))))))))).
% 2.70/1.48 thf(fact_227_Sup__upper, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [X3:A,A6:(set @ A)]: (((((member @ A) @ X3) @ A6) => (((ord_less_eq @ A) @ X3) @ ((complete_Sup_Sup @ A) @ A6))))))))).
% 2.70/1.48 thf(fact_228_Sup__least, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A6:(set @ A),Z2:A]: (((! [X:A]: (((((member @ A) @ X) @ A6) => (((ord_less_eq @ A) @ X) @ Z2)))) => (((ord_less_eq @ A) @ ((complete_Sup_Sup @ A) @ A6)) @ Z2)))))))).
% 2.70/1.48 thf(fact_229_Sup__mono, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A6:(set @ A),B6:(set @ A)]: (((! [A4:A]: (((((member @ A) @ A4) @ A6) => (? [X6:A]: (((((member @ A) @ X6) @ B6) & (((ord_less_eq @ A) @ A4) @ X6))))))) => (((ord_less_eq @ A) @ ((complete_Sup_Sup @ A) @ A6)) @ ((complete_Sup_Sup @ A) @ B6))))))))).
% 2.70/1.48 thf(fact_230_Sup__eqI, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A6:(set @ A),X3:A]: (((! [Y3:A]: (((((member @ A) @ Y3) @ A6) => (((ord_less_eq @ A) @ Y3) @ X3)))) => ((! [Y3:A]: (((! [Z4:A]: (((((member @ A) @ Z4) @ A6) => (((ord_less_eq @ A) @ Z4) @ Y3)))) => (((ord_less_eq @ A) @ X3) @ Y3)))) => (((complete_Sup_Sup @ A) @ A6) = X3))))))))).
% 2.70/1.48 thf(fact_231_Union__upper, axiom, (! [A:$tType,B6:(set @ A),A6:(set @ (set @ A))]: (((((member @ (set @ A)) @ B6) @ A6) => (((ord_less_eq @ (set @ A)) @ B6) @ ((complete_Sup_Sup @ (set @ A)) @ A6)))))).
% 2.70/1.49 thf(fact_232_Union__least, axiom, (! [A:$tType,A6:(set @ (set @ A)),C4:(set @ A)]: (((! [X8:(set @ A)]: (((((member @ (set @ A)) @ X8) @ A6) => (((ord_less_eq @ (set @ A)) @ X8) @ C4)))) => (((ord_less_eq @ (set @ A)) @ ((complete_Sup_Sup @ (set @ A)) @ A6)) @ C4))))).
% 2.70/1.49 thf(fact_233_Union__mono, axiom, (! [A:$tType,A6:(set @ (set @ A)),B6:(set @ (set @ A))]: (((((ord_less_eq @ (set @ (set @ A))) @ A6) @ B6) => (((ord_less_eq @ (set @ A)) @ ((complete_Sup_Sup @ (set @ A)) @ A6)) @ ((complete_Sup_Sup @ (set @ A)) @ B6)))))).
% 2.70/1.49 thf(fact_234_SUP__eq, axiom, (! [B:$tType,A:$tType,C:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A6:(set @ B),B6:(set @ C),F:(B > A),G3:(C > A)]: (((! [I:B]: (((((member @ B) @ I) @ A6) => (? [X6:C]: (((((member @ C) @ X6) @ B6) & (((ord_less_eq @ A) @ (F @ I)) @ (G3 @ X6)))))))) => ((! [J:C]: (((((member @ C) @ J) @ B6) => (? [X6:B]: (((((member @ B) @ X6) @ A6) & (((ord_less_eq @ A) @ (G3 @ J)) @ (F @ X6)))))))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ F) @ A6)) = ((complete_Sup_Sup @ A) @ ((((image @ C) @ A) @ G3) @ B6))))))))))).
% 2.70/1.49 thf(fact_235_inj__image__subset__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A),B6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A6)) @ ((((image @ A) @ B) @ F) @ B6)) = (((ord_less_eq @ (set @ A)) @ A6) @ B6)))))).
% 2.70/1.49 thf(fact_236_the__inv__into__into, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A),X3:B,B6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A6) => ((((member @ B) @ X3) @ ((((image @ A) @ B) @ F) @ A6)) => ((((ord_less_eq @ (set @ A)) @ A6) @ B6) => (((member @ A) @ (((((the_inv_into @ A) @ B) @ A6) @ F) @ X3)) @ B6))))))).
% 2.70/1.49 thf(fact_237_Zorn__Lemma, axiom, (! [A:$tType,A6:(set @ (set @ A))]: (((! [X:(set @ (set @ A))]: (((((member @ (set @ (set @ A))) @ X) @ ((chains2 @ A) @ A6)) => (((member @ (set @ A)) @ ((complete_Sup_Sup @ (set @ A)) @ X)) @ A6)))) => (? [X:(set @ A)]: (((((member @ (set @ A)) @ X) @ A6) & (! [Xa:(set @ A)]: (((((member @ (set @ A)) @ Xa) @ A6) => ((((ord_less_eq @ (set @ A)) @ X) @ Xa) => (Xa = X)))))))))))).
% 2.70/1.49 thf(fact_238_inj__image__Compl__subset, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => (((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ ((uminus_uminus @ (set @ A)) @ A6))) @ ((uminus_uminus @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A6))))))).
% 2.70/1.49 thf(fact_239_ComplI, axiom, (! [A:$tType,C3:A,A6:(set @ A)]: (((~ ((((member @ A) @ C3) @ A6))) => (((member @ A) @ C3) @ ((uminus_uminus @ (set @ A)) @ A6)))))).
% 2.70/1.49 thf(fact_240_Compl__iff, axiom, (! [A:$tType,C3:A,A6:(set @ A)]: (((((member @ A) @ C3) @ ((uminus_uminus @ (set @ A)) @ A6)) = (~ ((((member @ A) @ C3) @ A6))))))).
% 2.70/1.49 thf(fact_241_Compl__eq__Compl__iff, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A6) = ((uminus_uminus @ (set @ A)) @ B6)) = (A6 = B6))))).
% 2.70/1.49 thf(fact_242_Compl__subset__Compl__iff, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A6)) @ ((uminus_uminus @ (set @ A)) @ B6)) = (((ord_less_eq @ (set @ A)) @ B6) @ A6))))).
% 2.70/1.49 thf(fact_243_Compl__anti__mono, axiom, (! [A:$tType,A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) => (((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ B6)) @ ((uminus_uminus @ (set @ A)) @ A6)))))).
% 2.70/1.49 thf(fact_244_sp_092_060_094sub_062_092_060mu_062_Orel__mono, axiom, (! [A:$tType,C:$tType,G:$tType,D:$tType,B:$tType,R1:(A > (C > $o)),R1a:(A > (C > $o)),R22:(B > (D > $o)),R2a:(B > (D > $o))]: (((((ord_less_eq @ (A > (C > $o))) @ R1) @ R1a) => ((((ord_less_eq @ (B > (D > $o))) @ R22) @ R2a) => (((ord_less_eq @ ((((stream901396144_sp_mu @ G) @ A) @ B) > ((((stream901396144_sp_mu @ G) @ C) @ D) > $o))) @ (((((((stream1924447089_sp_mu @ A) @ C) @ B) @ D) @ G) @ R1) @ R22)) @ (((((((stream1924447089_sp_mu @ A) @ C) @ B) @ D) @ G) @ R1a) @ R2a))))))).
% 2.70/1.49 thf(fact_245_chainsD2, axiom, (! [A:$tType,C3:(set @ (set @ A)),S4:(set @ (set @ A))]: (((((member @ (set @ (set @ A))) @ C3) @ ((chains2 @ A) @ S4)) => (((ord_less_eq @ (set @ (set @ A))) @ C3) @ S4))))).
% 2.70/1.49 thf(fact_246_Collect__case__prod__mono, axiom, (! [B:$tType,A:$tType,A6:(A > (B > $o)),B6:(A > (B > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ A6) @ B6) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ ((collect @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ A6))) @ ((collect @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ B6))))))).
% 2.70/1.49 thf(fact_247_ComplD, axiom, (! [A:$tType,C3:A,A6:(set @ A)]: (((((member @ A) @ C3) @ ((uminus_uminus @ (set @ A)) @ A6)) => (~ ((((member @ A) @ C3) @ A6))))))).
% 2.70/1.49 thf(fact_248_double__complement, axiom, (! [A:$tType,A6:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A6)) = A6)))).
% 2.70/1.49 thf(fact_249_chainsD, axiom, (! [A:$tType,C3:(set @ (set @ A)),S4:(set @ (set @ A)),X3:(set @ A),Y:(set @ A)]: (((((member @ (set @ (set @ A))) @ C3) @ ((chains2 @ A) @ S4)) => ((((member @ (set @ A)) @ X3) @ C3) => ((((member @ (set @ A)) @ Y) @ C3) => ((((ord_less_eq @ (set @ A)) @ X3) @ Y) | (((ord_less_eq @ (set @ A)) @ Y) @ X3)))))))).
% 2.70/1.49 thf(fact_250_Zorn__Lemma2, axiom, (! [A:$tType,A6:(set @ (set @ A))]: (((! [X:(set @ (set @ A))]: (((((member @ (set @ (set @ A))) @ X) @ ((chains2 @ A) @ A6)) => (? [Xa:(set @ A)]: (((((member @ (set @ A)) @ Xa) @ A6) & (! [Xb:(set @ A)]: (((((member @ (set @ A)) @ Xb) @ X) => (((ord_less_eq @ (set @ A)) @ Xb) @ Xa)))))))))) => (? [X:(set @ A)]: (((((member @ (set @ A)) @ X) @ A6) & (! [Xa:(set @ A)]: (((((member @ (set @ A)) @ Xa) @ A6) => ((((ord_less_eq @ (set @ A)) @ X) @ Xa) => (Xa = X)))))))))))).
% 2.70/1.49 thf(fact_251_surj__Compl__image__subset, axiom, (! [A:$tType,B:$tType,F:(B > A),A6:(set @ B)]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ ((((image @ B) @ A) @ F) @ A6))) @ ((((image @ B) @ A) @ F) @ ((uminus_uminus @ (set @ B)) @ A6))))))).
% 2.70/1.49 thf(fact_252_mono__Chains, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),S:(set @ ((product_prod @ A) @ A))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R) @ S) => (((ord_less_eq @ (set @ (set @ A))) @ ((chains @ A) @ R)) @ ((chains @ A) @ S)))))).
% 2.70/1.49 thf(fact_253_relChain__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (((bNF_Ca1785829860lChain @ A) @ B) = (^ [R3:(set @ ((product_prod @ A) @ A)),As:(A > B)]: ((! [I2:A,J2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ I2) @ J2)) @ R3) => (((ord_less_eq @ B) @ (As @ I2)) @ (As @ J2)))))))))))).
% 2.70/1.49 thf(fact_254_chain__subset__def, axiom, (! [A:$tType]: (((chain_subset @ A) = (^ [C6:(set @ (set @ A))]: ((! [X4:(set @ A)]: (((((member @ (set @ A)) @ X4) @ C6) => (! [Y5:(set @ A)]: (((((member @ (set @ A)) @ Y5) @ C6) => ((((ord_less_eq @ (set @ A)) @ X4) @ Y5) | (((ord_less_eq @ (set @ A)) @ Y5) @ X4)))))))))))))).
% 2.70/1.49 thf(fact_255_vimage__subsetI, axiom, (! [B:$tType,A:$tType,F:(A > B),B6:(set @ B),A6:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((ord_less_eq @ (set @ B)) @ B6) @ ((((image @ A) @ B) @ F) @ A6)) => (((ord_less_eq @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ B6)) @ A6)))))).
% 2.70/1.49 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice, axiom, (! [A8:$tType,A9:$tType]: ((((comple187826305attice @ A9) @ (type2 @ A9)) => ((comple187826305attice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.70/1.49 thf(tcon_fun___Complete__Lattices_OSup, axiom, (! [A8:$tType,A9:$tType]: ((((complete_Sup @ A9) @ (type2 @ A9)) => ((complete_Sup @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.70/1.49 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A8:$tType,A9:$tType]: ((((order_top @ A9) @ (type2 @ A9)) => ((order_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.70/1.49 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.70/1.49 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.70/1.49 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1, axiom, (! [A8:$tType]: (((comple187826305attice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.70/1.49 thf(tcon_Set_Oset___Complete__Lattices_OSup_2, axiom, (! [A8:$tType]: (((complete_Sup @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.70/1.49 thf(tcon_Set_Oset___Orderings_Oorder__top_3, axiom, (! [A8:$tType]: (((order_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.70/1.49 thf(tcon_Set_Oset___Orderings_Otop_4, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.70/1.49 thf(tcon_Set_Oset___Orderings_Oord_5, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.70/1.49 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_6, axiom, ((comple187826305attice @ $o) @ (type2 @ $o))).
% 2.70/1.49 thf(tcon_HOL_Obool___Complete__Lattices_OSup_7, axiom, ((complete_Sup @ $o) @ (type2 @ $o))).
% 2.70/1.49 thf(tcon_HOL_Obool___Orderings_Oorder__top_8, axiom, ((order_top @ $o) @ (type2 @ $o))).
% 2.70/1.49 thf(tcon_HOL_Obool___Orderings_Otop_9, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.70/1.49 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.70/1.49 thf(conj_0, hypothesis, (! [B8:b,Sp2:c,Fsp:(((stream901396144_sp_mu @ d) @ a) @ ((stream1273403375_sp_nu @ d) @ a))]: (((x = ((((product_Pair @ (((stream901396144_sp_mu @ a) @ b) @ c)) @ (((stream901396144_sp_mu @ d) @ a) @ ((stream1273403375_sp_nu @ d) @ a))) @ (((((stream1370332830mu_Put @ b) @ c) @ a) @ B8) @ Sp2)) @ Fsp)) => p)))).
% 2.70/1.49 thf(conj_1, hypothesis, (! [F5:(a > (((stream901396144_sp_mu @ a) @ b) @ c)),B8:a,Sp2:((stream1273403375_sp_nu @ d) @ a)]: (((x = ((((product_Pair @ (((stream901396144_sp_mu @ a) @ b) @ c)) @ (((stream901396144_sp_mu @ d) @ a) @ ((stream1273403375_sp_nu @ d) @ a))) @ ((((stream1294929701mu_Get @ a) @ b) @ c) @ F5)) @ (((((stream1370332830mu_Put @ a) @ ((stream1273403375_sp_nu @ d) @ a)) @ d) @ B8) @ Sp2))) => p)))).
% 2.70/1.49 thf(conj_2, hypothesis, (! [F5:(a > (((stream901396144_sp_mu @ a) @ b) @ c)),G4:(d > (((stream901396144_sp_mu @ d) @ a) @ ((stream1273403375_sp_nu @ d) @ a)))]: (((x = ((((product_Pair @ (((stream901396144_sp_mu @ a) @ b) @ c)) @ (((stream901396144_sp_mu @ d) @ a) @ ((stream1273403375_sp_nu @ d) @ a))) @ ((((stream1294929701mu_Get @ a) @ b) @ c) @ F5)) @ ((((stream1294929701mu_Get @ d) @ a) @ ((stream1273403375_sp_nu @ d) @ a)) @ G4))) => p)))).
% 2.70/1.49 thf(conj_3, conjecture, p).
% 2.70/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2DTF27294.p
% 2.70/1.49 ------------------------
% 2.97/1.54 ---- Cleaned THF ---
% 2.97/1.54 thf(ty_t_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060nu_062,type,
% 2.97/1.54 stream1273403375_sp_nu: $tType > $tType > $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_t_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream901396144_sp_mu: $tType > $tType > $tType > $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_t_Product__Type_Oprod,type,
% 2.97/1.54 product_prod: $tType > $tType > $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_t_Stream_Ostream,type,
% 2.97/1.54 stream: $tType > $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_t_Set_Oset,type,
% 2.97/1.54 set: $tType > $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_t_Nat_Onat,type,
% 2.97/1.54 nat: $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_t_itself,type,
% 2.97/1.54 itself: $tType > $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_tf_d,type,
% 2.97/1.54 d: $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_tf_c,type,
% 2.97/1.54 c: $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_tf_b,type,
% 2.97/1.54 b: $tType ).
% 2.97/1.54
% 2.97/1.54 thf(ty_tf_a,type,
% 2.97/1.54 a: $tType ).
% 2.97/1.54
% 2.97/1.54 thf(sy_cl_HOL_Otype,type,
% 2.97/1.54 type:
% 2.97/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_cl_Orderings_Oord,type,
% 2.97/1.54 ord:
% 2.97/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_cl_Orderings_Otop,type,
% 2.97/1.54 top:
% 2.97/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_cl_Orderings_Oorder__top,type,
% 2.97/1.54 order_top:
% 2.97/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_cl_Complete__Lattices_OSup,type,
% 2.97/1.54 complete_Sup:
% 2.97/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 2.97/1.54 comple187826305attice:
% 2.97/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain,type,
% 2.97/1.54 bNF_Ca1785829860lChain:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( A > B ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_BNF__Def_OfstOp,type,
% 2.97/1.54 bNF_fstOp:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > ( product_prod @ A @ C ) > ( product_prod @ A @ B ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_BNF__Def_Opick__middlep,type,
% 2.97/1.54 bNF_pick_middlep:
% 2.97/1.54 !>[B: $tType,A: $tType,C: $tType] : ( ( B > A > $o ) > ( A > C > $o ) > B > C > A ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_BNF__Def_OsndOp,type,
% 2.97/1.54 bNF_sndOp:
% 2.97/1.54 !>[C: $tType,A: $tType,B: $tType] : ( ( C > A > $o ) > ( A > B > $o ) > ( product_prod @ C @ B ) > ( product_prod @ A @ B ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Complete__Lattices_OSup__class_OSup,type,
% 2.97/1.54 complete_Sup_Sup:
% 2.97/1.54 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Fun_Oinj__on,type,
% 2.97/1.54 inj_on:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Fun_Othe__inv__into,type,
% 2.97/1.54 the_inv_into:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > B > A ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.97/1.54 uminus_uminus:
% 2.97/1.54 !>[A: $tType] : ( A > A ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.97/1.54 ord_less_eq:
% 2.97/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.97/1.54 top_top:
% 2.97/1.54 !>[A: $tType] : A ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_OPair,type,
% 2.97/1.54 product_Pair:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oapfst,type,
% 2.97/1.54 product_apfst:
% 2.97/1.54 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( product_prod @ A @ B ) > ( product_prod @ C @ B ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oapsnd,type,
% 2.97/1.54 product_apsnd:
% 2.97/1.54 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( product_prod @ A @ B ) > ( product_prod @ A @ C ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Ocurry,type,
% 2.97/1.54 product_curry:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.97/1.54 produc2004651681e_prod:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Omap__prod,type,
% 2.97/1.54 product_map_prod:
% 2.97/1.54 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C ) > ( B > D ) > ( product_prod @ A @ B ) > ( product_prod @ C @ D ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 2.97/1.54 product_rec_bool:
% 2.97/1.54 !>[T: $tType] : ( T > T > $o > T ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.97/1.54 product_rec_prod:
% 2.97/1.54 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 2.97/1.54 product_case_prod:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 2.97/1.54 product_fst:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 2.97/1.54 product_snd:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 2.97/1.54 product_swap:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Pure_Otype,type,
% 2.97/1.54 type2:
% 2.97/1.54 !>[A: $tType] : ( itself @ A ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Set_OCollect,type,
% 2.97/1.54 collect:
% 2.97/1.54 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Set_Obind,type,
% 2.97/1.54 bind:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > ( set @ B ) ) > ( set @ B ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Set_Oimage,type,
% 2.97/1.54 image:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Set_Ovimage,type,
% 2.97/1.54 vimage:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Orun_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream5064451run_mu:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( stream901396144_sp_mu @ A @ B @ C ) > ( stream @ A ) > ( product_prod @ ( product_prod @ B @ C ) @ ( stream @ A ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_OGet,type,
% 2.97/1.54 stream1294929701mu_Get:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > ( stream901396144_sp_mu @ A @ B @ C ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_OPut,type,
% 2.97/1.54 stream1370332830mu_Put:
% 2.97/1.54 !>[B: $tType,C: $tType,A: $tType] : ( B > C > ( stream901396144_sp_mu @ A @ B @ C ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Ocase__sp_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream160000856_sp_mu:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > D ) > ( B > C > D ) > ( stream901396144_sp_mu @ A @ B @ C ) > D ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Opred__sp_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream123009735_sp_mu:
% 2.97/1.54 !>[A: $tType,B: $tType,E: $tType] : ( ( A > $o ) > ( B > $o ) > ( stream901396144_sp_mu @ E @ A @ B ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Orec__sp_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream674629690_sp_mu:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType,G: $tType] : ( ( ( A > ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ G ) ) > G ) > ( B > C > G ) > ( stream901396144_sp_mu @ A @ B @ C ) > G ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Orel__sp_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream1924447089_sp_mu:
% 2.97/1.54 !>[A: $tType,C: $tType,B: $tType,D: $tType,E: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( stream901396144_sp_mu @ E @ A @ B ) > ( stream901396144_sp_mu @ E @ C @ D ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Oset1__sp_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream2074884121_sp_mu:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( stream901396144_sp_mu @ A @ B @ C ) > ( set @ B ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osp_092_060_094sub_062_092_060mu_062_Oset2__sp_092_060_094sub_062_092_060mu_062,type,
% 2.97/1.54 stream1259315544_sp_mu:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( ( stream901396144_sp_mu @ A @ B @ C ) > ( set @ C ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Stream__Processor__Mirabelle__rrumbueyrq_Osub,type,
% 2.97/1.54 stream152839592le_sub:
% 2.97/1.54 !>[A: $tType,B: $tType,C: $tType] : ( set @ ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream901396144_sp_mu @ A @ B @ C ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Wellfounded_Olex__prod,type,
% 2.97/1.54 lex_prod:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Wellfounded_Omeasure,type,
% 2.97/1.54 measure:
% 2.97/1.54 !>[A: $tType] : ( ( A > nat ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Wellfounded_Owf,type,
% 2.97/1.54 wf:
% 2.97/1.54 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Wfrec_Osame__fst,type,
% 2.97/1.54 same_fst:
% 2.97/1.54 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Zorn_OChains,type,
% 2.97/1.54 chains:
% 2.97/1.54 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( set @ A ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Zorn_Ochain__subset,type,
% 2.97/1.54 chain_subset:
% 2.97/1.54 !>[A: $tType] : ( ( set @ ( set @ A ) ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_Zorn_Ochains,type,
% 2.97/1.54 chains2:
% 2.97/1.54 !>[A: $tType] : ( ( set @ ( set @ A ) ) > ( set @ ( set @ ( set @ A ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_c_member,type,
% 2.97/1.54 member:
% 2.97/1.54 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.97/1.54
% 2.97/1.54 thf(sy_v_P,type,
% 2.97/1.54 p: $o ).
% 2.97/1.54
% 2.97/1.54 thf(sy_v_x,type,
% 2.97/1.54 x: product_prod @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_0_sp_092_060_094sub_062_092_060mu_062_Oinject_I1_J,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C ),Y1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( ( ( stream1294929701mu_Get @ A @ B @ C @ X1 )
% 2.97/1.54 = ( stream1294929701mu_Get @ A @ B @ C @ Y1 ) )
% 2.97/1.54 = ( X1 = Y1 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_1_sp_092_060_094sub_062_092_060mu_062_Oinject_I2_J,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,X21: B,X22: C,Y21: B,Y22: C] :
% 2.97/1.54 ( ( ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 )
% 2.97/1.54 = ( stream1370332830mu_Put @ B @ C @ A @ Y21 @ Y22 ) )
% 2.97/1.54 = ( ( X21 = Y21 )
% 2.97/1.54 & ( X22 = Y22 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_2_sp_092_060_094sub_062_092_060mu_062_Odistinct_I1_J,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C ),X21: B,X22: C] :
% 2.97/1.54 ( ( stream1294929701mu_Get @ A @ B @ C @ X1 )
% 2.97/1.54 != ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_3_sp_092_060_094sub_062_092_060mu_062_Oexhaust,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,Y: stream901396144_sp_mu @ A @ B @ C] :
% 2.97/1.54 ( ! [X12: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( stream1294929701mu_Get @ A @ B @ C @ X12 ) )
% 2.97/1.54 => ~ ! [X212: B,X222: C] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( stream1370332830mu_Put @ B @ C @ A @ X212 @ X222 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_4_subI,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,F: A > ( stream901396144_sp_mu @ A @ B @ C ),A2: A] : ( member @ ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream901396144_sp_mu @ A @ B @ C ) ) @ ( product_Pair @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( F @ A2 ) @ ( stream1294929701mu_Get @ A @ B @ C @ F ) ) @ ( stream152839592le_sub @ A @ B @ C ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_5_prod_Oinject,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 2.97/1.54 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 2.97/1.54 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.97/1.54 = ( ( X1 = Y1 )
% 2.97/1.54 & ( X2 = Y2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_6_old_Oprod_Oinject,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.97/1.54 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.97/1.54 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.97/1.54 = ( ( A2 = A3 )
% 2.97/1.54 & ( B2 = B3 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_7_run_092_060_094sub_062_092_060mu_062_Osimps_I2_J,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,B2: B,Sp: C,S: stream @ A] :
% 2.97/1.54 ( ( stream5064451run_mu @ A @ B @ C @ ( stream1370332830mu_Put @ B @ C @ A @ B2 @ Sp ) @ S )
% 2.97/1.54 = ( product_Pair @ ( product_prod @ B @ C ) @ ( stream @ A ) @ ( product_Pair @ B @ C @ B2 @ Sp ) @ S ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_8_surj__pair,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 2.97/1.54 ? [X: A,Y3: B] :
% 2.97/1.54 ( P
% 2.97/1.54 = ( product_Pair @ A @ B @ X @ Y3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_9_prod__cases,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 2.97/1.54 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.97/1.54 => ( P2 @ P ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_10_Pair__inject,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.97/1.54 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.97/1.54 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.97/1.54 => ~ ( ( A2 = A3 )
% 2.97/1.54 => ( B2 != B3 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_11_prod__cases3,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.97/1.54 ~ ! [A4: A,B4: B,C2: C] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_12_prod__cases4,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.97/1.54 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_13_prod__cases5,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.97/1.54 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_14_prod__cases6,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 2.97/1.54 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_15_prod__cases7,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 2.97/1.54 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2,G2: G] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_16_old_Oprod_Oinducts,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.97/1.54 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.97/1.54 => ( P2 @ Prod ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_17_old_Oprod_Oexhaust,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.97/1.54 ~ ! [A4: A,B4: B] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_18_prod__induct7,axiom,
% 2.97/1.54 ! [G: $tType,F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 2.97/1.54 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) )
% 2.97/1.54 => ( P2 @ X3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_19_prod__induct6,axiom,
% 2.97/1.54 ! [F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 2.97/1.54 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F3: F2] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 2.97/1.54 => ( P2 @ X3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_20_prod__induct5,axiom,
% 2.97/1.54 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.97/1.54 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.97/1.54 => ( P2 @ X3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_21_prod__induct4,axiom,
% 2.97/1.54 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.97/1.54 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 2.97/1.54 => ( P2 @ X3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_22_prod__induct3,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.97/1.54 ( ! [A4: A,B4: B,C2: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 2.97/1.54 => ( P2 @ X3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_23_old_Oprod_Orec,axiom,
% 2.97/1.54 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.97/1.54 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.97/1.54 = ( F1 @ A2 @ B2 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_24_internal__case__prod__conv,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 2.97/1.54 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.97/1.54 = ( C3 @ A2 @ B2 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_25_ssubst__Pair__rhs,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,R: A,S: B,R2: set @ ( product_prod @ A @ B ),S2: B] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S ) @ R2 )
% 2.97/1.54 => ( ( S2 = S )
% 2.97/1.54 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_26_curry__conv,axiom,
% 2.97/1.54 ! [A: $tType,C: $tType,B: $tType] :
% 2.97/1.54 ( ( product_curry @ B @ C @ A )
% 2.97/1.54 = ( ^ [F4: ( product_prod @ B @ C ) > A,A5: B,B5: C] : ( F4 @ ( product_Pair @ B @ C @ A5 @ B5 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_27_sp_092_060_094sub_062_092_060mu_062_Osimps_I6_J,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,D: $tType,C: $tType,F1: ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > D,F22: B > C > D,X21: B,X22: C] :
% 2.97/1.54 ( ( stream160000856_sp_mu @ A @ B @ C @ D @ F1 @ F22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) )
% 2.97/1.54 = ( F22 @ X21 @ X22 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_28_sp_092_060_094sub_062_092_060mu_062_Osimps_I5_J,axiom,
% 2.97/1.54 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: ( A > ( stream901396144_sp_mu @ A @ B @ C ) ) > D,F22: B > C > D,X1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( ( stream160000856_sp_mu @ A @ B @ C @ D @ F1 @ F22 @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) )
% 2.97/1.54 = ( F1 @ X1 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_29_curryI,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.97/1.54 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.97/1.54 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_30_sp_092_060_094sub_062_092_060mu_062_Osimps_I8_J,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,G: $tType,C: $tType,F1: ( A > ( product_prod @ ( stream901396144_sp_mu @ A @ B @ C ) @ G ) ) > G,F22: B > C > G,X21: B,X22: C] :
% 2.97/1.54 ( ( stream674629690_sp_mu @ A @ B @ C @ G @ F1 @ F22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) )
% 2.97/1.54 = ( F22 @ X21 @ X22 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_31_sp_092_060_094sub_062_092_060mu_062_Opred__inject_I2_J,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,P1: B > $o,P22: C > $o,A2: B,Aa: C] :
% 2.97/1.54 ( ( stream123009735_sp_mu @ B @ C @ A @ P1 @ P22 @ ( stream1370332830mu_Put @ B @ C @ A @ A2 @ Aa ) )
% 2.97/1.54 = ( ( P1 @ A2 )
% 2.97/1.54 & ( P22 @ Aa ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_32_swap__simp,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,X3: B,Y: A] :
% 2.97/1.54 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) )
% 2.97/1.54 = ( product_Pair @ A @ B @ Y @ X3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_33_swap__swap,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,P: product_prod @ A @ B] :
% 2.97/1.54 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P ) )
% 2.97/1.54 = P ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_34_curryD,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.97/1.54 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 2.97/1.54 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_35_curryE,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.97/1.54 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 2.97/1.54 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_36_pair__in__swap__image,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,Y: A,X3: B,A6: set @ ( product_prod @ B @ A )] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y @ X3 ) @ ( image @ ( product_prod @ B @ A ) @ ( product_prod @ A @ B ) @ ( product_swap @ B @ A ) @ A6 ) )
% 2.97/1.54 = ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ X3 @ Y ) @ A6 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_37_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I2_J,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,D: $tType,C: $tType,G: $tType,R1: A > C > $o,R22: B > D > $o,Y21: A,Y22: B,X1: G > ( stream901396144_sp_mu @ G @ C @ D )] :
% 2.97/1.54 ~ ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 @ ( stream1370332830mu_Put @ A @ B @ G @ Y21 @ Y22 ) @ ( stream1294929701mu_Get @ G @ C @ D @ X1 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_38_sp_092_060_094sub_062_092_060mu_062_Orel__distinct_I1_J,axiom,
% 2.97/1.54 ! [B: $tType,C: $tType,E: $tType,A: $tType,F2: $tType,R1: B > E > $o,R22: C > F2 > $o,X1: A > ( stream901396144_sp_mu @ A @ B @ C ),Y21: E,Y22: F2] :
% 2.97/1.54 ~ ( stream1924447089_sp_mu @ B @ E @ C @ F2 @ A @ R1 @ R22 @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) @ ( stream1370332830mu_Put @ E @ F2 @ A @ Y21 @ Y22 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_39_internal__case__prod__def,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType] :
% 2.97/1.54 ( ( produc2004651681e_prod @ A @ B @ C )
% 2.97/1.54 = ( product_case_prod @ A @ B @ C ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_40_wf__sub,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType] : ( wf @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( stream152839592le_sub @ A @ B @ C ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_41_apsnd__conv,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,F: C > B,X3: A,Y: C] :
% 2.97/1.54 ( ( product_apsnd @ C @ B @ A @ F @ ( product_Pair @ A @ C @ X3 @ Y ) )
% 2.97/1.54 = ( product_Pair @ A @ B @ X3 @ ( F @ Y ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_42_old_Obool_Osimps_I5_J,axiom,
% 2.97/1.54 ! [T: $tType,F1: T,F22: T] :
% 2.97/1.54 ( ( product_rec_bool @ T @ F1 @ F22 @ $true )
% 2.97/1.54 = F1 ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_43_old_Obool_Osimps_I6_J,axiom,
% 2.97/1.54 ! [T: $tType,F1: T,F22: T] :
% 2.97/1.54 ( ( product_rec_bool @ T @ F1 @ F22 @ $false )
% 2.97/1.54 = F22 ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_44_apfst__conv,axiom,
% 2.97/1.54 ! [C: $tType,A: $tType,B: $tType,F: C > A,X3: C,Y: B] :
% 2.97/1.54 ( ( product_apfst @ C @ A @ B @ F @ ( product_Pair @ C @ B @ X3 @ Y ) )
% 2.97/1.54 = ( product_Pair @ A @ B @ ( F @ X3 ) @ Y ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_45_mem__Collect__eq,axiom,
% 2.97/1.54 ! [A: $tType,A2: A,P2: A > $o] :
% 2.97/1.54 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 2.97/1.54 = ( P2 @ A2 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_46_Collect__mem__eq,axiom,
% 2.97/1.54 ! [A: $tType,A6: set @ A] :
% 2.97/1.54 ( ( collect @ A
% 2.97/1.54 @ ^ [X4: A] : ( member @ A @ X4 @ A6 ) )
% 2.97/1.54 = A6 ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_47_Collect__cong,axiom,
% 2.97/1.54 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.97/1.54 ( ! [X: A] :
% 2.97/1.54 ( ( P2 @ X )
% 2.97/1.54 = ( Q @ X ) )
% 2.97/1.54 => ( ( collect @ A @ P2 )
% 2.97/1.54 = ( collect @ A @ Q ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_48_ext,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,F: A > B,G3: A > B] :
% 2.97/1.54 ( ! [X: A] :
% 2.97/1.54 ( ( F @ X )
% 2.97/1.54 = ( G3 @ X ) )
% 2.97/1.54 => ( F = G3 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_49_curry__case__prod,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,F: A > B > C] :
% 2.97/1.54 ( ( product_curry @ A @ B @ C @ ( product_case_prod @ A @ B @ C @ F ) )
% 2.97/1.54 = F ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_50_case__prod__curry,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,F: ( product_prod @ A @ B ) > C] :
% 2.97/1.54 ( ( product_case_prod @ A @ B @ C @ ( product_curry @ A @ B @ C @ F ) )
% 2.97/1.54 = F ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_51_sp_092_060_094sub_062_092_060mu_062_Orel__eq,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,G: $tType] :
% 2.97/1.54 ( ( stream1924447089_sp_mu @ A @ A @ B @ B @ G
% 2.97/1.54 @ ^ [Y4: A,Z: A] : ( Y4 = Z )
% 2.97/1.54 @ ^ [Y4: B,Z: B] : ( Y4 = Z ) )
% 2.97/1.54 = ( ^ [Y4: stream901396144_sp_mu @ G @ A @ B,Z: stream901396144_sp_mu @ G @ A @ B] : ( Y4 = Z ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_52_sp_092_060_094sub_062_092_060mu_062_Orel__refl,axiom,
% 2.97/1.54 ! [D: $tType,C: $tType,G: $tType,R1a: C > C > $o,R2a: D > D > $o,X3: stream901396144_sp_mu @ G @ C @ D] :
% 2.97/1.54 ( ! [X: C] : ( R1a @ X @ X )
% 2.97/1.54 => ( ! [X: D] : ( R2a @ X @ X )
% 2.97/1.54 => ( stream1924447089_sp_mu @ C @ C @ D @ D @ G @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_53_apsnd__apfst__commute,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,C: $tType,D: $tType,F: C > B,G3: D > A,P: product_prod @ D @ C] :
% 2.97/1.54 ( ( product_apsnd @ C @ B @ A @ F @ ( product_apfst @ D @ A @ C @ G3 @ P ) )
% 2.97/1.54 = ( product_apfst @ D @ A @ B @ G3 @ ( product_apsnd @ C @ B @ D @ F @ P ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_54_mem__case__prodE,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,Z2: A,C3: B > C > ( set @ A ),P: product_prod @ B @ C] :
% 2.97/1.54 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C3 @ P ) )
% 2.97/1.54 => ~ ! [X: B,Y3: C] :
% 2.97/1.54 ( ( P
% 2.97/1.54 = ( product_Pair @ B @ C @ X @ Y3 ) )
% 2.97/1.54 => ~ ( member @ A @ Z2 @ ( C3 @ X @ Y3 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_55_old_Oprod_Ocase,axiom,
% 2.97/1.54 ! [A: $tType,C: $tType,B: $tType,F: A > B > C,X1: A,X2: B] :
% 2.97/1.54 ( ( product_case_prod @ A @ B @ C @ F @ ( product_Pair @ A @ B @ X1 @ X2 ) )
% 2.97/1.54 = ( F @ X1 @ X2 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_56_sp_092_060_094sub_062_092_060mu_062_Orel__intros_I2_J,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,E: $tType,A: $tType,F2: $tType,R1: B > E > $o,X21: B,Y21: E,R22: C > F2 > $o,X22: C,Y22: F2] :
% 2.97/1.54 ( ( R1 @ X21 @ Y21 )
% 2.97/1.54 => ( ( R22 @ X22 @ Y22 )
% 2.97/1.54 => ( stream1924447089_sp_mu @ B @ E @ C @ F2 @ A @ R1 @ R22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) @ ( stream1370332830mu_Put @ E @ F2 @ A @ Y21 @ Y22 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_57_sp_092_060_094sub_062_092_060mu_062_Orel__inject_I2_J,axiom,
% 2.97/1.54 ! [A: $tType,E: $tType,B: $tType,C: $tType,F2: $tType,R1: B > E > $o,R22: C > F2 > $o,X21: B,X22: C,Y21: E,Y22: F2] :
% 2.97/1.54 ( ( stream1924447089_sp_mu @ B @ E @ C @ F2 @ A @ R1 @ R22 @ ( stream1370332830mu_Put @ B @ C @ A @ X21 @ X22 ) @ ( stream1370332830mu_Put @ E @ F2 @ A @ Y21 @ Y22 ) )
% 2.97/1.54 = ( ( R1 @ X21 @ Y21 )
% 2.97/1.54 & ( R22 @ X22 @ Y22 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_58_image__eqI,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,B2: A,F: B > A,X3: B,A6: set @ B] :
% 2.97/1.54 ( ( B2
% 2.97/1.54 = ( F @ X3 ) )
% 2.97/1.54 => ( ( member @ B @ X3 @ A6 )
% 2.97/1.54 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A6 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_59_wf__def,axiom,
% 2.97/1.54 ! [A: $tType] :
% 2.97/1.54 ( ( wf @ A )
% 2.97/1.54 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 2.97/1.54 ! [P3: A > $o] :
% 2.97/1.54 ( ! [X4: A] :
% 2.97/1.54 ( ! [Y5: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X4 ) @ R3 )
% 2.97/1.54 => ( P3 @ Y5 ) )
% 2.97/1.54 => ( P3 @ X4 ) )
% 2.97/1.54 => ( ^ [P4: A > $o] :
% 2.97/1.54 ! [X5: A] : ( P4 @ X5 )
% 2.97/1.54 @ P3 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_60_wfE__min,axiom,
% 2.97/1.54 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),X3: A,Q: set @ A] :
% 2.97/1.54 ( ( wf @ A @ R2 )
% 2.97/1.54 => ( ( member @ A @ X3 @ Q )
% 2.97/1.54 => ~ ! [Z3: A] :
% 2.97/1.54 ( ( member @ A @ Z3 @ Q )
% 2.97/1.54 => ~ ! [Y6: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ Z3 ) @ R2 )
% 2.97/1.54 => ~ ( member @ A @ Y6 @ Q ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_61_wfI__min,axiom,
% 2.97/1.54 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 2.97/1.54 ( ! [X: A,Q2: set @ A] :
% 2.97/1.54 ( ( member @ A @ X @ Q2 )
% 2.97/1.54 => ? [Xa: A] :
% 2.97/1.54 ( ( member @ A @ Xa @ Q2 )
% 2.97/1.54 & ! [Y3: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ Xa ) @ R2 )
% 2.97/1.54 => ~ ( member @ A @ Y3 @ Q2 ) ) ) )
% 2.97/1.54 => ( wf @ A @ R2 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_62_wfUNIVI,axiom,
% 2.97/1.54 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 2.97/1.54 ( ! [P5: A > $o,X: A] :
% 2.97/1.54 ( ! [Xa: A] :
% 2.97/1.54 ( ! [Y3: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ Xa ) @ R )
% 2.97/1.54 => ( P5 @ Y3 ) )
% 2.97/1.54 => ( P5 @ Xa ) )
% 2.97/1.54 => ( P5 @ X ) )
% 2.97/1.54 => ( wf @ A @ R ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_63_wf__asym,axiom,
% 2.97/1.54 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A,X3: A] :
% 2.97/1.54 ( ( wf @ A @ R )
% 2.97/1.54 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ X3 ) @ R )
% 2.97/1.54 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ A2 ) @ R ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_64_wf__induct,axiom,
% 2.97/1.54 ! [A: $tType,R: set @ ( product_prod @ A @ A ),P2: A > $o,A2: A] :
% 2.97/1.54 ( ( wf @ A @ R )
% 2.97/1.54 => ( ! [X: A] :
% 2.97/1.54 ( ! [Y6: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X ) @ R )
% 2.97/1.54 => ( P2 @ Y6 ) )
% 2.97/1.54 => ( P2 @ X ) )
% 2.97/1.54 => ( P2 @ A2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_65_wf__irrefl,axiom,
% 2.97/1.54 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A] :
% 2.97/1.54 ( ( wf @ A @ R )
% 2.97/1.54 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ R ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_66_rev__image__eqI,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,X3: A,A6: set @ A,B2: B,F: A > B] :
% 2.97/1.54 ( ( member @ A @ X3 @ A6 )
% 2.97/1.54 => ( ( B2
% 2.97/1.54 = ( F @ X3 ) )
% 2.97/1.54 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A6 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_67_ball__imageD,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: B > A,A6: set @ B,P2: A > $o] :
% 2.97/1.54 ( ! [X: A] :
% 2.97/1.54 ( ( member @ A @ X @ ( image @ B @ A @ F @ A6 ) )
% 2.97/1.54 => ( P2 @ X ) )
% 2.97/1.54 => ! [X6: B] :
% 2.97/1.54 ( ( member @ B @ X6 @ A6 )
% 2.97/1.54 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_68_image__cong,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,M: set @ A,N: set @ A,F: A > B,G3: A > B] :
% 2.97/1.54 ( ( M = N )
% 2.97/1.54 => ( ! [X: A] :
% 2.97/1.54 ( ( member @ A @ X @ N )
% 2.97/1.54 => ( ( F @ X )
% 2.97/1.54 = ( G3 @ X ) ) )
% 2.97/1.54 => ( ( image @ A @ B @ F @ M )
% 2.97/1.54 = ( image @ A @ B @ G3 @ N ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_69_bex__imageD,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: B > A,A6: set @ B,P2: A > $o] :
% 2.97/1.54 ( ? [X6: A] :
% 2.97/1.54 ( ( member @ A @ X6 @ ( image @ B @ A @ F @ A6 ) )
% 2.97/1.54 & ( P2 @ X6 ) )
% 2.97/1.54 => ? [X: B] :
% 2.97/1.54 ( ( member @ B @ X @ A6 )
% 2.97/1.54 & ( P2 @ ( F @ X ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_70_image__iff,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,Z2: A,F: B > A,A6: set @ B] :
% 2.97/1.54 ( ( member @ A @ Z2 @ ( image @ B @ A @ F @ A6 ) )
% 2.97/1.54 = ( ? [X4: B] :
% 2.97/1.54 ( ( member @ B @ X4 @ A6 )
% 2.97/1.54 & ( Z2
% 2.97/1.54 = ( F @ X4 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_71_imageI,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,X3: A,A6: set @ A,F: A > B] :
% 2.97/1.54 ( ( member @ A @ X3 @ A6 )
% 2.97/1.54 => ( member @ B @ ( F @ X3 ) @ ( image @ A @ B @ F @ A6 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_72_wf__induct__rule,axiom,
% 2.97/1.54 ! [A: $tType,R: set @ ( product_prod @ A @ A ),P2: A > $o,A2: A] :
% 2.97/1.54 ( ( wf @ A @ R )
% 2.97/1.54 => ( ! [X: A] :
% 2.97/1.54 ( ! [Y6: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X ) @ R )
% 2.97/1.54 => ( P2 @ Y6 ) )
% 2.97/1.54 => ( P2 @ X ) )
% 2.97/1.54 => ( P2 @ A2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_73_wf__eq__minimal,axiom,
% 2.97/1.54 ! [A: $tType] :
% 2.97/1.54 ( ( wf @ A )
% 2.97/1.54 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 2.97/1.54 ! [Q3: set @ A] :
% 2.97/1.54 ( ? [X4: A] : ( member @ A @ X4 @ Q3 )
% 2.97/1.54 => ? [X4: A] :
% 2.97/1.54 ( ( member @ A @ X4 @ Q3 )
% 2.97/1.54 & ! [Y5: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X4 ) @ R3 )
% 2.97/1.54 => ~ ( member @ A @ Y5 @ Q3 ) ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_74_wf__not__refl,axiom,
% 2.97/1.54 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A] :
% 2.97/1.54 ( ( wf @ A @ R )
% 2.97/1.54 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ R ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_75_wf__not__sym,axiom,
% 2.97/1.54 ! [A: $tType,R: set @ ( product_prod @ A @ A ),A2: A,X3: A] :
% 2.97/1.54 ( ( wf @ A @ R )
% 2.97/1.54 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ X3 ) @ R )
% 2.97/1.54 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ A2 ) @ R ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_76_wf__measure,axiom,
% 2.97/1.54 ! [A: $tType,F: A > nat] : ( wf @ A @ ( measure @ A @ F ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_77_dependent__wf__choice,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ A ),P2: ( A > B ) > A > B > $o] :
% 2.97/1.54 ( ( wf @ A @ R2 )
% 2.97/1.54 => ( ! [F3: A > B,G2: A > B,X: A,R4: B] :
% 2.97/1.54 ( ! [Z4: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z4 @ X ) @ R2 )
% 2.97/1.54 => ( ( F3 @ Z4 )
% 2.97/1.54 = ( G2 @ Z4 ) ) )
% 2.97/1.54 => ( ( P2 @ F3 @ X @ R4 )
% 2.97/1.54 = ( P2 @ G2 @ X @ R4 ) ) )
% 2.97/1.54 => ( ! [X: A,F3: A > B] :
% 2.97/1.54 ( ! [Y6: A] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X ) @ R2 )
% 2.97/1.54 => ( P2 @ F3 @ Y6 @ ( F3 @ Y6 ) ) )
% 2.97/1.54 => ? [X13: B] : ( P2 @ F3 @ X @ X13 ) )
% 2.97/1.54 => ? [F3: A > B] :
% 2.97/1.54 ! [X6: A] : ( P2 @ F3 @ X6 @ ( F3 @ X6 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_78_split__cong,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,Q4: product_prod @ A @ B,F: A > B > C,G3: A > B > C,P: product_prod @ A @ B] :
% 2.97/1.54 ( ! [X: A,Y3: B] :
% 2.97/1.54 ( ( ( product_Pair @ A @ B @ X @ Y3 )
% 2.97/1.54 = Q4 )
% 2.97/1.54 => ( ( F @ X @ Y3 )
% 2.97/1.54 = ( G3 @ X @ Y3 ) ) )
% 2.97/1.54 => ( ( P = Q4 )
% 2.97/1.54 => ( ( product_case_prod @ A @ B @ C @ F @ P )
% 2.97/1.54 = ( product_case_prod @ A @ B @ C @ G3 @ Q4 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_79_wf__lex__prod,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,Ra: set @ ( product_prod @ A @ A ),Rb: set @ ( product_prod @ B @ B )] :
% 2.97/1.54 ( ( wf @ A @ Ra )
% 2.97/1.54 => ( ( wf @ B @ Rb )
% 2.97/1.54 => ( wf @ ( product_prod @ A @ B ) @ ( lex_prod @ A @ B @ Ra @ Rb ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_80_in__lex__prod,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B,R: set @ ( product_prod @ A @ A ),S: set @ ( product_prod @ B @ B )] :
% 2.97/1.54 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ ( lex_prod @ A @ B @ R @ S ) )
% 2.97/1.54 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A3 ) @ R )
% 2.97/1.54 | ( ( A2 = A3 )
% 2.97/1.54 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B3 ) @ S ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_81_surj__swap,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType] :
% 2.97/1.54 ( ( image @ ( product_prod @ B @ A ) @ ( product_prod @ A @ B ) @ ( product_swap @ B @ A ) @ ( top_top @ ( set @ ( product_prod @ B @ A ) ) ) )
% 2.97/1.54 = ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_82_Sup_OSUP__cong,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,A6: set @ B,B6: set @ B,C4: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 2.97/1.54 ( ( A6 = B6 )
% 2.97/1.54 => ( ! [X: B] :
% 2.97/1.54 ( ( member @ B @ X @ B6 )
% 2.97/1.54 => ( ( C4 @ X )
% 2.97/1.54 = ( D3 @ X ) ) )
% 2.97/1.54 => ( ( Sup @ ( image @ B @ A @ C4 @ A6 ) )
% 2.97/1.54 = ( Sup @ ( image @ B @ A @ D3 @ B6 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_83_UNIV__I,axiom,
% 2.97/1.54 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_84_UNIV__witness,axiom,
% 2.97/1.54 ! [A: $tType] :
% 2.97/1.54 ? [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_85_UNIV__eq__I,axiom,
% 2.97/1.54 ! [A: $tType,A6: set @ A] :
% 2.97/1.54 ( ! [X: A] : ( member @ A @ X @ A6 )
% 2.97/1.54 => ( ( top_top @ ( set @ A ) )
% 2.97/1.54 = A6 ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_86_range__eqI,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,B2: A,F: B > A,X3: B] :
% 2.97/1.54 ( ( B2
% 2.97/1.54 = ( F @ X3 ) )
% 2.97/1.54 => ( member @ A @ B2 @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_87_rangeI,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: B > A,X3: B] : ( member @ A @ ( F @ X3 ) @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_88_sp_092_060_094sub_062_092_060mu_062_Oinduct,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,P2: ( stream901396144_sp_mu @ A @ B @ C ) > $o,Sp_mu: stream901396144_sp_mu @ A @ B @ C] :
% 2.97/1.54 ( ! [X: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( ! [Xa: stream901396144_sp_mu @ A @ B @ C] :
% 2.97/1.54 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ Xa @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ X @ ( top_top @ ( set @ A ) ) ) )
% 2.97/1.54 => ( P2 @ Xa ) )
% 2.97/1.54 => ( P2 @ ( stream1294929701mu_Get @ A @ B @ C @ X ) ) )
% 2.97/1.54 => ( ! [X1a: B,X23: C] : ( P2 @ ( stream1370332830mu_Put @ B @ C @ A @ X1a @ X23 ) )
% 2.97/1.54 => ( P2 @ Sp_mu ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_89_Inf_OINF__cong,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,A6: set @ B,B6: set @ B,C4: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 2.97/1.54 ( ( A6 = B6 )
% 2.97/1.54 => ( ! [X: B] :
% 2.97/1.54 ( ( member @ B @ X @ B6 )
% 2.97/1.54 => ( ( C4 @ X )
% 2.97/1.54 = ( D3 @ X ) ) )
% 2.97/1.54 => ( ( Inf @ ( image @ B @ A @ C4 @ A6 ) )
% 2.97/1.54 = ( Inf @ ( image @ B @ A @ D3 @ B6 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_90_iso__tuple__UNIV__I,axiom,
% 2.97/1.54 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_91_top__apply,axiom,
% 2.97/1.54 ! [C: $tType,D: $tType] :
% 2.97/1.54 ( ( top @ C @ ( type2 @ C ) )
% 2.97/1.54 => ( ( top_top @ ( D > C ) )
% 2.97/1.54 = ( ^ [X4: D] : ( top_top @ C ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_92_surjD,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 2.97/1.54 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 2.97/1.54 = ( top_top @ ( set @ A ) ) )
% 2.97/1.54 => ? [X: B] :
% 2.97/1.54 ( Y
% 2.97/1.54 = ( F @ X ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_93_surjE,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 2.97/1.54 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 2.97/1.54 = ( top_top @ ( set @ A ) ) )
% 2.97/1.54 => ~ ! [X: B] :
% 2.97/1.54 ( Y
% 2.97/1.54 != ( F @ X ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_94_surjI,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,G3: B > A,F: A > B] :
% 2.97/1.54 ( ! [X: A] :
% 2.97/1.54 ( ( G3 @ ( F @ X ) )
% 2.97/1.54 = X )
% 2.97/1.54 => ( ( image @ B @ A @ G3 @ ( top_top @ ( set @ B ) ) )
% 2.97/1.54 = ( top_top @ ( set @ A ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_95_surj__def,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,F: B > A] :
% 2.97/1.54 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 2.97/1.54 = ( top_top @ ( set @ A ) ) )
% 2.97/1.54 = ( ! [Y5: A] :
% 2.97/1.54 ? [X4: B] :
% 2.97/1.54 ( Y5
% 2.97/1.54 = ( F @ X4 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_96_top__set__def,axiom,
% 2.97/1.54 ! [A: $tType] :
% 2.97/1.54 ( ( top_top @ ( set @ A ) )
% 2.97/1.54 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_97_sp_092_060_094sub_062_092_060mu_062_Oset__cases_I2_J,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,E3: C,A2: stream901396144_sp_mu @ A @ B @ C] :
% 2.97/1.54 ( ( member @ C @ E3 @ ( stream1259315544_sp_mu @ A @ B @ C @ A2 ) )
% 2.97/1.54 => ( ! [Z3: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( ( A2
% 2.97/1.54 = ( stream1294929701mu_Get @ A @ B @ C @ Z3 ) )
% 2.97/1.54 => ! [X: stream901396144_sp_mu @ A @ B @ C] :
% 2.97/1.54 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ X @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ Z3 @ ( top_top @ ( set @ A ) ) ) )
% 2.97/1.54 => ~ ( member @ C @ E3 @ ( stream1259315544_sp_mu @ A @ B @ C @ X ) ) ) )
% 2.97/1.54 => ~ ! [Z1: B] :
% 2.97/1.54 ( A2
% 2.97/1.54 != ( stream1370332830mu_Put @ B @ C @ A @ Z1 @ E3 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_98_sp_092_060_094sub_062_092_060mu_062_Oset__cases_I1_J,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,E3: B,A2: stream901396144_sp_mu @ A @ B @ C] :
% 2.97/1.54 ( ( member @ B @ E3 @ ( stream2074884121_sp_mu @ A @ B @ C @ A2 ) )
% 2.97/1.54 => ( ! [Z3: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( ( A2
% 2.97/1.54 = ( stream1294929701mu_Get @ A @ B @ C @ Z3 ) )
% 2.97/1.54 => ! [X: stream901396144_sp_mu @ A @ B @ C] :
% 2.97/1.54 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ X @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ Z3 @ ( top_top @ ( set @ A ) ) ) )
% 2.97/1.54 => ~ ( member @ B @ E3 @ ( stream2074884121_sp_mu @ A @ B @ C @ X ) ) ) )
% 2.97/1.54 => ~ ! [Z22: C] :
% 2.97/1.54 ( A2
% 2.97/1.54 != ( stream1370332830mu_Put @ B @ C @ A @ E3 @ Z22 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_99_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I3_J,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,Xc: stream901396144_sp_mu @ A @ B @ C,Aa: A > ( stream901396144_sp_mu @ A @ B @ C ),Xe: C] :
% 2.97/1.54 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ Xc @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ Aa @ ( top_top @ ( set @ A ) ) ) )
% 2.97/1.54 => ( ( member @ C @ Xe @ ( stream1259315544_sp_mu @ A @ B @ C @ Xc ) )
% 2.97/1.54 => ( member @ C @ Xe @ ( stream1259315544_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ Aa ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_100_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I1_J,axiom,
% 2.97/1.54 ! [C: $tType,B: $tType,A: $tType,X3: stream901396144_sp_mu @ A @ B @ C,A2: A > ( stream901396144_sp_mu @ A @ B @ C ),Xa2: B] :
% 2.97/1.54 ( ( member @ ( stream901396144_sp_mu @ A @ B @ C ) @ X3 @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ A2 @ ( top_top @ ( set @ A ) ) ) )
% 2.97/1.54 => ( ( member @ B @ Xa2 @ ( stream2074884121_sp_mu @ A @ B @ C @ X3 ) )
% 2.97/1.54 => ( member @ B @ Xa2 @ ( stream2074884121_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ A2 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_101_map__prod__surj,axiom,
% 2.97/1.54 ! [A: $tType,C: $tType,D: $tType,B: $tType,F: A > B,G3: C > D] :
% 2.97/1.54 ( ( ( image @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.54 = ( top_top @ ( set @ B ) ) )
% 2.97/1.54 => ( ( ( image @ C @ D @ G3 @ ( top_top @ ( set @ C ) ) )
% 2.97/1.54 = ( top_top @ ( set @ D ) ) )
% 2.97/1.54 => ( ( image @ ( product_prod @ A @ C ) @ ( product_prod @ B @ D ) @ ( product_map_prod @ A @ B @ C @ D @ F @ G3 ) @ ( top_top @ ( set @ ( product_prod @ A @ C ) ) ) )
% 2.97/1.54 = ( top_top @ ( set @ ( product_prod @ B @ D ) ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_102_top1I,axiom,
% 2.97/1.54 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_103_map__prod__simp,axiom,
% 2.97/1.54 ! [C: $tType,A: $tType,B: $tType,D: $tType,F: C > A,G3: D > B,A2: C,B2: D] :
% 2.97/1.54 ( ( product_map_prod @ C @ A @ D @ B @ F @ G3 @ ( product_Pair @ C @ D @ A2 @ B2 ) )
% 2.97/1.54 = ( product_Pair @ A @ B @ ( F @ A2 ) @ ( G3 @ B2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_104_map__prod__imageI,axiom,
% 2.97/1.54 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: A,B2: B,R2: set @ ( product_prod @ A @ B ),F: A > C,G3: B > D] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R2 )
% 2.97/1.54 => ( member @ ( product_prod @ C @ D ) @ ( product_Pair @ C @ D @ ( F @ A2 ) @ ( G3 @ B2 ) ) @ ( image @ ( product_prod @ A @ B ) @ ( product_prod @ C @ D ) @ ( product_map_prod @ A @ C @ B @ D @ F @ G3 ) @ R2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_105_sp_092_060_094sub_062_092_060mu_062_Orel__refl__strong,axiom,
% 2.97/1.54 ! [C: $tType,A: $tType,B: $tType,X3: stream901396144_sp_mu @ B @ A @ C,R1a: A > A > $o,R2a: C > C > $o] :
% 2.97/1.54 ( ! [Z1: A] :
% 2.97/1.54 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ B @ A @ C @ X3 ) )
% 2.97/1.54 => ( R1a @ Z1 @ Z1 ) )
% 2.97/1.54 => ( ! [Z22: C] :
% 2.97/1.54 ( ( member @ C @ Z22 @ ( stream1259315544_sp_mu @ B @ A @ C @ X3 ) )
% 2.97/1.54 => ( R2a @ Z22 @ Z22 ) )
% 2.97/1.54 => ( stream1924447089_sp_mu @ A @ A @ C @ C @ B @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_106_sp_092_060_094sub_062_092_060mu_062_Orel__mono__strong,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,D: $tType,C: $tType,G: $tType,R1: A > C > $o,R22: B > D > $o,X3: stream901396144_sp_mu @ G @ A @ B,Y: stream901396144_sp_mu @ G @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 2.97/1.54 ( ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 @ X3 @ Y )
% 2.97/1.54 => ( ! [Z1: A,Y12: C] :
% 2.97/1.54 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ X3 ) )
% 2.97/1.54 => ( ( member @ C @ Y12 @ ( stream2074884121_sp_mu @ G @ C @ D @ Y ) )
% 2.97/1.54 => ( ( R1 @ Z1 @ Y12 )
% 2.97/1.54 => ( R1a @ Z1 @ Y12 ) ) ) )
% 2.97/1.54 => ( ! [Z22: B,Y23: D] :
% 2.97/1.54 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ X3 ) )
% 2.97/1.54 => ( ( member @ D @ Y23 @ ( stream1259315544_sp_mu @ G @ C @ D @ Y ) )
% 2.97/1.54 => ( ( R22 @ Z22 @ Y23 )
% 2.97/1.54 => ( R2a @ Z22 @ Y23 ) ) ) )
% 2.97/1.54 => ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1a @ R2a @ X3 @ Y ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_107_sp_092_060_094sub_062_092_060mu_062_Orel__cong,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,D: $tType,C: $tType,G: $tType,X3: stream901396144_sp_mu @ G @ A @ B,Ya: stream901396144_sp_mu @ G @ A @ B,Y: stream901396144_sp_mu @ G @ C @ D,Xa2: stream901396144_sp_mu @ G @ C @ D,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 2.97/1.54 ( ( X3 = Ya )
% 2.97/1.54 => ( ( Y = Xa2 )
% 2.97/1.54 => ( ! [Z1: A,Y12: C] :
% 2.97/1.54 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ Ya ) )
% 2.97/1.54 => ( ( member @ C @ Y12 @ ( stream2074884121_sp_mu @ G @ C @ D @ Xa2 ) )
% 2.97/1.54 => ( ( R1 @ Z1 @ Y12 )
% 2.97/1.54 = ( R1a @ Z1 @ Y12 ) ) ) )
% 2.97/1.54 => ( ! [Z22: B,Y23: D] :
% 2.97/1.54 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ Ya ) )
% 2.97/1.54 => ( ( member @ D @ Y23 @ ( stream1259315544_sp_mu @ G @ C @ D @ Xa2 ) )
% 2.97/1.54 => ( ( R22 @ Z22 @ Y23 )
% 2.97/1.54 = ( R2a @ Z22 @ Y23 ) ) ) )
% 2.97/1.54 => ( ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 @ X3 @ Y )
% 2.97/1.54 = ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1a @ R2a @ Ya @ Xa2 ) ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_108_sp_092_060_094sub_062_092_060mu_062_Opred__mono__strong,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,G: $tType,P1: A > $o,P22: B > $o,X3: stream901396144_sp_mu @ G @ A @ B,P1a: A > $o,P2a: B > $o] :
% 2.97/1.54 ( ( stream123009735_sp_mu @ A @ B @ G @ P1 @ P22 @ X3 )
% 2.97/1.54 => ( ! [Z1: A] :
% 2.97/1.54 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ X3 ) )
% 2.97/1.54 => ( ( P1 @ Z1 )
% 2.97/1.54 => ( P1a @ Z1 ) ) )
% 2.97/1.54 => ( ! [Z22: B] :
% 2.97/1.54 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ X3 ) )
% 2.97/1.54 => ( ( P22 @ Z22 )
% 2.97/1.54 => ( P2a @ Z22 ) ) )
% 2.97/1.54 => ( stream123009735_sp_mu @ A @ B @ G @ P1a @ P2a @ X3 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_109_sp_092_060_094sub_062_092_060mu_062_Opred__cong,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,G: $tType,X3: stream901396144_sp_mu @ G @ A @ B,Ya: stream901396144_sp_mu @ G @ A @ B,P1: A > $o,P1a: A > $o,P22: B > $o,P2a: B > $o] :
% 2.97/1.54 ( ( X3 = Ya )
% 2.97/1.54 => ( ! [Z1: A] :
% 2.97/1.54 ( ( member @ A @ Z1 @ ( stream2074884121_sp_mu @ G @ A @ B @ Ya ) )
% 2.97/1.54 => ( ( P1 @ Z1 )
% 2.97/1.54 = ( P1a @ Z1 ) ) )
% 2.97/1.54 => ( ! [Z22: B] :
% 2.97/1.54 ( ( member @ B @ Z22 @ ( stream1259315544_sp_mu @ G @ A @ B @ Ya ) )
% 2.97/1.54 => ( ( P22 @ Z22 )
% 2.97/1.54 = ( P2a @ Z22 ) ) )
% 2.97/1.54 => ( ( stream123009735_sp_mu @ A @ B @ G @ P1 @ P22 @ X3 )
% 2.97/1.54 = ( stream123009735_sp_mu @ A @ B @ G @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_110_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I2_J,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,A1: B,A22: C] : ( member @ B @ A1 @ ( stream2074884121_sp_mu @ A @ B @ C @ ( stream1370332830mu_Put @ B @ C @ A @ A1 @ A22 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_111_sp_092_060_094sub_062_092_060mu_062_Oset__intros_I4_J,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,C: $tType,A2a: C,A1a: B] : ( member @ C @ A2a @ ( stream1259315544_sp_mu @ A @ B @ C @ ( stream1370332830mu_Put @ B @ C @ A @ A1a @ A2a ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_112_prod__fun__imageE,axiom,
% 2.97/1.54 ! [B: $tType,A: $tType,D: $tType,C: $tType,C3: product_prod @ A @ B,F: C > A,G3: D > B,R2: set @ ( product_prod @ C @ D )] :
% 2.97/1.54 ( ( member @ ( product_prod @ A @ B ) @ C3 @ ( image @ ( product_prod @ C @ D ) @ ( product_prod @ A @ B ) @ ( product_map_prod @ C @ A @ D @ B @ F @ G3 ) @ R2 ) )
% 2.97/1.54 => ~ ! [X: C,Y3: D] :
% 2.97/1.54 ( ( C3
% 2.97/1.54 = ( product_Pair @ A @ B @ ( F @ X ) @ ( G3 @ Y3 ) ) )
% 2.97/1.54 => ~ ( member @ ( product_prod @ C @ D ) @ ( product_Pair @ C @ D @ X @ Y3 ) @ R2 ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_113_top__empty__eq,axiom,
% 2.97/1.54 ! [A: $tType] :
% 2.97/1.54 ( ( top_top @ ( A > $o ) )
% 2.97/1.54 = ( ^ [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_114_top__conj_I2_J,axiom,
% 2.97/1.54 ! [A: $tType,P2: $o,X3: A] :
% 2.97/1.54 ( ( P2
% 2.97/1.54 & ( top_top @ ( A > $o ) @ X3 ) )
% 2.97/1.54 = P2 ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_115_top__conj_I1_J,axiom,
% 2.97/1.54 ! [A: $tType,X3: A,P2: $o] :
% 2.97/1.54 ( ( ( top_top @ ( A > $o ) @ X3 )
% 2.97/1.54 & P2 )
% 2.97/1.54 = P2 ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_116_sp_092_060_094sub_062_092_060mu_062_Osimps_I15_J,axiom,
% 2.97/1.54 ! [B: $tType,C: $tType,A: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( ( stream2074884121_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) )
% 2.97/1.54 = ( complete_Sup_Sup @ ( set @ B ) @ ( image @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( set @ B ) @ ( stream2074884121_sp_mu @ A @ B @ C ) @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ X1 @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_117_sp_092_060_094sub_062_092_060mu_062_Osimps_I17_J,axiom,
% 2.97/1.54 ! [B: $tType,C: $tType,A: $tType,X1: A > ( stream901396144_sp_mu @ A @ B @ C )] :
% 2.97/1.54 ( ( stream1259315544_sp_mu @ A @ B @ C @ ( stream1294929701mu_Get @ A @ B @ C @ X1 ) )
% 2.97/1.54 = ( complete_Sup_Sup @ ( set @ C ) @ ( image @ ( stream901396144_sp_mu @ A @ B @ C ) @ ( set @ C ) @ ( stream1259315544_sp_mu @ A @ B @ C ) @ ( image @ A @ ( stream901396144_sp_mu @ A @ B @ C ) @ X1 @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_118_UN__ball__bex__simps_I3_J,axiom,
% 2.97/1.54 ! [D: $tType,A6: set @ ( set @ D ),P2: D > $o] :
% 2.97/1.54 ( ( ? [X4: D] :
% 2.97/1.54 ( ( member @ D @ X4 @ ( complete_Sup_Sup @ ( set @ D ) @ A6 ) )
% 2.97/1.54 & ( P2 @ X4 ) ) )
% 2.97/1.54 = ( ? [X4: set @ D] :
% 2.97/1.54 ( ( member @ ( set @ D ) @ X4 @ A6 )
% 2.97/1.54 & ? [Y5: D] :
% 2.97/1.54 ( ( member @ D @ Y5 @ X4 )
% 2.97/1.54 & ( P2 @ Y5 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_119_UN__ball__bex__simps_I1_J,axiom,
% 2.97/1.54 ! [A: $tType,A6: set @ ( set @ A ),P2: A > $o] :
% 2.97/1.54 ( ( ! [X4: A] :
% 2.97/1.54 ( ( member @ A @ X4 @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) )
% 2.97/1.54 => ( P2 @ X4 ) ) )
% 2.97/1.54 = ( ! [X4: set @ A] :
% 2.97/1.54 ( ( member @ ( set @ A ) @ X4 @ A6 )
% 2.97/1.54 => ! [Y5: A] :
% 2.97/1.54 ( ( member @ A @ Y5 @ X4 )
% 2.97/1.54 => ( P2 @ Y5 ) ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_120_UnionI,axiom,
% 2.97/1.54 ! [A: $tType,X7: set @ A,C4: set @ ( set @ A ),A6: A] :
% 2.97/1.54 ( ( member @ ( set @ A ) @ X7 @ C4 )
% 2.97/1.54 => ( ( member @ A @ A6 @ X7 )
% 2.97/1.54 => ( member @ A @ A6 @ ( complete_Sup_Sup @ ( set @ A ) @ C4 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_121_Union__iff,axiom,
% 2.97/1.54 ! [A: $tType,A6: A,C4: set @ ( set @ A )] :
% 2.97/1.54 ( ( member @ A @ A6 @ ( complete_Sup_Sup @ ( set @ A ) @ C4 ) )
% 2.97/1.54 = ( ? [X4: set @ A] :
% 2.97/1.54 ( ( member @ ( set @ A ) @ X4 @ C4 )
% 2.97/1.54 & ( member @ A @ A6 @ X4 ) ) ) ) ).
% 2.97/1.54
% 2.97/1.54 thf(fact_122_ball__UN,axiom,
% 2.97/1.54 ! [A: $tType,B: $tType,B6: B > ( set @ A ),A6: set @ B,P2: A > $o] :
% 2.97/1.54 ( ( ! [X4: A] :
% 2.97/1.54 ( ( member @ A @ X4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B6 @ A6 ) ) )
% 2.97/1.55 => ( P2 @ X4 ) ) )
% 2.97/1.55 = ( ! [X4: B] :
% 2.97/1.55 ( ( member @ B @ X4 @ A6 )
% 2.97/1.55 => ! [Y5: A] :
% 2.97/1.55 ( ( member @ A @ Y5 @ ( B6 @ X4 ) )
% 2.97/1.55 => ( P2 @ Y5 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_123_bex__UN,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,B6: B > ( set @ A ),A6: set @ B,P2: A > $o] :
% 2.97/1.55 ( ( ? [X4: A] :
% 2.97/1.55 ( ( member @ A @ X4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B6 @ A6 ) ) )
% 2.97/1.55 & ( P2 @ X4 ) ) )
% 2.97/1.55 = ( ? [X4: B] :
% 2.97/1.55 ( ( member @ B @ X4 @ A6 )
% 2.97/1.55 & ? [Y5: A] :
% 2.97/1.55 ( ( member @ A @ Y5 @ ( B6 @ X4 ) )
% 2.97/1.55 & ( P2 @ Y5 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_124_UN__ball__bex__simps_I2_J,axiom,
% 2.97/1.55 ! [C: $tType,B: $tType,B6: B > ( set @ C ),A6: set @ B,P2: C > $o] :
% 2.97/1.55 ( ( ! [X4: C] :
% 2.97/1.55 ( ( member @ C @ X4 @ ( complete_Sup_Sup @ ( set @ C ) @ ( image @ B @ ( set @ C ) @ B6 @ A6 ) ) )
% 2.97/1.55 => ( P2 @ X4 ) ) )
% 2.97/1.55 = ( ! [X4: B] :
% 2.97/1.55 ( ( member @ B @ X4 @ A6 )
% 2.97/1.55 => ! [Y5: C] :
% 2.97/1.55 ( ( member @ C @ Y5 @ ( B6 @ X4 ) )
% 2.97/1.55 => ( P2 @ Y5 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_125_UN__ball__bex__simps_I4_J,axiom,
% 2.97/1.55 ! [F2: $tType,E: $tType,B6: E > ( set @ F2 ),A6: set @ E,P2: F2 > $o] :
% 2.97/1.55 ( ( ? [X4: F2] :
% 2.97/1.55 ( ( member @ F2 @ X4 @ ( complete_Sup_Sup @ ( set @ F2 ) @ ( image @ E @ ( set @ F2 ) @ B6 @ A6 ) ) )
% 2.97/1.55 & ( P2 @ X4 ) ) )
% 2.97/1.55 = ( ? [X4: E] :
% 2.97/1.55 ( ( member @ E @ X4 @ A6 )
% 2.97/1.55 & ? [Y5: F2] :
% 2.97/1.55 ( ( member @ F2 @ Y5 @ ( B6 @ X4 ) )
% 2.97/1.55 & ( P2 @ Y5 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_126_Sup__UNIV,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ( ( complete_Sup_Sup @ A @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 = ( top_top @ A ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_127_Union__UNIV,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( complete_Sup_Sup @ ( set @ A ) @ ( top_top @ ( set @ ( set @ A ) ) ) )
% 2.97/1.55 = ( top_top @ ( set @ A ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_128_UnionE,axiom,
% 2.97/1.55 ! [A: $tType,A6: A,C4: set @ ( set @ A )] :
% 2.97/1.55 ( ( member @ A @ A6 @ ( complete_Sup_Sup @ ( set @ A ) @ C4 ) )
% 2.97/1.55 => ~ ! [X8: set @ A] :
% 2.97/1.55 ( ( member @ A @ A6 @ X8 )
% 2.97/1.55 => ~ ( member @ ( set @ A ) @ X8 @ C4 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_129_SUP__cong,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType] :
% 2.97/1.55 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A6: set @ B,B6: set @ B,C4: B > A,D3: B > A] :
% 2.97/1.55 ( ( A6 = B6 )
% 2.97/1.55 => ( ! [X: B] :
% 2.97/1.55 ( ( member @ B @ X @ B6 )
% 2.97/1.55 => ( ( C4 @ X )
% 2.97/1.55 = ( D3 @ X ) ) )
% 2.97/1.55 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ C4 @ A6 ) )
% 2.97/1.55 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ D3 @ B6 ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_130_same__fstI,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,P2: A > $o,X3: A,Y7: B,Y: B,R2: A > ( set @ ( product_prod @ B @ B ) )] :
% 2.97/1.55 ( ( P2 @ X3 )
% 2.97/1.55 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y7 @ Y ) @ ( R2 @ X3 ) )
% 2.97/1.55 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y7 ) @ ( product_Pair @ A @ B @ X3 @ Y ) ) @ ( same_fst @ A @ B @ P2 @ R2 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_131_wf__same__fst,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,P2: A > $o,R2: A > ( set @ ( product_prod @ B @ B ) )] :
% 2.97/1.55 ( ! [X: A] :
% 2.97/1.55 ( ( P2 @ X )
% 2.97/1.55 => ( wf @ B @ ( R2 @ X ) ) )
% 2.97/1.55 => ( wf @ ( product_prod @ A @ B ) @ ( same_fst @ A @ B @ P2 @ R2 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_132_wf__map__prod__image,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F: A > B] :
% 2.97/1.55 ( ( wf @ A @ R )
% 2.97/1.55 => ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( wf @ B @ ( image @ ( product_prod @ A @ A ) @ ( product_prod @ B @ B ) @ ( product_map_prod @ A @ B @ A @ B @ F @ F ) @ R ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_133_member__bind,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,X3: A,P2: set @ B,F: B > ( set @ A )] :
% 2.97/1.55 ( ( member @ A @ X3 @ ( bind @ B @ A @ P2 @ F ) )
% 2.97/1.55 = ( member @ A @ X3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ P2 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_134_inj__apfst,axiom,
% 2.97/1.55 ! [B: $tType,C: $tType,A: $tType,F: A > C] :
% 2.97/1.55 ( ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ C @ B ) @ ( product_apfst @ A @ C @ B @ F ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 2.97/1.55 = ( inj_on @ A @ C @ F @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_135_inj__apsnd,axiom,
% 2.97/1.55 ! [A: $tType,C: $tType,B: $tType,F: B > C] :
% 2.97/1.55 ( ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ A @ C ) @ ( product_apsnd @ B @ C @ A @ F ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 2.97/1.55 = ( inj_on @ B @ C @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_136_inj__on__image__iff,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,A6: set @ A,G3: A > B,F: A > A] :
% 2.97/1.55 ( ! [X: A] :
% 2.97/1.55 ( ( member @ A @ X @ A6 )
% 2.97/1.55 => ! [Xa3: A] :
% 2.97/1.55 ( ( member @ A @ Xa3 @ A6 )
% 2.97/1.55 => ( ( ( G3 @ ( F @ X ) )
% 2.97/1.55 = ( G3 @ ( F @ Xa3 ) ) )
% 2.97/1.55 = ( ( G3 @ X )
% 2.97/1.55 = ( G3 @ Xa3 ) ) ) ) )
% 2.97/1.55 => ( ( inj_on @ A @ A @ F @ A6 )
% 2.97/1.55 => ( ( inj_on @ A @ B @ G3 @ ( image @ A @ A @ F @ A6 ) )
% 2.97/1.55 = ( inj_on @ A @ B @ G3 @ A6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_137_inj__on__image,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A6: set @ ( set @ A )] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) )
% 2.97/1.55 => ( inj_on @ ( set @ A ) @ ( set @ B ) @ ( image @ A @ B @ F ) @ A6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_138_inj__swap,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,A6: set @ ( product_prod @ A @ B )] : ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ B @ A ) @ ( product_swap @ A @ B ) @ A6 ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_139_inj__eq,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,X3: A,Y: A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( ( F @ X3 )
% 2.97/1.55 = ( F @ Y ) )
% 2.97/1.55 = ( X3 = Y ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_140_injI,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B] :
% 2.97/1.55 ( ! [X: A,Y3: A] :
% 2.97/1.55 ( ( ( F @ X )
% 2.97/1.55 = ( F @ Y3 ) )
% 2.97/1.55 => ( X = Y3 ) )
% 2.97/1.55 => ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_141_injD,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,X3: A,Y: A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( ( F @ X3 )
% 2.97/1.55 = ( F @ Y ) )
% 2.97/1.55 => ( X3 = Y ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_142_range__ex1__eq,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,B2: B] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( member @ B @ B2 @ ( image @ A @ B @ F @ ( top_top @ ( set @ A ) ) ) )
% 2.97/1.55 = ( ? [X4: A] :
% 2.97/1.55 ( ( B2
% 2.97/1.55 = ( F @ X4 ) )
% 2.97/1.55 & ! [Y5: A] :
% 2.97/1.55 ( ( B2
% 2.97/1.55 = ( F @ Y5 ) )
% 2.97/1.55 => ( Y5 = X4 ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_143_inj__image__eq__iff,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( ( image @ A @ B @ F @ A6 )
% 2.97/1.55 = ( image @ A @ B @ F @ B6 ) )
% 2.97/1.55 = ( A6 = B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_144_inj__image__mem__iff,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A2: A,A6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A6 ) )
% 2.97/1.55 = ( member @ A @ A2 @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_145_bind__UNION,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType] :
% 2.97/1.55 ( ( bind @ B @ A )
% 2.97/1.55 = ( ^ [A7: set @ B,F4: B > ( set @ A )] : ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F4 @ A7 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_146_prod_Oinj__map,axiom,
% 2.97/1.55 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F22: B > D] :
% 2.97/1.55 ( ( inj_on @ A @ C @ F1 @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( inj_on @ B @ D @ F22 @ ( top_top @ ( set @ B ) ) )
% 2.97/1.55 => ( inj_on @ ( product_prod @ A @ B ) @ ( product_prod @ C @ D ) @ ( product_map_prod @ A @ C @ B @ D @ F1 @ F22 ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_147_the__inv__into__onto,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ A6 )
% 2.97/1.55 => ( ( image @ B @ A @ ( the_inv_into @ A @ B @ A6 @ F ) @ ( image @ A @ B @ F @ A6 ) )
% 2.97/1.55 = A6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_148_range__fst,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType] :
% 2.97/1.55 ( ( image @ ( product_prod @ A @ B ) @ A @ ( product_fst @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 2.97/1.55 = ( top_top @ ( set @ A ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_149_range__snd,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType] :
% 2.97/1.55 ( ( image @ ( product_prod @ B @ A ) @ A @ ( product_snd @ B @ A ) @ ( top_top @ ( set @ ( product_prod @ B @ A ) ) ) )
% 2.97/1.55 = ( top_top @ ( set @ A ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_150_fst__map__prod,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: C > A,G3: D > B,X3: product_prod @ C @ D] :
% 2.97/1.55 ( ( product_fst @ A @ B @ ( product_map_prod @ C @ A @ D @ B @ F @ G3 @ X3 ) )
% 2.97/1.55 = ( F @ ( product_fst @ C @ D @ X3 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_151_snd__map__prod,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: C > B,G3: D > A,X3: product_prod @ C @ D] :
% 2.97/1.55 ( ( product_snd @ B @ A @ ( product_map_prod @ C @ B @ D @ A @ F @ G3 @ X3 ) )
% 2.97/1.55 = ( G3 @ ( product_snd @ C @ D @ X3 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_152_fst__apfst,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,C: $tType,F: C > A,X3: product_prod @ C @ B] :
% 2.97/1.55 ( ( product_fst @ A @ B @ ( product_apfst @ C @ A @ B @ F @ X3 ) )
% 2.97/1.55 = ( F @ ( product_fst @ C @ B @ X3 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_153_apfst__eq__conv,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,C: $tType,F: C > A,X3: product_prod @ C @ B,G3: C > A] :
% 2.97/1.55 ( ( ( product_apfst @ C @ A @ B @ F @ X3 )
% 2.97/1.55 = ( product_apfst @ C @ A @ B @ G3 @ X3 ) )
% 2.97/1.55 = ( ( F @ ( product_fst @ C @ B @ X3 ) )
% 2.97/1.55 = ( G3 @ ( product_fst @ C @ B @ X3 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_154_snd__apfst,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,C: $tType,F: C > B,X3: product_prod @ C @ A] :
% 2.97/1.55 ( ( product_snd @ B @ A @ ( product_apfst @ C @ B @ A @ F @ X3 ) )
% 2.97/1.55 = ( product_snd @ C @ A @ X3 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_155_fst__apsnd,axiom,
% 2.97/1.55 ! [B: $tType,C: $tType,A: $tType,F: C > B,X3: product_prod @ A @ C] :
% 2.97/1.55 ( ( product_fst @ A @ B @ ( product_apsnd @ C @ B @ A @ F @ X3 ) )
% 2.97/1.55 = ( product_fst @ A @ C @ X3 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_156_snd__apsnd,axiom,
% 2.97/1.55 ! [A: $tType,C: $tType,B: $tType,F: C > A,X3: product_prod @ B @ C] :
% 2.97/1.55 ( ( product_snd @ B @ A @ ( product_apsnd @ C @ A @ B @ F @ X3 ) )
% 2.97/1.55 = ( F @ ( product_snd @ B @ C @ X3 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_157_apsnd__eq__conv,axiom,
% 2.97/1.55 ! [B: $tType,C: $tType,A: $tType,F: C > B,X3: product_prod @ A @ C,G3: C > B] :
% 2.97/1.55 ( ( ( product_apsnd @ C @ B @ A @ F @ X3 )
% 2.97/1.55 = ( product_apsnd @ C @ B @ A @ G3 @ X3 ) )
% 2.97/1.55 = ( ( F @ ( product_snd @ A @ C @ X3 ) )
% 2.97/1.55 = ( G3 @ ( product_snd @ A @ C @ X3 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_158_prod_Ocollapse,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.97/1.55 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 2.97/1.55 = Prod ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_159_snd__swap,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,X3: product_prod @ A @ B] :
% 2.97/1.55 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X3 ) )
% 2.97/1.55 = ( product_fst @ A @ B @ X3 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_160_fst__swap,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,X3: product_prod @ B @ A] :
% 2.97/1.55 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X3 ) )
% 2.97/1.55 = ( product_snd @ B @ A @ X3 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_161_apfst__apsnd,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,D: $tType,C: $tType,F: C > A,G3: D > B,X3: product_prod @ C @ D] :
% 2.97/1.55 ( ( product_apfst @ C @ A @ B @ F @ ( product_apsnd @ D @ B @ C @ G3 @ X3 ) )
% 2.97/1.55 = ( product_Pair @ A @ B @ ( F @ ( product_fst @ C @ D @ X3 ) ) @ ( G3 @ ( product_snd @ C @ D @ X3 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_162_apsnd__apfst,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,F: C > B,G3: D > A,X3: product_prod @ D @ C] :
% 2.97/1.55 ( ( product_apsnd @ C @ B @ A @ F @ ( product_apfst @ D @ A @ C @ G3 @ X3 ) )
% 2.97/1.55 = ( product_Pair @ A @ B @ ( G3 @ ( product_fst @ D @ C @ X3 ) ) @ ( F @ ( product_snd @ D @ C @ X3 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_163_surjective__pairing,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,T2: product_prod @ A @ B] :
% 2.97/1.55 ( T2
% 2.97/1.55 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T2 ) @ ( product_snd @ A @ B @ T2 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_164_prod_Oexhaust__sel,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.97/1.55 ( Prod
% 2.97/1.55 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_165_prod_Osplit__sel__asm,axiom,
% 2.97/1.55 ! [C: $tType,B: $tType,A: $tType,P2: C > $o,F: A > B > C,Prod: product_prod @ A @ B] :
% 2.97/1.55 ( ( P2 @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 2.97/1.55 = ( ~ ( ( Prod
% 2.97/1.55 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) )
% 2.97/1.55 & ~ ( P2 @ ( F @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_166_prod_Osplit__sel,axiom,
% 2.97/1.55 ! [C: $tType,B: $tType,A: $tType,P2: C > $o,F: A > B > C,Prod: product_prod @ A @ B] :
% 2.97/1.55 ( ( P2 @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 2.97/1.55 = ( ( Prod
% 2.97/1.55 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) )
% 2.97/1.55 => ( P2 @ ( F @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_167_prod__eqI,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,P: product_prod @ A @ B,Q4: product_prod @ A @ B] :
% 2.97/1.55 ( ( ( product_fst @ A @ B @ P )
% 2.97/1.55 = ( product_fst @ A @ B @ Q4 ) )
% 2.97/1.55 => ( ( ( product_snd @ A @ B @ P )
% 2.97/1.55 = ( product_snd @ A @ B @ Q4 ) )
% 2.97/1.55 => ( P = Q4 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_168_prod_Oexpand,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 2.97/1.55 ( ( ( ( product_fst @ A @ B @ Prod )
% 2.97/1.55 = ( product_fst @ A @ B @ Prod2 ) )
% 2.97/1.55 & ( ( product_snd @ A @ B @ Prod )
% 2.97/1.55 = ( product_snd @ A @ B @ Prod2 ) ) )
% 2.97/1.55 => ( Prod = Prod2 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_169_prod__eq__iff,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType] :
% 2.97/1.55 ( ( ^ [Y4: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y4 = Z ) )
% 2.97/1.55 = ( ^ [S3: product_prod @ A @ B,T3: product_prod @ A @ B] :
% 2.97/1.55 ( ( ( product_fst @ A @ B @ S3 )
% 2.97/1.55 = ( product_fst @ A @ B @ T3 ) )
% 2.97/1.55 & ( ( product_snd @ A @ B @ S3 )
% 2.97/1.55 = ( product_snd @ A @ B @ T3 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_170_case__prod__beta,axiom,
% 2.97/1.55 ! [A: $tType,C: $tType,B: $tType] :
% 2.97/1.55 ( ( product_case_prod @ B @ C @ A )
% 2.97/1.55 = ( ^ [F4: B > C > A,P6: product_prod @ B @ C] : ( F4 @ ( product_fst @ B @ C @ P6 ) @ ( product_snd @ B @ C @ P6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_171_prod_Ocase__eq__if,axiom,
% 2.97/1.55 ! [C: $tType,B: $tType,A: $tType] :
% 2.97/1.55 ( ( product_case_prod @ A @ B @ C )
% 2.97/1.55 = ( ^ [F4: A > B > C,Prod3: product_prod @ A @ B] : ( F4 @ ( product_fst @ A @ B @ Prod3 ) @ ( product_snd @ A @ B @ Prod3 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_172_Product__Type_OCollect__case__prodD,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,X3: product_prod @ A @ B,A6: A > B > $o] :
% 2.97/1.55 ( ( member @ ( product_prod @ A @ B ) @ X3 @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ A6 ) ) )
% 2.97/1.55 => ( A6 @ ( product_fst @ A @ B @ X3 ) @ ( product_snd @ A @ B @ X3 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_173_fst__conv,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,X1: A,X2: B] :
% 2.97/1.55 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X2 ) )
% 2.97/1.55 = X1 ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_174_fst__eqD,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,X3: A,Y: B,A2: A] :
% 2.97/1.55 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 2.97/1.55 = A2 )
% 2.97/1.55 => ( X3 = A2 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_175_snd__conv,axiom,
% 2.97/1.55 ! [Aa2: $tType,A: $tType,X1: Aa2,X2: A] :
% 2.97/1.55 ( ( product_snd @ Aa2 @ A @ ( product_Pair @ Aa2 @ A @ X1 @ X2 ) )
% 2.97/1.55 = X2 ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_176_snd__eqD,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,X3: B,Y: A,A2: A] :
% 2.97/1.55 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) )
% 2.97/1.55 = A2 )
% 2.97/1.55 => ( Y = A2 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_177_prod_Oswap__def,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType] :
% 2.97/1.55 ( ( product_swap @ A @ B )
% 2.97/1.55 = ( ^ [P6: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P6 ) @ ( product_fst @ A @ B @ P6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_178_inj__on__the__inv__into,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ A6 )
% 2.97/1.55 => ( inj_on @ B @ A @ ( the_inv_into @ A @ B @ A6 @ F ) @ ( image @ A @ B @ F @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_179_f__the__inv__into__f,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,F: A > B,A6: set @ A,Y: B] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ A6 )
% 2.97/1.55 => ( ( member @ B @ Y @ ( image @ A @ B @ F @ A6 ) )
% 2.97/1.55 => ( ( F @ ( the_inv_into @ A @ B @ A6 @ F @ Y ) )
% 2.97/1.55 = Y ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_180_the__inv__f__f,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,X3: A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( the_inv_into @ A @ B @ ( top_top @ ( set @ A ) ) @ F @ ( F @ X3 ) )
% 2.97/1.55 = X3 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_181_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,P2: A > B > $o,X3: A,Y: B,A2: product_prod @ A @ B] :
% 2.97/1.55 ( ( P2 @ X3 @ Y )
% 2.97/1.55 => ( ( A2
% 2.97/1.55 = ( product_Pair @ A @ B @ X3 @ Y ) )
% 2.97/1.55 => ( P2 @ ( product_fst @ A @ B @ A2 ) @ ( product_snd @ A @ B @ A2 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_182_conjI__realizer,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,P2: A > $o,P: A,Q: B > $o,Q4: B] :
% 2.97/1.55 ( ( P2 @ P )
% 2.97/1.55 => ( ( Q @ Q4 )
% 2.97/1.55 => ( ( P2 @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P @ Q4 ) ) )
% 2.97/1.55 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P @ Q4 ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_183_exI__realizer,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,P2: A > B > $o,Y: A,X3: B] :
% 2.97/1.55 ( ( P2 @ Y @ X3 )
% 2.97/1.55 => ( P2 @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_184_eq__snd__iff,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,B2: A,P: product_prod @ B @ A] :
% 2.97/1.55 ( ( B2
% 2.97/1.55 = ( product_snd @ B @ A @ P ) )
% 2.97/1.55 = ( ? [A5: B] :
% 2.97/1.55 ( P
% 2.97/1.55 = ( product_Pair @ B @ A @ A5 @ B2 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_185_sndI,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,X3: product_prod @ A @ B,Y: A,Z2: B] :
% 2.97/1.55 ( ( X3
% 2.97/1.55 = ( product_Pair @ A @ B @ Y @ Z2 ) )
% 2.97/1.55 => ( ( product_snd @ A @ B @ X3 )
% 2.97/1.55 = Z2 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_186_eq__fst__iff,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,A2: A,P: product_prod @ A @ B] :
% 2.97/1.55 ( ( A2
% 2.97/1.55 = ( product_fst @ A @ B @ P ) )
% 2.97/1.55 = ( ? [B5: B] :
% 2.97/1.55 ( P
% 2.97/1.55 = ( product_Pair @ A @ B @ A2 @ B5 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_187_fstI,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,X3: product_prod @ A @ B,Y: A,Z2: B] :
% 2.97/1.55 ( ( X3
% 2.97/1.55 = ( product_Pair @ A @ B @ Y @ Z2 ) )
% 2.97/1.55 => ( ( product_fst @ A @ B @ X3 )
% 2.97/1.55 = Y ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_188_Collect__split__mono__strong,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,X7: set @ A,A6: set @ ( product_prod @ A @ B ),Y8: set @ B,P2: A > B > $o,Q: A > B > $o] :
% 2.97/1.55 ( ( X7
% 2.97/1.55 = ( image @ ( product_prod @ A @ B ) @ A @ ( product_fst @ A @ B ) @ A6 ) )
% 2.97/1.55 => ( ( Y8
% 2.97/1.55 = ( image @ ( product_prod @ A @ B ) @ B @ ( product_snd @ A @ B ) @ A6 ) )
% 2.97/1.55 => ( ! [X: A] :
% 2.97/1.55 ( ( member @ A @ X @ X7 )
% 2.97/1.55 => ! [Xa3: B] :
% 2.97/1.55 ( ( member @ B @ Xa3 @ Y8 )
% 2.97/1.55 => ( ( P2 @ X @ Xa3 )
% 2.97/1.55 => ( Q @ X @ Xa3 ) ) ) )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ A6 @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ P2 ) ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ A6 @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ Q ) ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_189_sndOp__def,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,C: $tType] :
% 2.97/1.55 ( ( bNF_sndOp @ C @ A @ B )
% 2.97/1.55 = ( ^ [P3: C > A > $o,Q3: A > B > $o,Ac: product_prod @ C @ B] : ( product_Pair @ A @ B @ ( bNF_pick_middlep @ C @ A @ B @ P3 @ Q3 @ ( product_fst @ C @ B @ Ac ) @ ( product_snd @ C @ B @ Ac ) ) @ ( product_snd @ C @ B @ Ac ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_190_fstOp__def,axiom,
% 2.97/1.55 ! [C: $tType,B: $tType,A: $tType] :
% 2.97/1.55 ( ( bNF_fstOp @ A @ B @ C )
% 2.97/1.55 = ( ^ [P3: A > B > $o,Q3: B > C > $o,Ac: product_prod @ A @ C] : ( product_Pair @ A @ B @ ( product_fst @ A @ C @ Ac ) @ ( bNF_pick_middlep @ A @ B @ C @ P3 @ Q3 @ ( product_fst @ A @ C @ Ac ) @ ( product_snd @ A @ C @ Ac ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_191_subset__antisym,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ A6 )
% 2.97/1.55 => ( A6 = B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_192_subsetI,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ! [X: A] :
% 2.97/1.55 ( ( member @ A @ X @ A6 )
% 2.97/1.55 => ( member @ A @ X @ B6 ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ A6 @ B6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_193_inj__on__image__mem__iff__alt,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,B6: set @ A,A6: set @ A,A2: A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ B6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A6 ) )
% 2.97/1.55 => ( ( member @ A @ A2 @ B6 )
% 2.97/1.55 => ( member @ A @ A2 @ A6 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_194_inj__on__image__mem__iff,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,B6: set @ A,A2: A,A6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ B6 )
% 2.97/1.55 => ( ( member @ A @ A2 @ B6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A6 ) )
% 2.97/1.55 = ( member @ A @ A2 @ A6 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_195_inj__on__image__eq__iff,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,C4: set @ A,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ C4 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ C4 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 2.97/1.55 => ( ( ( image @ A @ B @ F @ A6 )
% 2.97/1.55 = ( image @ A @ B @ F @ B6 ) )
% 2.97/1.55 = ( A6 = B6 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_196_image__mono,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,A6: set @ A,B6: set @ A,F: A > B] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) @ ( image @ A @ B @ F @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_197_image__subsetI,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,A6: set @ A,F: A > B,B6: set @ B] :
% 2.97/1.55 ( ! [X: A] :
% 2.97/1.55 ( ( member @ A @ X @ A6 )
% 2.97/1.55 => ( member @ B @ ( F @ X ) @ B6 ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) @ B6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_198_subset__imageE,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,B6: set @ A,F: B > A,A6: set @ B] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ B6 @ ( image @ B @ A @ F @ A6 ) )
% 2.97/1.55 => ~ ! [C5: set @ B] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ B ) @ C5 @ A6 )
% 2.97/1.55 => ( B6
% 2.97/1.55 != ( image @ B @ A @ F @ C5 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_199_image__subset__iff,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,F: B > A,A6: set @ B,B6: set @ A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ F @ A6 ) @ B6 )
% 2.97/1.55 = ( ! [X4: B] :
% 2.97/1.55 ( ( member @ B @ X4 @ A6 )
% 2.97/1.55 => ( member @ A @ ( F @ X4 ) @ B6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_200_subset__image__iff,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,B6: set @ A,F: B > A,A6: set @ B] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ B6 @ ( image @ B @ A @ F @ A6 ) )
% 2.97/1.55 = ( ? [AA: set @ B] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ B ) @ AA @ A6 )
% 2.97/1.55 & ( B6
% 2.97/1.55 = ( image @ B @ A @ F @ AA ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_201_subrelI,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.97/1.55 ( ! [X: A,Y3: B] :
% 2.97/1.55 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y3 ) @ R )
% 2.97/1.55 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y3 ) @ S ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_202_wf__subset,axiom,
% 2.97/1.55 ! [A: $tType,R: set @ ( product_prod @ A @ A ),P: set @ ( product_prod @ A @ A )] :
% 2.97/1.55 ( ( wf @ A @ R )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ P @ R )
% 2.97/1.55 => ( wf @ A @ P ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_203_Collect__mono__iff,axiom,
% 2.97/1.55 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 2.97/1.55 = ( ! [X4: A] :
% 2.97/1.55 ( ( P2 @ X4 )
% 2.97/1.55 => ( Q @ X4 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_204_contra__subsetD,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A,C3: A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ~ ( member @ A @ C3 @ B6 )
% 2.97/1.55 => ~ ( member @ A @ C3 @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_205_set__eq__subset,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 2.97/1.55 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 2.97/1.55 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_206_subset__trans,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A,C4: set @ A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ A6 @ C4 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_207_Collect__mono,axiom,
% 2.97/1.55 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.97/1.55 ( ! [X: A] :
% 2.97/1.55 ( ( P2 @ X )
% 2.97/1.55 => ( Q @ X ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_208_subset__refl,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A] : ( ord_less_eq @ ( set @ A ) @ A6 @ A6 ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_209_rev__subsetD,axiom,
% 2.97/1.55 ! [A: $tType,C3: A,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( member @ A @ C3 @ A6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( member @ A @ C3 @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_210_subset__iff,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 2.97/1.55 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.97/1.55 ! [T3: A] :
% 2.97/1.55 ( ( member @ A @ T3 @ A7 )
% 2.97/1.55 => ( member @ A @ T3 @ B7 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_211_set__rev__mp,axiom,
% 2.97/1.55 ! [A: $tType,X3: A,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( member @ A @ X3 @ A6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( member @ A @ X3 @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_212_equalityD2,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( A6 = B6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_213_equalityD1,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( A6 = B6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ A6 @ B6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_214_subset__eq,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 2.97/1.55 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.97/1.55 ! [X4: A] :
% 2.97/1.55 ( ( member @ A @ X4 @ A7 )
% 2.97/1.55 => ( member @ A @ X4 @ B7 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_215_equalityE,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( A6 = B6 )
% 2.97/1.55 => ~ ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_216_subsetCE,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A,C3: A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( member @ A @ C3 @ A6 )
% 2.97/1.55 => ( member @ A @ C3 @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_217_subsetD,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A,C3: A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( member @ A @ C3 @ A6 )
% 2.97/1.55 => ( member @ A @ C3 @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_218_in__mono,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A,X3: A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( member @ A @ X3 @ A6 )
% 2.97/1.55 => ( member @ A @ X3 @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_219_set__mp,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A,X3: A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ( member @ A @ X3 @ A6 )
% 2.97/1.55 => ( member @ A @ X3 @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_220_subset__UNIV,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A] : ( ord_less_eq @ ( set @ A ) @ A6 @ ( top_top @ ( set @ A ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_221_top_Oextremum__uniqueI,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( order_top @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A2: A] :
% 2.97/1.55 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 2.97/1.55 => ( A2
% 2.97/1.55 = ( top_top @ A ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_222_top_Oextremum__unique,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( order_top @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A2: A] :
% 2.97/1.55 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 2.97/1.55 = ( A2
% 2.97/1.55 = ( top_top @ A ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_223_top__greatest,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( order_top @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( top_top @ A ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_224_Sup__subset__mono,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ ( complete_Sup_Sup @ A @ B6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_225_Sup__upper2,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [U: A,A6: set @ A,V: A] :
% 2.97/1.55 ( ( member @ A @ U @ A6 )
% 2.97/1.55 => ( ( ord_less_eq @ A @ V @ U )
% 2.97/1.55 => ( ord_less_eq @ A @ V @ ( complete_Sup_Sup @ A @ A6 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_226_Sup__le__iff,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A6: set @ A,B2: A] :
% 2.97/1.55 ( ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ B2 )
% 2.97/1.55 = ( ! [X4: A] :
% 2.97/1.55 ( ( member @ A @ X4 @ A6 )
% 2.97/1.55 => ( ord_less_eq @ A @ X4 @ B2 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_227_Sup__upper,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [X3: A,A6: set @ A] :
% 2.97/1.55 ( ( member @ A @ X3 @ A6 )
% 2.97/1.55 => ( ord_less_eq @ A @ X3 @ ( complete_Sup_Sup @ A @ A6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_228_Sup__least,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A6: set @ A,Z2: A] :
% 2.97/1.55 ( ! [X: A] :
% 2.97/1.55 ( ( member @ A @ X @ A6 )
% 2.97/1.55 => ( ord_less_eq @ A @ X @ Z2 ) )
% 2.97/1.55 => ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ Z2 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_229_Sup__mono,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ! [A4: A] :
% 2.97/1.55 ( ( member @ A @ A4 @ A6 )
% 2.97/1.55 => ? [X6: A] :
% 2.97/1.55 ( ( member @ A @ X6 @ B6 )
% 2.97/1.55 & ( ord_less_eq @ A @ A4 @ X6 ) ) )
% 2.97/1.55 => ( ord_less_eq @ A @ ( complete_Sup_Sup @ A @ A6 ) @ ( complete_Sup_Sup @ A @ B6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_230_Sup__eqI,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A6: set @ A,X3: A] :
% 2.97/1.55 ( ! [Y3: A] :
% 2.97/1.55 ( ( member @ A @ Y3 @ A6 )
% 2.97/1.55 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 2.97/1.55 => ( ! [Y3: A] :
% 2.97/1.55 ( ! [Z4: A] :
% 2.97/1.55 ( ( member @ A @ Z4 @ A6 )
% 2.97/1.55 => ( ord_less_eq @ A @ Z4 @ Y3 ) )
% 2.97/1.55 => ( ord_less_eq @ A @ X3 @ Y3 ) )
% 2.97/1.55 => ( ( complete_Sup_Sup @ A @ A6 )
% 2.97/1.55 = X3 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_231_Union__upper,axiom,
% 2.97/1.55 ! [A: $tType,B6: set @ A,A6: set @ ( set @ A )] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ B6 @ A6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ B6 @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_232_Union__least,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ ( set @ A ),C4: set @ A] :
% 2.97/1.55 ( ! [X8: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ X8 @ A6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ X8 @ C4 ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) @ C4 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_233_Union__mono,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ ( set @ A ),B6: set @ ( set @ A )] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ ( set @ A ) ) @ A6 @ B6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ A6 ) @ ( complete_Sup_Sup @ ( set @ A ) @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_234_SUP__eq,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,C: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.97/1.55 => ! [A6: set @ B,B6: set @ C,F: B > A,G3: C > A] :
% 2.97/1.55 ( ! [I: B] :
% 2.97/1.55 ( ( member @ B @ I @ A6 )
% 2.97/1.55 => ? [X6: C] :
% 2.97/1.55 ( ( member @ C @ X6 @ B6 )
% 2.97/1.55 & ( ord_less_eq @ A @ ( F @ I ) @ ( G3 @ X6 ) ) ) )
% 2.97/1.55 => ( ! [J: C] :
% 2.97/1.55 ( ( member @ C @ J @ B6 )
% 2.97/1.55 => ? [X6: B] :
% 2.97/1.55 ( ( member @ B @ X6 @ A6 )
% 2.97/1.55 & ( ord_less_eq @ A @ ( G3 @ J ) @ ( F @ X6 ) ) ) )
% 2.97/1.55 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ A6 ) )
% 2.97/1.55 = ( complete_Sup_Sup @ A @ ( image @ C @ A @ G3 @ B6 ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_235_inj__image__subset__iff,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) @ ( image @ A @ B @ F @ B6 ) )
% 2.97/1.55 = ( ord_less_eq @ ( set @ A ) @ A6 @ B6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_236_the__inv__into__into,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,X3: B,B6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ A6 )
% 2.97/1.55 => ( ( member @ B @ X3 @ ( image @ A @ B @ F @ A6 ) )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( member @ A @ ( the_inv_into @ A @ B @ A6 @ F @ X3 ) @ B6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_237_Zorn__Lemma,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ ( set @ A )] :
% 2.97/1.55 ( ! [X: set @ ( set @ A )] :
% 2.97/1.55 ( ( member @ ( set @ ( set @ A ) ) @ X @ ( chains2 @ A @ A6 ) )
% 2.97/1.55 => ( member @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ X ) @ A6 ) )
% 2.97/1.55 => ? [X: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ X @ A6 )
% 2.97/1.55 & ! [Xa: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ Xa @ A6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ X @ Xa )
% 2.97/1.55 => ( Xa = X ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_238_inj__image__Compl__subset,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ ( uminus_uminus @ ( set @ A ) @ A6 ) ) @ ( uminus_uminus @ ( set @ B ) @ ( image @ A @ B @ F @ A6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_239_ComplI,axiom,
% 2.97/1.55 ! [A: $tType,C3: A,A6: set @ A] :
% 2.97/1.55 ( ~ ( member @ A @ C3 @ A6 )
% 2.97/1.55 => ( member @ A @ C3 @ ( uminus_uminus @ ( set @ A ) @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_240_Compl__iff,axiom,
% 2.97/1.55 ! [A: $tType,C3: A,A6: set @ A] :
% 2.97/1.55 ( ( member @ A @ C3 @ ( uminus_uminus @ ( set @ A ) @ A6 ) )
% 2.97/1.55 = ( ~ ( member @ A @ C3 @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_241_Compl__eq__Compl__iff,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( ( uminus_uminus @ ( set @ A ) @ A6 )
% 2.97/1.55 = ( uminus_uminus @ ( set @ A ) @ B6 ) )
% 2.97/1.55 = ( A6 = B6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_242_Compl__subset__Compl__iff,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A6 ) @ ( uminus_uminus @ ( set @ A ) @ B6 ) )
% 2.97/1.55 = ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_243_Compl__anti__mono,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A,B6: set @ A] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B6 ) @ ( uminus_uminus @ ( set @ A ) @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_244_sp_092_060_094sub_062_092_060mu_062_Orel__mono,axiom,
% 2.97/1.55 ! [A: $tType,C: $tType,G: $tType,D: $tType,B: $tType,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 2.97/1.55 ( ( ord_less_eq @ ( A > C > $o ) @ R1 @ R1a )
% 2.97/1.55 => ( ( ord_less_eq @ ( B > D > $o ) @ R22 @ R2a )
% 2.97/1.55 => ( ord_less_eq @ ( ( stream901396144_sp_mu @ G @ A @ B ) > ( stream901396144_sp_mu @ G @ C @ D ) > $o ) @ ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1 @ R22 ) @ ( stream1924447089_sp_mu @ A @ C @ B @ D @ G @ R1a @ R2a ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_245_chainsD2,axiom,
% 2.97/1.55 ! [A: $tType,C3: set @ ( set @ A ),S4: set @ ( set @ A )] :
% 2.97/1.55 ( ( member @ ( set @ ( set @ A ) ) @ C3 @ ( chains2 @ A @ S4 ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ C3 @ S4 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_246_Collect__case__prod__mono,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,A6: A > B > $o,B6: A > B > $o] :
% 2.97/1.55 ( ( ord_less_eq @ ( A > B > $o ) @ A6 @ B6 )
% 2.97/1.55 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ A6 ) ) @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ B6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_247_ComplD,axiom,
% 2.97/1.55 ! [A: $tType,C3: A,A6: set @ A] :
% 2.97/1.55 ( ( member @ A @ C3 @ ( uminus_uminus @ ( set @ A ) @ A6 ) )
% 2.97/1.55 => ~ ( member @ A @ C3 @ A6 ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_248_double__complement,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ A] :
% 2.97/1.55 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A6 ) )
% 2.97/1.55 = A6 ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_249_chainsD,axiom,
% 2.97/1.55 ! [A: $tType,C3: set @ ( set @ A ),S4: set @ ( set @ A ),X3: set @ A,Y: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ ( set @ A ) ) @ C3 @ ( chains2 @ A @ S4 ) )
% 2.97/1.55 => ( ( member @ ( set @ A ) @ X3 @ C3 )
% 2.97/1.55 => ( ( member @ ( set @ A ) @ Y @ C3 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ X3 @ Y )
% 2.97/1.55 | ( ord_less_eq @ ( set @ A ) @ Y @ X3 ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_250_Zorn__Lemma2,axiom,
% 2.97/1.55 ! [A: $tType,A6: set @ ( set @ A )] :
% 2.97/1.55 ( ! [X: set @ ( set @ A )] :
% 2.97/1.55 ( ( member @ ( set @ ( set @ A ) ) @ X @ ( chains2 @ A @ A6 ) )
% 2.97/1.55 => ? [Xa: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ Xa @ A6 )
% 2.97/1.55 & ! [Xb: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ Xb @ X )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ Xb @ Xa ) ) ) )
% 2.97/1.55 => ? [X: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ X @ A6 )
% 2.97/1.55 & ! [Xa: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ Xa @ A6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ X @ Xa )
% 2.97/1.55 => ( Xa = X ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_251_surj__Compl__image__subset,axiom,
% 2.97/1.55 ! [A: $tType,B: $tType,F: B > A,A6: set @ B] :
% 2.97/1.55 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 2.97/1.55 = ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ ( image @ B @ A @ F @ A6 ) ) @ ( image @ B @ A @ F @ ( uminus_uminus @ ( set @ B ) @ A6 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_252_mono__Chains,axiom,
% 2.97/1.55 ! [A: $tType,R: set @ ( product_prod @ A @ A ),S: set @ ( product_prod @ A @ A )] :
% 2.97/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ S )
% 2.97/1.55 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( chains @ A @ R ) @ ( chains @ A @ S ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_253_relChain__def,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType] :
% 2.97/1.55 ( ( ord @ B @ ( type2 @ B ) )
% 2.97/1.55 => ( ( bNF_Ca1785829860lChain @ A @ B )
% 2.97/1.55 = ( ^ [R3: set @ ( product_prod @ A @ A ),As: A > B] :
% 2.97/1.55 ! [I2: A,J2: A] :
% 2.97/1.55 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ I2 @ J2 ) @ R3 )
% 2.97/1.55 => ( ord_less_eq @ B @ ( As @ I2 ) @ ( As @ J2 ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_254_chain__subset__def,axiom,
% 2.97/1.55 ! [A: $tType] :
% 2.97/1.55 ( ( chain_subset @ A )
% 2.97/1.55 = ( ^ [C6: set @ ( set @ A )] :
% 2.97/1.55 ! [X4: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ X4 @ C6 )
% 2.97/1.55 => ! [Y5: set @ A] :
% 2.97/1.55 ( ( member @ ( set @ A ) @ Y5 @ C6 )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ A ) @ X4 @ Y5 )
% 2.97/1.55 | ( ord_less_eq @ ( set @ A ) @ Y5 @ X4 ) ) ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(fact_255_vimage__subsetI,axiom,
% 2.97/1.55 ! [B: $tType,A: $tType,F: A > B,B6: set @ B,A6: set @ A] :
% 2.97/1.55 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 2.97/1.55 => ( ( ord_less_eq @ ( set @ B ) @ B6 @ ( image @ A @ B @ F @ A6 ) )
% 2.97/1.55 => ( ord_less_eq @ ( set @ A ) @ ( vimage @ A @ B @ F @ B6 ) @ A6 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 2.97/1.55 ! [A8: $tType,A9: $tType] :
% 2.97/1.55 ( ( comple187826305attice @ A9 @ ( type2 @ A9 ) )
% 2.97/1.55 => ( comple187826305attice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 2.97/1.55 ! [A8: $tType,A9: $tType] :
% 2.97/1.55 ( ( complete_Sup @ A9 @ ( type2 @ A9 ) )
% 2.97/1.55 => ( complete_Sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 2.97/1.55 ! [A8: $tType,A9: $tType] :
% 2.97/1.55 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 2.97/1.55 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_fun___Orderings_Otop,axiom,
% 2.97/1.55 ! [A8: $tType,A9: $tType] :
% 2.97/1.55 ( ( top @ A9 @ ( type2 @ A9 ) )
% 2.97/1.55 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_fun___Orderings_Oord,axiom,
% 2.97/1.55 ! [A8: $tType,A9: $tType] :
% 2.97/1.55 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 2.97/1.55 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 2.97/1.55 ! [A8: $tType] : ( comple187826305attice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_Set_Oset___Complete__Lattices_OSup_2,axiom,
% 2.97/1.55 ! [A8: $tType] : ( complete_Sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_Set_Oset___Orderings_Oorder__top_3,axiom,
% 2.97/1.55 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 2.97/1.55 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 2.97/1.55 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_6,axiom,
% 2.97/1.55 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_HOL_Obool___Complete__Lattices_OSup_7,axiom,
% 2.97/1.55 complete_Sup @ $o @ ( type2 @ $o ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_HOL_Obool___Orderings_Oorder__top_8,axiom,
% 2.97/1.55 order_top @ $o @ ( type2 @ $o ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_HOL_Obool___Orderings_Otop_9,axiom,
% 2.97/1.55 top @ $o @ ( type2 @ $o ) ).
% 2.97/1.55
% 2.97/1.55 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 2.97/1.55 ord @ $o @ ( type2 @ $o ) ).
% 2.97/1.55
% 2.97/1.55 thf(conj_0,hypothesis,
% 2.97/1.55 ! [B8: b,Sp2: c,Fsp: stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a )] :
% 2.97/1.55 ( ( x
% 2.97/1.55 = ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1370332830mu_Put @ b @ c @ a @ B8 @ Sp2 ) @ Fsp ) )
% 2.97/1.55 => p ) ).
% 2.97/1.55
% 2.97/1.55 thf(conj_1,hypothesis,
% 2.97/1.55 ! [F5: a > ( stream901396144_sp_mu @ a @ b @ c ),B8: a,Sp2: stream1273403375_sp_nu @ d @ a] :
% 2.97/1.55 ( ( x
% 2.97/1.55 = ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ F5 ) @ ( stream1370332830mu_Put @ a @ ( stream1273403375_sp_nu @ d @ a ) @ d @ B8 @ Sp2 ) ) )
% 2.97/1.55 => p ) ).
% 2.97/1.55
% 2.97/1.55 thf(conj_2,hypothesis,
% 2.97/1.55 ! [F5: a > ( stream901396144_sp_mu @ a @ b @ c ),G4: d > ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) )] :
% 2.97/1.55 ( ( x
% 2.97/1.55 = ( product_Pair @ ( stream901396144_sp_mu @ a @ b @ c ) @ ( stream901396144_sp_mu @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) ) @ ( stream1294929701mu_Get @ a @ b @ c @ F5 ) @ ( stream1294929701mu_Get @ d @ a @ ( stream1273403375_sp_nu @ d @ a ) @ G4 ) ) )
% 2.97/1.55 => p ) ).
% 2.97/1.55
% 2.97/1.55 thf(conj_3,conjecture,
% 2.97/1.55 p ).
% 2.97/1.55 ------------------------
% 2.97/1.57 % (27399)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/183Mi)
% 2.97/1.57 % (27402)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/2Mi)
% 2.97/1.57 % (27401)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/27Mi)
% 2.97/1.57 % (27400)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/4Mi)
% 2.97/1.57 % (27404)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/275Mi)
% 2.97/1.57 % (27405)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/18Mi)
% 2.97/1.57 % (27403)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/2Mi)
% 2.97/1.58 % (27402)Instruction limit reached!
% 2.97/1.58 % (27402)------------------------------
% 2.97/1.58 % (27402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.58 % (27402)Termination reason: Unknown
% 2.97/1.58 % (27402)Termination phase: shuffling
% 2.97/1.58 % (27403)Instruction limit reached!
% 2.97/1.58 % (27403)------------------------------
% 2.97/1.58 % (27403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.58 % (27403)Termination reason: Unknown
% 2.97/1.58 % (27403)Termination phase: shuffling
% 2.97/1.58
% 2.97/1.58 % (27403)Memory used [KB]: 1535
% 2.97/1.58 % (27403)Time elapsed: 0.003 s
% 2.97/1.58 % (27403)Instructions burned: 3 (million)
% 2.97/1.58 % (27403)------------------------------
% 2.97/1.58 % (27403)------------------------------
% 2.97/1.58
% 2.97/1.58 % (27402)Memory used [KB]: 1535
% 2.97/1.58 % (27402)Time elapsed: 0.003 s
% 2.97/1.58 % (27402)Instructions burned: 3 (million)
% 2.97/1.58 % (27402)------------------------------
% 2.97/1.58 % (27402)------------------------------
% 2.97/1.58 % (27400)Instruction limit reached!
% 2.97/1.58 % (27400)------------------------------
% 2.97/1.58 % (27400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.58 % (27400)Termination reason: Unknown
% 2.97/1.58 % (27400)Termination phase: shuffling
% 2.97/1.58
% 2.97/1.58 % (27400)Memory used [KB]: 1535
% 2.97/1.58 % (27400)Time elapsed: 0.004 s
% 2.97/1.58 % (27400)Instructions burned: 5 (million)
% 2.97/1.58 % (27400)------------------------------
% 2.97/1.58 % (27400)------------------------------
% 2.97/1.58 % (27405)Instruction limit reached!
% 2.97/1.58 % (27405)------------------------------
% 2.97/1.58 % (27405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.58 % (27405)Termination reason: Unknown
% 2.97/1.58 % (27405)Termination phase: shuffling
% 2.97/1.58
% 2.97/1.58 % (27405)Memory used [KB]: 1918
% 2.97/1.58 % (27405)Time elapsed: 0.011 s
% 2.97/1.58 % (27405)Instructions burned: 19 (million)
% 2.97/1.58 % (27405)------------------------------
% 2.97/1.58 % (27405)------------------------------
% 2.97/1.59 % (27401)Instruction limit reached!
% 2.97/1.59 % (27401)------------------------------
% 2.97/1.59 % (27401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.59 % (27401)Termination reason: Unknown
% 2.97/1.59 % (27401)Termination phase: shuffling
% 2.97/1.59
% 2.97/1.59 % (27401)Memory used [KB]: 2046
% 2.97/1.59 % (27401)Time elapsed: 0.015 s
% 2.97/1.59 % (27401)Instructions burned: 27 (million)
% 2.97/1.59 % (27401)------------------------------
% 2.97/1.59 % (27401)------------------------------
% 2.97/1.59 % (27406)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/3Mi)
% 2.97/1.59 % (27407)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/37Mi)
% 2.97/1.59 % (27408)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/15Mi)
% 2.97/1.59 % (27406)Instruction limit reached!
% 2.97/1.59 % (27406)------------------------------
% 2.97/1.59 % (27406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.59 % (27406)Termination reason: Unknown
% 2.97/1.59 % (27406)Termination phase: shuffling
% 2.97/1.59
% 2.97/1.59 % (27406)Memory used [KB]: 1535
% 2.97/1.59 % (27406)Time elapsed: 0.003 s
% 2.97/1.59 % (27406)Instructions burned: 3 (million)
% 2.97/1.59 % (27406)------------------------------
% 2.97/1.59 % (27406)------------------------------
% 3.02/1.60 % (27409)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/3Mi)
% 3.02/1.60 % (27408)Instruction limit reached!
% 3.02/1.60 % (27408)------------------------------
% 3.02/1.60 % (27408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (27408)Termination reason: Unknown
% 3.02/1.60 % (27408)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (27408)Memory used [KB]: 1918
% 3.02/1.60 % (27408)Time elapsed: 0.010 s
% 3.02/1.60 % (27408)Instructions burned: 16 (million)
% 3.02/1.60 % (27408)------------------------------
% 3.02/1.60 % (27408)------------------------------
% 3.02/1.60 % (27409)Instruction limit reached!
% 3.02/1.60 % (27409)------------------------------
% 3.02/1.60 % (27409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (27409)Termination reason: Unknown
% 3.02/1.60 % (27409)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (27409)Memory used [KB]: 1535
% 3.02/1.60 % (27409)Time elapsed: 0.003 s
% 3.02/1.60 % (27409)Instructions burned: 4 (million)
% 3.02/1.60 % (27409)------------------------------
% 3.02/1.60 % (27409)------------------------------
% 3.02/1.61 % (27410)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/1041Mi)
% 3.02/1.61 % (27407)Instruction limit reached!
% 3.02/1.61 % (27407)------------------------------
% 3.02/1.61 % (27407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (27407)Termination reason: Unknown
% 3.02/1.61 % (27407)Termination phase: shuffling
% 3.02/1.61
% 3.02/1.61 % (27407)Memory used [KB]: 2302
% 3.02/1.61 % (27407)Time elapsed: 0.019 s
% 3.02/1.61 % (27407)Instructions burned: 38 (million)
% 3.02/1.61 % (27407)------------------------------
% 3.02/1.61 % (27407)------------------------------
% 3.02/1.61 % (27411)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/7Mi)
% 3.02/1.62 % (27411)Instruction limit reached!
% 3.02/1.62 % (27411)------------------------------
% 3.02/1.62 % (27411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (27411)Termination reason: Unknown
% 3.02/1.62 % (27411)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (27411)Memory used [KB]: 1663
% 3.02/1.62 % (27411)Time elapsed: 0.005 s
% 3.02/1.62 % (27411)Instructions burned: 7 (million)
% 3.02/1.62 % (27411)------------------------------
% 3.02/1.62 % (27411)------------------------------
% 3.02/1.62 % (27412)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/16Mi)
% 3.02/1.62 % (27399)Instruction limit reached!
% 3.02/1.62 % (27399)------------------------------
% 3.02/1.62 % (27399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (27399)Termination reason: Unknown
% 3.02/1.62 % (27399)Termination phase: Saturation
% 3.02/1.62
% 3.02/1.62 % (27399)Memory used [KB]: 7547
% 3.02/1.62 % (27399)Time elapsed: 0.056 s
% 3.02/1.62 % (27399)Instructions burned: 184 (million)
% 3.02/1.62 % (27399)------------------------------
% 3.02/1.62 % (27399)------------------------------
% 3.02/1.63 % (27414)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/3Mi)
% 3.02/1.63 % (27413)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/3Mi)
% 3.02/1.63 % (27412)Instruction limit reached!
% 3.02/1.63 % (27412)------------------------------
% 3.02/1.63 % (27412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63 % (27412)Termination reason: Unknown
% 3.02/1.63 % (27412)Termination phase: shuffling
% 3.02/1.63
% 3.02/1.63 % (27412)Memory used [KB]: 1918
% 3.02/1.63 % (27412)Time elapsed: 0.010 s
% 3.02/1.63 % (27412)Instructions burned: 17 (million)
% 3.02/1.63 % (27412)------------------------------
% 3.02/1.63 % (27412)------------------------------
% 3.02/1.63 % (27413)Instruction limit reached!
% 3.02/1.63 % (27413)------------------------------
% 3.02/1.63 % (27413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63 % (27413)Termination reason: Unknown
% 3.02/1.63 % (27413)Termination phase: shuffling
% 3.02/1.63 % (27414)Instruction limit reached!
% 3.02/1.63 % (27414)------------------------------
% 3.02/1.63 % (27414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63
% 3.02/1.63 % (27413)Memory used [KB]: 1535
% 3.02/1.63 % (27413)Time elapsed: 0.003 s
% 3.02/1.63 % (27413)Instructions burned: 3 (million)
% 3.02/1.63 % (27413)------------------------------
% 3.02/1.63 % (27413)------------------------------
% 3.02/1.63 % (27414)Termination reason: Unknown
% 3.02/1.63 % (27414)Termination phase: shuffling
% 3.02/1.63
% 3.02/1.63 % (27414)Memory used [KB]: 1535
% 3.02/1.63 % (27414)Time elapsed: 0.003 s
% 3.02/1.63 % (27414)Instructions burned: 3 (million)
% 3.02/1.63 % (27414)------------------------------
% 3.02/1.63 % (27414)------------------------------
% 3.02/1.63 % (27415)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/7Mi)
% 3.02/1.63 % (27416)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/3Mi)
% 3.02/1.63 % (27416)Instruction limit reached!
% 3.02/1.63 % (27416)------------------------------
% 3.02/1.63 % (27416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63 % (27416)Termination reason: Unknown
% 3.02/1.63 % (27416)Termination phase: shuffling
% 3.02/1.63
% 3.02/1.63 % (27416)Memory used [KB]: 1535
% 3.02/1.63 % (27416)Time elapsed: 0.002 s
% 3.02/1.63 % (27416)Instructions burned: 3 (million)
% 3.02/1.63 % (27416)------------------------------
% 3.02/1.63 % (27416)------------------------------
% 3.02/1.63 % (27415)Instruction limit reached!
% 3.02/1.63 % (27415)------------------------------
% 3.02/1.63 % (27415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63 % (27415)Termination reason: Unknown
% 3.02/1.63 % (27415)Termination phase: shuffling
% 3.02/1.63
% 3.02/1.63 % (27415)Memory used [KB]: 1663
% 3.02/1.63 % (27415)Time elapsed: 0.005 s
% 3.02/1.63 % (27415)Instructions burned: 7 (million)
% 3.02/1.63 % (27415)------------------------------
% 3.02/1.63 % (27415)------------------------------
% 3.02/1.64 % (27417)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/4Mi)
% 3.02/1.64 % (27420)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/6Mi)
% 3.02/1.64 % (27419)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/710Mi)
% 3.02/1.64 % (27417)Instruction limit reached!
% 3.02/1.64 % (27417)------------------------------
% 3.02/1.64 % (27417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (27417)Termination reason: Unknown
% 3.02/1.64 % (27417)Termination phase: shuffling
% 3.02/1.64
% 3.02/1.64 % (27417)Memory used [KB]: 1535
% 3.02/1.64 % (27417)Time elapsed: 0.003 s
% 3.02/1.64 % (27417)Instructions burned: 4 (million)
% 3.02/1.64 % (27417)------------------------------
% 3.02/1.64 % (27417)------------------------------
% 3.02/1.64 % (27418)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/18Mi)
% 3.02/1.65 % (27420)Instruction limit reached!
% 3.02/1.65 % (27420)------------------------------
% 3.02/1.65 % (27420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.65 % (27420)Termination reason: Unknown
% 3.02/1.65 % (27420)Termination phase: shuffling
% 3.02/1.65
% 3.02/1.65 % (27420)Memory used [KB]: 1663
% 3.02/1.65 % (27420)Time elapsed: 0.003 s
% 3.02/1.65 % (27420)Instructions burned: 6 (million)
% 3.02/1.65 % (27420)------------------------------
% 3.02/1.65 % (27420)------------------------------
% 3.02/1.65 % (27421)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/902Mi)
% 3.02/1.65 % (27418)Instruction limit reached!
% 3.02/1.65 % (27418)------------------------------
% 3.02/1.65 % (27418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.65 % (27418)Termination reason: Unknown
% 3.02/1.65 % (27418)Termination phase: shuffling
% 3.02/1.65
% 3.02/1.65 % (27418)Memory used [KB]: 1918
% 3.02/1.65 % (27418)Time elapsed: 0.011 s
% 3.02/1.65 % (27418)Instructions burned: 19 (million)
% 3.02/1.65 % (27418)------------------------------
% 3.02/1.65 % (27418)------------------------------
% 3.02/1.65 % (27423)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/5Mi)
% 3.02/1.66 % (27423)Instruction limit reached!
% 3.02/1.66 % (27423)------------------------------
% 3.02/1.66 % (27423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66 % (27423)Termination reason: Unknown
% 3.02/1.66 % (27423)Termination phase: shuffling
% 3.02/1.66
% 3.02/1.66 % (27423)Memory used [KB]: 1663
% 3.02/1.66 % (27423)Time elapsed: 0.003 s
% 3.02/1.66 % (27423)Instructions burned: 7 (million)
% 3.02/1.66 % (27423)------------------------------
% 3.02/1.66 % (27423)------------------------------
% 3.02/1.66 % (27422)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/21Mi)
% 3.02/1.67 % (27425)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/377Mi)
% 3.02/1.67 % (27424)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/6Mi)
% 3.02/1.67 % (27422)Instruction limit reached!
% 3.02/1.67 % (27422)------------------------------
% 3.02/1.67 % (27422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67 % (27422)Termination reason: Unknown
% 3.02/1.67 % (27422)Termination phase: shuffling
% 3.02/1.67
% 3.02/1.67 % (27422)Memory used [KB]: 1918
% 3.02/1.67 % (27422)Time elapsed: 0.012 s
% 3.02/1.67 % (27422)Instructions burned: 21 (million)
% 3.02/1.67 % (27422)------------------------------
% 3.02/1.67 % (27422)------------------------------
% 3.02/1.67 % (27424)Instruction limit reached!
% 3.02/1.67 % (27424)------------------------------
% 3.02/1.67 % (27424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67 % (27424)Termination reason: Unknown
% 3.02/1.67 % (27424)Termination phase: shuffling
% 3.02/1.67
% 3.02/1.67 % (27424)Memory used [KB]: 1663
% 3.02/1.67 % (27424)Time elapsed: 0.004 s
% 3.02/1.67 % (27424)Instructions burned: 6 (million)
% 3.02/1.67 % (27424)------------------------------
% 3.02/1.67 % (27424)------------------------------
% 3.02/1.69 % (27426)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_27294 for (2998ds/779Mi)
% 3.02/1.69 % (27427)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_27294 for (2998ds/19Mi)
% 3.02/1.70 % (27427)Instruction limit reached!
% 3.02/1.70 % (27427)------------------------------
% 3.02/1.70 % (27427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.70 % (27427)Termination reason: Unknown
% 3.02/1.70 % (27427)Termination phase: shuffling
% 3.02/1.70
% 3.02/1.70 % (27427)Memory used [KB]: 1918
% 3.02/1.70 % (27427)Time elapsed: 0.010 s
% 3.02/1.70 % (27427)Instructions burned: 19 (million)
% 3.02/1.70 % (27427)------------------------------
% 3.02/1.70 % (27427)------------------------------
% 3.02/1.71 % (27404)Instruction limit reached!
% 3.02/1.71 % (27404)------------------------------
% 3.02/1.71 % (27404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (27404)Termination reason: Unknown
% 3.02/1.71 % (27404)Termination phase: Saturation
% 3.02/1.71
% 3.02/1.71 % (27404)Memory used [KB]: 7419
% 3.02/1.71 % (27404)Time elapsed: 0.134 s
% 3.02/1.71 % (27404)Instructions burned: 276 (million)
% 3.02/1.71 % (27404)------------------------------
% 3.02/1.71 % (27404)------------------------------
% 3.02/1.71 % (27428)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27294 for (2998ds/879Mi)
% 3.02/1.72 % (27429)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27294 for (2998ds/17Mi)
% 3.02/1.73 % (27429)Instruction limit reached!
% 3.02/1.73 % (27429)------------------------------
% 3.02/1.73 % (27429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.73 % (27429)Termination reason: Unknown
% 3.02/1.73 % (27429)Termination phase: shuffling
% 3.02/1.73
% 3.02/1.73 % (27429)Memory used [KB]: 1918
% 3.02/1.73 % (27429)Time elapsed: 0.010 s
% 3.02/1.73 % (27429)Instructions burned: 17 (million)
% 3.02/1.73 % (27429)------------------------------
% 3.02/1.73 % (27429)------------------------------
% 3.02/1.75 % (27430)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2998ds/3Mi)
% 3.02/1.75 % (27430)Instruction limit reached!
% 3.02/1.75 % (27430)------------------------------
% 3.02/1.75 % (27430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.75 % (27430)Termination reason: Unknown
% 3.02/1.75 % (27430)Termination phase: shuffling
% 3.02/1.75
% 3.02/1.75 % (27430)Memory used [KB]: 1535
% 3.02/1.75 % (27430)Time elapsed: 0.004 s
% 3.02/1.75 % (27430)Instructions burned: 4 (million)
% 3.02/1.75 % (27430)------------------------------
% 3.02/1.75 % (27430)------------------------------
% 3.02/1.77 % (27431)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27294 for (2998ds/30Mi)
% 3.02/1.78 % (27431)Instruction limit reached!
% 3.02/1.78 % (27431)------------------------------
% 3.02/1.78 % (27431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.78 % (27431)Termination reason: Unknown
% 3.02/1.78 % (27431)Termination phase: shuffling
% 3.02/1.78
% 3.02/1.78 % (27431)Memory used [KB]: 2174
% 3.02/1.78 % (27431)Time elapsed: 0.017 s
% 3.02/1.78 % (27431)Instructions burned: 30 (million)
% 3.02/1.78 % (27431)------------------------------
% 3.02/1.78 % (27431)------------------------------
% 3.02/1.80 % (27432)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27294 for (2997ds/127Mi)
% 3.02/1.83 % (27425)Instruction limit reached!
% 3.02/1.83 % (27425)------------------------------
% 3.02/1.83 % (27425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.83 % (27425)Termination reason: Unknown
% 3.02/1.83 % (27425)Termination phase: Saturation
% 3.02/1.83
% 3.02/1.83 % (27425)Memory used [KB]: 8827
% 3.02/1.83 % (27425)Time elapsed: 0.167 s
% 3.02/1.83 % (27425)Instructions burned: 378 (million)
% 3.02/1.83 % (27425)------------------------------
% 3.02/1.83 % (27425)------------------------------
% 3.02/1.84 % (27433)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27294 for (2997ds/100Mi)
% 3.02/1.86 % (27432)Instruction limit reached!
% 3.02/1.86 % (27432)------------------------------
% 3.02/1.86 % (27432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.86 % (27432)Termination reason: Unknown
% 3.02/1.86 % (27432)Termination phase: Saturation
% 3.02/1.86
% 3.02/1.86 % (27432)Memory used [KB]: 7291
% 3.02/1.86 % (27432)Time elapsed: 0.062 s
% 3.02/1.86 % (27432)Instructions burned: 127 (million)
% 3.02/1.86 % (27432)------------------------------
% 3.02/1.86 % (27432)------------------------------
% 3.02/1.88 % (27433)Instruction limit reached!
% 3.02/1.88 % (27433)------------------------------
% 3.02/1.88 % (27433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.88 % (27433)Termination reason: Unknown
% 3.02/1.88 % (27433)Termination phase: Preprocessing 3
% 3.02/1.88
% 3.02/1.88 % (27433)Memory used [KB]: 2814
% 3.02/1.88 % (27433)Time elapsed: 0.036 s
% 3.02/1.88 % (27433)Instructions burned: 100 (million)
% 3.02/1.88 % (27433)------------------------------
% 3.02/1.88 % (27433)------------------------------
% 3.02/1.88 % (27434)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2997ds/3Mi)
% 3.02/1.88 % (27434)Instruction limit reached!
% 3.02/1.88 % (27434)------------------------------
% 3.02/1.88 % (27434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.88 % (27434)Termination reason: Unknown
% 3.02/1.88 % (27434)Termination phase: shuffling
% 3.02/1.88
% 3.02/1.88 % (27434)Memory used [KB]: 1535
% 3.02/1.88 % (27434)Time elapsed: 0.003 s
% 3.02/1.88 % (27434)Instructions burned: 3 (million)
% 3.02/1.88 % (27434)------------------------------
% 3.02/1.88 % (27434)------------------------------
% 3.02/1.89 % (27435)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_27294 for (2996ds/20Mi)
% 3.02/1.89 % (27436)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_27294 for (2996ds/86Mi)
% 3.02/1.90 % (27435)Instruction limit reached!
% 3.02/1.90 % (27435)------------------------------
% 3.02/1.90 % (27435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.90 % (27435)Termination reason: Unknown
% 3.02/1.90 % (27435)Termination phase: shuffling
% 3.02/1.90
% 3.02/1.90 % (27435)Memory used [KB]: 1918
% 3.02/1.90 % (27435)Time elapsed: 0.012 s
% 3.02/1.90 % (27435)Instructions burned: 21 (million)
% 3.02/1.90 % (27435)------------------------------
% 3.02/1.90 % (27435)------------------------------
% 3.02/1.91 % (27437)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_27294 for (2996ds/107Mi)
% 3.02/1.94 % (27436)Instruction limit reached!
% 3.02/1.94 % (27436)------------------------------
% 3.02/1.94 % (27436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.94 % (27436)Termination reason: Unknown
% 3.02/1.94 % (27436)Termination phase: Function definition elimination
% 3.02/1.94
% 3.02/1.94 % (27436)Memory used [KB]: 2686
% 3.02/1.94 % (27436)Time elapsed: 0.043 s
% 3.02/1.94 % (27436)Instructions burned: 87 (million)
% 3.02/1.94 % (27436)------------------------------
% 3.02/1.94 % (27436)------------------------------
% 3.02/1.95 % (27437)Instruction limit reached!
% 3.02/1.95 % (27437)------------------------------
% 3.02/1.95 % (27437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.95 % (27437)Termination reason: Unknown
% 3.02/1.95 % (27437)Termination phase: Saturation
% 3.02/1.95
% 3.02/1.95 % (27437)Memory used [KB]: 7291
% 3.02/1.95 % (27437)Time elapsed: 0.041 s
% 3.02/1.95 % (27437)Instructions burned: 110 (million)
% 3.02/1.95 % (27437)------------------------------
% 3.02/1.95 % (27437)------------------------------
% 3.02/1.95 % (27438)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_27294 for (2996ds/39Mi)
% 3.02/1.96 % (27439)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_27294 for (2996ds/448Mi)
% 3.02/1.97 % (27419)Instruction limit reached!
% 3.02/1.97 % (27419)------------------------------
% 3.02/1.97 % (27419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.97 % (27419)Termination reason: Unknown
% 3.02/1.97 % (27419)Termination phase: Saturation
% 3.02/1.97
% 3.02/1.97 % (27419)Memory used [KB]: 8571
% 3.02/1.97 % (27419)Time elapsed: 0.324 s
% 3.02/1.97 % (27419)Instructions burned: 710 (million)
% 3.02/1.97 % (27419)------------------------------
% 3.02/1.97 % (27419)------------------------------
% 3.02/1.97 % (27438)Instruction limit reached!
% 3.02/1.97 % (27438)------------------------------
% 3.02/1.97 % (27438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.97 % (27438)Termination reason: Unknown
% 3.02/1.97 % (27438)Termination phase: shuffling
% 3.02/1.97
% 3.02/1.97 % (27438)Memory used [KB]: 2302
% 3.02/1.97 % (27438)Time elapsed: 0.020 s
% 3.02/1.97 % (27438)Instructions burned: 40 (million)
% 3.02/1.97 % (27438)------------------------------
% 3.02/1.97 % (27438)------------------------------
% 3.02/1.98 % (27440)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_27294 for (2995ds/46Mi)
% 3.02/1.98 % (27442)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_27294 for (2995ds/98Mi)
% 3.02/2.00 % (27440)Instruction limit reached!
% 3.02/2.00 % (27440)------------------------------
% 3.02/2.00 % (27440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/2.00 % (27440)Termination reason: Unknown
% 3.02/2.00 % (27440)Termination phase: SInE selection
% 3.02/2.00
% 3.02/2.00 % (27440)Memory used [KB]: 2046
% 3.02/2.00 % (27440)Time elapsed: 0.024 s
% 3.02/2.00 % (27440)Instructions burned: 46 (million)
% 3.02/2.00 % (27440)------------------------------
% 3.02/2.00 % (27440)------------------------------
% 3.02/2.02 % (27442)Instruction limit reached!
% 3.02/2.02 % (27442)------------------------------
% 3.02/2.02 % (27442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/2.02 % (27442)Termination reason: Unknown
% 3.02/2.02 % (27442)Termination phase: Preprocessing 3
% 3.02/2.02
% 3.02/2.02 % (27442)Memory used [KB]: 2814
% 3.02/2.02 % (27442)Time elapsed: 0.037 s
% 3.02/2.02 % (27442)Instructions burned: 98 (million)
% 3.02/2.02 % (27442)------------------------------
% 3.02/2.02 % (27442)------------------------------
% 6.18/2.03 % (27443)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_27294 for (2995ds/507Mi)
% 6.18/2.04 % (27444)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_27294 for (2995ds/149Mi)
% 6.18/2.06 % (27421)Instruction limit reached!
% 6.18/2.06 % (27421)------------------------------
% 6.18/2.06 % (27421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.06 % (27421)Termination reason: Unknown
% 6.18/2.06 % (27421)Termination phase: Saturation
% 6.18/2.06
% 6.18/2.06 % (27421)Memory used [KB]: 9338
% 6.18/2.06 % (27421)Time elapsed: 0.408 s
% 6.18/2.06 % (27421)Instructions burned: 903 (million)
% 6.18/2.06 % (27421)------------------------------
% 6.18/2.06 % (27421)------------------------------
% 6.18/2.07 % (27426)Instruction limit reached!
% 6.18/2.07 % (27426)------------------------------
% 6.18/2.07 % (27426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.07 % (27426)Termination reason: Unknown
% 6.18/2.07 % (27426)Termination phase: Saturation
% 6.18/2.07
% 6.18/2.07 % (27426)Memory used [KB]: 9210
% 6.18/2.07 % (27426)Time elapsed: 0.383 s
% 6.18/2.07 % (27426)Instructions burned: 779 (million)
% 6.18/2.07 % (27426)------------------------------
% 6.18/2.07 % (27426)------------------------------
% 6.18/2.08 % (27445)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/39Mi)
% 6.18/2.08 % (27410)Instruction limit reached!
% 6.18/2.08 % (27410)------------------------------
% 6.18/2.08 % (27410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.08 % (27410)Termination reason: Unknown
% 6.18/2.08 % (27410)Termination phase: Saturation
% 6.18/2.08
% 6.18/2.08 % (27410)Memory used [KB]: 10234
% 6.18/2.08 % (27410)Time elapsed: 0.471 s
% 6.18/2.08 % (27410)Instructions burned: 1041 (million)
% 6.18/2.08 % (27410)------------------------------
% 6.18/2.08 % (27410)------------------------------
% 6.18/2.08 % (27446)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/6Mi)
% 6.18/2.08 % (27446)Instruction limit reached!
% 6.18/2.08 % (27446)------------------------------
% 6.18/2.08 % (27446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.08 % (27446)Termination reason: Unknown
% 6.18/2.08 % (27446)Termination phase: shuffling
% 6.18/2.08
% 6.18/2.08 % (27446)Memory used [KB]: 1663
% 6.18/2.08 % (27446)Time elapsed: 0.003 s
% 6.18/2.08 % (27446)Instructions burned: 6 (million)
% 6.18/2.08 % (27446)------------------------------
% 6.18/2.08 % (27446)------------------------------
% 6.18/2.09 % (27448)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/47Mi)
% 6.18/2.09 % (27447)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/1087Mi)
% 6.18/2.09 % (27445)Instruction limit reached!
% 6.18/2.09 % (27445)------------------------------
% 6.18/2.09 % (27445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.09 % (27445)Termination reason: Unknown
% 6.18/2.09 % (27445)Termination phase: Property scanning
% 6.18/2.09
% 6.18/2.09 % (27445)Memory used [KB]: 2174
% 6.18/2.09 % (27445)Time elapsed: 0.021 s
% 6.18/2.09 % (27445)Instructions burned: 40 (million)
% 6.18/2.09 % (27445)------------------------------
% 6.18/2.09 % (27445)------------------------------
% 6.18/2.10 % (27428)Instruction limit reached!
% 6.18/2.10 % (27428)------------------------------
% 6.18/2.10 % (27428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.10 % (27428)Termination reason: Unknown
% 6.18/2.10 % (27428)Termination phase: Saturation
% 6.18/2.10
% 6.18/2.10 % (27428)Memory used [KB]: 8827
% 6.18/2.10 % (27428)Time elapsed: 0.386 s
% 6.18/2.10 % (27428)Instructions burned: 879 (million)
% 6.18/2.10 % (27428)------------------------------
% 6.18/2.10 % (27428)------------------------------
% 6.18/2.10 % (27448)Instruction limit reached!
% 6.18/2.10 % (27448)------------------------------
% 6.18/2.10 % (27448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.10 % (27448)Termination reason: Unknown
% 6.18/2.10 % (27448)Termination phase: Preprocessing 2
% 6.18/2.10
% 6.18/2.10 % (27448)Memory used [KB]: 2302
% 6.18/2.10 % (27448)Time elapsed: 0.016 s
% 6.18/2.10 % (27448)Instructions burned: 48 (million)
% 6.18/2.10 % (27448)------------------------------
% 6.18/2.10 % (27448)------------------------------
% 6.18/2.11 % (27444)Instruction limit reached!
% 6.18/2.11 % (27444)------------------------------
% 6.18/2.11 % (27444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.11 % (27444)Termination reason: Unknown
% 6.18/2.11 % (27444)Termination phase: Saturation
% 6.18/2.11
% 6.18/2.11 % (27444)Memory used [KB]: 7291
% 6.18/2.11 % (27444)Time elapsed: 0.072 s
% 6.18/2.11 % (27444)Instructions burned: 150 (million)
% 6.18/2.11 % (27444)------------------------------
% 6.18/2.11 % (27444)------------------------------
% 6.18/2.11 % (27449)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/44Mi)
% 6.18/2.11 % (27451)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/62Mi)
% 6.18/2.11 % (27450)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/432Mi)
% 6.18/2.12 % (27452)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/31Mi)
% 6.69/2.13 % (27449)Instruction limit reached!
% 6.69/2.13 % (27449)------------------------------
% 6.69/2.13 % (27449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.13 % (27449)Termination reason: Unknown
% 6.69/2.13 % (27449)Termination phase: shuffling
% 6.69/2.13
% 6.69/2.13 % (27449)Memory used [KB]: 2302
% 6.69/2.13 % (27449)Time elapsed: 0.022 s
% 6.69/2.13 % (27449)Instructions burned: 44 (million)
% 6.69/2.13 % (27449)------------------------------
% 6.69/2.13 % (27449)------------------------------
% 6.69/2.13 % (27451)Instruction limit reached!
% 6.69/2.13 % (27451)------------------------------
% 6.69/2.13 % (27451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.13 % (27451)Termination reason: Unknown
% 6.69/2.13 % (27451)Termination phase: Property scanning
% 6.69/2.13
% 6.69/2.13 % (27451)Memory used [KB]: 2686
% 6.69/2.13 % (27451)Time elapsed: 0.021 s
% 6.69/2.13 % (27451)Instructions burned: 62 (million)
% 6.69/2.13 % (27451)------------------------------
% 6.69/2.13 % (27451)------------------------------
% 6.69/2.14 % (27452)Instruction limit reached!
% 6.69/2.14 % (27452)------------------------------
% 6.69/2.14 % (27452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.14 % (27452)Termination reason: Unknown
% 6.69/2.14 % (27452)Termination phase: Property scanning
% 6.69/2.14
% 6.69/2.14 % (27452)Memory used [KB]: 2174
% 6.69/2.14 % (27452)Time elapsed: 0.017 s
% 6.69/2.14 % (27452)Instructions burned: 31 (million)
% 6.69/2.14 % (27452)------------------------------
% 6.69/2.14 % (27452)------------------------------
% 6.69/2.14 % (27453)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/96Mi)
% 6.69/2.14 % (27439)Instruction limit reached!
% 6.69/2.14 % (27439)------------------------------
% 6.69/2.14 % (27439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.14 % (27439)Termination reason: Unknown
% 6.69/2.14 % (27439)Termination phase: Saturation
% 6.69/2.14
% 6.69/2.14 % (27439)Memory used [KB]: 9594
% 6.69/2.14 % (27439)Time elapsed: 0.189 s
% 6.69/2.14 % (27439)Instructions burned: 449 (million)
% 6.69/2.14 % (27439)------------------------------
% 6.69/2.14 % (27439)------------------------------
% 6.69/2.15 % (27454)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/453Mi)
% 6.69/2.15 % (27455)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/71Mi)
% 6.69/2.16 % (27456)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27294 for (2994ds/83Mi)
% 6.69/2.17 % (27453)Instruction limit reached!
% 6.69/2.17 % (27453)------------------------------
% 6.69/2.17 % (27453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.17 % (27453)Termination reason: Unknown
% 6.69/2.17 % (27453)Termination phase: Property scanning
% 6.69/2.17
% 6.69/2.17 % (27453)Memory used [KB]: 2686
% 6.69/2.17 % (27453)Time elapsed: 0.031 s
% 6.69/2.17 % (27453)Instructions burned: 97 (million)
% 6.69/2.17 % (27453)------------------------------
% 6.69/2.17 % (27453)------------------------------
% 6.69/2.18 % (27457)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27294 for (2993ds/11Mi)
% 6.69/2.18 % (27457)Instruction limit reached!
% 6.69/2.18 % (27457)------------------------------
% 6.69/2.18 % (27457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.18 % (27457)Termination reason: Unknown
% 6.69/2.18 % (27457)Termination phase: shuffling
% 6.69/2.18
% 6.69/2.18 % (27457)Memory used [KB]: 1791
% 6.69/2.18 % (27457)Time elapsed: 0.005 s
% 6.69/2.18 % (27457)Instructions burned: 14 (million)
% 6.69/2.18 % (27457)------------------------------
% 6.69/2.18 % (27457)------------------------------
% 6.69/2.19 % (27455)Instruction limit reached!
% 6.69/2.19 % (27455)------------------------------
% 6.69/2.19 % (27455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.19 % (27455)Termination reason: Unknown
% 6.69/2.19 % (27455)Termination phase: Property scanning
% 6.69/2.19
% 6.69/2.19 % (27455)Memory used [KB]: 2814
% 6.69/2.19 % (27455)Time elapsed: 0.036 s
% 6.69/2.19 % (27455)Instructions burned: 71 (million)
% 6.69/2.19 % (27455)------------------------------
% 6.69/2.19 % (27455)------------------------------
% 6.69/2.19 % (27458)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_27294 for (2993ds/41Mi)
% 6.92/2.20 % (27456)Instruction limit reached!
% 6.92/2.20 % (27456)------------------------------
% 6.92/2.20 % (27456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.20 % (27456)Termination reason: Unknown
% 6.92/2.20 % (27456)Termination phase: Saturation
% 6.92/2.20
% 6.92/2.20 % (27456)Memory used [KB]: 7036
% 6.92/2.20 % (27456)Time elapsed: 0.042 s
% 6.92/2.20 % (27456)Instructions burned: 83 (million)
% 6.92/2.20 % (27456)------------------------------
% 6.92/2.20 % (27456)------------------------------
% 6.92/2.20 % (27459)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27294 for (2993ds/6Mi)
% 6.92/2.21 % (27458)Instruction limit reached!
% 6.92/2.21 % (27458)------------------------------
% 6.92/2.21 % (27458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.21 % (27458)Termination reason: Unknown
% 6.92/2.21 % (27458)Termination phase: shuffling
% 6.92/2.21
% 6.92/2.21 % (27458)Memory used [KB]: 2302
% 6.92/2.21 % (27458)Time elapsed: 0.013 s
% 6.92/2.21 % (27458)Instructions burned: 41 (million)
% 6.92/2.21 % (27458)------------------------------
% 6.92/2.21 % (27458)------------------------------
% 6.92/2.21 % (27459)Instruction limit reached!
% 6.92/2.21 % (27459)------------------------------
% 6.92/2.21 % (27459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.21 % (27459)Termination reason: Unknown
% 6.92/2.21 % (27459)Termination phase: shuffling
% 6.92/2.21
% 6.92/2.21 % (27459)Memory used [KB]: 1663
% 6.92/2.21 % (27459)Time elapsed: 0.004 s
% 6.92/2.21 % (27459)Instructions burned: 6 (million)
% 6.92/2.21 % (27459)------------------------------
% 6.92/2.21 % (27459)------------------------------
% 6.92/2.22 % (27460)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27294 for (2993ds/150Mi)
% 6.92/2.22 % (27461)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27294 for (2993ds/343Mi)
% 6.92/2.22 % (27462)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_27294 for (2993ds/109Mi)
% 6.92/2.26 % (27460)Instruction limit reached!
% 6.92/2.26 % (27460)------------------------------
% 6.92/2.26 % (27460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.26 % (27460)Termination reason: Unknown
% 6.92/2.26 % (27460)Termination phase: Saturation
% 6.92/2.26
% 6.92/2.26 % (27460)Memory used [KB]: 7547
% 6.92/2.26 % (27460)Time elapsed: 0.046 s
% 6.92/2.26 % (27460)Instructions burned: 152 (million)
% 6.92/2.26 % (27460)------------------------------
% 6.92/2.26 % (27460)------------------------------
% 6.92/2.27 % (27463)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_27294 for (2992ds/253Mi)
% 6.92/2.27 % (27443)Instruction limit reached!
% 6.92/2.27 % (27443)------------------------------
% 6.92/2.27 % (27443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.27 % (27443)Termination reason: Unknown
% 6.92/2.27 % (27443)Termination phase: Saturation
% 6.92/2.27
% 6.92/2.27 % (27443)Memory used [KB]: 9083
% 6.92/2.27 % (27443)Time elapsed: 0.249 s
% 6.92/2.27 % (27443)Instructions burned: 508 (million)
% 6.92/2.27 % (27443)------------------------------
% 6.92/2.27 % (27443)------------------------------
% 6.92/2.27 % (27462)Instruction limit reached!
% 6.92/2.27 % (27462)------------------------------
% 6.92/2.27 % (27462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.27 % (27462)Termination reason: Unknown
% 6.92/2.27 % (27462)Termination phase: Property scanning
% 6.92/2.27
% 6.92/2.27 % (27462)Memory used [KB]: 2686
% 6.92/2.27 % (27462)Time elapsed: 0.053 s
% 6.92/2.27 % (27462)Instructions burned: 109 (million)
% 6.92/2.27 % (27462)------------------------------
% 6.92/2.27 % (27462)------------------------------
% 6.92/2.29 % (27464)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27294 for (2992ds/140Mi)
% 6.92/2.29 % (27465)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_27294 for (2992ds/614Mi)
% 7.40/2.33 % (27450)Instruction limit reached!
% 7.40/2.33 % (27450)------------------------------
% 7.40/2.33 % (27450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.33 % (27450)Termination reason: Unknown
% 7.40/2.33 % (27450)Termination phase: Saturation
% 7.40/2.33
% 7.40/2.33 % (27450)Memory used [KB]: 4605
% 7.40/2.33 % (27450)Time elapsed: 0.214 s
% 7.40/2.33 % (27450)Instructions burned: 432 (million)
% 7.40/2.33 % (27450)------------------------------
% 7.40/2.33 % (27450)------------------------------
% 7.40/2.34 % (27466)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_27294 for (2992ds/202Mi)
% 7.40/2.36 % (27464)Instruction limit reached!
% 7.40/2.36 % (27464)------------------------------
% 7.40/2.36 % (27464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.36 % (27464)Termination reason: Unknown
% 7.40/2.36 % (27464)Termination phase: Saturation
% 7.40/2.36
% 7.40/2.36 % (27464)Memory used [KB]: 7675
% 7.40/2.36 % (27464)Time elapsed: 0.070 s
% 7.40/2.36 % (27464)Instructions burned: 140 (million)
% 7.40/2.36 % (27464)------------------------------
% 7.40/2.36 % (27464)------------------------------
% 7.40/2.36 % (27454)Instruction limit reached!
% 7.40/2.36 % (27454)------------------------------
% 7.40/2.36 % (27454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.36 % (27454)Termination reason: Unknown
% 7.40/2.36 % (27454)Termination phase: Saturation
% 7.40/2.36
% 7.40/2.36 % (27454)Memory used [KB]: 9083
% 7.40/2.36 % (27454)Time elapsed: 0.212 s
% 7.40/2.36 % (27454)Instructions burned: 454 (million)
% 7.40/2.36 % (27454)------------------------------
% 7.40/2.36 % (27454)------------------------------
% 7.40/2.36 % (27461)Instruction limit reached!
% 7.40/2.36 % (27461)------------------------------
% 7.40/2.36 % (27461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.36 % (27461)Termination reason: Unknown
% 7.40/2.36 % (27461)Termination phase: Saturation
% 7.40/2.36
% 7.40/2.36 % (27461)Memory used [KB]: 8571
% 7.40/2.36 % (27461)Time elapsed: 0.143 s
% 7.40/2.36 % (27461)Instructions burned: 343 (million)
% 7.40/2.36 % (27461)------------------------------
% 7.40/2.36 % (27461)------------------------------
% 7.40/2.38 % (27468)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_27294 for (2991ds/283Mi)
% 7.40/2.38 % (27469)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27294 for (2991ds/134Mi)
% 7.40/2.38 % (27467)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_27294 for (2992ds/339Mi)
% 7.40/2.38 % (27463)Instruction limit reached!
% 7.40/2.38 % (27463)------------------------------
% 7.40/2.38 % (27463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.38 % (27463)Termination reason: Unknown
% 7.40/2.38 % (27463)Termination phase: Saturation
% 7.40/2.38
% 7.40/2.38 % (27463)Memory used [KB]: 8187
% 7.40/2.38 % (27463)Time elapsed: 0.113 s
% 7.40/2.38 % (27463)Instructions burned: 254 (million)
% 7.40/2.38 % (27463)------------------------------
% 7.40/2.38 % (27463)------------------------------
% 8.22/2.40 % (27470)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27294 for (2991ds/298Mi)
% 8.22/2.44 % (27469)Instruction limit reached!
% 8.22/2.44 % (27469)------------------------------
% 8.22/2.44 % (27469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.44 % (27469)Termination reason: Unknown
% 8.22/2.44 % (27469)Termination phase: Saturation
% 8.22/2.44
% 8.22/2.44 % (27469)Memory used [KB]: 7291
% 8.22/2.44 % (27469)Time elapsed: 0.065 s
% 8.22/2.44 % (27469)Instructions burned: 134 (million)
% 8.22/2.44 % (27469)------------------------------
% 8.22/2.44 % (27469)------------------------------
% 8.22/2.44 % (27466)Instruction limit reached!
% 8.22/2.44 % (27466)------------------------------
% 8.22/2.44 % (27466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.44 % (27466)Termination reason: Unknown
% 8.22/2.44 % (27466)Termination phase: Saturation
% 8.22/2.44
% 8.22/2.44 % (27466)Memory used [KB]: 7803
% 8.22/2.44 % (27466)Time elapsed: 0.103 s
% 8.22/2.44 % (27466)Instructions burned: 202 (million)
% 8.22/2.44 % (27466)------------------------------
% 8.22/2.44 % (27466)------------------------------
% 8.22/2.46 % (27473)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_27294 for (2991ds/258Mi)
% 8.22/2.47 % (27472)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27294 for (2991ds/192Mi)
% 8.42/2.51 % (27467)Instruction limit reached!
% 8.42/2.51 % (27467)------------------------------
% 8.42/2.51 % (27467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.51 % (27467)Termination reason: Unknown
% 8.42/2.51 % (27467)Termination phase: Saturation
% 8.42/2.51
% 8.42/2.51 % (27467)Memory used [KB]: 8315
% 8.42/2.51 % (27467)Time elapsed: 0.126 s
% 8.42/2.51 % (27467)Instructions burned: 341 (million)
% 8.42/2.51 % (27467)------------------------------
% 8.42/2.51 % (27467)------------------------------
% 8.42/2.51 % (27468)Instruction limit reached!
% 8.42/2.51 % (27468)------------------------------
% 8.42/2.51 % (27468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.51 % (27468)Termination reason: Unknown
% 8.42/2.51 % (27468)Termination phase: Saturation
% 8.42/2.51
% 8.42/2.51 % (27468)Memory used [KB]: 8059
% 8.42/2.51 % (27468)Time elapsed: 0.139 s
% 8.42/2.51 % (27468)Instructions burned: 283 (million)
% 8.42/2.51 % (27468)------------------------------
% 8.42/2.51 % (27468)------------------------------
% 8.42/2.52 % (27474)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_27294 for (2990ds/90Mi)
% 8.42/2.53 % (27470)Instruction limit reached!
% 8.42/2.53 % (27470)------------------------------
% 8.42/2.53 % (27470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.53 % (27470)Termination reason: Unknown
% 8.42/2.53 % (27470)Termination phase: Saturation
% 8.42/2.53
% 8.42/2.53 % (27470)Memory used [KB]: 8955
% 8.42/2.53 % (27470)Time elapsed: 0.105 s
% 8.42/2.53 % (27470)Instructions burned: 301 (million)
% 8.42/2.53 % (27470)------------------------------
% 8.42/2.53 % (27470)------------------------------
% 8.42/2.53 % (27475)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_27294 for (2990ds/231Mi)
% 8.42/2.54 % (27476)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_27294 for (2990ds/458Mi)
% 8.42/2.57 % (27474)Instruction limit reached!
% 8.42/2.57 % (27474)------------------------------
% 8.42/2.57 % (27474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.57 % (27474)Termination reason: Unknown
% 8.42/2.57 % (27474)Termination phase: Equality resolution with deletion
% 8.42/2.57
% 8.42/2.57 % (27474)Memory used [KB]: 2686
% 8.42/2.57 % (27474)Time elapsed: 0.046 s
% 8.42/2.57 % (27474)Instructions burned: 91 (million)
% 8.42/2.57 % (27474)------------------------------
% 8.42/2.57 % (27474)------------------------------
% 8.42/2.57 % (27472)Instruction limit reached!
% 8.42/2.57 % (27472)------------------------------
% 8.42/2.57 % (27472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.57 % (27472)Termination reason: Unknown
% 8.42/2.57 % (27472)Termination phase: Saturation
% 8.42/2.57
% 8.42/2.57 % (27472)Memory used [KB]: 4093
% 8.42/2.57 % (27472)Time elapsed: 0.087 s
% 8.42/2.57 % (27472)Instructions burned: 193 (million)
% 8.42/2.57 % (27472)------------------------------
% 8.42/2.57 % (27472)------------------------------
% 8.42/2.58 % (27477)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/31Mi)
% 8.42/2.59 % (27473)Instruction limit reached!
% 8.42/2.59 % (27473)------------------------------
% 8.42/2.59 % (27473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.59 % (27473)Termination reason: Unknown
% 8.42/2.59 % (27473)Termination phase: Saturation
% 8.42/2.59
% 8.42/2.59 % (27473)Memory used [KB]: 8187
% 8.42/2.59 % (27473)Time elapsed: 0.127 s
% 8.42/2.59 % (27473)Instructions burned: 258 (million)
% 8.42/2.59 % (27473)------------------------------
% 8.42/2.59 % (27473)------------------------------
% 8.42/2.59 % (27465)Instruction limit reached!
% 8.42/2.59 % (27465)------------------------------
% 8.42/2.59 % (27465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.59 % (27465)Termination reason: Unknown
% 8.42/2.59 % (27465)Termination phase: Saturation
% 8.42/2.59
% 8.42/2.59 % (27465)Memory used [KB]: 9210
% 8.42/2.59 % (27465)Time elapsed: 0.299 s
% 8.42/2.59 % (27465)Instructions burned: 615 (million)
% 8.42/2.59 % (27465)------------------------------
% 8.42/2.59 % (27465)------------------------------
% 8.42/2.59 % (27478)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/297Mi)
% 9.43/2.60 % (27475)Instruction limit reached!
% 9.43/2.60 % (27475)------------------------------
% 9.43/2.60 % (27475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.60 % (27475)Termination reason: Unknown
% 9.43/2.60 % (27475)Termination phase: Saturation
% 9.43/2.60
% 9.43/2.60 % (27475)Memory used [KB]: 7675
% 9.43/2.60 % (27475)Time elapsed: 0.091 s
% 9.43/2.60 % (27475)Instructions burned: 231 (million)
% 9.43/2.60 % (27475)------------------------------
% 9.43/2.60 % (27475)------------------------------
% 9.43/2.60 % (27477)Instruction limit reached!
% 9.43/2.60 % (27477)------------------------------
% 9.43/2.60 % (27477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.60 % (27477)Termination reason: Unknown
% 9.43/2.60 % (27477)Termination phase: Property scanning
% 9.43/2.60
% 9.43/2.60 % (27477)Memory used [KB]: 2046
% 9.43/2.60 % (27477)Time elapsed: 0.018 s
% 9.43/2.60 % (27477)Instructions burned: 32 (million)
% 9.43/2.60 % (27477)------------------------------
% 9.43/2.60 % (27477)------------------------------
% 9.43/2.60 % (27479)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/987Mi)
% 9.43/2.60 % (27480)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/182Mi)
% 9.43/2.61 % (27447)Instruction limit reached!
% 9.43/2.61 % (27447)------------------------------
% 9.43/2.61 % (27447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.61 % (27447)Termination reason: Unknown
% 9.43/2.61 % (27447)Termination phase: Saturation
% 9.43/2.61
% 9.43/2.61 % (27447)Memory used [KB]: 8315
% 9.43/2.61 % (27447)Time elapsed: 0.510 s
% 9.43/2.61 % (27447)Instructions burned: 1088 (million)
% 9.43/2.61 % (27447)------------------------------
% 9.43/2.61 % (27447)------------------------------
% 9.43/2.61 % (27481)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/182Mi)
% 9.43/2.62 % (27482)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/154Mi)
% 9.43/2.63 % (27483)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/79Mi)
% 9.43/2.66 % (27483)Instruction limit reached!
% 9.43/2.66 % (27483)------------------------------
% 9.43/2.66 % (27483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.66 % (27483)Termination reason: Unknown
% 9.43/2.66 % (27483)Termination phase: Property scanning
% 9.43/2.66
% 9.43/2.66 % (27483)Memory used [KB]: 2686
% 9.43/2.66 % (27483)Time elapsed: 0.034 s
% 9.43/2.66 % (27483)Instructions burned: 81 (million)
% 9.43/2.66 % (27483)------------------------------
% 9.43/2.66 % (27483)------------------------------
% 9.43/2.67 % (27484)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_27294 for (2989ds/216Mi)
% 9.43/2.67 % (27482)Instruction limit reached!
% 9.43/2.67 % (27482)------------------------------
% 9.43/2.67 % (27482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.68 % (27482)Termination reason: Unknown
% 9.43/2.68 % (27482)Termination phase: Saturation
% 9.43/2.68
% 9.43/2.68 % (27482)Memory used [KB]: 3198
% 9.43/2.68 % (27482)Time elapsed: 0.062 s
% 9.43/2.68 % (27482)Instructions burned: 156 (million)
% 9.43/2.68 % (27482)------------------------------
% 9.43/2.68 % (27482)------------------------------
% 9.43/2.69 % (27480)Instruction limit reached!
% 9.43/2.69 % (27480)------------------------------
% 9.43/2.69 % (27480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.69 % (27480)Termination reason: Unknown
% 9.43/2.69 % (27480)Termination phase: Saturation
% 9.43/2.69
% 9.43/2.69 % (27480)Memory used [KB]: 7547
% 9.43/2.69 % (27480)Time elapsed: 0.087 s
% 9.43/2.69 % (27480)Instructions burned: 182 (million)
% 9.43/2.69 % (27480)------------------------------
% 9.43/2.69 % (27480)------------------------------
% 9.43/2.69 % (27485)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_27294 for (2988ds/114Mi)
% 10.30/2.70 % (27481)Instruction limit reached!
% 10.30/2.70 % (27481)------------------------------
% 10.30/2.70 % (27481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.70 % (27481)Termination reason: Unknown
% 10.30/2.70 % (27481)Termination phase: Saturation
% 10.30/2.70
% 10.30/2.70 % (27481)Memory used [KB]: 7675
% 10.30/2.70 % (27481)Time elapsed: 0.111 s
% 10.30/2.70 % (27481)Instructions burned: 182 (million)
% 10.30/2.70 % (27481)------------------------------
% 10.30/2.70 % (27481)------------------------------
% 10.30/2.71 % (27486)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_27294 for (2988ds/922Mi)
% 10.30/2.72 % (27487)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_27294 for (2988ds/182Mi)
% 10.30/2.73 % (27478)Instruction limit reached!
% 10.30/2.73 % (27478)------------------------------
% 10.30/2.73 % (27478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.73 % (27478)Termination reason: Unknown
% 10.30/2.73 % (27478)Termination phase: Saturation
% 10.30/2.73
% 10.30/2.73 % (27478)Memory used [KB]: 7931
% 10.30/2.73 % (27478)Time elapsed: 0.142 s
% 10.30/2.73 % (27478)Instructions burned: 297 (million)
% 10.30/2.73 % (27478)------------------------------
% 10.30/2.73 % (27478)------------------------------
% 10.30/2.75 % (27488)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_27294 for (2988ds/164Mi)
% 10.30/2.75 % (27485)Instruction limit reached!
% 10.30/2.75 % (27485)------------------------------
% 10.30/2.75 % (27485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.75 % (27485)Termination reason: Unknown
% 10.30/2.75 % (27485)Termination phase: Property scanning
% 10.30/2.75
% 10.30/2.75 % (27485)Memory used [KB]: 2686
% 10.30/2.75 % (27485)Time elapsed: 0.056 s
% 10.30/2.75 % (27485)Instructions burned: 115 (million)
% 10.30/2.75 % (27485)------------------------------
% 10.30/2.75 % (27485)------------------------------
% 10.30/2.75 % (27476)Instruction limit reached!
% 10.30/2.75 % (27476)------------------------------
% 10.30/2.75 % (27476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.75 % (27476)Termination reason: Unknown
% 10.30/2.75 % (27476)Termination phase: Saturation
% 10.30/2.75
% 10.30/2.75 % (27476)Memory used [KB]: 8827
% 10.30/2.75 % (27476)Time elapsed: 0.186 s
% 10.30/2.75 % (27476)Instructions burned: 458 (million)
% 10.30/2.75 % (27476)------------------------------
% 10.30/2.75 % (27476)------------------------------
% 10.30/2.76 % (27490)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_27294 for (2987ds/368Mi)
% 10.30/2.76 % (27489)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_27294 for (2988ds/50Mi)
% 10.30/2.77 % (27484)Instruction limit reached!
% 10.30/2.77 % (27484)------------------------------
% 10.30/2.77 % (27484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.77 % (27484)Termination reason: Unknown
% 10.30/2.77 % (27484)Termination phase: Saturation
% 10.30/2.77
% 10.30/2.77 % (27484)Memory used [KB]: 7675
% 10.30/2.77 % (27484)Time elapsed: 0.101 s
% 10.30/2.77 % (27484)Instructions burned: 216 (million)
% 10.30/2.77 % (27484)------------------------------
% 10.30/2.77 % (27484)------------------------------
% 10.30/2.79 % (27489)Instruction limit reached!
% 10.30/2.79 % (27489)------------------------------
% 10.30/2.79 % (27489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.79 % (27489)Termination reason: Unknown
% 10.30/2.79 % (27489)Termination phase: shuffling
% 10.30/2.79
% 10.30/2.79 % (27489)Memory used [KB]: 2686
% 10.30/2.79 % (27489)Time elapsed: 0.025 s
% 10.30/2.79 % (27489)Instructions burned: 51 (million)
% 10.30/2.79 % (27489)------------------------------
% 10.30/2.79 % (27489)------------------------------
% 10.30/2.79 % (27492)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_27294 for (2987ds/1021Mi)
% 10.97/2.80 % (27487)Instruction limit reached!
% 10.97/2.80 % (27487)------------------------------
% 10.97/2.80 % (27487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.97/2.80 % (27487)Termination reason: Unknown
% 10.97/2.80 % (27487)Termination phase: Saturation
% 10.97/2.80
% 10.97/2.80 % (27487)Memory used [KB]: 7547
% 10.97/2.80 % (27487)Time elapsed: 0.085 s
% 10.97/2.80 % (27487)Instructions burned: 183 (million)
% 10.97/2.80 % (27487)------------------------------
% 10.97/2.80 % (27487)------------------------------
% 10.97/2.80 % (27493)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_27294 for (2987ds/267Mi)
% 10.97/2.82 % (27488)Instruction limit reached!
% 10.97/2.82 % (27488)------------------------------
% 10.97/2.82 % (27488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.97/2.82 % (27488)Termination reason: Unknown
% 10.97/2.82 % (27488)Termination phase: Saturation
% 10.97/2.82
% 10.97/2.82 % (27488)Memory used [KB]: 2942
% 10.97/2.82 % (27488)Time elapsed: 0.077 s
% 10.97/2.82 % (27488)Instructions burned: 165 (million)
% 10.97/2.82 % (27488)------------------------------
% 10.97/2.82 % (27488)------------------------------
% 10.97/2.82 % (27494)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_27294 for (2987ds/204Mi)
% 10.97/2.84 % (27495)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_27294 for (2987ds/26Mi)
% 10.97/2.85 % (27495)Instruction limit reached!
% 10.97/2.85 % (27495)------------------------------
% 10.97/2.85 % (27495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.97/2.85 % (27495)Termination reason: Unknown
% 10.97/2.85 % (27495)Termination phase: shuffling
% 10.97/2.85
% 10.97/2.85 % (27495)Memory used [KB]: 2046
% 10.97/2.85 % (27495)Time elapsed: 0.014 s
% 10.97/2.85 % (27495)Instructions burned: 26 (million)
% 10.97/2.85 % (27495)------------------------------
% 10.97/2.85 % (27495)------------------------------
% 10.97/2.87 % (27496)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_27294 for (2986ds/53Mi)
% 11.20/2.90 % (27496)Instruction limit reached!
% 11.20/2.90 % (27496)------------------------------
% 11.20/2.90 % (27496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.20/2.90 % (27496)Termination reason: Unknown
% 11.20/2.90 % (27496)Termination phase: Property scanning
% 11.20/2.90
% 11.20/2.90 % (27496)Memory used [KB]: 2686
% 11.20/2.90 % (27496)Time elapsed: 0.018 s
% 11.20/2.90 % (27496)Instructions burned: 54 (million)
% 11.20/2.90 % (27496)------------------------------
% 11.20/2.90 % (27496)------------------------------
% 11.20/2.91 % (27494)Instruction limit reached!
% 11.20/2.91 % (27494)------------------------------
% 11.20/2.91 % (27494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.20/2.91 % (27494)Termination reason: Unknown
% 11.20/2.91 % (27494)Termination phase: Saturation
% 11.20/2.91
% 11.20/2.91 % (27494)Memory used [KB]: 7675
% 11.20/2.91 % (27494)Time elapsed: 0.106 s
% 11.20/2.91 % (27494)Instructions burned: 205 (million)
% 11.20/2.91 % (27494)------------------------------
% 11.20/2.91 % (27494)------------------------------
% 11.20/2.92 % (27497)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_27294 for (2986ds/4436Mi)
% 11.20/2.92 % (27498)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_27294 for (2986ds/1539Mi)
% 11.20/2.93 % (27493)Instruction limit reached!
% 11.20/2.93 % (27493)------------------------------
% 11.20/2.93 % (27493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.20/2.93 % (27493)Termination reason: Unknown
% 11.20/2.93 % (27493)Termination phase: Saturation
% 11.20/2.93
% 11.20/2.93 % (27493)Memory used [KB]: 7931
% 11.20/2.93 % (27493)Time elapsed: 0.130 s
% 11.20/2.93 % (27493)Instructions burned: 267 (million)
% 11.20/2.93 % (27493)------------------------------
% 11.20/2.93 % (27493)------------------------------
% 11.20/2.94 % (27490)Instruction limit reached!
% 11.20/2.94 % (27490)------------------------------
% 11.20/2.94 % (27490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.20/2.94 % (27490)Termination reason: Unknown
% 11.20/2.94 % (27490)Termination phase: Saturation
% 11.20/2.94
% 11.20/2.94 % (27490)Memory used [KB]: 8571
% 11.20/2.94 % (27490)Time elapsed: 0.178 s
% 11.20/2.94 % (27490)Instructions burned: 369 (million)
% 11.20/2.94 % (27490)------------------------------
% 11.20/2.94 % (27490)------------------------------
% 11.20/2.95 % (27499)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_27294 for (2986ds/408Mi)
% 11.20/2.95 % (27500)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_27294 for (2986ds/5205Mi)
% 12.97/3.05 % (27479)Instruction limit reached!
% 12.97/3.05 % (27479)------------------------------
% 12.97/3.05 % (27479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.05 % (27479)Termination reason: Unknown
% 12.97/3.05 % (27479)Termination phase: Saturation
% 12.97/3.05
% 12.97/3.05 % (27479)Memory used [KB]: 9978
% 12.97/3.05 % (27479)Time elapsed: 0.469 s
% 12.97/3.05 % (27479)Instructions burned: 988 (million)
% 12.97/3.05 % (27479)------------------------------
% 12.97/3.05 % (27479)------------------------------
% 12.97/3.07 % (27501)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_27294 for (2985ds/1913Mi)
% 13.62/3.14 % (27499)Instruction limit reached!
% 13.62/3.14 % (27499)------------------------------
% 13.62/3.14 % (27499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.62/3.14 % (27499)Termination reason: Unknown
% 13.62/3.14 % (27499)Termination phase: Saturation
% 13.62/3.14
% 13.62/3.14 % (27499)Memory used [KB]: 9338
% 13.62/3.14 % (27499)Time elapsed: 0.197 s
% 13.62/3.14 % (27499)Instructions burned: 408 (million)
% 13.62/3.14 % (27499)------------------------------
% 13.62/3.14 % (27499)------------------------------
% 13.62/3.16 % (27486)Instruction limit reached!
% 13.62/3.16 % (27486)------------------------------
% 13.62/3.16 % (27486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.62/3.16 % (27486)Termination reason: Unknown
% 13.62/3.16 % (27486)Termination phase: Saturation
% 13.62/3.16
% 13.62/3.16 % (27486)Memory used [KB]: 8187
% 13.62/3.16 % (27486)Time elapsed: 0.453 s
% 13.62/3.16 % (27486)Instructions burned: 923 (million)
% 13.62/3.16 % (27486)------------------------------
% 13.62/3.16 % (27486)------------------------------
% 13.62/3.16 % (27502)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_27294 for (2984ds/4350Mi)
% 13.62/3.17 % (27503)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_27294 for (2983ds/68Mi)
% 13.96/3.21 % (27503)Instruction limit reached!
% 13.96/3.21 % (27503)------------------------------
% 13.96/3.21 % (27503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.21 % (27503)Termination reason: Unknown
% 13.96/3.21 % (27503)Termination phase: Preprocessing 3
% 13.96/3.21
% 13.96/3.21 % (27503)Memory used [KB]: 2558
% 13.96/3.21 % (27503)Time elapsed: 0.037 s
% 13.96/3.21 % (27503)Instructions burned: 69 (million)
% 13.96/3.21 % (27503)------------------------------
% 13.96/3.21 % (27503)------------------------------
% 13.96/3.23 % (27504)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_27294 for (2983ds/358Mi)
% 13.96/3.25 % (27492)Instruction limit reached!
% 13.96/3.25 % (27492)------------------------------
% 13.96/3.25 % (27492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.25 % (27492)Termination reason: Unknown
% 13.96/3.25 % (27492)Termination phase: Saturation
% 13.96/3.25
% 13.96/3.25 % (27492)Memory used [KB]: 10618
% 13.96/3.25 % (27492)Time elapsed: 0.467 s
% 13.96/3.25 % (27492)Instructions burned: 1022 (million)
% 13.96/3.25 % (27492)------------------------------
% 13.96/3.25 % (27492)------------------------------
% 13.96/3.27 % (27505)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_27294 for (2983ds/31Mi)
% 13.96/3.29 % (27505)Instruction limit reached!
% 13.96/3.29 % (27505)------------------------------
% 13.96/3.29 % (27505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.29 % (27505)Termination reason: Unknown
% 13.96/3.29 % (27505)Termination phase: Property scanning
% 13.96/3.29
% 13.96/3.29 % (27505)Memory used [KB]: 2046
% 13.96/3.29 % (27505)Time elapsed: 0.018 s
% 13.96/3.29 % (27505)Instructions burned: 31 (million)
% 13.96/3.29 % (27505)------------------------------
% 13.96/3.29 % (27505)------------------------------
% 14.42/3.30 % (27506)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_27294 for (2982ds/279Mi)
% 14.42/3.37 % (27506)Refutation not found, incomplete strategy
% 14.42/3.37 % (27506)------------------------------
% 14.42/3.37 % (27506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.37 % (27506)Termination reason: Refutation not found, incomplete strategy
% 14.42/3.37
% 14.42/3.37
% 14.42/3.37 % (27506)Memory used [KB]: 7419
% 14.42/3.37 % (27506)Time elapsed: 0.064 s
% 14.42/3.37 % (27506)Instructions burned: 133 (million)
% 14.42/3.37 % (27506)------------------------------
% 14.42/3.37 % (27506)------------------------------
% 14.42/3.38 % (27504)Instruction limit reached!
% 14.42/3.38 % (27504)------------------------------
% 14.42/3.38 % (27504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.38 % (27504)Termination reason: Unknown
% 14.42/3.38 % (27504)Termination phase: Saturation
% 14.42/3.38
% 14.42/3.38 % (27504)Memory used [KB]: 8315
% 14.42/3.38 % (27504)Time elapsed: 0.147 s
% 14.42/3.38 % (27504)Instructions burned: 358 (million)
% 14.42/3.38 % (27504)------------------------------
% 14.42/3.38 % (27504)------------------------------
% 14.42/3.39 % (27508)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_27294 for (2981ds/258Mi)
% 14.42/3.39 % (27509)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_27294 for (2981ds/26Mi)
% 14.95/3.40 % (27509)Instruction limit reached!
% 14.95/3.40 % (27509)------------------------------
% 14.95/3.40 % (27509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.95/3.40 % (27509)Termination reason: Unknown
% 14.95/3.40 % (27509)Termination phase: shuffling
% 14.95/3.40
% 14.95/3.40 % (27509)Memory used [KB]: 2046
% 14.95/3.40 % (27509)Time elapsed: 0.014 s
% 14.95/3.40 % (27509)Instructions burned: 27 (million)
% 14.95/3.40 % (27509)------------------------------
% 14.95/3.40 % (27509)------------------------------
% 14.95/3.42 % (27510)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_27294 for (2981ds/995Mi)
% 14.95/3.48 % (27508)Instruction limit reached!
% 14.95/3.48 % (27508)------------------------------
% 14.95/3.48 % (27508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.95/3.48 % (27508)Termination reason: Unknown
% 14.95/3.48 % (27508)Termination phase: Saturation
% 14.95/3.48
% 14.95/3.48 % (27508)Memory used [KB]: 8315
% 14.95/3.48 % (27508)Time elapsed: 0.082 s
% 14.95/3.48 % (27508)Instructions burned: 260 (million)
% 14.95/3.48 % (27508)------------------------------
% 14.95/3.48 % (27508)------------------------------
% 15.37/3.50 % (27511)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_27294 for (2980ds/373Mi)
% 15.37/3.50 % (27498)First to succeed.
% 15.37/3.51 % (27498)Refutation found. Thanks to Tanya!
% 15.37/3.51 % SZS status Theorem for DTF2THF_27294
% 15.37/3.51 % SZS output start Proof for DTF2THF_27294
% 15.37/3.51 thf(type_def_5, type, itself: ($tType) > $tType).
% 15.37/3.51 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 15.37/3.51 thf(type_def_8, type, set: ($tType) > $tType).
% 15.37/3.51 thf(type_def_9, type, stream901396144_sp_mu: ($tType * $tType * $tType) > $tType).
% 15.37/3.51 thf(type_def_10, type, stream: ($tType) > $tType).
% 15.37/3.51 thf(type_def_11, type, nat: $tType).
% 15.37/3.51 thf(type_def_12, type, a: $tType).
% 15.37/3.51 thf(type_def_13, type, b: $tType).
% 15.37/3.51 thf(type_def_14, type, c: $tType).
% 15.37/3.51 thf(type_def_15, type, d: $tType).
% 15.37/3.51 thf(type_def_16, type, stream1273403375_sp_nu: ($tType * $tType) > $tType).
% 15.37/3.51 thf(func_def_0, type, stream1273403375_sp_nu: ($tType * $tType) > $tType).
% 15.37/3.51 thf(func_def_1, type, stream901396144_sp_mu: ($tType * $tType * $tType) > $tType).
% 15.37/3.51 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 15.37/3.51 thf(func_def_3, type, stream: ($tType) > $tType).
% 15.37/3.51 thf(func_def_4, type, set: ($tType) > $tType).
% 15.37/3.51 thf(func_def_5, type, nat: $tType).
% 15.37/3.51 thf(func_def_6, type, itself: ($tType) > $tType).
% 15.37/3.51 thf(func_def_7, type, d: $tType).
% 15.37/3.51 thf(func_def_8, type, c: $tType).
% 15.37/3.51 thf(func_def_9, type, b: $tType).
% 15.37/3.51 thf(func_def_10, type, a: $tType).
% 15.37/3.51 thf(func_def_11, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 15.37/3.51 thf(func_def_12, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 15.37/3.51 thf(func_def_13, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 15.37/3.51 thf(func_def_14, type, order_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 15.37/3.51 thf(func_def_15, type, complete_Sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 15.37/3.51 thf(func_def_16, type, comple187826305attice: !>[X0: $tType]:(itself @ X0 > $o)).
% 15.37/3.51 thf(func_def_17, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X1) > $o)).
% 15.37/3.51 thf(func_def_18, type, bNF_fstOp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X0 @ X1)).
% 15.37/3.51 thf(func_def_19, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1)).
% 15.37/3.51 thf(func_def_20, type, bNF_sndOp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2)).
% 15.37/3.51 thf(func_def_21, type, complete_Sup_Sup: !>[X0: $tType]:(set @ X0 > X0)).
% 15.37/3.51 thf(func_def_22, type, inj_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > $o)).
% 15.37/3.51 thf(func_def_23, type, the_inv_into: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > X1) > X1 > X0)).
% 15.37/3.51 thf(func_def_24, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 15.37/3.51 thf(func_def_25, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 15.37/3.51 thf(func_def_26, type, top_top: !>[X0: $tType]:(X0)).
% 15.37/3.51 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 15.37/3.51 thf(func_def_28, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2)).
% 15.37/3.51 thf(func_def_29, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1)).
% 15.37/3.51 thf(func_def_30, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2)).
% 15.37/3.51 thf(func_def_31, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 15.37/3.51 thf(func_def_32, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3)).
% 15.37/3.51 thf(func_def_33, type, product_rec_bool: !>[X0: $tType]:(X0 > X0 > $o > X0)).
% 15.37/3.51 thf(func_def_34, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 15.37/3.51 thf(func_def_35, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 15.37/3.51 thf(func_def_36, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 15.37/3.51 thf(func_def_37, type, product_snd: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 15.37/3.51 thf(func_def_38, type, product_swap: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > product_prod @ X1 @ X0)).
% 15.37/3.51 thf(func_def_39, type, type2: !>[X0: $tType]:(itself @ X0)).
% 15.37/3.51 thf(func_def_40, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 15.37/3.51 thf(func_def_41, type, bind: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > set @ X1) > set @ X1)).
% 15.37/3.51 thf(func_def_42, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 15.37/3.51 thf(func_def_43, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 15.37/3.51 thf(func_def_44, type, stream5064451run_mu: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X0 @ X1 @ X2 > stream @ X0 > product_prod @ product_prod @ X1 @ X2 @ stream @ X0)).
% 15.37/3.51 thf(func_def_45, type, stream1294929701mu_Get: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > stream901396144_sp_mu @ X0 @ X1 @ X2) > stream901396144_sp_mu @ X0 @ X1 @ X2)).
% 15.37/3.51 thf(func_def_46, type, stream1370332830mu_Put: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > X1 > stream901396144_sp_mu @ X2 @ X0 @ X1)).
% 15.37/3.51 thf(func_def_47, type, stream160000856_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > stream901396144_sp_mu @ X0 @ X1 @ X2) > X3) > (X1 > X2 > X3) > stream901396144_sp_mu @ X0 @ X1 @ X2 > X3)).
% 15.37/3.51 thf(func_def_48, type, stream123009735_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > $o) > (X1 > $o) > stream901396144_sp_mu @ X2 @ X0 @ X1 > $o)).
% 15.37/3.51 thf(func_def_49, type, stream674629690_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ stream901396144_sp_mu @ X0 @ X1 @ X2 @ X3) > X3) > (X1 > X2 > X3) > stream901396144_sp_mu @ X0 @ X1 @ X2 > X3)).
% 15.37/3.51 thf(func_def_50, type, stream1924447089_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > stream901396144_sp_mu @ X4 @ X0 @ X2 > stream901396144_sp_mu @ X4 @ X1 @ X3 > $o)).
% 15.37/3.51 thf(func_def_51, type, stream2074884121_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X0 @ X1 @ X2 > set @ X1)).
% 15.37/3.51 thf(func_def_52, type, stream1259315544_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X0 @ X1 @ X2 > set @ X2)).
% 15.37/3.51 thf(func_def_53, type, stream152839592le_sub: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ product_prod @ stream901396144_sp_mu @ X0 @ X1 @ X2 @ stream901396144_sp_mu @ X0 @ X1 @ X2)).
% 15.37/3.51 thf(func_def_54, type, lex_prod: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 15.37/3.51 thf(func_def_55, type, measure: !>[X0: $tType]:((X0 > nat) > set @ product_prod @ X0 @ X0)).
% 15.37/3.51 thf(func_def_56, type, wf: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 15.37/3.51 thf(func_def_57, type, same_fst: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 15.37/3.51 thf(func_def_58, type, chains: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ set @ X0)).
% 15.37/3.51 thf(func_def_59, type, chain_subset: !>[X0: $tType]:(set @ set @ X0 > $o)).
% 15.37/3.51 thf(func_def_60, type, chains2: !>[X0: $tType]:(set @ set @ X0 > set @ set @ set @ X0)).
% 15.37/3.51 thf(func_def_61, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 15.37/3.51 thf(func_def_63, type, x: product_prod @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a).
% 15.37/3.51 thf(func_def_79, type, sP0: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > (X0 > $o) > $o)).
% 15.37/3.51 thf(func_def_80, type, sP1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(stream901396144_sp_mu @ X2 @ X3 @ X4 > (X1 > X3 > $o) > (X1 > X3 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > $o)).
% 15.37/3.51 thf(func_def_81, type, sP2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(stream901396144_sp_mu @ X2 @ X4 @ X3 > (X0 > X3 > $o) > (X0 > X3 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > $o)).
% 15.37/3.51 thf(func_def_82, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 15.37/3.51 thf(func_def_83, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 15.37/3.51 thf(func_def_84, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 15.37/3.51 thf(func_def_85, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 15.37/3.51 thf(func_def_86, type, sK7: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_87, type, sK8: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_88, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0)).
% 15.37/3.51 thf(func_def_89, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2)).
% 15.37/3.51 thf(func_def_90, type, sK11: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_91, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 15.37/3.51 thf(func_def_92, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 15.37/3.51 thf(func_def_93, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 15.37/3.51 thf(func_def_94, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 15.37/3.51 thf(func_def_95, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 15.37/3.51 thf(func_def_96, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_97, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_98, type, sK19: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_99, type, sK20: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_100, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_101, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > (X1 > $o) > X1)).
% 15.37/3.51 thf(func_def_102, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(stream901396144_sp_mu @ X2 @ X3 @ X4 > (X1 > X3 > $o) > (X1 > X3 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X1)).
% 15.37/3.51 thf(func_def_103, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(stream901396144_sp_mu @ X2 @ X3 @ X4 > (X1 > X3 > $o) > (X1 > X3 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X3)).
% 15.37/3.51 thf(func_def_104, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((X1 > X2 > $o) > stream901396144_sp_mu @ X4 @ X3 @ X2 > stream901396144_sp_mu @ X4 @ X0 @ X1 > (X1 > X2 > $o) > X1)).
% 15.37/3.51 thf(func_def_105, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((X1 > X2 > $o) > stream901396144_sp_mu @ X4 @ X3 @ X2 > stream901396144_sp_mu @ X4 @ X0 @ X1 > (X1 > X2 > $o) > X2)).
% 15.37/3.51 thf(func_def_106, type, sK27: !>[X0: $tType]:(X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_107, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 15.37/3.51 thf(func_def_108, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 15.37/3.51 thf(func_def_109, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 15.37/3.51 thf(func_def_110, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 15.37/3.51 thf(func_def_111, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 15.37/3.51 thf(func_def_112, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 15.37/3.51 thf(func_def_113, type, sK34: !>[X0: $tType]:(set @ set @ X0 > set @ set @ X0)).
% 15.37/3.51 thf(func_def_114, type, sK35: !>[X0: $tType]:(set @ set @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_115, type, sK36: !>[X0: $tType]:(set @ X0 > X0)).
% 15.37/3.51 thf(func_def_116, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 15.37/3.51 thf(func_def_117, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 15.37/3.51 thf(func_def_118, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_119, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_120, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 15.37/3.51 thf(func_def_121, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 15.37/3.51 thf(func_def_122, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 15.37/3.51 thf(func_def_123, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 15.37/3.51 thf(func_def_124, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 15.37/3.51 thf(func_def_125, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X2 > X0)).
% 15.37/3.51 thf(func_def_126, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X2 > X1 > stream901396144_sp_mu @ X1 @ X0 @ X2)).
% 15.37/3.51 thf(func_def_127, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X2 > stream901396144_sp_mu @ X1 @ X0 @ X2)).
% 15.37/3.51 thf(func_def_128, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 15.37/3.51 thf(func_def_129, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_130, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_131, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 15.37/3.51 thf(func_def_132, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 15.37/3.51 thf(func_def_133, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 15.37/3.51 thf(func_def_134, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 15.37/3.51 thf(func_def_135, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 15.37/3.51 thf(func_def_136, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 15.37/3.51 thf(func_def_137, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 15.37/3.51 thf(func_def_138, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_139, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_140, type, sK61: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_141, type, sK62: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 15.37/3.51 thf(func_def_142, type, sK63: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_143, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(stream901396144_sp_mu @ X2 @ X4 @ X3 > (X0 > X3 > $o) > (X0 > X3 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X0)).
% 15.37/3.51 thf(func_def_144, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(stream901396144_sp_mu @ X2 @ X4 @ X3 > (X0 > X3 > $o) > (X0 > X3 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X3)).
% 15.37/3.51 thf(func_def_145, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((X0 > X3 > $o) > (X0 > X3 > $o) > stream901396144_sp_mu @ X4 @ X3 @ X2 > stream901396144_sp_mu @ X4 @ X0 @ X1 > X0)).
% 15.37/3.51 thf(func_def_146, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((X0 > X3 > $o) > (X0 > X3 > $o) > stream901396144_sp_mu @ X4 @ X3 @ X2 > stream901396144_sp_mu @ X4 @ X0 @ X1 > X3)).
% 15.37/3.51 thf(func_def_147, type, sK68: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 15.37/3.51 thf(func_def_148, type, sK69: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 15.37/3.51 thf(func_def_149, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3)).
% 15.37/3.51 thf(func_def_150, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2)).
% 15.37/3.51 thf(func_def_151, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X1)).
% 15.37/3.51 thf(func_def_152, type, sK73: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X1 > X0)).
% 15.37/3.51 thf(func_def_153, type, sK74: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > X0 > $o) > X1 > X0)).
% 15.37/3.51 thf(func_def_154, type, sK75: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X1 > X0)).
% 15.37/3.51 thf(func_def_155, type, sK76: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X1 > X0)).
% 15.37/3.51 thf(func_def_156, type, sK77: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X1)).
% 15.37/3.51 thf(func_def_157, type, sK78: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X0)).
% 15.37/3.51 thf(func_def_158, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X0)).
% 15.37/3.51 thf(func_def_159, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X1 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X1)).
% 15.37/3.51 thf(func_def_160, type, sK81: !>[X0: $tType]:(set @ set @ X0 > X0 > set @ X0)).
% 15.37/3.51 thf(func_def_161, type, sK82: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_162, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > $o) > (X1 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X1)).
% 15.37/3.51 thf(func_def_163, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > $o) > (X0 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X0)).
% 15.37/3.51 thf(func_def_164, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 15.37/3.51 thf(func_def_165, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 15.37/3.51 thf(func_def_166, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 15.37/3.51 thf(func_def_167, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 15.37/3.51 thf(func_def_168, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 15.37/3.51 thf(func_def_169, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 15.37/3.51 thf(func_def_170, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 15.37/3.51 thf(func_def_171, type, sK92: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 15.37/3.51 thf(func_def_172, type, sK93: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_173, type, sK94: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > $o)).
% 15.37/3.51 thf(func_def_174, type, sK95: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_175, type, sK96: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_176, type, sK97: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_177, type, sK98: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_178, type, sK99: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X0)).
% 15.37/3.51 thf(func_def_179, type, sK100: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_180, type, sK101: !>[X0: $tType, X1: $tType]:((X1 > X1) > (X1 > X0) > set @ X1 > X1)).
% 15.37/3.51 thf(func_def_181, type, sK102: !>[X0: $tType, X1: $tType]:((X1 > X1) > (X1 > X0) > set @ X1 > X1)).
% 15.37/3.51 thf(func_def_182, type, sK103: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_183, type, sK104: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_184, type, sK105: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_185, type, sK106: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 15.37/3.51 thf(func_def_186, type, sK107: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 15.37/3.51 thf(func_def_187, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X2)).
% 15.37/3.51 thf(func_def_188, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_189, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X0 > X1 > stream901396144_sp_mu @ X1 @ X0 @ X2)).
% 15.37/3.51 thf(func_def_190, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X0 > stream901396144_sp_mu @ X1 @ X0 @ X2)).
% 15.37/3.51 thf(func_def_191, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X0 > X2)).
% 15.37/3.51 thf(func_def_192, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2)).
% 15.37/3.51 thf(func_def_193, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1)).
% 15.37/3.51 thf(func_def_194, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X0)).
% 15.37/3.51 thf(func_def_195, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X2)).
% 15.37/3.51 thf(func_def_196, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType]:(stream901396144_sp_mu @ X1 @ X0 @ X2 > X1 > stream901396144_sp_mu @ X1 @ X0 @ X2)).
% 15.37/3.51 thf(func_def_197, type, sK118: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_198, type, sK119: !>[X0: $tType]:(set @ X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_199, type, sK120: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > X1) > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_200, type, sK121: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_201, type, sK122: !>[X0: $tType]:(X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_202, type, sK123: !>[X0: $tType]:(X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_203, type, sK124: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_204, type, sK125: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_205, type, sK126: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 15.37/3.51 thf(func_def_206, type, sK127: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 15.37/3.51 thf(func_def_207, type, sK128: !>[X0: $tType]:(set @ set @ X0 > set @ set @ X0)).
% 15.37/3.51 thf(func_def_208, type, sK129: !>[X0: $tType]:(set @ X0 > set @ set @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_209, type, sK130: !>[X0: $tType]:(set @ set @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_210, type, sK131: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > set @ X0 > set @ X1)).
% 15.37/3.51 thf(func_def_211, type, sK132: !>[X0: $tType]:(set @ X0 > set @ set @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_212, type, sK133: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_213, type, sK134: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X1)).
% 15.37/3.51 thf(func_def_214, type, sK135: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X0)).
% 15.37/3.51 thf(func_def_215, type, sK136: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X1)).
% 15.37/3.51 thf(func_def_216, type, sK137: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_217, type, sK138: !>[X0: $tType]:(X0)).
% 15.37/3.51 thf(func_def_218, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 15.37/3.51 thf(func_def_219, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 15.37/3.51 thf(func_def_220, type, sK141: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 15.37/3.51 thf(func_def_221, type, sK142: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_222, type, sK143: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_223, type, sK144: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 15.37/3.51 thf(func_def_224, type, sK145: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 15.37/3.51 thf(func_def_225, type, sK146: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X1 @ X0 > $o) > X2 > stream901396144_sp_mu @ X2 @ X1 @ X0)).
% 15.37/3.51 thf(func_def_226, type, sK147: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X1 @ X0 > $o) > X1)).
% 15.37/3.51 thf(func_def_227, type, sK148: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X1 @ X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_228, type, sK149: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > X1)).
% 15.37/3.51 thf(func_def_230, type, sK151: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_231, type, sK152: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1)).
% 15.37/3.51 thf(func_def_232, type, sK153: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_233, type, sK154: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_234, type, sK155: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_235, type, sK156: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_236, type, sK157: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0 > X1)).
% 15.37/3.51 thf(func_def_237, type, sK158: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_238, type, sK159: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_239, type, sK160: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_240, type, sK161: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_241, type, sK162: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_242, type, sK163: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_243, type, sK164: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_244, type, sK165: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_245, type, sK166: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_246, type, sK167: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_247, type, sK168: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_248, type, sK169: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_249, type, sK170: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_250, type, sK171: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_251, type, sK172: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_252, type, sK173: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_253, type, sK174: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_254, type, sK175: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_255, type, sK176: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > set @ X0 > set @ X1)).
% 15.37/3.51 thf(func_def_256, type, sK177: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > set @ X0)).
% 15.37/3.51 thf(func_def_257, type, sK178: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_258, type, sK179: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_259, type, sK180: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_260, type, sK181: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_261, type, sK182: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_262, type, sK183: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_263, type, sK184: !>[X0: $tType]:((X0 > nat) > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_264, type, sK185: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_265, type, sK186: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_266, type, sK187: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_267, type, sK188: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_268, type, sK189: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_269, type, sK190: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_270, type, sK191: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_271, type, sK192: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_272, type, sK193: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_273, type, sK194: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_274, type, sK195: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_275, type, sK196: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_276, type, sK197: !>[X0: $tType, X1: $tType]:((X0 > X1) > X1)).
% 15.37/3.51 thf(func_def_277, type, sK198: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1) > X0)).
% 15.37/3.51 thf(func_def_278, type, sK199: !>[X0: $tType, X1: $tType]:(X0 > X1 > (X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_279, type, sK200: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_280, type, sK201: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1)).
% 15.37/3.51 thf(func_def_281, type, sK202: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_282, type, sK203: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_283, type, sK204: !>[X0: $tType]:(set @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_284, type, sK205: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1)).
% 15.37/3.51 thf(func_def_285, type, sK206: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_286, type, sK207: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_287, type, sK208: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X0 @ X0) > set @ product_prod @ X1 @ X0 > (X1 > $o) > product_prod @ X1 @ X0)).
% 15.37/3.51 thf(func_def_288, type, sK209: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_289, type, sK210: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_290, type, sK211: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_291, type, sK212: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_292, type, sK213: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_293, type, sK214: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_294, type, sK215: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > X0 > X1)).
% 15.37/3.51 thf(func_def_295, type, sK216: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_296, type, sK217: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ stream901396144_sp_mu @ X1 @ X2 @ X0 > stream901396144_sp_mu @ X1 @ X2 @ X0)).
% 15.37/3.51 thf(func_def_297, type, sK218: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_298, type, sK219: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > set @ X0)).
% 15.37/3.51 thf(func_def_299, type, sK220: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 15.37/3.51 thf(func_def_300, type, sK221: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_301, type, sK222: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_302, type, sK223: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_303, type, sK224: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_304, type, sK225: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_305, type, sK226: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_306, type, sK227: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_307, type, sK228: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_308, type, sK229: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_309, type, sK230: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_310, type, sK231: !>[X0: $tType, X1: $tType]:(set @ X1 > set @ X0 > (X1 > X0) > X1)).
% 15.37/3.51 thf(func_def_311, type, sK232: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_312, type, sK233: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_313, type, sK234: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X1 > set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X0 > product_prod @ X0 @ X1)).
% 15.37/3.51 thf(func_def_314, type, sK235: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_315, type, sK236: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_316, type, sK237: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_317, type, sK238: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_318, type, sK239: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_319, type, sK240: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X1 > set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X0 > product_prod @ X0 @ X1)).
% 15.37/3.51 thf(func_def_320, type, sK241: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_321, type, sK242: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_322, type, sK243: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_323, type, sK244: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X1 > set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X0 > product_prod @ X0 @ X1)).
% 15.37/3.51 thf(func_def_324, type, sK245: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_325, type, sK246: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_326, type, sK247: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_327, type, sK248: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_328, type, sK249: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_329, type, sK250: !>[X0: $tType]:(X0 > set @ set @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_330, type, sK251: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_331, type, sK252: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0 > X0)).
% 15.37/3.51 thf(func_def_332, type, sK253: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > set @ X0)).
% 15.37/3.51 thf(func_def_333, type, sK254: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X0)).
% 15.37/3.51 thf(func_def_334, type, sK255: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X0 @ X0) > set @ product_prod @ X1 @ X0 > (X1 > $o) > product_prod @ X1 @ X0)).
% 15.37/3.51 thf(func_def_335, type, sK256: !>[X0: $tType, X1: $tType]:(X0 > (X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X0)).
% 15.37/3.51 thf(func_def_336, type, sK257: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X0 @ X0) > set @ product_prod @ X1 @ X0 > (X1 > $o) > product_prod @ X1 @ X0)).
% 15.37/3.51 thf(func_def_337, type, sK258: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_338, type, sK259: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_339, type, sK260: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0)).
% 15.37/3.51 thf(func_def_340, type, sK261: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 15.37/3.51 thf(func_def_341, type, sK262: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_342, type, sK263: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X0 > set @ product_prod @ X1 @ X1 > X0)).
% 15.37/3.51 thf(func_def_343, type, sK264: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0)).
% 15.37/3.51 thf(func_def_344, type, sK265: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X0 > set @ product_prod @ X1 @ X1 > X0)).
% 15.37/3.51 thf(func_def_345, type, sK266: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1)).
% 15.37/3.51 thf(func_def_346, type, sK267: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_347, type, sK268: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 15.37/3.51 thf(func_def_348, type, sK269: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0 > X1)).
% 15.37/3.51 thf(func_def_349, type, ph270: !>[X0: $tType]:(X0)).
% 15.37/3.51 thf(func_def_350, type, sK271: a).
% 15.37/3.51 thf(f3710,plain,(
% 15.37/3.51 $false),
% 15.37/3.51 inference(avatar_sat_refutation,[status(thm)],[f2764,f2790,f3021,f3420,f3709])).
% 15.37/3.51 thf(f3709,plain,(
% 15.37/3.51 spl150_1 | ~spl150_10 | ~spl150_12),
% 15.37/3.51 inference(avatar_contradiction_clause,[status(thm)],[f3708])).
% 15.37/3.51 thf(f3708,plain,(
% 15.37/3.51 $false | (spl150_1 | ~spl150_10 | ~spl150_12)),
% 15.37/3.51 inference(subsumption_resolution,[status(thm)],[f3705,f1463])).
% 15.37/3.51 thf(f1463,plain,(
% 15.37/3.51 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X0 @ X1] : (((product_Pair @ X0 @ X1 @ (sK126 @ X0 @ X1 @ X2) @ (sK127 @ X0 @ X1 @ X2)) = X2)) )),
% 15.37/3.51 inference(cnf_transformation,[status(thm)],[f1135])).
% 15.37/3.51 thf(f1135,plain,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : ((product_Pair @ X0 @ X1 @ (sK126 @ X0 @ X1 @ X2) @ (sK127 @ X0 @ X1 @ X2)) = X2)),
% 15.37/3.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK126,sK127])],[f831,f1134])).
% 15.37/3.51 thf(f1134,plain,(
% 15.37/3.51 ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X0 @ X1] : (? [X3 : X0,X4 : X1] : ((product_Pair @ X0 @ X1 @ X3 @ X4) = X2) => ((product_Pair @ X0 @ X1 @ (sK126 @ X0 @ X1 @ X2) @ (sK127 @ X0 @ X1 @ X2)) = X2))),
% 15.37/3.51 introduced(definition,[],[choice_axiom])).
% 15.37/3.51 thf(f831,plain,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : ? [X3 : X0,X4 : X1] : ((product_Pair @ X0 @ X1 @ X3 @ X4) = X2)),
% 15.37/3.51 inference(ennf_transformation,[status(thm)],[f699])).
% 15.37/3.51 thf(f699,plain,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : ~! [X3 : X0,X4 : X1] : ((product_Pair @ X0 @ X1 @ X3 @ X4) != X2)),
% 15.37/3.51 inference(rectify,[status(thm)],[f18])).
% 15.37/3.51 thf(f18,axiom,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X13 : product_prod @ X0 @ X1] : ~! [X30 : X0,X31 : X1] : ((product_Pair @ X0 @ X1 @ X30 @ X31) != X13)),
% 15.37/3.51 file('/export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2THF_27294.p',fact_17_old_Oprod_Oexhaust)).
% 15.37/3.51 thf(f3705,plain,(
% 15.37/3.51 (x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) @ (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))) | (spl150_1 | ~spl150_10 | ~spl150_12)),
% 15.37/3.51 inference(superposition,[status(thm)],[f3097,f3419])).
% 15.37/3.51 thf(f3419,plain,(
% 15.37/3.51 ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK117 @ a @ d @ stream1273403375_sp_nu @ d @ a @ (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))) = (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)) | ~spl150_12),
% 15.37/3.51 inference(avatar_component_clause,[status(thm)],[f3417])).
% 15.37/3.51 thf(f3417,definition,(
% 15.37/3.51 spl150_12 <=> ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK117 @ a @ d @ stream1273403375_sp_nu @ d @ a @ (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))) = (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))),
% 15.37/3.51 introduced(definition,[new_symbols(naming,[spl150_12])],[avatar_definition])).
% 15.37/3.51 thf(f3097,plain,(
% 15.37/3.51 ( ! [X0 : d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0)))) ) | (spl150_1 | ~spl150_10)),
% 15.37/3.51 inference(superposition,[status(thm)],[f2771,f3020])).
% 15.37/3.51 thf(f3020,plain,(
% 15.37/3.51 ((sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) = (stream1294929701mu_Get @ a @ b @ c @ (sK117 @ b @ a @ c @ (sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)))) | ~spl150_10),
% 15.37/3.51 inference(avatar_component_clause,[status(thm)],[f3018])).
% 15.37/3.51 thf(f3018,definition,(
% 15.37/3.51 spl150_10 <=> ((sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) = (stream1294929701mu_Get @ a @ b @ c @ (sK117 @ b @ a @ c @ (sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))))),
% 15.37/3.51 introduced(definition,[new_symbols(naming,[spl150_10])],[avatar_definition])).
% 15.37/3.51 thf(f2771,plain,(
% 15.37/3.51 ( ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1)))) ) | spl150_1),
% 15.37/3.51 inference(subsumption_resolution,[status(thm)],[f1174,f2763])).
% 15.37/3.51 thf(f2763,plain,(
% 15.37/3.51 (p != $true) | spl150_1),
% 15.37/3.51 inference(avatar_component_clause,[status(thm)],[f2761])).
% 15.37/3.51 thf(f2761,definition,(
% 15.37/3.51 spl150_1 <=> (p = $true)),
% 15.37/3.51 introduced(definition,[new_symbols(naming,[spl150_1])],[avatar_definition])).
% 15.37/3.51 thf(f1174,plain,(
% 15.37/3.51 ( ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1))) | (p = $true)) )),
% 15.37/3.51 inference(cnf_transformation,[status(thm)],[f947])).
% 15.37/3.51 thf(f947,plain,(
% 15.37/3.51 ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1))) | (p = $true))),
% 15.37/3.51 inference(ennf_transformation,[status(thm)],[f609])).
% 15.37/3.51 thf(f609,plain,(
% 15.37/3.51 ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1))) => (p = $true))),
% 15.37/3.51 inference(fool_elimination,[status(thm)],[f608])).
% 15.37/3.51 thf(f608,plain,(
% 15.37/3.51 ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1))) => p)),
% 15.37/3.51 inference(rectify,[status(thm)],[f274])).
% 15.37/3.51 thf(f274,axiom,(
% 15.37/3.51 ! [X138 : a > stream901396144_sp_mu @ a @ b @ c,X139 : d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X138) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X139))) => p)),
% 15.37/3.51 file('/export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2THF_27294.p',conj_2)).
% 15.37/3.51 thf(f3420,plain,(
% 15.37/3.51 spl150_12 | ~spl150_4 | ~spl150_10),
% 15.37/3.51 inference(avatar_split_clause,[status(thm)],[f3341,f3018,f2788,f3417])).
% 15.37/3.51 thf(f2788,definition,(
% 15.37/3.51 spl150_4 <=> ! [X2 : stream1273403375_sp_nu @ d @ a,X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : a] : (x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2)))),
% 15.37/3.51 introduced(definition,[new_symbols(naming,[spl150_4])],[avatar_definition])).
% 15.37/3.51 thf(f3341,plain,(
% 15.37/3.51 ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK117 @ a @ d @ stream1273403375_sp_nu @ d @ a @ (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))) = (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)) | (~spl150_4 | ~spl150_10)),
% 15.37/3.51 inference(trivial_inequality_removal,[status(thm)],[f3340])).
% 15.37/3.51 thf(f3340,plain,(
% 15.37/3.51 ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK117 @ a @ d @ stream1273403375_sp_nu @ d @ a @ (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))) = (sK127 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)) | (x != x) | (~spl150_4 | ~spl150_10)),
% 15.37/3.51 inference(superposition,[status(thm)],[f3095,f1463])).
% 15.37/3.51 thf(f3095,plain,(
% 15.37/3.51 ( ! [X0 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) @ X0)) | ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK117 @ a @ d @ stream1273403375_sp_nu @ d @ a @ X0)) = X0)) ) | (~spl150_4 | ~spl150_10)),
% 15.37/3.51 inference(superposition,[status(thm)],[f2925,f3020])).
% 15.37/3.51 thf(f2925,plain,(
% 15.37/3.51 ( ! [X0 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a,X1 : a > stream901396144_sp_mu @ a @ b @ c] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X1) @ X0)) | ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK117 @ a @ d @ stream1273403375_sp_nu @ d @ a @ X0)) = X0)) ) | ~spl150_4),
% 15.37/3.51 inference(superposition,[status(thm)],[f2789,f1414])).
% 15.37/3.51 thf(f1414,plain,(
% 15.37/3.51 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (((stream1370332830mu_Put @ X0 @ X2 @ X1 @ (sK115 @ X0 @ X1 @ X2 @ X3) @ (sK116 @ X0 @ X1 @ X2 @ X3)) = X3) | ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ (sK117 @ X0 @ X1 @ X2 @ X3)) = X3)) )),
% 15.37/3.51 inference(cnf_transformation,[status(thm)],[f1119])).
% 15.37/3.51 thf(f1119,plain,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (((stream1370332830mu_Put @ X0 @ X2 @ X1 @ (sK115 @ X0 @ X1 @ X2 @ X3) @ (sK116 @ X0 @ X1 @ X2 @ X3)) = X3) | ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ (sK117 @ X0 @ X1 @ X2 @ X3)) = X3))),
% 15.37/3.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK115,sK116,sK117])],[f1116,f1118,f1117])).
% 15.37/3.51 thf(f1117,plain,(
% 15.37/3.51 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (? [X4 : X0,X5 : X2] : ((stream1370332830mu_Put @ X0 @ X2 @ X1 @ X4 @ X5) = X3) => ((stream1370332830mu_Put @ X0 @ X2 @ X1 @ (sK115 @ X0 @ X1 @ X2 @ X3) @ (sK116 @ X0 @ X1 @ X2 @ X3)) = X3))),
% 15.37/3.51 introduced(definition,[],[choice_axiom])).
% 15.37/3.51 thf(f1118,plain,(
% 15.37/3.51 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (? [X6 : X1 > stream901396144_sp_mu @ X1 @ X0 @ X2] : ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ X6) = X3) => ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ (sK117 @ X0 @ X1 @ X2 @ X3)) = X3))),
% 15.37/3.51 introduced(definition,[],[choice_axiom])).
% 15.37/3.51 thf(f1116,plain,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (? [X4 : X0,X5 : X2] : ((stream1370332830mu_Put @ X0 @ X2 @ X1 @ X4 @ X5) = X3) | ? [X6 : X1 > stream901396144_sp_mu @ X1 @ X0 @ X2] : ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ X6) = X3))),
% 15.37/3.51 inference(rectify,[status(thm)],[f794])).
% 15.37/3.51 thf(f794,plain,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (? [X5 : X0,X6 : X2] : ((stream1370332830mu_Put @ X0 @ X2 @ X1 @ X5 @ X6) = X3) | ? [X4 : X1 > stream901396144_sp_mu @ X1 @ X0 @ X2] : ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ X4) = X3))),
% 15.37/3.51 inference(ennf_transformation,[status(thm)],[f704])).
% 15.37/3.51 thf(f704,plain,(
% 15.37/3.51 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (! [X4 : X1 > stream901396144_sp_mu @ X1 @ X0 @ X2] : ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ X4) != X3) => ~! [X5 : X0,X6 : X2] : ((stream1370332830mu_Put @ X0 @ X2 @ X1 @ X5 @ X6) != X3))),
% 15.37/3.51 inference(rectify,[status(thm)],[f4])).
% 15.37/3.51 thf(f4,axiom,(
% 15.37/3.51 ! [X1 : $tType,X0 : $tType,X2 : $tType,X13 : stream901396144_sp_mu @ X0 @ X1 @ X2] : (! [X14 : X0 > stream901396144_sp_mu @ X0 @ X1 @ X2] : ((stream1294929701mu_Get @ X0 @ X1 @ X2 @ X14) != X13) => ~! [X15 : X1,X16 : X2] : ((stream1370332830mu_Put @ X1 @ X2 @ X0 @ X15 @ X16) != X13))),
% 15.37/3.51 file('/export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2THF_27294.p',fact_3_sp_092_060_094sub_062_092_060mu_062_Oexhaust)).
% 15.37/3.51 thf(f2789,plain,(
% 15.37/3.51 ( ! [X2 : stream1273403375_sp_nu @ d @ a,X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2)))) ) | ~spl150_4),
% 15.37/3.51 inference(avatar_component_clause,[status(thm)],[f2788])).
% 15.37/3.51 thf(f3021,plain,(
% 15.37/3.51 spl150_10 | spl150_1),
% 15.37/3.51 inference(avatar_split_clause,[status(thm)],[f2955,f2761,f3018])).
% 15.37/3.51 thf(f2955,plain,(
% 15.37/3.51 ((sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) = (stream1294929701mu_Get @ a @ b @ c @ (sK117 @ b @ a @ c @ (sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)))) | spl150_1),
% 15.37/3.51 inference(equality_resolution,[status(thm)],[f2933])).
% 15.37/3.51 thf(f2933,plain,(
% 15.37/3.51 ( ! [X0 : product_prod @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != X0) | ((sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0) = (stream1294929701mu_Get @ a @ b @ c @ (sK117 @ b @ a @ c @ (sK126 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0))))) ) | spl150_1),
% 15.37/3.51 inference(superposition,[status(thm)],[f2924,f1463])).
% 15.37/3.51 thf(f2924,plain,(
% 15.37/3.51 ( ! [X0 : stream901396144_sp_mu @ a @ b @ c,X1 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0 @ X1)) | ((stream1294929701mu_Get @ a @ b @ c @ (sK117 @ b @ a @ c @ X0)) = X0)) ) | spl150_1),
% 15.37/3.51 inference(superposition,[status(thm)],[f2765,f1414])).
% 15.37/3.51 thf(f2765,plain,(
% 15.37/3.51 ( ! [X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a,X0 : b,X1 : c] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2))) ) | spl150_1),
% 15.37/3.51 inference(subsumption_resolution,[status(thm)],[f1456,f2763])).
% 15.37/3.51 thf(f1456,plain,(
% 15.37/3.51 ( ! [X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a,X0 : b,X1 : c] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2)) | (p = $true)) )),
% 15.37/3.51 inference(cnf_transformation,[status(thm)],[f786])).
% 15.37/3.51 thf(f786,plain,(
% 15.37/3.51 ! [X0 : b,X1 : c,X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((p = $true) | (x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2)))),
% 15.37/3.51 inference(ennf_transformation,[status(thm)],[f373])).
% 15.37/3.51 thf(f373,plain,(
% 15.37/3.51 ! [X0 : b,X1 : c,X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2)) => (p = $true))),
% 15.37/3.51 inference(fool_elimination,[status(thm)],[f372])).
% 15.37/3.51 thf(f372,plain,(
% 15.37/3.51 ! [X0 : b,X1 : c,X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2)) => p)),
% 15.37/3.51 inference(rectify,[status(thm)],[f272])).
% 15.37/3.51 thf(f272,axiom,(
% 15.37/3.51 ! [X135 : b,X136 : c,X137 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X135 @ X136) @ X137)) => p)),
% 15.37/3.51 file('/export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2THF_27294.p',conj_0)).
% 15.37/3.51 thf(f2790,plain,(
% 15.37/3.51 spl150_4 | spl150_1),
% 15.37/3.51 inference(avatar_split_clause,[status(thm)],[f1382,f2761,f2788])).
% 15.37/3.51 thf(f1382,plain,(
% 15.37/3.51 ( ! [X2 : stream1273403375_sp_nu @ d @ a,X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : a] : ((x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2))) | (p = $true)) )),
% 15.37/3.51 inference(cnf_transformation,[status(thm)],[f967])).
% 15.37/3.51 thf(f967,plain,(
% 15.37/3.51 ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : a,X2 : stream1273403375_sp_nu @ d @ a] : ((p = $true) | (x != (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2))))),
% 15.37/3.51 inference(ennf_transformation,[status(thm)],[f315])).
% 15.37/3.51 thf(f315,plain,(
% 15.37/3.51 ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : a,X2 : stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2))) => (p = $true))),
% 15.37/3.51 inference(fool_elimination,[status(thm)],[f314])).
% 15.37/3.51 thf(f314,plain,(
% 15.37/3.51 ! [X0 : a > stream901396144_sp_mu @ a @ b @ c,X1 : a,X2 : stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2))) => p)),
% 15.37/3.51 inference(rectify,[status(thm)],[f273])).
% 15.37/3.51 thf(f273,axiom,(
% 15.37/3.51 ! [X138 : a > stream901396144_sp_mu @ a @ b @ c,X135 : a,X136 : stream1273403375_sp_nu @ d @ a] : ((x = (product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X138) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X135 @ X136))) => p)),
% 15.37/3.51 file('/export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2THF_27294.p',conj_1)).
% 15.37/3.51 thf(f2764,plain,(
% 15.37/3.51 ~spl150_1),
% 15.37/3.51 inference(avatar_split_clause,[status(thm)],[f1376,f2761])).
% 15.37/3.51 thf(f1376,plain,(
% 15.37/3.51 (p != $true)),
% 15.37/3.51 inference(cnf_transformation,[status(thm)],[f714])).
% 15.37/3.51 thf(f714,plain,(
% 15.37/3.51 (p != $true)),
% 15.37/3.51 inference(flattening,[status(thm)],[f399])).
% 15.37/3.51 thf(f399,plain,(
% 15.37/3.51 ~(p = $true)),
% 15.37/3.51 inference(fool_elimination,[status(thm)],[f398])).
% 15.37/3.51 thf(f398,plain,(
% 15.37/3.51 ~p),
% 15.37/3.51 inference(rectify,[status(thm)],[f276])).
% 15.37/3.51 thf(f276,negated_conjecture,(
% 15.37/3.51 ~p),
% 15.37/3.51 inference(negated_conjecture,[status(cth)],[f275])).
% 15.37/3.51 thf(f275,conjecture,(
% 15.37/3.51 p),
% 15.37/3.51 file('/export/starexec/sandbox2/tmp/tmp.NF0sOmq8cm/DTF2THF_27294.p',conj_3)).
% 15.37/3.51 % SZS output end Proof for DTF2THF_27294
% 15.37/3.51 % (27498)------------------------------
% 15.37/3.51 % (27498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.37/3.51 % (27498)Termination reason: Refutation
% 15.37/3.51
% 15.37/3.51 % (27498)Memory used [KB]: 12409
% 15.37/3.51 % (27498)Time elapsed: 0.589 s
% 15.37/3.51 % (27498)Instructions burned: 1382 (million)
% 15.37/3.51 % (27498)------------------------------
% 15.37/3.51 % (27498)------------------------------
% 15.37/3.51 % (27398)Success in time 1.951 s
%------------------------------------------------------------------------------