%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT245^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 08:45:17 AM UTC 2026
% Result : Theorem 80.13s 12.89s
% Output : Refutation 80.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT245^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 06:11:41 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : DAT245^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.45 % Domain : Data Structures
% 0.18/0.45 % Problem : Infinite streams (sequences/lists) 108
% 0.18/0.45 % Version : [Bla16] axioms : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.18/0.45 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.18/0.45 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bla16]
% 0.18/0.45 % Names : stream__108.p [Bla16]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.67 v9.0.0, 1.00 v8.1.0, 0.75 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.18/0.45 % Syntax : Number of formulae : 341 ( 132 unt; 50 typ; 0 def)
% 0.18/0.45 % Number of atoms : 796 ( 258 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 13 ( 2 avg)
% 0.18/0.45 % Number of connectives : 3890 ( 79 ~; 9 |; 56 &;3424 @)
% 0.18/0.45 % ( 0 <=>; 322 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 18 ( 7 avg)
% 0.18/0.45 % Number of types : 2 ( 1 usr)
% 0.18/0.45 % Number of type conns : 187 ( 187 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 52 ( 49 usr; 5 con; 0-7 aty)
% 0.18/0.45 % Number of variables : 1030 ( 51 ^; 914 !; 18 ?;1030 :)
% 0.18/0.45 % ( 47 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.45 % SPC : TH1_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.18/0.45 % 2016-07-13 14:40:45.745
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 %----Could-be-implicit typings (4)
% 0.18/0.45 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream,type,
% 0.18/0.45 stream170649215stream: $tType > $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_t_Set_Oset,type,
% 0.18/0.45 set: $tType > $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_t_itself,type,
% 0.18/0.45 itself: $tType > $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_tf_a,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 %----Explicit typings (46)
% 0.18/0.45 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.18/0.45 bounded_lattice:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_HOL_Otype,type,
% 0.18/0.45 type:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Groups_Ouminus,type,
% 0.18/0.45 uminus:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Obot,type,
% 0.18/0.45 bot:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.18/0.45 ord:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.18/0.45 order:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Groups_Ogroup__add,type,
% 0.18/0.45 group_add:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Ono__bot,type,
% 0.18/0.45 no_bot:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Ono__top,type,
% 0.18/0.45 no_top:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.18/0.45 linorder:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.18/0.45 preorder:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.18/0.45 order_bot:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.18/0.45 boolean_algebra:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.18/0.45 semilattice_inf:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.18/0.45 ordered_ab_group_add:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.18/0.45 bounded_lattice_bot:
% 0.18/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.18/0.45 minus_minus:
% 0.18/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.18/0.45 uminus_uminus:
% 0.18/0.45 !>[A: $tType] : ( A > A ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_If,type,
% 0.18/0.45 if:
% 0.18/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.18/0.45 inf_inf:
% 0.18/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.18/0.45 bot_bot:
% 0.18/0.45 !>[A: $tType] : A ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.18/0.45 ord_less:
% 0.18/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.18/0.45 ord_less_eq:
% 0.18/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oorder__class_Oantimono,type,
% 0.18/0.45 order_antimono:
% 0.18/0.45 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Pure_Otype,type,
% 0.18/0.45 type2:
% 0.18/0.45 !>[A: $tType] : ( itself @ A ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Relation_Oinv__imagep,type,
% 0.18/0.45 inv_imagep:
% 0.18/0.45 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_OBall,type,
% 0.18/0.45 ball:
% 0.18/0.45 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_OCollect,type,
% 0.18/0.45 collect:
% 0.18/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oinsert,type,
% 0.18/0.45 insert:
% 0.18/0.45 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Ois__empty,type,
% 0.18/0.45 is_empty:
% 0.18/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Ois__singleton,type,
% 0.18/0.45 is_singleton:
% 0.18/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Opairwise,type,
% 0.18/0.45 pairwise:
% 0.18/0.45 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oremove,type,
% 0.18/0.45 remove:
% 0.18/0.45 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Othe__elem,type,
% 0.18/0.45 the_elem:
% 0.18/0.45 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember,type,
% 0.18/0.45 stream1586597341member:
% 0.18/0.45 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_OSCons,type,
% 0.18/0.45 stream641971652_SCons:
% 0.18/0.45 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocase__stream,type,
% 0.18/0.45 stream1342653232stream:
% 0.18/0.45 !>[A: $tType,B: $tType] : ( ( A > ( stream170649215stream @ A ) > B ) > ( stream170649215stream @ A ) > B ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocorec__stream,type,
% 0.18/0.45 stream660621732stream:
% 0.18/0.45 !>[C: $tType,A: $tType] : ( ( C > A ) > ( C > $o ) > ( C > ( stream170649215stream @ A ) ) > ( C > C ) > C > ( stream170649215stream @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Opred__stream,type,
% 0.18/0.45 stream1153105665stream:
% 0.18/0.45 !>[A: $tType] : ( ( A > $o ) > ( stream170649215stream @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osset,type,
% 0.18/0.45 stream30925839e_sset:
% 0.18/0.45 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( set @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreams,type,
% 0.18/0.45 stream2015131171treams:
% 0.18/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( stream170649215stream @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreamsp,type,
% 0.18/0.45 stream86250253reamsp:
% 0.18/0.45 !>[A: $tType] : ( ( A > $o ) > ( stream170649215stream @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member,type,
% 0.18/0.45 member:
% 0.18/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_A,type,
% 0.18/0.45 a2: set @ a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_s,type,
% 0.18/0.45 s: stream170649215stream @ a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_sa____,type,
% 0.18/0.45 sa: stream170649215stream @ a ).
% 0.18/0.45
% 0.18/0.45 %----Relevant facts (256)
% 0.18/0.45 thf(fact_0_streams,axiom,
% 0.18/0.45 ord_less_eq @ ( set @ a ) @ ( stream30925839e_sset @ a @ sa ) @ a2 ).
% 0.18/0.45
% 0.18/0.45 % streams
% 0.18/0.45 thf(fact_1_assms,axiom,
% 0.18/0.45 ord_less_eq @ ( set @ a ) @ ( stream30925839e_sset @ a @ s ) @ a2 ).
% 0.18/0.45
% 0.18/0.45 % assms
% 0.18/0.45 thf(fact_2_stream_Oinject,axiom,
% 0.18/0.45 ! [A: $tType,X1: A,X2: stream170649215stream @ A,Y1: A,Y2: stream170649215stream @ A] :
% 0.18/0.45 ( ( ( stream641971652_SCons @ A @ X1 @ X2 )
% 0.18/0.45 = ( stream641971652_SCons @ A @ Y1 @ Y2 ) )
% 0.18/0.45 = ( ( X1 = Y1 )
% 0.18/0.45 & ( X2 = Y2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % stream.inject
% 0.18/0.45 thf(fact_3_stream_Oset__intros_I2_J,axiom,
% 0.18/0.45 ! [A: $tType,X: A,A2: stream170649215stream @ A,A1: A] :
% 0.18/0.45 ( ( member @ A @ X @ ( stream30925839e_sset @ A @ A2 ) )
% 0.18/0.45 => ( member @ A @ X @ ( stream30925839e_sset @ A @ ( stream641971652_SCons @ A @ A1 @ A2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % stream.set_intros(2)
% 0.18/0.45 thf(fact_4_stream_Oset__intros_I1_J,axiom,
% 0.18/0.45 ! [A: $tType,A1: A,A2: stream170649215stream @ A] : ( member @ A @ A1 @ ( stream30925839e_sset @ A @ ( stream641971652_SCons @ A @ A1 @ A2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % stream.set_intros(1)
% 0.18/0.45 thf(fact_5_streams_Ocases,axiom,
% 0.18/0.45 ! [A: $tType,A3: stream170649215stream @ A,A4: set @ A] :
% 0.18/0.45 ( ( member @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A4 ) )
% 0.18/0.45 => ~ ! [A5: A,S: stream170649215stream @ A] :
% 0.18/0.45 ( ( A3
% 0.18/0.45 = ( stream641971652_SCons @ A @ A5 @ S ) )
% 0.18/0.45 => ( ( member @ A @ A5 @ A4 )
% 0.18/0.45 => ~ ( member @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A4 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % streams.cases
% 0.18/0.45 thf(fact_6_streams_Osimps,axiom,
% 0.18/0.45 ! [A: $tType,A3: stream170649215stream @ A,A4: set @ A] :
% 0.18/0.45 ( ( member @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A4 ) )
% 0.18/0.45 = ( ? [A6: A,S2: stream170649215stream @ A] :
% 0.18/0.45 ( ( A3
% 0.18/0.45 = ( stream641971652_SCons @ A @ A6 @ S2 ) )
% 0.18/0.45 & ( member @ A @ A6 @ A4 )
% 0.18/0.45 & ( member @ ( stream170649215stream @ A ) @ S2 @ ( stream2015131171treams @ A @ A4 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % streams.simps
% 0.18/0.45 thf(fact_7_stream_Oexhaust,axiom,
% 0.18/0.45 ! [A: $tType,Y: stream170649215stream @ A] :
% 0.18/0.45 ~ ! [X12: A,X22: stream170649215stream @ A] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( stream641971652_SCons @ A @ X12 @ X22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % stream.exhaust
% 0.18/0.45 thf(fact_8_streams__Stream,axiom,
% 0.18/0.45 ! [A: $tType,X: A,S3: stream170649215stream @ A,A4: set @ A] :
% 0.18/0.45 ( ( member @ ( stream170649215stream @ A ) @ ( stream641971652_SCons @ A @ X @ S3 ) @ ( stream2015131171treams @ A @ A4 ) )
% 0.18/0.45 = ( ( member @ A @ X @ A4 )
% 0.18/0.45 & ( member @ ( stream170649215stream @ A ) @ S3 @ ( stream2015131171treams @ A @ A4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % streams_Stream
% 0.18/0.45 thf(fact_9_stream_Oset__cases,axiom,
% 0.18/0.45 ! [A: $tType,E: A,A3: stream170649215stream @ A] :
% 0.18/0.45 ( ( member @ A @ E @ ( stream30925839e_sset @ A @ A3 ) )
% 0.18/0.45 => ( ! [Z2: stream170649215stream @ A] :
% 0.18/0.45 ( A3
% 0.18/0.45 != ( stream641971652_SCons @ A @ E @ Z2 ) )
% 0.18/0.45 => ~ ! [Z1: A,Z2: stream170649215stream @ A] :
% 0.18/0.45 ( ( A3
% 0.18/0.45 = ( stream641971652_SCons @ A @ Z1 @ Z2 ) )
% 0.18/0.45 => ~ ( member @ A @ E @ ( stream30925839e_sset @ A @ Z2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % stream.set_cases
% 0.18/0.45 thf(fact_10_streams_Ocoinduct,axiom,
% 0.18/0.45 ! [A: $tType,X3: ( stream170649215stream @ A ) > $o,X: stream170649215stream @ A,A4: set @ A] :
% 0.18/0.45 ( ( X3 @ X )
% 0.18/0.45 => ( ! [X4: stream170649215stream @ A] :
% 0.18/0.45 ( ( X3 @ X4 )
% 0.18/0.45 => ? [A7: A,S4: stream170649215stream @ A] :
% 0.18/0.45 ( ( X4
% 0.18/0.45 = ( stream641971652_SCons @ A @ A7 @ S4 ) )
% 0.18/0.45 & ( member @ A @ A7 @ A4 )
% 0.18/0.45 & ( ( X3 @ S4 )
% 0.18/0.45 | ( member @ ( stream170649215stream @ A ) @ S4 @ ( stream2015131171treams @ A @ A4 ) ) ) ) )
% 0.18/0.45 => ( member @ ( stream170649215stream @ A ) @ X @ ( stream2015131171treams @ A @ A4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % streams.coinduct
% 0.18/0.45 thf(fact_11_stream_Oset__induct,axiom,
% 0.18/0.45 ! [A: $tType,X: A,A3: stream170649215stream @ A,P: A > ( stream170649215stream @ A ) > $o] :
% 0.18/0.45 ( ( member @ A @ X @ ( stream30925839e_sset @ A @ A3 ) )
% 0.18/0.45 => ( ! [Z1: A,Z2: stream170649215stream @ A] : ( P @ Z1 @ ( stream641971652_SCons @ A @ Z1 @ Z2 ) )
% 0.18/0.45 => ( ! [Z1: A,Z2: stream170649215stream @ A,Xa: A] :
% 0.18/0.45 ( ( member @ A @ Xa @ ( stream30925839e_sset @ A @ Z2 ) )
% 0.18/0.45 => ( ( P @ Xa @ Z2 )
% 0.18/0.45 => ( P @ Xa @ ( stream641971652_SCons @ A @ Z1 @ Z2 ) ) ) )
% 0.18/0.45 => ( P @ X @ A3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % stream.set_induct
% 0.18/0.45 thf(fact_12_smember__code,axiom,
% 0.18/0.45 ! [A: $tType,X: A,Y: A,S3: stream170649215stream @ A] :
% 0.18/0.45 ( ( stream1586597341member @ A @ X @ ( stream641971652_SCons @ A @ Y @ S3 ) )
% 0.18/0.45 = ( ( X != Y )
% 0.18/0.45 => ( stream1586597341member @ A @ X @ S3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smember_code
% 0.18/0.45 thf(fact_13_subsetI,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.45 ( ! [X4: A] :
% 0.18/0.45 ( ( member @ A @ X4 @ A4 )
% 0.18/0.45 => ( member @ A @ X4 @ B2 ) )
% 0.18/0.45 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % subsetI
% 0.18/0.45 thf(fact_14_subset__antisym,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A4 )
% 0.18/0.45 => ( A4 = B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % subset_antisym
% 0.18/0.45 thf(fact_15_order__refl,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_refl
% 0.18/0.45 thf(fact_16_Stream__Mirabelle__hbrgyiwlrc_Osmember__def,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( stream1586597341member @ A )
% 0.18/0.45 = ( ^ [X5: A,S2: stream170649215stream @ A] : ( member @ A @ X5 @ ( stream30925839e_sset @ A @ S2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Stream_Mirabelle_hbrgyiwlrc.smember_def
% 0.18/0.45 thf(fact_17_set__mp,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,X: A] :
% 0.18/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.45 => ( ( member @ A @ X @ A4 )
% 0.18/0.45 => ( member @ A @ X @ B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % set_mp
% 0.18/0.45 thf(fact_18_in__mono,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,X: A] :
% 0.18/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.45 => ( ( member @ A @ X @ A4 )
% 0.18/0.45 => ( member @ A @ X @ B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % in_mono
% 0.18/0.45 thf(fact_19_subsetD,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.18/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.45 => ( ( member @ A @ C2 @ A4 )
% 0.18/0.45 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % subsetD
% 0.18/0.45 thf(fact_20_subsetCE,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.18/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.45 => ( ( member @ A @ C2 @ A4 )
% 0.18/0.45 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % subsetCE
% 0.18/0.45 thf(fact_21_equalityE,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.45 ( ( A4 = B2 )
% 0.18/0.45 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.45 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % equalityE
% 0.18/0.45 thf(fact_22_subset__eq,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.18/0.45 = ( ^ [A8: set @ A,B3: set @ A] :
% 0.18/0.45 ! [X5: A] :
% 0.18/0.45 ( ( member @ A @ X5 @ A8 )
% 0.18/0.45 => ( member @ A @ X5 @ B3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % subset_eq
% 0.18/0.45 thf(fact_23_equalityD1,axiom,
% 0.18/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.45 ( ( A4 = B2 )
% 0.18/0.45 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % equalityD1
% 0.18/0.45 thf(fact_24_dual__order_Oantisym,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [B4: A,A3: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.18/0.45 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.45 => ( A3 = B4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.antisym
% 0.18/0.45 thf(fact_25_dual__order_Otrans,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [B4: A,A3: A,C2: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.18/0.45 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.18/0.45 => ( ord_less_eq @ A @ C2 @ A3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.trans
% 0.18/0.45 thf(fact_26_linorder__wlog,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [P: A > A > $o,A3: A,B4: A] :
% 0.18/0.45 ( ! [A5: A,B5: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.18/0.45 => ( P @ A5 @ B5 ) )
% 0.18/0.45 => ( ! [A5: A,B5: A] :
% 0.18/0.45 ( ( P @ B5 @ A5 )
% 0.18/0.45 => ( P @ A5 @ B5 ) )
% 0.18/0.45 => ( P @ A3 @ B4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_wlog
% 0.18/0.45 thf(fact_27_dual__order_Orefl,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.refl
% 0.18/0.45 thf(fact_28_order__trans,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [X: A,Y: A,Z: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.45 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.18/0.45 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_trans
% 0.18/0.45 thf(fact_29_order__class_Oorder_Oantisym,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [A3: A,B4: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.45 => ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.18/0.45 => ( A3 = B4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_class.order.antisym
% 0.18/0.45 thf(fact_30_ord__le__eq__trans,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [A3: A,B4: A,C2: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.45 => ( ( B4 = C2 )
% 0.18/0.45 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_le_eq_trans
% 0.18/0.45 thf(fact_31_ord__eq__le__trans,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [A3: A,B4: A,C2: A] :
% 0.18/0.45 ( ( A3 = B4 )
% 0.18/0.45 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.18/0.45 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_le_trans
% 0.18/0.45 thf(fact_32_antisym__conv,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [Y: A,X: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ Y @ X )
% 0.18/0.45 => ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.45 = ( X = Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % antisym_conv
% 0.18/0.45 thf(fact_33_le__cases3,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [X: A,Y: A,Z: A] :
% 0.18/0.45 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.45 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.18/0.45 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.18/0.45 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.18/0.45 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.18/0.45 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.18/0.45 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.18/0.45 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.18/0.45 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.18/0.45 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.18/0.45 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.18/0.45 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_cases3
% 0.18/0.45 thf(fact_34_order_Otrans,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [A3: A,B4: A,C2: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.45 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.18/0.45 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.trans
% 0.18/0.45 thf(fact_35_le__cases,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [X: A,Y: A] :
% 0.18/0.45 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.18/0.45 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_cases
% 0.18/0.45 thf(fact_36_eq__refl,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [X: A,Y: A] :
% 0.18/0.45 ( ( X = Y )
% 0.18/0.45 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eq_refl
% 0.18/0.45 thf(fact_37_linear,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [X: A,Y: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.45 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linear
% 0.18/0.45 thf(fact_38_antisym,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ! [X: A,Y: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.45 => ( ( ord_less_eq @ A @ Y @ X )
% 0.18/0.45 => ( X = Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % antisym
% 0.18/0.45 thf(fact_39_eq__iff,axiom,
% 0.18/0.45 ! [A: $tType] :
% 0.18/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.45 => ( ( ^ [Y3: A,Z3: A] : ( Y3 = Z3 ) )
% 0.18/0.45 = ( ^ [X5: A,Y4: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.18/0.45 & ( ord_less_eq @ A @ Y4 @ X5 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eq_iff
% 0.18/0.45 thf(fact_40_ord__le__eq__subst,axiom,
% 0.18/0.45 ! [A: $tType,B: $tType] :
% 0.18/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.18/0.45 => ! [A3: A,B4: A,F: A > B,C2: B] :
% 0.18/0.45 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.45 => ( ( ( F @ B4 )
% 0.18/0.45 = C2 )
% 0.18/0.45 => ( ! [X4: A,Y5: A] :
% 0.18/0.45 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.18/0.45 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.45 => ( ord_less_eq @ B @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_le_eq_subst
% 0.18/0.45 thf(fact_41_ord__eq__le__subst,axiom,
% 0.18/0.45 ! [A: $tType,B: $tType] :
% 0.18/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.18/0.45 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.18/0.45 ( ( A3
% 0.18/0.46 = ( F @ B4 ) )
% 0.18/0.46 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.18/0.46 => ( ! [X4: B,Y5: B] :
% 0.18/0.46 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.46 => ( ord_less_eq @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ord_eq_le_subst
% 0.18/0.46 thf(fact_42_order__subst2,axiom,
% 0.18/0.46 ! [A: $tType,C: $tType] :
% 0.18/0.46 ( ( ( order @ C @ ( type2 @ C ) )
% 0.18/0.46 & ( order @ A @ ( type2 @ A ) ) )
% 0.18/0.46 => ! [A3: A,B4: A,F: A > C,C2: C] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.46 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.18/0.46 => ( ! [X4: A,Y5: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.46 => ( ord_less_eq @ C @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % order_subst2
% 0.18/0.46 thf(fact_43_order__subst1,axiom,
% 0.18/0.46 ! [A: $tType,B: $tType] :
% 0.18/0.46 ( ( ( order @ B @ ( type2 @ B ) )
% 0.18/0.46 & ( order @ A @ ( type2 @ A ) ) )
% 0.18/0.46 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ ( F @ B4 ) )
% 0.18/0.46 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.18/0.46 => ( ! [X4: B,Y5: B] :
% 0.18/0.46 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.46 => ( ord_less_eq @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % order_subst1
% 0.18/0.46 thf(fact_44_le__fun__def,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.18/0.46 = ( ^ [F2: A > B,G: A > B] :
% 0.18/0.46 ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G @ X5 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_fun_def
% 0.18/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,P: A > $o] :
% 0.18/0.46 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.18/0.46 = ( P @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % mem_Collect_eq
% 0.18/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( collect @ A
% 0.18/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ A4 ) )
% 0.18/0.46 = A4 ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_mem_eq
% 0.18/0.46 thf(fact_47_Collect__cong,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.18/0.46 ( ! [X4: A] :
% 0.18/0.46 ( ( P @ X4 )
% 0.18/0.46 = ( Q @ X4 ) )
% 0.18/0.46 => ( ( collect @ A @ P )
% 0.18/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_cong
% 0.18/0.46 thf(fact_48_ext,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.18/0.46 ( ! [X4: A] :
% 0.18/0.46 ( ( F @ X4 )
% 0.18/0.46 = ( G2 @ X4 ) )
% 0.18/0.46 => ( F = G2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % ext
% 0.18/0.46 thf(fact_49_le__funI,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.46 => ! [F: A > B,G2: A > B] :
% 0.18/0.46 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G2 @ X4 ) )
% 0.18/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_funI
% 0.18/0.46 thf(fact_50_le__funE,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.46 => ! [F: A > B,G2: A > B,X: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.18/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_funE
% 0.18/0.46 thf(fact_51_le__funD,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.46 => ! [F: A > B,G2: A > B,X: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.18/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_funD
% 0.18/0.46 thf(fact_52_Collect__mono__iff,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.18/0.46 = ( ! [X5: A] :
% 0.18/0.46 ( ( P @ X5 )
% 0.18/0.46 => ( Q @ X5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_mono_iff
% 0.18/0.46 thf(fact_53_contra__subsetD,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ~ ( member @ A @ C2 @ B2 )
% 0.18/0.46 => ~ ( member @ A @ C2 @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % contra_subsetD
% 0.18/0.46 thf(fact_54_set__eq__subset,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ^ [Y3: set @ A,Z3: set @ A] : ( Y3 = Z3 ) )
% 0.18/0.46 = ( ^ [A8: set @ A,B3: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A8 @ B3 )
% 0.18/0.46 & ( ord_less_eq @ ( set @ A ) @ B3 @ A8 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % set_eq_subset
% 0.18/0.46 thf(fact_55_subset__trans,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_trans
% 0.18/0.46 thf(fact_56_Collect__mono,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.18/0.46 ( ! [X4: A] :
% 0.18/0.46 ( ( P @ X4 )
% 0.18/0.46 => ( Q @ X4 ) )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_mono
% 0.18/0.46 thf(fact_57_subset__refl,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.18/0.46
% 0.18/0.46 % subset_refl
% 0.18/0.46 thf(fact_58_rev__subsetD,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_subsetD
% 0.18/0.46 thf(fact_59_subset__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.18/0.46 = ( ^ [A8: set @ A,B3: set @ A] :
% 0.18/0.46 ! [T: A] :
% 0.18/0.46 ( ( member @ A @ T @ A8 )
% 0.18/0.46 => ( member @ A @ T @ B3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_iff
% 0.18/0.46 thf(fact_60_set__rev__mp,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( member @ A @ X @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % set_rev_mp
% 0.18/0.46 thf(fact_61_equalityD2,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( A4 = B2 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % equalityD2
% 0.18/0.46 thf(fact_62_stream_Oset,axiom,
% 0.18/0.46 ! [A: $tType,X1: A,X2: stream170649215stream @ A] :
% 0.18/0.46 ( ( stream30925839e_sset @ A @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.18/0.46 = ( insert @ A @ X1 @ ( stream30925839e_sset @ A @ X2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.set
% 0.18/0.46 thf(fact_63_stream_Opred__inject,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o,A3: A,Aa: stream170649215stream @ A] :
% 0.18/0.46 ( ( stream1153105665stream @ A @ P @ ( stream641971652_SCons @ A @ A3 @ Aa ) )
% 0.18/0.46 = ( ( P @ A3 )
% 0.18/0.46 & ( stream1153105665stream @ A @ P @ Aa ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.pred_inject
% 0.18/0.46 thf(fact_64_antimono__def,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.46 & ( order @ B @ ( type2 @ B ) ) )
% 0.18/0.46 => ( ( order_antimono @ A @ B )
% 0.18/0.46 = ( ^ [F2: A > B] :
% 0.18/0.46 ! [X5: A,Y4: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.18/0.46 => ( ord_less_eq @ B @ ( F2 @ Y4 ) @ ( F2 @ X5 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % antimono_def
% 0.18/0.46 thf(fact_65_antimonoI,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.46 & ( order @ B @ ( type2 @ B ) ) )
% 0.18/0.46 => ! [F: A > B] :
% 0.18/0.46 ( ! [X4: A,Y5: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less_eq @ B @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 0.18/0.46 => ( order_antimono @ A @ B @ F ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % antimonoI
% 0.18/0.46 thf(fact_66_antimonoE,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.46 & ( order @ B @ ( type2 @ B ) ) )
% 0.18/0.46 => ! [F: A > B,X: A,Y: A] :
% 0.18/0.46 ( ( order_antimono @ A @ B @ F )
% 0.18/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.46 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % antimonoE
% 0.18/0.46 thf(fact_67_antimonoD,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( ( order @ A @ ( type2 @ A ) )
% 0.18/0.46 & ( order @ B @ ( type2 @ B ) ) )
% 0.18/0.46 => ! [F: A > B,X: A,Y: A] :
% 0.18/0.46 ( ( order_antimono @ A @ B @ F )
% 0.18/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.46 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % antimonoD
% 0.18/0.46 thf(fact_68_streamsp_Ocoinduct,axiom,
% 0.18/0.46 ! [A: $tType,X3: ( stream170649215stream @ A ) > $o,X: stream170649215stream @ A,A4: A > $o] :
% 0.18/0.46 ( ( X3 @ X )
% 0.18/0.46 => ( ! [X4: stream170649215stream @ A] :
% 0.18/0.46 ( ( X3 @ X4 )
% 0.18/0.46 => ? [A7: A,S4: stream170649215stream @ A] :
% 0.18/0.46 ( ( X4
% 0.18/0.46 = ( stream641971652_SCons @ A @ A7 @ S4 ) )
% 0.18/0.46 & ( A4 @ A7 )
% 0.18/0.46 & ( ( X3 @ S4 )
% 0.18/0.46 | ( stream86250253reamsp @ A @ A4 @ S4 ) ) ) )
% 0.18/0.46 => ( stream86250253reamsp @ A @ A4 @ X ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % streamsp.coinduct
% 0.18/0.46 thf(fact_69_streamsp_Osimps,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( stream86250253reamsp @ A )
% 0.18/0.46 = ( ^ [A8: A > $o,A6: stream170649215stream @ A] :
% 0.18/0.46 ? [B6: A,S2: stream170649215stream @ A] :
% 0.18/0.46 ( ( A6
% 0.18/0.46 = ( stream641971652_SCons @ A @ B6 @ S2 ) )
% 0.18/0.46 & ( A8 @ B6 )
% 0.18/0.46 & ( stream86250253reamsp @ A @ A8 @ S2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % streamsp.simps
% 0.18/0.46 thf(fact_70_streamsp_Ocases,axiom,
% 0.18/0.46 ! [A: $tType,A4: A > $o,A3: stream170649215stream @ A] :
% 0.18/0.46 ( ( stream86250253reamsp @ A @ A4 @ A3 )
% 0.18/0.46 => ~ ! [A5: A,S: stream170649215stream @ A] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( stream641971652_SCons @ A @ A5 @ S ) )
% 0.18/0.46 => ( ( A4 @ A5 )
% 0.18/0.46 => ~ ( stream86250253reamsp @ A @ A4 @ S ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % streamsp.cases
% 0.18/0.46 thf(fact_71_stream_Ocase,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType,F: A > ( stream170649215stream @ A ) > B,X1: A,X2: stream170649215stream @ A] :
% 0.18/0.46 ( ( stream1342653232stream @ A @ B @ F @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.18/0.46 = ( F @ X1 @ X2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.case
% 0.18/0.46 thf(fact_72_insertCI,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,B2: set @ A,B4: A] :
% 0.18/0.46 ( ( ~ ( member @ A @ A3 @ B2 )
% 0.18/0.46 => ( A3 = B4 ) )
% 0.18/0.46 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertCI
% 0.18/0.46 thf(fact_73_insert__iff,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.18/0.46 = ( ( A3 = B4 )
% 0.18/0.46 | ( member @ A @ A3 @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_iff
% 0.18/0.46 thf(fact_74_insert__absorb2,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A] :
% 0.18/0.46 ( ( insert @ A @ X @ ( insert @ A @ X @ A4 ) )
% 0.18/0.46 = ( insert @ A @ X @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_absorb2
% 0.18/0.46 thf(fact_75_insert__subset,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.18/0.46 = ( ( member @ A @ X @ B2 )
% 0.18/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_subset
% 0.18/0.46 thf(fact_76_insertE,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.18/0.46 => ( ( A3 != B4 )
% 0.18/0.46 => ( member @ A @ A3 @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertE
% 0.18/0.46 thf(fact_77_insertI1,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,B2: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertI1
% 0.18/0.46 thf(fact_78_insertI2,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,B2: set @ A,B4: A] :
% 0.18/0.46 ( ( member @ A @ A3 @ B2 )
% 0.18/0.46 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertI2
% 0.18/0.46 thf(fact_79_Set_Oset__insert,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ X @ A4 )
% 0.18/0.46 => ~ ! [B7: set @ A] :
% 0.18/0.46 ( ( A4
% 0.18/0.46 = ( insert @ A @ X @ B7 ) )
% 0.18/0.46 => ( member @ A @ X @ B7 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Set.set_insert
% 0.18/0.46 thf(fact_80_insert__ident,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ~ ( member @ A @ X @ B2 )
% 0.18/0.46 => ( ( ( insert @ A @ X @ A4 )
% 0.18/0.46 = ( insert @ A @ X @ B2 ) )
% 0.18/0.46 = ( A4 = B2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_ident
% 0.18/0.46 thf(fact_81_insert__absorb,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ A3 @ A4 )
% 0.18/0.46 => ( ( insert @ A @ A3 @ A4 )
% 0.18/0.46 = A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_absorb
% 0.18/0.46 thf(fact_82_insert__eq__iff,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A,B4: A,B2: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ A3 @ A4 )
% 0.18/0.46 => ( ~ ( member @ A @ B4 @ B2 )
% 0.18/0.46 => ( ( ( insert @ A @ A3 @ A4 )
% 0.18/0.46 = ( insert @ A @ B4 @ B2 ) )
% 0.18/0.46 = ( ( ( A3 = B4 )
% 0.18/0.46 => ( A4 = B2 ) )
% 0.18/0.46 & ( ( A3 != B4 )
% 0.18/0.46 => ? [C4: set @ A] :
% 0.18/0.46 ( ( A4
% 0.18/0.46 = ( insert @ A @ B4 @ C4 ) )
% 0.18/0.46 & ~ ( member @ A @ B4 @ C4 )
% 0.18/0.46 & ( B2
% 0.18/0.46 = ( insert @ A @ A3 @ C4 ) )
% 0.18/0.46 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_eq_iff
% 0.18/0.46 thf(fact_83_insert__commute,axiom,
% 0.18/0.46 ! [A: $tType,X: A,Y: A,A4: set @ A] :
% 0.18/0.46 ( ( insert @ A @ X @ ( insert @ A @ Y @ A4 ) )
% 0.18/0.46 = ( insert @ A @ Y @ ( insert @ A @ X @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_commute
% 0.18/0.46 thf(fact_84_mk__disjoint__insert,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ A3 @ A4 )
% 0.18/0.46 => ? [B7: set @ A] :
% 0.18/0.46 ( ( A4
% 0.18/0.46 = ( insert @ A @ A3 @ B7 ) )
% 0.18/0.46 & ~ ( member @ A @ A3 @ B7 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % mk_disjoint_insert
% 0.18/0.46 thf(fact_85_insert__mono,axiom,
% 0.18/0.46 ! [A: $tType,C3: set @ A,D: set @ A,A3: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C3 ) @ ( insert @ A @ A3 @ D ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_mono
% 0.18/0.46 thf(fact_86_subset__insert,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.18/0.46 = ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_insert
% 0.18/0.46 thf(fact_87_subset__insertI,axiom,
% 0.18/0.46 ! [A: $tType,B2: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( insert @ A @ A3 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_insertI
% 0.18/0.46 thf(fact_88_subset__insertI2,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,B4: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_insertI2
% 0.18/0.46 thf(fact_89_stream_Opred__cong,axiom,
% 0.18/0.46 ! [A: $tType,X: stream170649215stream @ A,Ya: stream170649215stream @ A,P: A > $o,Pa: A > $o] :
% 0.18/0.46 ( ( X = Ya )
% 0.18/0.46 => ( ! [Z4: A] :
% 0.18/0.46 ( ( member @ A @ Z4 @ ( stream30925839e_sset @ A @ Ya ) )
% 0.18/0.46 => ( ( P @ Z4 )
% 0.18/0.46 = ( Pa @ Z4 ) ) )
% 0.18/0.46 => ( ( stream1153105665stream @ A @ P @ X )
% 0.18/0.46 = ( stream1153105665stream @ A @ Pa @ Ya ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.pred_cong
% 0.18/0.46 thf(fact_90_stream_Opred__mono__strong,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o,X: stream170649215stream @ A,Pa: A > $o] :
% 0.18/0.46 ( ( stream1153105665stream @ A @ P @ X )
% 0.18/0.46 => ( ! [Z4: A] :
% 0.18/0.46 ( ( member @ A @ Z4 @ ( stream30925839e_sset @ A @ X ) )
% 0.18/0.46 => ( ( P @ Z4 )
% 0.18/0.46 => ( Pa @ Z4 ) ) )
% 0.18/0.46 => ( stream1153105665stream @ A @ Pa @ X ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.pred_mono_strong
% 0.18/0.46 thf(fact_91_insert__subsetI,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A,X3: set @ A] :
% 0.18/0.46 ( ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ X3 @ A4 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ X3 ) @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_subsetI
% 0.18/0.46 thf(fact_92_singleton__insert__inj__eq_H,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A,B4: A] :
% 0.18/0.46 ( ( ( insert @ A @ A3 @ A4 )
% 0.18/0.46 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 = ( ( A3 = B4 )
% 0.18/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_insert_inj_eq'
% 0.18/0.46 thf(fact_93_singleton__insert__inj__eq,axiom,
% 0.18/0.46 ! [A: $tType,B4: A,A3: A,A4: set @ A] :
% 0.18/0.46 ( ( ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( insert @ A @ A3 @ A4 ) )
% 0.18/0.46 = ( ( A3 = B4 )
% 0.18/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_insert_inj_eq
% 0.18/0.46 thf(fact_94_stream_Opred__set,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( stream1153105665stream @ A )
% 0.18/0.46 = ( ^ [P2: A > $o,X5: stream170649215stream @ A] :
% 0.18/0.46 ! [Y4: A] :
% 0.18/0.46 ( ( member @ A @ Y4 @ ( stream30925839e_sset @ A @ X5 ) )
% 0.18/0.46 => ( P2 @ Y4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.pred_set
% 0.18/0.46 thf(fact_95_subset__singletonD,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,X: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 => ( ( A4
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 | ( A4
% 0.18/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_singletonD
% 0.18/0.46 thf(fact_96_subset__singleton__iff,axiom,
% 0.18/0.46 ! [A: $tType,X3: set @ A,A3: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ X3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 = ( ( X3
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 | ( X3
% 0.18/0.46 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_singleton_iff
% 0.18/0.46 thf(fact_97_stream_Ocorec__code,axiom,
% 0.18/0.46 ! [A: $tType,C: $tType] :
% 0.18/0.46 ( ( stream660621732stream @ C @ A )
% 0.18/0.46 = ( ^ [G1: C > A,Q2: C > $o,G21: C > ( stream170649215stream @ A ),G22: C > C,A6: C] : ( stream641971652_SCons @ A @ ( G1 @ A6 ) @ ( if @ ( stream170649215stream @ A ) @ ( Q2 @ A6 ) @ ( G21 @ A6 ) @ ( stream660621732stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ ( G22 @ A6 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.corec_code
% 0.18/0.46 thf(fact_98_bot__apply,axiom,
% 0.18/0.46 ! [C: $tType,D2: $tType] :
% 0.18/0.46 ( ( bot @ C @ ( type2 @ C ) )
% 0.18/0.46 => ( ( bot_bot @ ( D2 > C ) )
% 0.18/0.46 = ( ^ [X5: D2] : ( bot_bot @ C ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_apply
% 0.18/0.46 thf(fact_99_empty__Collect__eq,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o] :
% 0.18/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.18/0.46 = ( collect @ A @ P ) )
% 0.18/0.46 = ( ! [X5: A] :
% 0.18/0.46 ~ ( P @ X5 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_Collect_eq
% 0.18/0.46 thf(fact_100_Collect__empty__eq,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o] :
% 0.18/0.46 ( ( ( collect @ A @ P )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( ! [X5: A] :
% 0.18/0.46 ~ ( P @ X5 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_empty_eq
% 0.18/0.46 thf(fact_101_all__not__in__conv,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( ! [X5: A] :
% 0.18/0.46 ~ ( member @ A @ X5 @ A4 ) )
% 0.18/0.46 = ( A4
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % all_not_in_conv
% 0.18/0.46 thf(fact_102_empty__iff,axiom,
% 0.18/0.46 ! [A: $tType,C2: A] :
% 0.18/0.46 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_iff
% 0.18/0.46 thf(fact_103_empty__subsetI,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.18/0.46
% 0.18/0.46 % empty_subsetI
% 0.18/0.46 thf(fact_104_subset__empty,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( A4
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_empty
% 0.18/0.46 thf(fact_105_singletonI,axiom,
% 0.18/0.46 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % singletonI
% 0.18/0.46 thf(fact_106_ball__empty,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o,X6: A] :
% 0.18/0.46 ( ( member @ A @ X6 @ ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 => ( P @ X6 ) ) ).
% 0.18/0.46
% 0.18/0.46 % ball_empty
% 0.18/0.46 thf(fact_107_subset__emptyI,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ! [X4: A] :
% 0.18/0.46 ~ ( member @ A @ X4 @ A4 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_emptyI
% 0.18/0.46 thf(fact_108_stream_Ocorec__disc,axiom,
% 0.18/0.46 ! [A: $tType,C: $tType] :
% 0.18/0.46 ( ( stream660621732stream @ C @ A )
% 0.18/0.46 = ( stream660621732stream @ C @ A ) ) ).
% 0.18/0.46
% 0.18/0.46 % stream.corec_disc
% 0.18/0.46 thf(fact_109_bot__fun__def,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( bot @ B @ ( type2 @ B ) )
% 0.18/0.46 => ( ( bot_bot @ ( A > B ) )
% 0.18/0.46 = ( ^ [X5: A] : ( bot_bot @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_fun_def
% 0.18/0.46 thf(fact_110_ex__in__conv,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( ? [X5: A] : ( member @ A @ X5 @ A4 ) )
% 0.18/0.46 = ( A4
% 0.18/0.46 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ex_in_conv
% 0.18/0.46 thf(fact_111_equals0I,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ! [Y5: A] :
% 0.18/0.46 ~ ( member @ A @ Y5 @ A4 )
% 0.18/0.46 => ( A4
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % equals0I
% 0.18/0.46 thf(fact_112_equals0D,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,A3: A] :
% 0.18/0.46 ( ( A4
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % equals0D
% 0.18/0.46 thf(fact_113_Ball__def,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ball @ A )
% 0.18/0.46 = ( ^ [A8: set @ A,P2: A > $o] :
% 0.18/0.46 ! [X5: A] :
% 0.18/0.46 ( ( member @ A @ X5 @ A8 )
% 0.18/0.46 => ( P2 @ X5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Ball_def
% 0.18/0.46 thf(fact_114_emptyE,axiom,
% 0.18/0.46 ! [A: $tType,A3: A] :
% 0.18/0.46 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % emptyE
% 0.18/0.46 thf(fact_115_bot_Oextremum__uniqueI,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.18/0.46 => ( A3
% 0.18/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot.extremum_uniqueI
% 0.18/0.46 thf(fact_116_bot_Oextremum__unique,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.18/0.46 = ( A3
% 0.18/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot.extremum_unique
% 0.18/0.46 thf(fact_117_bot_Oextremum,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot.extremum
% 0.18/0.46 thf(fact_118_singleton__inject,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,B4: A] :
% 0.18/0.46 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 => ( A3 = B4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_inject
% 0.18/0.46 thf(fact_119_insert__not__empty,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A] :
% 0.18/0.46 ( ( insert @ A @ A3 @ A4 )
% 0.18/0.46 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_not_empty
% 0.18/0.46 thf(fact_120_doubleton__eq__iff,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,B4: A,C2: A,D3: A] :
% 0.18/0.46 ( ( ( insert @ A @ A3 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 = ( insert @ A @ C2 @ ( insert @ A @ D3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.18/0.46 = ( ( ( A3 = C2 )
% 0.18/0.46 & ( B4 = D3 ) )
% 0.18/0.46 | ( ( A3 = D3 )
% 0.18/0.46 & ( B4 = C2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % doubleton_eq_iff
% 0.18/0.46 thf(fact_121_singleton__iff,axiom,
% 0.18/0.46 ! [A: $tType,B4: A,A3: A] :
% 0.18/0.46 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 = ( B4 = A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_iff
% 0.18/0.46 thf(fact_122_singletonD,axiom,
% 0.18/0.46 ! [A: $tType,B4: A,A3: A] :
% 0.18/0.46 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 => ( B4 = A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % singletonD
% 0.18/0.46 thf(fact_123_the__elem__eq,axiom,
% 0.18/0.46 ! [A: $tType,X: A] :
% 0.18/0.46 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 = X ) ).
% 0.18/0.46
% 0.18/0.46 % the_elem_eq
% 0.18/0.46 thf(fact_124_is__singletonI,axiom,
% 0.18/0.46 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonI
% 0.18/0.46 thf(fact_125_Ball__Collect,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ball @ A )
% 0.18/0.46 = ( ^ [A8: set @ A,P2: A > $o] : ( ord_less_eq @ ( set @ A ) @ A8 @ ( collect @ A @ P2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Ball_Collect
% 0.18/0.46 thf(fact_126_Set_Ois__empty__def,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( is_empty @ A )
% 0.18/0.46 = ( ^ [A8: set @ A] :
% 0.18/0.46 ( A8
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Set.is_empty_def
% 0.18/0.46 thf(fact_127_is__singletonE,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( is_singleton @ A @ A4 )
% 0.18/0.46 => ~ ! [X4: A] :
% 0.18/0.46 ( A4
% 0.18/0.46 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonE
% 0.18/0.46 thf(fact_128_bot__set__def,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.18/0.46 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_set_def
% 0.18/0.46 thf(fact_129_is__singleton__the__elem,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( is_singleton @ A )
% 0.18/0.46 = ( ^ [A8: set @ A] :
% 0.18/0.46 ( A8
% 0.18/0.46 = ( insert @ A @ ( the_elem @ A @ A8 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singleton_the_elem
% 0.18/0.46 thf(fact_130_is__singletonI_H,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( A4
% 0.18/0.46 != ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 => ( ! [X4: A,Y5: A] :
% 0.18/0.46 ( ( member @ A @ X4 @ A4 )
% 0.18/0.46 => ( ( member @ A @ Y5 @ A4 )
% 0.18/0.46 => ( X4 = Y5 ) ) )
% 0.18/0.46 => ( is_singleton @ A @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonI'
% 0.18/0.46 thf(fact_131_is__singleton__def,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( is_singleton @ A )
% 0.18/0.46 = ( ^ [A8: set @ A] :
% 0.18/0.46 ? [X5: A] :
% 0.18/0.46 ( A8
% 0.18/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singleton_def
% 0.18/0.46 thf(fact_132_pairwise__singleton,axiom,
% 0.18/0.46 ! [A: $tType,P: A > A > $o,A4: A] : ( pairwise @ A @ P @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % pairwise_singleton
% 0.18/0.46 thf(fact_133_subset__Compl__singleton,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B4: A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.18/0.46 = ( ~ ( member @ A @ B4 @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_Compl_singleton
% 0.18/0.46 thf(fact_134_ball__reg,axiom,
% 0.18/0.46 ! [A: $tType,R: set @ A,P: A > $o,Q: A > $o] :
% 0.18/0.46 ( ! [X4: A] :
% 0.18/0.46 ( ( member @ A @ X4 @ R )
% 0.18/0.46 => ( ( P @ X4 )
% 0.18/0.46 => ( Q @ X4 ) ) )
% 0.18/0.46 => ( ! [X4: A] :
% 0.18/0.46 ( ( member @ A @ X4 @ R )
% 0.18/0.46 => ( P @ X4 ) )
% 0.18/0.46 => ! [X6: A] :
% 0.18/0.46 ( ( member @ A @ X6 @ R )
% 0.18/0.46 => ( Q @ X6 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ball_reg
% 0.18/0.46 thf(fact_135_bot__empty__eq,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( bot_bot @ ( A > $o ) )
% 0.18/0.46 = ( ^ [X5: A] : ( member @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_empty_eq
% 0.18/0.46 thf(fact_136_Compl__eq__Compl__iff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ( uminus_uminus @ ( set @ A ) @ A4 )
% 0.18/0.46 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.18/0.46 = ( A4 = B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compl_eq_Compl_iff
% 0.18/0.46 thf(fact_137_Compl__iff,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.18/0.46 = ( ~ ( member @ A @ C2 @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compl_iff
% 0.18/0.46 thf(fact_138_ComplI,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ C2 @ A4 )
% 0.18/0.46 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ComplI
% 0.18/0.46 thf(fact_139_Compl__anti__mono,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compl_anti_mono
% 0.18/0.46 thf(fact_140_Compl__subset__Compl__iff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.18/0.46 = ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compl_subset_Compl_iff
% 0.18/0.46 thf(fact_141_double__complement,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.18/0.46 = A4 ) ).
% 0.18/0.46
% 0.18/0.46 % double_complement
% 0.18/0.46 thf(fact_142_pairwise__def,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( pairwise @ A )
% 0.18/0.46 = ( ^ [R2: A > A > $o,S5: set @ A] :
% 0.18/0.46 ! [X5: A] :
% 0.18/0.46 ( ( member @ A @ X5 @ S5 )
% 0.18/0.46 => ! [Y4: A] :
% 0.18/0.46 ( ( member @ A @ Y4 @ S5 )
% 0.18/0.46 => ( ( X5 != Y4 )
% 0.18/0.46 => ( R2 @ X5 @ Y4 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % pairwise_def
% 0.18/0.46 thf(fact_143_ComplD,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.18/0.46 => ~ ( member @ A @ C2 @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % ComplD
% 0.18/0.46 thf(fact_144_subset__Compl__self__eq,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.18/0.46 = ( A4
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_Compl_self_eq
% 0.18/0.46 thf(fact_145_pairwise__empty,axiom,
% 0.18/0.46 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % pairwise_empty
% 0.18/0.46 thf(fact_146_pairwise__subset,axiom,
% 0.18/0.46 ! [A: $tType,P: A > A > $o,S6: set @ A,T2: set @ A] :
% 0.18/0.46 ( ( pairwise @ A @ P @ S6 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ T2 @ S6 )
% 0.18/0.46 => ( pairwise @ A @ P @ T2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % pairwise_subset
% 0.18/0.46 thf(fact_147_pairwise__insert,axiom,
% 0.18/0.46 ! [A: $tType,R3: A > A > $o,X: A,S3: set @ A] :
% 0.18/0.46 ( ( pairwise @ A @ R3 @ ( insert @ A @ X @ S3 ) )
% 0.18/0.46 = ( ! [Y4: A] :
% 0.18/0.46 ( ( ( member @ A @ Y4 @ S3 )
% 0.18/0.46 & ( Y4 != X ) )
% 0.18/0.46 => ( ( R3 @ X @ Y4 )
% 0.18/0.46 & ( R3 @ Y4 @ X ) ) )
% 0.18/0.46 & ( pairwise @ A @ R3 @ S3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % pairwise_insert
% 0.18/0.46 thf(fact_148_neg__le__iff__le,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [B4: A,A3: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A3 ) )
% 0.18/0.46 = ( ord_less_eq @ A @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % neg_le_iff_le
% 0.18/0.46 thf(fact_149_compl__le__compl__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A,Y: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) )
% 0.18/0.46 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % compl_le_compl_iff
% 0.18/0.46 thf(fact_150_uminus__apply,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( uminus @ B @ ( type2 @ B ) )
% 0.18/0.46 => ( ( uminus_uminus @ ( A > B ) )
% 0.18/0.46 = ( ^ [A8: A > B,X5: A] : ( uminus_uminus @ B @ ( A8 @ X5 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % uminus_apply
% 0.18/0.46 thf(fact_151_add_Oinverse__inverse,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A] :
% 0.18/0.46 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A3 ) )
% 0.18/0.46 = A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % add.inverse_inverse
% 0.18/0.46 thf(fact_152_compl__eq__compl__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A,Y: A] :
% 0.18/0.46 ( ( ( uminus_uminus @ A @ X )
% 0.18/0.46 = ( uminus_uminus @ A @ Y ) )
% 0.18/0.46 = ( X = Y ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % compl_eq_compl_iff
% 0.18/0.46 thf(fact_153_double__compl,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A] :
% 0.18/0.46 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.18/0.46 = X ) ) ).
% 0.18/0.46
% 0.18/0.46 % double_compl
% 0.18/0.46 thf(fact_154_neg__equal__iff__equal,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A] :
% 0.18/0.46 ( ( ( uminus_uminus @ A @ A3 )
% 0.18/0.46 = ( uminus_uminus @ A @ B4 ) )
% 0.18/0.46 = ( A3 = B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % neg_equal_iff_equal
% 0.18/0.46 thf(fact_155_minus__equation__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A] :
% 0.18/0.46 ( ( ( uminus_uminus @ A @ A3 )
% 0.18/0.46 = B4 )
% 0.18/0.46 = ( ( uminus_uminus @ A @ B4 )
% 0.18/0.46 = A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % minus_equation_iff
% 0.18/0.46 thf(fact_156_equation__minus__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( uminus_uminus @ A @ B4 ) )
% 0.18/0.46 = ( B4
% 0.18/0.46 = ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % equation_minus_iff
% 0.18/0.46 thf(fact_157_fun__Compl__def,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( uminus @ B @ ( type2 @ B ) )
% 0.18/0.46 => ( ( uminus_uminus @ ( A > B ) )
% 0.18/0.46 = ( ^ [A8: A > B,X5: A] : ( uminus_uminus @ B @ ( A8 @ X5 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % fun_Compl_def
% 0.18/0.46 thf(fact_158_le__imp__neg__le,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.46 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_imp_neg_le
% 0.18/0.46 thf(fact_159_minus__le__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A3 ) @ B4 )
% 0.18/0.46 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % minus_le_iff
% 0.18/0.46 thf(fact_160_le__minus__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ ( uminus_uminus @ A @ B4 ) )
% 0.18/0.46 = ( ord_less_eq @ A @ B4 @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_minus_iff
% 0.18/0.46 thf(fact_161_compl__le__swap2,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [Y: A,X: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ X )
% 0.18/0.46 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ Y ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % compl_le_swap2
% 0.18/0.46 thf(fact_162_compl__le__swap1,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [Y: A,X: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ Y @ ( uminus_uminus @ A @ X ) )
% 0.18/0.46 => ( ord_less_eq @ A @ X @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % compl_le_swap1
% 0.18/0.46 thf(fact_163_compl__mono,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A,Y: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.46 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ ( uminus_uminus @ A @ X ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % compl_mono
% 0.18/0.46 thf(fact_164_Collect__empty__eq__bot,axiom,
% 0.18/0.46 ! [A: $tType,P: A > $o] :
% 0.18/0.46 ( ( ( collect @ A @ P )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( P
% 0.18/0.46 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_empty_eq_bot
% 0.18/0.46 thf(fact_165_in__inv__imagep,axiom,
% 0.18/0.46 ! [B: $tType,A: $tType] :
% 0.18/0.46 ( ( inv_imagep @ A @ B )
% 0.18/0.46 = ( ^ [R4: A > A > $o,F2: B > A,X5: B,Y4: B] : ( R4 @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % in_inv_imagep
% 0.18/0.46 thf(fact_166_Compl__insert,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A] :
% 0.18/0.46 ( ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compl_insert
% 0.18/0.46 thf(fact_167_Diff__idemp,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ B2 )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_idemp
% 0.18/0.46 thf(fact_168_Diff__iff,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 = ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_iff
% 0.18/0.46 thf(fact_169_DiffI,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 => ( ~ ( member @ A @ C2 @ B2 )
% 0.18/0.46 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % DiffI
% 0.18/0.46 thf(fact_170_minus__diff__eq,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A] :
% 0.18/0.46 ( ( uminus_uminus @ A @ ( minus_minus @ A @ A3 @ B4 ) )
% 0.18/0.46 = ( minus_minus @ A @ B4 @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % minus_diff_eq
% 0.18/0.46 thf(fact_171_Diff__cancel,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ A4 @ A4 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_cancel
% 0.18/0.46 thf(fact_172_empty__Diff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_Diff
% 0.18/0.46 thf(fact_173_Diff__empty,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = A4 ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_empty
% 0.18/0.46 thf(fact_174_Diff__insert0,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_insert0
% 0.18/0.46 thf(fact_175_insert__Diff1,axiom,
% 0.18/0.46 ! [A: $tType,X: A,B2: set @ A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ X @ B2 )
% 0.18/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_Diff1
% 0.18/0.46 thf(fact_176_Diff__eq__empty__iff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ( minus_minus @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_eq_empty_iff
% 0.18/0.46 thf(fact_177_insert__Diff__single,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A] :
% 0.18/0.46 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.18/0.46 = ( insert @ A @ A3 @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_Diff_single
% 0.18/0.46 thf(fact_178_diff__mono,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A,D3: A,C2: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.46 => ( ( ord_less_eq @ A @ D3 @ C2 )
% 0.18/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ D3 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_mono
% 0.18/0.46 thf(fact_179_diff__left__mono,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [B4: A,A3: A,C2: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.18/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ C2 @ A3 ) @ ( minus_minus @ A @ C2 @ B4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_left_mono
% 0.18/0.46 thf(fact_180_diff__right__mono,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A,C2: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ C2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_right_mono
% 0.18/0.46 thf(fact_181_diff__eq__diff__less__eq,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A,C2: A,D3: A] :
% 0.18/0.46 ( ( ( minus_minus @ A @ A3 @ B4 )
% 0.18/0.46 = ( minus_minus @ A @ C2 @ D3 ) )
% 0.18/0.46 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.46 = ( ord_less_eq @ A @ C2 @ D3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_eq_diff_less_eq
% 0.18/0.46 thf(fact_182_Diff__mono,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,C3: set @ A,D: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ D @ B2 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ ( minus_minus @ ( set @ A ) @ C3 @ D ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_mono
% 0.18/0.46 thf(fact_183_Diff__subset,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ A4 ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_subset
% 0.18/0.46 thf(fact_184_double__diff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.18/0.46 => ( ( minus_minus @ ( set @ A ) @ B2 @ ( minus_minus @ ( set @ A ) @ C3 @ A4 ) )
% 0.18/0.46 = A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % double_diff
% 0.18/0.46 thf(fact_185_insert__Diff__if,axiom,
% 0.18/0.46 ! [A: $tType,X: A,B2: set @ A,A4: set @ A] :
% 0.18/0.46 ( ( ( member @ A @ X @ B2 )
% 0.18/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) )
% 0.18/0.46 & ( ~ ( member @ A @ X @ B2 )
% 0.18/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.18/0.46 = ( insert @ A @ X @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_Diff_if
% 0.18/0.46 thf(fact_186_DiffD2,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % DiffD2
% 0.18/0.46 thf(fact_187_DiffD1,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 => ( member @ A @ C2 @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % DiffD1
% 0.18/0.46 thf(fact_188_DiffE,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 => ~ ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % DiffE
% 0.18/0.46 thf(fact_189_Diff__insert,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,A3: A,B2: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_insert
% 0.18/0.46 thf(fact_190_insert__Diff,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ A3 @ A4 )
% 0.18/0.46 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.18/0.46 = A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_Diff
% 0.18/0.46 thf(fact_191_Diff__insert2,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,A3: A,B2: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_insert2
% 0.18/0.46 thf(fact_192_Diff__insert__absorb,axiom,
% 0.18/0.46 ! [A: $tType,X: A,A4: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.18/0.46 = A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_insert_absorb
% 0.18/0.46 thf(fact_193_subset__Diff__insert,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,X: A,C3: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ ( insert @ A @ X @ C3 ) ) )
% 0.18/0.46 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) )
% 0.18/0.46 & ~ ( member @ A @ X @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_Diff_insert
% 0.18/0.46 thf(fact_194_Diff__single__insert,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,X: A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_single_insert
% 0.18/0.46 thf(fact_195_subset__insert__iff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,X: A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.18/0.46 = ( ( ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) )
% 0.18/0.46 & ( ~ ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % subset_insert_iff
% 0.18/0.46 thf(fact_196_remove__def,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( remove @ A )
% 0.18/0.46 = ( ^ [X5: A,A8: set @ A] : ( minus_minus @ ( set @ A ) @ A8 @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % remove_def
% 0.18/0.46 thf(fact_197_psubset__insert__iff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,X: A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.18/0.46 = ( ( ( member @ A @ X @ B2 )
% 0.18/0.46 => ( ord_less @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 & ( ~ ( member @ A @ X @ B2 )
% 0.18/0.46 => ( ( ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ord_less @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) )
% 0.18/0.46 & ( ~ ( member @ A @ X @ A4 )
% 0.18/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubset_insert_iff
% 0.18/0.46 thf(fact_198_disjoint__eq__subset__Compl,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( ord_less_eq @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % disjoint_eq_subset_Compl
% 0.18/0.46 thf(fact_199_IntI,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 => ( ( member @ A @ C2 @ B2 )
% 0.18/0.46 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % IntI
% 0.18/0.46 thf(fact_200_Int__iff,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 = ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 & ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_iff
% 0.18/0.46 thf(fact_201_member__remove,axiom,
% 0.18/0.46 ! [A: $tType,X: A,Y: A,A4: set @ A] :
% 0.18/0.46 ( ( member @ A @ X @ ( remove @ A @ Y @ A4 ) )
% 0.18/0.46 = ( ( member @ A @ X @ A4 )
% 0.18/0.46 & ( X != Y ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % member_remove
% 0.18/0.46 thf(fact_202_le__inf__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A,Y: A,Z: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.18/0.46 = ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.46 & ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_inf_iff
% 0.18/0.46 thf(fact_203_inf_Obounded__iff,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A,B4: A,C2: A] :
% 0.18/0.46 ( ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C2 ) )
% 0.18/0.46 = ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.18/0.46 & ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inf.bounded_iff
% 0.18/0.46 thf(fact_204_neg__less__iff__less,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [B4: A,A3: A] :
% 0.18/0.46 ( ( ord_less @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A3 ) )
% 0.18/0.46 = ( ord_less @ A @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % neg_less_iff_less
% 0.18/0.46 thf(fact_205_inf__bot__right,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A] :
% 0.18/0.46 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 0.18/0.46 = ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inf_bot_right
% 0.18/0.46 thf(fact_206_inf__bot__left,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A] :
% 0.18/0.46 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 0.18/0.46 = ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inf_bot_left
% 0.18/0.46 thf(fact_207_Int__subset__iff,axiom,
% 0.18/0.46 ! [A: $tType,C3: set @ A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 = ( ( ord_less_eq @ ( set @ A ) @ C3 @ A4 )
% 0.18/0.46 & ( ord_less_eq @ ( set @ A ) @ C3 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_subset_iff
% 0.18/0.46 thf(fact_208_Int__insert__right__if1,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ A3 @ A4 )
% 0.18/0.46 => ( ( inf_inf @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.18/0.46 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_insert_right_if1
% 0.18/0.46 thf(fact_209_Int__insert__right__if0,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ A3 @ A4 )
% 0.18/0.46 => ( ( inf_inf @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_insert_right_if0
% 0.18/0.46 thf(fact_210_insert__inter__insert,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A4 ) @ ( insert @ A @ A3 @ B2 ) )
% 0.18/0.46 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_inter_insert
% 0.18/0.46 thf(fact_211_Int__insert__left__if1,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,C3: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ A3 @ C3 )
% 0.18/0.46 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C3 )
% 0.18/0.46 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_insert_left_if1
% 0.18/0.46 thf(fact_212_Int__insert__left__if0,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,C3: set @ A,B2: set @ A] :
% 0.18/0.46 ( ~ ( member @ A @ A3 @ C3 )
% 0.18/0.46 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C3 )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_insert_left_if0
% 0.18/0.46 thf(fact_213_psubsetI,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ( A4 != B2 )
% 0.18/0.46 => ( ord_less @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubsetI
% 0.18/0.46 thf(fact_214_compl__inf__bot,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A] :
% 0.18/0.46 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ X )
% 0.18/0.46 = ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % compl_inf_bot
% 0.18/0.46 thf(fact_215_inf__compl__bot,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A] :
% 0.18/0.46 ( ( inf_inf @ A @ X @ ( uminus_uminus @ A @ X ) )
% 0.18/0.46 = ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inf_compl_bot
% 0.18/0.46 thf(fact_216_inf__compl__bot__left1,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A,Y: A] :
% 0.18/0.46 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ ( inf_inf @ A @ X @ Y ) )
% 0.18/0.46 = ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inf_compl_bot_left1
% 0.18/0.46 thf(fact_217_inf__compl__bot__left2,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A,Y: A] :
% 0.18/0.46 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 0.18/0.46 = ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inf_compl_bot_left2
% 0.18/0.46 thf(fact_218_inf__compl__bot__right,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A,Y: A] :
% 0.18/0.46 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ ( uminus_uminus @ A @ X ) ) )
% 0.18/0.46 = ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inf_compl_bot_right
% 0.18/0.46 thf(fact_219_insert__disjoint_I1_J,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A4 ) @ B2 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( ~ ( member @ A @ A3 @ B2 )
% 0.18/0.46 & ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_disjoint(1)
% 0.18/0.46 thf(fact_220_insert__disjoint_I2_J,axiom,
% 0.18/0.46 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A4 ) @ B2 ) )
% 0.18/0.46 = ( ~ ( member @ A @ A3 @ B2 )
% 0.18/0.46 & ( ( bot_bot @ ( set @ A ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_disjoint(2)
% 0.18/0.46 thf(fact_221_disjoint__insert_I1_J,axiom,
% 0.18/0.46 ! [A: $tType,B2: set @ A,A3: A,A4: set @ A] :
% 0.18/0.46 ( ( ( inf_inf @ ( set @ A ) @ B2 @ ( insert @ A @ A3 @ A4 ) )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( ~ ( member @ A @ A3 @ B2 )
% 0.18/0.46 & ( ( inf_inf @ ( set @ A ) @ B2 @ A4 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % disjoint_insert(1)
% 0.18/0.46 thf(fact_222_disjoint__insert_I2_J,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B4: A,B2: set @ A] :
% 0.18/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ B2 ) ) )
% 0.18/0.46 = ( ~ ( member @ A @ B4 @ A4 )
% 0.18/0.46 & ( ( bot_bot @ ( set @ A ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % disjoint_insert(2)
% 0.18/0.46 thf(fact_223_Diff__disjoint,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ A4 ) )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_disjoint
% 0.18/0.46 thf(fact_224_Compl__disjoint,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compl_disjoint
% 0.18/0.46 thf(fact_225_Compl__disjoint2,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) @ A4 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compl_disjoint2
% 0.18/0.46 thf(fact_226_Diff__Compl,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_Compl
% 0.18/0.46 thf(fact_227_psubset__imp__ex__mem,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ord_less @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ? [B5: A] : ( member @ A @ B5 @ ( minus_minus @ ( set @ A ) @ B2 @ A4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubset_imp_ex_mem
% 0.18/0.46 thf(fact_228_Diff__Int__distrib2,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ C3 )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_Int_distrib2
% 0.18/0.46 thf(fact_229_Diff__Int__distrib,axiom,
% 0.18/0.46 ! [A: $tType,C3: set @ A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ C3 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C3 @ A4 ) @ ( inf_inf @ ( set @ A ) @ C3 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_Int_distrib
% 0.18/0.46 thf(fact_230_Diff__Diff__Int,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_Diff_Int
% 0.18/0.46 thf(fact_231_Diff__Int2,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,C3: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.18/0.46 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Diff_Int2
% 0.18/0.46 thf(fact_232_Int__Diff,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.18/0.46 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) @ C3 )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_Diff
% 0.18/0.46 thf(fact_233_Int__emptyI,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ! [X4: A] :
% 0.18/0.46 ( ( member @ A @ X4 @ A4 )
% 0.18/0.46 => ~ ( member @ A @ X4 @ B2 ) )
% 0.18/0.46 => ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_emptyI
% 0.18/0.46 thf(fact_234_Int__empty__left,axiom,
% 0.18/0.46 ! [A: $tType,B2: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_empty_left
% 0.18/0.46 thf(fact_235_Int__empty__right,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_empty_right
% 0.18/0.46 thf(fact_236_disjoint__iff__not__equal,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.18/0.46 = ( ! [X5: A] :
% 0.18/0.46 ( ( member @ A @ X5 @ A4 )
% 0.18/0.46 => ! [Y4: A] :
% 0.18/0.46 ( ( member @ A @ Y4 @ B2 )
% 0.18/0.46 => ( X5 != Y4 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % disjoint_iff_not_equal
% 0.18/0.46 thf(fact_237_bot_Oextremum__strict,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A] :
% 0.18/0.46 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot.extremum_strict
% 0.18/0.46 thf(fact_238_bot_Onot__eq__extremum,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [A3: A] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 != ( bot_bot @ A ) )
% 0.18/0.46 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot.not_eq_extremum
% 0.18/0.46 thf(fact_239_not__psubset__empty,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ~ ( ord_less @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % not_psubset_empty
% 0.18/0.46 thf(fact_240_IntE,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 => ~ ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 => ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % IntE
% 0.18/0.46 thf(fact_241_IntD1,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 => ( member @ A @ C2 @ A4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % IntD1
% 0.18/0.46 thf(fact_242_IntD2,axiom,
% 0.18/0.46 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 => ( member @ A @ C2 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % IntD2
% 0.18/0.46 thf(fact_243_psubsetD,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.18/0.46 ( ( ord_less @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ( member @ A @ C2 @ A4 )
% 0.18/0.46 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubsetD
% 0.18/0.46 thf(fact_244_Int__assoc,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) @ C3 )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_assoc
% 0.18/0.46 thf(fact_245_Int__absorb,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ A4 )
% 0.18/0.46 = A4 ) ).
% 0.18/0.46
% 0.18/0.46 % Int_absorb
% 0.18/0.46 thf(fact_246_Int__commute,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.18/0.46 = ( ^ [A8: set @ A,B3: set @ A] : ( inf_inf @ ( set @ A ) @ B3 @ A8 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_commute
% 0.18/0.46 thf(fact_247_psubset__trans,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.18/0.46 ( ( ord_less @ ( set @ A ) @ A4 @ B2 )
% 0.18/0.46 => ( ( ord_less @ ( set @ A ) @ B2 @ C3 )
% 0.18/0.46 => ( ord_less @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubset_trans
% 0.18/0.46 thf(fact_248_Int__left__absorb,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_left_absorb
% 0.18/0.46 thf(fact_249_Int__left__commute,axiom,
% 0.18/0.46 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.18/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.18/0.46 = ( inf_inf @ ( set @ A ) @ B2 @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Int_left_commute
% 0.18/0.46 thf(fact_250_ord__eq__less__subst,axiom,
% 0.18/0.46 ! [A: $tType,B: $tType] :
% 0.18/0.46 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.46 & ( ord @ A @ ( type2 @ A ) ) )
% 0.18/0.46 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( F @ B4 ) )
% 0.18/0.46 => ( ( ord_less @ B @ B4 @ C2 )
% 0.18/0.46 => ( ! [X4: B,Y5: B] :
% 0.18/0.46 ( ( ord_less @ B @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.46 => ( ord_less @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ord_eq_less_subst
% 0.18/0.46 thf(fact_251_ord__less__eq__subst,axiom,
% 0.18/0.46 ! [A: $tType,B: $tType] :
% 0.18/0.46 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.18/0.46 & ( ord @ A @ ( type2 @ A ) ) )
% 0.18/0.46 => ! [A3: A,B4: A,F: A > B,C2: B] :
% 0.18/0.46 ( ( ord_less @ A @ A3 @ B4 )
% 0.18/0.46 => ( ( ( F @ B4 )
% 0.18/0.46 = C2 )
% 0.18/0.46 => ( ! [X4: A,Y5: A] :
% 0.18/0.46 ( ( ord_less @ A @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.46 => ( ord_less @ B @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ord_less_eq_subst
% 0.18/0.46 thf(fact_252_order__less__subst1,axiom,
% 0.18/0.46 ! [A: $tType,B: $tType] :
% 0.18/0.46 ( ( ( order @ B @ ( type2 @ B ) )
% 0.18/0.46 & ( order @ A @ ( type2 @ A ) ) )
% 0.18/0.46 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.18/0.46 ( ( ord_less @ A @ A3 @ ( F @ B4 ) )
% 0.18/0.46 => ( ( ord_less @ B @ B4 @ C2 )
% 0.18/0.46 => ( ! [X4: B,Y5: B] :
% 0.18/0.46 ( ( ord_less @ B @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.46 => ( ord_less @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % order_less_subst1
% 0.18/0.46 thf(fact_253_order__less__subst2,axiom,
% 0.18/0.46 ! [A: $tType,C: $tType] :
% 0.18/0.46 ( ( ( order @ C @ ( type2 @ C ) )
% 0.18/0.46 & ( order @ A @ ( type2 @ A ) ) )
% 0.18/0.46 => ! [A3: A,B4: A,F: A > C,C2: C] :
% 0.18/0.46 ( ( ord_less @ A @ A3 @ B4 )
% 0.18/0.46 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 0.18/0.46 => ( ! [X4: A,Y5: A] :
% 0.18/0.46 ( ( ord_less @ A @ X4 @ Y5 )
% 0.18/0.46 => ( ord_less @ C @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.18/0.46 => ( ord_less @ C @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % order_less_subst2
% 0.18/0.46 thf(fact_254_lt__ex,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A] :
% 0.18/0.46 ? [Y5: A] : ( ord_less @ A @ Y5 @ X ) ) ).
% 0.18/0.46
% 0.18/0.46 % lt_ex
% 0.18/0.46 thf(fact_255_gt__ex,axiom,
% 0.18/0.46 ! [A: $tType] :
% 0.18/0.46 ( ( no_top @ A @ ( type2 @ A ) )
% 0.18/0.46 => ! [X: A] :
% 0.18/0.46 ? [X12: A] : ( ord_less @ A @ X @ X12 ) ) ).
% 0.18/0.46
% 0.18/0.46 % gt_ex
% 0.18/0.46
% 0.18/0.46 %----Type constructors (31)
% 0.18/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.18/0.46 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.18/0.46 ! [A9: $tType] : ( bounded_lattice @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( bounded_lattice @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( bounded_lattice @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( bounded_lattice @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( bounded_lattice_bot @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( semilattice_inf @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( semilattice_inf @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( boolean_algebra @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( boolean_algebra @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( order_bot @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( order_bot @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( preorder @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( preorder @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( order @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( order @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( ord @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( ord @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Orderings_Obot,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( bot @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( bot @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.18/0.46 ! [A9: $tType,A10: $tType] :
% 0.18/0.46 ( ( uminus @ A10 @ ( type2 @ A10 ) )
% 0.18/0.46 => ( uminus @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 0.18/0.46 ! [A9: $tType] : ( bounded_lattice_bot @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 0.18/0.46 ! [A9: $tType] : ( semilattice_inf @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_5,axiom,
% 0.18/0.46 ! [A9: $tType] : ( boolean_algebra @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 0.18/0.46 ! [A9: $tType] : ( order_bot @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 0.18/0.46 ! [A9: $tType] : ( preorder @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 0.18/0.46 ! [A9: $tType] : ( order @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 0.18/0.46 ! [A9: $tType] : ( ord @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 0.18/0.46 ! [A9: $tType] : ( bot @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_Set_Oset___Groups_Ouminus_11,axiom,
% 0.18/0.46 ! [A9: $tType] : ( uminus @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 0.18/0.46 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_13,axiom,
% 0.18/0.46 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_14,axiom,
% 0.18/0.46 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15,axiom,
% 0.18/0.46 order_bot @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 0.18/0.46 preorder @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.18/0.46 linorder @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_17,axiom,
% 0.18/0.46 order @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Orderings_Oord_18,axiom,
% 0.18/0.46 ord @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Orderings_Obot_19,axiom,
% 0.18/0.46 bot @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 thf(tcon_HOL_Obool___Groups_Ouminus_20,axiom,
% 0.18/0.46 uminus @ $o @ ( type2 @ $o ) ).
% 0.18/0.46
% 0.18/0.46 %----Helper facts (3)
% 0.18/0.46 thf(help_If_3_1_T,axiom,
% 0.18/0.46 ! [P: $o] :
% 0.18/0.46 ( ( P = $true )
% 0.18/0.46 | ( P = $false ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(help_If_2_1_T,axiom,
% 0.18/0.46 ! [A: $tType,X: A,Y: A] :
% 0.18/0.46 ( ( if @ A @ $false @ X @ Y )
% 0.18/0.46 = Y ) ).
% 0.18/0.46
% 0.18/0.46 thf(help_If_1_1_T,axiom,
% 0.18/0.46 ! [A: $tType,X: A,Y: A] :
% 0.18/0.46 ( ( if @ A @ $true @ X @ Y )
% 0.18/0.46 = X ) ).
% 0.18/0.46
% 0.18/0.46 %----Conjectures (1)
% 0.18/0.46 thf(conj_0,conjecture,
% 0.18/0.46 ? [A7: a,S4: stream170649215stream @ a] :
% 0.18/0.46 ( ( sa
% 0.18/0.46 = ( stream641971652_SCons @ a @ A7 @ S4 ) )
% 0.18/0.46 & ( member @ a @ A7 @ a2 )
% 0.18/0.46 & ( ? [Sa: stream170649215stream @ a] :
% 0.18/0.46 ( ( S4 = Sa )
% 0.18/0.46 & ( ord_less_eq @ ( set @ a ) @ ( stream30925839e_sset @ a @ Sa ) @ a2 ) )
% 0.18/0.46 | ( member @ ( stream170649215stream @ a ) @ S4 @ ( stream2015131171treams @ a @ a2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 0.30/1.50 ---- Embedded in THF ---
% 0.30/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.50 %%% Generated on Tue Feb 24 06:11:42 EST 2026
% 0.30/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.50 %%% Logic specification used:
% 0.30/1.50 %%% thf(spec, logic, $$dhol).
% 0.30/1.50
% 0.30/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2DTF5740.p
% 0.30/1.50 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream, type, stream170649215stream: ($tType > $tType)).
% 0.30/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.30/1.50 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.30/1.50 thf(ty_tf_a, type, a: $tType).
% 0.30/1.50 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 0.30/1.50 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 0.30/1.50 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.30/1.50 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 0.30/1.50 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 0.30/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.30/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.30/1.50 thf(sy_c_Orderings_Oorder__class_Oantimono, type, order_antimono: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.30/1.50 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.30/1.50 thf(sy_c_Relation_Oinv__imagep, type, inv_imagep: (!> [B:$tType,A:$tType]: (((B > (B > $o)) > ((A > B) > (A > (A > $o))))))).
% 0.30/1.50 thf(sy_c_Set_OBall, type, ball: (!> [A:$tType]: (((set @ A) > ((A > $o) > $o))))).
% 0.30/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.30/1.50 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 0.30/1.50 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.30/1.50 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.30/1.50 thf(sy_c_Set_Opairwise, type, pairwise: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 0.30/1.50 thf(sy_c_Set_Oremove, type, remove: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 0.30/1.50 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember, type, stream1586597341member: (!> [A:$tType]: ((A > ((stream170649215stream @ A) > $o))))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_OSCons, type, stream641971652_SCons: (!> [A:$tType]: ((A > ((stream170649215stream @ A) > (stream170649215stream @ A)))))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocase__stream, type, stream1342653232stream: (!> [A:$tType,B:$tType]: (((A > ((stream170649215stream @ A) > B)) > ((stream170649215stream @ A) > B))))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocorec__stream, type, stream660621732stream: (!> [C:$tType,A:$tType]: (((C > A) > ((C > $o) > ((C > (stream170649215stream @ A)) > ((C > C) > (C > (stream170649215stream @ A))))))))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Opred__stream, type, stream1153105665stream: (!> [A:$tType]: (((A > $o) > ((stream170649215stream @ A) > $o))))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osset, type, stream30925839e_sset: (!> [A:$tType]: (((stream170649215stream @ A) > (set @ A))))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreams, type, stream2015131171treams: (!> [A:$tType]: (((set @ A) > (set @ (stream170649215stream @ A)))))).
% 0.30/1.50 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreamsp, type, stream86250253reamsp: (!> [A:$tType]: (((A > $o) > ((stream170649215stream @ A) > $o))))).
% 0.30/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.30/1.50 thf(sy_v_A, type, a2: (set @ a)).
% 0.30/1.50 thf(sy_v_s, type, s: (stream170649215stream @ a)).
% 0.30/1.50 thf(sy_v_sa____, type, sa: (stream170649215stream @ a)).
% 0.30/1.50 thf(fact_0_streams, axiom, (((ord_less_eq @ (set @ a)) @ ((stream30925839e_sset @ a) @ sa)) @ a2)).
% 0.30/1.50 thf(fact_1_assms, axiom, (((ord_less_eq @ (set @ a)) @ ((stream30925839e_sset @ a) @ s)) @ a2)).
% 0.30/1.50 thf(fact_2_stream_Oinject, axiom, (! [A:$tType,X1:A,X2:(stream170649215stream @ A),Y1:A,Y2:(stream170649215stream @ A)]: ((((((stream641971652_SCons @ A) @ X1) @ X2) = (((stream641971652_SCons @ A) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 0.30/1.50 thf(fact_3_stream_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A2:(stream170649215stream @ A),A1:A]: (((((member @ A) @ X) @ ((stream30925839e_sset @ A) @ A2)) => (((member @ A) @ X) @ ((stream30925839e_sset @ A) @ (((stream641971652_SCons @ A) @ A1) @ A2))))))).
% 0.30/1.50 thf(fact_4_stream_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A2:(stream170649215stream @ A)]: ((((member @ A) @ A1) @ ((stream30925839e_sset @ A) @ (((stream641971652_SCons @ A) @ A1) @ A2)))))).
% 0.30/1.50 thf(fact_5_streams_Ocases, axiom, (! [A:$tType,A3:(stream170649215stream @ A),A4:(set @ A)]: (((((member @ (stream170649215stream @ A)) @ A3) @ ((stream2015131171treams @ A) @ A4)) => (~ ((! [A5:A,S:(stream170649215stream @ A)]: (((A3 = (((stream641971652_SCons @ A) @ A5) @ S)) => ((((member @ A) @ A5) @ A4) => (~ ((((member @ (stream170649215stream @ A)) @ S) @ ((stream2015131171treams @ A) @ A4)))))))))))))).
% 0.30/1.50 thf(fact_6_streams_Osimps, axiom, (! [A:$tType,A3:(stream170649215stream @ A),A4:(set @ A)]: (((((member @ (stream170649215stream @ A)) @ A3) @ ((stream2015131171treams @ A) @ A4)) = (? [A6:A,S2:(stream170649215stream @ A)]: (((A3 = (((stream641971652_SCons @ A) @ A6) @ S2)) & ((((member @ A) @ A6) @ A4) & (((member @ (stream170649215stream @ A)) @ S2) @ ((stream2015131171treams @ A) @ A4)))))))))).
% 0.30/1.50 thf(fact_7_stream_Oexhaust, axiom, (! [A:$tType,Y:(stream170649215stream @ A)]: ((~ ((! [X12:A,X22:(stream170649215stream @ A)]: ((Y != (((stream641971652_SCons @ A) @ X12) @ X22))))))))).
% 0.30/1.50 thf(fact_8_streams__Stream, axiom, (! [A:$tType,X:A,S3:(stream170649215stream @ A),A4:(set @ A)]: (((((member @ (stream170649215stream @ A)) @ (((stream641971652_SCons @ A) @ X) @ S3)) @ ((stream2015131171treams @ A) @ A4)) = ((((member @ A) @ X) @ A4) & (((member @ (stream170649215stream @ A)) @ S3) @ ((stream2015131171treams @ A) @ A4))))))).
% 0.30/1.50 thf(fact_9_stream_Oset__cases, axiom, (! [A:$tType,E:A,A3:(stream170649215stream @ A)]: (((((member @ A) @ E) @ ((stream30925839e_sset @ A) @ A3)) => ((! [Z2:(stream170649215stream @ A)]: ((A3 != (((stream641971652_SCons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(stream170649215stream @ A)]: (((A3 = (((stream641971652_SCons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((stream30925839e_sset @ A) @ Z2)))))))))))))).
% 0.30/1.50 thf(fact_10_streams_Ocoinduct, axiom, (! [A:$tType,X3:((stream170649215stream @ A) > $o),X:(stream170649215stream @ A),A4:(set @ A)]: (((X3 @ X) => ((! [X4:(stream170649215stream @ A)]: (((X3 @ X4) => (? [A7:A,S4:(stream170649215stream @ A)]: (((X4 = (((stream641971652_SCons @ A) @ A7) @ S4)) & ((((member @ A) @ A7) @ A4) & ((X3 @ S4) | (((member @ (stream170649215stream @ A)) @ S4) @ ((stream2015131171treams @ A) @ A4)))))))))) => (((member @ (stream170649215stream @ A)) @ X) @ ((stream2015131171treams @ A) @ A4))))))).
% 0.30/1.50 thf(fact_11_stream_Oset__induct, axiom, (! [A:$tType,X:A,A3:(stream170649215stream @ A),P:(A > ((stream170649215stream @ A) > $o))]: (((((member @ A) @ X) @ ((stream30925839e_sset @ A) @ A3)) => ((! [Z1:A,Z2:(stream170649215stream @ A)]: (((P @ Z1) @ (((stream641971652_SCons @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(stream170649215stream @ A),Xa:A]: (((((member @ A) @ Xa) @ ((stream30925839e_sset @ A) @ Z2)) => (((P @ Xa) @ Z2) => ((P @ Xa) @ (((stream641971652_SCons @ A) @ Z1) @ Z2)))))) => ((P @ X) @ A3))))))).
% 0.30/1.50 thf(fact_12_smember__code, axiom, (! [A:$tType,X:A,Y:A,S3:(stream170649215stream @ A)]: (((((stream1586597341member @ A) @ X) @ (((stream641971652_SCons @ A) @ Y) @ S3)) = ((X != Y) => (((stream1586597341member @ A) @ X) @ S3)))))).
% 0.30/1.50 thf(fact_13_subsetI, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A4) => (((member @ A) @ X4) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B2))))).
% 0.30/1.50 thf(fact_14_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A4) => (A4 = B2)))))).
% 0.30/1.50 thf(fact_15_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 0.30/1.50 thf(fact_16_Stream__Mirabelle__hbrgyiwlrc_Osmember__def, axiom, (! [A:$tType]: (((stream1586597341member @ A) = (^ [X5:A,S2:(stream170649215stream @ A)]: ((((member @ A) @ X5) @ ((stream30925839e_sset @ A) @ S2)))))))).
% 0.30/1.50 thf(fact_17_set__mp, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B2)))))).
% 0.30/1.50 thf(fact_18_in__mono, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B2)))))).
% 0.30/1.50 thf(fact_19_subsetD, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B2)))))).
% 0.30/1.50 thf(fact_20_subsetCE, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B2)))))).
% 0.30/1.50 thf(fact_21_equalityE, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((A4 = B2) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => (~ ((((ord_less_eq @ (set @ A)) @ B2) @ A4)))))))))).
% 0.30/1.50 thf(fact_22_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A8:(set @ A),B3:(set @ A)]: ((! [X5:A]: (((((member @ A) @ X5) @ A8) => (((member @ A) @ X5) @ B3)))))))))).
% 0.30/1.50 thf(fact_23_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((A4 = B2) => (((ord_less_eq @ (set @ A)) @ A4) @ B2))))).
% 0.30/1.50 thf(fact_24_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A3:A]: (((((ord_less_eq @ A) @ B4) @ A3) => ((((ord_less_eq @ A) @ A3) @ B4) => (A3 = B4))))))))).
% 0.30/1.50 thf(fact_25_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A3:A,C2:A]: (((((ord_less_eq @ A) @ B4) @ A3) => ((((ord_less_eq @ A) @ C2) @ B4) => (((ord_less_eq @ A) @ C2) @ A3))))))))).
% 0.30/1.50 thf(fact_26_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A3:A,B4:A]: (((! [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) => ((P @ A5) @ B5)))) => ((! [A5:A,B5:A]: ((((P @ B5) @ A5) => ((P @ A5) @ B5)))) => ((P @ A3) @ B4))))))))).
% 0.30/1.50 thf(fact_27_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 0.30/1.50 thf(fact_28_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 0.30/1.50 thf(fact_29_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ B4) @ A3) => (A3 = B4))))))))).
% 0.30/1.50 thf(fact_30_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((B4 = C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 0.30/1.50 thf(fact_31_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B4:A,C2:A]: (((A3 = B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 0.30/1.50 thf(fact_32_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.30/1.50 thf(fact_33_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z)))) => (((((ord_less_eq @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X)))) => (~ (((((ord_less_eq @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 0.30/1.50 thf(fact_34_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 0.30/1.50 thf(fact_35_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.30/1.50 thf(fact_36_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.30/1.50 thf(fact_37_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.30/1.50 thf(fact_38_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 0.30/1.50 thf(fact_39_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y3:A,Z3:A]: ((Y3 = Z3))) = (^ [X5:A,Y4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X5))))))))).
% 0.30/1.50 thf(fact_40_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,B4:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A3) @ B4) => (((F @ B4) = C2) => ((! [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) => (((ord_less_eq @ B) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ B) @ (F @ A3)) @ C2)))))))))).
% 0.30/1.50 thf(fact_41_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,F:(B > A),B4:B,C2:B]: (((A3 = (F @ B4)) => ((((ord_less_eq @ B) @ B4) @ C2) => ((! [X4:B,Y5:B]: (((((ord_less_eq @ B) @ X4) @ Y5) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A3) @ (F @ C2))))))))))).
% 0.30/1.50 thf(fact_42_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,B4:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ C) @ (F @ B4)) @ C2) => ((! [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) => (((ord_less_eq @ C) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ C) @ (F @ A3)) @ C2)))))))))).
% 0.30/1.50 thf(fact_43_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,F:(B > A),B4:B,C2:B]: (((((ord_less_eq @ A) @ A3) @ (F @ B4)) => ((((ord_less_eq @ B) @ B4) @ C2) => ((! [X4:B,Y5:B]: (((((ord_less_eq @ B) @ X4) @ Y5) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A3) @ (F @ C2))))))))))).
% 0.30/1.50 thf(fact_44_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G:(A > B)]: ((! [X5:A]: ((((ord_less_eq @ B) @ (F2 @ X5)) @ (G @ X5))))))))))).
% 0.30/1.50 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 0.30/1.50 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X5:A]: ((((member @ A) @ X5) @ A4)))) = A4)))).
% 0.30/1.50 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.30/1.50 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X4:A]: (((F @ X4) = (G2 @ X4)))) => (F = G2))))).
% 0.30/1.50 thf(fact_49_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G2:(A > B)]: (((! [X4:A]: ((((ord_less_eq @ B) @ (F @ X4)) @ (G2 @ X4)))) => (((ord_less_eq @ (A > B)) @ F) @ G2)))))))).
% 0.30/1.50 thf(fact_50_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X)) @ (G2 @ X))))))))).
% 0.30/1.50 thf(fact_51_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X)) @ (G2 @ X))))))))).
% 0.30/1.50 thf(fact_52_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X5:A]: (((P @ X5) => (Q @ X5)))))))).
% 0.30/1.50 thf(fact_53_contra__subsetD, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((~ ((((member @ A) @ C2) @ B2))) => (~ ((((member @ A) @ C2) @ A4)))))))).
% 0.30/1.50 thf(fact_54_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z3:(set @ A)]: ((Y3 = Z3))) = (^ [A8:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A8) @ B3) & (((ord_less_eq @ (set @ A)) @ B3) @ A8)))))))).
% 0.30/1.50 thf(fact_55_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C3) => (((ord_less_eq @ (set @ A)) @ A4) @ C3)))))).
% 0.30/1.50 thf(fact_56_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) => (Q @ X4)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 0.30/1.50 thf(fact_57_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 0.30/1.50 thf(fact_58_rev__subsetD, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B2) => (((member @ A) @ C2) @ B2)))))).
% 0.30/1.50 thf(fact_59_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A8:(set @ A),B3:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A8) => (((member @ A) @ T) @ B3)))))))))).
% 0.30/1.50 thf(fact_60_set__rev__mp, axiom, (! [A:$tType,X:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ X) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B2) => (((member @ A) @ X) @ B2)))))).
% 0.30/1.50 thf(fact_61_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((A4 = B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A4))))).
% 0.30/1.50 thf(fact_62_stream_Oset, axiom, (! [A:$tType,X1:A,X2:(stream170649215stream @ A)]: ((((stream30925839e_sset @ A) @ (((stream641971652_SCons @ A) @ X1) @ X2)) = (((insert @ A) @ X1) @ ((stream30925839e_sset @ A) @ X2)))))).
% 0.30/1.50 thf(fact_63_stream_Opred__inject, axiom, (! [A:$tType,P:(A > $o),A3:A,Aa:(stream170649215stream @ A)]: (((((stream1153105665stream @ A) @ P) @ (((stream641971652_SCons @ A) @ A3) @ Aa)) = ((P @ A3) & (((stream1153105665stream @ A) @ P) @ Aa)))))).
% 0.30/1.50 thf(fact_64_antimono__def, axiom, (! [B:$tType,A:$tType]: (((((order @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (((order_antimono @ A) @ B) = (^ [F2:(A > B)]: ((! [X5:A,Y4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) => (((ord_less_eq @ B) @ (F2 @ Y4)) @ (F2 @ X5)))))))))))).
% 0.30/1.50 thf(fact_65_antimonoI, axiom, (! [B:$tType,A:$tType]: (((((order @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F:(A > B)]: (((! [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) => (((ord_less_eq @ B) @ (F @ Y5)) @ (F @ X4))))) => (((order_antimono @ A) @ B) @ F)))))))).
% 0.30/1.50 thf(fact_66_antimonoE, axiom, (! [B:$tType,A:$tType]: (((((order @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F:(A > B),X:A,Y:A]: (((((order_antimono @ A) @ B) @ F) => ((((ord_less_eq @ A) @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 0.30/1.50 thf(fact_67_antimonoD, axiom, (! [B:$tType,A:$tType]: (((((order @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F:(A > B),X:A,Y:A]: (((((order_antimono @ A) @ B) @ F) => ((((ord_less_eq @ A) @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 0.30/1.50 thf(fact_68_streamsp_Ocoinduct, axiom, (! [A:$tType,X3:((stream170649215stream @ A) > $o),X:(stream170649215stream @ A),A4:(A > $o)]: (((X3 @ X) => ((! [X4:(stream170649215stream @ A)]: (((X3 @ X4) => (? [A7:A,S4:(stream170649215stream @ A)]: (((X4 = (((stream641971652_SCons @ A) @ A7) @ S4)) & ((A4 @ A7) & ((X3 @ S4) | (((stream86250253reamsp @ A) @ A4) @ S4))))))))) => (((stream86250253reamsp @ A) @ A4) @ X)))))).
% 0.30/1.50 thf(fact_69_streamsp_Osimps, axiom, (! [A:$tType]: (((stream86250253reamsp @ A) = (^ [A8:(A > $o),A6:(stream170649215stream @ A)]: ((? [B6:A,S2:(stream170649215stream @ A)]: (((A6 = (((stream641971652_SCons @ A) @ B6) @ S2)) & ((A8 @ B6) & (((stream86250253reamsp @ A) @ A8) @ S2))))))))))).
% 0.30/1.50 thf(fact_70_streamsp_Ocases, axiom, (! [A:$tType,A4:(A > $o),A3:(stream170649215stream @ A)]: (((((stream86250253reamsp @ A) @ A4) @ A3) => (~ ((! [A5:A,S:(stream170649215stream @ A)]: (((A3 = (((stream641971652_SCons @ A) @ A5) @ S)) => ((A4 @ A5) => (~ ((((stream86250253reamsp @ A) @ A4) @ S))))))))))))).
% 0.30/1.50 thf(fact_71_stream_Ocase, axiom, (! [B:$tType,A:$tType,F:(A > ((stream170649215stream @ A) > B)),X1:A,X2:(stream170649215stream @ A)]: ((((((stream1342653232stream @ A) @ B) @ F) @ (((stream641971652_SCons @ A) @ X1) @ X2)) = ((F @ X1) @ X2))))).
% 0.30/1.50 thf(fact_72_insertCI, axiom, (! [A:$tType,A3:A,B2:(set @ A),B4:A]: ((((~ ((((member @ A) @ A3) @ B2))) => (A3 = B4)) => (((member @ A) @ A3) @ (((insert @ A) @ B4) @ B2)))))).
% 0.30/1.50 thf(fact_73_insert__iff, axiom, (! [A:$tType,A3:A,B4:A,A4:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B4) @ A4)) = ((A3 = B4) | (((member @ A) @ A3) @ A4)))))).
% 0.30/1.50 thf(fact_74_insert__absorb2, axiom, (! [A:$tType,X:A,A4:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A4)) = (((insert @ A) @ X) @ A4))))).
% 0.30/1.50 thf(fact_75_insert__subset, axiom, (! [A:$tType,X:A,A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A4)) @ B2) = ((((member @ A) @ X) @ B2) & (((ord_less_eq @ (set @ A)) @ A4) @ B2)))))).
% 0.30/1.50 thf(fact_76_insertE, axiom, (! [A:$tType,A3:A,B4:A,A4:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B4) @ A4)) => ((A3 != B4) => (((member @ A) @ A3) @ A4)))))).
% 0.30/1.50 thf(fact_77_insertI1, axiom, (! [A:$tType,A3:A,B2:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B2))))).
% 0.30/1.50 thf(fact_78_insertI2, axiom, (! [A:$tType,A3:A,B2:(set @ A),B4:A]: (((((member @ A) @ A3) @ B2) => (((member @ A) @ A3) @ (((insert @ A) @ B4) @ B2)))))).
% 0.30/1.50 thf(fact_79_Set_Oset__insert, axiom, (! [A:$tType,X:A,A4:(set @ A)]: (((((member @ A) @ X) @ A4) => (~ ((! [B7:(set @ A)]: (((A4 = (((insert @ A) @ X) @ B7)) => (((member @ A) @ X) @ B7)))))))))).
% 0.30/1.50 thf(fact_80_insert__ident, axiom, (! [A:$tType,X:A,A4:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ A4))) => ((~ ((((member @ A) @ X) @ B2))) => (((((insert @ A) @ X) @ A4) = (((insert @ A) @ X) @ B2)) = (A4 = B2))))))).
% 0.30/1.50 thf(fact_81_insert__absorb, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => ((((insert @ A) @ A3) @ A4) = A4))))).
% 0.30/1.50 thf(fact_82_insert__eq__iff, axiom, (! [A:$tType,A3:A,A4:(set @ A),B4:A,B2:(set @ A)]: (((~ ((((member @ A) @ A3) @ A4))) => ((~ ((((member @ A) @ B4) @ B2))) => (((((insert @ A) @ A3) @ A4) = (((insert @ A) @ B4) @ B2)) = (((A3 = B4) => (A4 = B2)) & ((A3 != B4) => (? [C4:(set @ A)]: (((A4 = (((insert @ A) @ B4) @ C4)) & ((~ ((((member @ A) @ B4) @ C4))) & ((B2 = (((insert @ A) @ A3) @ C4)) & (~ ((((member @ A) @ A3) @ C4)))))))))))))))).
% 0.30/1.50 thf(fact_83_insert__commute, axiom, (! [A:$tType,X:A,Y:A,A4:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y) @ A4)) = (((insert @ A) @ Y) @ (((insert @ A) @ X) @ A4)))))).
% 0.30/1.50 thf(fact_84_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => (? [B7:(set @ A)]: (((A4 = (((insert @ A) @ A3) @ B7)) & (~ ((((member @ A) @ A3) @ B7)))))))))).
% 0.30/1.50 thf(fact_85_insert__mono, axiom, (! [A:$tType,C3:(set @ A),D:(set @ A),A3:A]: (((((ord_less_eq @ (set @ A)) @ C3) @ D) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A3) @ C3)) @ (((insert @ A) @ A3) @ D)))))).
% 0.30/1.50 thf(fact_86_subset__insert, axiom, (! [A:$tType,X:A,A4:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ A4))) => ((((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ B2)) = (((ord_less_eq @ (set @ A)) @ A4) @ B2)))))).
% 0.30/1.50 thf(fact_87_subset__insertI, axiom, (! [A:$tType,B2:(set @ A),A3:A]: ((((ord_less_eq @ (set @ A)) @ B2) @ (((insert @ A) @ A3) @ B2))))).
% 0.30/1.50 thf(fact_88_subset__insertI2, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),B4:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B4) @ B2)))))).
% 0.30/1.50 thf(fact_89_stream_Opred__cong, axiom, (! [A:$tType,X:(stream170649215stream @ A),Ya:(stream170649215stream @ A),P:(A > $o),Pa:(A > $o)]: (((X = Ya) => ((! [Z4:A]: (((((member @ A) @ Z4) @ ((stream30925839e_sset @ A) @ Ya)) => ((P @ Z4) = (Pa @ Z4))))) => ((((stream1153105665stream @ A) @ P) @ X) = (((stream1153105665stream @ A) @ Pa) @ Ya))))))).
% 0.30/1.50 thf(fact_90_stream_Opred__mono__strong, axiom, (! [A:$tType,P:(A > $o),X:(stream170649215stream @ A),Pa:(A > $o)]: (((((stream1153105665stream @ A) @ P) @ X) => ((! [Z4:A]: (((((member @ A) @ Z4) @ ((stream30925839e_sset @ A) @ X)) => ((P @ Z4) => (Pa @ Z4))))) => (((stream1153105665stream @ A) @ Pa) @ X)))))).
% 0.30/1.50 thf(fact_91_insert__subsetI, axiom, (! [A:$tType,X:A,A4:(set @ A),X3:(set @ A)]: (((((member @ A) @ X) @ A4) => ((((ord_less_eq @ (set @ A)) @ X3) @ A4) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ X3)) @ A4)))))).
% 0.30/1.50 thf(fact_92_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A3:A,A4:(set @ A),B4:A]: ((((((insert @ A) @ A3) @ A4) = (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) = ((A3 = B4) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A))))))))).
% 0.30/1.50 thf(fact_93_singleton__insert__inj__eq, axiom, (! [A:$tType,B4:A,A3:A,A4:(set @ A)]: ((((((insert @ A) @ B4) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A3) @ A4)) = ((A3 = B4) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A))))))))).
% 0.30/1.50 thf(fact_94_stream_Opred__set, axiom, (! [A:$tType]: (((stream1153105665stream @ A) = (^ [P2:(A > $o),X5:(stream170649215stream @ A)]: ((! [Y4:A]: (((((member @ A) @ Y4) @ ((stream30925839e_sset @ A) @ X5)) => (P2 @ Y4)))))))))).
% 0.30/1.50 thf(fact_95_subset__singletonD, axiom, (! [A:$tType,A4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) => ((A4 = (bot_bot @ (set @ A))) | (A4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 0.30/1.50 thf(fact_96_subset__singleton__iff, axiom, (! [A:$tType,X3:(set @ A),A3:A]: (((((ord_less_eq @ (set @ A)) @ X3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = ((X3 = (bot_bot @ (set @ A))) | (X3 = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))))).
% 0.30/1.50 thf(fact_97_stream_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((stream660621732stream @ C) @ A) = (^ [G1:(C > A),Q2:(C > $o),G21:(C > (stream170649215stream @ A)),G22:(C > C),A6:C]: ((((stream641971652_SCons @ A) @ (G1 @ A6)) @ ((((if @ (stream170649215stream @ A)) @ (Q2 @ A6)) @ (G21 @ A6)) @ (((((((stream660621732stream @ C) @ A) @ G1) @ Q2) @ G21) @ G22) @ (G22 @ A6)))))))))).
% 0.30/1.50 thf(fact_98_bot__apply, axiom, (! [C:$tType,D2:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D2 > C)) = (^ [X5:D2]: ((bot_bot @ C)))))))).
% 0.30/1.50 thf(fact_99_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X5:A]: ((~ ((P @ X5))))))))).
% 0.30/1.50 thf(fact_100_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X5:A]: ((~ ((P @ X5))))))))).
% 0.30/1.50 thf(fact_101_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X5:A]: ((~ ((((member @ A) @ X5) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_102_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_103_empty__subsetI, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4)))).
% 0.30/1.50 thf(fact_104_subset__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_105_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_106_ball__empty, axiom, (! [A:$tType,P:(A > $o),X6:A]: (((((member @ A) @ X6) @ (bot_bot @ (set @ A))) => (P @ X6))))).
% 0.30/1.50 thf(fact_107_subset__emptyI, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A4))))) => (((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_108_stream_Ocorec__disc, axiom, (! [A:$tType,C:$tType]: ((((stream660621732stream @ C) @ A) = ((stream660621732stream @ C) @ A))))).
% 0.30/1.50 thf(fact_109_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X5:A]: ((bot_bot @ B)))))))).
% 0.30/1.50 thf(fact_110_ex__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((? [X5:A]: ((((member @ A) @ X5) @ A4))) = (A4 != (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_111_equals0I, axiom, (! [A:$tType,A4:(set @ A)]: (((! [Y5:A]: ((~ ((((member @ A) @ Y5) @ A4))))) => (A4 = (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_112_equals0D, axiom, (! [A:$tType,A4:(set @ A),A3:A]: (((A4 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A4))))))).
% 0.30/1.50 thf(fact_113_Ball__def, axiom, (! [A:$tType]: (((ball @ A) = (^ [A8:(set @ A),P2:(A > $o)]: ((! [X5:A]: (((((member @ A) @ X5) @ A8) => (P2 @ X5)))))))))).
% 0.30/1.50 thf(fact_114_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_115_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ A3) @ (bot_bot @ A)) => (A3 = (bot_bot @ A))))))))).
% 0.30/1.50 thf(fact_116_bot_Oextremum__unique, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ A3) @ (bot_bot @ A)) = (A3 = (bot_bot @ A))))))))).
% 0.30/1.50 thf(fact_117_bot_Oextremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A3))))))).
% 0.30/1.50 thf(fact_118_singleton__inject, axiom, (! [A:$tType,A3:A,B4:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) => (A3 = B4))))).
% 0.30/1.50 thf(fact_119_insert__not__empty, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((insert @ A) @ A3) @ A4) != (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_120_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B4:A,C2:A,D3:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D3) @ (bot_bot @ (set @ A))))) = (((A3 = C2) & (B4 = D3)) | ((A3 = D3) & (B4 = C2))))))).
% 0.30/1.50 thf(fact_121_singleton__iff, axiom, (! [A:$tType,B4:A,A3:A]: (((((member @ A) @ B4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B4 = A3))))).
% 0.30/1.50 thf(fact_122_singletonD, axiom, (! [A:$tType,B4:A,A3:A]: (((((member @ A) @ B4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B4 = A3))))).
% 0.30/1.50 thf(fact_123_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 0.30/1.50 thf(fact_124_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_125_Ball__Collect, axiom, (! [A:$tType]: (((ball @ A) = (^ [A8:(set @ A),P2:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ A8) @ ((collect @ A) @ P2)))))))).
% 0.30/1.50 thf(fact_126_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A8:(set @ A)]: ((A8 = (bot_bot @ (set @ A))))))))).
% 0.30/1.50 thf(fact_127_is__singletonE, axiom, (! [A:$tType,A4:(set @ A)]: ((((is_singleton @ A) @ A4) => (~ ((! [X4:A]: ((A4 != (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 0.30/1.50 thf(fact_128_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 0.30/1.50 thf(fact_129_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A8:(set @ A)]: ((A8 = (((insert @ A) @ ((the_elem @ A) @ A8)) @ (bot_bot @ (set @ A)))))))))).
% 0.30/1.50 thf(fact_130_is__singletonI_H, axiom, (! [A:$tType,A4:(set @ A)]: (((A4 != (bot_bot @ (set @ A))) => ((! [X4:A,Y5:A]: (((((member @ A) @ X4) @ A4) => ((((member @ A) @ Y5) @ A4) => (X4 = Y5))))) => ((is_singleton @ A) @ A4)))))).
% 0.30/1.50 thf(fact_131_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A8:(set @ A)]: ((? [X5:A]: ((A8 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))))))))))).
% 0.30/1.50 thf(fact_132_pairwise__singleton, axiom, (! [A:$tType,P:(A > (A > $o)),A4:A]: ((((pairwise @ A) @ P) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_133_subset__Compl__singleton, axiom, (! [A:$tType,A4:(set @ A),B4:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ ((uminus_uminus @ (set @ A)) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A))))) = (~ ((((member @ A) @ B4) @ A4))))))).
% 0.30/1.50 thf(fact_134_ball__reg, axiom, (! [A:$tType,R:(set @ A),P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ R) => ((P @ X4) => (Q @ X4))))) => ((! [X4:A]: (((((member @ A) @ X4) @ R) => (P @ X4)))) => (! [X6:A]: (((((member @ A) @ X6) @ R) => (Q @ X6))))))))).
% 0.30/1.50 thf(fact_135_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X5:A]: ((((member @ A) @ X5) @ (bot_bot @ (set @ A))))))))).
% 0.30/1.50 thf(fact_136_Compl__eq__Compl__iff, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A4) = ((uminus_uminus @ (set @ A)) @ B2)) = (A4 = B2))))).
% 0.30/1.50 thf(fact_137_Compl__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A4)) = (~ ((((member @ A) @ C2) @ A4))))))).
% 0.30/1.50 thf(fact_138_ComplI, axiom, (! [A:$tType,C2:A,A4:(set @ A)]: (((~ ((((member @ A) @ C2) @ A4))) => (((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A4)))))).
% 0.30/1.50 thf(fact_139_Compl__anti__mono, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => (((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ B2)) @ ((uminus_uminus @ (set @ A)) @ A4)))))).
% 0.30/1.50 thf(fact_140_Compl__subset__Compl__iff, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A4)) @ ((uminus_uminus @ (set @ A)) @ B2)) = (((ord_less_eq @ (set @ A)) @ B2) @ A4))))).
% 0.30/1.50 thf(fact_141_double__complement, axiom, (! [A:$tType,A4:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A4)) = A4)))).
% 0.30/1.50 thf(fact_142_pairwise__def, axiom, (! [A:$tType]: (((pairwise @ A) = (^ [R2:(A > (A > $o)),S5:(set @ A)]: ((! [X5:A]: (((((member @ A) @ X5) @ S5) => (! [Y4:A]: (((((member @ A) @ Y4) @ S5) => ((X5 != Y4) => ((R2 @ X5) @ Y4)))))))))))))).
% 0.30/1.50 thf(fact_143_ComplD, axiom, (! [A:$tType,C2:A,A4:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A4)) => (~ ((((member @ A) @ C2) @ A4))))))).
% 0.30/1.50 thf(fact_144_subset__Compl__self__eq, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ ((uminus_uminus @ (set @ A)) @ A4)) = (A4 = (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_145_pairwise__empty, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((pairwise @ A) @ P) @ (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_146_pairwise__subset, axiom, (! [A:$tType,P:(A > (A > $o)),S6:(set @ A),T2:(set @ A)]: (((((pairwise @ A) @ P) @ S6) => ((((ord_less_eq @ (set @ A)) @ T2) @ S6) => (((pairwise @ A) @ P) @ T2)))))).
% 0.30/1.50 thf(fact_147_pairwise__insert, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A,S3:(set @ A)]: (((((pairwise @ A) @ R3) @ (((insert @ A) @ X) @ S3)) = ((! [Y4:A]: ((((((member @ A) @ Y4) @ S3) & (Y4 != X)) => (((R3 @ X) @ Y4) & ((R3 @ Y4) @ X))))) & (((pairwise @ A) @ R3) @ S3)))))).
% 0.30/1.50 thf(fact_148_neg__le__iff__le, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B4:A,A3:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B4)) @ ((uminus_uminus @ A) @ A3)) = (((ord_less_eq @ A) @ A3) @ B4)))))))).
% 0.30/1.50 thf(fact_149_compl__le__compl__iff, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X)) @ ((uminus_uminus @ A) @ Y)) = (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.30/1.50 thf(fact_150_uminus__apply, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A8:(A > B),X5:A]: (((uminus_uminus @ B) @ (A8 @ X5))))))))).
% 0.30/1.50 thf(fact_151_add_Oinverse__inverse, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A3)) = A3))))))).
% 0.30/1.50 thf(fact_152_compl__eq__compl__iff, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((uminus_uminus @ A) @ X) = ((uminus_uminus @ A) @ Y)) = (X = Y)))))))).
% 0.30/1.50 thf(fact_153_double__compl, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ X)) = X))))))).
% 0.30/1.50 thf(fact_154_neg__equal__iff__equal, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: (((((uminus_uminus @ A) @ A3) = ((uminus_uminus @ A) @ B4)) = (A3 = B4)))))))).
% 0.30/1.50 thf(fact_155_minus__equation__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: (((((uminus_uminus @ A) @ A3) = B4) = (((uminus_uminus @ A) @ B4) = A3)))))))).
% 0.30/1.50 thf(fact_156_equation__minus__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: (((A3 = ((uminus_uminus @ A) @ B4)) = (B4 = ((uminus_uminus @ A) @ A3))))))))).
% 0.30/1.50 thf(fact_157_fun__Compl__def, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A8:(A > B),X5:A]: (((uminus_uminus @ B) @ (A8 @ X5))))))))).
% 0.30/1.50 thf(fact_158_le__imp__neg__le, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B4)) @ ((uminus_uminus @ A) @ A3))))))))).
% 0.30/1.50 thf(fact_159_minus__le__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ A3)) @ B4) = (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B4)) @ A3)))))))).
% 0.30/1.50 thf(fact_160_le__minus__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ ((uminus_uminus @ A) @ B4)) = (((ord_less_eq @ A) @ B4) @ ((uminus_uminus @ A) @ A3))))))))).
% 0.30/1.50 thf(fact_161_compl__le__swap2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y)) @ X) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X)) @ Y)))))))).
% 0.30/1.50 thf(fact_162_compl__le__swap1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ ((uminus_uminus @ A) @ X)) => (((ord_less_eq @ A) @ X) @ ((uminus_uminus @ A) @ Y))))))))).
% 0.30/1.50 thf(fact_163_compl__mono, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y)) @ ((uminus_uminus @ A) @ X))))))))).
% 0.30/1.50 thf(fact_164_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 0.30/1.50 thf(fact_165_in__inv__imagep, axiom, (! [B:$tType,A:$tType]: ((((inv_imagep @ A) @ B) = (^ [R4:(A > (A > $o)),F2:(B > A),X5:B,Y4:B]: (((R4 @ (F2 @ X5)) @ (F2 @ Y4)))))))).
% 0.30/1.50 thf(fact_166_Compl__insert, axiom, (! [A:$tType,X:A,A4:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ (((insert @ A) @ X) @ A4)) = (((minus_minus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A4)) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_167_Diff__idemp, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) @ B2) = (((minus_minus @ (set @ A)) @ A4) @ B2))))).
% 0.30/1.50 thf(fact_168_Diff__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) = ((((member @ A) @ C2) @ A4) & (~ ((((member @ A) @ C2) @ B2)))))))).
% 0.30/1.50 thf(fact_169_DiffI, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B2))))))).
% 0.30/1.50 thf(fact_170_minus__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A]: ((((uminus_uminus @ A) @ (((minus_minus @ A) @ A3) @ B4)) = (((minus_minus @ A) @ B4) @ A3)))))))).
% 0.30/1.50 thf(fact_171_Diff__cancel, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ A4) = (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_172_empty__Diff, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4) = (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_173_Diff__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = A4)))).
% 0.30/1.50 thf(fact_174_Diff__insert0, axiom, (! [A:$tType,X:A,A4:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ A4))) => ((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ B2)) = (((minus_minus @ (set @ A)) @ A4) @ B2)))))).
% 0.30/1.50 thf(fact_175_insert__Diff1, axiom, (! [A:$tType,X:A,B2:(set @ A),A4:(set @ A)]: (((((member @ A) @ X) @ B2) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A4)) @ B2) = (((minus_minus @ (set @ A)) @ A4) @ B2)))))).
% 0.30/1.50 thf(fact_176_Diff__eq__empty__iff, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: ((((((minus_minus @ (set @ A)) @ A4) @ B2) = (bot_bot @ (set @ A))) = (((ord_less_eq @ (set @ A)) @ A4) @ B2))))).
% 0.30/1.50 thf(fact_177_insert__Diff__single, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A3) @ A4))))).
% 0.30/1.50 thf(fact_178_diff__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A,D3:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ D3) @ C2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A3) @ C2)) @ (((minus_minus @ A) @ B4) @ D3)))))))))).
% 0.30/1.50 thf(fact_179_diff__left__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B4:A,A3:A,C2:A]: (((((ord_less_eq @ A) @ B4) @ A3) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C2) @ A3)) @ (((minus_minus @ A) @ C2) @ B4))))))))).
% 0.30/1.50 thf(fact_180_diff__right__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B4) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A3) @ C2)) @ (((minus_minus @ A) @ B4) @ C2))))))))).
% 0.30/1.50 thf(fact_181_diff__eq__diff__less__eq, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B4:A,C2:A,D3:A]: ((((((minus_minus @ A) @ A3) @ B4) = (((minus_minus @ A) @ C2) @ D3)) => ((((ord_less_eq @ A) @ A3) @ B4) = (((ord_less_eq @ A) @ C2) @ D3))))))))).
% 0.30/1.50 thf(fact_182_Diff__mono, axiom, (! [A:$tType,A4:(set @ A),C3:(set @ A),D:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C3) => ((((ord_less_eq @ (set @ A)) @ D) @ B2) => (((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) @ (((minus_minus @ (set @ A)) @ C3) @ D))))))).
% 0.30/1.50 thf(fact_183_Diff__subset, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) @ A4)))).
% 0.30/1.50 thf(fact_184_double__diff, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C3) => ((((minus_minus @ (set @ A)) @ B2) @ (((minus_minus @ (set @ A)) @ C3) @ A4)) = A4)))))).
% 0.30/1.50 thf(fact_185_insert__Diff__if, axiom, (! [A:$tType,X:A,B2:(set @ A),A4:(set @ A)]: ((((((member @ A) @ X) @ B2) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A4)) @ B2) = (((minus_minus @ (set @ A)) @ A4) @ B2))) & ((~ ((((member @ A) @ X) @ B2))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A4)) @ B2) = (((insert @ A) @ X) @ (((minus_minus @ (set @ A)) @ A4) @ B2)))))))).
% 0.30/1.50 thf(fact_186_DiffD2, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) => (~ ((((member @ A) @ C2) @ B2))))))).
% 0.30/1.50 thf(fact_187_DiffD1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) => (((member @ A) @ C2) @ A4))))).
% 0.30/1.50 thf(fact_188_DiffE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) => (~ (((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B2)))))))).
% 0.30/1.50 thf(fact_189_Diff__insert, axiom, (! [A:$tType,A4:(set @ A),A3:A,B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B2)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_190_insert__Diff, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => ((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = A4))))).
% 0.30/1.50 thf(fact_191_Diff__insert2, axiom, (! [A:$tType,A4:(set @ A),A3:A,B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B2)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) @ B2))))).
% 0.30/1.50 thf(fact_192_Diff__insert__absorb, axiom, (! [A:$tType,X:A,A4:(set @ A)]: (((~ ((((member @ A) @ X) @ A4))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A4)) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = A4))))).
% 0.30/1.50 thf(fact_193_subset__Diff__insert, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),X:A,C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ B2) @ (((insert @ A) @ X) @ C3))) = ((((ord_less_eq @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ B2) @ C3)) & (~ ((((member @ A) @ X) @ A4)))))))).
% 0.30/1.50 thf(fact_194_Diff__single__insert, axiom, (! [A:$tType,A4:(set @ A),X:A,B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) @ B2) => (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ B2)))))).
% 0.30/1.50 thf(fact_195_subset__insert__iff, axiom, (! [A:$tType,A4:(set @ A),X:A,B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ B2)) = (((((member @ A) @ X) @ A4) => (((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) @ B2)) & ((~ ((((member @ A) @ X) @ A4))) => (((ord_less_eq @ (set @ A)) @ A4) @ B2))))))).
% 0.30/1.50 thf(fact_196_remove__def, axiom, (! [A:$tType]: (((remove @ A) = (^ [X5:A,A8:(set @ A)]: ((((minus_minus @ (set @ A)) @ A8) @ (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))))))))).
% 0.30/1.50 thf(fact_197_psubset__insert__iff, axiom, (! [A:$tType,A4:(set @ A),X:A,B2:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ B2)) = (((((member @ A) @ X) @ B2) => (((ord_less @ (set @ A)) @ A4) @ B2)) & ((~ ((((member @ A) @ X) @ B2))) => (((((member @ A) @ X) @ A4) => (((ord_less @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) @ B2)) & ((~ ((((member @ A) @ X) @ A4))) => (((ord_less_eq @ (set @ A)) @ A4) @ B2))))))))).
% 0.30/1.50 thf(fact_198_disjoint__eq__subset__Compl, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A4) @ B2) = (bot_bot @ (set @ A))) = (((ord_less_eq @ (set @ A)) @ A4) @ ((uminus_uminus @ (set @ A)) @ B2)))))).
% 0.30/1.50 thf(fact_199_IntI, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B2))))))).
% 0.30/1.50 thf(fact_200_Int__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) = ((((member @ A) @ C2) @ A4) & (((member @ A) @ C2) @ B2)))))).
% 0.30/1.50 thf(fact_201_member__remove, axiom, (! [A:$tType,X:A,Y:A,A4:(set @ A)]: (((((member @ A) @ X) @ (((remove @ A) @ Y) @ A4)) = ((((member @ A) @ X) @ A4) & (X != Y)))))).
% 0.30/1.50 thf(fact_202_le__inf__iff, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = ((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ X) @ Z))))))))).
% 0.30/1.50 thf(fact_203_inf_Obounded__iff, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A3:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ (((inf_inf @ A) @ B4) @ C2)) = ((((ord_less_eq @ A) @ A3) @ B4) & (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 0.30/1.50 thf(fact_204_neg__less__iff__less, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B4:A,A3:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ B4)) @ ((uminus_uminus @ A) @ A3)) = (((ord_less @ A) @ A3) @ B4)))))))).
% 0.30/1.50 thf(fact_205_inf__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 0.30/1.50 thf(fact_206_inf__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X) = (bot_bot @ A)))))))).
% 0.30/1.50 thf(fact_207_Int__subset__iff, axiom, (! [A:$tType,C3:(set @ A),A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C3) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) = ((((ord_less_eq @ (set @ A)) @ C3) @ A4) & (((ord_less_eq @ (set @ A)) @ C3) @ B2)))))).
% 0.30/1.50 thf(fact_208_Int__insert__right__if1, axiom, (! [A:$tType,A3:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ A3) @ A4) => ((((inf_inf @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B2)) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ A4) @ B2))))))).
% 0.30/1.50 thf(fact_209_Int__insert__right__if0, axiom, (! [A:$tType,A3:A,A4:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ A3) @ A4))) => ((((inf_inf @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B2)) = (((inf_inf @ (set @ A)) @ A4) @ B2)))))).
% 0.30/1.50 thf(fact_210_insert__inter__insert, axiom, (! [A:$tType,A3:A,A4:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ A4)) @ (((insert @ A) @ A3) @ B2)) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ A4) @ B2)))))).
% 0.30/1.50 thf(fact_211_Int__insert__left__if1, axiom, (! [A:$tType,A3:A,C3:(set @ A),B2:(set @ A)]: (((((member @ A) @ A3) @ C3) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C3) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ B2) @ C3))))))).
% 0.30/1.50 thf(fact_212_Int__insert__left__if0, axiom, (! [A:$tType,A3:A,C3:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ A3) @ C3))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C3) = (((inf_inf @ (set @ A)) @ B2) @ C3)))))).
% 0.30/1.50 thf(fact_213_psubsetI, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((A4 != B2) => (((ord_less @ (set @ A)) @ A4) @ B2)))))).
% 0.30/1.50 thf(fact_214_compl__inf__bot, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ X) = (bot_bot @ A)))))))).
% 0.30/1.50 thf(fact_215_inf__compl__bot, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ ((uminus_uminus @ A) @ X)) = (bot_bot @ A)))))))).
% 0.30/1.50 thf(fact_216_inf__compl__bot__left1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ (((inf_inf @ A) @ X) @ Y)) = (bot_bot @ A)))))))).
% 0.30/1.50 thf(fact_217_inf__compl__bot__left2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ Y)) = (bot_bot @ A)))))))).
% 0.30/1.50 thf(fact_218_inf__compl__bot__right, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ ((uminus_uminus @ A) @ X))) = (bot_bot @ A)))))))).
% 0.30/1.50 thf(fact_219_insert__disjoint_I1_J, axiom, (! [A:$tType,A3:A,A4:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ A4)) @ B2) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A3) @ B2))) & ((((inf_inf @ (set @ A)) @ A4) @ B2) = (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_220_insert__disjoint_I2_J, axiom, (! [A:$tType,A3:A,A4:(set @ A),B2:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ A4)) @ B2)) = ((~ ((((member @ A) @ A3) @ B2))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A4) @ B2))))))).
% 0.30/1.50 thf(fact_221_disjoint__insert_I1_J, axiom, (! [A:$tType,B2:(set @ A),A3:A,A4:(set @ A)]: ((((((inf_inf @ (set @ A)) @ B2) @ (((insert @ A) @ A3) @ A4)) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A3) @ B2))) & ((((inf_inf @ (set @ A)) @ B2) @ A4) = (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_222_disjoint__insert_I2_J, axiom, (! [A:$tType,A4:(set @ A),B4:A,B2:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A4) @ (((insert @ A) @ B4) @ B2))) = ((~ ((((member @ A) @ B4) @ A4))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A4) @ B2))))))).
% 0.30/1.50 thf(fact_223_Diff__disjoint, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ B2) @ A4)) = (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_224_Compl__disjoint, axiom, (! [A:$tType,A4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ ((uminus_uminus @ (set @ A)) @ A4)) = (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_225_Compl__disjoint2, axiom, (! [A:$tType,A4:(set @ A)]: (((((inf_inf @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A4)) @ A4) = (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_226_Diff__Compl, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ ((uminus_uminus @ (set @ A)) @ B2)) = (((inf_inf @ (set @ A)) @ A4) @ B2))))).
% 0.30/1.50 thf(fact_227_psubset__imp__ex__mem, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B2) => (? [B5:A]: ((((member @ A) @ B5) @ (((minus_minus @ (set @ A)) @ B2) @ A4)))))))).
% 0.30/1.50 thf(fact_228_Diff__Int__distrib2, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) @ C3) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ C3)) @ (((inf_inf @ (set @ A)) @ B2) @ C3)))))).
% 0.30/1.50 thf(fact_229_Diff__Int__distrib, axiom, (! [A:$tType,C3:(set @ A),A4:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ C3) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ C3) @ A4)) @ (((inf_inf @ (set @ A)) @ C3) @ B2)))))).
% 0.30/1.50 thf(fact_230_Diff__Diff__Int, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ A4) @ B2)) = (((inf_inf @ (set @ A)) @ A4) @ B2))))).
% 0.30/1.50 thf(fact_231_Diff__Int2, axiom, (! [A:$tType,A4:(set @ A),C3:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ C3)) @ (((inf_inf @ (set @ A)) @ B2) @ C3)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ C3)) @ B2))))).
% 0.30/1.50 thf(fact_232_Int__Diff, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) @ C3) = (((inf_inf @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ B2) @ C3)))))).
% 0.30/1.50 thf(fact_233_Int__emptyI, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A4) => (~ ((((member @ A) @ X4) @ B2)))))) => ((((inf_inf @ (set @ A)) @ A4) @ B2) = (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_234_Int__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_235_Int__empty__right, axiom, (! [A:$tType,A4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 0.30/1.50 thf(fact_236_disjoint__iff__not__equal, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A4) @ B2) = (bot_bot @ (set @ A))) = (! [X5:A]: (((((member @ A) @ X5) @ A4) => (! [Y4:A]: (((((member @ A) @ Y4) @ B2) => (X5 != Y4))))))))))).
% 0.30/1.50 thf(fact_237_bot_Oextremum__strict, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ (bot_bot @ A)))))))))).
% 0.30/1.50 thf(fact_238_bot_Onot__eq__extremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: (((A3 != (bot_bot @ A)) = (((ord_less @ A) @ (bot_bot @ A)) @ A3)))))))).
% 0.30/1.50 thf(fact_239_not__psubset__empty, axiom, (! [A:$tType,A4:(set @ A)]: ((~ ((((ord_less @ (set @ A)) @ A4) @ (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_240_IntE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) => (~ (((((member @ A) @ C2) @ A4) => (~ ((((member @ A) @ C2) @ B2)))))))))).
% 0.30/1.50 thf(fact_241_IntD1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) => (((member @ A) @ C2) @ A4))))).
% 0.30/1.50 thf(fact_242_IntD2, axiom, (! [A:$tType,C2:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) => (((member @ A) @ C2) @ B2))))).
% 0.30/1.50 thf(fact_243_psubsetD, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:A]: (((((ord_less @ (set @ A)) @ A4) @ B2) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B2)))))).
% 0.30/1.50 thf(fact_244_Int__assoc, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) @ C3) = (((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ B2) @ C3)))))).
% 0.30/1.50 thf(fact_245_Int__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ A4) = A4)))).
% 0.30/1.50 thf(fact_246_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A8:(set @ A),B3:(set @ A)]: ((((inf_inf @ (set @ A)) @ B3) @ A8))))))).
% 0.30/1.50 thf(fact_247_psubset__trans, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B2) => ((((ord_less @ (set @ A)) @ B2) @ C3) => (((ord_less @ (set @ A)) @ A4) @ C3)))))).
% 0.30/1.50 thf(fact_248_Int__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ A4) @ B2)) = (((inf_inf @ (set @ A)) @ A4) @ B2))))).
% 0.30/1.50 thf(fact_249_Int__left__commute, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ B2) @ C3)) = (((inf_inf @ (set @ A)) @ B2) @ (((inf_inf @ (set @ A)) @ A4) @ C3)))))).
% 0.30/1.50 thf(fact_250_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,F:(B > A),B4:B,C2:B]: (((A3 = (F @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X4:B,Y5:B]: (((((ord_less @ B) @ X4) @ Y5) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ A) @ A3) @ (F @ C2))))))))))).
% 0.30/1.50 thf(fact_251_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,B4:A,F:(A > B),C2:B]: (((((ord_less @ A) @ A3) @ B4) => (((F @ B4) = C2) => ((! [X4:A,Y5:A]: (((((ord_less @ A) @ X4) @ Y5) => (((ord_less @ B) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ B) @ (F @ A3)) @ C2)))))))))).
% 0.30/1.50 thf(fact_252_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,F:(B > A),B4:B,C2:B]: (((((ord_less @ A) @ A3) @ (F @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X4:B,Y5:B]: (((((ord_less @ B) @ X4) @ Y5) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ A) @ A3) @ (F @ C2))))))))))).
% 0.30/1.50 thf(fact_253_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,B4:A,F:(A > C),C2:C]: (((((ord_less @ A) @ A3) @ B4) => ((((ord_less @ C) @ (F @ B4)) @ C2) => ((! [X4:A,Y5:A]: (((((ord_less @ A) @ X4) @ Y5) => (((ord_less @ C) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ C) @ (F @ A3)) @ C2)))))))))).
% 0.30/1.50 thf(fact_254_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y5:A]: ((((ord_less @ A) @ Y5) @ X))))))))).
% 0.30/1.50 thf(fact_255_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X:A]: ((? [X12:A]: ((((ord_less @ A) @ X) @ X12))))))))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A9:$tType]: (((bounded_lattice @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A9:$tType,A10:$tType]: ((((bounded_lattice @ A10) @ (type2 @ A10)) => ((bounded_lattice @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A9:$tType,A10:$tType]: ((((bounded_lattice @ A10) @ (type2 @ A10)) => ((bounded_lattice_bot @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A9:$tType,A10:$tType]: ((((semilattice_inf @ A10) @ (type2 @ A10)) => ((semilattice_inf @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A9:$tType,A10:$tType]: ((((boolean_algebra @ A10) @ (type2 @ A10)) => ((boolean_algebra @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A9:$tType,A10:$tType]: ((((order_bot @ A10) @ (type2 @ A10)) => ((order_bot @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A9:$tType,A10:$tType]: ((((preorder @ A10) @ (type2 @ A10)) => ((preorder @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A9:$tType,A10:$tType]: ((((order @ A10) @ (type2 @ A10)) => ((order @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A9:$tType,A10:$tType]: ((((ord @ A10) @ (type2 @ A10)) => ((ord @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Orderings_Obot, axiom, (! [A9:$tType,A10:$tType]: ((((bot @ A10) @ (type2 @ A10)) => ((bot @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_fun___Groups_Ouminus, axiom, (! [A9:$tType,A10:$tType]: ((((uminus @ A10) @ (type2 @ A10)) => ((uminus @ (A9 > A10)) @ (type2 @ (A9 > A10))))))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3, axiom, (! [A9:$tType]: (((bounded_lattice_bot @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4, axiom, (! [A9:$tType]: (((semilattice_inf @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_5, axiom, (! [A9:$tType]: (((boolean_algebra @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Orderings_Oorder__bot_6, axiom, (! [A9:$tType]: (((order_bot @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_7, axiom, (! [A9:$tType]: (((preorder @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Orderings_Oorder_8, axiom, (! [A9:$tType]: (((order @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Orderings_Oord_9, axiom, (! [A9:$tType]: (((ord @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Orderings_Obot_10, axiom, (! [A9:$tType]: (((bot @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Groups_Ouminus_11, axiom, (! [A9:$tType]: (((uminus @ (set @ A9)) @ (type2 @ (set @ A9)))))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12, axiom, ((bounded_lattice_bot @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_13, axiom, ((semilattice_inf @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_14, axiom, ((boolean_algebra @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15, axiom, ((order_bot @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_16, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_17, axiom, ((order @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Orderings_Oord_18, axiom, ((ord @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Orderings_Obot_19, axiom, ((bot @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Groups_Ouminus_20, axiom, ((uminus @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.30/1.50 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 0.30/1.50 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 0.30/1.50 thf(conj_0, conjecture, (? [A7:a,S4:(stream170649215stream @ a)]: (((sa = (((stream641971652_SCons @ a) @ A7) @ S4)) & ((((member @ a) @ A7) @ a2) & ((? [Sa:(stream170649215stream @ a)]: (((S4 = Sa) & (((ord_less_eq @ (set @ a)) @ ((stream30925839e_sset @ a) @ Sa)) @ a2)))) | (((member @ (stream170649215stream @ a)) @ S4) @ ((stream2015131171treams @ a) @ a2)))))))).
% 0.30/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2DTF5740.p
% 0.30/1.50 ------------------------
% 0.30/1.53 ---- Cleaned THF ---
% 0.30/1.53 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream,type,
% 0.30/1.53 stream170649215stream: $tType > $tType ).
% 0.30/1.53
% 0.30/1.53 thf(ty_t_Set_Oset,type,
% 0.30/1.53 set: $tType > $tType ).
% 0.30/1.53
% 0.30/1.53 thf(ty_t_itself,type,
% 0.30/1.53 itself: $tType > $tType ).
% 0.30/1.53
% 0.30/1.53 thf(ty_tf_a,type,
% 0.30/1.53 a: $tType ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/1.53 bounded_lattice:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_HOL_Otype,type,
% 0.30/1.53 type:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Groups_Ouminus,type,
% 0.30/1.53 uminus:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Obot,type,
% 0.30/1.53 bot:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Oord,type,
% 0.30/1.53 ord:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Oorder,type,
% 0.30/1.53 order:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Groups_Ogroup__add,type,
% 0.30/1.53 group_add:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Ono__bot,type,
% 0.30/1.53 no_bot:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Ono__top,type,
% 0.30/1.53 no_top:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/1.53 linorder:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/1.53 preorder:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.30/1.53 order_bot:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.30/1.53 boolean_algebra:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.30/1.53 semilattice_inf:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.30/1.53 ordered_ab_group_add:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.30/1.53 bounded_lattice_bot:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.30/1.53 minus_minus:
% 0.30/1.53 !>[A: $tType] : ( A > A > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.30/1.53 uminus_uminus:
% 0.30/1.53 !>[A: $tType] : ( A > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_If,type,
% 0.30/1.53 if:
% 0.30/1.53 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.30/1.53 inf_inf:
% 0.30/1.53 !>[A: $tType] : ( A > A > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/1.53 bot_bot:
% 0.30/1.53 !>[A: $tType] : A ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.30/1.53 ord_less:
% 0.30/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/1.53 ord_less_eq:
% 0.30/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Orderings_Oorder__class_Oantimono,type,
% 0.30/1.53 order_antimono:
% 0.30/1.53 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Pure_Otype,type,
% 0.30/1.53 type2:
% 0.30/1.53 !>[A: $tType] : ( itself @ A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Relation_Oinv__imagep,type,
% 0.30/1.53 inv_imagep:
% 0.30/1.53 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_OBall,type,
% 0.30/1.53 ball:
% 0.30/1.53 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_OCollect,type,
% 0.30/1.53 collect:
% 0.30/1.53 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_Oinsert,type,
% 0.30/1.53 insert:
% 0.30/1.53 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_Ois__empty,type,
% 0.30/1.53 is_empty:
% 0.30/1.53 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_Ois__singleton,type,
% 0.30/1.53 is_singleton:
% 0.30/1.53 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_Opairwise,type,
% 0.30/1.53 pairwise:
% 0.30/1.53 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_Oremove,type,
% 0.30/1.53 remove:
% 0.30/1.53 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_Othe__elem,type,
% 0.30/1.53 the_elem:
% 0.30/1.53 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember,type,
% 0.30/1.53 stream1586597341member:
% 0.30/1.53 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_OSCons,type,
% 0.30/1.53 stream641971652_SCons:
% 0.30/1.53 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocase__stream,type,
% 0.30/1.53 stream1342653232stream:
% 0.30/1.53 !>[A: $tType,B: $tType] : ( ( A > ( stream170649215stream @ A ) > B ) > ( stream170649215stream @ A ) > B ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocorec__stream,type,
% 0.30/1.53 stream660621732stream:
% 0.30/1.53 !>[C: $tType,A: $tType] : ( ( C > A ) > ( C > $o ) > ( C > ( stream170649215stream @ A ) ) > ( C > C ) > C > ( stream170649215stream @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Opred__stream,type,
% 0.30/1.53 stream1153105665stream:
% 0.30/1.53 !>[A: $tType] : ( ( A > $o ) > ( stream170649215stream @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osset,type,
% 0.30/1.53 stream30925839e_sset:
% 0.30/1.53 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( set @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreams,type,
% 0.30/1.53 stream2015131171treams:
% 0.30/1.53 !>[A: $tType] : ( ( set @ A ) > ( set @ ( stream170649215stream @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreamsp,type,
% 0.30/1.53 stream86250253reamsp:
% 0.30/1.53 !>[A: $tType] : ( ( A > $o ) > ( stream170649215stream @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_member,type,
% 0.30/1.53 member:
% 0.30/1.53 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_v_A,type,
% 0.30/1.53 a2: set @ a ).
% 0.30/1.53
% 0.30/1.53 thf(sy_v_s,type,
% 0.30/1.53 s: stream170649215stream @ a ).
% 0.30/1.53
% 0.30/1.53 thf(sy_v_sa____,type,
% 0.30/1.53 sa: stream170649215stream @ a ).
% 0.30/1.53
% 0.30/1.53 thf(fact_0_streams,axiom,
% 0.30/1.53 ord_less_eq @ ( set @ a ) @ ( stream30925839e_sset @ a @ sa ) @ a2 ).
% 0.30/1.53
% 0.30/1.53 thf(fact_1_assms,axiom,
% 0.30/1.53 ord_less_eq @ ( set @ a ) @ ( stream30925839e_sset @ a @ s ) @ a2 ).
% 0.30/1.53
% 0.30/1.53 thf(fact_2_stream_Oinject,axiom,
% 0.30/1.53 ! [A: $tType,X1: A,X2: stream170649215stream @ A,Y1: A,Y2: stream170649215stream @ A] :
% 0.30/1.53 ( ( ( stream641971652_SCons @ A @ X1 @ X2 )
% 0.30/1.53 = ( stream641971652_SCons @ A @ Y1 @ Y2 ) )
% 0.30/1.53 = ( ( X1 = Y1 )
% 0.30/1.53 & ( X2 = Y2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_3_stream_Oset__intros_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A2: stream170649215stream @ A,A1: A] :
% 0.30/1.53 ( ( member @ A @ X @ ( stream30925839e_sset @ A @ A2 ) )
% 0.30/1.53 => ( member @ A @ X @ ( stream30925839e_sset @ A @ ( stream641971652_SCons @ A @ A1 @ A2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_4_stream_Oset__intros_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,A1: A,A2: stream170649215stream @ A] : ( member @ A @ A1 @ ( stream30925839e_sset @ A @ ( stream641971652_SCons @ A @ A1 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_5_streams_Ocases,axiom,
% 0.30/1.53 ! [A: $tType,A3: stream170649215stream @ A,A4: set @ A] :
% 0.30/1.53 ( ( member @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A4 ) )
% 0.30/1.53 => ~ ! [A5: A,S: stream170649215stream @ A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( stream641971652_SCons @ A @ A5 @ S ) )
% 0.30/1.53 => ( ( member @ A @ A5 @ A4 )
% 0.30/1.53 => ~ ( member @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A4 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_6_streams_Osimps,axiom,
% 0.30/1.53 ! [A: $tType,A3: stream170649215stream @ A,A4: set @ A] :
% 0.30/1.53 ( ( member @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A4 ) )
% 0.30/1.53 = ( ? [A6: A,S2: stream170649215stream @ A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( stream641971652_SCons @ A @ A6 @ S2 ) )
% 0.30/1.53 & ( member @ A @ A6 @ A4 )
% 0.30/1.53 & ( member @ ( stream170649215stream @ A ) @ S2 @ ( stream2015131171treams @ A @ A4 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_7_stream_Oexhaust,axiom,
% 0.30/1.53 ! [A: $tType,Y: stream170649215stream @ A] :
% 0.30/1.53 ~ ! [X12: A,X22: stream170649215stream @ A] :
% 0.30/1.53 ( Y
% 0.30/1.53 != ( stream641971652_SCons @ A @ X12 @ X22 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_8_streams__Stream,axiom,
% 0.30/1.53 ! [A: $tType,X: A,S3: stream170649215stream @ A,A4: set @ A] :
% 0.30/1.53 ( ( member @ ( stream170649215stream @ A ) @ ( stream641971652_SCons @ A @ X @ S3 ) @ ( stream2015131171treams @ A @ A4 ) )
% 0.30/1.53 = ( ( member @ A @ X @ A4 )
% 0.30/1.53 & ( member @ ( stream170649215stream @ A ) @ S3 @ ( stream2015131171treams @ A @ A4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_9_stream_Oset__cases,axiom,
% 0.30/1.53 ! [A: $tType,E: A,A3: stream170649215stream @ A] :
% 0.30/1.53 ( ( member @ A @ E @ ( stream30925839e_sset @ A @ A3 ) )
% 0.30/1.53 => ( ! [Z2: stream170649215stream @ A] :
% 0.30/1.53 ( A3
% 0.30/1.53 != ( stream641971652_SCons @ A @ E @ Z2 ) )
% 0.30/1.53 => ~ ! [Z1: A,Z2: stream170649215stream @ A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( stream641971652_SCons @ A @ Z1 @ Z2 ) )
% 0.30/1.53 => ~ ( member @ A @ E @ ( stream30925839e_sset @ A @ Z2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_10_streams_Ocoinduct,axiom,
% 0.30/1.53 ! [A: $tType,X3: ( stream170649215stream @ A ) > $o,X: stream170649215stream @ A,A4: set @ A] :
% 0.30/1.53 ( ( X3 @ X )
% 0.30/1.53 => ( ! [X4: stream170649215stream @ A] :
% 0.30/1.53 ( ( X3 @ X4 )
% 0.30/1.53 => ? [A7: A,S4: stream170649215stream @ A] :
% 0.30/1.53 ( ( X4
% 0.30/1.53 = ( stream641971652_SCons @ A @ A7 @ S4 ) )
% 0.30/1.53 & ( member @ A @ A7 @ A4 )
% 0.30/1.53 & ( ( X3 @ S4 )
% 0.30/1.53 | ( member @ ( stream170649215stream @ A ) @ S4 @ ( stream2015131171treams @ A @ A4 ) ) ) ) )
% 0.30/1.53 => ( member @ ( stream170649215stream @ A ) @ X @ ( stream2015131171treams @ A @ A4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_11_stream_Oset__induct,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A3: stream170649215stream @ A,P: A > ( stream170649215stream @ A ) > $o] :
% 0.30/1.53 ( ( member @ A @ X @ ( stream30925839e_sset @ A @ A3 ) )
% 0.30/1.53 => ( ! [Z1: A,Z2: stream170649215stream @ A] : ( P @ Z1 @ ( stream641971652_SCons @ A @ Z1 @ Z2 ) )
% 0.30/1.53 => ( ! [Z1: A,Z2: stream170649215stream @ A,Xa: A] :
% 0.30/1.53 ( ( member @ A @ Xa @ ( stream30925839e_sset @ A @ Z2 ) )
% 0.30/1.53 => ( ( P @ Xa @ Z2 )
% 0.30/1.53 => ( P @ Xa @ ( stream641971652_SCons @ A @ Z1 @ Z2 ) ) ) )
% 0.30/1.53 => ( P @ X @ A3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_12_smember__code,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A,S3: stream170649215stream @ A] :
% 0.30/1.53 ( ( stream1586597341member @ A @ X @ ( stream641971652_SCons @ A @ Y @ S3 ) )
% 0.30/1.53 = ( ( X != Y )
% 0.30/1.53 => ( stream1586597341member @ A @ X @ S3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_13_subsetI,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ! [X4: A] :
% 0.30/1.53 ( ( member @ A @ X4 @ A4 )
% 0.30/1.53 => ( member @ A @ X4 @ B2 ) )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_14_subset__antisym,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A4 )
% 0.30/1.53 => ( A4 = B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_15_order__refl,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_16_Stream__Mirabelle__hbrgyiwlrc_Osmember__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( stream1586597341member @ A )
% 0.30/1.53 = ( ^ [X5: A,S2: stream170649215stream @ A] : ( member @ A @ X5 @ ( stream30925839e_sset @ A @ S2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_17_set__mp,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( member @ A @ X @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_18_in__mono,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( member @ A @ X @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_19_subsetD,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_20_subsetCE,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_21_equalityE,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( A4 = B2 )
% 0.30/1.53 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_22_subset__eq,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/1.53 = ( ^ [A8: set @ A,B3: set @ A] :
% 0.30/1.53 ! [X5: A] :
% 0.30/1.53 ( ( member @ A @ X5 @ A8 )
% 0.30/1.53 => ( member @ A @ X5 @ B3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_23_equalityD1,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( A4 = B2 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_24_dual__order_Oantisym,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B4: A,A3: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( A3 = B4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_25_dual__order_Otrans,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B4: A,A3: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.30/1.53 => ( ord_less_eq @ A @ C2 @ A3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_26_linorder__wlog,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [P: A > A > $o,A3: A,B4: A] :
% 0.30/1.53 ( ! [A5: A,B5: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.30/1.53 => ( P @ A5 @ B5 ) )
% 0.30/1.53 => ( ! [A5: A,B5: A] :
% 0.30/1.53 ( ( P @ B5 @ A5 )
% 0.30/1.53 => ( P @ A5 @ B5 ) )
% 0.30/1.53 => ( P @ A3 @ B4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_27_dual__order_Orefl,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_28_order__trans,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.30/1.53 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_29_order__class_Oorder_Oantisym,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/1.53 => ( A3 = B4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_30_ord__le__eq__trans,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ord @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( B4 = C2 )
% 0.30/1.53 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_31_ord__eq__le__trans,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ord @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A,C2: A] :
% 0.30/1.53 ( ( A3 = B4 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.30/1.53 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_32_antisym__conv,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [Y: A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/1.53 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 = ( X = Y ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_33_le__cases3,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.30/1.53 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.30/1.53 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.30/1.53 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.30/1.53 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.30/1.53 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_34_order_Otrans,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.30/1.53 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_35_le__cases,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_36_eq__refl,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( X = Y )
% 0.30/1.53 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_37_linear,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_38_antisym,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ( ( ord_less_eq @ A @ Y @ X )
% 0.30/1.53 => ( X = Y ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_39_eq__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( ^ [Y3: A,Z3: A] : ( Y3 = Z3 ) )
% 0.30/1.53 = ( ^ [X5: A,Y4: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/1.53 & ( ord_less_eq @ A @ Y4 @ X5 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_40_ord__le__eq__subst,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType] :
% 0.30/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,B4: A,F: A > B,C2: B] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( ( F @ B4 )
% 0.30/1.53 = C2 )
% 0.30/1.53 => ( ! [X4: A,Y5: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_41_ord__eq__le__subst,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType] :
% 0.30/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( F @ B4 ) )
% 0.30/1.53 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.30/1.53 => ( ! [X4: B,Y5: B] :
% 0.30/1.53 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less_eq @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_42_order__subst2,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType] :
% 0.30/1.53 ( ( ( order @ C @ ( type2 @ C ) )
% 0.30/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,B4: A,F: A > C,C2: C] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.30/1.53 => ( ! [X4: A,Y5: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less_eq @ C @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_43_order__subst1,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType] :
% 0.30/1.53 ( ( ( order @ B @ ( type2 @ B ) )
% 0.30/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ ( F @ B4 ) )
% 0.30/1.53 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.30/1.53 => ( ! [X4: B,Y5: B] :
% 0.30/1.53 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less_eq @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_44_le__fun__def,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/1.53 = ( ^ [F2: A > B,G: A > B] :
% 0.30/1.53 ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G @ X5 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,P: A > $o] :
% 0.30/1.53 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.30/1.53 = ( P @ A3 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( collect @ A
% 0.30/1.53 @ ^ [X5: A] : ( member @ A @ X5 @ A4 ) )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_47_Collect__cong,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/1.53 ( ! [X4: A] :
% 0.30/1.53 ( ( P @ X4 )
% 0.30/1.53 = ( Q @ X4 ) )
% 0.30/1.53 => ( ( collect @ A @ P )
% 0.30/1.53 = ( collect @ A @ Q ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_48_ext,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.30/1.53 ( ! [X4: A] :
% 0.30/1.53 ( ( F @ X4 )
% 0.30/1.53 = ( G2 @ X4 ) )
% 0.30/1.53 => ( F = G2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_49_le__funI,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 => ! [F: A > B,G2: A > B] :
% 0.30/1.53 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G2 @ X4 ) )
% 0.30/1.53 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_50_le__funE,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 => ! [F: A > B,G2: A > B,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_51_le__funD,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 => ! [F: A > B,G2: A > B,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_52_Collect__mono__iff,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.30/1.53 = ( ! [X5: A] :
% 0.30/1.53 ( ( P @ X5 )
% 0.30/1.53 => ( Q @ X5 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_53_contra__subsetD,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ~ ( member @ A @ C2 @ B2 )
% 0.30/1.53 => ~ ( member @ A @ C2 @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_54_set__eq__subset,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ^ [Y3: set @ A,Z3: set @ A] : ( Y3 = Z3 ) )
% 0.30/1.53 = ( ^ [A8: set @ A,B3: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A8 @ B3 )
% 0.30/1.53 & ( ord_less_eq @ ( set @ A ) @ B3 @ A8 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_55_subset__trans,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_56_Collect__mono,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/1.53 ( ! [X4: A] :
% 0.30/1.53 ( ( P @ X4 )
% 0.30/1.53 => ( Q @ X4 ) )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_57_subset__refl,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_58_rev__subsetD,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_59_subset__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/1.53 = ( ^ [A8: set @ A,B3: set @ A] :
% 0.30/1.53 ! [T: A] :
% 0.30/1.53 ( ( member @ A @ T @ A8 )
% 0.30/1.53 => ( member @ A @ T @ B3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_60_set__rev__mp,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( member @ A @ X @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_61_equalityD2,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( A4 = B2 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_62_stream_Oset,axiom,
% 0.30/1.53 ! [A: $tType,X1: A,X2: stream170649215stream @ A] :
% 0.30/1.53 ( ( stream30925839e_sset @ A @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.30/1.53 = ( insert @ A @ X1 @ ( stream30925839e_sset @ A @ X2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_63_stream_Opred__inject,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,A3: A,Aa: stream170649215stream @ A] :
% 0.30/1.53 ( ( stream1153105665stream @ A @ P @ ( stream641971652_SCons @ A @ A3 @ Aa ) )
% 0.30/1.53 = ( ( P @ A3 )
% 0.30/1.53 & ( stream1153105665stream @ A @ P @ Aa ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_64_antimono__def,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 & ( order @ B @ ( type2 @ B ) ) )
% 0.30/1.53 => ( ( order_antimono @ A @ B )
% 0.30/1.53 = ( ^ [F2: A > B] :
% 0.30/1.53 ! [X5: A,Y4: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F2 @ Y4 ) @ ( F2 @ X5 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_65_antimonoI,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 & ( order @ B @ ( type2 @ B ) ) )
% 0.30/1.53 => ! [F: A > B] :
% 0.30/1.53 ( ! [X4: A,Y5: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 0.30/1.53 => ( order_antimono @ A @ B @ F ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_66_antimonoE,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 & ( order @ B @ ( type2 @ B ) ) )
% 0.30/1.53 => ! [F: A > B,X: A,Y: A] :
% 0.30/1.53 ( ( order_antimono @ A @ B @ F )
% 0.30/1.53 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_67_antimonoD,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( ( order @ A @ ( type2 @ A ) )
% 0.30/1.53 & ( order @ B @ ( type2 @ B ) ) )
% 0.30/1.53 => ! [F: A > B,X: A,Y: A] :
% 0.30/1.53 ( ( order_antimono @ A @ B @ F )
% 0.30/1.53 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_68_streamsp_Ocoinduct,axiom,
% 0.30/1.53 ! [A: $tType,X3: ( stream170649215stream @ A ) > $o,X: stream170649215stream @ A,A4: A > $o] :
% 0.30/1.53 ( ( X3 @ X )
% 0.30/1.53 => ( ! [X4: stream170649215stream @ A] :
% 0.30/1.53 ( ( X3 @ X4 )
% 0.30/1.53 => ? [A7: A,S4: stream170649215stream @ A] :
% 0.30/1.53 ( ( X4
% 0.30/1.53 = ( stream641971652_SCons @ A @ A7 @ S4 ) )
% 0.30/1.53 & ( A4 @ A7 )
% 0.30/1.53 & ( ( X3 @ S4 )
% 0.30/1.53 | ( stream86250253reamsp @ A @ A4 @ S4 ) ) ) )
% 0.30/1.53 => ( stream86250253reamsp @ A @ A4 @ X ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_69_streamsp_Osimps,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( stream86250253reamsp @ A )
% 0.30/1.53 = ( ^ [A8: A > $o,A6: stream170649215stream @ A] :
% 0.30/1.53 ? [B6: A,S2: stream170649215stream @ A] :
% 0.30/1.53 ( ( A6
% 0.30/1.53 = ( stream641971652_SCons @ A @ B6 @ S2 ) )
% 0.30/1.53 & ( A8 @ B6 )
% 0.30/1.53 & ( stream86250253reamsp @ A @ A8 @ S2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_70_streamsp_Ocases,axiom,
% 0.30/1.53 ! [A: $tType,A4: A > $o,A3: stream170649215stream @ A] :
% 0.30/1.53 ( ( stream86250253reamsp @ A @ A4 @ A3 )
% 0.30/1.53 => ~ ! [A5: A,S: stream170649215stream @ A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( stream641971652_SCons @ A @ A5 @ S ) )
% 0.30/1.53 => ( ( A4 @ A5 )
% 0.30/1.53 => ~ ( stream86250253reamsp @ A @ A4 @ S ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_71_stream_Ocase,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,F: A > ( stream170649215stream @ A ) > B,X1: A,X2: stream170649215stream @ A] :
% 0.30/1.53 ( ( stream1342653232stream @ A @ B @ F @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.30/1.53 = ( F @ X1 @ X2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_72_insertCI,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,B2: set @ A,B4: A] :
% 0.30/1.53 ( ( ~ ( member @ A @ A3 @ B2 )
% 0.30/1.53 => ( A3 = B4 ) )
% 0.30/1.53 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_73_insert__iff,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.30/1.53 = ( ( A3 = B4 )
% 0.30/1.53 | ( member @ A @ A3 @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_74_insert__absorb2,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A] :
% 0.30/1.53 ( ( insert @ A @ X @ ( insert @ A @ X @ A4 ) )
% 0.30/1.53 = ( insert @ A @ X @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_75_insert__subset,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.30/1.53 = ( ( member @ A @ X @ B2 )
% 0.30/1.53 & ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_76_insertE,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.30/1.53 => ( ( A3 != B4 )
% 0.30/1.53 => ( member @ A @ A3 @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_77_insertI1,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,B2: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_78_insertI2,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,B2: set @ A,B4: A] :
% 0.30/1.53 ( ( member @ A @ A3 @ B2 )
% 0.30/1.53 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_79_Set_Oset__insert,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ~ ! [B7: set @ A] :
% 0.30/1.53 ( ( A4
% 0.30/1.53 = ( insert @ A @ X @ B7 ) )
% 0.30/1.53 => ( member @ A @ X @ B7 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_80_insert__ident,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ~ ( member @ A @ X @ B2 )
% 0.30/1.53 => ( ( ( insert @ A @ X @ A4 )
% 0.30/1.53 = ( insert @ A @ X @ B2 ) )
% 0.30/1.53 = ( A4 = B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_81_insert__absorb,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ A3 @ A4 )
% 0.30/1.53 => ( ( insert @ A @ A3 @ A4 )
% 0.30/1.53 = A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_82_insert__eq__iff,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A,B4: A,B2: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ A3 @ A4 )
% 0.30/1.53 => ( ~ ( member @ A @ B4 @ B2 )
% 0.30/1.53 => ( ( ( insert @ A @ A3 @ A4 )
% 0.30/1.53 = ( insert @ A @ B4 @ B2 ) )
% 0.30/1.53 = ( ( ( A3 = B4 )
% 0.30/1.53 => ( A4 = B2 ) )
% 0.30/1.53 & ( ( A3 != B4 )
% 0.30/1.53 => ? [C4: set @ A] :
% 0.30/1.53 ( ( A4
% 0.30/1.53 = ( insert @ A @ B4 @ C4 ) )
% 0.30/1.53 & ~ ( member @ A @ B4 @ C4 )
% 0.30/1.53 & ( B2
% 0.30/1.53 = ( insert @ A @ A3 @ C4 ) )
% 0.30/1.53 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_83_insert__commute,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A,A4: set @ A] :
% 0.30/1.53 ( ( insert @ A @ X @ ( insert @ A @ Y @ A4 ) )
% 0.30/1.53 = ( insert @ A @ Y @ ( insert @ A @ X @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_84_mk__disjoint__insert,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ A3 @ A4 )
% 0.30/1.53 => ? [B7: set @ A] :
% 0.30/1.53 ( ( A4
% 0.30/1.53 = ( insert @ A @ A3 @ B7 ) )
% 0.30/1.53 & ~ ( member @ A @ A3 @ B7 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_85_insert__mono,axiom,
% 0.30/1.53 ! [A: $tType,C3: set @ A,D: set @ A,A3: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C3 ) @ ( insert @ A @ A3 @ D ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_86_subset__insert,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.30/1.53 = ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_87_subset__insertI,axiom,
% 0.30/1.53 ! [A: $tType,B2: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( insert @ A @ A3 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_88_subset__insertI2,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,B4: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_89_stream_Opred__cong,axiom,
% 0.30/1.53 ! [A: $tType,X: stream170649215stream @ A,Ya: stream170649215stream @ A,P: A > $o,Pa: A > $o] :
% 0.30/1.53 ( ( X = Ya )
% 0.30/1.53 => ( ! [Z4: A] :
% 0.30/1.53 ( ( member @ A @ Z4 @ ( stream30925839e_sset @ A @ Ya ) )
% 0.30/1.53 => ( ( P @ Z4 )
% 0.30/1.53 = ( Pa @ Z4 ) ) )
% 0.30/1.53 => ( ( stream1153105665stream @ A @ P @ X )
% 0.30/1.53 = ( stream1153105665stream @ A @ Pa @ Ya ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_90_stream_Opred__mono__strong,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,X: stream170649215stream @ A,Pa: A > $o] :
% 0.30/1.53 ( ( stream1153105665stream @ A @ P @ X )
% 0.30/1.53 => ( ! [Z4: A] :
% 0.30/1.53 ( ( member @ A @ Z4 @ ( stream30925839e_sset @ A @ X ) )
% 0.30/1.53 => ( ( P @ Z4 )
% 0.30/1.53 => ( Pa @ Z4 ) ) )
% 0.30/1.53 => ( stream1153105665stream @ A @ Pa @ X ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_91_insert__subsetI,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A,X3: set @ A] :
% 0.30/1.53 ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ X3 @ A4 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ X3 ) @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_92_singleton__insert__inj__eq_H,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A,B4: A] :
% 0.30/1.53 ( ( ( insert @ A @ A3 @ A4 )
% 0.30/1.53 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 = ( ( A3 = B4 )
% 0.30/1.53 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_93_singleton__insert__inj__eq,axiom,
% 0.30/1.53 ! [A: $tType,B4: A,A3: A,A4: set @ A] :
% 0.30/1.53 ( ( ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( insert @ A @ A3 @ A4 ) )
% 0.30/1.53 = ( ( A3 = B4 )
% 0.30/1.53 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_94_stream_Opred__set,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( stream1153105665stream @ A )
% 0.30/1.53 = ( ^ [P2: A > $o,X5: stream170649215stream @ A] :
% 0.30/1.53 ! [Y4: A] :
% 0.30/1.53 ( ( member @ A @ Y4 @ ( stream30925839e_sset @ A @ X5 ) )
% 0.30/1.53 => ( P2 @ Y4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_95_subset__singletonD,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 => ( ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 | ( A4
% 0.30/1.53 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_96_subset__singleton__iff,axiom,
% 0.30/1.53 ! [A: $tType,X3: set @ A,A3: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ X3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 = ( ( X3
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 | ( X3
% 0.30/1.53 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_97_stream_Ocorec__code,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType] :
% 0.30/1.53 ( ( stream660621732stream @ C @ A )
% 0.30/1.53 = ( ^ [G1: C > A,Q2: C > $o,G21: C > ( stream170649215stream @ A ),G22: C > C,A6: C] : ( stream641971652_SCons @ A @ ( G1 @ A6 ) @ ( if @ ( stream170649215stream @ A ) @ ( Q2 @ A6 ) @ ( G21 @ A6 ) @ ( stream660621732stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ ( G22 @ A6 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_98_bot__apply,axiom,
% 0.30/1.53 ! [C: $tType,D2: $tType] :
% 0.30/1.53 ( ( bot @ C @ ( type2 @ C ) )
% 0.30/1.53 => ( ( bot_bot @ ( D2 > C ) )
% 0.30/1.53 = ( ^ [X5: D2] : ( bot_bot @ C ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_99_empty__Collect__eq,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o] :
% 0.30/1.53 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/1.53 = ( collect @ A @ P ) )
% 0.30/1.53 = ( ! [X5: A] :
% 0.30/1.53 ~ ( P @ X5 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_100_Collect__empty__eq,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o] :
% 0.30/1.53 ( ( ( collect @ A @ P )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ! [X5: A] :
% 0.30/1.53 ~ ( P @ X5 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_101_all__not__in__conv,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( ! [X5: A] :
% 0.30/1.53 ~ ( member @ A @ X5 @ A4 ) )
% 0.30/1.53 = ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_102_empty__iff,axiom,
% 0.30/1.53 ! [A: $tType,C2: A] :
% 0.30/1.53 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_103_empty__subsetI,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_104_subset__empty,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_105_singletonI,axiom,
% 0.30/1.53 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_106_ball__empty,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,X6: A] :
% 0.30/1.53 ( ( member @ A @ X6 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 => ( P @ X6 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_107_subset__emptyI,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ! [X4: A] :
% 0.30/1.53 ~ ( member @ A @ X4 @ A4 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_108_stream_Ocorec__disc,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType] :
% 0.30/1.53 ( ( stream660621732stream @ C @ A )
% 0.30/1.53 = ( stream660621732stream @ C @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_109_bot__fun__def,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( bot @ B @ ( type2 @ B ) )
% 0.30/1.53 => ( ( bot_bot @ ( A > B ) )
% 0.30/1.53 = ( ^ [X5: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_110_ex__in__conv,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( ? [X5: A] : ( member @ A @ X5 @ A4 ) )
% 0.30/1.53 = ( A4
% 0.30/1.53 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_111_equals0I,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ! [Y5: A] :
% 0.30/1.53 ~ ( member @ A @ Y5 @ A4 )
% 0.30/1.53 => ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_112_equals0D,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,A3: A] :
% 0.30/1.53 ( ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_113_Ball__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ball @ A )
% 0.30/1.53 = ( ^ [A8: set @ A,P2: A > $o] :
% 0.30/1.53 ! [X5: A] :
% 0.30/1.53 ( ( member @ A @ X5 @ A8 )
% 0.30/1.53 => ( P2 @ X5 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_114_emptyE,axiom,
% 0.30/1.53 ! [A: $tType,A3: A] :
% 0.30/1.53 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_115_bot_Oextremum__uniqueI,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.30/1.53 => ( A3
% 0.30/1.53 = ( bot_bot @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_116_bot_Oextremum__unique,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.30/1.53 = ( A3
% 0.30/1.53 = ( bot_bot @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_117_bot_Oextremum,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A3 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_118_singleton__inject,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,B4: A] :
% 0.30/1.53 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 => ( A3 = B4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_119_insert__not__empty,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/1.53 ( ( insert @ A @ A3 @ A4 )
% 0.30/1.53 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_120_doubleton__eq__iff,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,B4: A,C2: A,D3: A] :
% 0.30/1.53 ( ( ( insert @ A @ A3 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 = ( insert @ A @ C2 @ ( insert @ A @ D3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/1.53 = ( ( ( A3 = C2 )
% 0.30/1.53 & ( B4 = D3 ) )
% 0.30/1.53 | ( ( A3 = D3 )
% 0.30/1.53 & ( B4 = C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_121_singleton__iff,axiom,
% 0.30/1.53 ! [A: $tType,B4: A,A3: A] :
% 0.30/1.53 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 = ( B4 = A3 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_122_singletonD,axiom,
% 0.30/1.53 ! [A: $tType,B4: A,A3: A] :
% 0.30/1.53 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 => ( B4 = A3 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_123_the__elem__eq,axiom,
% 0.30/1.53 ! [A: $tType,X: A] :
% 0.30/1.53 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 = X ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_124_is__singletonI,axiom,
% 0.30/1.53 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_125_Ball__Collect,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ball @ A )
% 0.30/1.53 = ( ^ [A8: set @ A,P2: A > $o] : ( ord_less_eq @ ( set @ A ) @ A8 @ ( collect @ A @ P2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_126_Set_Ois__empty__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( is_empty @ A )
% 0.30/1.53 = ( ^ [A8: set @ A] :
% 0.30/1.53 ( A8
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_127_is__singletonE,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( is_singleton @ A @ A4 )
% 0.30/1.53 => ~ ! [X4: A] :
% 0.30/1.53 ( A4
% 0.30/1.53 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_128_bot__set__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bot_bot @ ( set @ A ) )
% 0.30/1.53 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_129_is__singleton__the__elem,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( is_singleton @ A )
% 0.30/1.53 = ( ^ [A8: set @ A] :
% 0.30/1.53 ( A8
% 0.30/1.53 = ( insert @ A @ ( the_elem @ A @ A8 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_130_is__singletonI_H,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( A4
% 0.30/1.53 != ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 => ( ! [X4: A,Y5: A] :
% 0.30/1.53 ( ( member @ A @ X4 @ A4 )
% 0.30/1.53 => ( ( member @ A @ Y5 @ A4 )
% 0.30/1.53 => ( X4 = Y5 ) ) )
% 0.30/1.53 => ( is_singleton @ A @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_131_is__singleton__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( is_singleton @ A )
% 0.30/1.53 = ( ^ [A8: set @ A] :
% 0.30/1.53 ? [X5: A] :
% 0.30/1.53 ( A8
% 0.30/1.53 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_132_pairwise__singleton,axiom,
% 0.30/1.53 ! [A: $tType,P: A > A > $o,A4: A] : ( pairwise @ A @ P @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_133_subset__Compl__singleton,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/1.53 = ( ~ ( member @ A @ B4 @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_134_ball__reg,axiom,
% 0.30/1.53 ! [A: $tType,R: set @ A,P: A > $o,Q: A > $o] :
% 0.30/1.53 ( ! [X4: A] :
% 0.30/1.53 ( ( member @ A @ X4 @ R )
% 0.30/1.53 => ( ( P @ X4 )
% 0.30/1.53 => ( Q @ X4 ) ) )
% 0.30/1.53 => ( ! [X4: A] :
% 0.30/1.53 ( ( member @ A @ X4 @ R )
% 0.30/1.53 => ( P @ X4 ) )
% 0.30/1.53 => ! [X6: A] :
% 0.30/1.53 ( ( member @ A @ X6 @ R )
% 0.30/1.53 => ( Q @ X6 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_135_bot__empty__eq,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bot_bot @ ( A > $o ) )
% 0.30/1.53 = ( ^ [X5: A] : ( member @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_136_Compl__eq__Compl__iff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ( uminus_uminus @ ( set @ A ) @ A4 )
% 0.30/1.53 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.30/1.53 = ( A4 = B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_137_Compl__iff,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.30/1.53 = ( ~ ( member @ A @ C2 @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_138_ComplI,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_139_Compl__anti__mono,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_140_Compl__subset__Compl__iff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.30/1.53 = ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_141_double__complement,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_142_pairwise__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( pairwise @ A )
% 0.30/1.53 = ( ^ [R2: A > A > $o,S5: set @ A] :
% 0.30/1.53 ! [X5: A] :
% 0.30/1.53 ( ( member @ A @ X5 @ S5 )
% 0.30/1.53 => ! [Y4: A] :
% 0.30/1.53 ( ( member @ A @ Y4 @ S5 )
% 0.30/1.53 => ( ( X5 != Y4 )
% 0.30/1.53 => ( R2 @ X5 @ Y4 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_143_ComplD,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.30/1.53 => ~ ( member @ A @ C2 @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_144_subset__Compl__self__eq,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.30/1.53 = ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_145_pairwise__empty,axiom,
% 0.30/1.53 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_146_pairwise__subset,axiom,
% 0.30/1.53 ! [A: $tType,P: A > A > $o,S6: set @ A,T2: set @ A] :
% 0.30/1.53 ( ( pairwise @ A @ P @ S6 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ T2 @ S6 )
% 0.30/1.53 => ( pairwise @ A @ P @ T2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_147_pairwise__insert,axiom,
% 0.30/1.53 ! [A: $tType,R3: A > A > $o,X: A,S3: set @ A] :
% 0.30/1.53 ( ( pairwise @ A @ R3 @ ( insert @ A @ X @ S3 ) )
% 0.30/1.53 = ( ! [Y4: A] :
% 0.30/1.53 ( ( ( member @ A @ Y4 @ S3 )
% 0.30/1.53 & ( Y4 != X ) )
% 0.30/1.53 => ( ( R3 @ X @ Y4 )
% 0.30/1.53 & ( R3 @ Y4 @ X ) ) )
% 0.30/1.53 & ( pairwise @ A @ R3 @ S3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_148_neg__le__iff__le,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B4: A,A3: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A3 ) )
% 0.30/1.53 = ( ord_less_eq @ A @ A3 @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_149_compl__le__compl__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) )
% 0.30/1.53 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_150_uminus__apply,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( uminus @ B @ ( type2 @ B ) )
% 0.30/1.53 => ( ( uminus_uminus @ ( A > B ) )
% 0.30/1.53 = ( ^ [A8: A > B,X5: A] : ( uminus_uminus @ B @ ( A8 @ X5 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_151_add_Oinverse__inverse,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A] :
% 0.30/1.53 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A3 ) )
% 0.30/1.53 = A3 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_152_compl__eq__compl__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ( uminus_uminus @ A @ X )
% 0.30/1.53 = ( uminus_uminus @ A @ Y ) )
% 0.30/1.53 = ( X = Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_153_double__compl,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.30/1.53 = X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_154_neg__equal__iff__equal,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( ( uminus_uminus @ A @ A3 )
% 0.30/1.53 = ( uminus_uminus @ A @ B4 ) )
% 0.30/1.53 = ( A3 = B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_155_minus__equation__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( ( uminus_uminus @ A @ A3 )
% 0.30/1.53 = B4 )
% 0.30/1.53 = ( ( uminus_uminus @ A @ B4 )
% 0.30/1.53 = A3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_156_equation__minus__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( uminus_uminus @ A @ B4 ) )
% 0.30/1.53 = ( B4
% 0.30/1.53 = ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_157_fun__Compl__def,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( uminus @ B @ ( type2 @ B ) )
% 0.30/1.53 => ( ( uminus_uminus @ ( A > B ) )
% 0.30/1.53 = ( ^ [A8: A > B,X5: A] : ( uminus_uminus @ B @ ( A8 @ X5 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_158_le__imp__neg__le,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_159_minus__le__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A3 ) @ B4 )
% 0.30/1.53 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ A3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_160_le__minus__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ ( uminus_uminus @ A @ B4 ) )
% 0.30/1.53 = ( ord_less_eq @ A @ B4 @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_161_compl__le__swap2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [Y: A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ X )
% 0.30/1.53 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_162_compl__le__swap1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [Y: A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ Y @ ( uminus_uminus @ A @ X ) )
% 0.30/1.53 => ( ord_less_eq @ A @ X @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_163_compl__mono,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ ( uminus_uminus @ A @ X ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_164_Collect__empty__eq__bot,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o] :
% 0.30/1.53 ( ( ( collect @ A @ P )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( P
% 0.30/1.53 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_165_in__inv__imagep,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( inv_imagep @ A @ B )
% 0.30/1.53 = ( ^ [R4: A > A > $o,F2: B > A,X5: B,Y4: B] : ( R4 @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_166_Compl__insert,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A] :
% 0.30/1.53 ( ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_167_Diff__idemp,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ B2 )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_168_Diff__iff,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 = ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_169_DiffI,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( ~ ( member @ A @ C2 @ B2 )
% 0.30/1.53 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_170_minus__diff__eq,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A] :
% 0.30/1.53 ( ( uminus_uminus @ A @ ( minus_minus @ A @ A3 @ B4 ) )
% 0.30/1.53 = ( minus_minus @ A @ B4 @ A3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_171_Diff__cancel,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ A4 @ A4 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_172_empty__Diff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_173_Diff__empty,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_174_Diff__insert0,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_175_insert__Diff1,axiom,
% 0.30/1.53 ! [A: $tType,X: A,B2: set @ A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ X @ B2 )
% 0.30/1.53 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_176_Diff__eq__empty__iff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ( minus_minus @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_177_insert__Diff__single,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/1.53 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/1.53 = ( insert @ A @ A3 @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_178_diff__mono,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A,D3: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ D3 @ C2 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ D3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_179_diff__left__mono,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B4: A,A3: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ C2 @ A3 ) @ ( minus_minus @ A @ C2 @ B4 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_180_diff__right__mono,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_181_diff__eq__diff__less__eq,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A,C2: A,D3: A] :
% 0.30/1.53 ( ( ( minus_minus @ A @ A3 @ B4 )
% 0.30/1.53 = ( minus_minus @ A @ C2 @ D3 ) )
% 0.30/1.53 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 = ( ord_less_eq @ A @ C2 @ D3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_182_Diff__mono,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,C3: set @ A,D: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ D @ B2 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ ( minus_minus @ ( set @ A ) @ C3 @ D ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_183_Diff__subset,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_184_double__diff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.30/1.53 => ( ( minus_minus @ ( set @ A ) @ B2 @ ( minus_minus @ ( set @ A ) @ C3 @ A4 ) )
% 0.30/1.53 = A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_185_insert__Diff__if,axiom,
% 0.30/1.53 ! [A: $tType,X: A,B2: set @ A,A4: set @ A] :
% 0.30/1.53 ( ( ( member @ A @ X @ B2 )
% 0.30/1.53 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) )
% 0.30/1.53 & ( ~ ( member @ A @ X @ B2 )
% 0.30/1.53 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B2 )
% 0.30/1.53 = ( insert @ A @ X @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_186_DiffD2,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_187_DiffD1,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 => ( member @ A @ C2 @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_188_DiffE,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 => ~ ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_189_Diff__insert,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,A3: A,B2: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_190_insert__Diff,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ A3 @ A4 )
% 0.30/1.53 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/1.53 = A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_191_Diff__insert2,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,A3: A,B2: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_192_Diff__insert__absorb,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A4: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/1.53 = A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_193_subset__Diff__insert,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,X: A,C3: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ ( insert @ A @ X @ C3 ) ) )
% 0.30/1.53 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) )
% 0.30/1.53 & ~ ( member @ A @ X @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_194_Diff__single__insert,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,X: A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_195_subset__insert__iff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,X: A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.30/1.53 = ( ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) )
% 0.30/1.53 & ( ~ ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_196_remove__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( remove @ A )
% 0.30/1.53 = ( ^ [X5: A,A8: set @ A] : ( minus_minus @ ( set @ A ) @ A8 @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_197_psubset__insert__iff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,X: A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less @ ( set @ A ) @ A4 @ ( insert @ A @ X @ B2 ) )
% 0.30/1.53 = ( ( ( member @ A @ X @ B2 )
% 0.30/1.53 => ( ord_less @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 & ( ~ ( member @ A @ X @ B2 )
% 0.30/1.53 => ( ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ord_less @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) )
% 0.30/1.53 & ( ~ ( member @ A @ X @ A4 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_198_disjoint__eq__subset__Compl,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ord_less_eq @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_199_IntI,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( ( member @ A @ C2 @ B2 )
% 0.30/1.53 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_200_Int__iff,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 = ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 & ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_201_member__remove,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( remove @ A @ Y @ A4 ) )
% 0.30/1.53 = ( ( member @ A @ X @ A4 )
% 0.30/1.53 & ( X != Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_202_le__inf__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.30/1.53 = ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 & ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_203_inf_Obounded__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A,B4: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C2 ) )
% 0.30/1.53 = ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/1.53 & ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_204_neg__less__iff__less,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B4: A,A3: A] :
% 0.30/1.53 ( ( ord_less @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A3 ) )
% 0.30/1.53 = ( ord_less @ A @ A3 @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_205_inf__bot__right,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 0.30/1.53 = ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_206_inf__bot__left,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 0.30/1.53 = ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_207_Int__subset__iff,axiom,
% 0.30/1.53 ! [A: $tType,C3: set @ A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 = ( ( ord_less_eq @ ( set @ A ) @ C3 @ A4 )
% 0.30/1.53 & ( ord_less_eq @ ( set @ A ) @ C3 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_208_Int__insert__right__if1,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ A3 @ A4 )
% 0.30/1.53 => ( ( inf_inf @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.30/1.53 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_209_Int__insert__right__if0,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ A3 @ A4 )
% 0.30/1.53 => ( ( inf_inf @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B2 ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_210_insert__inter__insert,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A4 ) @ ( insert @ A @ A3 @ B2 ) )
% 0.30/1.53 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_211_Int__insert__left__if1,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,C3: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ A3 @ C3 )
% 0.30/1.53 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C3 )
% 0.30/1.53 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_212_Int__insert__left__if0,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,C3: set @ A,B2: set @ A] :
% 0.30/1.53 ( ~ ( member @ A @ A3 @ C3 )
% 0.30/1.53 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C3 )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_213_psubsetI,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( A4 != B2 )
% 0.30/1.53 => ( ord_less @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_214_compl__inf__bot,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ X )
% 0.30/1.53 = ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_215_inf__compl__bot,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( inf_inf @ A @ X @ ( uminus_uminus @ A @ X ) )
% 0.30/1.53 = ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_216_inf__compl__bot__left1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ ( inf_inf @ A @ X @ Y ) )
% 0.30/1.53 = ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_217_inf__compl__bot__left2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 0.30/1.53 = ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_218_inf__compl__bot__right,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ ( uminus_uminus @ A @ X ) ) )
% 0.30/1.53 = ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_219_insert__disjoint_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A4 ) @ B2 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ~ ( member @ A @ A3 @ B2 )
% 0.30/1.53 & ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_220_insert__disjoint_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,A3: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A4 ) @ B2 ) )
% 0.30/1.53 = ( ~ ( member @ A @ A3 @ B2 )
% 0.30/1.53 & ( ( bot_bot @ ( set @ A ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_221_disjoint__insert_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,B2: set @ A,A3: A,A4: set @ A] :
% 0.30/1.53 ( ( ( inf_inf @ ( set @ A ) @ B2 @ ( insert @ A @ A3 @ A4 ) )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ~ ( member @ A @ A3 @ B2 )
% 0.30/1.53 & ( ( inf_inf @ ( set @ A ) @ B2 @ A4 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_222_disjoint__insert_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: A,B2: set @ A] :
% 0.30/1.53 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ B2 ) ) )
% 0.30/1.53 = ( ~ ( member @ A @ B4 @ A4 )
% 0.30/1.53 & ( ( bot_bot @ ( set @ A ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_223_Diff__disjoint,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ A4 ) )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_224_Compl__disjoint,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ A4 ) )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_225_Compl__disjoint2,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A4 ) @ A4 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_226_Diff__Compl,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ A4 @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_227_psubset__imp__ex__mem,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ord_less @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ? [B5: A] : ( member @ A @ B5 @ ( minus_minus @ ( set @ A ) @ B2 @ A4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_228_Diff__Int__distrib2,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) @ C3 )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_229_Diff__Int__distrib,axiom,
% 0.30/1.53 ! [A: $tType,C3: set @ A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ C3 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C3 @ A4 ) @ ( inf_inf @ ( set @ A ) @ C3 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_230_Diff__Diff__Int,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_231_Diff__Int2,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,C3: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.30/1.53 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_232_Int__Diff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) @ C3 )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_233_Int__emptyI,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ! [X4: A] :
% 0.30/1.53 ( ( member @ A @ X4 @ A4 )
% 0.30/1.53 => ~ ( member @ A @ X4 @ B2 ) )
% 0.30/1.53 => ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_234_Int__empty__left,axiom,
% 0.30/1.53 ! [A: $tType,B2: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_235_Int__empty__right,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_236_disjoint__iff__not__equal,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ! [X5: A] :
% 0.30/1.53 ( ( member @ A @ X5 @ A4 )
% 0.30/1.53 => ! [Y4: A] :
% 0.30/1.53 ( ( member @ A @ Y4 @ B2 )
% 0.30/1.53 => ( X5 != Y4 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_237_bot_Oextremum__strict,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A] :
% 0.30/1.53 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_238_bot_Onot__eq__extremum,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A3: A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 != ( bot_bot @ A ) )
% 0.30/1.53 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_239_not__psubset__empty,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ~ ( ord_less @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_240_IntE,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 => ~ ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_241_IntD1,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 => ( member @ A @ C2 @ A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_242_IntD2,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 => ( member @ A @ C2 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_243_psubsetD,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C2: A] :
% 0.30/1.53 ( ( ord_less @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_244_Int__assoc,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) @ C3 )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_245_Int__absorb,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ A4 @ A4 )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_246_Int__commute,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) )
% 0.30/1.53 = ( ^ [A8: set @ A,B3: set @ A] : ( inf_inf @ ( set @ A ) @ B3 @ A8 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_247_psubset__trans,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( ord_less @ ( set @ A ) @ A4 @ B2 )
% 0.30/1.53 => ( ( ord_less @ ( set @ A ) @ B2 @ C3 )
% 0.30/1.53 => ( ord_less @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_248_Int__left__absorb,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ A4 @ B2 ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_249_Int__left__commute,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.30/1.53 = ( inf_inf @ ( set @ A ) @ B2 @ ( inf_inf @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_250_ord__eq__less__subst,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType] :
% 0.30/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( F @ B4 ) )
% 0.30/1.53 => ( ( ord_less @ B @ B4 @ C2 )
% 0.30/1.53 => ( ! [X4: B,Y5: B] :
% 0.30/1.53 ( ( ord_less @ B @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_251_ord__less__eq__subst,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType] :
% 0.30/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.30/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,B4: A,F: A > B,C2: B] :
% 0.30/1.53 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( ( F @ B4 )
% 0.30/1.53 = C2 )
% 0.30/1.53 => ( ! [X4: A,Y5: A] :
% 0.30/1.53 ( ( ord_less @ A @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less @ B @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_252_order__less__subst1,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType] :
% 0.30/1.53 ( ( ( order @ B @ ( type2 @ B ) )
% 0.30/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,F: B > A,B4: B,C2: B] :
% 0.30/1.53 ( ( ord_less @ A @ A3 @ ( F @ B4 ) )
% 0.30/1.53 => ( ( ord_less @ B @ B4 @ C2 )
% 0.30/1.53 => ( ! [X4: B,Y5: B] :
% 0.30/1.53 ( ( ord_less @ B @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less @ A @ A3 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_253_order__less__subst2,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType] :
% 0.30/1.53 ( ( ( order @ C @ ( type2 @ C ) )
% 0.30/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 0.30/1.53 => ! [A3: A,B4: A,F: A > C,C2: C] :
% 0.30/1.53 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/1.53 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 0.30/1.53 => ( ! [X4: A,Y5: A] :
% 0.30/1.53 ( ( ord_less @ A @ X4 @ Y5 )
% 0.30/1.53 => ( ord_less @ C @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.30/1.53 => ( ord_less @ C @ ( F @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_254_lt__ex,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ? [Y5: A] : ( ord_less @ A @ Y5 @ X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_255_gt__ex,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( no_top @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ? [X12: A] : ( ord_less @ A @ X @ X12 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/1.53 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/1.53 ! [A9: $tType] : ( bounded_lattice @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( bounded_lattice @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( bounded_lattice @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( bounded_lattice @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( bounded_lattice_bot @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( semilattice_inf @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( semilattice_inf @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( boolean_algebra @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( boolean_algebra @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( order_bot @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( order_bot @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( preorder @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( preorder @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( order @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( order @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( ord @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( ord @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( bot @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( bot @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.30/1.53 ! [A9: $tType,A10: $tType] :
% 0.30/1.53 ( ( uminus @ A10 @ ( type2 @ A10 ) )
% 0.30/1.53 => ( uminus @ ( A9 > A10 ) @ ( type2 @ ( A9 > A10 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 0.30/1.53 ! [A9: $tType] : ( bounded_lattice_bot @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 0.30/1.53 ! [A9: $tType] : ( semilattice_inf @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_5,axiom,
% 0.30/1.53 ! [A9: $tType] : ( boolean_algebra @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 0.30/1.53 ! [A9: $tType] : ( order_bot @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 0.30/1.53 ! [A9: $tType] : ( preorder @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 0.30/1.53 ! [A9: $tType] : ( order @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 0.30/1.53 ! [A9: $tType] : ( ord @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 0.30/1.53 ! [A9: $tType] : ( bot @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Groups_Ouminus_11,axiom,
% 0.30/1.53 ! [A9: $tType] : ( uminus @ ( set @ A9 ) @ ( type2 @ ( set @ A9 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 0.30/1.53 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_13,axiom,
% 0.30/1.53 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_14,axiom,
% 0.30/1.53 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15,axiom,
% 0.30/1.53 order_bot @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 0.30/1.53 preorder @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/1.53 linorder @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_17,axiom,
% 0.30/1.53 order @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Orderings_Oord_18,axiom,
% 0.30/1.53 ord @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Orderings_Obot_19,axiom,
% 0.30/1.53 bot @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Groups_Ouminus_20,axiom,
% 0.30/1.53 uminus @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(help_If_3_1_T,axiom,
% 0.30/1.53 ! [P: $o] :
% 0.30/1.53 ( ( P = $true )
% 0.30/1.53 | ( P = $false ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(help_If_2_1_T,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A] :
% 0.30/1.53 ( ( if @ A @ $false @ X @ Y )
% 0.30/1.53 = Y ) ).
% 0.30/1.53
% 0.30/1.53 thf(help_If_1_1_T,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A] :
% 0.30/1.53 ( ( if @ A @ $true @ X @ Y )
% 0.30/1.53 = X ) ).
% 0.30/1.53
% 0.30/1.53 thf(conj_0,conjecture,
% 0.30/1.53 ? [A7: a,S4: stream170649215stream @ a] :
% 0.30/1.53 ( ( sa
% 0.30/1.53 = ( stream641971652_SCons @ a @ A7 @ S4 ) )
% 0.30/1.53 & ( member @ a @ A7 @ a2 )
% 0.30/1.53 & ( ? [Sa: stream170649215stream @ a] :
% 0.30/1.53 ( ( S4 = Sa )
% 0.30/1.53 & ( ord_less_eq @ ( set @ a ) @ ( stream30925839e_sset @ a @ Sa ) @ a2 ) )
% 0.30/1.53 | ( member @ ( stream170649215stream @ a ) @ S4 @ ( stream2015131171treams @ a @ a2 ) ) ) ) ).
% 0.30/1.53 ------------------------
% 0.30/1.56 % (6113)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/2Mi)
% 0.30/1.56 % (6111)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_5740 for (2999ds/4Mi)
% 0.30/1.56 % (6113)Instruction limit reached!
% 0.30/1.56 % (6113)------------------------------
% 0.30/1.56 % (6113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.56 % (6113)Termination reason: Unknown
% 0.30/1.56 % (6113)Termination phase: shuffling
% 0.30/1.56
% 0.30/1.56 % (6113)Memory used [KB]: 1279
% 0.30/1.56 % (6113)Time elapsed: 0.002 s
% 0.30/1.56 % (6113)Instructions burned: 2 (million)
% 0.30/1.56 % (6113)------------------------------
% 0.30/1.56 % (6113)------------------------------
% 0.30/1.56 % (6115)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_5740 for (2999ds/275Mi)
% 0.30/1.56 % (6111)Instruction limit reached!
% 0.30/1.56 % (6111)------------------------------
% 0.30/1.56 % (6111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.56 % (6111)Termination reason: Unknown
% 0.30/1.56 % (6111)Termination phase: shuffling
% 0.30/1.56
% 0.30/1.56 % (6111)Memory used [KB]: 1407
% 0.30/1.56 % (6111)Time elapsed: 0.002 s
% 0.30/1.56 % (6111)Instructions burned: 4 (million)
% 0.30/1.56 % (6111)------------------------------
% 0.30/1.56 % (6111)------------------------------
% 0.30/1.57 % (6114)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_5740 for (2999ds/2Mi)
% 0.30/1.57 % (6114)Instruction limit reached!
% 0.30/1.57 % (6114)------------------------------
% 0.30/1.57 % (6114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.57 % (6114)Termination reason: Unknown
% 0.30/1.57 % (6114)Termination phase: shuffling
% 0.30/1.57
% 0.30/1.57 % (6114)Memory used [KB]: 1279
% 0.30/1.57 % (6114)Time elapsed: 0.004 s
% 0.30/1.57 % (6114)Instructions burned: 3 (million)
% 0.30/1.57 % (6114)------------------------------
% 0.30/1.57 % (6114)------------------------------
% 0.30/1.57 % (6110)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/183Mi)
% 0.30/1.57 % (6112)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_5740 for (2999ds/27Mi)
% 0.30/1.57 % (6116)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/18Mi)
% 0.30/1.57 % (6117)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/3Mi)
% 0.30/1.57 % (6118)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_5740 for (2999ds/37Mi)
% 0.30/1.58 % (6117)Instruction limit reached!
% 0.30/1.58 % (6117)------------------------------
% 0.30/1.58 % (6117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (6117)Termination reason: Unknown
% 0.30/1.58 % (6117)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (6117)Memory used [KB]: 1407
% 0.30/1.58 % (6117)Time elapsed: 0.003 s
% 0.30/1.58 % (6117)Instructions burned: 6 (million)
% 0.30/1.58 % (6117)------------------------------
% 0.30/1.58 % (6117)------------------------------
% 0.30/1.58 % (6116)Instruction limit reached!
% 0.30/1.58 % (6116)------------------------------
% 0.30/1.58 % (6116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (6116)Termination reason: Unknown
% 0.30/1.58 % (6116)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (6116)Memory used [KB]: 1663
% 0.30/1.58 % (6116)Time elapsed: 0.014 s
% 0.30/1.58 % (6116)Instructions burned: 18 (million)
% 0.30/1.58 % (6116)------------------------------
% 0.30/1.58 % (6116)------------------------------
% 0.30/1.58 % (6120)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_5740 for (2999ds/3Mi)
% 0.30/1.59 % (6118)Instruction limit reached!
% 0.30/1.59 % (6118)------------------------------
% 0.30/1.59 % (6118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (6118)Termination reason: Unknown
% 0.30/1.59 % (6118)Termination phase: Property scanning
% 0.30/1.59
% 0.30/1.59 % (6118)Memory used [KB]: 2046
% 0.30/1.59 % (6118)Time elapsed: 0.012 s
% 0.30/1.59 % (6118)Instructions burned: 39 (million)
% 0.30/1.59 % (6118)------------------------------
% 0.30/1.59 % (6118)------------------------------
% 0.30/1.59 % (6120)Instruction limit reached!
% 0.30/1.59 % (6120)------------------------------
% 0.30/1.59 % (6120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (6120)Termination reason: Unknown
% 0.30/1.59 % (6120)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (6120)Memory used [KB]: 1407
% 0.30/1.59 % (6120)Time elapsed: 0.002 s
% 0.30/1.59 % (6120)Instructions burned: 3 (million)
% 0.30/1.59 % (6120)------------------------------
% 0.30/1.59 % (6120)------------------------------
% 0.30/1.59 % (6119)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_5740 for (2999ds/15Mi)
% 0.30/1.59 % (6112)Instruction limit reached!
% 0.30/1.59 % (6112)------------------------------
% 0.30/1.59 % (6112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (6112)Termination reason: Unknown
% 0.30/1.59 % (6112)Termination phase: Property scanning
% 0.30/1.59
% 0.30/1.59 % (6112)Memory used [KB]: 1791
% 0.30/1.59 % (6112)Time elapsed: 0.018 s
% 0.30/1.59 % (6112)Instructions burned: 28 (million)
% 0.30/1.59 % (6112)------------------------------
% 0.30/1.59 % (6112)------------------------------
% 0.30/1.59 % (6119)Instruction limit reached!
% 0.30/1.59 % (6119)------------------------------
% 0.30/1.59 % (6119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (6119)Termination reason: Unknown
% 0.30/1.59 % (6119)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (6119)Memory used [KB]: 1663
% 0.30/1.59 % (6119)Time elapsed: 0.009 s
% 0.30/1.59 % (6119)Instructions burned: 15 (million)
% 0.30/1.59 % (6119)------------------------------
% 0.30/1.59 % (6119)------------------------------
% 0.30/1.59 % (6122)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/7Mi)
% 0.30/1.60 % (6123)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/16Mi)
% 2.92/1.60 % (6122)Instruction limit reached!
% 2.92/1.60 % (6122)------------------------------
% 2.92/1.60 % (6122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (6122)Termination reason: Unknown
% 2.92/1.60 % (6122)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (6122)Memory used [KB]: 1535
% 2.92/1.60 % (6122)Time elapsed: 0.004 s
% 2.92/1.60 % (6122)Instructions burned: 9 (million)
% 2.92/1.60 % (6122)------------------------------
% 2.92/1.60 % (6122)------------------------------
% 2.92/1.60 % (6121)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_5740 for (2999ds/1041Mi)
% 2.92/1.60 % (6123)Instruction limit reached!
% 2.92/1.60 % (6123)------------------------------
% 2.92/1.60 % (6123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (6123)Termination reason: Unknown
% 2.92/1.60 % (6123)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (6123)Memory used [KB]: 1663
% 2.92/1.60 % (6123)Time elapsed: 0.007 s
% 2.92/1.60 % (6123)Instructions burned: 18 (million)
% 2.92/1.60 % (6123)------------------------------
% 2.92/1.60 % (6123)------------------------------
% 2.92/1.60 % (6124)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_5740 for (2999ds/3Mi)
% 2.92/1.60 % (6124)Instruction limit reached!
% 2.92/1.60 % (6124)------------------------------
% 2.92/1.60 % (6124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (6124)Termination reason: Unknown
% 2.92/1.60 % (6124)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (6124)Memory used [KB]: 1279
% 2.92/1.60 % (6124)Time elapsed: 0.002 s
% 2.92/1.60 % (6124)Instructions burned: 3 (million)
% 2.92/1.60 % (6124)------------------------------
% 2.92/1.60 % (6124)------------------------------
% 2.92/1.60 % (6125)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_5740 for (2999ds/3Mi)
% 2.92/1.61 % (6125)Instruction limit reached!
% 2.92/1.61 % (6125)------------------------------
% 2.92/1.61 % (6125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (6125)Termination reason: Unknown
% 2.92/1.61 % (6125)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (6125)Memory used [KB]: 1407
% 2.92/1.61 % (6125)Time elapsed: 0.003 s
% 2.92/1.61 % (6125)Instructions burned: 5 (million)
% 2.92/1.61 % (6125)------------------------------
% 2.92/1.61 % (6125)------------------------------
% 2.92/1.61 % (6126)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/7Mi)
% 2.92/1.61 % (6126)Instruction limit reached!
% 2.92/1.61 % (6126)------------------------------
% 2.92/1.61 % (6126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (6126)Termination reason: Unknown
% 2.92/1.61 % (6126)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (6126)Memory used [KB]: 1535
% 2.92/1.61 % (6126)Time elapsed: 0.004 s
% 2.92/1.61 % (6126)Instructions burned: 9 (million)
% 2.92/1.61 % (6126)------------------------------
% 2.92/1.61 % (6126)------------------------------
% 2.92/1.61 % (6127)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/3Mi)
% 2.92/1.61 % (6127)Instruction limit reached!
% 2.92/1.61 % (6127)------------------------------
% 2.92/1.61 % (6127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (6127)Termination reason: Unknown
% 2.92/1.61 % (6127)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (6127)Memory used [KB]: 1407
% 2.92/1.61 % (6127)Time elapsed: 0.002 s
% 2.92/1.61 % (6127)Instructions burned: 4 (million)
% 2.92/1.61 % (6127)------------------------------
% 2.92/1.61 % (6127)------------------------------
% 2.92/1.61 % (6128)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/4Mi)
% 2.92/1.61 % (6128)Instruction limit reached!
% 2.92/1.61 % (6128)------------------------------
% 2.92/1.61 % (6128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (6128)Termination reason: Unknown
% 2.92/1.61 % (6128)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (6128)Memory used [KB]: 1407
% 2.92/1.61 % (6128)Time elapsed: 0.003 s
% 2.92/1.61 % (6128)Instructions burned: 4 (million)
% 2.92/1.61 % (6128)------------------------------
% 2.92/1.61 % (6128)------------------------------
% 2.92/1.62 % (6129)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/18Mi)
% 2.92/1.62 % (6130)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/710Mi)
% 2.92/1.62 % (6131)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/6Mi)
% 2.92/1.62 % (6129)Instruction limit reached!
% 2.92/1.62 % (6129)------------------------------
% 2.92/1.62 % (6129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (6129)Termination reason: Unknown
% 2.92/1.62 % (6129)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (6129)Memory used [KB]: 1663
% 2.92/1.62 % (6129)Time elapsed: 0.007 s
% 2.92/1.62 % (6129)Instructions burned: 18 (million)
% 2.92/1.62 % (6129)------------------------------
% 2.92/1.62 % (6129)------------------------------
% 2.92/1.62 % (6131)Instruction limit reached!
% 2.92/1.62 % (6131)------------------------------
% 2.92/1.62 % (6131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (6131)Termination reason: Unknown
% 2.92/1.62 % (6131)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (6131)Memory used [KB]: 1407
% 2.92/1.62 % (6131)Time elapsed: 0.003 s
% 2.92/1.62 % (6131)Instructions burned: 6 (million)
% 2.92/1.62 % (6131)------------------------------
% 2.92/1.62 % (6131)------------------------------
% 2.92/1.62 % (6132)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_5740 for (2999ds/902Mi)
% 2.92/1.63 % (6133)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_5740 for (2999ds/21Mi)
% 2.92/1.63 % (6134)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/5Mi)
% 2.92/1.63 % (6134)Instruction limit reached!
% 2.92/1.63 % (6134)------------------------------
% 2.92/1.63 % (6134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (6134)Termination reason: Unknown
% 2.92/1.63 % (6134)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (6134)Memory used [KB]: 1407
% 2.92/1.63 % (6134)Time elapsed: 0.003 s
% 2.92/1.63 % (6134)Instructions burned: 5 (million)
% 2.92/1.63 % (6134)------------------------------
% 2.92/1.63 % (6134)------------------------------
% 2.92/1.64 % (6133)Instruction limit reached!
% 2.92/1.64 % (6133)------------------------------
% 2.92/1.64 % (6133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (6133)Termination reason: Unknown
% 2.92/1.64 % (6133)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (6133)Memory used [KB]: 1791
% 2.92/1.64 % (6133)Time elapsed: 0.008 s
% 2.92/1.64 % (6133)Instructions burned: 21 (million)
% 2.92/1.64 % (6133)------------------------------
% 2.92/1.64 % (6133)------------------------------
% 2.92/1.64 % (6135)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_5740 for (2999ds/6Mi)
% 2.92/1.65 % (6135)Instruction limit reached!
% 2.92/1.65 % (6135)------------------------------
% 2.92/1.65 % (6135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (6135)Termination reason: Unknown
% 2.92/1.65 % (6135)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (6135)Memory used [KB]: 1407
% 2.92/1.65 % (6135)Time elapsed: 0.003 s
% 2.92/1.65 % (6135)Instructions burned: 7 (million)
% 2.92/1.65 % (6135)------------------------------
% 2.92/1.65 % (6135)------------------------------
% 2.92/1.65 % (6136)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5740 for (2999ds/377Mi)
% 2.92/1.65 % (6137)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_5740 for (2999ds/779Mi)
% 2.92/1.66 % (6115)Instruction limit reached!
% 2.92/1.66 % (6115)------------------------------
% 2.92/1.66 % (6115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (6115)Termination reason: Unknown
% 2.92/1.66 % (6115)Termination phase: Saturation
% 2.92/1.66
% 2.92/1.66 % (6115)Memory used [KB]: 7036
% 2.92/1.66 % (6115)Time elapsed: 0.094 s
% 2.92/1.66 % (6115)Instructions burned: 277 (million)
% 2.92/1.66 % (6115)------------------------------
% 2.92/1.66 % (6115)------------------------------
% 2.92/1.67 % (6138)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_5740 for (2998ds/19Mi)
% 2.92/1.67 % (6138)Instruction limit reached!
% 2.92/1.67 % (6138)------------------------------
% 2.92/1.67 % (6138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (6138)Termination reason: Unknown
% 2.92/1.67 % (6138)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (6138)Memory used [KB]: 1663
% 2.92/1.67 % (6138)Time elapsed: 0.008 s
% 2.92/1.67 % (6138)Instructions burned: 21 (million)
% 2.92/1.67 % (6138)------------------------------
% 2.92/1.67 % (6138)------------------------------
% 2.92/1.67 % (6110)Instruction limit reached!
% 2.92/1.67 % (6110)------------------------------
% 2.92/1.67 % (6110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (6110)Termination reason: Unknown
% 2.92/1.67 % (6110)Termination phase: Saturation
% 2.92/1.67
% 2.92/1.67 % (6110)Memory used [KB]: 7164
% 2.92/1.67 % (6110)Time elapsed: 0.105 s
% 2.92/1.67 % (6110)Instructions burned: 183 (million)
% 2.92/1.67 % (6110)------------------------------
% 2.92/1.67 % (6110)------------------------------
% 2.92/1.68 % (6139)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5740 for (2998ds/879Mi)
% 2.92/1.69 % (6140)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5740 for (2998ds/17Mi)
% 2.92/1.70 % (6140)Instruction limit reached!
% 2.92/1.70 % (6140)------------------------------
% 2.92/1.70 % (6140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.70 % (6140)Termination reason: Unknown
% 2.92/1.70 % (6140)Termination phase: shuffling
% 2.92/1.70
% 2.92/1.70 % (6140)Memory used [KB]: 1663
% 2.92/1.70 % (6140)Time elapsed: 0.009 s
% 2.92/1.70 % (6140)Instructions burned: 19 (million)
% 2.92/1.70 % (6140)------------------------------
% 2.92/1.70 % (6140)------------------------------
% 2.92/1.71 % (6141)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5740 for (2998ds/3Mi)
% 2.92/1.71 % (6141)Instruction limit reached!
% 2.92/1.71 % (6141)------------------------------
% 2.92/1.71 % (6141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.71 % (6141)Termination reason: Unknown
% 2.92/1.71 % (6141)Termination phase: shuffling
% 2.92/1.71
% 2.92/1.71 % (6141)Memory used [KB]: 1407
% 2.92/1.71 % (6141)Time elapsed: 0.003 s
% 2.92/1.71 % (6141)Instructions burned: 4 (million)
% 2.92/1.71 % (6141)------------------------------
% 2.92/1.71 % (6141)------------------------------
% 2.92/1.72 % (6142)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5740 for (2998ds/30Mi)
% 2.92/1.73 % (6142)Instruction limit reached!
% 2.92/1.73 % (6142)------------------------------
% 2.92/1.73 % (6142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (6142)Termination reason: Unknown
% 2.92/1.73 % (6142)Termination phase: Property scanning
% 2.92/1.73
% 2.92/1.73 % (6142)Memory used [KB]: 1918
% 2.92/1.73 % (6142)Time elapsed: 0.012 s
% 2.92/1.73 % (6142)Instructions burned: 30 (million)
% 2.92/1.73 % (6142)------------------------------
% 2.92/1.73 % (6142)------------------------------
% 2.92/1.74 % (6143)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5740 for (2998ds/127Mi)
% 2.92/1.76 % (6136)Instruction limit reached!
% 2.92/1.76 % (6136)------------------------------
% 2.92/1.76 % (6136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.76 % (6136)Termination reason: Unknown
% 2.92/1.76 % (6136)Termination phase: Saturation
% 2.92/1.76
% 2.92/1.76 % (6136)Memory used [KB]: 7803
% 2.92/1.76 % (6136)Time elapsed: 0.118 s
% 2.92/1.76 % (6136)Instructions burned: 379 (million)
% 2.92/1.76 % (6136)------------------------------
% 2.92/1.76 % (6136)------------------------------
% 2.92/1.77 % (6144)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5740 for (2997ds/100Mi)
% 2.92/1.78 % (6143)Instruction limit reached!
% 2.92/1.78 % (6143)------------------------------
% 2.92/1.78 % (6143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.78 % (6143)Termination reason: Unknown
% 2.92/1.78 % (6143)Termination phase: Saturation
% 2.92/1.78
% 2.92/1.78 % (6143)Memory used [KB]: 6780
% 2.92/1.78 % (6143)Time elapsed: 0.042 s
% 2.92/1.78 % (6143)Instructions burned: 129 (million)
% 2.92/1.78 % (6143)------------------------------
% 2.92/1.78 % (6143)------------------------------
% 2.92/1.79 % (6145)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_5740 for (2997ds/3Mi)
% 2.92/1.79 % (6145)Instruction limit reached!
% 2.92/1.79 % (6145)------------------------------
% 2.92/1.79 % (6145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.79 % (6145)Termination reason: Unknown
% 2.92/1.79 % (6145)Termination phase: shuffling
% 2.92/1.79
% 2.92/1.79 % (6145)Memory used [KB]: 1407
% 2.92/1.79 % (6145)Time elapsed: 0.003 s
% 2.92/1.79 % (6145)Instructions burned: 4 (million)
% 2.92/1.79 % (6145)------------------------------
% 2.92/1.79 % (6145)------------------------------
% 2.92/1.80 % (6144)Instruction limit reached!
% 2.92/1.80 % (6144)------------------------------
% 2.92/1.80 % (6144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.80 % (6144)Termination reason: Unknown
% 2.92/1.80 % (6144)Termination phase: Property scanning
% 2.92/1.80
% 2.92/1.80 % (6144)Memory used [KB]: 2174
% 2.92/1.80 % (6144)Time elapsed: 0.028 s
% 2.92/1.80 % (6144)Instructions burned: 102 (million)
% 2.92/1.80 % (6144)------------------------------
% 2.92/1.80 % (6144)------------------------------
% 2.92/1.80 % (6146)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_5740 for (2997ds/20Mi)
% 2.92/1.81 % (6146)Instruction limit reached!
% 2.92/1.81 % (6146)------------------------------
% 2.92/1.81 % (6146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (6146)Termination reason: Unknown
% 2.92/1.81 % (6146)Termination phase: shuffling
% 2.92/1.81
% 2.92/1.81 % (6146)Memory used [KB]: 1663
% 2.92/1.81 % (6146)Time elapsed: 0.009 s
% 2.92/1.81 % (6146)Instructions burned: 20 (million)
% 2.92/1.81 % (6146)------------------------------
% 2.92/1.81 % (6146)------------------------------
% 2.92/1.81 % (6147)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_5740 for (2997ds/86Mi)
% 2.92/1.82 % (6148)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_5740 for (2997ds/107Mi)
% 2.92/1.83 % (6130)Instruction limit reached!
% 2.92/1.83 % (6130)------------------------------
% 2.92/1.83 % (6130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.83 % (6130)Termination reason: Unknown
% 2.92/1.83 % (6130)Termination phase: Saturation
% 2.92/1.83
% 2.92/1.83 % (6130)Memory used [KB]: 7675
% 2.92/1.83 % (6130)Time elapsed: 0.214 s
% 2.92/1.83 % (6130)Instructions burned: 711 (million)
% 2.92/1.83 % (6130)------------------------------
% 2.92/1.83 % (6130)------------------------------
% 2.92/1.83 % (6147)Instruction limit reached!
% 2.92/1.83 % (6147)------------------------------
% 2.92/1.83 % (6147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.83 % (6147)Termination reason: Unknown
% 2.92/1.83 % (6147)Termination phase: Saturation
% 2.92/1.83
% 2.92/1.83 % (6147)Memory used [KB]: 6652
% 2.92/1.83 % (6147)Time elapsed: 0.026 s
% 2.92/1.83 % (6147)Instructions burned: 86 (million)
% 2.92/1.83 % (6147)------------------------------
% 2.92/1.83 % (6147)------------------------------
% 2.92/1.84 % (6149)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_5740 for (2997ds/39Mi)
% 2.92/1.84 % (6150)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_5740 for (2996ds/448Mi)
% 2.92/1.85 % (6148)Instruction limit reached!
% 2.92/1.85 % (6148)------------------------------
% 2.92/1.85 % (6148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.85 % (6148)Termination reason: Unknown
% 2.92/1.85 % (6148)Termination phase: Saturation
% 2.92/1.85
% 2.92/1.85 % (6148)Memory used [KB]: 6652
% 2.92/1.85 % (6148)Time elapsed: 0.036 s
% 2.92/1.85 % (6149)Instruction limit reached!
% 2.92/1.85 % (6149)------------------------------
% 2.92/1.85 % (6149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.85 % (6148)Instructions burned: 108 (million)
% 2.92/1.85 % (6149)Termination reason: Unknown
% 2.92/1.85 % (6148)------------------------------
% 2.92/1.85 % (6148)------------------------------
% 2.92/1.85 % (6149)Termination phase: Property scanning
% 2.92/1.85
% 2.92/1.85 % (6149)Memory used [KB]: 2046
% 2.92/1.85 % (6149)Time elapsed: 0.012 s
% 2.92/1.85 % (6149)Instructions burned: 41 (million)
% 2.92/1.85 % (6149)------------------------------
% 2.92/1.85 % (6149)------------------------------
% 2.92/1.86 % (6152)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_5740 for (2996ds/98Mi)
% 2.92/1.86 % (6151)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_5740 for (2996ds/46Mi)
% 2.92/1.88 % (6151)Instruction limit reached!
% 2.92/1.88 % (6151)------------------------------
% 2.92/1.88 % (6151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.88 % (6151)Termination reason: Unknown
% 2.92/1.88 % (6151)Termination phase: Preprocessing 3
% 2.92/1.88
% 2.92/1.88 % (6151)Memory used [KB]: 1918
% 2.92/1.88 % (6151)Time elapsed: 0.017 s
% 2.92/1.88 % (6151)Instructions burned: 46 (million)
% 2.92/1.88 % (6151)------------------------------
% 2.92/1.88 % (6151)------------------------------
% 2.92/1.89 % (6152)Instruction limit reached!
% 2.92/1.89 % (6152)------------------------------
% 2.92/1.89 % (6152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (6152)Termination reason: Unknown
% 2.92/1.89 % (6152)Termination phase: Property scanning
% 2.92/1.89
% 2.92/1.89 % (6152)Memory used [KB]: 2174
% 2.92/1.89 % (6152)Time elapsed: 0.027 s
% 2.92/1.89 % (6152)Instructions burned: 99 (million)
% 2.92/1.89 % (6152)------------------------------
% 2.92/1.89 % (6152)------------------------------
% 2.92/1.89 % (6153)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_5740 for (2996ds/507Mi)
% 2.92/1.89 % (6137)Instruction limit reached!
% 2.92/1.89 % (6137)------------------------------
% 2.92/1.89 % (6137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (6137)Termination reason: Unknown
% 2.92/1.89 % (6137)Termination phase: Saturation
% 2.92/1.89
% 2.92/1.89 % (6137)Memory used [KB]: 7803
% 2.92/1.89 % (6137)Time elapsed: 0.237 s
% 2.92/1.89 % (6137)Instructions burned: 781 (million)
% 2.92/1.89 % (6137)------------------------------
% 2.92/1.89 % (6137)------------------------------
% 2.92/1.90 % (6154)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_5740 for (2996ds/149Mi)
% 2.92/1.90 % (6155)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5740 for (2996ds/39Mi)
% 2.92/1.91 % (6155)Instruction limit reached!
% 2.92/1.91 % (6155)------------------------------
% 2.92/1.91 % (6155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.91 % (6155)Termination reason: Unknown
% 2.92/1.91 % (6155)Termination phase: Preprocessing 3
% 2.92/1.91
% 2.92/1.91 % (6155)Memory used [KB]: 1918
% 2.92/1.91 % (6155)Time elapsed: 0.013 s
% 2.92/1.91 % (6155)Instructions burned: 39 (million)
% 2.92/1.91 % (6155)------------------------------
% 2.92/1.91 % (6155)------------------------------
% 2.92/1.92 % (6132)Instruction limit reached!
% 2.92/1.92 % (6132)------------------------------
% 2.92/1.92 % (6132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.92 % (6132)Termination reason: Unknown
% 2.92/1.92 % (6132)Termination phase: Saturation
% 2.92/1.92
% 2.92/1.92 % (6132)Memory used [KB]: 8315
% 2.92/1.92 % (6132)Time elapsed: 0.293 s
% 2.92/1.92 % (6132)Instructions burned: 904 (million)
% 2.92/1.92 % (6132)------------------------------
% 2.92/1.92 % (6132)------------------------------
% 2.92/1.92 % (6156)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_5740 for (2996ds/6Mi)
% 2.92/1.92 % (6156)Instruction limit reached!
% 2.92/1.92 % (6156)------------------------------
% 2.92/1.92 % (6156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.92 % (6156)Termination reason: Unknown
% 2.92/1.92 % (6156)Termination phase: shuffling
% 2.92/1.92
% 2.92/1.92 % (6156)Memory used [KB]: 1407
% 2.92/1.92 % (6156)Time elapsed: 0.003 s
% 2.92/1.92 % (6156)Instructions burned: 8 (million)
% 2.92/1.92 % (6156)------------------------------
% 2.92/1.92 % (6156)------------------------------
% 2.92/1.92 % (6157)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_5740 for (2996ds/1087Mi)
% 2.92/1.93 % (6158)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_5740 for (2996ds/47Mi)
% 2.92/1.94 % (6154)Instruction limit reached!
% 2.92/1.94 % (6154)------------------------------
% 2.92/1.94 % (6154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (6154)Termination reason: Unknown
% 2.92/1.94 % (6154)Termination phase: Saturation
% 2.92/1.94
% 2.92/1.94 % (6154)Memory used [KB]: 6908
% 2.92/1.94 % (6154)Time elapsed: 0.045 s
% 2.92/1.94 % (6154)Instructions burned: 149 (million)
% 2.92/1.94 % (6154)------------------------------
% 2.92/1.94 % (6154)------------------------------
% 2.92/1.95 % (6158)Instruction limit reached!
% 2.92/1.95 % (6158)------------------------------
% 2.92/1.95 % (6158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.95 % (6158)Termination reason: Unknown
% 2.92/1.95 % (6158)Termination phase: Property scanning
% 2.92/1.95
% 2.92/1.95 % (6158)Memory used [KB]: 2046
% 2.92/1.95 % (6158)Time elapsed: 0.016 s
% 2.92/1.95 % (6158)Instructions burned: 47 (million)
% 2.92/1.95 % (6158)------------------------------
% 2.92/1.95 % (6158)------------------------------
% 2.92/1.95 % (6159)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_5740 for (2995ds/44Mi)
% 2.92/1.95 % (6139)Instruction limit reached!
% 2.92/1.95 % (6139)------------------------------
% 2.92/1.95 % (6139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.95 % (6139)Termination reason: Unknown
% 2.92/1.95 % (6139)Termination phase: Saturation
% 2.92/1.95
% 2.92/1.95 % (6139)Memory used [KB]: 7547
% 2.92/1.95 % (6139)Time elapsed: 0.270 s
% 2.92/1.95 % (6139)Instructions burned: 881 (million)
% 2.92/1.95 % (6139)------------------------------
% 2.92/1.95 % (6139)------------------------------
% 2.92/1.96 % (6160)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_5740 for (2995ds/432Mi)
% 2.92/1.96 % (6161)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_5740 for (2995ds/62Mi)
% 2.92/1.96 % (6159)Instruction limit reached!
% 2.92/1.96 % (6159)------------------------------
% 2.92/1.96 % (6159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.96 % (6159)Termination reason: Unknown
% 2.92/1.96 % (6159)Termination phase: Property scanning
% 2.92/1.96
% 2.92/1.96 % (6159)Memory used [KB]: 2046
% 2.92/1.96 % (6159)Time elapsed: 0.013 s
% 2.92/1.96 % (6159)Instructions burned: 44 (million)
% 2.92/1.96 % (6159)------------------------------
% 2.92/1.96 % (6159)------------------------------
% 2.92/1.97 % (6162)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_5740 for (2995ds/31Mi)
% 2.92/1.98 % (6121)Instruction limit reached!
% 2.92/1.98 % (6121)------------------------------
% 2.92/1.98 % (6121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (6121)Termination reason: Unknown
% 2.92/1.98 % (6121)Termination phase: Saturation
% 2.92/1.98
% 2.92/1.98 % (6121)Memory used [KB]: 9722
% 2.92/1.98 % (6121)Time elapsed: 0.378 s
% 2.92/1.98 % (6121)Instructions burned: 1041 (million)
% 2.92/1.98 % (6121)------------------------------
% 2.92/1.98 % (6121)------------------------------
% 2.92/1.98 % (6161)Instruction limit reached!
% 2.92/1.98 % (6161)------------------------------
% 2.92/1.98 % (6161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (6161)Termination reason: Unknown
% 2.92/1.98 % (6161)Termination phase: Property scanning
% 2.92/1.98
% 2.92/1.98 % (6161)Memory used [KB]: 2046
% 2.92/1.98 % (6161)Time elapsed: 0.017 s
% 2.92/1.98 % (6161)Instructions burned: 62 (million)
% 2.92/1.98 % (6161)------------------------------
% 2.92/1.98 % (6161)------------------------------
% 2.92/1.98 % (6150)Instruction limit reached!
% 2.92/1.98 % (6150)------------------------------
% 2.92/1.98 % (6150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (6150)Termination reason: Unknown
% 2.92/1.98 % (6150)Termination phase: Saturation
% 2.92/1.98
% 2.92/1.98 % (6150)Memory used [KB]: 7803
% 2.92/1.98 % (6150)Time elapsed: 0.135 s
% 2.92/1.98 % (6150)Instructions burned: 449 (million)
% 2.92/1.98 % (6150)------------------------------
% 2.92/1.98 % (6150)------------------------------
% 2.92/1.98 % (6162)Instruction limit reached!
% 2.92/1.98 % (6162)------------------------------
% 2.92/1.98 % (6162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (6162)Termination reason: Unknown
% 2.92/1.98 % (6162)Termination phase: Preprocessing 1
% 2.92/1.98
% 2.92/1.98 % (6162)Memory used [KB]: 1791
% 2.92/1.98 % (6162)Time elapsed: 0.011 s
% 2.92/1.98 % (6162)Instructions burned: 34 (million)
% 2.92/1.98 % (6162)------------------------------
% 2.92/1.98 % (6162)------------------------------
% 2.92/1.99 % (6164)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_5740 for (2995ds/453Mi)
% 2.92/1.99 % (6163)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_5740 for (2995ds/96Mi)
% 2.92/1.99 % (6165)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_5740 for (2995ds/71Mi)
% 2.92/1.99 % (6166)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_5740 for (2995ds/83Mi)
% 2.92/2.01 % (6165)Instruction limit reached!
% 2.92/2.01 % (6165)------------------------------
% 2.92/2.01 % (6165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/2.01 % (6165)Termination reason: Unknown
% 2.92/2.01 % (6165)Termination phase: Property scanning
% 2.92/2.01
% 2.92/2.01 % (6165)Memory used [KB]: 2174
% 2.92/2.01 % (6165)Time elapsed: 0.022 s
% 2.92/2.01 % (6165)Instructions burned: 72 (million)
% 2.92/2.01 % (6165)------------------------------
% 2.92/2.01 % (6165)------------------------------
% 6.06/2.02 % (6166)Instruction limit reached!
% 6.06/2.02 % (6166)------------------------------
% 6.06/2.02 % (6166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.02 % (6166)Termination reason: Unknown
% 6.06/2.02 % (6166)Termination phase: Saturation
% 6.06/2.02
% 6.06/2.02 % (6166)Memory used [KB]: 6524
% 6.06/2.02 % (6166)Time elapsed: 0.026 s
% 6.06/2.02 % (6166)Instructions burned: 86 (million)
% 6.06/2.02 % (6166)------------------------------
% 6.06/2.02 % (6166)------------------------------
% 6.06/2.02 % (6163)Instruction limit reached!
% 6.06/2.02 % (6163)------------------------------
% 6.06/2.02 % (6163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.02 % (6163)Termination reason: Unknown
% 6.06/2.02 % (6163)Termination phase: Saturation
% 6.06/2.02
% 6.06/2.02 % (6163)Memory used [KB]: 6652
% 6.06/2.02 % (6163)Time elapsed: 0.032 s
% 6.06/2.02 % (6163)Instructions burned: 98 (million)
% 6.06/2.02 % (6163)------------------------------
% 6.06/2.02 % (6163)------------------------------
% 6.06/2.02 % (6167)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_5740 for (2995ds/11Mi)
% 6.06/2.02 % (6167)Instruction limit reached!
% 6.06/2.02 % (6167)------------------------------
% 6.06/2.02 % (6167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.02 % (6167)Termination reason: Unknown
% 6.06/2.02 % (6167)Termination phase: shuffling
% 6.06/2.02
% 6.06/2.02 % (6167)Memory used [KB]: 1663
% 6.06/2.02 % (6167)Time elapsed: 0.005 s
% 6.06/2.02 % (6167)Instructions burned: 14 (million)
% 6.06/2.02 % (6167)------------------------------
% 6.06/2.02 % (6167)------------------------------
% 6.06/2.03 % (6168)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_5740 for (2995ds/41Mi)
% 6.06/2.03 % (6169)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5740 for (2995ds/6Mi)
% 6.06/2.03 % (6169)Instruction limit reached!
% 6.06/2.03 % (6169)------------------------------
% 6.06/2.03 % (6169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.03 % (6169)Termination reason: Unknown
% 6.06/2.03 % (6169)Termination phase: shuffling
% 6.06/2.03
% 6.06/2.03 % (6169)Memory used [KB]: 1407
% 6.06/2.03 % (6169)Time elapsed: 0.003 s
% 6.06/2.03 % (6169)Instructions burned: 6 (million)
% 6.06/2.03 % (6169)------------------------------
% 6.06/2.03 % (6169)------------------------------
% 6.06/2.03 % (6170)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_5740 for (2995ds/150Mi)
% 6.06/2.04 % (6168)Instruction limit reached!
% 6.06/2.04 % (6168)------------------------------
% 6.06/2.04 % (6168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.04 % (6168)Termination reason: Unknown
% 6.06/2.04 % (6168)Termination phase: Property scanning
% 6.06/2.04
% 6.06/2.04 % (6168)Memory used [KB]: 2046
% 6.06/2.04 % (6168)Time elapsed: 0.013 s
% 6.06/2.04 % (6168)Instructions burned: 44 (million)
% 6.06/2.04 % (6168)------------------------------
% 6.06/2.04 % (6168)------------------------------
% 6.06/2.04 % (6171)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_5740 for (2995ds/343Mi)
% 6.06/2.05 % (6172)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_5740 for (2994ds/109Mi)
% 6.06/2.06 % (6153)Instruction limit reached!
% 6.06/2.06 % (6153)------------------------------
% 6.06/2.06 % (6153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.06 % (6153)Termination reason: Unknown
% 6.06/2.06 % (6153)Termination phase: Saturation
% 6.06/2.06
% 6.06/2.06 % (6153)Memory used [KB]: 7931
% 6.06/2.06 % (6153)Time elapsed: 0.169 s
% 6.06/2.06 % (6153)Instructions burned: 507 (million)
% 6.06/2.06 % (6153)------------------------------
% 6.06/2.06 % (6153)------------------------------
% 6.06/2.07 % (6173)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_5740 for (2994ds/253Mi)
% 6.06/2.08 % (6170)Instruction limit reached!
% 6.06/2.08 % (6170)------------------------------
% 6.06/2.08 % (6170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.08 % (6170)Termination reason: Unknown
% 6.06/2.08 % (6170)Termination phase: Saturation
% 6.06/2.08
% 6.06/2.08 % (6170)Memory used [KB]: 6908
% 6.06/2.08 % (6170)Time elapsed: 0.047 s
% 6.06/2.08 % (6170)Instructions burned: 151 (million)
% 6.06/2.08 % (6170)------------------------------
% 6.06/2.08 % (6170)------------------------------
% 6.06/2.08 % (6172)Instruction limit reached!
% 6.06/2.08 % (6172)------------------------------
% 6.06/2.08 % (6172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.08 % (6172)Termination reason: Unknown
% 6.06/2.08 % (6172)Termination phase: Saturation
% 6.06/2.08
% 6.06/2.08 % (6172)Memory used [KB]: 6652
% 6.06/2.08 % (6172)Time elapsed: 0.034 s
% 6.06/2.08 % (6172)Instructions burned: 111 (million)
% 6.06/2.08 % (6172)------------------------------
% 6.06/2.08 % (6172)------------------------------
% 6.06/2.09 % (6174)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_5740 for (2994ds/140Mi)
% 6.06/2.09 % (6175)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_5740 for (2994ds/614Mi)
% 6.06/2.09 % (6160)Instruction limit reached!
% 6.06/2.09 % (6160)------------------------------
% 6.06/2.09 % (6160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.09 % (6160)Termination reason: Unknown
% 6.06/2.09 % (6160)Termination phase: Saturation
% 6.06/2.09
% 6.06/2.09 % (6160)Memory used [KB]: 3326
% 6.06/2.09 % (6160)Time elapsed: 0.134 s
% 6.06/2.09 % (6160)Instructions burned: 433 (million)
% 6.06/2.09 % (6160)------------------------------
% 6.06/2.09 % (6160)------------------------------
% 6.06/2.10 % (6176)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_5740 for (2994ds/202Mi)
% 6.61/2.12 % (6164)Instruction limit reached!
% 6.61/2.12 % (6164)------------------------------
% 6.61/2.12 % (6164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.12 % (6164)Termination reason: Unknown
% 6.61/2.12 % (6164)Termination phase: Saturation
% 6.61/2.12
% 6.61/2.12 % (6164)Memory used [KB]: 7803
% 6.61/2.12 % (6164)Time elapsed: 0.133 s
% 6.61/2.12 % (6164)Instructions burned: 455 (million)
% 6.61/2.12 % (6164)------------------------------
% 6.61/2.12 % (6164)------------------------------
% 6.61/2.13 % (6177)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_5740 for (2994ds/339Mi)
% 6.61/2.13 % (6174)Instruction limit reached!
% 6.61/2.13 % (6174)------------------------------
% 6.61/2.13 % (6174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.13 % (6174)Termination reason: Unknown
% 6.61/2.13 % (6174)Termination phase: Saturation
% 6.61/2.13
% 6.61/2.13 % (6174)Memory used [KB]: 6908
% 6.61/2.13 % (6174)Time elapsed: 0.046 s
% 6.61/2.13 % (6174)Instructions burned: 140 (million)
% 6.61/2.13 % (6174)------------------------------
% 6.61/2.13 % (6174)------------------------------
% 6.61/2.14 % (6178)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_5740 for (2994ds/283Mi)
% 6.61/2.14 % (6173)Instruction limit reached!
% 6.61/2.14 % (6173)------------------------------
% 6.61/2.14 % (6173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.14 % (6173)Termination reason: Unknown
% 6.61/2.14 % (6173)Termination phase: Saturation
% 6.61/2.14
% 6.61/2.14 % (6173)Memory used [KB]: 7164
% 6.61/2.14 % (6173)Time elapsed: 0.080 s
% 6.61/2.14 % (6173)Instructions burned: 253 (million)
% 6.61/2.14 % (6173)------------------------------
% 6.61/2.14 % (6173)------------------------------
% 6.61/2.15 % (6171)Instruction limit reached!
% 6.61/2.15 % (6171)------------------------------
% 6.61/2.15 % (6171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.15 % (6171)Termination reason: Unknown
% 6.61/2.15 % (6171)Termination phase: Saturation
% 6.61/2.15
% 6.61/2.15 % (6171)Memory used [KB]: 7419
% 6.61/2.15 % (6171)Time elapsed: 0.109 s
% 6.61/2.15 % (6171)Instructions burned: 343 (million)
% 6.61/2.15 % (6171)------------------------------
% 6.61/2.15 % (6171)------------------------------
% 6.61/2.15 % (6179)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_5740 for (2993ds/134Mi)
% 6.61/2.16 % (6180)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_5740 for (2993ds/298Mi)
% 6.61/2.16 % (6176)Instruction limit reached!
% 6.61/2.16 % (6176)------------------------------
% 6.61/2.16 % (6176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.16 % (6176)Termination reason: Unknown
% 6.61/2.16 % (6176)Termination phase: Saturation
% 6.61/2.16
% 6.61/2.16 % (6176)Memory used [KB]: 6908
% 6.61/2.16 % (6176)Time elapsed: 0.064 s
% 6.61/2.16 % (6176)Instructions burned: 203 (million)
% 6.61/2.16 % (6176)------------------------------
% 6.61/2.16 % (6176)------------------------------
% 6.61/2.17 % (6181)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_5740 for (2993ds/192Mi)
% 6.61/2.19 % (6179)Instruction limit reached!
% 6.61/2.19 % (6179)------------------------------
% 6.61/2.19 % (6179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.19 % (6179)Termination reason: Unknown
% 6.61/2.19 % (6179)Termination phase: Saturation
% 6.61/2.19
% 6.61/2.19 % (6179)Memory used [KB]: 6780
% 6.61/2.19 % (6179)Time elapsed: 0.040 s
% 6.61/2.19 % (6179)Instructions burned: 135 (million)
% 6.61/2.19 % (6179)------------------------------
% 6.61/2.19 % (6179)------------------------------
% 7.08/2.20 % (6182)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_5740 for (2993ds/258Mi)
% 7.08/2.23 % (6178)Instruction limit reached!
% 7.08/2.23 % (6178)------------------------------
% 7.08/2.23 % (6178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.23 % (6178)Termination reason: Unknown
% 7.08/2.23 % (6178)Termination phase: Saturation
% 7.08/2.23
% 7.08/2.23 % (6178)Memory used [KB]: 7547
% 7.08/2.23 % (6178)Time elapsed: 0.089 s
% 7.08/2.23 % (6178)Instructions burned: 283 (million)
% 7.08/2.23 % (6178)------------------------------
% 7.08/2.23 % (6178)------------------------------
% 7.08/2.23 % (6177)Instruction limit reached!
% 7.08/2.23 % (6177)------------------------------
% 7.08/2.23 % (6177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.23 % (6177)Termination reason: Unknown
% 7.08/2.23 % (6177)Termination phase: Saturation
% 7.08/2.23
% 7.08/2.23 % (6177)Memory used [KB]: 7419
% 7.08/2.23 % (6177)Time elapsed: 0.102 s
% 7.08/2.23 % (6177)Instructions burned: 341 (million)
% 7.08/2.23 % (6177)------------------------------
% 7.08/2.23 % (6177)------------------------------
% 7.08/2.23 % (6181)Instruction limit reached!
% 7.08/2.23 % (6181)------------------------------
% 7.08/2.23 % (6181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.23 % (6181)Termination reason: Unknown
% 7.08/2.23 % (6181)Termination phase: Saturation
% 7.08/2.23
% 7.08/2.23 % (6181)Memory used [KB]: 7803
% 7.08/2.23 % (6181)Time elapsed: 0.061 s
% 7.08/2.23 % (6181)Instructions burned: 194 (million)
% 7.08/2.23 % (6181)------------------------------
% 7.08/2.23 % (6181)------------------------------
% 7.08/2.24 % (6183)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_5740 for (2993ds/90Mi)
% 7.08/2.24 % (6184)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_5740 for (2993ds/231Mi)
% 7.08/2.24 % (6185)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_5740 for (2993ds/458Mi)
% 7.08/2.24 % (6180)Instruction limit reached!
% 7.08/2.24 % (6180)------------------------------
% 7.08/2.24 % (6180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.24 % (6180)Termination reason: Unknown
% 7.08/2.24 % (6180)Termination phase: Saturation
% 7.08/2.24
% 7.08/2.24 % (6180)Memory used [KB]: 7931
% 7.08/2.24 % (6180)Time elapsed: 0.089 s
% 7.08/2.24 % (6180)Instructions burned: 300 (million)
% 7.08/2.24 % (6180)------------------------------
% 7.08/2.24 % (6180)------------------------------
% 7.08/2.25 % (6186)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_5740 for (2992ds/31Mi)
% 7.08/2.26 % (6186)Instruction limit reached!
% 7.08/2.26 % (6186)------------------------------
% 7.08/2.26 % (6186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.26 % (6186)Termination reason: Unknown
% 7.08/2.26 % (6186)Termination phase: Preprocessing 1
% 7.08/2.26
% 7.08/2.26 % (6186)Memory used [KB]: 1791
% 7.08/2.26 % (6186)Time elapsed: 0.011 s
% 7.08/2.26 % (6186)Instructions burned: 34 (million)
% 7.08/2.26 % (6186)------------------------------
% 7.08/2.26 % (6186)------------------------------
% 7.08/2.26 % (6183)Instruction limit reached!
% 7.08/2.26 % (6183)------------------------------
% 7.08/2.26 % (6183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.26 % (6183)Termination reason: Unknown
% 7.08/2.26 % (6183)Termination phase: Saturation
% 7.08/2.26
% 7.08/2.26 % (6183)Memory used [KB]: 6652
% 7.08/2.26 % (6183)Time elapsed: 0.027 s
% 7.08/2.26 % (6183)Instructions burned: 90 (million)
% 7.08/2.26 % (6183)------------------------------
% 7.08/2.26 % (6183)------------------------------
% 7.08/2.27 % (6187)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_5740 for (2992ds/297Mi)
% 7.08/2.27 % (6188)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_5740 for (2992ds/987Mi)
% 7.08/2.28 % (6175)Instruction limit reached!
% 7.08/2.28 % (6175)------------------------------
% 7.08/2.28 % (6175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.28 % (6175)Termination reason: Unknown
% 7.08/2.28 % (6175)Termination phase: Saturation
% 7.08/2.28
% 7.08/2.28 % (6175)Memory used [KB]: 7931
% 7.08/2.28 % (6175)Time elapsed: 0.192 s
% 7.08/2.28 % (6175)Instructions burned: 614 (million)
% 7.08/2.28 % (6175)------------------------------
% 7.08/2.28 % (6175)------------------------------
% 7.08/2.28 % (6182)Instruction limit reached!
% 7.08/2.28 % (6182)------------------------------
% 7.08/2.28 % (6182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.28 % (6182)Termination reason: Unknown
% 7.08/2.28 % (6182)Termination phase: Saturation
% 7.08/2.28
% 7.08/2.28 % (6182)Memory used [KB]: 7164
% 7.08/2.28 % (6182)Time elapsed: 0.081 s
% 7.08/2.28 % (6182)Instructions burned: 259 (million)
% 7.08/2.28 % (6182)------------------------------
% 7.08/2.28 % (6182)------------------------------
% 7.08/2.29 % (6189)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_5740 for (2992ds/182Mi)
% 7.08/2.29 % (6190)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_5740 for (2992ds/182Mi)
% 7.90/2.30 % (6184)Instruction limit reached!
% 7.90/2.30 % (6184)------------------------------
% 7.90/2.30 % (6184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.30 % (6184)Termination reason: Unknown
% 7.90/2.30 % (6184)Termination phase: Saturation
% 7.90/2.30
% 7.90/2.30 % (6184)Memory used [KB]: 6908
% 7.90/2.30 % (6184)Time elapsed: 0.061 s
% 7.90/2.30 % (6184)Instructions burned: 231 (million)
% 7.90/2.30 % (6184)------------------------------
% 7.90/2.30 % (6184)------------------------------
% 7.90/2.31 % (6191)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_5740 for (2992ds/154Mi)
% 7.90/2.34 % (6157)Instruction limit reached!
% 7.90/2.34 % (6157)------------------------------
% 7.90/2.34 % (6157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.34 % (6157)Termination reason: Unknown
% 7.90/2.34 % (6157)Termination phase: Saturation
% 7.90/2.34
% 7.90/2.34 % (6157)Memory used [KB]: 7931
% 7.90/2.34 % (6157)Time elapsed: 0.413 s
% 7.90/2.34 % (6157)Instructions burned: 1088 (million)
% 7.90/2.34 % (6157)------------------------------
% 7.90/2.34 % (6157)------------------------------
% 7.90/2.34 % (6189)Instruction limit reached!
% 7.90/2.34 % (6189)------------------------------
% 7.90/2.34 % (6189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.34 % (6189)Termination reason: Unknown
% 7.90/2.34 % (6189)Termination phase: Saturation
% 7.90/2.34
% 7.90/2.34 % (6189)Memory used [KB]: 7036
% 7.90/2.34 % (6189)Time elapsed: 0.054 s
% 7.90/2.34 % (6189)Instructions burned: 182 (million)
% 7.90/2.34 % (6189)------------------------------
% 7.90/2.34 % (6189)------------------------------
% 7.90/2.35 % (6190)Instruction limit reached!
% 7.90/2.35 % (6190)------------------------------
% 7.90/2.35 % (6190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.35 % (6190)Termination reason: Unknown
% 7.90/2.35 % (6190)Termination phase: Saturation
% 7.90/2.35
% 7.90/2.35 % (6190)Memory used [KB]: 7036
% 7.90/2.35 % (6190)Time elapsed: 0.057 s
% 7.90/2.35 % (6190)Instructions burned: 183 (million)
% 7.90/2.35 % (6190)------------------------------
% 7.90/2.35 % (6190)------------------------------
% 7.90/2.35 % (6192)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_5740 for (2992ds/79Mi)
% 7.90/2.35 % (6191)Instruction limit reached!
% 7.90/2.35 % (6191)------------------------------
% 7.90/2.35 % (6191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.35 % (6191)Termination reason: Unknown
% 7.90/2.35 % (6191)Termination phase: Saturation
% 7.90/2.35
% 7.90/2.35 % (6191)Memory used [KB]: 2686
% 7.90/2.35 % (6191)Time elapsed: 0.043 s
% 7.90/2.35 % (6191)Instructions burned: 155 (million)
% 7.90/2.35 % (6191)------------------------------
% 7.90/2.35 % (6191)------------------------------
% 7.90/2.35 % (6193)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_5740 for (2992ds/216Mi)
% 7.90/2.36 % (6187)Instruction limit reached!
% 7.90/2.36 % (6187)------------------------------
% 7.90/2.36 % (6187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.36 % (6187)Termination reason: Unknown
% 7.90/2.36 % (6187)Termination phase: Saturation
% 7.90/2.36
% 7.90/2.36 % (6187)Memory used [KB]: 7419
% 7.90/2.36 % (6187)Time elapsed: 0.084 s
% 7.90/2.36 % (6187)Instructions burned: 298 (million)
% 7.90/2.36 % (6187)------------------------------
% 7.90/2.36 % (6187)------------------------------
% 7.90/2.36 % (6194)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_5740 for (2992ds/114Mi)
% 7.90/2.36 % (6195)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_5740 for (2991ds/922Mi)
% 7.90/2.37 % (6196)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_5740 for (2991ds/182Mi)
% 7.90/2.37 % (6192)Instruction limit reached!
% 7.90/2.37 % (6192)------------------------------
% 7.90/2.37 % (6192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.37 % (6192)Termination reason: Unknown
% 7.90/2.37 % (6192)Termination phase: Saturation
% 7.90/2.37
% 7.90/2.37 % (6192)Memory used [KB]: 6652
% 7.90/2.37 % (6192)Time elapsed: 0.027 s
% 7.90/2.37 % (6192)Instructions burned: 81 (million)
% 7.90/2.37 % (6192)------------------------------
% 7.90/2.37 % (6192)------------------------------
% 7.90/2.38 % (6185)Refutation not found, non-redundant clauses discarded% (6185)------------------------------
% 7.90/2.38 % (6185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.38 % (6185)Termination reason: Refutation not found, non-redundant clauses discarded
% 7.90/2.38
% 7.90/2.38 % (6185)Memory used [KB]: 7675
% 7.90/2.38 % (6185)Time elapsed: 0.137 s
% 7.90/2.38 % (6185)Instructions burned: 437 (million)
% 7.90/2.38 % (6185)------------------------------
% 7.90/2.38 % (6185)------------------------------
% 7.90/2.38 % (6197)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_5740 for (2991ds/164Mi)
% 7.90/2.39 % (6198)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_5740 for (2991ds/50Mi)
% 7.90/2.39 % (6194)Instruction limit reached!
% 7.90/2.39 % (6194)------------------------------
% 7.90/2.39 % (6194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.39 % (6194)Termination reason: Unknown
% 7.90/2.39 % (6194)Termination phase: Saturation
% 7.90/2.39
% 7.90/2.39 % (6194)Memory used [KB]: 6780
% 7.90/2.39 % (6194)Time elapsed: 0.034 s
% 7.90/2.39 % (6194)Instructions burned: 114 (million)
% 7.90/2.39 % (6194)------------------------------
% 7.90/2.39 % (6194)------------------------------
% 8.52/2.40 % (6199)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_5740 for (2991ds/368Mi)
% 8.52/2.40 % (6198)Instruction limit reached!
% 8.52/2.40 % (6198)------------------------------
% 8.52/2.40 % (6198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.40 % (6198)Termination reason: Unknown
% 8.52/2.40 % (6198)Termination phase: Property scanning
% 8.52/2.40
% 8.52/2.40 % (6198)Memory used [KB]: 2046
% 8.52/2.40 % (6198)Time elapsed: 0.015 s
% 8.52/2.40 % (6198)Instructions burned: 53 (million)
% 8.52/2.40 % (6198)------------------------------
% 8.52/2.40 % (6198)------------------------------
% 8.52/2.41 % (6200)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_5740 for (2991ds/1021Mi)
% 8.52/2.41 % (6193)Instruction limit reached!
% 8.52/2.41 % (6193)------------------------------
% 8.52/2.41 % (6193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.41 % (6193)Termination reason: Unknown
% 8.52/2.41 % (6193)Termination phase: Saturation
% 8.52/2.41
% 8.52/2.41 % (6193)Memory used [KB]: 7291
% 8.52/2.41 % (6193)Time elapsed: 0.062 s
% 8.52/2.41 % (6193)Instructions burned: 216 (million)
% 8.52/2.41 % (6193)------------------------------
% 8.52/2.41 % (6193)------------------------------
% 8.52/2.42 % (6196)Instruction limit reached!
% 8.52/2.42 % (6196)------------------------------
% 8.52/2.42 % (6196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.42 % (6196)Termination reason: Unknown
% 8.52/2.42 % (6196)Termination phase: Saturation
% 8.52/2.42
% 8.52/2.42 % (6196)Memory used [KB]: 7036
% 8.52/2.42 % (6196)Time elapsed: 0.052 s
% 8.52/2.42 % (6196)Instructions burned: 183 (million)
% 8.52/2.42 % (6196)------------------------------
% 8.52/2.42 % (6196)------------------------------
% 8.52/2.42 % (6201)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_5740 for (2991ds/267Mi)
% 8.52/2.43 % (6202)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_5740 for (2991ds/204Mi)
% 8.52/2.43 % (6197)Instruction limit reached!
% 8.52/2.43 % (6197)------------------------------
% 8.52/2.43 % (6197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.43 % (6197)Termination reason: Unknown
% 8.52/2.43 % (6197)Termination phase: Saturation
% 8.52/2.43
% 8.52/2.43 % (6197)Memory used [KB]: 2302
% 8.52/2.43 % (6197)Time elapsed: 0.050 s
% 8.52/2.43 % (6197)Instructions burned: 165 (million)
% 8.52/2.43 % (6197)------------------------------
% 8.52/2.43 % (6197)------------------------------
% 8.52/2.44 % (6203)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_5740 for (2991ds/26Mi)
% 8.52/2.45 % (6203)Instruction limit reached!
% 8.52/2.45 % (6203)------------------------------
% 8.52/2.45 % (6203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.45 % (6203)Termination reason: Unknown
% 8.52/2.45 % (6203)Termination phase: shuffling
% 8.52/2.45
% 8.52/2.45 % (6203)Memory used [KB]: 1791
% 8.52/2.45 % (6203)Time elapsed: 0.010 s
% 8.52/2.45 % (6203)Instructions burned: 28 (million)
% 8.52/2.45 % (6203)------------------------------
% 8.52/2.45 % (6203)------------------------------
% 8.52/2.46 % (6204)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_5740 for (2990ds/53Mi)
% 8.52/2.48 % (6204)Instruction limit reached!
% 8.52/2.48 % (6204)------------------------------
% 8.52/2.48 % (6204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.48 % (6204)Termination reason: Unknown
% 8.52/2.48 % (6204)Termination phase: Property scanning
% 8.52/2.48
% 8.52/2.48 % (6204)Memory used [KB]: 2046
% 8.52/2.48 % (6204)Time elapsed: 0.017 s
% 8.52/2.48 % (6204)Instructions burned: 53 (million)
% 8.52/2.48 % (6204)------------------------------
% 8.52/2.48 % (6204)------------------------------
% 8.52/2.49 % (6205)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_5740 for (2990ds/4436Mi)
% 8.52/2.49 % (6202)Instruction limit reached!
% 8.52/2.49 % (6202)------------------------------
% 8.52/2.49 % (6202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.49 % (6202)Termination reason: Unknown
% 8.52/2.49 % (6202)Termination phase: Saturation
% 8.52/2.49
% 8.52/2.49 % (6202)Memory used [KB]: 7036
% 8.52/2.49 % (6202)Time elapsed: 0.086 s
% 8.52/2.49 % (6202)Instructions burned: 204 (million)
% 8.52/2.49 % (6202)------------------------------
% 8.52/2.49 % (6202)------------------------------
% 8.85/2.50 % (6206)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_5740 for (2990ds/1539Mi)
% 8.85/2.51 % (6201)Instruction limit reached!
% 8.85/2.51 % (6201)------------------------------
% 8.85/2.51 % (6201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.51 % (6201)Termination reason: Unknown
% 8.85/2.51 % (6201)Termination phase: Saturation
% 8.85/2.51
% 8.85/2.51 % (6201)Memory used [KB]: 7419
% 8.85/2.51 % (6201)Time elapsed: 0.105 s
% 8.85/2.51 % (6201)Instructions burned: 268 (million)
% 8.85/2.51 % (6201)------------------------------
% 8.85/2.51 % (6201)------------------------------
% 8.85/2.51 % (6199)Instruction limit reached!
% 8.85/2.51 % (6199)------------------------------
% 8.85/2.51 % (6199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.51 % (6199)Termination reason: Unknown
% 8.85/2.51 % (6199)Termination phase: Saturation
% 8.85/2.51
% 8.85/2.51 % (6199)Memory used [KB]: 7547
% 8.85/2.51 % (6199)Time elapsed: 0.137 s
% 8.85/2.51 % (6199)Instructions burned: 368 (million)
% 8.85/2.51 % (6199)------------------------------
% 8.85/2.51 % (6199)------------------------------
% 8.85/2.52 % (6207)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_5740 for (2990ds/408Mi)
% 8.85/2.52 % (6208)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_5740 for (2990ds/5205Mi)
% 8.85/2.58 % (6188)Instruction limit reached!
% 8.85/2.58 % (6188)------------------------------
% 8.85/2.58 % (6188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.58 % (6188)Termination reason: Unknown
% 8.85/2.58 % (6188)Termination phase: Saturation
% 8.85/2.58
% 8.85/2.58 % (6188)Memory used [KB]: 8059
% 8.85/2.58 % (6188)Time elapsed: 0.302 s
% 8.85/2.58 % (6188)Instructions burned: 988 (million)
% 8.85/2.58 % (6188)------------------------------
% 8.85/2.58 % (6188)------------------------------
% 8.85/2.59 % (6209)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_5740 for (2989ds/1913Mi)
% 9.38/2.64 % (6207)Instruction limit reached!
% 9.38/2.64 % (6207)------------------------------
% 9.38/2.64 % (6207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.64 % (6207)Termination reason: Unknown
% 9.38/2.64 % (6207)Termination phase: Saturation
% 9.38/2.64
% 9.38/2.64 % (6207)Memory used [KB]: 8059
% 9.38/2.64 % (6207)Time elapsed: 0.128 s
% 9.38/2.64 % (6207)Instructions burned: 408 (million)
% 9.38/2.64 % (6207)------------------------------
% 9.38/2.64 % (6207)------------------------------
% 9.38/2.65 % (6195)Instruction limit reached!
% 9.38/2.65 % (6195)------------------------------
% 9.38/2.65 % (6195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.65 % (6195)Termination reason: Unknown
% 9.38/2.65 % (6195)Termination phase: Saturation
% 9.38/2.65
% 9.38/2.65 % (6195)Memory used [KB]: 7547
% 9.38/2.65 % (6195)Time elapsed: 0.292 s
% 9.38/2.65 % (6195)Instructions burned: 924 (million)
% 9.38/2.65 % (6195)------------------------------
% 9.38/2.65 % (6195)------------------------------
% 9.38/2.65 % (6210)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_5740 for (2988ds/4350Mi)
% 9.38/2.66 % (6211)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_5740 for (2988ds/68Mi)
% 9.38/2.68 % (6211)Instruction limit reached!
% 9.38/2.68 % (6211)------------------------------
% 9.38/2.68 % (6211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.68 % (6211)Termination reason: Unknown
% 9.38/2.68 % (6211)Termination phase: Property scanning
% 9.38/2.68
% 9.38/2.68 % (6211)Memory used [KB]: 2046
% 9.38/2.68 % (6211)Time elapsed: 0.021 s
% 9.38/2.68 % (6211)Instructions burned: 68 (million)
% 9.38/2.68 % (6211)------------------------------
% 9.38/2.68 % (6211)------------------------------
% 9.38/2.69 % (6212)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_5740 for (2988ds/358Mi)
% 9.85/2.73 % (6200)Instruction limit reached!
% 9.85/2.73 % (6200)------------------------------
% 9.85/2.73 % (6200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.85/2.73 % (6200)Termination reason: Unknown
% 9.85/2.73 % (6200)Termination phase: Saturation
% 9.85/2.73
% 9.85/2.73 % (6200)Memory used [KB]: 8187
% 9.85/2.73 % (6200)Time elapsed: 0.343 s
% 9.85/2.73 % (6200)Instructions burned: 1021 (million)
% 9.85/2.73 % (6200)------------------------------
% 9.85/2.73 % (6200)------------------------------
% 9.85/2.74 % (6213)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_5740 for (2988ds/31Mi)
% 9.85/2.75 % (6213)Instruction limit reached!
% 9.85/2.75 % (6213)------------------------------
% 9.85/2.75 % (6213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.85/2.75 % (6213)Termination reason: Unknown
% 9.85/2.75 % (6213)Termination phase: Property scanning
% 9.85/2.75
% 9.85/2.75 % (6213)Memory used [KB]: 1791
% 9.85/2.75 % (6213)Time elapsed: 0.011 s
% 9.85/2.75 % (6213)Instructions burned: 33 (million)
% 9.85/2.75 % (6213)------------------------------
% 9.85/2.75 % (6213)------------------------------
% 9.85/2.76 % (6214)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_5740 for (2987ds/279Mi)
% 10.20/2.80 % (6214)Refutation not found, incomplete strategy
% 10.20/2.80 % (6214)------------------------------
% 10.20/2.80 % (6214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.80 % (6214)Termination reason: Refutation not found, incomplete strategy
% 10.20/2.80
% 10.20/2.80
% 10.20/2.80 % (6214)Memory used [KB]: 7036
% 10.20/2.80 % (6214)Time elapsed: 0.045 s
% 10.20/2.80 % (6214)Instructions burned: 158 (million)
% 10.20/2.80 % (6214)------------------------------
% 10.20/2.80 % (6214)------------------------------
% 10.20/2.80 % (6212)Instruction limit reached!
% 10.20/2.80 % (6212)------------------------------
% 10.20/2.80 % (6212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.80 % (6212)Termination reason: Unknown
% 10.20/2.80 % (6212)Termination phase: Saturation
% 10.20/2.80
% 10.20/2.80 % (6212)Memory used [KB]: 7291
% 10.20/2.80 % (6212)Time elapsed: 0.116 s
% 10.20/2.80 % (6212)Instructions burned: 359 (million)
% 10.20/2.80 % (6212)------------------------------
% 10.20/2.80 % (6212)------------------------------
% 10.20/2.81 % (6215)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_5740 for (2987ds/258Mi)
% 10.20/2.81 % (6216)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_5740 for (2987ds/26Mi)
% 10.20/2.82 % (6216)Instruction limit reached!
% 10.20/2.82 % (6216)------------------------------
% 10.20/2.82 % (6216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.82 % (6216)Termination reason: Unknown
% 10.20/2.82 % (6216)Termination phase: shuffling
% 10.20/2.82
% 10.20/2.82 % (6216)Memory used [KB]: 1791
% 10.20/2.82 % (6216)Time elapsed: 0.008 s
% 10.20/2.82 % (6216)Instructions burned: 26 (million)
% 10.20/2.82 % (6216)------------------------------
% 10.20/2.82 % (6216)------------------------------
% 10.20/2.83 % (6217)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_5740 for (2987ds/995Mi)
% 10.39/2.90 % (6215)Instruction limit reached!
% 10.39/2.90 % (6215)------------------------------
% 10.39/2.90 % (6215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.90 % (6215)Termination reason: Unknown
% 10.39/2.90 % (6215)Termination phase: Saturation
% 10.39/2.90
% 10.39/2.90 % (6215)Memory used [KB]: 7291
% 10.39/2.90 % (6215)Time elapsed: 0.083 s
% 10.39/2.90 % (6215)Instructions burned: 259 (million)
% 10.39/2.90 % (6215)------------------------------
% 10.39/2.90 % (6215)------------------------------
% 10.39/2.91 % (6218)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_5740 for (2986ds/373Mi)
% 10.39/2.98 % (6206)Instruction limit reached!
% 10.39/2.98 % (6206)------------------------------
% 10.39/2.98 % (6206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.98 % (6206)Termination reason: Unknown
% 10.39/2.98 % (6206)Termination phase: Saturation
% 10.39/2.98
% 10.39/2.98 % (6206)Memory used [KB]: 9978
% 10.39/2.98 % (6206)Time elapsed: 0.480 s
% 10.39/2.98 % (6206)Instructions burned: 1539 (million)
% 10.39/2.98 % (6206)------------------------------
% 10.39/2.98 % (6206)------------------------------
% 10.39/2.99 % (6219)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_5740 for (2985ds/253Mi)
% 10.39/3.02 % (6218)Instruction limit reached!
% 10.39/3.02 % (6218)------------------------------
% 10.39/3.02 % (6218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/3.02 % (6218)Termination reason: Unknown
% 10.39/3.02 % (6218)Termination phase: Saturation
% 10.39/3.02
% 10.39/3.02 % (6218)Memory used [KB]: 7547
% 10.39/3.02 % (6218)Time elapsed: 0.116 s
% 10.39/3.02 % (6218)Instructions burned: 373 (million)
% 10.39/3.02 % (6218)------------------------------
% 10.39/3.02 % (6218)------------------------------
% 13.17/3.03 % (6220)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_5740 for (2985ds/832Mi)
% 13.17/3.06 % (6219)Instruction limit reached!
% 13.17/3.06 % (6219)------------------------------
% 13.17/3.06 % (6219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.06 % (6219)Termination reason: Unknown
% 13.17/3.06 % (6219)Termination phase: Saturation
% 13.17/3.06
% 13.17/3.06 % (6219)Memory used [KB]: 7547
% 13.17/3.06 % (6219)Time elapsed: 0.072 s
% 13.17/3.06 % (6219)Instructions burned: 255 (million)
% 13.17/3.06 % (6219)------------------------------
% 13.17/3.06 % (6219)------------------------------
% 13.17/3.07 % (6221)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_5740 for (2984ds/668Mi)
% 13.74/3.13 % (6217)Instruction limit reached!
% 13.74/3.13 % (6217)------------------------------
% 13.74/3.13 % (6217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.13 % (6217)Termination reason: Unknown
% 13.74/3.13 % (6217)Termination phase: Saturation
% 13.74/3.13
% 13.74/3.13 % (6217)Memory used [KB]: 9338
% 13.74/3.13 % (6217)Time elapsed: 0.302 s
% 13.74/3.13 % (6217)Instructions burned: 996 (million)
% 13.74/3.13 % (6217)------------------------------
% 13.74/3.13 % (6217)------------------------------
% 13.74/3.14 % (6222)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=40:si=on:rtra=on_0 on DTF2THF_5740 for (2984ds/40Mi)
% 13.74/3.15 % (6222)Instruction limit reached!
% 13.74/3.15 % (6222)------------------------------
% 13.74/3.15 % (6222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.15 % (6222)Termination reason: Unknown
% 13.74/3.15 % (6222)Termination phase: Property scanning
% 13.74/3.15
% 13.74/3.15 % (6222)Memory used [KB]: 2046
% 13.74/3.15 % (6222)Time elapsed: 0.013 s
% 13.74/3.15 % (6222)Instructions burned: 43 (million)
% 13.74/3.15 % (6222)------------------------------
% 13.74/3.15 % (6222)------------------------------
% 13.74/3.16 % (6223)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_5740 for (2983ds/294Mi)
% 13.74/3.18 % (6209)Instruction limit reached!
% 13.74/3.18 % (6209)------------------------------
% 13.74/3.18 % (6209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.18 % (6209)Termination reason: Unknown
% 13.74/3.18 % (6209)Termination phase: Saturation
% 13.74/3.18
% 13.74/3.18 % (6209)Memory used [KB]: 3454
% 13.74/3.18 % (6209)Time elapsed: 0.597 s
% 13.74/3.18 % (6209)Instructions burned: 1915 (million)
% 13.74/3.18 % (6209)------------------------------
% 13.74/3.18 % (6209)------------------------------
% 13.74/3.19 % (6224)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_5740 for (2983ds/187Mi)
% 13.74/3.19 % (6223)Refutation not found, incomplete strategy
% 13.74/3.19 % (6223)------------------------------
% 13.74/3.19 % (6223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.19 % (6223)Termination reason: Refutation not found, incomplete strategy
% 13.74/3.19
% 13.74/3.19
% 13.74/3.19 % (6223)Memory used [KB]: 6908
% 13.74/3.19 % (6223)Time elapsed: 0.031 s
% 13.74/3.19 % (6223)Instructions burned: 108 (million)
% 13.74/3.19 % (6223)------------------------------
% 13.74/3.19 % (6223)------------------------------
% 14.09/3.20 % (6225)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_5740 for (2983ds/371Mi)
% 14.09/3.25 % (6224)Instruction limit reached!
% 14.09/3.25 % (6224)------------------------------
% 14.09/3.25 % (6224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.25 % (6224)Termination reason: Unknown
% 14.09/3.25 % (6224)Termination phase: Saturation
% 14.09/3.25
% 14.09/3.25 % (6224)Memory used [KB]: 7036
% 14.09/3.25 % (6224)Time elapsed: 0.059 s
% 14.09/3.25 % (6224)Instructions burned: 188 (million)
% 14.09/3.25 % (6224)------------------------------
% 14.09/3.25 % (6224)------------------------------
% 14.09/3.26 % (6226)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_5740 for (2982ds/1827Mi)
% 14.09/3.27 % (6221)Instruction limit reached!
% 14.09/3.27 % (6221)------------------------------
% 14.09/3.27 % (6221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.27 % (6221)Termination reason: Unknown
% 14.09/3.27 % (6221)Termination phase: Saturation
% 14.09/3.27
% 14.09/3.27 % (6221)Memory used [KB]: 13816
% 14.09/3.27 % (6221)Time elapsed: 0.200 s
% 14.09/3.27 % (6221)Instructions burned: 668 (million)
% 14.09/3.27 % (6221)------------------------------
% 14.09/3.27 % (6221)------------------------------
% 14.09/3.28 % (6227)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_5740 for (2982ds/70Mi)
% 14.09/3.29 % (6220)Instruction limit reached!
% 14.09/3.29 % (6220)------------------------------
% 14.09/3.29 % (6220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.29 % (6220)Termination reason: Unknown
% 14.09/3.29 % (6220)Termination phase: Saturation
% 14.09/3.29
% 14.09/3.29 % (6220)Memory used [KB]: 8315
% 14.09/3.29 % (6220)Time elapsed: 0.256 s
% 14.09/3.29 % (6220)Instructions burned: 832 (million)
% 14.09/3.29 % (6220)------------------------------
% 14.09/3.29 % (6220)------------------------------
% 14.09/3.30 % (6228)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_5740 for (2982ds/316Mi)
% 14.09/3.30 % (6227)Instruction limit reached!
% 14.09/3.30 % (6227)------------------------------
% 14.09/3.30 % (6227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.30 % (6227)Termination reason: Unknown
% 14.09/3.30 % (6227)Termination phase: Preprocessing 3
% 14.09/3.30
% 14.09/3.30 % (6227)Memory used [KB]: 2174
% 14.09/3.30 % (6227)Time elapsed: 0.021 s
% 14.09/3.30 % (6227)Instructions burned: 73 (million)
% 14.09/3.30 % (6227)------------------------------
% 14.09/3.30 % (6227)------------------------------
% 14.97/3.31 % (6229)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_5740 for (2982ds/932Mi)
% 14.97/3.32 % (6225)Instruction limit reached!
% 14.97/3.32 % (6225)------------------------------
% 14.97/3.32 % (6225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.97/3.32 % (6225)Termination reason: Unknown
% 14.97/3.32 % (6225)Termination phase: Saturation
% 14.97/3.32
% 14.97/3.32 % (6225)Memory used [KB]: 7291
% 14.97/3.32 % (6225)Time elapsed: 0.116 s
% 14.97/3.32 % (6225)Instructions burned: 371 (million)
% 14.97/3.32 % (6225)------------------------------
% 14.97/3.32 % (6225)------------------------------
% 14.97/3.33 % (6230)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_5740 for (2982ds/4714Mi)
% 14.97/3.35 % (6228)Refutation not found, incomplete strategy
% 14.97/3.35 % (6228)------------------------------
% 14.97/3.35 % (6228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.97/3.35 % (6228)Termination reason: Refutation not found, incomplete strategy
% 14.97/3.35
% 14.97/3.35
% 14.97/3.35 % (6228)Memory used [KB]: 7419
% 14.97/3.35 % (6228)Time elapsed: 0.055 s
% 14.97/3.35 % (6228)Instructions burned: 199 (million)
% 14.97/3.35 % (6228)------------------------------
% 14.97/3.35 % (6228)------------------------------
% 14.97/3.36 % (6231)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_5740 for (2981ds/8250Mi)
% 14.97/3.38 % (6230)Refutation not found, incomplete strategy
% 14.97/3.38 % (6230)------------------------------
% 14.97/3.38 % (6230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.97/3.38 % (6230)Termination reason: Refutation not found, incomplete strategy
% 14.97/3.38
% 14.97/3.38
% 14.97/3.38 % (6230)Memory used [KB]: 7675
% 14.97/3.38 % (6230)Time elapsed: 0.058 s
% 14.97/3.38 % (6230)Instructions burned: 203 (million)
% 14.97/3.38 % (6230)------------------------------
% 14.97/3.38 % (6230)------------------------------
% 14.97/3.39 % (6232)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_5740 for (2981ds/770Mi)
% 15.83/3.58 % (6229)Instruction limit reached!
% 15.83/3.58 % (6229)------------------------------
% 15.83/3.58 % (6229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.83/3.58 % (6229)Termination reason: Unknown
% 15.83/3.58 % (6229)Termination phase: Saturation
% 15.83/3.58
% 15.83/3.58 % (6229)Memory used [KB]: 9338
% 15.83/3.58 % (6229)Time elapsed: 0.274 s
% 15.83/3.58 % (6229)Instructions burned: 935 (million)
% 15.83/3.58 % (6229)------------------------------
% 15.83/3.58 % (6229)------------------------------
% 15.83/3.59 % (6233)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_5740 for (2979ds/794Mi)
% 16.41/3.62 % (6232)Instruction limit reached!
% 16.41/3.62 % (6232)------------------------------
% 16.41/3.62 % (6232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.41/3.62 % (6232)Termination reason: Unknown
% 16.41/3.62 % (6232)Termination phase: Saturation
% 16.41/3.62
% 16.41/3.62 % (6232)Memory used [KB]: 8443
% 16.41/3.62 % (6232)Time elapsed: 0.230 s
% 16.41/3.62 % (6232)Instructions burned: 772 (million)
% 16.41/3.62 % (6232)------------------------------
% 16.41/3.62 % (6232)------------------------------
% 16.41/3.63 % (6234)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_5740 for (2979ds/464Mi)
% 16.94/3.78 % (6234)Instruction limit reached!
% 16.94/3.78 % (6234)------------------------------
% 16.94/3.78 % (6234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.94/3.78 % (6234)Termination reason: Unknown
% 16.94/3.78 % (6234)Termination phase: Saturation
% 16.94/3.78
% 16.94/3.78 % (6234)Memory used [KB]: 7547
% 16.94/3.78 % (6234)Time elapsed: 0.145 s
% 16.94/3.78 % (6234)Instructions burned: 465 (million)
% 16.94/3.78 % (6234)------------------------------
% 16.94/3.78 % (6234)------------------------------
% 16.94/3.79 % (6235)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_5740 for (2977ds/1376Mi)
% 17.40/3.84 % (6233)Instruction limit reached!
% 17.40/3.84 % (6233)------------------------------
% 17.40/3.84 % (6233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.84 % (6233)Termination reason: Unknown
% 17.40/3.84 % (6233)Termination phase: Saturation
% 17.40/3.84
% 17.40/3.84 % (6233)Memory used [KB]: 4989
% 17.40/3.84 % (6233)Time elapsed: 0.249 s
% 17.40/3.84 % (6233)Instructions burned: 796 (million)
% 17.40/3.84 % (6233)------------------------------
% 17.40/3.84 % (6233)------------------------------
% 17.40/3.84 % (6226)Instruction limit reached!
% 17.40/3.84 % (6226)------------------------------
% 17.40/3.84 % (6226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.84 % (6226)Termination reason: Unknown
% 17.40/3.84 % (6226)Termination phase: Saturation
% 17.40/3.84
% 17.40/3.84 % (6226)Memory used [KB]: 9083
% 17.40/3.84 % (6226)Time elapsed: 0.580 s
% 17.40/3.84 % (6226)Instructions burned: 1828 (million)
% 17.40/3.84 % (6226)------------------------------
% 17.40/3.84 % (6226)------------------------------
% 17.40/3.85 % (6236)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_5740 for (2977ds/906Mi)
% 17.40/3.85 % (6237)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_5740 for (2977ds/434Mi)
% 17.40/3.85 % (6205)Instruction limit reached!
% 17.40/3.85 % (6205)------------------------------
% 17.40/3.85 % (6205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.85 % (6205)Termination reason: Unknown
% 17.40/3.85 % (6205)Termination phase: Saturation
% 17.40/3.85
% 17.40/3.85 % (6205)Memory used [KB]: 10874
% 17.40/3.85 % (6205)Time elapsed: 1.370 s
% 17.40/3.85 % (6205)Instructions burned: 4437 (million)
% 17.40/3.85 % (6205)------------------------------
% 17.40/3.85 % (6205)------------------------------
% 17.40/3.86 % (6238)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_5740 for (2976ds/865Mi)
% 18.52/3.97 % (6210)Instruction limit reached!
% 18.52/3.97 % (6210)------------------------------
% 18.52/3.97 % (6210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.52/3.97 % (6210)Termination reason: Unknown
% 18.52/3.97 % (6210)Termination phase: Saturation
% 18.52/3.97
% 18.52/3.97 % (6210)Memory used [KB]: 12665
% 18.52/3.97 % (6210)Time elapsed: 1.315 s
% 18.52/3.97 % (6210)Instructions burned: 4351 (million)
% 18.52/3.97 % (6210)------------------------------
% 18.52/3.97 % (6210)------------------------------
% 18.52/3.98 % (6239)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_5740 for (2975ds/593Mi)
% 18.52/3.98 % (6237)Instruction limit reached!
% 18.52/3.98 % (6237)------------------------------
% 18.52/3.98 % (6237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.52/3.98 % (6237)Termination reason: Unknown
% 18.52/3.98 % (6237)Termination phase: Saturation
% 18.52/3.98
% 18.52/3.98 % (6237)Memory used [KB]: 7164
% 18.52/3.98 % (6237)Time elapsed: 0.137 s
% 18.52/3.98 % (6237)Instructions burned: 435 (million)
% 18.52/3.98 % (6237)------------------------------
% 18.52/3.98 % (6237)------------------------------
% 18.52/3.99 % (6240)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_5740 for (2975ds/443Mi)
% 20.18/4.10 % (6208)Instruction limit reached!
% 20.18/4.10 % (6208)------------------------------
% 20.18/4.10 % (6208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.10 % (6208)Termination reason: Unknown
% 20.18/4.10 % (6208)Termination phase: Saturation
% 20.18/4.10
% 20.18/4.10 % (6208)Memory used [KB]: 13816
% 20.18/4.10 % (6208)Time elapsed: 1.580 s
% 20.18/4.10 % (6208)Instructions burned: 5205 (million)
% 20.18/4.10 % (6208)------------------------------
% 20.18/4.10 % (6208)------------------------------
% 20.18/4.11 % (6241)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_5740 for (2974ds/594Mi)
% 20.18/4.12 % (6238)Instruction limit reached!
% 20.18/4.12 % (6238)------------------------------
% 20.18/4.12 % (6238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.12 % (6238)Termination reason: Unknown
% 20.18/4.12 % (6238)Termination phase: Saturation
% 20.18/4.12
% 20.18/4.12 % (6238)Memory used [KB]: 8315
% 20.18/4.12 % (6238)Time elapsed: 0.257 s
% 20.18/4.12 % (6238)Instructions burned: 865 (million)
% 20.18/4.12 % (6238)------------------------------
% 20.18/4.12 % (6238)------------------------------
% 20.89/4.13 % (6242)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_5740 for (2974ds/327Mi)
% 20.89/4.13 % (6240)Instruction limit reached!
% 20.89/4.13 % (6240)------------------------------
% 20.89/4.13 % (6240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.13 % (6240)Termination reason: Unknown
% 20.89/4.13 % (6240)Termination phase: Saturation
% 20.89/4.13
% 20.89/4.13 % (6240)Memory used [KB]: 7291
% 20.89/4.13 % (6240)Time elapsed: 0.142 s
% 20.89/4.13 % (6240)Instructions burned: 445 (million)
% 20.89/4.13 % (6240)------------------------------
% 20.89/4.13 % (6240)------------------------------
% 20.89/4.14 % (6243)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_5740 for (2974ds/5411Mi)
% 20.89/4.15 % (6239)Instruction limit reached!
% 20.89/4.15 % (6239)------------------------------
% 20.89/4.15 % (6239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.15 % (6239)Termination reason: Unknown
% 20.89/4.15 % (6239)Termination phase: Saturation
% 20.89/4.15
% 20.89/4.15 % (6239)Memory used [KB]: 8315
% 20.89/4.15 % (6239)Time elapsed: 0.179 s
% 20.89/4.15 % (6239)Instructions burned: 593 (million)
% 20.89/4.15 % (6239)------------------------------
% 20.89/4.15 % (6239)------------------------------
% 20.89/4.16 % (6236)Instruction limit reached!
% 20.89/4.16 % (6236)------------------------------
% 20.89/4.16 % (6236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.16 % (6236)Termination reason: Unknown
% 20.89/4.16 % (6236)Termination phase: Saturation
% 20.89/4.16
% 20.89/4.16 % (6236)Memory used [KB]: 10490
% 20.89/4.16 % (6236)Time elapsed: 0.313 s
% 20.89/4.16 % (6236)Instructions burned: 907 (million)
% 20.89/4.16 % (6236)------------------------------
% 20.89/4.16 % (6236)------------------------------
% 20.89/4.16 % (6244)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_5740 for (2973ds/1762Mi)
% 20.89/4.17 % (6245)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_5740 for (2973ds/96Mi)
% 20.89/4.19 % (6245)Instruction limit reached!
% 20.89/4.19 % (6245)------------------------------
% 20.89/4.19 % (6245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.19 % (6245)Termination reason: Unknown
% 20.89/4.19 % (6245)Termination phase: Property scanning
% 20.89/4.19
% 20.89/4.19 % (6245)Memory used [KB]: 2174
% 20.89/4.19 % (6245)Time elapsed: 0.028 s
% 20.89/4.19 % (6245)Instructions burned: 97 (million)
% 20.89/4.19 % (6245)------------------------------
% 20.89/4.19 % (6245)------------------------------
% 21.18/4.20 % (6246)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_5740 for (2973ds/503Mi)
% 21.18/4.21 % (6235)Instruction limit reached!
% 21.18/4.21 % (6235)------------------------------
% 21.18/4.21 % (6235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.21 % (6235)Termination reason: Unknown
% 21.18/4.21 % (6235)Termination phase: Saturation
% 21.18/4.21
% 21.18/4.21 % (6235)Memory used [KB]: 10874
% 21.18/4.21 % (6235)Time elapsed: 0.426 s
% 21.18/4.21 % (6235)Instructions burned: 1378 (million)
% 21.18/4.21 % (6235)------------------------------
% 21.18/4.21 % (6235)------------------------------
% 21.18/4.22 % (6247)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_5740 for (2973ds/90Mi)
% 21.18/4.23 % (6242)Instruction limit reached!
% 21.18/4.23 % (6242)------------------------------
% 21.18/4.23 % (6242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.23 % (6242)Termination reason: Unknown
% 21.18/4.23 % (6242)Termination phase: Saturation
% 21.18/4.23
% 21.18/4.23 % (6242)Memory used [KB]: 7547
% 21.18/4.23 % (6242)Time elapsed: 0.105 s
% 21.18/4.23 % (6242)Instructions burned: 327 (million)
% 21.18/4.23 % (6242)------------------------------
% 21.18/4.23 % (6242)------------------------------
% 21.18/4.24 % (6248)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_5740 for (2973ds/593Mi)
% 21.18/4.25 % (6247)Instruction limit reached!
% 21.18/4.25 % (6247)------------------------------
% 21.18/4.25 % (6247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.25 % (6247)Termination reason: Unknown
% 21.18/4.25 % (6247)Termination phase: Saturation
% 21.18/4.25
% 21.18/4.25 % (6247)Memory used [KB]: 6652
% 21.18/4.25 % (6247)Time elapsed: 0.029 s
% 21.18/4.25 % (6247)Instructions burned: 92 (million)
% 21.18/4.25 % (6247)------------------------------
% 21.18/4.25 % (6247)------------------------------
% 21.18/4.26 % (6249)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_5740 for (2972ds/1512Mi)
% 21.47/4.30 % (6241)Instruction limit reached!
% 21.47/4.30 % (6241)------------------------------
% 21.47/4.30 % (6241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.47/4.30 % (6241)Termination reason: Unknown
% 21.47/4.30 % (6241)Termination phase: Saturation
% 21.47/4.30
% 21.47/4.30 % (6241)Memory used [KB]: 7419
% 21.47/4.30 % (6241)Time elapsed: 0.190 s
% 21.47/4.30 % (6241)Instructions burned: 595 (million)
% 21.47/4.30 % (6241)------------------------------
% 21.47/4.30 % (6241)------------------------------
% 21.47/4.31 % (6250)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_5740 for (2972ds/569Mi)
% 21.47/4.36 % (6246)Instruction limit reached!
% 21.47/4.36 % (6246)------------------------------
% 21.47/4.36 % (6246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.47/4.36 % (6246)Termination reason: Unknown
% 21.47/4.36 % (6246)Termination phase: Saturation
% 21.47/4.36
% 21.47/4.36 % (6246)Memory used [KB]: 7931
% 21.47/4.36 % (6246)Time elapsed: 0.155 s
% 21.47/4.36 % (6246)Instructions burned: 504 (million)
% 21.47/4.36 % (6246)------------------------------
% 21.47/4.36 % (6246)------------------------------
% 21.47/4.37 % (6251)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_5740 for (2971ds/501Mi)
% 21.93/4.43 % (6248)Instruction limit reached!
% 21.93/4.43 % (6248)------------------------------
% 21.93/4.43 % (6248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.43 % (6248)Termination reason: Unknown
% 21.93/4.43 % (6248)Termination phase: Saturation
% 21.93/4.43
% 21.93/4.43 % (6248)Memory used [KB]: 8059
% 21.93/4.43 % (6248)Time elapsed: 0.189 s
% 21.93/4.43 % (6248)Instructions burned: 595 (million)
% 21.93/4.43 % (6248)------------------------------
% 21.93/4.43 % (6248)------------------------------
% 21.93/4.44 % (6252)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_5740 for (2971ds/562Mi)
% 21.93/4.48 % (6250)Instruction limit reached!
% 21.93/4.48 % (6250)------------------------------
% 21.93/4.48 % (6250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.48 % (6250)Termination reason: Unknown
% 21.93/4.48 % (6250)Termination phase: Saturation
% 21.93/4.48
% 21.93/4.48 % (6250)Memory used [KB]: 8059
% 21.93/4.48 % (6250)Time elapsed: 0.170 s
% 21.93/4.48 % (6250)Instructions burned: 569 (million)
% 21.93/4.48 % (6250)------------------------------
% 21.93/4.48 % (6250)------------------------------
% 21.93/4.49 % (6253)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_5740 for (2970ds/406Mi)
% 22.41/4.52 % (6251)Instruction limit reached!
% 22.41/4.52 % (6251)------------------------------
% 22.41/4.52 % (6251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.41/4.52 % (6251)Termination reason: Unknown
% 22.41/4.52 % (6251)Termination phase: Saturation
% 22.41/4.52
% 22.41/4.52 % (6251)Memory used [KB]: 8315
% 22.41/4.52 % (6251)Time elapsed: 0.155 s
% 22.41/4.52 % (6251)Instructions burned: 504 (million)
% 22.41/4.52 % (6251)------------------------------
% 22.41/4.52 % (6251)------------------------------
% 22.41/4.53 % (6254)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_5740 for (2970ds/582Mi)
% 22.67/4.60 % (6252)Instruction limit reached!
% 22.67/4.60 % (6252)------------------------------
% 22.67/4.60 % (6252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.67/4.60 % (6252)Termination reason: Unknown
% 22.67/4.60 % (6252)Termination phase: Saturation
% 22.67/4.60
% 22.67/4.60 % (6252)Memory used [KB]: 7803
% 22.67/4.60 % (6252)Time elapsed: 0.164 s
% 22.67/4.60 % (6252)Instructions burned: 562 (million)
% 22.67/4.60 % (6252)------------------------------
% 22.67/4.60 % (6252)------------------------------
% 22.67/4.61 % (6255)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_5740 for (2969ds/456Mi)
% 22.67/4.61 % (6253)Instruction limit reached!
% 22.67/4.61 % (6253)------------------------------
% 22.67/4.61 % (6253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.67/4.61 % (6253)Termination reason: Unknown
% 22.67/4.61 % (6253)Termination phase: Saturation
% 22.67/4.61
% 22.67/4.61 % (6253)Memory used [KB]: 7675
% 22.67/4.61 % (6253)Time elapsed: 0.125 s
% 22.67/4.61 % (6253)Instructions burned: 407 (million)
% 22.67/4.61 % (6253)------------------------------
% 22.67/4.61 % (6253)------------------------------
% 22.67/4.62 % (6256)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_5740 for (2969ds/393Mi)
% 22.67/4.69 % (6244)Instruction limit reached!
% 22.67/4.69 % (6244)------------------------------
% 22.67/4.69 % (6244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.67/4.69 % (6244)Termination reason: Unknown
% 22.67/4.69 % (6244)Termination phase: Saturation
% 22.67/4.69
% 22.67/4.69 % (6244)Memory used [KB]: 10746
% 22.67/4.69 % (6244)Time elapsed: 0.527 s
% 22.67/4.69 % (6244)Instructions burned: 1764 (million)
% 22.67/4.69 % (6244)------------------------------
% 22.67/4.69 % (6244)------------------------------
% 23.63/4.70 % (6257)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_5740 for (2968ds/1335Mi)
% 23.63/4.72 % (6254)Instruction limit reached!
% 23.63/4.72 % (6254)------------------------------
% 23.63/4.72 % (6254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.72 % (6254)Termination reason: Unknown
% 23.63/4.72 % (6254)Termination phase: Saturation
% 23.63/4.72
% 23.63/4.72 % (6254)Memory used [KB]: 7803
% 23.63/4.72 % (6254)Time elapsed: 0.187 s
% 23.63/4.72 % (6254)Instructions burned: 585 (million)
% 23.63/4.72 % (6254)------------------------------
% 23.63/4.72 % (6254)------------------------------
% 23.63/4.73 % (6258)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_5740 for (2968ds/3373Mi)
% 23.63/4.73 % (6249)Instruction limit reached!
% 23.63/4.73 % (6249)------------------------------
% 23.63/4.73 % (6249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.73 % (6249)Termination reason: Unknown
% 23.63/4.73 % (6249)Termination phase: Saturation
% 23.63/4.73
% 23.63/4.73 % (6249)Memory used [KB]: 8315
% 23.63/4.73 % (6249)Time elapsed: 0.472 s
% 23.63/4.73 % (6249)Instructions burned: 1514 (million)
% 23.63/4.73 % (6249)------------------------------
% 23.63/4.73 % (6249)------------------------------
% 23.63/4.74 % (6256)Instruction limit reached!
% 23.63/4.74 % (6256)------------------------------
% 23.63/4.74 % (6256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.74 % (6256)Termination reason: Unknown
% 23.63/4.74 % (6256)Termination phase: Saturation
% 23.63/4.74
% 23.63/4.74 % (6256)Memory used [KB]: 7419
% 23.63/4.74 % (6256)Time elapsed: 0.115 s
% 23.63/4.74 % (6256)Instructions burned: 395 (million)
% 23.63/4.74 % (6256)------------------------------
% 23.63/4.74 % (6256)------------------------------
% 23.63/4.74 % (6259)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_5740 for (2968ds/474Mi)
% 23.63/4.75 % (6260)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_5740 for (2968ds/157Mi)
% 23.63/4.75 % (6255)Instruction limit reached!
% 23.63/4.75 % (6255)------------------------------
% 23.63/4.75 % (6255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.75 % (6255)Termination reason: Unknown
% 23.63/4.75 % (6255)Termination phase: Saturation
% 23.63/4.75
% 23.63/4.75 % (6255)Memory used [KB]: 7675
% 23.63/4.75 % (6255)Time elapsed: 0.141 s
% 23.63/4.75 % (6255)Instructions burned: 456 (million)
% 23.63/4.75 % (6255)------------------------------
% 23.63/4.75 % (6255)------------------------------
% 23.63/4.76 % (6261)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_5740 for (2967ds/590Mi)
% 23.63/4.79 % (6260)Instruction limit reached!
% 23.63/4.79 % (6260)------------------------------
% 23.63/4.79 % (6260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.79 % (6260)Termination reason: Unknown
% 23.63/4.79 % (6260)Termination phase: Saturation
% 23.63/4.79
% 23.63/4.79 % (6260)Memory used [KB]: 6908
% 23.63/4.79 % (6260)Time elapsed: 0.044 s
% 23.63/4.79 % (6260)Instructions burned: 157 (million)
% 23.63/4.79 % (6260)------------------------------
% 23.63/4.79 % (6260)------------------------------
% 24.72/4.80 % (6262)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_5740 for (2967ds/104Mi)
% 24.72/4.83 % (6262)Instruction limit reached!
% 24.72/4.83 % (6262)------------------------------
% 24.72/4.83 % (6262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.72/4.83 % (6262)Termination reason: Unknown
% 24.72/4.83 % (6262)Termination phase: Saturation
% 24.72/4.83
% 24.72/4.83 % (6262)Memory used [KB]: 2430
% 24.72/4.83 % (6262)Time elapsed: 0.032 s
% 24.72/4.83 % (6262)Instructions burned: 106 (million)
% 24.72/4.83 % (6262)------------------------------
% 24.72/4.83 % (6262)------------------------------
% 24.72/4.84 % (6263)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_5740 for (2967ds/414Mi)
% 24.72/4.89 % (6259)Instruction limit reached!
% 24.72/4.89 % (6259)------------------------------
% 24.72/4.89 % (6259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.72/4.89 % (6259)Termination reason: Unknown
% 24.72/4.89 % (6259)Termination phase: Saturation
% 24.72/4.89
% 24.72/4.89 % (6259)Memory used [KB]: 8059
% 24.72/4.89 % (6259)Time elapsed: 0.147 s
% 24.72/4.89 % (6259)Instructions burned: 475 (million)
% 24.72/4.89 % (6259)------------------------------
% 24.72/4.89 % (6259)------------------------------
% 24.72/4.90 % (6264)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_5740 for (2966ds/715Mi)
% 25.01/4.94 % (6261)Instruction limit reached!
% 25.01/4.94 % (6261)------------------------------
% 25.01/4.94 % (6261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.01/4.94 % (6261)Termination reason: Unknown
% 25.01/4.94 % (6261)Termination phase: Saturation
% 25.01/4.94
% 25.01/4.94 % (6261)Memory used [KB]: 8315
% 25.01/4.94 % (6261)Time elapsed: 0.175 s
% 25.01/4.94 % (6261)Instructions burned: 592 (million)
% 25.01/4.94 % (6261)------------------------------
% 25.01/4.94 % (6261)------------------------------
% 25.01/4.95 % (6265)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_5740 for (2966ds/961Mi)
% 25.01/4.96 % (6263)Instruction limit reached!
% 25.01/4.96 % (6263)------------------------------
% 25.01/4.96 % (6263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.01/4.96 % (6263)Termination reason: Unknown
% 25.01/4.96 % (6263)Termination phase: Saturation
% 25.01/4.96
% 25.01/4.96 % (6263)Memory used [KB]: 7675
% 25.01/4.96 % (6263)Time elapsed: 0.123 s
% 25.01/4.96 % (6263)Instructions burned: 416 (million)
% 25.01/4.96 % (6263)------------------------------
% 25.01/4.96 % (6263)------------------------------
% 25.01/4.97 % (6266)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_5740 for (2965ds/1213Mi)
% 27.20/5.10 % (6257)Instruction limit reached!
% 27.20/5.10 % (6257)------------------------------
% 27.20/5.10 % (6257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.20/5.10 % (6257)Termination reason: Unknown
% 27.20/5.10 % (6257)Termination phase: Saturation
% 27.20/5.10
% 27.20/5.10 % (6257)Memory used [KB]: 8955
% 27.20/5.10 % (6257)Time elapsed: 0.401 s
% 27.20/5.10 % (6257)Instructions burned: 1335 (million)
% 27.20/5.10 % (6257)------------------------------
% 27.20/5.10 % (6257)------------------------------
% 27.20/5.11 % (6267)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_5740 for (2964ds/1979Mi)
% 27.20/5.12 % (6264)Instruction limit reached!
% 27.20/5.12 % (6264)------------------------------
% 27.20/5.12 % (6264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.20/5.12 % (6264)Termination reason: Unknown
% 27.20/5.12 % (6264)Termination phase: Saturation
% 27.20/5.12
% 27.20/5.12 % (6264)Memory used [KB]: 3709
% 27.20/5.12 % (6264)Time elapsed: 0.229 s
% 27.20/5.12 % (6264)Instructions burned: 715 (million)
% 27.20/5.12 % (6264)------------------------------
% 27.20/5.12 % (6264)------------------------------
% 27.93/5.13 % (6268)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_5740 for (2964ds/481Mi)
% 28.29/5.25 % (6265)Instruction limit reached!
% 28.29/5.25 % (6265)------------------------------
% 28.29/5.25 % (6265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.29/5.25 % (6265)Termination reason: Unknown
% 28.29/5.25 % (6265)Termination phase: Saturation
% 28.29/5.25
% 28.29/5.25 % (6265)Memory used [KB]: 7931
% 28.29/5.25 % (6265)Time elapsed: 0.301 s
% 28.29/5.25 % (6265)Instructions burned: 963 (million)
% 28.29/5.25 % (6265)------------------------------
% 28.29/5.25 % (6265)------------------------------
% 28.29/5.25 % (6231)Instruction limit reached!
% 28.29/5.25 % (6231)------------------------------
% 28.29/5.25 % (6231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.29/5.25 % (6231)Termination reason: Unknown
% 28.29/5.25 % (6231)Termination phase: Saturation
% 28.29/5.25
% 28.29/5.25 % (6231)Memory used [KB]: 10490
% 28.29/5.25 % (6231)Time elapsed: 1.889 s
% 28.29/5.25 % (6231)Instructions burned: 8252 (million)
% 28.29/5.25 % (6231)------------------------------
% 28.29/5.25 % (6231)------------------------------
% 28.29/5.26 % (6269)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_5740 for (2962ds/783Mi)
% 28.29/5.26 % (6270)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_5740 for (2962ds/432Mi)
% 28.29/5.28 % (6268)Instruction limit reached!
% 28.29/5.28 % (6268)------------------------------
% 28.29/5.28 % (6268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.29/5.28 % (6268)Termination reason: Unknown
% 28.29/5.28 % (6268)Termination phase: Saturation
% 28.29/5.28
% 28.29/5.28 % (6268)Memory used [KB]: 7675
% 28.29/5.28 % (6268)Time elapsed: 0.150 s
% 28.29/5.28 % (6268)Instructions burned: 481 (million)
% 28.29/5.28 % (6268)------------------------------
% 28.29/5.28 % (6268)------------------------------
% 28.29/5.29 % (6271)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_5740 for (2962ds/1670Mi)
% 28.86/5.35 % (6266)Instruction limit reached!
% 28.86/5.35 % (6266)------------------------------
% 28.86/5.35 % (6266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.86/5.35 % (6266)Termination reason: Unknown
% 28.86/5.35 % (6266)Termination phase: Saturation
% 28.86/5.35
% 28.86/5.35 % (6266)Memory used [KB]: 8699
% 28.86/5.35 % (6266)Time elapsed: 0.384 s
% 28.86/5.35 % (6266)Instructions burned: 1214 (million)
% 28.86/5.35 % (6266)------------------------------
% 28.86/5.35 % (6266)------------------------------
% 28.86/5.36 % (6272)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_5740 for (2961ds/90Mi)
% 28.86/5.39 % (6272)Instruction limit reached!
% 28.86/5.39 % (6272)------------------------------
% 28.86/5.39 % (6272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.86/5.39 % (6272)Termination reason: Unknown
% 28.86/5.39 % (6272)Termination phase: Saturation
% 28.86/5.39
% 28.86/5.39 % (6272)Memory used [KB]: 6652
% 28.86/5.39 % (6272)Time elapsed: 0.027 s
% 28.86/5.39 % (6272)Instructions burned: 91 (million)
% 28.86/5.39 % (6272)------------------------------
% 28.86/5.39 % (6272)------------------------------
% 28.86/5.39 % (6270)Instruction limit reached!
% 28.86/5.39 % (6270)------------------------------
% 28.86/5.39 % (6270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.86/5.39 % (6270)Termination reason: Unknown
% 28.86/5.39 % (6270)Termination phase: Saturation
% 28.86/5.39
% 28.86/5.39 % (6270)Memory used [KB]: 7547
% 28.86/5.39 % (6270)Time elapsed: 0.135 s
% 28.86/5.39 % (6270)Instructions burned: 433 (million)
% 28.86/5.39 % (6270)------------------------------
% 28.86/5.39 % (6270)------------------------------
% 29.31/5.40 % (6273)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_5740 for (2961ds/346Mi)
% 29.31/5.40 % (6274)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_5740 for (2961ds/401Mi)
% 29.52/5.50 % (6269)Instruction limit reached!
% 29.52/5.50 % (6269)------------------------------
% 29.52/5.50 % (6269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.52/5.50 % (6269)Termination reason: Unknown
% 29.52/5.50 % (6269)Termination phase: Saturation
% 29.52/5.50
% 29.52/5.50 % (6269)Memory used [KB]: 7931
% 29.52/5.50 % (6269)Time elapsed: 0.242 s
% 29.52/5.50 % (6269)Instructions burned: 785 (million)
% 29.52/5.50 % (6269)------------------------------
% 29.52/5.50 % (6269)------------------------------
% 29.52/5.51 % (6275)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_5740 for (2960ds/6454Mi)
% 29.52/5.51 % (6273)Instruction limit reached!
% 29.52/5.51 % (6273)------------------------------
% 29.52/5.51 % (6273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.52/5.51 % (6273)Termination reason: Unknown
% 29.52/5.51 % (6273)Termination phase: Saturation
% 29.52/5.51
% 29.52/5.51 % (6273)Memory used [KB]: 7547
% 29.52/5.51 % (6273)Time elapsed: 0.109 s
% 29.52/5.51 % (6273)Instructions burned: 348 (million)
% 29.52/5.51 % (6273)------------------------------
% 29.52/5.51 % (6273)------------------------------
% 29.52/5.52 % (6276)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_5740 for (2960ds/283Mi)
% 29.52/5.52 % (6274)Instruction limit reached!
% 29.52/5.52 % (6274)------------------------------
% 29.52/5.52 % (6274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.52/5.52 % (6274)Termination reason: Unknown
% 29.52/5.52 % (6274)Termination phase: Saturation
% 29.52/5.52
% 29.52/5.52 % (6274)Memory used [KB]: 8187
% 29.52/5.52 % (6274)Time elapsed: 0.122 s
% 29.52/5.52 % (6274)Instructions burned: 402 (million)
% 29.52/5.52 % (6274)------------------------------
% 29.52/5.52 % (6274)------------------------------
% 29.52/5.53 % (6277)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_5740 for (2960ds/865Mi)
% 30.22/5.61 % (6276)Instruction limit reached!
% 30.22/5.61 % (6276)------------------------------
% 30.22/5.61 % (6276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.22/5.61 % (6276)Termination reason: Unknown
% 30.22/5.61 % (6276)Termination phase: Saturation
% 30.22/5.61
% 30.22/5.61 % (6276)Memory used [KB]: 7547
% 30.22/5.61 % (6276)Time elapsed: 0.092 s
% 30.22/5.61 % (6276)Instructions burned: 283 (million)
% 30.22/5.61 % (6276)------------------------------
% 30.22/5.61 % (6276)------------------------------
% 30.22/5.62 % (6278)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_5740 for (2959ds/4528Mi)
% 30.51/5.73 % (6267)Instruction limit reached!
% 30.51/5.73 % (6267)------------------------------
% 30.51/5.73 % (6267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.51/5.73 % (6267)Termination reason: Unknown
% 30.51/5.73 % (6267)Termination phase: Saturation
% 30.51/5.73
% 30.51/5.73 % (6267)Memory used [KB]: 8187
% 30.51/5.73 % (6267)Time elapsed: 0.655 s
% 30.51/5.73 % (6267)Instructions burned: 1981 (million)
% 30.51/5.73 % (6267)------------------------------
% 30.51/5.73 % (6267)------------------------------
% 30.51/5.74 % (6279)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_5740 for (2958ds/1001Mi)
% 30.51/5.77 % (6243)Refutation not found, non-redundant clauses discarded% (6243)------------------------------
% 30.51/5.77 % (6243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.51/5.77 % (6243)Termination reason: Refutation not found, non-redundant clauses discarded
% 30.51/5.77
% 30.51/5.77 % (6243)Memory used [KB]: 9722
% 30.51/5.77 % (6243)Time elapsed: 1.625 s
% 30.51/5.77 % (6243)Instructions burned: 5387 (million)
% 30.51/5.77 % (6243)------------------------------
% 30.51/5.77 % (6243)------------------------------
% 30.51/5.78 % (6258)Instruction limit reached!
% 30.51/5.78 % (6258)------------------------------
% 30.51/5.78 % (6258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.51/5.78 % (6258)Termination reason: Unknown
% 30.51/5.78 % (6258)Termination phase: Saturation
% 30.51/5.78
% 30.51/5.78 % (6258)Memory used [KB]: 10746
% 30.51/5.78 % (6258)Time elapsed: 1.052 s
% 30.51/5.78 % (6258)Instructions burned: 3373 (million)
% 30.51/5.78 % (6258)------------------------------
% 30.51/5.78 % (6258)------------------------------
% 30.51/5.78 % (6280)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_5740 for (2957ds/102Mi)
% 30.51/5.79 % (6281)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_5740 for (2957ds/952Mi)
% 31.33/5.80 % (6271)Instruction limit reached!
% 31.33/5.80 % (6271)------------------------------
% 31.33/5.80 % (6271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.33/5.80 % (6271)Termination reason: Unknown
% 31.33/5.80 % (6271)Termination phase: Saturation
% 31.33/5.80
% 31.33/5.80 % (6271)Memory used [KB]: 9594
% 31.33/5.80 % (6271)Time elapsed: 0.508 s
% 31.33/5.80 % (6271)Instructions burned: 1671 (million)
% 31.33/5.80 % (6271)------------------------------
% 31.33/5.80 % (6271)------------------------------
% 31.33/5.81 % (6280)Instruction limit reached!
% 31.33/5.81 % (6280)------------------------------
% 31.33/5.81 % (6280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.33/5.81 % (6280)Termination reason: Unknown
% 31.33/5.81 % (6280)Termination phase: Property scanning
% 31.33/5.81
% 31.33/5.81 % (6280)Memory used [KB]: 2174
% 31.33/5.81 % (6280)Time elapsed: 0.029 s
% 31.33/5.81 % (6280)Instructions burned: 102 (million)
% 31.33/5.81 % (6280)------------------------------
% 31.33/5.81 % (6280)------------------------------
% 31.33/5.81 % (6277)Instruction limit reached!
% 31.33/5.81 % (6277)------------------------------
% 31.33/5.81 % (6277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.33/5.81 % (6277)Termination reason: Unknown
% 31.33/5.81 % (6277)Termination phase: Saturation
% 31.33/5.81
% 31.33/5.81 % (6277)Memory used [KB]: 9210
% 31.33/5.81 % (6277)Time elapsed: 0.276 s
% 31.33/5.81 % (6277)Instructions burned: 865 (million)
% 31.33/5.81 % (6277)------------------------------
% 31.33/5.81 % (6277)------------------------------
% 31.33/5.81 % (6282)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_5740 for (2957ds/578Mi)
% 31.33/5.82 % (6283)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_5740 for (2957ds/643Mi)
% 31.33/5.82 % (6284)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_5740 for (2957ds/865Mi)
% 32.18/5.98 % (6282)Instruction limit reached!
% 32.18/5.98 % (6282)------------------------------
% 32.18/5.98 % (6282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.18/5.98 % (6282)Termination reason: Unknown
% 32.18/5.98 % (6282)Termination phase: Saturation
% 32.18/5.98
% 32.18/5.98 % (6282)Memory used [KB]: 9083
% 32.18/5.98 % (6282)Time elapsed: 0.174 s
% 32.18/5.98 % (6282)Instructions burned: 578 (million)
% 32.18/5.98 % (6282)------------------------------
% 32.18/5.98 % (6282)------------------------------
% 32.18/5.99 % (6285)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_5740 for (2955ds/1174Mi)
% 32.18/6.01 % (6283)Instruction limit reached!
% 32.18/6.01 % (6283)------------------------------
% 32.18/6.01 % (6283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.18/6.01 % (6283)Termination reason: Unknown
% 32.18/6.01 % (6283)Termination phase: Saturation
% 32.18/6.01
% 32.18/6.01 % (6283)Memory used [KB]: 8955
% 32.18/6.01 % (6283)Time elapsed: 0.196 s
% 32.18/6.01 % (6283)Instructions burned: 644 (million)
% 32.18/6.01 % (6283)------------------------------
% 32.18/6.01 % (6283)------------------------------
% 32.18/6.02 % (6286)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_5740 for (2955ds/644Mi)
% 34.23/6.06 % (6279)Instruction limit reached!
% 34.23/6.06 % (6279)------------------------------
% 34.23/6.06 % (6279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.23/6.06 % (6279)Termination reason: Unknown
% 34.23/6.06 % (6279)Termination phase: Saturation
% 34.23/6.06
% 34.23/6.06 % (6279)Memory used [KB]: 8571
% 34.23/6.06 % (6279)Time elapsed: 0.314 s
% 34.23/6.06 % (6279)Instructions burned: 1003 (million)
% 34.23/6.06 % (6279)------------------------------
% 34.23/6.06 % (6279)------------------------------
% 34.23/6.07 % (6287)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_5740 for (2954ds/1201Mi)
% 34.23/6.08 % (6284)Instruction limit reached!
% 34.23/6.08 % (6284)------------------------------
% 34.23/6.08 % (6284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.23/6.08 % (6284)Termination reason: Unknown
% 34.23/6.08 % (6284)Termination phase: Saturation
% 34.23/6.08
% 34.23/6.08 % (6284)Memory used [KB]: 8955
% 34.23/6.08 % (6284)Time elapsed: 0.261 s
% 34.23/6.08 % (6284)Instructions burned: 867 (million)
% 34.23/6.08 % (6284)------------------------------
% 34.23/6.08 % (6284)------------------------------
% 34.23/6.08 % (6281)Instruction limit reached!
% 34.23/6.08 % (6281)------------------------------
% 34.23/6.08 % (6281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.23/6.08 % (6281)Termination reason: Unknown
% 34.23/6.08 % (6281)Termination phase: Saturation
% 34.23/6.08
% 34.23/6.08 % (6281)Memory used [KB]: 8571
% 34.23/6.08 % (6281)Time elapsed: 0.297 s
% 34.23/6.08 % (6281)Instructions burned: 953 (million)
% 34.23/6.08 % (6281)------------------------------
% 34.23/6.08 % (6281)------------------------------
% 34.23/6.09 % (6288)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_5740 for (2954ds/1046Mi)
% 34.23/6.09 % (6289)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_5740 for (2954ds/222Mi)
% 34.71/6.16 % (6289)Instruction limit reached!
% 34.71/6.16 % (6289)------------------------------
% 34.71/6.16 % (6289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.71/6.16 % (6289)Termination reason: Unknown
% 34.71/6.16 % (6289)Termination phase: Saturation
% 34.71/6.16
% 34.71/6.16 % (6289)Memory used [KB]: 7036
% 34.71/6.16 % (6289)Time elapsed: 0.064 s
% 34.71/6.16 % (6289)Instructions burned: 225 (million)
% 34.71/6.16 % (6289)------------------------------
% 34.71/6.16 % (6289)------------------------------
% 34.71/6.17 % (6290)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_5740 for (2953ds/68Mi)
% 34.71/6.19 % (6290)Instruction limit reached!
% 34.71/6.19 % (6290)------------------------------
% 34.71/6.19 % (6290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.71/6.19 % (6290)Termination reason: Unknown
% 34.71/6.19 % (6290)Termination phase: Property scanning
% 34.71/6.19
% 34.71/6.19 % (6290)Memory used [KB]: 2046
% 34.71/6.19 % (6290)Time elapsed: 0.022 s
% 34.71/6.19 % (6290)Instructions burned: 68 (million)
% 34.71/6.19 % (6290)------------------------------
% 34.71/6.19 % (6290)------------------------------
% 34.71/6.20 % (6291)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_5740 for (2953ds/454Mi)
% 35.04/6.22 % (6286)Instruction limit reached!
% 35.04/6.22 % (6286)------------------------------
% 35.04/6.22 % (6286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.22 % (6286)Termination reason: Unknown
% 35.04/6.22 % (6286)Termination phase: Saturation
% 35.04/6.22
% 35.04/6.22 % (6286)Memory used [KB]: 9083
% 35.04/6.22 % (6286)Time elapsed: 0.204 s
% 35.04/6.22 % (6286)Instructions burned: 645 (million)
% 35.04/6.22 % (6286)------------------------------
% 35.04/6.22 % (6286)------------------------------
% 35.04/6.23 % (6292)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_5740 for (2953ds/360Mi)
% 35.57/6.33 % (6291)Instruction limit reached!
% 35.57/6.33 % (6291)------------------------------
% 35.57/6.33 % (6291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.33 % (6291)Termination reason: Unknown
% 35.57/6.33 % (6291)Termination phase: Saturation
% 35.57/6.33
% 35.57/6.33 % (6291)Memory used [KB]: 12409
% 35.57/6.33 % (6291)Time elapsed: 0.137 s
% 35.57/6.33 % (6291)Instructions burned: 454 (million)
% 35.57/6.33 % (6291)------------------------------
% 35.57/6.33 % (6291)------------------------------
% 35.57/6.34 % (6293)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_5740 for (2952ds/157Mi)
% 35.57/6.34 % (6292)Instruction limit reached!
% 35.57/6.34 % (6292)------------------------------
% 35.57/6.34 % (6292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.34 % (6292)Termination reason: Unknown
% 35.57/6.34 % (6292)Termination phase: Saturation
% 35.57/6.34
% 35.57/6.34 % (6292)Memory used [KB]: 8059
% 35.57/6.34 % (6292)Time elapsed: 0.111 s
% 35.57/6.34 % (6292)Instructions burned: 360 (million)
% 35.57/6.34 % (6292)------------------------------
% 35.57/6.34 % (6292)------------------------------
% 35.57/6.35 % (6294)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_5740 for (2951ds/5061Mi)
% 35.57/6.36 % (6285)Instruction limit reached!
% 35.57/6.36 % (6285)------------------------------
% 35.57/6.36 % (6285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.36 % (6285)Termination reason: Unknown
% 35.57/6.36 % (6285)Termination phase: Saturation
% 35.57/6.36
% 35.57/6.36 % (6285)Memory used [KB]: 9210
% 35.57/6.36 % (6285)Time elapsed: 0.371 s
% 35.57/6.36 % (6285)Instructions burned: 1175 (million)
% 35.57/6.36 % (6285)------------------------------
% 35.57/6.36 % (6285)------------------------------
% 35.57/6.37 % (6295)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_5740 for (2951ds/2401Mi)
% 35.57/6.39 % (6293)Instruction limit reached!
% 35.57/6.39 % (6293)------------------------------
% 35.57/6.39 % (6293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.39 % (6293)Termination reason: Unknown
% 35.57/6.39 % (6293)Termination phase: Saturation
% 35.57/6.39
% 35.57/6.39 % (6293)Memory used [KB]: 6908
% 35.57/6.39 % (6293)Time elapsed: 0.044 s
% 35.57/6.39 % (6293)Instructions burned: 157 (million)
% 35.57/6.39 % (6293)------------------------------
% 35.57/6.39 % (6293)------------------------------
% 35.57/6.39 % (6296)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_5740 for (2951ds/5798Mi)
% 36.15/6.40 % (6288)Instruction limit reached!
% 36.15/6.40 % (6288)------------------------------
% 36.15/6.40 % (6288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.15/6.40 % (6288)Termination reason: Unknown
% 36.15/6.40 % (6288)Termination phase: Saturation
% 36.15/6.40
% 36.15/6.40 % (6288)Memory used [KB]: 9083
% 36.15/6.40 % (6288)Time elapsed: 0.319 s
% 36.15/6.40 % (6288)Instructions burned: 1047 (million)
% 36.15/6.40 % (6288)------------------------------
% 36.15/6.40 % (6288)------------------------------
% 36.15/6.41 % (6297)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_5740 for (2951ds/346Mi)
% 36.15/6.42 % (6287)Instruction limit reached!
% 36.15/6.42 % (6287)------------------------------
% 36.15/6.42 % (6287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.15/6.42 % (6287)Termination reason: Unknown
% 36.15/6.42 % (6287)Termination phase: Saturation
% 36.15/6.42
% 36.15/6.42 % (6287)Memory used [KB]: 9594
% 36.15/6.42 % (6287)Time elapsed: 0.357 s
% 36.15/6.42 % (6287)Instructions burned: 1203 (million)
% 36.15/6.42 % (6287)------------------------------
% 36.15/6.42 % (6287)------------------------------
% 36.15/6.43 % (6298)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_5740 for (2951ds/1321Mi)
% 37.05/6.52 % (6297)Instruction limit reached!
% 37.05/6.52 % (6297)------------------------------
% 37.05/6.52 % (6297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.05/6.52 % (6297)Termination reason: Unknown
% 37.05/6.52 % (6297)Termination phase: Saturation
% 37.05/6.52
% 37.05/6.52 % (6297)Memory used [KB]: 7547
% 37.05/6.52 % (6297)Time elapsed: 0.110 s
% 37.05/6.52 % (6297)Instructions burned: 349 (million)
% 37.05/6.52 % (6297)------------------------------
% 37.05/6.52 % (6297)------------------------------
% 37.05/6.53 % (6299)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_5740 for (2950ds/1312Mi)
% 37.76/6.82 % (6278)Instruction limit reached!
% 37.76/6.82 % (6278)------------------------------
% 37.76/6.82 % (6278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.76/6.82 % (6278)Termination reason: Unknown
% 37.76/6.82 % (6278)Termination phase: Saturation
% 37.76/6.82
% 37.76/6.82 % (6278)Memory used [KB]: 6140
% 37.76/6.82 % (6278)Time elapsed: 1.204 s
% 37.76/6.82 % (6278)Instructions burned: 4531 (million)
% 37.76/6.82 % (6278)------------------------------
% 37.76/6.82 % (6278)------------------------------
% 37.76/6.83 % (6300)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_5740 for (2947ds/672Mi)
% 37.76/6.83 % (6298)Instruction limit reached!
% 37.76/6.83 % (6298)------------------------------
% 37.76/6.83 % (6298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.76/6.83 % (6298)Termination reason: Unknown
% 37.76/6.83 % (6298)Termination phase: Saturation
% 37.76/6.83
% 37.76/6.83 % (6298)Memory used [KB]: 4989
% 37.76/6.83 % (6298)Time elapsed: 0.404 s
% 37.76/6.83 % (6298)Instructions burned: 1321 (million)
% 37.76/6.83 % (6298)------------------------------
% 37.76/6.83 % (6298)------------------------------
% 37.76/6.84 % (6301)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_5740 for (2947ds/1897Mi)
% 38.32/6.92 % (6299)Instruction limit reached!
% 38.32/6.92 % (6299)------------------------------
% 38.32/6.92 % (6299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.32/6.92 % (6299)Termination reason: Unknown
% 38.32/6.92 % (6299)Termination phase: Saturation
% 38.32/6.92
% 38.32/6.92 % (6299)Memory used [KB]: 9466
% 38.32/6.92 % (6299)Time elapsed: 0.390 s
% 38.32/6.92 % (6299)Instructions burned: 1315 (million)
% 38.32/6.92 % (6299)------------------------------
% 38.32/6.92 % (6299)------------------------------
% 38.32/6.93 % (6302)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_5740 for (2946ds/1202Mi)
% 41.25/7.05 % (6300)Instruction limit reached!
% 41.25/7.05 % (6300)------------------------------
% 41.25/7.05 % (6300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.25/7.05 % (6300)Termination reason: Unknown
% 41.25/7.05 % (6300)Termination phase: Saturation
% 41.25/7.05
% 41.25/7.05 % (6300)Memory used [KB]: 7803
% 41.25/7.05 % (6300)Time elapsed: 0.216 s
% 41.25/7.05 % (6300)Instructions burned: 672 (million)
% 41.25/7.05 % (6300)------------------------------
% 41.25/7.05 % (6300)------------------------------
% 41.25/7.06 % (6303)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_5740 for (2945ds/1493Mi)
% 41.25/7.09 % (6303)Refutation not found, incomplete strategy
% 41.25/7.09 % (6303)------------------------------
% 41.25/7.09 % (6303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.25/7.09 % (6303)Termination reason: Refutation not found, incomplete strategy
% 41.25/7.09
% 41.25/7.09
% 41.25/7.09 % (6303)Memory used [KB]: 7036
% 41.25/7.09 % (6303)Time elapsed: 0.039 s
% 41.25/7.09 % (6303)Instructions burned: 141 (million)
% 41.25/7.09 % (6303)------------------------------
% 41.25/7.09 % (6303)------------------------------
% 41.25/7.10 % (6304)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_5740 for (2944ds/7679Mi)
% 41.25/7.12 % (6295)Instruction limit reached!
% 41.25/7.12 % (6295)------------------------------
% 41.25/7.12 % (6295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.25/7.12 % (6295)Termination reason: Unknown
% 41.25/7.12 % (6295)Termination phase: Saturation
% 41.25/7.12
% 41.25/7.12 % (6295)Memory used [KB]: 7675
% 41.25/7.12 % (6295)Time elapsed: 0.745 s
% 41.25/7.12 % (6295)Instructions burned: 2403 (million)
% 41.25/7.12 % (6295)------------------------------
% 41.25/7.12 % (6295)------------------------------
% 41.95/7.13 % (6305)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_5740 for (2944ds/340Mi)
% 42.33/7.23 % (6305)Instruction limit reached!
% 42.33/7.23 % (6305)------------------------------
% 42.33/7.23 % (6305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.33/7.23 % (6305)Termination reason: Unknown
% 42.33/7.23 % (6305)Termination phase: Saturation
% 42.33/7.23
% 42.33/7.23 % (6305)Memory used [KB]: 8443
% 42.33/7.23 % (6305)Time elapsed: 0.108 s
% 42.33/7.23 % (6305)Instructions burned: 340 (million)
% 42.33/7.23 % (6305)------------------------------
% 42.33/7.23 % (6305)------------------------------
% 42.33/7.24 % (6306)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_5740 for (2943ds/3672Mi)
% 42.94/7.31 % (6302)Instruction limit reached!
% 42.94/7.31 % (6302)------------------------------
% 42.94/7.31 % (6302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.94/7.31 % (6302)Termination reason: Unknown
% 42.94/7.31 % (6302)Termination phase: Saturation
% 42.94/7.31
% 42.94/7.31 % (6302)Memory used [KB]: 4605
% 42.94/7.31 % (6302)Time elapsed: 0.383 s
% 42.94/7.31 % (6302)Instructions burned: 1202 (million)
% 42.94/7.31 % (6302)------------------------------
% 42.94/7.31 % (6302)------------------------------
% 42.94/7.32 % (6307)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_5740 for (2942ds/1535Mi)
% 43.37/7.43 % (6301)Instruction limit reached!
% 43.37/7.43 % (6301)------------------------------
% 43.37/7.43 % (6301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.37/7.43 % (6301)Termination reason: Unknown
% 43.37/7.43 % (6301)Termination phase: Saturation
% 43.37/7.43
% 43.37/7.43 % (6301)Memory used [KB]: 8955
% 43.37/7.43 % (6301)Time elapsed: 0.591 s
% 43.37/7.43 % (6301)Instructions burned: 1898 (million)
% 43.37/7.43 % (6301)------------------------------
% 43.37/7.43 % (6301)------------------------------
% 43.37/7.44 % (6308)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_5740 for (2941ds/4637Mi)
% 43.74/7.54 % (6275)Refutation not found, non-redundant clauses discarded% (6275)------------------------------
% 43.74/7.54 % (6275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.74/7.54 % (6275)Termination reason: Refutation not found, non-redundant clauses discarded
% 43.74/7.54
% 43.74/7.54 % (6275)Memory used [KB]: 11769
% 43.74/7.54 % (6275)Time elapsed: 2.029 s
% 43.74/7.54 % (6275)Instructions burned: 6445 (million)
% 43.74/7.54 % (6275)------------------------------
% 43.74/7.54 % (6275)------------------------------
% 43.74/7.55 % (6309)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_5740 for (2940ds/3174Mi)
% 44.18/7.78 % (6307)Instruction limit reached!
% 44.18/7.78 % (6307)------------------------------
% 44.18/7.78 % (6307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.18/7.78 % (6307)Termination reason: Unknown
% 44.18/7.78 % (6307)Termination phase: Saturation
% 44.18/7.78
% 44.18/7.78 % (6307)Memory used [KB]: 10618
% 44.18/7.78 % (6307)Time elapsed: 0.479 s
% 44.18/7.78 % (6307)Instructions burned: 1536 (million)
% 44.18/7.78 % (6307)------------------------------
% 44.18/7.78 % (6307)------------------------------
% 44.18/7.79 % (6310)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_5740 for (2937ds/307Mi)
% 44.84/7.87 % (6310)Instruction limit reached!
% 44.84/7.87 % (6310)------------------------------
% 44.84/7.87 % (6310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.84/7.87 % (6310)Termination reason: Unknown
% 44.84/7.87 % (6310)Termination phase: Saturation
% 44.84/7.87
% 44.84/7.87 % (6310)Memory used [KB]: 7419
% 44.84/7.87 % (6310)Time elapsed: 0.113 s
% 44.84/7.87 % (6310)Instructions burned: 310 (million)
% 44.84/7.87 % (6310)------------------------------
% 44.84/7.87 % (6310)------------------------------
% 44.84/7.88 % (6311)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_5740 for (2936ds/3619Mi)
% 45.15/7.93 % (6294)Instruction limit reached!
% 45.15/7.93 % (6294)------------------------------
% 45.15/7.93 % (6294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.15/7.93 % (6294)Termination reason: Unknown
% 45.15/7.93 % (6294)Termination phase: Saturation
% 45.15/7.93
% 45.15/7.93 % (6294)Memory used [KB]: 11513
% 45.15/7.93 % (6294)Time elapsed: 1.575 s
% 45.15/7.93 % (6294)Instructions burned: 5062 (million)
% 45.15/7.93 % (6294)------------------------------
% 45.15/7.93 % (6294)------------------------------
% 45.15/7.94 % (6312)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_5740 for (2936ds/2325Mi)
% 49.00/8.14 % (6296)Instruction limit reached!
% 49.00/8.14 % (6296)------------------------------
% 49.00/8.14 % (6296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.00/8.14 % (6296)Termination reason: Unknown
% 49.00/8.14 % (6296)Termination phase: Saturation
% 49.00/8.14
% 49.00/8.14 % (6296)Memory used [KB]: 9083
% 49.00/8.14 % (6296)Time elapsed: 1.747 s
% 49.00/8.14 % (6296)Instructions burned: 5798 (million)
% 49.00/8.14 % (6296)------------------------------
% 49.00/8.14 % (6296)------------------------------
% 49.00/8.15 % (6313)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_5740 for (2934ds/2341Mi)
% 50.06/8.37 % (6306)Instruction limit reached!
% 50.06/8.37 % (6306)------------------------------
% 50.06/8.37 % (6306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.06/8.37 % (6306)Termination reason: Unknown
% 50.06/8.37 % (6306)Termination phase: Saturation
% 50.06/8.37
% 50.06/8.37 % (6306)Memory used [KB]: 10746
% 50.06/8.37 % (6306)Time elapsed: 1.157 s
% 50.06/8.37 % (6306)Instructions burned: 3672 (million)
% 50.06/8.37 % (6306)------------------------------
% 50.06/8.37 % (6306)------------------------------
% 50.06/8.39 % (6314)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_5740 for (2931ds/7257Mi)
% 51.15/8.51 % (6309)Instruction limit reached!
% 51.15/8.51 % (6309)------------------------------
% 51.15/8.51 % (6309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.15/8.51 % (6309)Termination reason: Unknown
% 51.15/8.51 % (6309)Termination phase: Saturation
% 51.15/8.51
% 51.15/8.51 % (6309)Memory used [KB]: 10362
% 51.15/8.51 % (6309)Time elapsed: 0.984 s
% 51.15/8.51 % (6309)Instructions burned: 3174 (million)
% 51.15/8.51 % (6309)------------------------------
% 51.15/8.51 % (6309)------------------------------
% 51.15/8.52 % (6315)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_5740 for (2930ds/3710Mi)
% 51.57/8.64 % (6312)Instruction limit reached!
% 51.57/8.64 % (6312)------------------------------
% 51.57/8.64 % (6312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.57/8.64 % (6312)Termination reason: Unknown
% 51.57/8.64 % (6312)Termination phase: Saturation
% 51.57/8.64
% 51.57/8.64 % (6312)Memory used [KB]: 11385
% 51.57/8.64 % (6312)Time elapsed: 0.703 s
% 51.57/8.64 % (6312)Instructions burned: 2326 (million)
% 51.57/8.64 % (6312)------------------------------
% 51.57/8.64 % (6312)------------------------------
% 51.57/8.65 % (6316)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_5740 for (2929ds/326Mi)
% 51.92/8.75 % (6316)Instruction limit reached!
% 51.92/8.75 % (6316)------------------------------
% 51.92/8.75 % (6316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.92/8.75 % (6316)Termination reason: Unknown
% 51.92/8.75 % (6316)Termination phase: Saturation
% 51.92/8.75
% 51.92/8.75 % (6316)Memory used [KB]: 7164
% 51.92/8.75 % (6316)Time elapsed: 0.100 s
% 51.92/8.75 % (6316)Instructions burned: 328 (million)
% 51.92/8.75 % (6316)------------------------------
% 51.92/8.75 % (6316)------------------------------
% 51.92/8.76 % (6317)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_5740 for (2928ds/1100Mi)
% 51.92/8.80 % (6308)Instruction limit reached!
% 51.92/8.80 % (6308)------------------------------
% 51.92/8.80 % (6308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.92/8.80 % (6308)Termination reason: Unknown
% 51.92/8.80 % (6308)Termination phase: Saturation
% 51.92/8.80
% 51.92/8.80 % (6308)Memory used [KB]: 12920
% 51.92/8.80 % (6308)Time elapsed: 1.376 s
% 51.92/8.80 % (6308)Instructions burned: 4637 (million)
% 51.92/8.80 % (6308)------------------------------
% 51.92/8.80 % (6308)------------------------------
% 50.99/8.81 % (6318)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_5740 for (2927ds/406Mi)
% 50.99/8.88 % (6313)Instruction limit reached!
% 50.99/8.88 % (6313)------------------------------
% 50.99/8.88 % (6313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.99/8.88 % (6313)Termination reason: Unknown
% 50.99/8.88 % (6313)Termination phase: Saturation
% 50.99/8.88
% 50.99/8.88 % (6313)Memory used [KB]: 8443
% 50.99/8.88 % (6313)Time elapsed: 0.734 s
% 50.99/8.88 % (6313)Instructions burned: 2342 (million)
% 50.99/8.88 % (6313)------------------------------
% 50.99/8.88 % (6313)------------------------------
% 50.99/8.89 % (6319)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_5740 for (2926ds/1871Mi)
% 53.29/8.93 % (6318)Instruction limit reached!
% 53.29/8.93 % (6318)------------------------------
% 53.29/8.93 % (6318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.29/8.93 % (6318)Termination reason: Unknown
% 53.29/8.93 % (6318)Termination phase: Saturation
% 53.29/8.93
% 53.29/8.93 % (6318)Memory used [KB]: 7675
% 53.29/8.93 % (6318)Time elapsed: 0.127 s
% 53.29/8.93 % (6318)Instructions burned: 409 (million)
% 53.29/8.93 % (6318)------------------------------
% 53.29/8.93 % (6318)------------------------------
% 53.29/8.94 % (6320)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_5740 for (2926ds/1194Mi)
% 53.29/8.96 % (6311)Instruction limit reached!
% 53.29/8.96 % (6311)------------------------------
% 53.29/8.96 % (6311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.29/8.96 % (6311)Termination reason: Unknown
% 53.29/8.96 % (6311)Termination phase: Saturation
% 53.29/8.96
% 53.29/8.96 % (6311)Memory used [KB]: 11513
% 53.29/8.96 % (6311)Time elapsed: 1.074 s
% 53.29/8.96 % (6311)Instructions burned: 3619 (million)
% 53.29/8.96 % (6311)------------------------------
% 53.29/8.96 % (6311)------------------------------
% 53.29/8.97 % (6321)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_5740 for (2925ds/474Mi)
% 55.29/9.09 % (6317)Instruction limit reached!
% 55.29/9.09 % (6317)------------------------------
% 55.29/9.09 % (6317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.29/9.09 % (6317)Termination reason: Unknown
% 55.29/9.09 % (6317)Termination phase: Saturation
% 55.29/9.09
% 55.29/9.09 % (6317)Memory used [KB]: 9722
% 55.29/9.09 % (6317)Time elapsed: 0.338 s
% 55.29/9.09 % (6317)Instructions burned: 1100 (million)
% 55.29/9.09 % (6317)------------------------------
% 55.29/9.09 % (6317)------------------------------
% 55.29/9.10 % (6322)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_5740 for (2924ds/3115Mi)
% 55.29/9.11 % (6321)Instruction limit reached!
% 55.29/9.11 % (6321)------------------------------
% 55.29/9.11 % (6321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.29/9.11 % (6321)Termination reason: Unknown
% 55.29/9.11 % (6321)Termination phase: Saturation
% 55.29/9.11
% 55.29/9.11 % (6321)Memory used [KB]: 8059
% 55.29/9.11 % (6321)Time elapsed: 0.169 s
% 55.29/9.11 % (6321)Instructions burned: 476 (million)
% 55.29/9.11 % (6321)------------------------------
% 55.29/9.11 % (6321)------------------------------
% 55.29/9.12 % (6323)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_5740 for (2924ds/831Mi)
% 56.86/9.31 % (6320)Instruction limit reached!
% 56.86/9.31 % (6320)------------------------------
% 56.86/9.31 % (6320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.86/9.31 % (6320)Termination reason: Unknown
% 56.86/9.31 % (6320)Termination phase: Saturation
% 56.86/9.31
% 56.86/9.31 % (6320)Memory used [KB]: 8443
% 56.86/9.31 % (6320)Time elapsed: 0.390 s
% 56.86/9.31 % (6320)Instructions burned: 1196 (million)
% 56.86/9.31 % (6320)------------------------------
% 56.86/9.31 % (6320)------------------------------
% 56.86/9.32 % (6324)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_5740 for (2922ds/1188Mi)
% 56.86/9.34 % (6304)Instruction limit reached!
% 56.86/9.34 % (6304)------------------------------
% 56.86/9.34 % (6304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.86/9.34 % (6304)Termination reason: Unknown
% 56.86/9.34 % (6304)Termination phase: Saturation
% 56.86/9.34
% 56.86/9.34 % (6304)Memory used [KB]: 12537
% 56.86/9.34 % (6304)Time elapsed: 2.264 s
% 56.86/9.34 % (6304)Instructions burned: 7679 (million)
% 56.86/9.34 % (6304)------------------------------
% 56.86/9.34 % (6304)------------------------------
% 56.86/9.36 % (6325)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_5740 for (2921ds/2868Mi)
% 56.86/9.38 % (6323)Instruction limit reached!
% 56.86/9.38 % (6323)------------------------------
% 56.86/9.38 % (6323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.86/9.38 % (6323)Termination reason: Unknown
% 56.86/9.38 % (6323)Termination phase: Saturation
% 56.86/9.38
% 56.86/9.38 % (6323)Memory used [KB]: 8443
% 56.86/9.38 % (6323)Time elapsed: 0.259 s
% 56.86/9.38 % (6323)Instructions burned: 833 (million)
% 56.86/9.38 % (6323)------------------------------
% 56.86/9.38 % (6323)------------------------------
% 56.86/9.39 % (6326)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_5740 for (2921ds/1516Mi)
% 57.51/9.41 % (6325)Refutation not found, incomplete strategy
% 57.51/9.41 % (6325)------------------------------
% 57.51/9.41 % (6325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.51/9.41 % (6325)Termination reason: Refutation not found, incomplete strategy
% 57.51/9.41
% 57.51/9.41
% 57.51/9.41 % (6325)Memory used [KB]: 7547
% 57.51/9.41 % (6325)Time elapsed: 0.058 s
% 57.51/9.41 % (6325)Instructions burned: 207 (million)
% 57.51/9.41 % (6325)------------------------------
% 57.51/9.41 % (6325)------------------------------
% 57.51/9.42 % (6327)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_5740 for (2921ds/2321Mi)
% 57.51/9.48 % (6327)Refutation not found, incomplete strategy
% 57.51/9.48 % (6327)------------------------------
% 57.51/9.48 % (6327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.51/9.48 % (6327)Termination reason: Refutation not found, incomplete strategy
% 57.51/9.48
% 57.51/9.48
% 57.51/9.48 % (6327)Memory used [KB]: 7675
% 57.51/9.48 % (6327)Time elapsed: 0.061 s
% 57.51/9.48 % (6327)Instructions burned: 214 (million)
% 57.51/9.48 % (6327)------------------------------
% 57.51/9.48 % (6327)------------------------------
% 57.51/9.49 % (6319)Instruction limit reached!
% 57.51/9.49 % (6319)------------------------------
% 57.51/9.49 % (6319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.51/9.49 % (6319)Termination reason: Unknown
% 57.51/9.49 % (6319)Termination phase: Saturation
% 57.51/9.49
% 57.51/9.49 % (6319)Memory used [KB]: 10618
% 57.51/9.49 % (6319)Time elapsed: 0.619 s
% 57.51/9.49 % (6319)Instructions burned: 1871 (million)
% 57.51/9.49 % (6319)------------------------------
% 57.51/9.49 % (6319)------------------------------
% 57.51/9.49 % (6328)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_5740 for (2920ds/2812Mi)
% 57.95/9.50 % (6329)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_5740 for (2920ds/4604Mi)
% 58.16/9.60 % (6315)Instruction limit reached!
% 58.16/9.60 % (6315)------------------------------
% 58.16/9.60 % (6315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.16/9.60 % (6315)Termination reason: Unknown
% 58.16/9.60 % (6315)Termination phase: Saturation
% 58.16/9.60
% 58.16/9.60 % (6315)Memory used [KB]: 14072
% 58.16/9.60 % (6315)Time elapsed: 1.087 s
% 58.16/9.60 % (6315)Instructions burned: 3712 (million)
% 58.16/9.60 % (6315)------------------------------
% 58.16/9.60 % (6315)------------------------------
% 58.16/9.61 % (6330)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_5740 for (2919ds/2678Mi)
% 58.16/9.69 % (6324)Instruction limit reached!
% 58.16/9.69 % (6324)------------------------------
% 58.16/9.69 % (6324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.16/9.69 % (6324)Termination reason: Unknown
% 58.16/9.69 % (6324)Termination phase: Saturation
% 58.16/9.69
% 58.16/9.69 % (6324)Memory used [KB]: 9338
% 58.16/9.69 % (6324)Time elapsed: 0.367 s
% 58.16/9.69 % (6324)Instructions burned: 1191 (million)
% 58.16/9.69 % (6324)------------------------------
% 58.16/9.69 % (6324)------------------------------
% 58.16/9.70 % (6331)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_5740 for (2918ds/643Mi)
% 58.75/9.85 % (6326)Instruction limit reached!
% 58.75/9.85 % (6326)------------------------------
% 58.75/9.85 % (6326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.75/9.85 % (6326)Termination reason: Unknown
% 58.75/9.85 % (6326)Termination phase: Saturation
% 58.75/9.85
% 58.75/9.85 % (6326)Memory used [KB]: 7803
% 58.75/9.85 % (6326)Time elapsed: 0.461 s
% 58.75/9.85 % (6326)Instructions burned: 1517 (million)
% 58.75/9.85 % (6326)------------------------------
% 58.75/9.85 % (6326)------------------------------
% 58.75/9.86 % (6332)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_5740 for (2916ds/458Mi)
% 58.75/9.89 % (6331)Instruction limit reached!
% 58.75/9.89 % (6331)------------------------------
% 58.75/9.89 % (6331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.75/9.89 % (6331)Termination reason: Unknown
% 58.75/9.89 % (6331)Termination phase: Saturation
% 58.75/9.89
% 58.75/9.89 % (6331)Memory used [KB]: 8827
% 58.75/9.89 % (6331)Time elapsed: 0.198 s
% 58.75/9.89 % (6331)Instructions burned: 644 (million)
% 58.75/9.89 % (6331)------------------------------
% 58.75/9.89 % (6331)------------------------------
% 59.53/9.90 % (6333)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_5740 for (2916ds/2546Mi)
% 59.53/9.99 % (6332)Instruction limit reached!
% 59.53/9.99 % (6332)------------------------------
% 59.53/9.99 % (6332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.53/9.99 % (6332)Termination reason: Unknown
% 59.53/9.99 % (6332)Termination phase: Saturation
% 59.53/9.99
% 59.53/9.99 % (6332)Memory used [KB]: 7675
% 59.53/9.99 % (6332)Time elapsed: 0.134 s
% 59.53/9.99 % (6332)Instructions burned: 458 (million)
% 59.53/9.99 % (6332)------------------------------
% 59.53/9.99 % (6332)------------------------------
% 59.53/10.00 % (6334)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_5740 for (2915ds/1432Mi)
% 62.31/10.03 % (6322)Instruction limit reached!
% 62.31/10.03 % (6322)------------------------------
% 62.31/10.03 % (6322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.31/10.03 % (6322)Termination reason: Unknown
% 62.31/10.03 % (6322)Termination phase: Saturation
% 62.31/10.03
% 62.31/10.03 % (6322)Memory used [KB]: 11769
% 62.31/10.03 % (6322)Time elapsed: 0.925 s
% 62.31/10.03 % (6322)Instructions burned: 3116 (million)
% 62.31/10.03 % (6322)------------------------------
% 62.31/10.03 % (6322)------------------------------
% 62.31/10.04 % (6335)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_5740 for (2915ds/386Mi)
% 62.95/10.16 % (6335)Instruction limit reached!
% 62.95/10.16 % (6335)------------------------------
% 62.95/10.16 % (6335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.95/10.16 % (6335)Termination reason: Unknown
% 62.95/10.16 % (6335)Termination phase: Saturation
% 62.95/10.16
% 62.95/10.16 % (6335)Memory used [KB]: 8059
% 62.95/10.16 % (6335)Time elapsed: 0.119 s
% 62.95/10.16 % (6335)Instructions burned: 386 (million)
% 62.95/10.16 % (6335)------------------------------
% 62.95/10.16 % (6335)------------------------------
% 62.95/10.17 % (6336)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_5740 for (2913ds/360Mi)
% 63.52/10.27 % (6336)Instruction limit reached!
% 63.52/10.27 % (6336)------------------------------
% 63.52/10.27 % (6336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.52/10.27 % (6336)Termination reason: Unknown
% 63.52/10.27 % (6336)Termination phase: Saturation
% 63.52/10.27
% 63.52/10.27 % (6336)Memory used [KB]: 7931
% 63.52/10.27 % (6336)Time elapsed: 0.107 s
% 63.52/10.27 % (6336)Instructions burned: 362 (million)
% 63.52/10.27 % (6336)------------------------------
% 63.52/10.27 % (6336)------------------------------
% 63.52/10.28 % (6337)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_5740 for (2912ds/5446Mi)
% 64.23/10.38 % (6328)Instruction limit reached!
% 64.23/10.38 % (6328)------------------------------
% 64.23/10.38 % (6328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.23/10.38 % (6328)Termination reason: Unknown
% 64.23/10.38 % (6328)Termination phase: Saturation
% 64.23/10.38
% 64.23/10.38 % (6328)Memory used [KB]: 10618
% 64.23/10.38 % (6328)Time elapsed: 0.890 s
% 64.23/10.38 % (6328)Instructions burned: 2812 (million)
% 64.23/10.38 % (6328)------------------------------
% 64.23/10.38 % (6328)------------------------------
% 64.23/10.39 % (6338)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_5740 for (2911ds/2573Mi)
% 64.82/10.43 % (6330)Instruction limit reached!
% 64.82/10.43 % (6330)------------------------------
% 64.82/10.43 % (6330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.82/10.43 % (6330)Termination reason: Unknown
% 64.82/10.43 % (6330)Termination phase: Saturation
% 64.82/10.43
% 64.82/10.43 % (6330)Memory used [KB]: 9978
% 64.82/10.43 % (6330)Time elapsed: 0.813 s
% 64.82/10.43 % (6330)Instructions burned: 2680 (million)
% 64.82/10.43 % (6330)------------------------------
% 64.82/10.43 % (6330)------------------------------
% 64.82/10.43 % (6334)Instruction limit reached!
% 64.82/10.43 % (6334)------------------------------
% 64.82/10.43 % (6334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.82/10.43 % (6334)Termination reason: Unknown
% 64.82/10.43 % (6334)Termination phase: Saturation
% 64.82/10.43
% 64.82/10.43 % (6334)Memory used [KB]: 10490
% 64.82/10.43 % (6334)Time elapsed: 0.429 s
% 64.82/10.43 % (6334)Instructions burned: 1432 (million)
% 64.82/10.43 % (6334)------------------------------
% 64.82/10.43 % (6334)------------------------------
% 64.82/10.44 % (6339)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_5740 for (2911ds/2655Mi)
% 64.82/10.44 % (6340)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_5740 for (2911ds/2781Mi)
% 65.51/10.62 % (6314)Instruction limit reached!
% 65.51/10.62 % (6314)------------------------------
% 65.51/10.62 % (6314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.51/10.62 % (6314)Termination reason: Unknown
% 65.51/10.62 % (6314)Termination phase: Saturation
% 65.51/10.62
% 65.51/10.62 % (6314)Memory used [KB]: 13304
% 65.51/10.62 % (6314)Time elapsed: 2.237 s
% 65.51/10.62 % (6314)Instructions burned: 7257 (million)
% 65.51/10.62 % (6314)------------------------------
% 65.51/10.62 % (6314)------------------------------
% 65.51/10.63 % (6341)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_5740 for (2909ds/307Mi)
% 65.74/10.70 % (6333)Instruction limit reached!
% 65.74/10.70 % (6333)------------------------------
% 65.74/10.70 % (6333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.74/10.70 % (6333)Termination reason: Unknown
% 65.74/10.70 % (6333)Termination phase: Saturation
% 65.74/10.70
% 65.74/10.70 % (6333)Memory used [KB]: 10106
% 65.74/10.70 % (6333)Time elapsed: 0.801 s
% 65.74/10.70 % (6333)Instructions burned: 2549 (million)
% 65.74/10.70 % (6333)------------------------------
% 65.74/10.70 % (6333)------------------------------
% 65.74/10.71 % (6342)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_5740 for (2908ds/1548Mi)
% 65.74/10.72 % (6341)Instruction limit reached!
% 65.74/10.72 % (6341)------------------------------
% 65.74/10.72 % (6341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.74/10.72 % (6341)Termination reason: Unknown
% 65.74/10.72 % (6341)Termination phase: Saturation
% 65.74/10.72
% 65.74/10.72 % (6341)Memory used [KB]: 7419
% 65.74/10.72 % (6341)Time elapsed: 0.090 s
% 65.74/10.72 % (6341)Instructions burned: 310 (million)
% 65.74/10.72 % (6341)------------------------------
% 65.74/10.72 % (6341)------------------------------
% 65.74/10.73 % (6344)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_5740 for (2908ds/5214Mi)
% 65.96/10.87 % (6329)Instruction limit reached!
% 65.96/10.87 % (6329)------------------------------
% 65.96/10.87 % (6329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.96/10.87 % (6329)Termination reason: Unknown
% 65.96/10.87 % (6329)Termination phase: Saturation
% 65.96/10.87
% 65.96/10.87 % (6329)Memory used [KB]: 12153
% 65.96/10.87 % (6329)Time elapsed: 1.366 s
% 65.96/10.87 % (6329)Instructions burned: 4604 (million)
% 65.96/10.87 % (6329)------------------------------
% 65.96/10.87 % (6329)------------------------------
% 65.96/10.88 % (6345)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_5740 for (2906ds/3201Mi)
% 70.07/11.16 % (6338)Instruction limit reached!
% 70.07/11.16 % (6338)------------------------------
% 70.07/11.16 % (6338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.07/11.16 % (6338)Termination reason: Unknown
% 70.07/11.16 % (6338)Termination phase: Saturation
% 70.07/11.16
% 70.07/11.16 % (6338)Memory used [KB]: 11513
% 70.07/11.16 % (6338)Time elapsed: 0.768 s
% 70.07/11.16 % (6338)Instructions burned: 2575 (million)
% 70.07/11.16 % (6338)------------------------------
% 70.07/11.16 % (6338)------------------------------
% 70.07/11.17 % (6346)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_5740 for (2903ds/454Mi)
% 70.07/11.18 % (6342)Instruction limit reached!
% 70.07/11.18 % (6342)------------------------------
% 70.07/11.18 % (6342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.07/11.18 % (6342)Termination reason: Unknown
% 70.07/11.18 % (6342)Termination phase: Saturation
% 70.07/11.18
% 70.07/11.18 % (6342)Memory used [KB]: 9466
% 70.07/11.18 % (6342)Time elapsed: 0.469 s
% 70.07/11.18 % (6342)Instructions burned: 1549 (million)
% 70.07/11.18 % (6342)------------------------------
% 70.07/11.18 % (6342)------------------------------
% 70.07/11.19 % (6347)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_5740 for (2903ds/3049Mi)
% 70.53/11.22 % (6339)Instruction limit reached!
% 70.53/11.22 % (6339)------------------------------
% 70.53/11.22 % (6339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.53/11.22 % (6339)Termination reason: Unknown
% 70.53/11.22 % (6339)Termination phase: Saturation
% 70.53/11.22
% 70.53/11.22 % (6339)Memory used [KB]: 11001
% 70.53/11.22 % (6339)Time elapsed: 0.789 s
% 70.53/11.22 % (6339)Instructions burned: 2656 (million)
% 70.53/11.22 % (6339)------------------------------
% 70.53/11.22 % (6339)------------------------------
% 70.53/11.23 % (6348)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_5740 for (2903ds/7311Mi)
% 70.98/11.30 % (6340)Instruction limit reached!
% 70.98/11.30 % (6340)------------------------------
% 70.98/11.30 % (6340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.98/11.30 % (6340)Termination reason: Unknown
% 70.98/11.30 % (6340)Termination phase: Saturation
% 70.98/11.30
% 70.98/11.30 % (6340)Memory used [KB]: 4989
% 70.98/11.30 % (6340)Time elapsed: 0.862 s
% 70.98/11.30 % (6340)Instructions burned: 2781 (million)
% 70.98/11.30 % (6340)------------------------------
% 70.98/11.30 % (6340)------------------------------
% 70.98/11.31 % (6346)Instruction limit reached!
% 70.98/11.31 % (6346)------------------------------
% 70.98/11.31 % (6346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.98/11.31 % (6346)Termination reason: Unknown
% 70.98/11.31 % (6346)Termination phase: Saturation
% 70.98/11.31
% 70.98/11.31 % (6346)Memory used [KB]: 12665
% 70.98/11.31 % (6346)Time elapsed: 0.139 s
% 70.98/11.31 % (6346)Instructions burned: 455 (million)
% 70.98/11.31 % (6346)------------------------------
% 70.98/11.31 % (6346)------------------------------
% 70.98/11.31 % (6349)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_5740 for (2902ds/6804Mi)
% 70.98/11.32 % (6350)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_5740 for (2902ds/1683Mi)
% 72.65/11.83 % (6345)Instruction limit reached!
% 72.65/11.83 % (6345)------------------------------
% 72.65/11.83 % (6345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.65/11.83 % (6345)Termination reason: Unknown
% 72.65/11.83 % (6345)Termination phase: Saturation
% 72.65/11.83
% 72.65/11.83 % (6345)Memory used [KB]: 12281
% 72.65/11.83 % (6345)Time elapsed: 0.953 s
% 72.65/11.83 % (6345)Instructions burned: 3201 (million)
% 72.65/11.83 % (6345)------------------------------
% 72.65/11.83 % (6345)------------------------------
% 72.65/11.84 % (6351)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_5740 for (2897ds/4688Mi)
% 72.65/11.85 % (6350)Instruction limit reached!
% 72.65/11.85 % (6350)------------------------------
% 72.65/11.85 % (6350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.65/11.85 % (6350)Termination reason: Unknown
% 72.65/11.85 % (6350)Termination phase: Saturation
% 72.65/11.85
% 72.65/11.85 % (6350)Memory used [KB]: 9083
% 72.65/11.85 % (6350)Time elapsed: 0.533 s
% 72.65/11.85 % (6350)Instructions burned: 1686 (million)
% 72.65/11.85 % (6350)------------------------------
% 72.65/11.85 % (6350)------------------------------
% 72.65/11.86 % (6352)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_5740 for (2896ds/2207Mi)
% 73.44/12.01 % (6337)Instruction limit reached!
% 73.44/12.01 % (6337)------------------------------
% 73.44/12.01 % (6337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.44/12.01 % (6337)Termination reason: Unknown
% 73.44/12.01 % (6337)Termination phase: Saturation
% 73.44/12.01
% 73.44/12.01 % (6337)Memory used [KB]: 16247
% 73.44/12.01 % (6337)Time elapsed: 1.732 s
% 73.44/12.01 % (6337)Instructions burned: 5446 (million)
% 73.44/12.01 % (6337)------------------------------
% 73.44/12.01 % (6337)------------------------------
% 73.44/12.02 % (6353)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=8216:si=on:rtra=on_0 on DTF2THF_5740 for (2895ds/8216Mi)
% 76.98/12.17 % (6347)Instruction limit reached!
% 76.98/12.17 % (6347)------------------------------
% 76.98/12.17 % (6347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.98/12.17 % (6347)Termination reason: Unknown
% 76.98/12.17 % (6347)Termination phase: Saturation
% 76.98/12.17
% 76.98/12.17 % (6347)Memory used [KB]: 10362
% 76.98/12.17 % (6347)Time elapsed: 0.978 s
% 76.98/12.17 % (6347)Instructions burned: 3051 (million)
% 76.98/12.17 % (6347)------------------------------
% 76.98/12.17 % (6347)------------------------------
% 76.98/12.18 % (6354)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_5740 for (2893ds/430Mi)
% 77.91/12.30 % (6344)Refutation not found, non-redundant clauses discarded% (6344)------------------------------
% 77.91/12.30 % (6344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.91/12.30 % (6344)Termination reason: Refutation not found, non-redundant clauses discarded
% 77.91/12.30
% 77.91/12.30 % (6344)Memory used [KB]: 15607
% 77.91/12.30 % (6344)Time elapsed: 1.574 s
% 77.91/12.30 % (6344)Instructions burned: 5189 (million)
% 77.91/12.30 % (6344)------------------------------
% 77.91/12.30 % (6344)------------------------------
% 77.91/12.31 % (6354)Instruction limit reached!
% 77.91/12.31 % (6354)------------------------------
% 77.91/12.31 % (6354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.91/12.31 % (6354)Termination reason: Unknown
% 77.91/12.31 % (6354)Termination phase: Saturation
% 77.91/12.31
% 77.91/12.31 % (6354)Memory used [KB]: 7803
% 77.91/12.31 % (6354)Time elapsed: 0.130 s
% 77.91/12.31 % (6354)Instructions burned: 432 (million)
% 77.91/12.31 % (6354)------------------------------
% 77.91/12.31 % (6354)------------------------------
% 77.91/12.31 % (6355)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_5740 for (2892ds/2012Mi)
% 77.91/12.32 % (6356)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_5740 for (2892ds/631Mi)
% 78.86/12.57 % (6352)Instruction limit reached!
% 78.86/12.57 % (6352)------------------------------
% 78.86/12.57 % (6352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.86/12.57 % (6352)Termination reason: Unknown
% 78.86/12.57 % (6352)Termination phase: Saturation
% 78.86/12.57
% 78.86/12.57 % (6352)Memory used [KB]: 9210
% 78.86/12.57 % (6352)Time elapsed: 0.709 s
% 78.86/12.57 % (6352)Instructions burned: 2208 (million)
% 78.86/12.57 % (6352)------------------------------
% 78.86/12.57 % (6352)------------------------------
% 78.86/12.58 % (6357)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_5740 for (2889ds/8785Mi)
% 78.86/12.59 % (6356)Instruction limit reached!
% 78.86/12.59 % (6356)------------------------------
% 78.86/12.59 % (6356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.86/12.59 % (6356)Termination reason: Unknown
% 78.86/12.59 % (6356)Termination phase: Saturation
% 78.86/12.59
% 78.86/12.59 % (6356)Memory used [KB]: 8955
% 78.86/12.59 % (6356)Time elapsed: 0.289 s
% 78.86/12.59 % (6356)Instructions burned: 631 (million)
% 78.86/12.59 % (6356)------------------------------
% 78.86/12.59 % (6356)------------------------------
% 79.52/12.60 % (6358)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_5740 for (2889ds/739Mi)
% 80.13/12.84 % (6358)Instruction limit reached!
% 80.13/12.84 % (6358)------------------------------
% 80.13/12.84 % (6358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.13/12.84 % (6358)Termination reason: Unknown
% 80.13/12.84 % (6358)Termination phase: Saturation
% 80.13/12.84
% 80.13/12.84 % (6358)Memory used [KB]: 8059
% 80.13/12.84 % (6358)Time elapsed: 0.270 s
% 80.13/12.84 % (6358)Instructions burned: 739 (million)
% 80.13/12.84 % (6358)------------------------------
% 80.13/12.84 % (6358)------------------------------
% 80.13/12.85 % (6359)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_5740 for (2886ds/5473Mi)
% 80.13/12.89 % (6348)First to succeed.
% 80.13/12.89 % (6348)Refutation found. Thanks to Tanya!
% 80.13/12.89 % SZS status Theorem for DTF2THF_5740
% 80.13/12.89 % SZS output start Proof for DTF2THF_5740
% 80.13/12.89 thf(type_def_5, type, itself: ($tType) > $tType).
% 80.13/12.89 thf(type_def_7, type, set: ($tType) > $tType).
% 80.13/12.89 thf(type_def_8, type, stream170649215stream: ($tType) > $tType).
% 80.13/12.89 thf(type_def_9, type, a: $tType).
% 80.13/12.89 thf(func_def_0, type, stream170649215stream: ($tType) > $tType).
% 80.13/12.89 thf(func_def_1, type, set: ($tType) > $tType).
% 80.13/12.89 thf(func_def_2, type, itself: ($tType) > $tType).
% 80.13/12.89 thf(func_def_3, type, a: $tType).
% 80.13/12.89 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_6, type, uminus: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_7, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_8, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_9, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_10, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_11, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_12, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_13, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_14, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_15, type, order_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_16, type, boolean_algebra: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_17, type, semilattice_inf: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_18, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_19, type, bounded_lattice_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 80.13/12.89 thf(func_def_20, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 80.13/12.89 thf(func_def_21, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 80.13/12.89 thf(func_def_22, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 80.13/12.89 thf(func_def_23, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 80.13/12.89 thf(func_def_24, type, bot_bot: !>[X0: $tType]:(X0)).
% 80.13/12.89 thf(func_def_25, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 80.13/12.89 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 80.13/12.89 thf(func_def_27, type, order_antimono: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 80.13/12.89 thf(func_def_28, type, type2: !>[X0: $tType]:(itself @ X0)).
% 80.13/12.89 thf(func_def_29, type, inv_imagep: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o)).
% 80.13/12.89 thf(func_def_30, type, ball: !>[X0: $tType]:(set @ X0 > (X0 > $o) > $o)).
% 80.13/12.89 thf(func_def_31, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 80.13/12.89 thf(func_def_32, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 80.13/12.89 thf(func_def_33, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 80.13/12.89 thf(func_def_34, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 80.13/12.89 thf(func_def_35, type, pairwise: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 80.13/12.89 thf(func_def_36, type, remove: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 80.13/12.89 thf(func_def_37, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 80.13/12.89 thf(func_def_38, type, stream1586597341member: !>[X0: $tType]:(X0 > stream170649215stream @ X0 > $o)).
% 80.13/12.89 thf(func_def_39, type, stream641971652_SCons: !>[X0: $tType]:(X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_40, type, stream1342653232stream: !>[X0: $tType, X1: $tType]:((X0 > stream170649215stream @ X0 > X1) > stream170649215stream @ X0 > X1)).
% 80.13/12.89 thf(func_def_41, type, stream660621732stream: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > $o) > (X0 > stream170649215stream @ X1) > (X0 > X0) > X0 > stream170649215stream @ X1)).
% 80.13/12.89 thf(func_def_42, type, stream1153105665stream: !>[X0: $tType]:((X0 > $o) > stream170649215stream @ X0 > $o)).
% 80.13/12.89 thf(func_def_43, type, stream30925839e_sset: !>[X0: $tType]:(stream170649215stream @ X0 > set @ X0)).
% 80.13/12.89 thf(func_def_44, type, stream2015131171treams: !>[X0: $tType]:(set @ X0 > set @ stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_45, type, stream86250253reamsp: !>[X0: $tType]:((X0 > $o) > stream170649215stream @ X0 > $o)).
% 80.13/12.89 thf(func_def_46, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 80.13/12.89 thf(func_def_47, type, a2: set @ a).
% 80.13/12.89 thf(func_def_48, type, s: stream170649215stream @ a).
% 80.13/12.89 thf(func_def_49, type, sa: stream170649215stream @ a).
% 80.13/12.89 thf(func_def_65, type, sP0: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > $o)).
% 80.13/12.89 thf(func_def_66, type, sP1: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > $o)).
% 80.13/12.89 thf(func_def_67, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 80.13/12.89 thf(func_def_68, type, sK3: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > X0)).
% 80.13/12.89 thf(func_def_69, type, sK4: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_70, type, sK5: !>[X0: $tType]:(stream170649215stream @ X0 > X0 > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_71, type, sK6: !>[X0: $tType]:(stream170649215stream @ X0 > X0 > X0)).
% 80.13/12.89 thf(func_def_72, type, sK7: !>[X0: $tType]:(stream170649215stream @ X0 > X0 > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_73, type, sK8: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 80.13/12.89 thf(func_def_74, type, sK9: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set @ X0 > X0)).
% 80.13/12.89 thf(func_def_75, type, sK10: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 80.13/12.89 thf(func_def_76, type, sK11: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 80.13/12.89 thf(func_def_77, type, sK12: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > set @ X0)).
% 80.13/12.89 thf(func_def_78, type, sK13: !>[X0: $tType]:(set @ X0 > (stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_79, type, sK14: !>[X0: $tType]:((X0 > stream170649215stream @ X0 > $o) > X0)).
% 80.13/12.89 thf(func_def_80, type, sK15: !>[X0: $tType]:((X0 > stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_81, type, sK16: !>[X0: $tType]:((X0 > stream170649215stream @ X0 > $o) > X0)).
% 80.13/12.89 thf(func_def_82, type, sK17: !>[X0: $tType]:((X0 > stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_83, type, sK18: !>[X0: $tType]:((X0 > stream170649215stream @ X0 > $o) > X0)).
% 80.13/12.89 thf(func_def_84, type, sK19: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 80.13/12.89 thf(func_def_85, type, sK20: !>[X0: $tType]:(stream170649215stream @ X0 > X0)).
% 80.13/12.89 thf(func_def_86, type, sK21: !>[X0: $tType]:(stream170649215stream @ X0 > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_87, type, sK22: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > X0)).
% 80.13/12.89 thf(func_def_88, type, sK23: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 80.13/12.89 thf(func_def_90, type, ph25: !>[X0: $tType]:(X0)).
% 80.13/12.89 thf(f5633,plain,(
% 80.13/12.89 $false),
% 80.13/12.89 inference(subsumption_resolution,[status(thm)],[f5624,f1414])).
% 80.13/12.89 thf(f1414,plain,(
% 80.13/12.89 ($true = (member @ a @ (sK20 @ a @ sa) @ a2))),
% 80.13/12.89 inference(trivial_inequality_removal,[status(thm)],[f1411])).
% 80.13/12.89 thf(f1411,plain,(
% 80.13/12.89 ($true = (member @ a @ (sK20 @ a @ sa) @ a2)) | ($true != $true)),
% 80.13/12.89 inference(superposition,[status(thm)],[f1385,f1145])).
% 80.13/12.89 thf(f1145,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X1 : stream170649215stream @ X0] : (($true = (member @ X0 @ (sK20 @ X0 @ X1) @ (stream30925839e_sset @ X0 @ X1)))) )),
% 80.13/12.89 inference(superposition,[status(thm)],[f1010,f1095])).
% 80.13/12.89 thf(f1095,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X1 : stream170649215stream @ X0] : (((stream641971652_SCons @ X0 @ (sK20 @ X0 @ X1) @ (sK21 @ X0 @ X1)) = X1)) )),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f991])).
% 80.13/12.89 thf(f991,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ (sK20 @ X0 @ X1) @ (sK21 @ X0 @ X1)) = X1)),
% 80.13/12.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f888,f990])).
% 80.13/12.89 thf(f990,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : stream170649215stream @ X0] : (? [X2 : X0,X3 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ X2 @ X3) = X1) => ((stream641971652_SCons @ X0 @ (sK20 @ X0 @ X1) @ (sK21 @ X0 @ X1)) = X1))),
% 80.13/12.89 introduced(definition,[],[choice_axiom])).
% 80.13/12.89 thf(f888,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : stream170649215stream @ X0] : ? [X2 : X0,X3 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ X2 @ X3) = X1)),
% 80.13/12.89 inference(ennf_transformation,[status(thm)],[f558])).
% 80.13/12.89 thf(f558,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : stream170649215stream @ X0] : ~! [X2 : X0,X3 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ X2 @ X3) != X1)),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f557])).
% 80.13/12.89 thf(f557,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : stream170649215stream @ X0] : ~! [X2 : X0,X3 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ X2 @ X3) != X1)),
% 80.13/12.89 inference(rectify,[status(thm)],[f8])).
% 80.13/12.89 thf(f8,axiom,(
% 80.13/12.89 ! [X0 : $tType,X16 : stream170649215stream @ X0] : ~! [X17 : X0,X18 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ X17 @ X18) != X16)),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',fact_7_stream_Oexhaust)).
% 80.13/12.89 thf(f1010,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X2 : stream170649215stream @ X0,X1 : X0] : (($true = (member @ X0 @ X1 @ (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X1 @ X2))))) )),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f724])).
% 80.13/12.89 thf(f724,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : X0,X2 : stream170649215stream @ X0] : ($true = (member @ X0 @ X1 @ (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X1 @ X2))))),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f723])).
% 80.13/12.89 thf(f723,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : X0,X2 : stream170649215stream @ X0] : (member @ X0 @ X1 @ (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X1 @ X2)))),
% 80.13/12.89 inference(rectify,[status(thm)],[f5])).
% 80.13/12.89 thf(f5,axiom,(
% 80.13/12.89 ! [X0 : $tType,X9 : X0,X8 : stream170649215stream @ X0] : (member @ X0 @ X9 @ (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X9 @ X8)))),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',fact_4_stream_Oset__intros_I1_J)).
% 80.13/12.89 thf(f1385,plain,(
% 80.13/12.89 ( ! [X0 : a] : (($true != (member @ a @ X0 @ (stream30925839e_sset @ a @ sa))) | ($true = (member @ a @ X0 @ a2))) )),
% 80.13/12.89 inference(trivial_inequality_removal,[status(thm)],[f1384])).
% 80.13/12.89 thf(f1384,plain,(
% 80.13/12.89 ( ! [X0 : a] : (($true = (member @ a @ X0 @ a2)) | ($true != (member @ a @ X0 @ (stream30925839e_sset @ a @ sa))) | ($true != $true)) )),
% 80.13/12.89 inference(superposition,[status(thm)],[f1059,f1036])).
% 80.13/12.89 thf(f1036,plain,(
% 80.13/12.89 ((ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ sa) @ a2) = $true)),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f500])).
% 80.13/12.89 thf(f500,plain,(
% 80.13/12.89 ((ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ sa) @ a2) = $true)),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f499])).
% 80.13/12.89 thf(f499,plain,(
% 80.13/12.89 (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ sa) @ a2)),
% 80.13/12.89 inference(rectify,[status(thm)],[f1])).
% 80.13/12.89 thf(f1,axiom,(
% 80.13/12.89 (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ sa) @ a2)),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',fact_0_streams)).
% 80.13/12.89 thf(f1059,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X2 : set @ X0,X3 : X0,X1 : set @ X0] : (($true != (ord_less_eq @ set @ X0 @ X1 @ X2)) | ($true != (member @ X0 @ X3 @ X1)) | ($true = (member @ X0 @ X3 @ X2))) )),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f887])).
% 80.13/12.89 thf(f887,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : (($true != (ord_less_eq @ set @ X0 @ X1 @ X2)) | ($true != (member @ X0 @ X3 @ X1)) | ($true = (member @ X0 @ X3 @ X2)))),
% 80.13/12.89 inference(flattening,[status(thm)],[f886])).
% 80.13/12.89 thf(f886,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((($true = (member @ X0 @ X3 @ X2)) | ($true != (member @ X0 @ X3 @ X1))) | ($true != (ord_less_eq @ set @ X0 @ X1 @ X2)))),
% 80.13/12.89 inference(ennf_transformation,[status(thm)],[f830])).
% 80.13/12.89 thf(f830,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : (($true = (ord_less_eq @ set @ X0 @ X1 @ X2)) => (($true = (member @ X0 @ X3 @ X1)) => ($true = (member @ X0 @ X3 @ X2))))),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f829])).
% 80.13/12.89 thf(f829,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((member @ X0 @ X3 @ X1) => (member @ X0 @ X3 @ X2)))),
% 80.13/12.89 inference(rectify,[status(thm)],[f21])).
% 80.13/12.89 thf(f21,axiom,(
% 80.13/12.89 ! [X0 : $tType,X11 : set @ X0,X29 : set @ X0,X31 : X0] : ((ord_less_eq @ set @ X0 @ X11 @ X29) => ((member @ X0 @ X31 @ X11) => (member @ X0 @ X31 @ X29)))),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',fact_20_subsetCE)).
% 80.13/12.89 thf(f5624,plain,(
% 80.13/12.89 ($true != (member @ a @ (sK20 @ a @ sa) @ a2))),
% 80.13/12.89 inference(trivial_inequality_removal,[status(thm)],[f5621])).
% 80.13/12.89 thf(f5621,plain,(
% 80.13/12.89 (sa != sa) | ($true != (member @ a @ (sK20 @ a @ sa) @ a2))),
% 80.13/12.89 inference(superposition,[status(thm)],[f3326,f1095])).
% 80.13/12.89 thf(f3326,plain,(
% 80.13/12.89 ( ! [X0 : a] : ((sa != (stream641971652_SCons @ a @ X0 @ (sK21 @ a @ sa))) | ($true != (member @ a @ X0 @ a2))) )),
% 80.13/12.89 inference(trivial_inequality_removal,[status(thm)],[f3318])).
% 80.13/12.89 thf(f3318,plain,(
% 80.13/12.89 ( ! [X0 : a] : (($true != $true) | (sa != (stream641971652_SCons @ a @ X0 @ (sK21 @ a @ sa))) | ($true != (member @ a @ X0 @ a2))) )),
% 80.13/12.89 inference(superposition,[status(thm)],[f1135,f3288])).
% 80.13/12.89 thf(f3288,plain,(
% 80.13/12.89 ($true = (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ (sK21 @ a @ sa)) @ a2))),
% 80.13/12.89 inference(trivial_inequality_removal,[status(thm)],[f3263])).
% 80.13/12.89 thf(f3263,plain,(
% 80.13/12.89 ($true != $true) | ($true = (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ (sK21 @ a @ sa)) @ a2))),
% 80.13/12.89 inference(superposition,[status(thm)],[f1442,f3199])).
% 80.13/12.89 thf(f3199,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X1 : stream170649215stream @ X0] : (($true = (ord_less_eq @ set @ X0 @ (stream30925839e_sset @ X0 @ (sK21 @ X0 @ X1)) @ (stream30925839e_sset @ X0 @ X1)))) )),
% 80.13/12.89 inference(superposition,[status(thm)],[f1363,f1095])).
% 80.13/12.89 thf(f1363,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X2 : stream170649215stream @ X0,X1 : X0] : (($true = (ord_less_eq @ set @ X0 @ (stream30925839e_sset @ X0 @ X2) @ (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X1 @ X2))))) )),
% 80.13/12.89 inference(superposition,[status(thm)],[f1066,f1098])).
% 80.13/12.89 thf(f1098,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X2 : stream170649215stream @ X0,X1 : X0] : (((insert @ X0 @ X1 @ (stream30925839e_sset @ X0 @ X2)) = (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X1 @ X2)))) )),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f708])).
% 80.13/12.89 thf(f708,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : X0,X2 : stream170649215stream @ X0] : ((insert @ X0 @ X1 @ (stream30925839e_sset @ X0 @ X2)) = (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X1 @ X2)))),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f707])).
% 80.13/12.89 thf(f707,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : X0,X2 : stream170649215stream @ X0] : ((insert @ X0 @ X1 @ (stream30925839e_sset @ X0 @ X2)) = (stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X1 @ X2)))),
% 80.13/12.89 inference(rectify,[status(thm)],[f63])).
% 80.13/12.89 thf(f63,axiom,(
% 80.13/12.89 ! [X0 : $tType,X3 : X0,X4 : stream170649215stream @ X0] : ((stream30925839e_sset @ X0 @ (stream641971652_SCons @ X0 @ X3 @ X4)) = (insert @ X0 @ X3 @ (stream30925839e_sset @ X0 @ X4)))),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',fact_62_stream_Oset)).
% 80.13/12.89 thf(f1066,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X2 : X0,X1 : set @ X0] : (($true = (ord_less_eq @ set @ X0 @ X1 @ (insert @ X0 @ X2 @ X1)))) )),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f546])).
% 80.13/12.89 thf(f546,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : X0] : ($true = (ord_less_eq @ set @ X0 @ X1 @ (insert @ X0 @ X2 @ X1)))),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f545])).
% 80.13/12.89 thf(f545,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : X0] : (ord_less_eq @ set @ X0 @ X1 @ (insert @ X0 @ X2 @ X1))),
% 80.13/12.89 inference(rectify,[status(thm)],[f88])).
% 80.13/12.89 thf(f88,axiom,(
% 80.13/12.89 ! [X0 : $tType,X29 : set @ X0,X10 : X0] : (ord_less_eq @ set @ X0 @ X29 @ (insert @ X0 @ X10 @ X29))),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',fact_87_subset__insertI)).
% 80.13/12.89 thf(f1442,plain,(
% 80.13/12.89 ( ! [X0 : set @ a] : (($true != (ord_less_eq @ set @ a @ X0 @ (stream30925839e_sset @ a @ sa))) | ($true = (ord_less_eq @ set @ a @ X0 @ a2))) )),
% 80.13/12.89 inference(trivial_inequality_removal,[status(thm)],[f1439])).
% 80.13/12.89 thf(f1439,plain,(
% 80.13/12.89 ( ! [X0 : set @ a] : (($true = (ord_less_eq @ set @ a @ X0 @ a2)) | ($true != $true) | ($true != (ord_less_eq @ set @ a @ X0 @ (stream30925839e_sset @ a @ sa)))) )),
% 80.13/12.89 inference(superposition,[status(thm)],[f1040,f1036])).
% 80.13/12.89 thf(f1040,plain,(
% 80.13/12.89 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ X0,X1 : set @ X0] : (($true != (ord_less_eq @ set @ X0 @ X2 @ X3)) | ($true = (ord_less_eq @ set @ X0 @ X1 @ X3)) | ($true != (ord_less_eq @ set @ X0 @ X1 @ X2))) )),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f890])).
% 80.13/12.89 thf(f890,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : (($true != (ord_less_eq @ set @ X0 @ X2 @ X3)) | ($true != (ord_less_eq @ set @ X0 @ X1 @ X2)) | ($true = (ord_less_eq @ set @ X0 @ X1 @ X3)))),
% 80.13/12.89 inference(flattening,[status(thm)],[f889])).
% 80.13/12.89 thf(f889,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : ((($true = (ord_less_eq @ set @ X0 @ X1 @ X3)) | ($true != (ord_less_eq @ set @ X0 @ X2 @ X3))) | ($true != (ord_less_eq @ set @ X0 @ X1 @ X2)))),
% 80.13/12.89 inference(ennf_transformation,[status(thm)],[f866])).
% 80.13/12.89 thf(f866,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : (($true = (ord_less_eq @ set @ X0 @ X1 @ X2)) => (($true = (ord_less_eq @ set @ X0 @ X2 @ X3)) => ($true = (ord_less_eq @ set @ X0 @ X1 @ X3))))),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f865])).
% 80.13/12.89 thf(f865,plain,(
% 80.13/12.89 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((ord_less_eq @ set @ X0 @ X2 @ X3) => (ord_less_eq @ set @ X0 @ X1 @ X3)))),
% 80.13/12.89 inference(rectify,[status(thm)],[f56])).
% 80.13/12.89 thf(f56,axiom,(
% 80.13/12.89 ! [X0 : $tType,X11 : set @ X0,X29 : set @ X0,X46 : set @ X0] : ((ord_less_eq @ set @ X0 @ X11 @ X29) => ((ord_less_eq @ set @ X0 @ X29 @ X46) => (ord_less_eq @ set @ X0 @ X11 @ X46)))),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',fact_55_subset__trans)).
% 80.13/12.89 thf(f1135,plain,(
% 80.13/12.89 ( ! [X2 : stream170649215stream @ a,X0 : a] : (($true != (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ X2) @ a2)) | (sa != (stream641971652_SCons @ a @ X0 @ X2)) | ($true != (member @ a @ X0 @ a2))) )),
% 80.13/12.89 inference(equality_resolution,[status(thm)],[f1100])).
% 80.13/12.89 thf(f1100,plain,(
% 80.13/12.89 ( ! [X2 : stream170649215stream @ a,X0 : a,X1 : stream170649215stream @ a] : ((X1 != X2) | ($true != (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ X2) @ a2)) | (sa != (stream641971652_SCons @ a @ X0 @ X1)) | ($true != (member @ a @ X0 @ a2))) )),
% 80.13/12.89 inference(cnf_transformation,[status(thm)],[f938])).
% 80.13/12.89 thf(f938,plain,(
% 80.13/12.89 ! [X0 : a,X1 : stream170649215stream @ a] : ((($true != (member @ stream170649215stream @ a @ X1 @ (stream2015131171treams @ a @ a2))) & ! [X2 : stream170649215stream @ a] : ((X1 != X2) | ($true != (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ X2) @ a2)))) | (sa != (stream641971652_SCons @ a @ X0 @ X1)) | ($true != (member @ a @ X0 @ a2)))),
% 80.13/12.89 inference(ennf_transformation,[status(thm)],[f716])).
% 80.13/12.89 thf(f716,plain,(
% 80.13/12.89 ~? [X0 : a,X1 : stream170649215stream @ a] : (($true = (member @ a @ X0 @ a2)) & (sa = (stream641971652_SCons @ a @ X0 @ X1)) & (? [X2 : stream170649215stream @ a] : ((X1 = X2) & ($true = (ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ X2) @ a2))) | ($true = (member @ stream170649215stream @ a @ X1 @ (stream2015131171treams @ a @ a2)))))),
% 80.13/12.89 inference(fool_elimination,[status(thm)],[f715])).
% 80.13/12.89 thf(f715,plain,(
% 80.13/12.89 ~? [X0 : a,X1 : stream170649215stream @ a] : ((? [X2 : stream170649215stream @ a] : ((ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ X2) @ a2) & (X1 = X2)) | (member @ stream170649215stream @ a @ X1 @ (stream2015131171treams @ a @ a2))) & (member @ a @ X0 @ a2) & (sa = (stream641971652_SCons @ a @ X0 @ X1)))),
% 80.13/12.89 inference(rectify,[status(thm)],[f292])).
% 80.13/12.89 thf(f292,negated_conjecture,(
% 80.13/12.89 ~? [X25 : a,X26 : stream170649215stream @ a] : ((? [X73 : stream170649215stream @ a] : ((ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ X73) @ a2) & (X26 = X73)) | (member @ stream170649215stream @ a @ X26 @ (stream2015131171treams @ a @ a2))) & (member @ a @ X25 @ a2) & (sa = (stream641971652_SCons @ a @ X25 @ X26)))),
% 80.13/12.89 inference(negated_conjecture,[status(cth)],[f291])).
% 80.13/12.89 thf(f291,conjecture,(
% 80.13/12.89 ? [X25 : a,X26 : stream170649215stream @ a] : ((? [X73 : stream170649215stream @ a] : ((ord_less_eq @ set @ a @ (stream30925839e_sset @ a @ X73) @ a2) & (X26 = X73)) | (member @ stream170649215stream @ a @ X26 @ (stream2015131171treams @ a @ a2))) & (member @ a @ X25 @ a2) & (sa = (stream641971652_SCons @ a @ X25 @ X26)))),
% 80.13/12.89 file('/export/starexec/sandbox/tmp/tmp.OaYfS02p20/DTF2THF_5740.p',conj_0)).
% 80.13/12.89 % SZS output end Proof for DTF2THF_5740
% 80.13/12.89 % (6348)------------------------------
% 80.13/12.89 % (6348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.13/12.89 % (6348)Termination reason: Refutation
% 80.13/12.89
% 80.13/12.89 % (6348)Memory used [KB]: 12665
% 80.13/12.89 % (6348)Time elapsed: 1.655 s
% 80.13/12.89 % (6348)Instructions burned: 5553 (million)
% 80.13/12.89 % (6348)------------------------------
% 80.13/12.89 % (6348)------------------------------
% 80.13/12.89 % (6109)Success in time 11.356 s
%------------------------------------------------------------------------------