%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP111^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:38 AM UTC 2026
% Result : Theorem 15.48s 3.49s
% Output : Refutation 15.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP111^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:27:04 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : ITP111^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.45 % Domain : Interactive Theorem Proving
% 0.19/0.45 % Problem : Sledgehammer Lower_Semicontinuous problem prob_214__6249176_1
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Des21]
% 0.19/0.45 % Names : Lower_Semicontinuous/prob_214__6249176_1 [Des21]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.33 v9.1.0, 0.00 v8.1.0, 0.25 v7.5.0
% 0.19/0.45 % Syntax : Number of formulae : 358 ( 77 unt; 60 typ; 0 def)
% 0.19/0.45 % Number of atoms : 973 ( 342 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 7 ( 3 avg)
% 0.19/0.45 % Number of connectives : 3496 ( 99 ~; 32 |; 63 &;2858 @)
% 0.19/0.45 % ( 0 <=>; 444 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 17 ( 7 avg)
% 0.19/0.45 % Number of types : 4 ( 3 usr)
% 0.19/0.45 % Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 58 ( 57 usr; 3 con; 0-5 aty)
% 0.19/0.45 % Number of variables : 874 ( 9 ^; 773 !; 39 ?; 874 :)
% 0.19/0.45 % ( 53 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:25:45.493
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % Could-be-implicit typings (4)
% 0.19/0.45 thf(ty_t_Extended__Real_Oereal,type,
% 0.19/0.45 extended_ereal: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Real_Oreal,type,
% 0.19/0.45 real: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Set_Oset,type,
% 0.19/0.45 set: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_a,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 % Explicit typings (56)
% 0.19/0.45 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 0.19/0.45 real_V2090557954_space:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_HOL_Otype,type,
% 0.19/0.45 type:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Oidom,type,
% 0.19/0.45 idom:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Oring,type,
% 0.19/0.45 ring:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ozero,type,
% 0.19/0.45 zero:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Fields_Ofield,type,
% 0.19/0.45 field:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ouminus,type,
% 0.19/0.45 uminus:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.19/0.45 ord:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.45 order:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Omult__zero,type,
% 0.19/0.45 mult_zero:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ogroup__add,type,
% 0.19/0.45 group_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Ono__bot,type,
% 0.19/0.45 no_bot:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Ono__top,type,
% 0.19/0.45 no_top:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.45 linorder:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.19/0.45 preorder:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Owellorder,type,
% 0.19/0.45 wellorder:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Fields_Odivision__ring,type,
% 0.19/0.45 division_ring:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Osemidom__divide,type,
% 0.19/0.45 semidom_divide:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.19/0.45 semigroup_mult:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Odense__order,type,
% 0.19/0.45 dense_order:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.19/0.45 linordered_idom:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Olinordered__ring,type,
% 0.19/0.45 linordered_ring:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Fields_Olinordered__field,type,
% 0.19/0.45 linordered_field:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.19/0.45 ab_semigroup_mult:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.19/0.45 boolean_algebra:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.19/0.45 ordered_ab_group_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Topological__Spaces_Ot0__space,type,
% 0.19/0.45 topological_t0_space:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Topological__Spaces_Ot1__space,type,
% 0.19/0.45 topological_t1_space:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 0.19/0.45 linord581940658strict:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.19/0.45 linord219039673up_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 0.19/0.45 semiri1193490041visors:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Olinordered__semiring__strict,type,
% 0.19/0.45 linord20386208strict:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.19/0.45 linord1659791738miring:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Topological__Spaces_Odiscrete__topology,type,
% 0.19/0.45 topolo2133971006pology:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 0.19/0.45 topolo503727757_space:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.19/0.45 canoni770627133id_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Olinordered__comm__semiring__strict,type,
% 0.19/0.45 linord893533164strict:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 0.19/0.45 semiri1923998003cancel:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Euclidean__Division_Oeuclidean__ring__cancel,type,
% 0.19/0.45 euclid24285859cancel:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Euclidean__Division_Oeuclidean__semiring__cancel,type,
% 0.19/0.45 euclid191655569cancel:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.19/0.45 condit1656338222tinuum:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Extended__Nat_Oinfinity__class_Oinfinity,type,
% 0.19/0.45 extend1396239628finity:
% 0.19/0.45 !>[A: $tType] : A ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Extended__Real_Oereal_OMInfty,type,
% 0.19/0.45 extended_MInfty: extended_ereal ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Extended__Real_Oereal_OPInfty,type,
% 0.19/0.45 extended_PInfty: extended_ereal ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Extended__Real_Oereal_Orec__ereal,type,
% 0.19/0.45 extended_rec_ereal:
% 0.19/0.45 !>[A: $tType] : ( ( real > A ) > A > A > extended_ereal > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.19/0.45 times_times:
% 0.19/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.19/0.45 uminus_uminus:
% 0.19/0.45 !>[A: $tType] : ( A > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.19/0.45 zero_zero:
% 0.19/0.45 !>[A: $tType] : A ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Lower__Semicontinuous__Mirabelle__quczrylfpw_Olsc__at,type,
% 0.19/0.45 lower_582600101lsc_at:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( A > ( A > B ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.19/0.45 ord_less:
% 0.19/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Rings_Odivide__class_Odivide,type,
% 0.19/0.45 divide_divide:
% 0.19/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set_OCollect,type,
% 0.19/0.45 collect:
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Topological__Spaces_Oopen__class_Oopen,type,
% 0.19/0.45 topolo1751647064n_open:
% 0.19/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member,type,
% 0.19/0.45 member:
% 0.19/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_f,type,
% 0.19/0.45 f: a > extended_ereal ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_x0,type,
% 0.19/0.45 x0: a ).
% 0.19/0.45
% 0.19/0.45 % Relevant facts (255)
% 0.19/0.45 thf(fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 0.19/0.45 ( ( ( f @ x0 )
% 0.19/0.45 = ( extend1396239628finity @ extended_ereal ) )
% 0.19/0.45 => ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 0.19/0.45 = ( ! [C: extended_ereal] :
% 0.19/0.45 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 0.19/0.45 => ? [T: set @ a] :
% 0.19/0.45 ( ( topolo1751647064n_open @ a @ T )
% 0.19/0.45 & ( member @ a @ x0 @ T )
% 0.19/0.45 & ! [X: a] :
% 0.19/0.45 ( ( member @ a @ X @ T )
% 0.19/0.45 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>f x0 = \<infinity> \<Longrightarrow> lsc_at x0 f = (\<forall>C<f x0. \<exists>T. open T \<and> x0 \<in> T \<and> (\<forall>y\<in>T. C < f y))\<close>
% 0.19/0.45 thf(fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 0.19/0.45 ( ( ( f @ x0 )
% 0.19/0.45 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.19/0.45 => ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 0.19/0.45 = ( ! [C: extended_ereal] :
% 0.19/0.45 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 0.19/0.45 => ? [T: set @ a] :
% 0.19/0.45 ( ( topolo1751647064n_open @ a @ T )
% 0.19/0.45 & ( member @ a @ x0 @ T )
% 0.19/0.45 & ! [X: a] :
% 0.19/0.45 ( ( member @ a @ X @ T )
% 0.19/0.45 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>f x0 = - \<infinity> \<Longrightarrow> lsc_at x0 f = (\<forall>C<f x0. \<exists>T. open T \<and> x0 \<in> T \<and> (\<forall>y\<in>T. C < f y))\<close>
% 0.19/0.45 thf(fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 0.19/0.45 ( ( ( f @ x0 )
% 0.19/0.45 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.19/0.45 => ( ( ( f @ x0 )
% 0.19/0.45 != ( extend1396239628finity @ extended_ereal ) )
% 0.19/0.45 => ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 0.19/0.45 = ( ! [C: extended_ereal] :
% 0.19/0.45 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 0.19/0.45 => ? [T: set @ a] :
% 0.19/0.45 ( ( topolo1751647064n_open @ a @ T )
% 0.19/0.45 & ( member @ a @ x0 @ T )
% 0.19/0.45 & ! [X: a] :
% 0.19/0.45 ( ( member @ a @ X @ T )
% 0.19/0.45 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>\<lbrakk>f x0 \<noteq> - \<infinity>; f x0 \<noteq> \<infinity>\<rbrakk> \<Longrightarrow> lsc_at x0 f = (\<forall>C<f x0. \<exists>T. open T \<and> x0 \<in> T \<and> (\<forall>y\<in>T. C < f y))\<close>
% 0.19/0.45 thf(fact_3_lsc__at__MInfty,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( topolo503727757_space @ A )
% 0.19/0.45 => ! [F: A > extended_ereal,X0: A] :
% 0.19/0.45 ( ( ( F @ X0 )
% 0.19/0.45 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.19/0.45 => ( lower_582600101lsc_at @ A @ extended_ereal @ X0 @ F ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lsc_at_MInfty
% 0.19/0.45 thf(fact_4_t0__space,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( topological_t0_space @ A )
% 0.19/0.45 => ! [X2: A,Y: A] :
% 0.19/0.45 ( ( X2 != Y )
% 0.19/0.45 => ? [U: set @ A] :
% 0.19/0.45 ( ( topolo1751647064n_open @ A @ U )
% 0.19/0.45 & ( ( member @ A @ X2 @ U )
% 0.19/0.45 != ( member @ A @ Y @ U ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % t0_space
% 0.19/0.45 thf(fact_5_t1__space,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( topological_t1_space @ A )
% 0.19/0.45 => ! [X2: A,Y: A] :
% 0.19/0.45 ( ( X2 != Y )
% 0.19/0.45 => ? [U: set @ A] :
% 0.19/0.45 ( ( topolo1751647064n_open @ A @ U )
% 0.19/0.45 & ( member @ A @ X2 @ U )
% 0.19/0.45 & ~ ( member @ A @ Y @ U ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % t1_space
% 0.19/0.45 thf(fact_6_separation__t0,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( topological_t0_space @ A )
% 0.19/0.45 => ! [X2: A,Y: A] :
% 0.19/0.45 ( ( X2 != Y )
% 0.19/0.45 = ( ? [U2: set @ A] :
% 0.19/0.45 ( ( topolo1751647064n_open @ A @ U2 )
% 0.19/0.45 & ( ( member @ A @ X2 @ U2 )
% 0.19/0.45 != ( member @ A @ Y @ U2 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % separation_t0
% 0.19/0.45 thf(fact_7_separation__t1,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( topological_t1_space @ A )
% 0.19/0.45 => ! [X2: A,Y: A] :
% 0.19/0.45 ( ( X2 != Y )
% 0.19/0.45 = ( ? [U2: set @ A] :
% 0.19/0.45 ( ( topolo1751647064n_open @ A @ U2 )
% 0.19/0.45 & ( member @ A @ X2 @ U2 )
% 0.19/0.45 & ~ ( member @ A @ Y @ U2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % separation_t1
% 0.19/0.45 thf(fact_8_open__discrete,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( topolo2133971006pology @ A )
% 0.19/0.45 => ! [A2: set @ A] : ( topolo1751647064n_open @ A @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % open_discrete
% 0.19/0.45 thf(fact_9_minf_I11_J,axiom,
% 0.19/0.45 ! [C2: $tType,D: $tType] :
% 0.19/0.45 ( ( ord @ C2 )
% 0.19/0.45 => ! [F2: D] :
% 0.19/0.45 ? [Z: C2] :
% 0.19/0.45 ! [X3: C2] :
% 0.19/0.45 ( ( ord_less @ C2 @ X3 @ Z )
% 0.19/0.45 => ( F2 = F2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(11)
% 0.19/0.45 thf(fact_10_minf_I7_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z )
% 0.19/0.45 => ~ ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(7)
% 0.19/0.45 thf(fact_11_minf_I5_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z )
% 0.19/0.45 => ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(5)
% 0.19/0.45 thf(fact_12_minf_I4_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z )
% 0.19/0.45 => ( X3 != T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(4)
% 0.19/0.45 thf(fact_13_minf_I3_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z )
% 0.19/0.45 => ( X3 != T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(3)
% 0.19/0.45 thf(fact_14_minf_I2_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A )
% 0.19/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.19/0.45 ( ? [Z2: A] :
% 0.19/0.45 ! [X4: A] :
% 0.19/0.45 ( ( ord_less @ A @ X4 @ Z2 )
% 0.19/0.45 => ( ( P @ X4 )
% 0.19/0.45 = ( P2 @ X4 ) ) )
% 0.19/0.45 => ( ? [Z2: A] :
% 0.19/0.45 ! [X4: A] :
% 0.19/0.45 ( ( ord_less @ A @ X4 @ Z2 )
% 0.19/0.45 => ( ( Q @ X4 )
% 0.19/0.45 = ( Q2 @ X4 ) ) )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z )
% 0.19/0.45 => ( ( ( P @ X3 )
% 0.19/0.45 | ( Q @ X3 ) )
% 0.19/0.45 = ( ( P2 @ X3 )
% 0.19/0.45 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(2)
% 0.19/0.45 thf(fact_15_pinf_I1_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A )
% 0.19/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.19/0.45 ( ? [Z2: A] :
% 0.19/0.45 ! [X4: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z2 @ X4 )
% 0.19/0.45 => ( ( P @ X4 )
% 0.19/0.45 = ( P2 @ X4 ) ) )
% 0.19/0.45 => ( ? [Z2: A] :
% 0.19/0.45 ! [X4: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z2 @ X4 )
% 0.19/0.45 => ( ( Q @ X4 )
% 0.19/0.45 = ( Q2 @ X4 ) ) )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X3 )
% 0.19/0.45 => ( ( ( P @ X3 )
% 0.19/0.45 & ( Q @ X3 ) )
% 0.19/0.45 = ( ( P2 @ X3 )
% 0.19/0.45 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(1)
% 0.19/0.45 thf(fact_16_pinf_I2_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A )
% 0.19/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.19/0.45 ( ? [Z2: A] :
% 0.19/0.45 ! [X4: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z2 @ X4 )
% 0.19/0.45 => ( ( P @ X4 )
% 0.19/0.45 = ( P2 @ X4 ) ) )
% 0.19/0.45 => ( ? [Z2: A] :
% 0.19/0.45 ! [X4: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z2 @ X4 )
% 0.19/0.45 => ( ( Q @ X4 )
% 0.19/0.45 = ( Q2 @ X4 ) ) )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.45 => ( ( ( P @ X3 )
% 0.30/0.45 | ( Q @ X3 ) )
% 0.30/0.45 = ( ( P2 @ X3 )
% 0.30/0.45 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % pinf(2)
% 0.30/0.45 thf(fact_17_pinf_I3_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [T2: A] :
% 0.30/0.45 ? [Z: A] :
% 0.30/0.45 ! [X3: A] :
% 0.30/0.45 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.45 => ( X3 != T2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % pinf(3)
% 0.30/0.45 thf(fact_18_pinf_I4_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [T2: A] :
% 0.30/0.45 ? [Z: A] :
% 0.30/0.45 ! [X3: A] :
% 0.30/0.45 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.45 => ( X3 != T2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % pinf(4)
% 0.30/0.45 thf(fact_19_pinf_I5_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [T2: A] :
% 0.30/0.45 ? [Z: A] :
% 0.30/0.45 ! [X3: A] :
% 0.30/0.45 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.45 => ~ ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % pinf(5)
% 0.30/0.45 thf(fact_20_pinf_I7_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [T2: A] :
% 0.30/0.45 ? [Z: A] :
% 0.30/0.45 ! [X3: A] :
% 0.30/0.45 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.45 => ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % pinf(7)
% 0.30/0.45 thf(fact_21_pinf_I11_J,axiom,
% 0.30/0.45 ! [C2: $tType,D: $tType] :
% 0.30/0.45 ( ( ord @ C2 )
% 0.30/0.45 => ! [F2: D] :
% 0.30/0.45 ? [Z: C2] :
% 0.30/0.45 ! [X3: C2] :
% 0.30/0.45 ( ( ord_less @ C2 @ Z @ X3 )
% 0.30/0.45 => ( F2 = F2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % pinf(11)
% 0.30/0.45 thf(fact_22_minf_I1_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.45 ( ? [Z2: A] :
% 0.30/0.45 ! [X4: A] :
% 0.30/0.45 ( ( ord_less @ A @ X4 @ Z2 )
% 0.30/0.45 => ( ( P @ X4 )
% 0.30/0.45 = ( P2 @ X4 ) ) )
% 0.30/0.45 => ( ? [Z2: A] :
% 0.30/0.45 ! [X4: A] :
% 0.30/0.45 ( ( ord_less @ A @ X4 @ Z2 )
% 0.30/0.45 => ( ( Q @ X4 )
% 0.30/0.45 = ( Q2 @ X4 ) ) )
% 0.30/0.45 => ? [Z: A] :
% 0.30/0.45 ! [X3: A] :
% 0.30/0.45 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.45 => ( ( ( P @ X3 )
% 0.30/0.45 & ( Q @ X3 ) )
% 0.30/0.45 = ( ( P2 @ X3 )
% 0.30/0.45 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % minf(1)
% 0.30/0.45 thf(fact_23_ereal__MInfty__lessI,axiom,
% 0.30/0.45 ! [A3: extended_ereal] :
% 0.30/0.45 ( ( A3
% 0.30/0.45 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.45 => ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ A3 ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_MInfty_lessI
% 0.30/0.45 thf(fact_24_ereal__infty__less_I2_J,axiom,
% 0.30/0.45 ! [X2: extended_ereal] :
% 0.30/0.45 ( ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ X2 )
% 0.30/0.45 = ( X2
% 0.30/0.45 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_infty_less(2)
% 0.30/0.45 thf(fact_25_ereal__minus__less__minus,axiom,
% 0.30/0.45 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.45 ( ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) @ ( uminus_uminus @ extended_ereal @ B2 ) )
% 0.30/0.45 = ( ord_less @ extended_ereal @ B2 @ A3 ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_minus_less_minus
% 0.30/0.45 thf(fact_26_ereal__less__PInfty,axiom,
% 0.30/0.45 ! [A3: extended_ereal] :
% 0.30/0.45 ( ( A3
% 0.30/0.45 != ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.45 => ( ord_less @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_less_PInfty
% 0.30/0.45 thf(fact_27_ereal__infty__less_I1_J,axiom,
% 0.30/0.45 ! [X2: extended_ereal] :
% 0.30/0.45 ( ( ord_less @ extended_ereal @ X2 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.45 = ( X2
% 0.30/0.45 != ( extend1396239628finity @ extended_ereal ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_infty_less(1)
% 0.30/0.45 thf(fact_28_neg__less__iff__less,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ordered_ab_group_add @ A )
% 0.30/0.45 => ! [B2: A,A3: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) )
% 0.30/0.45 = ( ord_less @ A @ A3 @ B2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_less_iff_less
% 0.30/0.45 thf(fact_29_less__ereal_Osimps_I3_J,axiom,
% 0.30/0.45 ! [A3: extended_ereal] :
% 0.30/0.45 ~ ( ord_less @ extended_ereal @ A3 @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_ereal.simps(3)
% 0.30/0.45 thf(fact_30_less__ereal_Osimps_I6_J,axiom,
% 0.30/0.45 ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) ).
% 0.30/0.45
% 0.30/0.45 % less_ereal.simps(6)
% 0.30/0.45 thf(fact_31_ereal__uminus__eq__iff,axiom,
% 0.30/0.45 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.45 ( ( ( uminus_uminus @ extended_ereal @ A3 )
% 0.30/0.45 = ( uminus_uminus @ extended_ereal @ B2 ) )
% 0.30/0.45 = ( A3 = B2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_uminus_eq_iff
% 0.30/0.45 thf(fact_32_ereal__uminus__uminus,axiom,
% 0.30/0.45 ! [A3: extended_ereal] :
% 0.30/0.45 ( ( uminus_uminus @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) )
% 0.30/0.45 = A3 ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_uminus_uminus
% 0.30/0.45 thf(fact_33_neg__equal__iff__equal,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( group_add @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( ( uminus_uminus @ A @ A3 )
% 0.30/0.45 = ( uminus_uminus @ A @ B2 ) )
% 0.30/0.45 = ( A3 = B2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_equal_iff_equal
% 0.30/0.45 thf(fact_34_add_Oinverse__inverse,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( group_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A3 ) )
% 0.30/0.45 = A3 ) ) ).
% 0.30/0.45
% 0.30/0.45 % add.inverse_inverse
% 0.30/0.45 thf(fact_35_minus__equation__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( group_add @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( ( uminus_uminus @ A @ A3 )
% 0.30/0.45 = B2 )
% 0.30/0.45 = ( ( uminus_uminus @ A @ B2 )
% 0.30/0.45 = A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % minus_equation_iff
% 0.30/0.45 thf(fact_36_equation__minus__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( group_add @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( A3
% 0.30/0.45 = ( uminus_uminus @ A @ B2 ) )
% 0.30/0.45 = ( B2
% 0.30/0.45 = ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % equation_minus_iff
% 0.30/0.45 thf(fact_37_ereal__uminus__eq__reorder,axiom,
% 0.30/0.45 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.45 ( ( ( uminus_uminus @ extended_ereal @ A3 )
% 0.30/0.45 = B2 )
% 0.30/0.45 = ( A3
% 0.30/0.45 = ( uminus_uminus @ extended_ereal @ B2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_uminus_eq_reorder
% 0.30/0.45 thf(fact_38_less__minus__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ordered_ab_group_add @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 0.30/0.45 = ( ord_less @ A @ B2 @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_minus_iff
% 0.30/0.45 thf(fact_39_minus__less__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ordered_ab_group_add @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 0.30/0.45 = ( ord_less @ A @ ( uminus_uminus @ A @ B2 ) @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % minus_less_iff
% 0.30/0.45 thf(fact_40_MInfty__neq__PInfty_I1_J,axiom,
% 0.30/0.45 ( ( extend1396239628finity @ extended_ereal )
% 0.30/0.45 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % MInfty_neq_PInfty(1)
% 0.30/0.45 thf(fact_41_less__ereal_Osimps_I2_J,axiom,
% 0.30/0.45 ! [A3: extended_ereal] :
% 0.30/0.45 ~ ( ord_less @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 ) ).
% 0.30/0.45
% 0.30/0.45 % less_ereal.simps(2)
% 0.30/0.45 thf(fact_42_ereal__less__uminus__reorder,axiom,
% 0.30/0.45 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.45 ( ( ord_less @ extended_ereal @ A3 @ ( uminus_uminus @ extended_ereal @ B2 ) )
% 0.30/0.45 = ( ord_less @ extended_ereal @ B2 @ ( uminus_uminus @ extended_ereal @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_less_uminus_reorder
% 0.30/0.45 thf(fact_43_ereal__uminus__less__reorder,axiom,
% 0.30/0.45 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.45 ( ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) @ B2 )
% 0.30/0.45 = ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ B2 ) @ A3 ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_uminus_less_reorder
% 0.30/0.45 thf(fact_44_compl__eq__compl__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( boolean_algebra @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ( uminus_uminus @ A @ X2 )
% 0.30/0.45 = ( uminus_uminus @ A @ Y ) )
% 0.30/0.45 = ( X2 = Y ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_eq_compl_iff
% 0.30/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.45 ! [A: $tType,A3: A,P: A > $o] :
% 0.30/0.45 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.30/0.45 = ( P @ A3 ) ) ).
% 0.30/0.45
% 0.30/0.45 % mem_Collect_eq
% 0.30/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.45 ! [A: $tType,A2: set @ A] :
% 0.30/0.45 ( ( collect @ A
% 0.30/0.45 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 0.30/0.45 = A2 ) ).
% 0.30/0.45
% 0.30/0.45 % Collect_mem_eq
% 0.30/0.45 thf(fact_47_Collect__cong,axiom,
% 0.30/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.45 ( ! [X4: A] :
% 0.30/0.45 ( ( P @ X4 )
% 0.30/0.45 = ( Q @ X4 ) )
% 0.30/0.45 => ( ( collect @ A @ P )
% 0.30/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Collect_cong
% 0.30/0.45 thf(fact_48_ext,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.45 ( ! [X4: A] :
% 0.30/0.45 ( ( F @ X4 )
% 0.30/0.45 = ( G @ X4 ) )
% 0.30/0.45 => ( F = G ) ) ).
% 0.30/0.45
% 0.30/0.45 % ext
% 0.30/0.45 thf(fact_49_double__compl,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( boolean_algebra @ A )
% 0.30/0.45 => ! [X2: A] :
% 0.30/0.45 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X2 ) )
% 0.30/0.45 = X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % double_compl
% 0.30/0.45 thf(fact_50_uminus__apply,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( uminus @ B )
% 0.30/0.45 => ( ( uminus_uminus @ ( A > B ) )
% 0.30/0.45 = ( ^ [A4: A > B,X: A] : ( uminus_uminus @ B @ ( A4 @ X ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % uminus_apply
% 0.30/0.45 thf(fact_51_verit__minus__simplify_I4_J,axiom,
% 0.30/0.45 ! [B: $tType] :
% 0.30/0.45 ( ( group_add @ B )
% 0.30/0.45 => ! [B2: B] :
% 0.30/0.45 ( ( uminus_uminus @ B @ ( uminus_uminus @ B @ B2 ) )
% 0.30/0.45 = B2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % verit_minus_simplify(4)
% 0.30/0.45 thf(fact_52_verit__negate__coefficient_I2_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ordered_ab_group_add @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.45 => ( ord_less @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % verit_negate_coefficient(2)
% 0.30/0.45 thf(fact_53_compl__less__swap1,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( boolean_algebra @ A )
% 0.30/0.45 => ! [Y: A,X2: A] :
% 0.30/0.45 ( ( ord_less @ A @ Y @ ( uminus_uminus @ A @ X2 ) )
% 0.30/0.45 => ( ord_less @ A @ X2 @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_less_swap1
% 0.30/0.45 thf(fact_54_compl__less__swap2,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( boolean_algebra @ A )
% 0.30/0.45 => ! [Y: A,X2: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ Y ) @ X2 )
% 0.30/0.45 => ( ord_less @ A @ ( uminus_uminus @ A @ X2 ) @ Y ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_less_swap2
% 0.30/0.45 thf(fact_55_compl__less__compl__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( boolean_algebra @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ X2 ) @ ( uminus_uminus @ A @ Y ) )
% 0.30/0.45 = ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_less_compl_iff
% 0.30/0.45 thf(fact_56_MInfty__eq__minfinity,axiom,
% 0.30/0.45 ( extended_MInfty
% 0.30/0.45 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % MInfty_eq_minfinity
% 0.30/0.45 thf(fact_57_verit__comp__simplify1_I1_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.30/0.45
% 0.30/0.45 % verit_comp_simplify1(1)
% 0.30/0.45 thf(fact_58_verit__negate__coefficient_I3_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ordered_ab_group_add @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( A3 = B2 )
% 0.30/0.45 => ( ( uminus_uminus @ A @ A3 )
% 0.30/0.45 = ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % verit_negate_coefficient(3)
% 0.30/0.45 thf(fact_59_fun__Compl__def,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( uminus @ B )
% 0.30/0.45 => ( ( uminus_uminus @ ( A > B ) )
% 0.30/0.45 = ( ^ [A4: A > B,X: A] : ( uminus_uminus @ B @ ( A4 @ X ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % fun_Compl_def
% 0.30/0.45 thf(fact_60_uminus__ereal_Osimps_I2_J,axiom,
% 0.30/0.45 ( ( uminus_uminus @ extended_ereal @ extended_PInfty )
% 0.30/0.45 = extended_MInfty ) ).
% 0.30/0.45
% 0.30/0.45 % uminus_ereal.simps(2)
% 0.30/0.45 thf(fact_61_uminus__ereal_Osimps_I3_J,axiom,
% 0.30/0.45 ( ( uminus_uminus @ extended_ereal @ extended_MInfty )
% 0.30/0.45 = extended_PInfty ) ).
% 0.30/0.45
% 0.30/0.45 % uminus_ereal.simps(3)
% 0.30/0.45 thf(fact_62_ereal__less_I6_J,axiom,
% 0.30/0.45 ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( zero_zero @ extended_ereal ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_less(6)
% 0.30/0.45 thf(fact_63_ereal_Osimps_I13_J,axiom,
% 0.30/0.45 ! [A: $tType,F1: real > A,F22: A,F3: A] :
% 0.30/0.45 ( ( extended_rec_ereal @ A @ F1 @ F22 @ F3 @ extended_MInfty )
% 0.30/0.45 = F3 ) ).
% 0.30/0.45
% 0.30/0.45 % ereal.simps(13)
% 0.30/0.45 thf(fact_64_ex__gt__or__lt,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( condit1656338222tinuum @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ? [B3: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B3 )
% 0.30/0.45 | ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ex_gt_or_lt
% 0.30/0.45 thf(fact_65_linorder__neqE__linordered__idom,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linordered_idom @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( X2 != Y )
% 0.30/0.45 => ( ~ ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % linorder_neqE_linordered_idom
% 0.30/0.45 thf(fact_66_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [B2: A,A3: A] :
% 0.30/0.45 ( ( ord_less @ A @ B2 @ A3 )
% 0.30/0.45 => ( A3 != B2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % dual_order.strict_implies_not_eq
% 0.30/0.45 thf(fact_67_not__gr__zero,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( canoni770627133id_add @ A )
% 0.30/0.45 => ! [N: A] :
% 0.30/0.45 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.30/0.45 = ( N
% 0.30/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % not_gr_zero
% 0.30/0.45 thf(fact_68_neg__equal__zero,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linord219039673up_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( ( uminus_uminus @ A @ A3 )
% 0.30/0.45 = A3 )
% 0.30/0.45 = ( A3
% 0.30/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_equal_zero
% 0.30/0.45 thf(fact_69_equal__neg__zero,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linord219039673up_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( A3
% 0.30/0.45 = ( uminus_uminus @ A @ A3 ) )
% 0.30/0.45 = ( A3
% 0.30/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % equal_neg_zero
% 0.30/0.45 thf(fact_70_neg__equal__0__iff__equal,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( group_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( ( uminus_uminus @ A @ A3 )
% 0.30/0.45 = ( zero_zero @ A ) )
% 0.30/0.45 = ( A3
% 0.30/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_equal_0_iff_equal
% 0.30/0.45 thf(fact_71_neg__0__equal__iff__equal,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( group_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( ( zero_zero @ A )
% 0.30/0.45 = ( uminus_uminus @ A @ A3 ) )
% 0.30/0.45 = ( ( zero_zero @ A )
% 0.30/0.45 = A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_0_equal_iff_equal
% 0.30/0.45 thf(fact_72_add_Oinverse__neutral,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( group_add @ A )
% 0.30/0.45 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 0.30/0.45 = ( zero_zero @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % add.inverse_neutral
% 0.30/0.45 thf(fact_73_ereal__uminus__zero__iff,axiom,
% 0.30/0.45 ! [A3: extended_ereal] :
% 0.30/0.45 ( ( ( uminus_uminus @ extended_ereal @ A3 )
% 0.30/0.45 = ( zero_zero @ extended_ereal ) )
% 0.30/0.45 = ( A3
% 0.30/0.45 = ( zero_zero @ extended_ereal ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_uminus_zero_iff
% 0.30/0.45 thf(fact_74_ereal__uminus__zero,axiom,
% 0.30/0.45 ( ( uminus_uminus @ extended_ereal @ ( zero_zero @ extended_ereal ) )
% 0.30/0.45 = ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_uminus_zero
% 0.30/0.45 thf(fact_75_less__neg__neg,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linord219039673up_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ ( uminus_uminus @ A @ A3 ) )
% 0.30/0.45 = ( ord_less @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_neg_neg
% 0.30/0.45 thf(fact_76_neg__less__pos,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linord219039673up_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ A3 ) @ A3 )
% 0.30/0.45 = ( ord_less @ A @ ( zero_zero @ A ) @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_less_pos
% 0.30/0.45 thf(fact_77_neg__0__less__iff__less,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ordered_ab_group_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A3 ) )
% 0.30/0.45 = ( ord_less @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_0_less_iff_less
% 0.30/0.45 thf(fact_78_neg__less__0__iff__less,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ordered_ab_group_add @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ A3 ) @ ( zero_zero @ A ) )
% 0.30/0.45 = ( ord_less @ A @ ( zero_zero @ A ) @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_less_0_iff_less
% 0.30/0.45 thf(fact_79_neg__0__less__iff__less__erea,axiom,
% 0.30/0.45 ! [A3: extended_ereal] :
% 0.30/0.45 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ A3 ) )
% 0.30/0.45 = ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neg_0_less_iff_less_erea
% 0.30/0.45 thf(fact_80_ereal_Osimps_I12_J,axiom,
% 0.30/0.45 ! [A: $tType,F1: real > A,F22: A,F3: A] :
% 0.30/0.45 ( ( extended_rec_ereal @ A @ F1 @ F22 @ F3 @ extended_PInfty )
% 0.30/0.45 = F22 ) ).
% 0.30/0.45
% 0.30/0.45 % ereal.simps(12)
% 0.30/0.45 thf(fact_81_zero__reorient,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( zero @ A )
% 0.30/0.45 => ! [X2: A] :
% 0.30/0.45 ( ( ( zero_zero @ A )
% 0.30/0.45 = X2 )
% 0.30/0.45 = ( X2
% 0.30/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % zero_reorient
% 0.30/0.45 thf(fact_82_gr__zeroI,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( canoni770627133id_add @ A )
% 0.30/0.45 => ! [N: A] :
% 0.30/0.45 ( ( N
% 0.30/0.45 != ( zero_zero @ A ) )
% 0.30/0.45 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % gr_zeroI
% 0.30/0.45 thf(fact_83_not__less__zero,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( canoni770627133id_add @ A )
% 0.30/0.45 => ! [N: A] :
% 0.30/0.45 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % not_less_zero
% 0.30/0.45 thf(fact_84_gr__implies__not__zero,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( canoni770627133id_add @ A )
% 0.30/0.45 => ! [M: A,N: A] :
% 0.30/0.45 ( ( ord_less @ A @ M @ N )
% 0.30/0.45 => ( N
% 0.30/0.45 != ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % gr_implies_not_zero
% 0.30/0.45 thf(fact_85_zero__less__iff__neq__zero,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( canoni770627133id_add @ A )
% 0.30/0.45 => ! [N: A] :
% 0.30/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.30/0.45 = ( N
% 0.30/0.45 != ( zero_zero @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % zero_less_iff_neq_zero
% 0.30/0.45 thf(fact_86_Infty__neq__0_I1_J,axiom,
% 0.30/0.45 ( ( extend1396239628finity @ extended_ereal )
% 0.30/0.45 != ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.45
% 0.30/0.45 % Infty_neq_0(1)
% 0.30/0.45 thf(fact_87_infinity__ereal__def,axiom,
% 0.30/0.45 ( ( extend1396239628finity @ extended_ereal )
% 0.30/0.45 = extended_PInfty ) ).
% 0.30/0.45
% 0.30/0.45 % infinity_ereal_def
% 0.30/0.45 thf(fact_88_ereal_Odistinct_I5_J,axiom,
% 0.30/0.45 extended_PInfty != extended_MInfty ).
% 0.30/0.45
% 0.30/0.45 % ereal.distinct(5)
% 0.30/0.45 thf(fact_89_Infty__neq__0_I3_J,axiom,
% 0.30/0.45 ( ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.45 != ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.45
% 0.30/0.45 % Infty_neq_0(3)
% 0.30/0.45 thf(fact_90_ereal__less_I5_J,axiom,
% 0.30/0.45 ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) ).
% 0.30/0.45
% 0.30/0.45 % ereal_less(5)
% 0.30/0.45 thf(fact_91_ord__eq__less__subst,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType] :
% 0.30/0.45 ( ( ( ord @ B )
% 0.30/0.45 & ( ord @ A ) )
% 0.30/0.45 => ! [A3: A,F: B > A,B2: B,C3: B] :
% 0.30/0.45 ( ( A3
% 0.30/0.45 = ( F @ B2 ) )
% 0.30/0.45 => ( ( ord_less @ B @ B2 @ C3 )
% 0.30/0.45 => ( ! [X4: B,Y2: B] :
% 0.30/0.45 ( ( ord_less @ B @ X4 @ Y2 )
% 0.30/0.45 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.45 => ( ord_less @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ord_eq_less_subst
% 0.30/0.45 thf(fact_92_ord__less__eq__subst,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType] :
% 0.30/0.45 ( ( ( ord @ B )
% 0.30/0.45 & ( ord @ A ) )
% 0.30/0.45 => ! [A3: A,B2: A,F: A > B,C3: B] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.45 => ( ( ( F @ B2 )
% 0.30/0.45 = C3 )
% 0.30/0.45 => ( ! [X4: A,Y2: A] :
% 0.30/0.45 ( ( ord_less @ A @ X4 @ Y2 )
% 0.30/0.45 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.45 => ( ord_less @ B @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ord_less_eq_subst
% 0.30/0.45 thf(fact_93_order__less__subst1,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType] :
% 0.30/0.45 ( ( ( order @ B )
% 0.30/0.45 & ( order @ A ) )
% 0.30/0.45 => ! [A3: A,F: B > A,B2: B,C3: B] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ ( F @ B2 ) )
% 0.30/0.45 => ( ( ord_less @ B @ B2 @ C3 )
% 0.30/0.45 => ( ! [X4: B,Y2: B] :
% 0.30/0.45 ( ( ord_less @ B @ X4 @ Y2 )
% 0.30/0.45 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.45 => ( ord_less @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % order_less_subst1
% 0.30/0.45 thf(fact_94_order__less__subst2,axiom,
% 0.30/0.45 ! [A: $tType,C2: $tType] :
% 0.30/0.45 ( ( ( order @ C2 )
% 0.30/0.45 & ( order @ A ) )
% 0.30/0.45 => ! [A3: A,B2: A,F: A > C2,C3: C2] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.45 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C3 )
% 0.30/0.45 => ( ! [X4: A,Y2: A] :
% 0.30/0.45 ( ( ord_less @ A @ X4 @ Y2 )
% 0.30/0.45 => ( ord_less @ C2 @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.45 => ( ord_less @ C2 @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % order_less_subst2
% 0.30/0.45 thf(fact_95_lt__ex,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( no_bot @ A )
% 0.30/0.45 => ! [X2: A] :
% 0.30/0.45 ? [Y2: A] : ( ord_less @ A @ Y2 @ X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % lt_ex
% 0.30/0.45 thf(fact_96_gt__ex,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( no_top @ A )
% 0.30/0.45 => ! [X2: A] :
% 0.30/0.45 ? [X_1: A] : ( ord_less @ A @ X2 @ X_1 ) ) ).
% 0.30/0.45
% 0.30/0.45 % gt_ex
% 0.30/0.45 thf(fact_97_neqE,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( X2 != Y )
% 0.30/0.45 => ( ~ ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neqE
% 0.30/0.45 thf(fact_98_neq__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( X2 != Y )
% 0.30/0.45 = ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 | ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % neq_iff
% 0.30/0.45 thf(fact_99_order_Oasym,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.45 => ~ ( ord_less @ A @ B2 @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % order.asym
% 0.30/0.45 thf(fact_100_dense,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( dense_order @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ? [Z: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Z )
% 0.30/0.45 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % dense
% 0.30/0.45 thf(fact_101_less__imp__neq,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( X2 != Y ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_imp_neq
% 0.30/0.45 thf(fact_102_less__asym,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( preorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_asym
% 0.30/0.45 thf(fact_103_less__asym_H,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( preorder @ A )
% 0.30/0.45 => ! [A3: A,B2: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.45 => ~ ( ord_less @ A @ B2 @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_asym'
% 0.30/0.45 thf(fact_104_less__trans,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( preorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A,Z3: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( ( ord_less @ A @ Y @ Z3 )
% 0.30/0.45 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_trans
% 0.30/0.45 thf(fact_105_less__linear,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 | ( X2 = Y )
% 0.30/0.45 | ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_linear
% 0.30/0.45 thf(fact_106_less__irrefl,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( preorder @ A )
% 0.30/0.45 => ! [X2: A] :
% 0.30/0.45 ~ ( ord_less @ A @ X2 @ X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_irrefl
% 0.30/0.45 thf(fact_107_ord__eq__less__trans,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ord @ A )
% 0.30/0.45 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.45 ( ( A3 = B2 )
% 0.30/0.45 => ( ( ord_less @ A @ B2 @ C3 )
% 0.30/0.45 => ( ord_less @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ord_eq_less_trans
% 0.30/0.45 thf(fact_108_ord__less__eq__trans,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ord @ A )
% 0.30/0.45 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.45 => ( ( B2 = C3 )
% 0.30/0.45 => ( ord_less @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ord_less_eq_trans
% 0.30/0.45 thf(fact_109_dual__order_Oasym,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [B2: A,A3: A] :
% 0.30/0.45 ( ( ord_less @ A @ B2 @ A3 )
% 0.30/0.45 => ~ ( ord_less @ A @ A3 @ B2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % dual_order.asym
% 0.30/0.45 thf(fact_110_less__imp__not__eq,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( X2 != Y ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_imp_not_eq
% 0.30/0.45 thf(fact_111_less__not__sym,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( preorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_not_sym
% 0.30/0.45 thf(fact_112_less__induct,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( wellorder @ A )
% 0.30/0.45 => ! [P: A > $o,A3: A] :
% 0.30/0.45 ( ! [X4: A] :
% 0.30/0.45 ( ! [Y3: A] :
% 0.30/0.45 ( ( ord_less @ A @ Y3 @ X4 )
% 0.30/0.45 => ( P @ Y3 ) )
% 0.30/0.45 => ( P @ X4 ) )
% 0.30/0.45 => ( P @ A3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_induct
% 0.30/0.45 thf(fact_113_antisym__conv3,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [Y: A,X2: A] :
% 0.30/0.45 ( ~ ( ord_less @ A @ Y @ X2 )
% 0.30/0.45 => ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.30/0.45 = ( X2 = Y ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % antisym_conv3
% 0.30/0.45 thf(fact_114_less__imp__not__eq2,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( Y != X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_imp_not_eq2
% 0.30/0.45 thf(fact_115_less__imp__triv,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( preorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A,P: $o] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( ( ord_less @ A @ Y @ X2 )
% 0.30/0.45 => P ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_imp_triv
% 0.30/0.45 thf(fact_116_linorder__cases,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ~ ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ( ( X2 != Y )
% 0.30/0.45 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % linorder_cases
% 0.30/0.45 thf(fact_117_dual__order_Oirrefl,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [A3: A] :
% 0.30/0.45 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.30/0.45
% 0.30/0.45 % dual_order.irrefl
% 0.30/0.45 thf(fact_118_order_Ostrict__trans,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( order @ A )
% 0.30/0.45 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.45 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.45 => ( ( ord_less @ A @ B2 @ C3 )
% 0.30/0.45 => ( ord_less @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % order.strict_trans
% 0.30/0.45 thf(fact_119_less__imp__not__less,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( preorder @ A )
% 0.30/0.45 => ! [X2: A,Y: A] :
% 0.30/0.45 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.45 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % less_imp_not_less
% 0.30/0.45 thf(fact_120_exists__least__iff,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( wellorder @ A )
% 0.30/0.45 => ( ( ^ [P3: A > $o] :
% 0.30/0.45 ? [X5: A] : ( P3 @ X5 ) )
% 0.30/0.45 = ( ^ [P4: A > $o] :
% 0.30/0.45 ? [N2: A] :
% 0.30/0.45 ( ( P4 @ N2 )
% 0.30/0.45 & ! [M2: A] :
% 0.30/0.45 ( ( ord_less @ A @ M2 @ N2 )
% 0.30/0.45 => ~ ( P4 @ M2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % exists_least_iff
% 0.30/0.45 thf(fact_121_linorder__less__wlog,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [P: A > A > $o,A3: A,B2: A] :
% 0.30/0.45 ( ! [A5: A,B3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A5 @ B3 )
% 0.30/0.46 => ( P @ A5 @ B3 ) )
% 0.30/0.46 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 0.30/0.46 => ( ! [A5: A,B3: A] :
% 0.30/0.46 ( ( P @ B3 @ A5 )
% 0.30/0.46 => ( P @ A5 @ B3 ) )
% 0.30/0.46 => ( P @ A3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_less_wlog
% 0.30/0.46 thf(fact_122_dual__order_Ostrict__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A3: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ B2 )
% 0.30/0.46 => ( ord_less @ A @ C3 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_trans
% 0.30/0.46 thf(fact_123_not__less__iff__gr__or__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X2: A,Y: A] :
% 0.30/0.46 ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.30/0.46 = ( ( ord_less @ A @ Y @ X2 )
% 0.30/0.46 | ( X2 = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_iff_gr_or_eq
% 0.30/0.46 thf(fact_124_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.46 => ( A3 != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_implies_not_eq
% 0.30/0.46 thf(fact_125_field__lbound__gt__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [D1: A,D2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ D1 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ D2 )
% 0.30/0.46 => ? [E: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ E )
% 0.30/0.46 & ( ord_less @ A @ E @ D1 )
% 0.30/0.46 & ( ord_less @ A @ E @ D2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % field_lbound_gt_zero
% 0.30/0.46 thf(fact_126_less__numeral__extra_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_numeral_extra(3)
% 0.30/0.46 thf(fact_127_ereal__mult__eq__PInfty,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( ( times_times @ extended_ereal @ A3 @ B2 )
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 = ( ( ( A3
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 | ( ( A3
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) )
% 0.30/0.46 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_eq_PInfty
% 0.30/0.46 thf(fact_128_ereal__mult__eq__MInfty,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( ( times_times @ extended_ereal @ A3 @ B2 )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 = ( ( ( A3
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) )
% 0.30/0.46 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 | ( ( A3
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_eq_MInfty
% 0.30/0.46 thf(fact_129_ereal__mult__infty,axiom,
% 0.30/0.46 ! [A3: extended_ereal] :
% 0.30/0.46 ( ( ( A3
% 0.30/0.46 = ( zero_zero @ extended_ereal ) )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) )
% 0.30/0.46 & ( ( A3
% 0.30/0.46 != ( zero_zero @ extended_ereal ) )
% 0.30/0.46 => ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 & ( ~ ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_infty
% 0.30/0.46 thf(fact_130_ereal__infty__mult,axiom,
% 0.30/0.46 ! [A3: extended_ereal] :
% 0.30/0.46 ( ( ( A3
% 0.30/0.46 = ( zero_zero @ extended_ereal ) )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) )
% 0.30/0.46 & ( ( A3
% 0.30/0.46 != ( zero_zero @ extended_ereal ) )
% 0.30/0.46 => ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 )
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 & ( ~ ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_infty_mult
% 0.30/0.46 thf(fact_131_ereal__divide__Infty_I2_J,axiom,
% 0.30/0.46 ! [X2: extended_ereal] :
% 0.30/0.46 ( ( divide_divide @ extended_ereal @ X2 @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_divide_Infty(2)
% 0.30/0.46 thf(fact_132_mult__zero__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( mult_zero @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( times_times @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_zero_left
% 0.30/0.46 thf(fact_133_mult__zero__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( mult_zero @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( times_times @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_zero_right
% 0.30/0.46 thf(fact_134_mult__eq__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1193490041visors @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A3 @ B2 )
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 = ( ( A3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( B2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_eq_0_iff
% 0.30/0.46 thf(fact_135_mult__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ C3 @ A3 )
% 0.30/0.46 = ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A3 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel_left
% 0.30/0.46 thf(fact_136_mult__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [A3: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A3 @ C3 )
% 0.30/0.46 = ( times_times @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A3 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel_right
% 0.30/0.46 thf(fact_137_div__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_0
% 0.30/0.46 thf(fact_138_div__by__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_by_0
% 0.30/0.46 thf(fact_139_mult__minus__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( times_times @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 0.30/0.46 = ( uminus_uminus @ A @ ( times_times @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_minus_right
% 0.30/0.46 thf(fact_140_minus__mult__minus,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( times_times @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 0.30/0.46 = ( times_times @ A @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_mult_minus
% 0.30/0.46 thf(fact_141_mult__minus__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( times_times @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 0.30/0.46 = ( uminus_uminus @ A @ ( times_times @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_minus_left
% 0.30/0.46 thf(fact_142_ereal__mult__minus__left,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( times_times @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) @ B2 )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_minus_left
% 0.30/0.46 thf(fact_143_ereal__mult__minus__right,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( times_times @ extended_ereal @ A3 @ ( uminus_uminus @ extended_ereal @ B2 ) )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_minus_right
% 0.30/0.46 thf(fact_144_ereal__zero__times,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( ( times_times @ extended_ereal @ A3 @ B2 )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) )
% 0.30/0.46 = ( ( A3
% 0.30/0.46 = ( zero_zero @ extended_ereal ) )
% 0.30/0.46 | ( B2
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_zero_times
% 0.30/0.46 thf(fact_145_ereal__zero__mult,axiom,
% 0.30/0.46 ! [A3: extended_ereal] :
% 0.30/0.46 ( ( times_times @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_zero_mult
% 0.30/0.46 thf(fact_146_ereal__mult__zero,axiom,
% 0.30/0.46 ! [A3: extended_ereal] :
% 0.30/0.46 ( ( times_times @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_zero
% 0.30/0.46 thf(fact_147_ereal__uminus__divide,axiom,
% 0.30/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.30/0.46 ( ( divide_divide @ extended_ereal @ ( uminus_uminus @ extended_ereal @ X2 ) @ Y )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( divide_divide @ extended_ereal @ X2 @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_uminus_divide
% 0.30/0.46 thf(fact_148_ereal__divide__zero__left,axiom,
% 0.30/0.46 ! [A3: extended_ereal] :
% 0.30/0.46 ( ( divide_divide @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_divide_zero_left
% 0.30/0.46 thf(fact_149_ereal__times__divide__eq__left,axiom,
% 0.30/0.46 ! [B2: extended_ereal,C3: extended_ereal,A3: extended_ereal] :
% 0.30/0.46 ( ( times_times @ extended_ereal @ ( divide_divide @ extended_ereal @ B2 @ C3 ) @ A3 )
% 0.30/0.46 = ( divide_divide @ extended_ereal @ ( times_times @ extended_ereal @ B2 @ A3 ) @ C3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_times_divide_eq_left
% 0.30/0.46 thf(fact_150_nonzero__mult__div__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [B2: A,A3: A] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ B2 ) @ B2 )
% 0.30/0.46 = A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_div_cancel_right
% 0.30/0.46 thf(fact_151_nonzero__mult__div__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ B2 ) @ A3 )
% 0.30/0.46 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_div_cancel_left
% 0.30/0.46 thf(fact_152_ereal__divide__Infty_I1_J,axiom,
% 0.30/0.46 ! [X2: extended_ereal] :
% 0.30/0.46 ( ( divide_divide @ extended_ereal @ X2 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 = ( zero_zero @ extended_ereal ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_divide_Infty(1)
% 0.30/0.46 thf(fact_153_mult_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_mult @ A )
% 0.30/0.46 => ! [B2: A,A3: A,C3: A] :
% 0.30/0.46 ( ( times_times @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) )
% 0.30/0.46 = ( times_times @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult.left_commute
% 0.30/0.46 thf(fact_154_mult_Ocommute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_mult @ A )
% 0.30/0.46 => ( ( times_times @ A )
% 0.30/0.46 = ( ^ [A6: A,B4: A] : ( times_times @ A @ B4 @ A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult.commute
% 0.30/0.46 thf(fact_155_mult_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semigroup_mult @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( times_times @ A @ ( times_times @ A @ A3 @ B2 ) @ C3 )
% 0.30/0.46 = ( times_times @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult.assoc
% 0.30/0.46 thf(fact_156_ereal__times__divide__eq,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal,C3: extended_ereal] :
% 0.30/0.46 ( ( times_times @ extended_ereal @ A3 @ ( divide_divide @ extended_ereal @ B2 @ C3 ) )
% 0.30/0.46 = ( divide_divide @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) @ C3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_times_divide_eq
% 0.30/0.46 thf(fact_157_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_mult @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( times_times @ A @ ( times_times @ A @ A3 @ B2 ) @ C3 )
% 0.30/0.46 = ( times_times @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ab_semigroup_mult_class.mult_ac(1)
% 0.30/0.46 thf(fact_158_mult__not__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( mult_zero @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A3 @ B2 )
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( A3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_not_zero
% 0.30/0.46 thf(fact_159_divisors__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1193490041visors @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A3 @ B2 )
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( ( A3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( B2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divisors_zero
% 0.30/0.46 thf(fact_160_no__zero__divisors,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1193490041visors @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( B2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( times_times @ A @ A3 @ B2 )
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % no_zero_divisors
% 0.30/0.46 thf(fact_161_mult__left__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( times_times @ A @ C3 @ A3 )
% 0.30/0.46 = ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( A3 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_left_cancel
% 0.30/0.46 thf(fact_162_mult__right__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( times_times @ A @ A3 @ C3 )
% 0.30/0.46 = ( times_times @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( A3 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_right_cancel
% 0.30/0.46 thf(fact_163_square__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( idom @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A3 @ A3 )
% 0.30/0.46 = ( times_times @ A @ B2 @ B2 ) )
% 0.30/0.46 = ( ( A3 = B2 )
% 0.30/0.46 | ( A3
% 0.30/0.46 = ( uminus_uminus @ A @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % square_eq_iff
% 0.30/0.46 thf(fact_164_minus__mult__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( times_times @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 0.30/0.46 = ( times_times @ A @ A3 @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_mult_commute
% 0.30/0.46 thf(fact_165_times__ereal_Osimps_I6_J,axiom,
% 0.30/0.46 ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_ereal.simps(6)
% 0.30/0.46 thf(fact_166_ereal__right__mult__cong,axiom,
% 0.30/0.46 ! [C3: extended_ereal,D3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( C3 = D3 )
% 0.30/0.46 => ( ( ( D3
% 0.30/0.46 != ( zero_zero @ extended_ereal ) )
% 0.30/0.46 => ( A3 = B2 ) )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ C3 @ A3 )
% 0.30/0.46 = ( times_times @ extended_ereal @ D3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_right_mult_cong
% 0.30/0.46 thf(fact_167_ereal__left__mult__cong,axiom,
% 0.30/0.46 ! [C3: extended_ereal,D3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( C3 = D3 )
% 0.30/0.46 => ( ( ( D3
% 0.30/0.46 != ( zero_zero @ extended_ereal ) )
% 0.30/0.46 => ( A3 = B2 ) )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ A3 @ C3 )
% 0.30/0.46 = ( times_times @ extended_ereal @ B2 @ D3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_left_mult_cong
% 0.30/0.46 thf(fact_168_ereal__mult__divide,axiom,
% 0.30/0.46 ! [B2: extended_ereal,A3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ B2 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ( times_times @ extended_ereal @ B2 @ ( divide_divide @ extended_ereal @ A3 @ B2 ) )
% 0.30/0.46 = A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_divide
% 0.30/0.46 thf(fact_169_ereal__divide__less__iff,axiom,
% 0.30/0.46 ! [C3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ ( divide_divide @ extended_ereal @ A3 @ C3 ) @ B2 )
% 0.30/0.46 = ( ord_less @ extended_ereal @ A3 @ ( times_times @ extended_ereal @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_divide_less_iff
% 0.30/0.46 thf(fact_170_ereal__divide__less__pos,axiom,
% 0.30/0.46 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ X2 )
% 0.30/0.46 => ( ( X2
% 0.30/0.46 != ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ ( divide_divide @ extended_ereal @ Y @ X2 ) @ Z3 )
% 0.30/0.46 = ( ord_less @ extended_ereal @ Y @ ( times_times @ extended_ereal @ X2 @ Z3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_divide_less_pos
% 0.30/0.46 thf(fact_171_ereal__less__divide__iff,axiom,
% 0.30/0.46 ! [C3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ A3 @ ( divide_divide @ extended_ereal @ B2 @ C3 ) )
% 0.30/0.46 = ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_less_divide_iff
% 0.30/0.46 thf(fact_172_ereal__less__divide__pos,axiom,
% 0.30/0.46 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ X2 )
% 0.30/0.46 => ( ( X2
% 0.30/0.46 != ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ Y @ ( divide_divide @ extended_ereal @ Z3 @ X2 ) )
% 0.30/0.46 = ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ X2 @ Y ) @ Z3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_less_divide_pos
% 0.30/0.46 thf(fact_173_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord893533164strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.46 thf(fact_174_mult__less__cancel__right__disj,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A3: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 & ( ord_less @ A @ A3 @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_right_disj
% 0.30/0.46 thf(fact_175_mult__strict__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono
% 0.30/0.46 thf(fact_176_mult__strict__right__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [B2: A,A3: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono_neg
% 0.30/0.46 thf(fact_177_mult__less__cancel__left__disj,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 & ( ord_less @ A @ A3 @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_disj
% 0.30/0.46 thf(fact_178_mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono
% 0.30/0.46 thf(fact_179_mult__strict__left__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [B2: A,A3: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono_neg
% 0.30/0.46 thf(fact_180_mult__less__cancel__left__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( ord_less @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_pos
% 0.30/0.46 thf(fact_181_mult__less__cancel__left__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( ord_less @ A @ B2 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_neg
% 0.30/0.46 thf(fact_182_zero__less__mult__pos2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [B2: A,A3: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B2 @ A3 ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos2
% 0.30/0.46 thf(fact_183_zero__less__mult__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos
% 0.30/0.46 thf(fact_184_zero__less__mult__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_iff
% 0.30/0.46 thf(fact_185_mult__pos__neg2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ B2 @ A3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg2
% 0.30/0.46 thf(fact_186_mult__pos__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_pos
% 0.30/0.46 thf(fact_187_mult__pos__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A3 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg
% 0.30/0.46 thf(fact_188_mult__neg__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A3 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_neg_pos
% 0.30/0.46 thf(fact_189_mult__less__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( times_times @ A @ A3 @ B2 ) @ ( zero_zero @ A ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.30/0.46 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_0_iff
% 0.30/0.46 thf(fact_190_not__square__less__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_ring @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ~ ( ord_less @ A @ ( times_times @ A @ A3 @ A3 ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_square_less_zero
% 0.30/0.46 thf(fact_191_mult__neg__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_neg_neg
% 0.30/0.46 thf(fact_192_times__ereal_Osimps_I9_J,axiom,
% 0.30/0.46 ( ( times_times @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 = ( extend1396239628finity @ extended_ereal ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_ereal.simps(9)
% 0.30/0.46 thf(fact_193_times__ereal_Osimps_I8_J,axiom,
% 0.30/0.46 ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_ereal.simps(8)
% 0.30/0.46 thf(fact_194_times__ereal_Osimps_I7_J,axiom,
% 0.30/0.46 ( ( times_times @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_ereal.simps(7)
% 0.30/0.46 thf(fact_195_ereal__mult__less__0__iff,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) @ ( zero_zero @ extended_ereal ) )
% 0.30/0.46 = ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) )
% 0.30/0.46 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 0.30/0.46 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_less_0_iff
% 0.30/0.46 thf(fact_196_ereal__zero__less__0__iff,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( times_times @ extended_ereal @ A3 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 0.30/0.46 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_zero_less_0_iff
% 0.30/0.46 thf(fact_197_ereal__mult__mono__strict,axiom,
% 0.30/0.46 ! [B2: extended_ereal,C3: extended_ereal,A3: extended_ereal,D3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ C3 @ D3 )
% 0.30/0.46 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ ( times_times @ extended_ereal @ B2 @ D3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_mono_strict
% 0.30/0.46 thf(fact_198_ereal__mult__mono__strict_H,axiom,
% 0.30/0.46 ! [A3: extended_ereal,C3: extended_ereal,B2: extended_ereal,D3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ C3 @ D3 )
% 0.30/0.46 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ ( times_times @ extended_ereal @ B2 @ D3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_mono_strict'
% 0.30/0.46 thf(fact_199_ereal__mult__less__right,axiom,
% 0.30/0.46 ! [B2: extended_ereal,A3: extended_ereal,C3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ B2 @ A3 ) @ ( times_times @ extended_ereal @ C3 @ A3 ) )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ord_less @ extended_ereal @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_less_right
% 0.30/0.46 thf(fact_200_ereal__mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal,C3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ C3 @ A3 ) @ ( times_times @ extended_ereal @ C3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_strict_left_mono
% 0.30/0.46 thf(fact_201_ereal__mult__strict__right__mono,axiom,
% 0.30/0.46 ! [A3: extended_ereal,B2: extended_ereal,C3: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 0.30/0.46 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ ( times_times @ extended_ereal @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ereal_mult_strict_right_mono
% 0.30/0.46 thf(fact_202_div__mult__mult1__if,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid191655569cancel @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( zero_zero @ A ) ) )
% 0.30/0.46 & ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_mult1_if
% 0.30/0.46 thf(fact_203_div__mult__mult2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid191655569cancel @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_mult2
% 0.30/0.46 thf(fact_204_div__mult__mult1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid191655569cancel @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_mult1
% 0.30/0.46 thf(fact_205_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_right2
% 0.30/0.46 thf(fact_206_divide__eq__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ A3 @ B2 )
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 = ( ( A3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( B2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_eq_0_iff
% 0.30/0.46 thf(fact_207_divide__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ C3 @ A3 )
% 0.30/0.46 = ( divide_divide @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A3 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_cancel_left
% 0.30/0.46 thf(fact_208_divide__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A3: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ A3 @ C3 )
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A3 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_cancel_right
% 0.30/0.46 thf(fact_209_division__ring__divide__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % division_ring_divide_zero
% 0.30/0.46 thf(fact_210_times__divide__eq__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( times_times @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ A3 @ B2 ) @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_divide_eq_right
% 0.30/0.46 thf(fact_211_divide__divide__eq__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_eq_right
% 0.30/0.46 thf(fact_212_divide__divide__eq__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( divide_divide @ A @ A3 @ B2 ) @ C3 )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_eq_left
% 0.30/0.46 thf(fact_213_times__divide__eq__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [B2: A,C3: A,A3: A] :
% 0.30/0.46 ( ( times_times @ A @ ( divide_divide @ A @ B2 @ C3 ) @ A3 )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ B2 @ A3 ) @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_divide_eq_left
% 0.30/0.46 thf(fact_214_div__minus__minus,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid24285859cancel @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_minus_minus
% 0.30/0.46 thf(fact_215_mult__divide__mult__cancel__left__if,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( zero_zero @ A ) ) )
% 0.30/0.46 & ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_divide_mult_cancel_left_if
% 0.30/0.46 thf(fact_216_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_left
% 0.30/0.46 thf(fact_217_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_left2
% 0.30/0.46 thf(fact_218_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_right
% 0.30/0.46 thf(fact_219_linordered__field__no__lb,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ? [Y2: A] : ( ord_less @ A @ Y2 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_field_no_lb
% 0.30/0.46 thf(fact_220_linordered__field__no__ub,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_field_no_ub
% 0.30/0.46 thf(fact_221_divide__divide__eq__left_H,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( divide_divide @ A @ A3 @ B2 ) @ C3 )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ ( times_times @ A @ C3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_eq_left'
% 0.30/0.46 thf(fact_222_divide__divide__times__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [X2: A,Y: A,Z3: A,W: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( divide_divide @ A @ Z3 @ W ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ X2 @ W ) @ ( times_times @ A @ Y @ Z3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_times_eq
% 0.30/0.46 thf(fact_223_times__divide__times__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [X2: A,Y: A,Z3: A,W: A] :
% 0.30/0.46 ( ( times_times @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( divide_divide @ A @ Z3 @ W ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ X2 @ Z3 ) @ ( times_times @ A @ Y @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_divide_times_eq
% 0.30/0.46 thf(fact_224_div__minus__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid24285859cancel @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_minus_right
% 0.30/0.46 thf(fact_225_minus__divide__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( uminus_uminus @ A @ ( divide_divide @ A @ A3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_divide_left
% 0.30/0.46 thf(fact_226_minus__divide__divide,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_divide_divide
% 0.30/0.46 thf(fact_227_minus__divide__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( uminus_uminus @ A @ ( divide_divide @ A @ A3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_divide_right
% 0.30/0.46 thf(fact_228_divide__neg__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X2: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ Y @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X2 @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_neg_neg
% 0.30/0.46 thf(fact_229_divide__neg__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X2: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_neg_pos
% 0.30/0.46 thf(fact_230_divide__pos__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X2: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ X2 )
% 0.30/0.46 => ( ( ord_less @ A @ Y @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_pos_neg
% 0.30/0.46 thf(fact_231_divide__pos__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X2: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ X2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X2 @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_pos_pos
% 0.30/0.46 thf(fact_232_divide__less__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( divide_divide @ A @ A3 @ B2 ) @ ( zero_zero @ A ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.30/0.46 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_less_0_iff
% 0.30/0.46 thf(fact_233_divide__less__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A3: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( divide_divide @ A @ A3 @ C3 ) @ ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ord_less @ A @ A3 @ B2 ) )
% 0.30/0.46 & ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ B2 @ A3 ) )
% 0.30/0.46 & ( C3
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_less_cancel
% 0.30/0.46 thf(fact_234_zero__less__divide__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ A3 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_divide_iff
% 0.30/0.46 thf(fact_235_divide__strict__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ A3 @ C3 ) @ ( divide_divide @ A @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_right_mono
% 0.30/0.46 thf(fact_236_divide__strict__right__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [B2: A,A3: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ A3 @ C3 ) @ ( divide_divide @ A @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_right_mono_neg
% 0.30/0.46 thf(fact_237_frac__eq__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [Y: A,Z3: A,X2: A,W: A] :
% 0.30/0.46 ( ( Y
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( Z3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( divide_divide @ A @ X2 @ Y )
% 0.30/0.46 = ( divide_divide @ A @ W @ Z3 ) )
% 0.30/0.46 = ( ( times_times @ A @ X2 @ Z3 )
% 0.30/0.46 = ( times_times @ A @ W @ Y ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % frac_eq_eq
% 0.30/0.46 thf(fact_238_divide__eq__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [B2: A,C3: A,A3: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ B2 @ C3 )
% 0.30/0.46 = A3 )
% 0.30/0.46 = ( ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( B2
% 0.30/0.46 = ( times_times @ A @ A3 @ C3 ) ) )
% 0.30/0.46 & ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_eq_eq
% 0.30/0.46 thf(fact_239_eq__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( times_times @ A @ A3 @ C3 )
% 0.30/0.46 = B2 ) )
% 0.30/0.46 & ( ( C3
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_divide_eq
% 0.30/0.46 thf(fact_240_divide__eq__imp,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C3: A,B2: A,A3: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( B2
% 0.30/0.46 = ( times_times @ A @ A3 @ C3 ) )
% 0.30/0.46 => ( ( divide_divide @ A @ B2 @ C3 )
% 0.30/0.46 = A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_eq_imp
% 0.30/0.46 thf(fact_241_eq__divide__imp,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( times_times @ A @ A3 @ C3 )
% 0.30/0.46 = B2 )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_divide_imp
% 0.30/0.46 thf(fact_242_nonzero__divide__eq__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C3: A,B2: A,A3: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( divide_divide @ A @ B2 @ C3 )
% 0.30/0.46 = A3 )
% 0.30/0.46 = ( B2
% 0.30/0.46 = ( times_times @ A @ A3 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_divide_eq_eq
% 0.30/0.46 thf(fact_243_nonzero__eq__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( C3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( A3
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ( times_times @ A @ A3 @ C3 )
% 0.30/0.46 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_eq_divide_eq
% 0.30/0.46 thf(fact_244_nonzero__minus__divide__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [B2: A,A3: A] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( uminus_uminus @ A @ ( divide_divide @ A @ A3 @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ ( uminus_uminus @ A @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_minus_divide_right
% 0.30/0.46 thf(fact_245_nonzero__minus__divide__divide,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [B2: A,A3: A] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_minus_divide_divide
% 0.30/0.46 thf(fact_246_divide__strict__left__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ C3 @ A3 ) @ ( divide_divide @ A @ C3 @ B2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_left_mono_neg
% 0.30/0.46 thf(fact_247_divide__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [B2: A,A3: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ C3 @ A3 ) @ ( divide_divide @ A @ C3 @ B2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_left_mono
% 0.30/0.46 thf(fact_248_mult__imp__less__div__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [Y: A,Z3: A,X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 0.30/0.46 => ( ( ord_less @ A @ ( times_times @ A @ Z3 @ Y ) @ X2 )
% 0.30/0.46 => ( ord_less @ A @ Z3 @ ( divide_divide @ A @ X2 @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_imp_less_div_pos
% 0.30/0.46 thf(fact_249_mult__imp__div__pos__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [Y: A,X2: A,Z3: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 0.30/0.46 => ( ( ord_less @ A @ X2 @ ( times_times @ A @ Z3 @ Y ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ X2 @ Y ) @ Z3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_imp_div_pos_less
% 0.30/0.46 thf(fact_250_pos__less__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pos_less_divide_eq
% 0.30/0.46 thf(fact_251_pos__divide__less__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C3: A,B2: A,A3: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C3 ) @ A3 )
% 0.30/0.46 = ( ord_less @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pos_divide_less_eq
% 0.30/0.46 thf(fact_252_neg__less__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C3: A,A3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ord_less @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neg_less_divide_eq
% 0.30/0.46 thf(fact_253_neg__divide__less__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C3: A,B2: A,A3: A] :
% 0.30/0.46 ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C3 ) @ A3 )
% 0.30/0.46 = ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neg_divide_less_eq
% 0.30/0.46 thf(fact_254_less__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A3: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) )
% 0.30/0.46 & ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 0.30/0.46 => ( ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) ) )
% 0.30/0.46 & ( ~ ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ A3 @ ( zero_zero @ A ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_divide_eq
% 0.30/0.46
% 0.30/0.46 % Subclasses (4)
% 0.30/0.46 thf(subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( real_V2090557954_space @ A )
% 0.30/0.46 => ( type @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Ot0__space,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( real_V2090557954_space @ A )
% 0.30/0.46 => ( topological_t0_space @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Ot1__space,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( real_V2090557954_space @ A )
% 0.30/0.46 => ( topological_t1_space @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( real_V2090557954_space @ A )
% 0.30/0.46 => ( topolo503727757_space @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % Type constructors (37)
% 0.30/0.46 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( topolo503727757_space @ A8 )
% 0.30/0.46 => ( topolo503727757_space @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( boolean_algebra @ A8 )
% 0.30/0.46 => ( boolean_algebra @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( preorder @ A8 )
% 0.30/0.46 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( order @ A8 )
% 0.30/0.46 => ( order @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ord @ A8 )
% 0.30/0.46 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( uminus @ A8 )
% 0.30/0.46 => ( uminus @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_1,axiom,
% 0.30/0.46 ! [A7: $tType] : ( boolean_algebra @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Groups_Oab__semigroup__mult,axiom,
% 0.30/0.46 ! [A7: $tType] :
% 0.30/0.46 ( ( ab_semigroup_mult @ A7 )
% 0.30/0.46 => ( ab_semigroup_mult @ ( set @ A7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Groups_Osemigroup__mult,axiom,
% 0.30/0.46 ! [A7: $tType] :
% 0.30/0.46 ( ( semigroup_mult @ A7 )
% 0.30/0.46 => ( semigroup_mult @ ( set @ A7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.30/0.46 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.30/0.46 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 0.30/0.46 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Groups_Ouminus_5,axiom,
% 0.30/0.46 ! [A7: $tType] : ( uminus @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Groups_Ozero,axiom,
% 0.30/0.46 ! [A7: $tType] :
% 0.30/0.46 ( ( zero @ A7 )
% 0.30/0.46 => ( zero @ ( set @ A7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_6,axiom,
% 0.30/0.46 topolo503727757_space @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology,axiom,
% 0.30/0.46 topolo2133971006pology @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Topological__Spaces_Ot1__space,axiom,
% 0.30/0.46 topological_t1_space @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Topological__Spaces_Ot0__space,axiom,
% 0.30/0.46 topological_t0_space @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_7,axiom,
% 0.30/0.46 boolean_algebra @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 0.30/0.46 preorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.30/0.46 ord @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Groups_Ouminus_11,axiom,
% 0.30/0.46 uminus @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Conditionally__Complete__Lattices_Olinear__continuum,axiom,
% 0.30/0.46 condit1656338222tinuum @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_12,axiom,
% 0.30/0.46 topolo503727757_space @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Ot1__space_13,axiom,
% 0.30/0.46 topological_t1_space @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Ot0__space_14,axiom,
% 0.30/0.46 topological_t0_space @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Groups_Oab__semigroup__mult_15,axiom,
% 0.30/0.46 ab_semigroup_mult @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Orderings_Odense__order,axiom,
% 0.30/0.46 dense_order @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Groups_Osemigroup__mult_16,axiom,
% 0.30/0.46 semigroup_mult @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Orderings_Opreorder_17,axiom,
% 0.30/0.46 preorder @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Orderings_Olinorder_18,axiom,
% 0.30/0.46 linorder @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Orderings_Oorder_19,axiom,
% 0.30/0.46 order @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Orderings_Oord_20,axiom,
% 0.30/0.46 ord @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Groups_Ouminus_21,axiom,
% 0.30/0.46 uminus @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Extended__Real_Oereal___Groups_Ozero_22,axiom,
% 0.30/0.46 zero @ extended_ereal ).
% 0.30/0.46
% 0.30/0.46 % Free types (1)
% 0.30/0.46 thf(tfree_0,hypothesis,
% 0.30/0.46 real_V2090557954_space @ a ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 0.30/0.46 != ( ~ ! [C: extended_ereal] :
% 0.30/0.46 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 0.30/0.46 => ? [T: set @ a] :
% 0.30/0.46 ( ( topolo1751647064n_open @ a @ T )
% 0.30/0.46 & ( member @ a @ x0 @ T )
% 0.30/0.46 & ! [X: a] :
% 0.30/0.46 ( ( member @ a @ X @ T )
% 0.30/0.46 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.43/1.48 ---- Embedded in THF ---
% 2.43/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.43/1.48 %%% Generated on Tue Feb 24 08:27:05 EST 2026
% 2.43/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.43/1.48 %%% Logic specification used:
% 2.43/1.48 %%% thf(spec, logic, $$dhol).
% 2.43/1.48
% 2.43/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2DTF16074.p
% 2.43/1.48 thf(ty_t_Extended__Real_Oereal, type, extended_ereal: $tType).
% 2.43/1.48 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.43/1.48 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.43/1.48 thf(ty_tf_a, type, a: $tType).
% 2.43/1.48 thf(sy_cl_Real__Vector__Spaces_Ometric__space, type, real_V2090557954_space: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Oidom, type, idom: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Oring, type, ring: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Fields_Ofield, type, field: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Omult__zero, type, mult_zero: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Fields_Odivision__ring, type, division_ring: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Osemidom__divide, type, semidom_divide: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Olinordered__ring, type, linordered_ring: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Topological__Spaces_Ot0__space, type, topological_t0_space: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Topological__Spaces_Ot1__space, type, topological_t1_space: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Olinordered__ring__strict, type, linord581940658strict: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Osemiring__no__zero__divisors, type, semiri1193490041visors: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Olinordered__semiring__strict, type, linord20386208strict: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Topological__Spaces_Odiscrete__topology, type, topolo2133971006pology: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Topological__Spaces_Otopological__space, type, topolo503727757_space: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Olinordered__comm__semiring__strict, type, linord893533164strict: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel, type, semiri1923998003cancel: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Euclidean__Division_Oeuclidean__ring__cancel, type, euclid24285859cancel: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Euclidean__Division_Oeuclidean__semiring__cancel, type, euclid191655569cancel: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: ($o))).
% 2.43/1.48 thf(sy_c_Extended__Nat_Oinfinity__class_Oinfinity, type, extend1396239628finity: (!> [A:$tType]: (A))).
% 2.43/1.48 thf(sy_c_Extended__Real_Oereal_OMInfty, type, extended_MInfty: extended_ereal).
% 2.43/1.48 thf(sy_c_Extended__Real_Oereal_OPInfty, type, extended_PInfty: extended_ereal).
% 2.43/1.48 thf(sy_c_Extended__Real_Oereal_Orec__ereal, type, extended_rec_ereal: (!> [A:$tType]: (((real > A) > (A > (A > (extended_ereal > A))))))).
% 2.43/1.48 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 2.43/1.48 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.43/1.48 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.43/1.48 thf(sy_c_Lower__Semicontinuous__Mirabelle__quczrylfpw_Olsc__at, type, lower_582600101lsc_at: (!> [A:$tType,B:$tType]: ((A > ((A > B) > $o))))).
% 2.43/1.48 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.43/1.48 thf(sy_c_Rings_Odivide__class_Odivide, type, divide_divide: (!> [A:$tType]: ((A > (A > A))))).
% 2.43/1.48 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.43/1.48 thf(sy_c_Topological__Spaces_Oopen__class_Oopen, type, topolo1751647064n_open: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.43/1.48 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.43/1.48 thf(sy_v_f, type, f: (a > extended_ereal)).
% 2.43/1.48 thf(sy_v_x0, type, x0: a).
% 2.43/1.48 thf(fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062, axiom, (((f @ x0) = (extend1396239628finity @ extended_ereal)) => (((((lower_582600101lsc_at @ a) @ extended_ereal) @ x0) @ f) = (! [C:extended_ereal]: (((((ord_less @ extended_ereal) @ C) @ (f @ x0)) => (? [T:(set @ a)]: ((((topolo1751647064n_open @ a) @ T) & ((((member @ a) @ x0) @ T) & (! [X:a]: (((((member @ a) @ X) @ T) => (((ord_less @ extended_ereal) @ C) @ (f @ X))))))))))))))).
% 2.43/1.48 thf(fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062, axiom, (((f @ x0) = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) => (((((lower_582600101lsc_at @ a) @ extended_ereal) @ x0) @ f) = (! [C:extended_ereal]: (((((ord_less @ extended_ereal) @ C) @ (f @ x0)) => (? [T:(set @ a)]: ((((topolo1751647064n_open @ a) @ T) & ((((member @ a) @ x0) @ T) & (! [X:a]: (((((member @ a) @ X) @ T) => (((ord_less @ extended_ereal) @ C) @ (f @ X))))))))))))))).
% 2.43/1.48 thf(fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062, axiom, (((f @ x0) != ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) => (((f @ x0) != (extend1396239628finity @ extended_ereal)) => (((((lower_582600101lsc_at @ a) @ extended_ereal) @ x0) @ f) = (! [C:extended_ereal]: (((((ord_less @ extended_ereal) @ C) @ (f @ x0)) => (? [T:(set @ a)]: ((((topolo1751647064n_open @ a) @ T) & ((((member @ a) @ x0) @ T) & (! [X:a]: (((((member @ a) @ X) @ T) => (((ord_less @ extended_ereal) @ C) @ (f @ X)))))))))))))))).
% 2.43/1.48 thf(fact_3_lsc__at__MInfty, axiom, (! [A:$tType]: (((topolo503727757_space @ A) => (! [F:(A > extended_ereal),X0:A]: ((((F @ X0) = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) => ((((lower_582600101lsc_at @ A) @ extended_ereal) @ X0) @ F)))))))).
% 2.43/1.48 thf(fact_4_t0__space, axiom, (! [A:$tType]: (((topological_t0_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) => (? [U:(set @ A)]: ((((topolo1751647064n_open @ A) @ U) & ((((member @ A) @ X2) @ U) != (((member @ A) @ Y) @ U)))))))))))).
% 2.43/1.48 thf(fact_5_t1__space, axiom, (! [A:$tType]: (((topological_t1_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) => (? [U:(set @ A)]: ((((topolo1751647064n_open @ A) @ U) & ((((member @ A) @ X2) @ U) & (~ ((((member @ A) @ Y) @ U)))))))))))))).
% 2.43/1.48 thf(fact_6_separation__t0, axiom, (! [A:$tType]: (((topological_t0_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) = (? [U2:(set @ A)]: ((((topolo1751647064n_open @ A) @ U2) & ((((member @ A) @ X2) @ U2) != (((member @ A) @ Y) @ U2)))))))))))).
% 2.43/1.48 thf(fact_7_separation__t1, axiom, (! [A:$tType]: (((topological_t1_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) = (? [U2:(set @ A)]: ((((topolo1751647064n_open @ A) @ U2) & ((((member @ A) @ X2) @ U2) & (~ ((((member @ A) @ Y) @ U2)))))))))))))).
% 2.43/1.48 thf(fact_8_open__discrete, axiom, (! [A:$tType]: (((topolo2133971006pology @ A) => (! [A2:(set @ A)]: (((topolo1751647064n_open @ A) @ A2))))))).
% 2.43/1.48 thf(fact_9_minf_I11_J, axiom, (! [C2:$tType,D:$tType]: (((ord @ C2) => (! [F2:D]: ((? [Z:C2]: ((! [X3:C2]: (((((ord_less @ C2) @ X3) @ Z) => (F2 = F2)))))))))))).
% 2.43/1.48 thf(fact_10_minf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (~ ((((ord_less @ A) @ T2) @ X3)))))))))))))).
% 2.43/1.48 thf(fact_11_minf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (((ord_less @ A) @ X3) @ T2)))))))))))).
% 2.43/1.48 thf(fact_12_minf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (X3 != T2)))))))))))).
% 2.43/1.48 thf(fact_13_minf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (X3 != T2)))))))))))).
% 2.43/1.48 thf(fact_14_minf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z2) => ((P @ X4) = (P2 @ X4))))))) => ((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z2) => ((Q @ X4) = (Q2 @ X4))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (((P @ X3) | (Q @ X3)) = ((P2 @ X3) | (Q2 @ X3)))))))))))))))).
% 2.43/1.48 thf(fact_15_pinf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ Z2) @ X4) => ((P @ X4) = (P2 @ X4))))))) => ((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ Z2) @ X4) => ((Q @ X4) = (Q2 @ X4))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (((P @ X3) & (Q @ X3)) = ((P2 @ X3) & (Q2 @ X3)))))))))))))))).
% 2.43/1.48 thf(fact_16_pinf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ Z2) @ X4) => ((P @ X4) = (P2 @ X4))))))) => ((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ Z2) @ X4) => ((Q @ X4) = (Q2 @ X4))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (((P @ X3) | (Q @ X3)) = ((P2 @ X3) | (Q2 @ X3)))))))))))))))).
% 2.43/1.48 thf(fact_17_pinf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (X3 != T2)))))))))))).
% 2.43/1.48 thf(fact_18_pinf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (X3 != T2)))))))))))).
% 2.43/1.48 thf(fact_19_pinf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (~ ((((ord_less @ A) @ X3) @ T2)))))))))))))).
% 2.43/1.48 thf(fact_20_pinf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (((ord_less @ A) @ T2) @ X3)))))))))))).
% 2.43/1.48 thf(fact_21_pinf_I11_J, axiom, (! [C2:$tType,D:$tType]: (((ord @ C2) => (! [F2:D]: ((? [Z:C2]: ((! [X3:C2]: (((((ord_less @ C2) @ Z) @ X3) => (F2 = F2)))))))))))).
% 2.43/1.48 thf(fact_22_minf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z2) => ((P @ X4) = (P2 @ X4))))))) => ((? [Z2:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z2) => ((Q @ X4) = (Q2 @ X4))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (((P @ X3) & (Q @ X3)) = ((P2 @ X3) & (Q2 @ X3)))))))))))))))).
% 2.43/1.48 thf(fact_23_ereal__MInfty__lessI, axiom, (! [A3:extended_ereal]: (((A3 != ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) => (((ord_less @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) @ A3))))).
% 2.43/1.48 thf(fact_24_ereal__infty__less_I2_J, axiom, (! [X2:extended_ereal]: (((((ord_less @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) @ X2) = (X2 != ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))))))).
% 2.43/1.48 thf(fact_25_ereal__minus__less__minus, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((ord_less @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ A3)) @ ((uminus_uminus @ extended_ereal) @ B2)) = (((ord_less @ extended_ereal) @ B2) @ A3))))).
% 2.43/1.48 thf(fact_26_ereal__less__PInfty, axiom, (! [A3:extended_ereal]: (((A3 != (extend1396239628finity @ extended_ereal)) => (((ord_less @ extended_ereal) @ A3) @ (extend1396239628finity @ extended_ereal)))))).
% 2.43/1.48 thf(fact_27_ereal__infty__less_I1_J, axiom, (! [X2:extended_ereal]: (((((ord_less @ extended_ereal) @ X2) @ (extend1396239628finity @ extended_ereal)) = (X2 != (extend1396239628finity @ extended_ereal)))))).
% 2.43/1.48 thf(fact_28_neg__less__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B2:A,A3:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A3)) = (((ord_less @ A) @ A3) @ B2)))))))).
% 2.43/1.48 thf(fact_29_less__ereal_Osimps_I3_J, axiom, (! [A3:extended_ereal]: ((~ ((((ord_less @ extended_ereal) @ A3) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)))))))).
% 2.43/1.48 thf(fact_30_less__ereal_Osimps_I6_J, axiom, (((ord_less @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) @ (extend1396239628finity @ extended_ereal))).
% 2.43/1.48 thf(fact_31_ereal__uminus__eq__iff, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((uminus_uminus @ extended_ereal) @ A3) = ((uminus_uminus @ extended_ereal) @ B2)) = (A3 = B2))))).
% 2.43/1.48 thf(fact_32_ereal__uminus__uminus, axiom, (! [A3:extended_ereal]: ((((uminus_uminus @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ A3)) = A3)))).
% 2.43/1.48 thf(fact_33_neg__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A,B2:A]: (((((uminus_uminus @ A) @ A3) = ((uminus_uminus @ A) @ B2)) = (A3 = B2)))))))).
% 2.43/1.48 thf(fact_34_add_Oinverse__inverse, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A3)) = A3))))))).
% 2.43/1.48 thf(fact_35_minus__equation__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A,B2:A]: (((((uminus_uminus @ A) @ A3) = B2) = (((uminus_uminus @ A) @ B2) = A3)))))))).
% 2.43/1.48 thf(fact_36_equation__minus__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A,B2:A]: (((A3 = ((uminus_uminus @ A) @ B2)) = (B2 = ((uminus_uminus @ A) @ A3))))))))).
% 2.43/1.48 thf(fact_37_ereal__uminus__eq__reorder, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((uminus_uminus @ extended_ereal) @ A3) = B2) = (A3 = ((uminus_uminus @ extended_ereal) @ B2)))))).
% 2.43/1.48 thf(fact_38_less__minus__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ A3) @ ((uminus_uminus @ A) @ B2)) = (((ord_less @ A) @ B2) @ ((uminus_uminus @ A) @ A3))))))))).
% 2.43/1.48 thf(fact_39_minus__less__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A3)) @ B2) = (((ord_less @ A) @ ((uminus_uminus @ A) @ B2)) @ A3)))))))).
% 2.43/1.48 thf(fact_40_MInfty__neq__PInfty_I1_J, axiom, ((extend1396239628finity @ extended_ereal) != ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)))).
% 2.43/1.48 thf(fact_41_less__ereal_Osimps_I2_J, axiom, (! [A3:extended_ereal]: ((~ ((((ord_less @ extended_ereal) @ (extend1396239628finity @ extended_ereal)) @ A3)))))).
% 2.43/1.48 thf(fact_42_ereal__less__uminus__reorder, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((ord_less @ extended_ereal) @ A3) @ ((uminus_uminus @ extended_ereal) @ B2)) = (((ord_less @ extended_ereal) @ B2) @ ((uminus_uminus @ extended_ereal) @ A3)))))).
% 2.43/1.48 thf(fact_43_ereal__uminus__less__reorder, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((ord_less @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ A3)) @ B2) = (((ord_less @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ B2)) @ A3))))).
% 2.43/1.48 thf(fact_44_compl__eq__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X2:A,Y:A]: (((((uminus_uminus @ A) @ X2) = ((uminus_uminus @ A) @ Y)) = (X2 = Y)))))))).
% 2.43/1.48 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.43/1.48 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A2)))) = A2)))).
% 2.43/1.48 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.43/1.48 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.43/1.48 thf(fact_49_double__compl, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X2:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ X2)) = X2))))))).
% 2.43/1.48 thf(fact_50_uminus__apply, axiom, (! [B:$tType,A:$tType]: (((uminus @ B) => ((uminus_uminus @ (A > B)) = (^ [A4:(A > B),X:A]: (((uminus_uminus @ B) @ (A4 @ X))))))))).
% 2.43/1.48 thf(fact_51_verit__minus__simplify_I4_J, axiom, (! [B:$tType]: (((group_add @ B) => (! [B2:B]: ((((uminus_uminus @ B) @ ((uminus_uminus @ B) @ B2)) = B2))))))).
% 2.43/1.48 thf(fact_52_verit__negate__coefficient_I2_J, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ A3) @ B2) => (((ord_less @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A3))))))))).
% 2.43/1.48 thf(fact_53_compl__less__swap1, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y:A,X2:A]: (((((ord_less @ A) @ Y) @ ((uminus_uminus @ A) @ X2)) => (((ord_less @ A) @ X2) @ ((uminus_uminus @ A) @ Y))))))))).
% 2.43/1.48 thf(fact_54_compl__less__swap2, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y:A,X2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ Y)) @ X2) => (((ord_less @ A) @ ((uminus_uminus @ A) @ X2)) @ Y)))))))).
% 2.43/1.48 thf(fact_55_compl__less__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ X2)) @ ((uminus_uminus @ A) @ Y)) = (((ord_less @ A) @ Y) @ X2)))))))).
% 2.43/1.48 thf(fact_56_MInfty__eq__minfinity, axiom, (extended_MInfty = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)))).
% 2.43/1.48 thf(fact_57_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))))))).
% 2.43/1.48 thf(fact_58_verit__negate__coefficient_I3_J, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B2:A]: (((A3 = B2) => (((uminus_uminus @ A) @ A3) = ((uminus_uminus @ A) @ B2))))))))).
% 2.43/1.48 thf(fact_59_fun__Compl__def, axiom, (! [B:$tType,A:$tType]: (((uminus @ B) => ((uminus_uminus @ (A > B)) = (^ [A4:(A > B),X:A]: (((uminus_uminus @ B) @ (A4 @ X))))))))).
% 2.43/1.48 thf(fact_60_uminus__ereal_Osimps_I2_J, axiom, (((uminus_uminus @ extended_ereal) @ extended_PInfty) = extended_MInfty)).
% 2.43/1.48 thf(fact_61_uminus__ereal_Osimps_I3_J, axiom, (((uminus_uminus @ extended_ereal) @ extended_MInfty) = extended_PInfty)).
% 2.43/1.48 thf(fact_62_ereal__less_I6_J, axiom, (((ord_less @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) @ (zero_zero @ extended_ereal))).
% 2.43/1.48 thf(fact_63_ereal_Osimps_I13_J, axiom, (! [A:$tType,F1:(real > A),F22:A,F3:A]: (((((((extended_rec_ereal @ A) @ F1) @ F22) @ F3) @ extended_MInfty) = F3)))).
% 2.43/1.48 thf(fact_64_ex__gt__or__lt, axiom, (! [A:$tType]: (((condit1656338222tinuum @ A) => (! [A3:A]: ((? [B3:A]: (((((ord_less @ A) @ A3) @ B3) | (((ord_less @ A) @ B3) @ A3)))))))))).
% 2.43/1.48 thf(fact_65_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X2:A,Y:A]: (((X2 != Y) => ((~ ((((ord_less @ A) @ X2) @ Y))) => (((ord_less @ A) @ Y) @ X2))))))))).
% 2.43/1.48 thf(fact_66_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A3:A]: (((((ord_less @ A) @ B2) @ A3) => (A3 != B2)))))))).
% 2.43/1.48 thf(fact_67_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_68_neg__equal__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A3:A]: (((((uminus_uminus @ A) @ A3) = A3) = (A3 = (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_69_equal__neg__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A3:A]: (((A3 = ((uminus_uminus @ A) @ A3)) = (A3 = (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_70_neg__equal__0__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A]: (((((uminus_uminus @ A) @ A3) = (zero_zero @ A)) = (A3 = (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_71_neg__0__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A]: ((((zero_zero @ A) = ((uminus_uminus @ A) @ A3)) = ((zero_zero @ A) = A3)))))))).
% 2.43/1.48 thf(fact_72_add_Oinverse__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (((uminus_uminus @ A) @ (zero_zero @ A)) = (zero_zero @ A)))))).
% 2.43/1.48 thf(fact_73_ereal__uminus__zero__iff, axiom, (! [A3:extended_ereal]: (((((uminus_uminus @ extended_ereal) @ A3) = (zero_zero @ extended_ereal)) = (A3 = (zero_zero @ extended_ereal)))))).
% 2.43/1.48 thf(fact_74_ereal__uminus__zero, axiom, (((uminus_uminus @ extended_ereal) @ (zero_zero @ extended_ereal)) = (zero_zero @ extended_ereal))).
% 2.43/1.48 thf(fact_75_less__neg__neg, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A3:A]: (((((ord_less @ A) @ A3) @ ((uminus_uminus @ A) @ A3)) = (((ord_less @ A) @ A3) @ (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_76_neg__less__pos, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A3:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A3)) @ A3) = (((ord_less @ A) @ (zero_zero @ A)) @ A3)))))))).
% 2.43/1.48 thf(fact_77_neg__0__less__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((uminus_uminus @ A) @ A3)) = (((ord_less @ A) @ A3) @ (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_78_neg__less__0__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A3)) @ (zero_zero @ A)) = (((ord_less @ A) @ (zero_zero @ A)) @ A3)))))))).
% 2.43/1.48 thf(fact_79_neg__0__less__iff__less__erea, axiom, (! [A3:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ ((uminus_uminus @ extended_ereal) @ A3)) = (((ord_less @ extended_ereal) @ A3) @ (zero_zero @ extended_ereal)))))).
% 2.43/1.48 thf(fact_80_ereal_Osimps_I12_J, axiom, (! [A:$tType,F1:(real > A),F22:A,F3:A]: (((((((extended_rec_ereal @ A) @ F1) @ F22) @ F3) @ extended_PInfty) = F22)))).
% 2.43/1.48 thf(fact_81_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X2:A]: ((((zero_zero @ A) = X2) = (X2 = (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_82_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.43/1.48 thf(fact_83_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_84_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_85_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.43/1.48 thf(fact_86_Infty__neq__0_I1_J, axiom, ((extend1396239628finity @ extended_ereal) != (zero_zero @ extended_ereal))).
% 2.43/1.48 thf(fact_87_infinity__ereal__def, axiom, ((extend1396239628finity @ extended_ereal) = extended_PInfty)).
% 2.43/1.48 thf(fact_88_ereal_Odistinct_I5_J, axiom, (extended_PInfty != extended_MInfty)).
% 2.43/1.48 thf(fact_89_Infty__neq__0_I3_J, axiom, (((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)) != (zero_zero @ extended_ereal))).
% 2.43/1.48 thf(fact_90_ereal__less_I5_J, axiom, (((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ (extend1396239628finity @ extended_ereal))).
% 2.43/1.48 thf(fact_91_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F:(B > A),B2:B,C3:B]: (((A3 = (F @ B2)) => ((((ord_less @ B) @ B2) @ C3) => ((! [X4:B,Y2:B]: (((((ord_less @ B) @ X4) @ Y2) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less @ A) @ A3) @ (F @ C3))))))))))).
% 2.43/1.48 thf(fact_92_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B2:A,F:(A > B),C3:B]: (((((ord_less @ A) @ A3) @ B2) => (((F @ B2) = C3) => ((! [X4:A,Y2:A]: (((((ord_less @ A) @ X4) @ Y2) => (((ord_less @ B) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less @ B) @ (F @ A3)) @ C3)))))))))).
% 2.43/1.48 thf(fact_93_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F:(B > A),B2:B,C3:B]: (((((ord_less @ A) @ A3) @ (F @ B2)) => ((((ord_less @ B) @ B2) @ C3) => ((! [X4:B,Y2:B]: (((((ord_less @ B) @ X4) @ Y2) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less @ A) @ A3) @ (F @ C3))))))))))).
% 2.43/1.48 thf(fact_94_order__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A3:A,B2:A,F:(A > C2),C3:C2]: (((((ord_less @ A) @ A3) @ B2) => ((((ord_less @ C2) @ (F @ B2)) @ C3) => ((! [X4:A,Y2:A]: (((((ord_less @ A) @ X4) @ Y2) => (((ord_less @ C2) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less @ C2) @ (F @ A3)) @ C3)))))))))).
% 2.43/1.48 thf(fact_95_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X2:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X2))))))))).
% 2.43/1.48 thf(fact_96_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X2:A]: ((? [X_1:A]: ((((ord_less @ A) @ X2) @ X_1))))))))).
% 2.43/1.48 thf(fact_97_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((X2 != Y) => ((~ ((((ord_less @ A) @ X2) @ Y))) => (((ord_less @ A) @ Y) @ X2))))))))).
% 2.43/1.48 thf(fact_98_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((X2 != Y) = ((((ord_less @ A) @ X2) @ Y) | (((ord_less @ A) @ Y) @ X2))))))))).
% 2.43/1.48 thf(fact_99_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ A3) @ B2) => (~ ((((ord_less @ A) @ B2) @ A3)))))))))).
% 2.43/1.48 thf(fact_100_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X2) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 2.43/1.48 thf(fact_101_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (X2 != Y)))))))).
% 2.43/1.48 thf(fact_102_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (~ ((((ord_less @ A) @ Y) @ X2)))))))))).
% 2.43/1.48 thf(fact_103_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ A3) @ B2) => (~ ((((ord_less @ A) @ B2) @ A3)))))))))).
% 2.43/1.48 thf(fact_104_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X2) @ Z3))))))))).
% 2.43/1.48 thf(fact_105_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) | ((X2 = Y) | (((ord_less @ A) @ Y) @ X2))))))))).
% 2.43/1.48 thf(fact_106_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((~ ((((ord_less @ A) @ X2) @ X2))))))))).
% 2.43/1.48 thf(fact_107_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B2:A,C3:A]: (((A3 = B2) => ((((ord_less @ A) @ B2) @ C3) => (((ord_less @ A) @ A3) @ C3))))))))).
% 2.43/1.48 thf(fact_108_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ B2) => ((B2 = C3) => (((ord_less @ A) @ A3) @ C3))))))))).
% 2.43/1.48 thf(fact_109_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A3:A]: (((((ord_less @ A) @ B2) @ A3) => (~ ((((ord_less @ A) @ A3) @ B2)))))))))).
% 2.43/1.48 thf(fact_110_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (X2 != Y)))))))).
% 2.43/1.48 thf(fact_111_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (~ ((((ord_less @ A) @ Y) @ X2)))))))))).
% 2.43/1.48 thf(fact_112_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A3:A]: (((! [X4:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X4) => (P @ Y3)))) => (P @ X4)))) => (P @ A3)))))))).
% 2.43/1.48 thf(fact_113_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X2:A]: (((~ ((((ord_less @ A) @ Y) @ X2))) => ((~ ((((ord_less @ A) @ X2) @ Y))) = (X2 = Y))))))))).
% 2.43/1.48 thf(fact_114_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (Y != X2)))))))).
% 2.43/1.48 thf(fact_115_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,P:$o]: (((((ord_less @ A) @ X2) @ Y) => ((((ord_less @ A) @ Y) @ X2) => P)))))))).
% 2.43/1.48 thf(fact_116_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less @ A) @ X2) @ Y))) => ((X2 != Y) => (((ord_less @ A) @ Y) @ X2))))))))).
% 2.43/1.48 thf(fact_117_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))))))).
% 2.43/1.48 thf(fact_118_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ B2) => ((((ord_less @ A) @ B2) @ C3) => (((ord_less @ A) @ A3) @ C3))))))))).
% 2.43/1.48 thf(fact_119_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (~ ((((ord_less @ A) @ Y) @ X2)))))))))).
% 2.43/1.48 thf(fact_120_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P3:(A > $o)]: ((? [X5:A]: ((P3 @ X5))))) = (^ [P4:(A > $o)]: ((? [N2:A]: (((P4 @ N2) & (! [M2:A]: (((((ord_less @ A) @ M2) @ N2) => (~ ((P4 @ M2)))))))))))))))).
% 2.43/1.48 thf(fact_121_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B2:A]: (((! [A5:A,B3:A]: (((((ord_less @ A) @ A5) @ B3) => ((P @ A5) @ B3)))) => ((! [A5:A]: (((P @ A5) @ A5))) => ((! [A5:A,B3:A]: ((((P @ B3) @ A5) => ((P @ A5) @ B3)))) => ((P @ A3) @ B2)))))))))).
% 2.43/1.48 thf(fact_122_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A3:A,C3:A]: (((((ord_less @ A) @ B2) @ A3) => ((((ord_less @ A) @ C3) @ B2) => (((ord_less @ A) @ C3) @ A3))))))))).
% 2.43/1.48 thf(fact_123_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less @ A) @ X2) @ Y))) = ((((ord_less @ A) @ Y) @ X2) | (X2 = Y))))))))).
% 2.43/1.48 thf(fact_124_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ A3) @ B2) => (A3 != B2)))))))).
% 2.43/1.48 thf(fact_125_field__lbound__gt__zero, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [D1:A,D2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ D1) => ((((ord_less @ A) @ (zero_zero @ A)) @ D2) => (? [E:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ E) & ((((ord_less @ A) @ E) @ D1) & (((ord_less @ A) @ E) @ D2))))))))))))).
% 2.43/1.48 thf(fact_126_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.43/1.48 thf(fact_127_ereal__mult__eq__PInfty, axiom, (! [A3:extended_ereal,B2:extended_ereal]: ((((((times_times @ extended_ereal) @ A3) @ B2) = (extend1396239628finity @ extended_ereal)) = (((A3 = (extend1396239628finity @ extended_ereal)) & (((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ B2)) | (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) & (B2 = (extend1396239628finity @ extended_ereal))) | (((A3 = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) & (((ord_less @ extended_ereal) @ B2) @ (zero_zero @ extended_ereal))) | ((((ord_less @ extended_ereal) @ A3) @ (zero_zero @ extended_ereal)) & (B2 = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))))))))))).
% 2.43/1.48 thf(fact_128_ereal__mult__eq__MInfty, axiom, (! [A3:extended_ereal,B2:extended_ereal]: ((((((times_times @ extended_ereal) @ A3) @ B2) = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) = (((A3 = (extend1396239628finity @ extended_ereal)) & (((ord_less @ extended_ereal) @ B2) @ (zero_zero @ extended_ereal))) | (((((ord_less @ extended_ereal) @ A3) @ (zero_zero @ extended_ereal)) & (B2 = (extend1396239628finity @ extended_ereal))) | (((A3 = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) & (((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ B2)) | ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) & (B2 = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))))))))))).
% 2.43/1.48 thf(fact_129_ereal__mult__infty, axiom, (! [A3:extended_ereal]: ((((A3 = (zero_zero @ extended_ereal)) => ((((times_times @ extended_ereal) @ A3) @ (extend1396239628finity @ extended_ereal)) = (zero_zero @ extended_ereal))) & ((A3 != (zero_zero @ extended_ereal)) => (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) => ((((times_times @ extended_ereal) @ A3) @ (extend1396239628finity @ extended_ereal)) = (extend1396239628finity @ extended_ereal))) & ((~ ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3))) => ((((times_times @ extended_ereal) @ A3) @ (extend1396239628finity @ extended_ereal)) = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)))))))))).
% 2.43/1.48 thf(fact_130_ereal__infty__mult, axiom, (! [A3:extended_ereal]: ((((A3 = (zero_zero @ extended_ereal)) => ((((times_times @ extended_ereal) @ (extend1396239628finity @ extended_ereal)) @ A3) = (zero_zero @ extended_ereal))) & ((A3 != (zero_zero @ extended_ereal)) => (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) => ((((times_times @ extended_ereal) @ (extend1396239628finity @ extended_ereal)) @ A3) = (extend1396239628finity @ extended_ereal))) & ((~ ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3))) => ((((times_times @ extended_ereal) @ (extend1396239628finity @ extended_ereal)) @ A3) = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)))))))))).
% 2.43/1.48 thf(fact_131_ereal__divide__Infty_I2_J, axiom, (! [X2:extended_ereal]: (((((divide_divide @ extended_ereal) @ X2) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) = (zero_zero @ extended_ereal))))).
% 2.43/1.48 thf(fact_132_mult__zero__left, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A3:A]: (((((times_times @ A) @ (zero_zero @ A)) @ A3) = (zero_zero @ A)))))))).
% 2.43/1.48 thf(fact_133_mult__zero__right, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A3:A]: (((((times_times @ A) @ A3) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.43/1.48 thf(fact_134_mult__eq__0__iff, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A3:A,B2:A]: ((((((times_times @ A) @ A3) @ B2) = (zero_zero @ A)) = ((A3 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_135_mult__cancel__left, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C3:A,A3:A,B2:A]: ((((((times_times @ A) @ C3) @ A3) = (((times_times @ A) @ C3) @ B2)) = ((C3 = (zero_zero @ A)) | (A3 = B2))))))))).
% 2.43/1.48 thf(fact_136_mult__cancel__right, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [A3:A,C3:A,B2:A]: ((((((times_times @ A) @ A3) @ C3) = (((times_times @ A) @ B2) @ C3)) = ((C3 = (zero_zero @ A)) | (A3 = B2))))))))).
% 2.43/1.48 thf(fact_137_div__0, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [A3:A]: (((((divide_divide @ A) @ (zero_zero @ A)) @ A3) = (zero_zero @ A)))))))).
% 2.43/1.48 thf(fact_138_div__by__0, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [A3:A]: (((((divide_divide @ A) @ A3) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.43/1.48 thf(fact_139_mult__minus__right, axiom, (! [A:$tType]: (((ring @ A) => (! [A3:A,B2:A]: (((((times_times @ A) @ A3) @ ((uminus_uminus @ A) @ B2)) = ((uminus_uminus @ A) @ (((times_times @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_140_minus__mult__minus, axiom, (! [A:$tType]: (((ring @ A) => (! [A3:A,B2:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A3)) @ ((uminus_uminus @ A) @ B2)) = (((times_times @ A) @ A3) @ B2)))))))).
% 2.43/1.48 thf(fact_141_mult__minus__left, axiom, (! [A:$tType]: (((ring @ A) => (! [A3:A,B2:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A3)) @ B2) = ((uminus_uminus @ A) @ (((times_times @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_142_ereal__mult__minus__left, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((times_times @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ A3)) @ B2) = ((uminus_uminus @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ B2)))))).
% 2.43/1.48 thf(fact_143_ereal__mult__minus__right, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((times_times @ extended_ereal) @ A3) @ ((uminus_uminus @ extended_ereal) @ B2)) = ((uminus_uminus @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ B2)))))).
% 2.43/1.48 thf(fact_144_ereal__zero__times, axiom, (! [A3:extended_ereal,B2:extended_ereal]: ((((((times_times @ extended_ereal) @ A3) @ B2) = (zero_zero @ extended_ereal)) = ((A3 = (zero_zero @ extended_ereal)) | (B2 = (zero_zero @ extended_ereal))))))).
% 2.43/1.48 thf(fact_145_ereal__zero__mult, axiom, (! [A3:extended_ereal]: (((((times_times @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) = (zero_zero @ extended_ereal))))).
% 2.43/1.48 thf(fact_146_ereal__mult__zero, axiom, (! [A3:extended_ereal]: (((((times_times @ extended_ereal) @ A3) @ (zero_zero @ extended_ereal)) = (zero_zero @ extended_ereal))))).
% 2.43/1.48 thf(fact_147_ereal__uminus__divide, axiom, (! [X2:extended_ereal,Y:extended_ereal]: (((((divide_divide @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ X2)) @ Y) = ((uminus_uminus @ extended_ereal) @ (((divide_divide @ extended_ereal) @ X2) @ Y)))))).
% 2.43/1.48 thf(fact_148_ereal__divide__zero__left, axiom, (! [A3:extended_ereal]: (((((divide_divide @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) = (zero_zero @ extended_ereal))))).
% 2.43/1.48 thf(fact_149_ereal__times__divide__eq__left, axiom, (! [B2:extended_ereal,C3:extended_ereal,A3:extended_ereal]: (((((times_times @ extended_ereal) @ (((divide_divide @ extended_ereal) @ B2) @ C3)) @ A3) = (((divide_divide @ extended_ereal) @ (((times_times @ extended_ereal) @ B2) @ A3)) @ C3))))).
% 2.43/1.48 thf(fact_150_nonzero__mult__div__cancel__right, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [B2:A,A3:A]: (((B2 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A3) @ B2)) @ B2) = A3)))))))).
% 2.43/1.48 thf(fact_151_nonzero__mult__div__cancel__left, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [A3:A,B2:A]: (((A3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A3) @ B2)) @ A3) = B2)))))))).
% 2.43/1.48 thf(fact_152_ereal__divide__Infty_I1_J, axiom, (! [X2:extended_ereal]: (((((divide_divide @ extended_ereal) @ X2) @ (extend1396239628finity @ extended_ereal)) = (zero_zero @ extended_ereal))))).
% 2.43/1.48 thf(fact_153_mult_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [B2:A,A3:A,C3:A]: (((((times_times @ A) @ B2) @ (((times_times @ A) @ A3) @ C3)) = (((times_times @ A) @ A3) @ (((times_times @ A) @ B2) @ C3))))))))).
% 2.43/1.48 thf(fact_154_mult_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => ((times_times @ A) = (^ [A6:A,B4:A]: ((((times_times @ A) @ B4) @ A6)))))))).
% 2.43/1.48 thf(fact_155_mult_Oassoc, axiom, (! [A:$tType]: (((semigroup_mult @ A) => (! [A3:A,B2:A,C3:A]: (((((times_times @ A) @ (((times_times @ A) @ A3) @ B2)) @ C3) = (((times_times @ A) @ A3) @ (((times_times @ A) @ B2) @ C3))))))))).
% 2.43/1.48 thf(fact_156_ereal__times__divide__eq, axiom, (! [A3:extended_ereal,B2:extended_ereal,C3:extended_ereal]: (((((times_times @ extended_ereal) @ A3) @ (((divide_divide @ extended_ereal) @ B2) @ C3)) = (((divide_divide @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ B2)) @ C3))))).
% 2.43/1.48 thf(fact_157_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [A3:A,B2:A,C3:A]: (((((times_times @ A) @ (((times_times @ A) @ A3) @ B2)) @ C3) = (((times_times @ A) @ A3) @ (((times_times @ A) @ B2) @ C3))))))))).
% 2.43/1.48 thf(fact_158_mult__not__zero, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A3:A,B2:A]: ((((((times_times @ A) @ A3) @ B2) != (zero_zero @ A)) => ((A3 != (zero_zero @ A)) & (B2 != (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_159_divisors__zero, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A3:A,B2:A]: ((((((times_times @ A) @ A3) @ B2) = (zero_zero @ A)) => ((A3 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_160_no__zero__divisors, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A3:A,B2:A]: (((A3 != (zero_zero @ A)) => ((B2 != (zero_zero @ A)) => ((((times_times @ A) @ A3) @ B2) != (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_161_mult__left__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => (((((times_times @ A) @ C3) @ A3) = (((times_times @ A) @ C3) @ B2)) = (A3 = B2))))))))).
% 2.43/1.48 thf(fact_162_mult__right__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => (((((times_times @ A) @ A3) @ C3) = (((times_times @ A) @ B2) @ C3)) = (A3 = B2))))))))).
% 2.43/1.48 thf(fact_163_square__eq__iff, axiom, (! [A:$tType]: (((idom @ A) => (! [A3:A,B2:A]: ((((((times_times @ A) @ A3) @ A3) = (((times_times @ A) @ B2) @ B2)) = ((A3 = B2) | (A3 = ((uminus_uminus @ A) @ B2)))))))))).
% 2.43/1.48 thf(fact_164_minus__mult__commute, axiom, (! [A:$tType]: (((ring @ A) => (! [A3:A,B2:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A3)) @ B2) = (((times_times @ A) @ A3) @ ((uminus_uminus @ A) @ B2))))))))).
% 2.43/1.48 thf(fact_165_times__ereal_Osimps_I6_J, axiom, ((((times_times @ extended_ereal) @ (extend1396239628finity @ extended_ereal)) @ (extend1396239628finity @ extended_ereal)) = (extend1396239628finity @ extended_ereal))).
% 2.43/1.48 thf(fact_166_ereal__right__mult__cong, axiom, (! [C3:extended_ereal,D3:extended_ereal,A3:extended_ereal,B2:extended_ereal]: (((C3 = D3) => (((D3 != (zero_zero @ extended_ereal)) => (A3 = B2)) => ((((times_times @ extended_ereal) @ C3) @ A3) = (((times_times @ extended_ereal) @ D3) @ B2))))))).
% 2.43/1.48 thf(fact_167_ereal__left__mult__cong, axiom, (! [C3:extended_ereal,D3:extended_ereal,A3:extended_ereal,B2:extended_ereal]: (((C3 = D3) => (((D3 != (zero_zero @ extended_ereal)) => (A3 = B2)) => ((((times_times @ extended_ereal) @ A3) @ C3) = (((times_times @ extended_ereal) @ B2) @ D3))))))).
% 2.43/1.48 thf(fact_168_ereal__mult__divide, axiom, (! [B2:extended_ereal,A3:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ B2) => ((((ord_less @ extended_ereal) @ B2) @ (extend1396239628finity @ extended_ereal)) => ((((times_times @ extended_ereal) @ B2) @ (((divide_divide @ extended_ereal) @ A3) @ B2)) = A3)))))).
% 2.43/1.48 thf(fact_169_ereal__divide__less__iff, axiom, (! [C3:extended_ereal,A3:extended_ereal,B2:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ C3) => ((((ord_less @ extended_ereal) @ C3) @ (extend1396239628finity @ extended_ereal)) => ((((ord_less @ extended_ereal) @ (((divide_divide @ extended_ereal) @ A3) @ C3)) @ B2) = (((ord_less @ extended_ereal) @ A3) @ (((times_times @ extended_ereal) @ B2) @ C3)))))))).
% 2.43/1.48 thf(fact_170_ereal__divide__less__pos, axiom, (! [X2:extended_ereal,Y:extended_ereal,Z3:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ X2) => ((X2 != (extend1396239628finity @ extended_ereal)) => ((((ord_less @ extended_ereal) @ (((divide_divide @ extended_ereal) @ Y) @ X2)) @ Z3) = (((ord_less @ extended_ereal) @ Y) @ (((times_times @ extended_ereal) @ X2) @ Z3)))))))).
% 2.43/1.48 thf(fact_171_ereal__less__divide__iff, axiom, (! [C3:extended_ereal,A3:extended_ereal,B2:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ C3) => ((((ord_less @ extended_ereal) @ C3) @ (extend1396239628finity @ extended_ereal)) => ((((ord_less @ extended_ereal) @ A3) @ (((divide_divide @ extended_ereal) @ B2) @ C3)) = (((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ C3)) @ B2))))))).
% 2.43/1.48 thf(fact_172_ereal__less__divide__pos, axiom, (! [X2:extended_ereal,Y:extended_ereal,Z3:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ X2) => ((X2 != (extend1396239628finity @ extended_ereal)) => ((((ord_less @ extended_ereal) @ Y) @ (((divide_divide @ extended_ereal) @ Z3) @ X2)) = (((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ X2) @ Y)) @ Z3))))))).
% 2.43/1.48 thf(fact_173_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom, (! [A:$tType]: (((linord893533164strict @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C3) => (((ord_less @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)))))))))).
% 2.43/1.48 thf(fact_174_mult__less__cancel__right__disj, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A3:A,C3:A,B2:A]: (((((ord_less @ A) @ (((times_times @ A) @ A3) @ C3)) @ (((times_times @ A) @ B2) @ C3)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C3) & (((ord_less @ A) @ A3) @ B2)) | ((((ord_less @ A) @ C3) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ A3)))))))))).
% 2.43/1.48 thf(fact_175_mult__strict__right__mono, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C3) => (((ord_less @ A) @ (((times_times @ A) @ A3) @ C3)) @ (((times_times @ A) @ B2) @ C3)))))))))).
% 2.43/1.48 thf(fact_176_mult__strict__right__mono__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [B2:A,A3:A,C3:A]: (((((ord_less @ A) @ B2) @ A3) => ((((ord_less @ A) @ C3) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ A3) @ C3)) @ (((times_times @ A) @ B2) @ C3)))))))))).
% 2.43/1.48 thf(fact_177_mult__less__cancel__left__disj, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C3:A,A3:A,B2:A]: (((((ord_less @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C3) & (((ord_less @ A) @ A3) @ B2)) | ((((ord_less @ A) @ C3) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ A3)))))))))).
% 2.43/1.48 thf(fact_178_mult__strict__left__mono, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C3) => (((ord_less @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)))))))))).
% 2.43/1.48 thf(fact_179_mult__strict__left__mono__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [B2:A,A3:A,C3:A]: (((((ord_less @ A) @ B2) @ A3) => ((((ord_less @ A) @ C3) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)))))))))).
% 2.43/1.48 thf(fact_180_mult__less__cancel__left__pos, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C3:A,A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ C3) => ((((ord_less @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (((ord_less @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_181_mult__less__cancel__left__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C3:A,A3:A,B2:A]: (((((ord_less @ A) @ C3) @ (zero_zero @ A)) => ((((ord_less @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (((ord_less @ A) @ B2) @ A3))))))))).
% 2.43/1.48 thf(fact_182_zero__less__mult__pos2, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [B2:A,A3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ B2) @ A3)) => ((((ord_less @ A) @ (zero_zero @ A)) @ A3) => (((ord_less @ A) @ (zero_zero @ A)) @ B2))))))))).
% 2.43/1.48 thf(fact_183_zero__less__mult__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A3) @ B2)) => ((((ord_less @ A) @ (zero_zero @ A)) @ A3) => (((ord_less @ A) @ (zero_zero @ A)) @ B2))))))))).
% 2.43/1.48 thf(fact_184_zero__less__mult__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A3) @ B2)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A3) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less @ A) @ A3) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.43/1.48 thf(fact_185_mult__pos__neg2, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A3) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ B2) @ A3)) @ (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_186_mult__pos__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A3) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A3) @ B2)))))))))).
% 2.43/1.48 thf(fact_187_mult__pos__neg, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A3) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ A3) @ B2)) @ (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_188_mult__neg__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ A3) @ (zero_zero @ A)) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (((times_times @ A) @ A3) @ B2)) @ (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_189_mult__less__0__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (((times_times @ A) @ A3) @ B2)) @ (zero_zero @ A)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A3) & (((ord_less @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less @ A) @ A3) @ (zero_zero @ A)) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.43/1.48 thf(fact_190_not__square__less__zero, axiom, (! [A:$tType]: (((linordered_ring @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ (((times_times @ A) @ A3) @ A3)) @ (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_191_mult__neg__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ A3) @ (zero_zero @ A)) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A3) @ B2)))))))))).
% 2.43/1.48 thf(fact_192_times__ereal_Osimps_I9_J, axiom, ((((times_times @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) = (extend1396239628finity @ extended_ereal))).
% 2.43/1.48 thf(fact_193_times__ereal_Osimps_I8_J, axiom, ((((times_times @ extended_ereal) @ (extend1396239628finity @ extended_ereal)) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)))).
% 2.43/1.48 thf(fact_194_times__ereal_Osimps_I7_J, axiom, ((((times_times @ extended_ereal) @ ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal))) @ (extend1396239628finity @ extended_ereal)) = ((uminus_uminus @ extended_ereal) @ (extend1396239628finity @ extended_ereal)))).
% 2.43/1.48 thf(fact_195_ereal__mult__less__0__iff, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ B2)) @ (zero_zero @ extended_ereal)) = (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) & (((ord_less @ extended_ereal) @ B2) @ (zero_zero @ extended_ereal))) | ((((ord_less @ extended_ereal) @ A3) @ (zero_zero @ extended_ereal)) & (((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ B2))))))).
% 2.43/1.48 thf(fact_196_ereal__zero__less__0__iff, axiom, (! [A3:extended_ereal,B2:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ (((times_times @ extended_ereal) @ A3) @ B2)) = (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) & (((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ B2)) | ((((ord_less @ extended_ereal) @ A3) @ (zero_zero @ extended_ereal)) & (((ord_less @ extended_ereal) @ B2) @ (zero_zero @ extended_ereal)))))))).
% 2.43/1.48 thf(fact_197_ereal__mult__mono__strict, axiom, (! [B2:extended_ereal,C3:extended_ereal,A3:extended_ereal,D3:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ B2) => ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ C3) => ((((ord_less @ extended_ereal) @ A3) @ B2) => ((((ord_less @ extended_ereal) @ C3) @ D3) => (((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ C3)) @ (((times_times @ extended_ereal) @ B2) @ D3))))))))).
% 2.43/1.48 thf(fact_198_ereal__mult__mono__strict_H, axiom, (! [A3:extended_ereal,C3:extended_ereal,B2:extended_ereal,D3:extended_ereal]: (((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) => ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ C3) => ((((ord_less @ extended_ereal) @ A3) @ B2) => ((((ord_less @ extended_ereal) @ C3) @ D3) => (((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ C3)) @ (((times_times @ extended_ereal) @ B2) @ D3))))))))).
% 2.43/1.48 thf(fact_199_ereal__mult__less__right, axiom, (! [B2:extended_ereal,A3:extended_ereal,C3:extended_ereal]: (((((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ B2) @ A3)) @ (((times_times @ extended_ereal) @ C3) @ A3)) => ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ A3) => ((((ord_less @ extended_ereal) @ A3) @ (extend1396239628finity @ extended_ereal)) => (((ord_less @ extended_ereal) @ B2) @ C3))))))).
% 2.43/1.48 thf(fact_200_ereal__mult__strict__left__mono, axiom, (! [A3:extended_ereal,B2:extended_ereal,C3:extended_ereal]: (((((ord_less @ extended_ereal) @ A3) @ B2) => ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ C3) => ((((ord_less @ extended_ereal) @ C3) @ (extend1396239628finity @ extended_ereal)) => (((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ C3) @ A3)) @ (((times_times @ extended_ereal) @ C3) @ B2)))))))).
% 2.43/1.48 thf(fact_201_ereal__mult__strict__right__mono, axiom, (! [A3:extended_ereal,B2:extended_ereal,C3:extended_ereal]: (((((ord_less @ extended_ereal) @ A3) @ B2) => ((((ord_less @ extended_ereal) @ (zero_zero @ extended_ereal)) @ C3) => ((((ord_less @ extended_ereal) @ C3) @ (extend1396239628finity @ extended_ereal)) => (((ord_less @ extended_ereal) @ (((times_times @ extended_ereal) @ A3) @ C3)) @ (((times_times @ extended_ereal) @ B2) @ C3)))))))).
% 2.43/1.48 thf(fact_202_div__mult__mult1__if, axiom, (! [A:$tType]: (((euclid191655569cancel @ A) => (! [C3:A,A3:A,B2:A]: ((((C3 = (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (zero_zero @ A))) & ((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (((divide_divide @ A) @ A3) @ B2)))))))))).
% 2.43/1.48 thf(fact_203_div__mult__mult2, axiom, (! [A:$tType]: (((euclid191655569cancel @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A3) @ C3)) @ (((times_times @ A) @ B2) @ C3)) = (((divide_divide @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_204_div__mult__mult1, axiom, (! [A:$tType]: (((euclid191655569cancel @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (((divide_divide @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_205_nonzero__mult__divide__mult__cancel__right2, axiom, (! [A:$tType]: (((field @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A3) @ C3)) @ (((times_times @ A) @ C3) @ B2)) = (((divide_divide @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_206_divide__eq__0__iff, axiom, (! [A:$tType]: (((field @ A) => (! [A3:A,B2:A]: ((((((divide_divide @ A) @ A3) @ B2) = (zero_zero @ A)) = ((A3 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_207_divide__cancel__left, axiom, (! [A:$tType]: (((field @ A) => (! [C3:A,A3:A,B2:A]: ((((((divide_divide @ A) @ C3) @ A3) = (((divide_divide @ A) @ C3) @ B2)) = ((C3 = (zero_zero @ A)) | (A3 = B2))))))))).
% 2.43/1.48 thf(fact_208_divide__cancel__right, axiom, (! [A:$tType]: (((field @ A) => (! [A3:A,C3:A,B2:A]: ((((((divide_divide @ A) @ A3) @ C3) = (((divide_divide @ A) @ B2) @ C3)) = ((C3 = (zero_zero @ A)) | (A3 = B2))))))))).
% 2.43/1.48 thf(fact_209_division__ring__divide__zero, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A3:A]: (((((divide_divide @ A) @ A3) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.43/1.48 thf(fact_210_times__divide__eq__right, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A3:A,B2:A,C3:A]: (((((times_times @ A) @ A3) @ (((divide_divide @ A) @ B2) @ C3)) = (((divide_divide @ A) @ (((times_times @ A) @ A3) @ B2)) @ C3)))))))).
% 2.43/1.48 thf(fact_211_divide__divide__eq__right, axiom, (! [A:$tType]: (((field @ A) => (! [A3:A,B2:A,C3:A]: (((((divide_divide @ A) @ A3) @ (((divide_divide @ A) @ B2) @ C3)) = (((divide_divide @ A) @ (((times_times @ A) @ A3) @ C3)) @ B2)))))))).
% 2.43/1.48 thf(fact_212_divide__divide__eq__left, axiom, (! [A:$tType]: (((field @ A) => (! [A3:A,B2:A,C3:A]: (((((divide_divide @ A) @ (((divide_divide @ A) @ A3) @ B2)) @ C3) = (((divide_divide @ A) @ A3) @ (((times_times @ A) @ B2) @ C3))))))))).
% 2.43/1.48 thf(fact_213_times__divide__eq__left, axiom, (! [A:$tType]: (((field @ A) => (! [B2:A,C3:A,A3:A]: (((((times_times @ A) @ (((divide_divide @ A) @ B2) @ C3)) @ A3) = (((divide_divide @ A) @ (((times_times @ A) @ B2) @ A3)) @ C3)))))))).
% 2.43/1.48 thf(fact_214_div__minus__minus, axiom, (! [A:$tType]: (((euclid24285859cancel @ A) => (! [A3:A,B2:A]: (((((divide_divide @ A) @ ((uminus_uminus @ A) @ A3)) @ ((uminus_uminus @ A) @ B2)) = (((divide_divide @ A) @ A3) @ B2)))))))).
% 2.43/1.48 thf(fact_215_mult__divide__mult__cancel__left__if, axiom, (! [A:$tType]: (((field @ A) => (! [C3:A,A3:A,B2:A]: ((((C3 = (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (zero_zero @ A))) & ((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (((divide_divide @ A) @ A3) @ B2)))))))))).
% 2.43/1.48 thf(fact_216_nonzero__mult__divide__mult__cancel__left, axiom, (! [A:$tType]: (((field @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ C3) @ B2)) = (((divide_divide @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_217_nonzero__mult__divide__mult__cancel__left2, axiom, (! [A:$tType]: (((field @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C3) @ A3)) @ (((times_times @ A) @ B2) @ C3)) = (((divide_divide @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_218_nonzero__mult__divide__mult__cancel__right, axiom, (! [A:$tType]: (((field @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A3) @ C3)) @ (((times_times @ A) @ B2) @ C3)) = (((divide_divide @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_219_linordered__field__no__lb, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X3))))))))).
% 2.43/1.48 thf(fact_220_linordered__field__no__ub, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A]: ((? [X_1:A]: ((((ord_less @ A) @ X3) @ X_1))))))))).
% 2.43/1.48 thf(fact_221_divide__divide__eq__left_H, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A3:A,B2:A,C3:A]: (((((divide_divide @ A) @ (((divide_divide @ A) @ A3) @ B2)) @ C3) = (((divide_divide @ A) @ A3) @ (((times_times @ A) @ C3) @ B2))))))))).
% 2.43/1.48 thf(fact_222_divide__divide__times__eq, axiom, (! [A:$tType]: (((field @ A) => (! [X2:A,Y:A,Z3:A,W:A]: (((((divide_divide @ A) @ (((divide_divide @ A) @ X2) @ Y)) @ (((divide_divide @ A) @ Z3) @ W)) = (((divide_divide @ A) @ (((times_times @ A) @ X2) @ W)) @ (((times_times @ A) @ Y) @ Z3))))))))).
% 2.43/1.48 thf(fact_223_times__divide__times__eq, axiom, (! [A:$tType]: (((field @ A) => (! [X2:A,Y:A,Z3:A,W:A]: (((((times_times @ A) @ (((divide_divide @ A) @ X2) @ Y)) @ (((divide_divide @ A) @ Z3) @ W)) = (((divide_divide @ A) @ (((times_times @ A) @ X2) @ Z3)) @ (((times_times @ A) @ Y) @ W))))))))).
% 2.43/1.48 thf(fact_224_div__minus__right, axiom, (! [A:$tType]: (((euclid24285859cancel @ A) => (! [A3:A,B2:A]: (((((divide_divide @ A) @ A3) @ ((uminus_uminus @ A) @ B2)) = (((divide_divide @ A) @ ((uminus_uminus @ A) @ A3)) @ B2)))))))).
% 2.43/1.48 thf(fact_225_minus__divide__left, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A3:A,B2:A]: ((((uminus_uminus @ A) @ (((divide_divide @ A) @ A3) @ B2)) = (((divide_divide @ A) @ ((uminus_uminus @ A) @ A3)) @ B2)))))))).
% 2.43/1.48 thf(fact_226_minus__divide__divide, axiom, (! [A:$tType]: (((field @ A) => (! [A3:A,B2:A]: (((((divide_divide @ A) @ ((uminus_uminus @ A) @ A3)) @ ((uminus_uminus @ A) @ B2)) = (((divide_divide @ A) @ A3) @ B2)))))))).
% 2.43/1.48 thf(fact_227_minus__divide__right, axiom, (! [A:$tType]: (((field @ A) => (! [A3:A,B2:A]: ((((uminus_uminus @ A) @ (((divide_divide @ A) @ A3) @ B2)) = (((divide_divide @ A) @ A3) @ ((uminus_uminus @ A) @ B2))))))))).
% 2.43/1.48 thf(fact_228_divide__neg__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ (zero_zero @ A)) => ((((ord_less @ A) @ Y) @ (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ X2) @ Y)))))))))).
% 2.43/1.48 thf(fact_229_divide__neg__pos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ (zero_zero @ A)) => ((((ord_less @ A) @ (zero_zero @ A)) @ Y) => (((ord_less @ A) @ (((divide_divide @ A) @ X2) @ Y)) @ (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_230_divide__pos__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ X2) => ((((ord_less @ A) @ Y) @ (zero_zero @ A)) => (((ord_less @ A) @ (((divide_divide @ A) @ X2) @ Y)) @ (zero_zero @ A)))))))))).
% 2.43/1.48 thf(fact_231_divide__pos__pos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ X2) => ((((ord_less @ A) @ (zero_zero @ A)) @ Y) => (((ord_less @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ X2) @ Y)))))))))).
% 2.43/1.48 thf(fact_232_divide__less__0__iff, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (((divide_divide @ A) @ A3) @ B2)) @ (zero_zero @ A)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A3) & (((ord_less @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less @ A) @ A3) @ (zero_zero @ A)) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.43/1.48 thf(fact_233_divide__less__cancel, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A3:A,C3:A,B2:A]: (((((ord_less @ A) @ (((divide_divide @ A) @ A3) @ C3)) @ (((divide_divide @ A) @ B2) @ C3)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C3) => (((ord_less @ A) @ A3) @ B2)) & (((((ord_less @ A) @ C3) @ (zero_zero @ A)) => (((ord_less @ A) @ B2) @ A3)) & (C3 != (zero_zero @ A))))))))))).
% 2.43/1.48 thf(fact_234_zero__less__divide__iff, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ A3) @ B2)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A3) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less @ A) @ A3) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.43/1.48 thf(fact_235_divide__strict__right__mono, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C3) => (((ord_less @ A) @ (((divide_divide @ A) @ A3) @ C3)) @ (((divide_divide @ A) @ B2) @ C3)))))))))).
% 2.43/1.48 thf(fact_236_divide__strict__right__mono__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [B2:A,A3:A,C3:A]: (((((ord_less @ A) @ B2) @ A3) => ((((ord_less @ A) @ C3) @ (zero_zero @ A)) => (((ord_less @ A) @ (((divide_divide @ A) @ A3) @ C3)) @ (((divide_divide @ A) @ B2) @ C3)))))))))).
% 2.43/1.48 thf(fact_237_frac__eq__eq, axiom, (! [A:$tType]: (((field @ A) => (! [Y:A,Z3:A,X2:A,W:A]: (((Y != (zero_zero @ A)) => ((Z3 != (zero_zero @ A)) => (((((divide_divide @ A) @ X2) @ Y) = (((divide_divide @ A) @ W) @ Z3)) = ((((times_times @ A) @ X2) @ Z3) = (((times_times @ A) @ W) @ Y))))))))))).
% 2.43/1.48 thf(fact_238_divide__eq__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [B2:A,C3:A,A3:A]: ((((((divide_divide @ A) @ B2) @ C3) = A3) = (((C3 != (zero_zero @ A)) => (B2 = (((times_times @ A) @ A3) @ C3))) & ((C3 = (zero_zero @ A)) => (A3 = (zero_zero @ A))))))))))).
% 2.43/1.48 thf(fact_239_eq__divide__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A3:A,B2:A,C3:A]: (((A3 = (((divide_divide @ A) @ B2) @ C3)) = (((C3 != (zero_zero @ A)) => ((((times_times @ A) @ A3) @ C3) = B2)) & ((C3 = (zero_zero @ A)) => (A3 = (zero_zero @ A))))))))))).
% 2.43/1.48 thf(fact_240_divide__eq__imp, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C3:A,B2:A,A3:A]: (((C3 != (zero_zero @ A)) => ((B2 = (((times_times @ A) @ A3) @ C3)) => ((((divide_divide @ A) @ B2) @ C3) = A3))))))))).
% 2.43/1.48 thf(fact_241_eq__divide__imp, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => (((((times_times @ A) @ A3) @ C3) = B2) => (A3 = (((divide_divide @ A) @ B2) @ C3)))))))))).
% 2.43/1.48 thf(fact_242_nonzero__divide__eq__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C3:A,B2:A,A3:A]: (((C3 != (zero_zero @ A)) => (((((divide_divide @ A) @ B2) @ C3) = A3) = (B2 = (((times_times @ A) @ A3) @ C3)))))))))).
% 2.43/1.48 thf(fact_243_nonzero__eq__divide__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C3:A,A3:A,B2:A]: (((C3 != (zero_zero @ A)) => ((A3 = (((divide_divide @ A) @ B2) @ C3)) = ((((times_times @ A) @ A3) @ C3) = B2))))))))).
% 2.43/1.48 thf(fact_244_nonzero__minus__divide__right, axiom, (! [A:$tType]: (((division_ring @ A) => (! [B2:A,A3:A]: (((B2 != (zero_zero @ A)) => (((uminus_uminus @ A) @ (((divide_divide @ A) @ A3) @ B2)) = (((divide_divide @ A) @ A3) @ ((uminus_uminus @ A) @ B2)))))))))).
% 2.43/1.48 thf(fact_245_nonzero__minus__divide__divide, axiom, (! [A:$tType]: (((division_ring @ A) => (! [B2:A,A3:A]: (((B2 != (zero_zero @ A)) => ((((divide_divide @ A) @ ((uminus_uminus @ A) @ A3)) @ ((uminus_uminus @ A) @ B2)) = (((divide_divide @ A) @ A3) @ B2))))))))).
% 2.43/1.48 thf(fact_246_divide__strict__left__mono__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ B2) => ((((ord_less @ A) @ C3) @ (zero_zero @ A)) => ((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A3) @ B2)) => (((ord_less @ A) @ (((divide_divide @ A) @ C3) @ A3)) @ (((divide_divide @ A) @ C3) @ B2))))))))))).
% 2.43/1.48 thf(fact_247_divide__strict__left__mono, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [B2:A,A3:A,C3:A]: (((((ord_less @ A) @ B2) @ A3) => ((((ord_less @ A) @ (zero_zero @ A)) @ C3) => ((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A3) @ B2)) => (((ord_less @ A) @ (((divide_divide @ A) @ C3) @ A3)) @ (((divide_divide @ A) @ C3) @ B2))))))))))).
% 2.43/1.48 thf(fact_248_mult__imp__less__div__pos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [Y:A,Z3:A,X2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ Y) => ((((ord_less @ A) @ (((times_times @ A) @ Z3) @ Y)) @ X2) => (((ord_less @ A) @ Z3) @ (((divide_divide @ A) @ X2) @ Y)))))))))).
% 2.43/1.48 thf(fact_249_mult__imp__div__pos__less, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [Y:A,X2:A,Z3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ Y) => ((((ord_less @ A) @ X2) @ (((times_times @ A) @ Z3) @ Y)) => (((ord_less @ A) @ (((divide_divide @ A) @ X2) @ Y)) @ Z3))))))))).
% 2.43/1.48 thf(fact_250_pos__less__divide__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C3:A,A3:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ C3) => ((((ord_less @ A) @ A3) @ (((divide_divide @ A) @ B2) @ C3)) = (((ord_less @ A) @ (((times_times @ A) @ A3) @ C3)) @ B2))))))))).
% 2.43/1.48 thf(fact_251_pos__divide__less__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C3:A,B2:A,A3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ C3) => ((((ord_less @ A) @ (((divide_divide @ A) @ B2) @ C3)) @ A3) = (((ord_less @ A) @ B2) @ (((times_times @ A) @ A3) @ C3)))))))))).
% 2.43/1.48 thf(fact_252_neg__less__divide__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C3:A,A3:A,B2:A]: (((((ord_less @ A) @ C3) @ (zero_zero @ A)) => ((((ord_less @ A) @ A3) @ (((divide_divide @ A) @ B2) @ C3)) = (((ord_less @ A) @ B2) @ (((times_times @ A) @ A3) @ C3)))))))))).
% 2.43/1.48 thf(fact_253_neg__divide__less__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C3:A,B2:A,A3:A]: (((((ord_less @ A) @ C3) @ (zero_zero @ A)) => ((((ord_less @ A) @ (((divide_divide @ A) @ B2) @ C3)) @ A3) = (((ord_less @ A) @ (((times_times @ A) @ A3) @ C3)) @ B2))))))))).
% 2.43/1.48 thf(fact_254_less__divide__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A3:A,B2:A,C3:A]: (((((ord_less @ A) @ A3) @ (((divide_divide @ A) @ B2) @ C3)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C3) => (((ord_less @ A) @ (((times_times @ A) @ A3) @ C3)) @ B2)) & ((~ ((((ord_less @ A) @ (zero_zero @ A)) @ C3))) => (((((ord_less @ A) @ C3) @ (zero_zero @ A)) => (((ord_less @ A) @ B2) @ (((times_times @ A) @ A3) @ C3))) & ((~ ((((ord_less @ A) @ C3) @ (zero_zero @ A)))) => (((ord_less @ A) @ A3) @ (zero_zero @ A))))))))))))).
% 2.43/1.48 thf(subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => (type @ A))))).
% 2.43/1.48 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Ot0__space, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => (topological_t0_space @ A))))).
% 2.43/1.48 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Ot1__space, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => (topological_t1_space @ A))))).
% 2.43/1.48 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => (topolo503727757_space @ A))))).
% 2.43/1.48 thf(tcon_fun___Topological__Spaces_Otopological__space, axiom, (! [A7:$tType,A8:$tType]: (((topolo503727757_space @ A8) => (topolo503727757_space @ (A7 > A8)))))).
% 2.43/1.48 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A7:$tType,A8:$tType]: (((boolean_algebra @ A8) => (boolean_algebra @ (A7 > A8)))))).
% 2.43/1.48 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.43/1.48 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.43/1.48 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.43/1.48 thf(tcon_fun___Groups_Ouminus, axiom, (! [A7:$tType,A8:$tType]: (((uminus @ A8) => (uminus @ (A7 > A8)))))).
% 2.43/1.48 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_1, axiom, (! [A7:$tType]: ((boolean_algebra @ (set @ A7))))).
% 2.43/1.48 thf(tcon_Set_Oset___Groups_Oab__semigroup__mult, axiom, (! [A7:$tType]: (((ab_semigroup_mult @ A7) => (ab_semigroup_mult @ (set @ A7)))))).
% 2.43/1.48 thf(tcon_Set_Oset___Groups_Osemigroup__mult, axiom, (! [A7:$tType]: (((semigroup_mult @ A7) => (semigroup_mult @ (set @ A7)))))).
% 2.43/1.48 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.43/1.48 thf(tcon_Set_Oset___Orderings_Oorder_3, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.43/1.48 thf(tcon_Set_Oset___Orderings_Oord_4, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.43/1.48 thf(tcon_Set_Oset___Groups_Ouminus_5, axiom, (! [A7:$tType]: ((uminus @ (set @ A7))))).
% 2.43/1.48 thf(tcon_Set_Oset___Groups_Ozero, axiom, (! [A7:$tType]: (((zero @ A7) => (zero @ (set @ A7)))))).
% 2.43/1.48 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_6, axiom, (topolo503727757_space @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology, axiom, (topolo2133971006pology @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Topological__Spaces_Ot1__space, axiom, (topological_t1_space @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Topological__Spaces_Ot0__space, axiom, (topological_t0_space @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_7, axiom, (boolean_algebra @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Orderings_Opreorder_8, axiom, (preorder @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, (order @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, (ord @ $o)).
% 2.43/1.48 thf(tcon_HOL_Obool___Groups_Ouminus_11, axiom, (uminus @ $o)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Conditionally__Complete__Lattices_Olinear__continuum, axiom, (condit1656338222tinuum @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_12, axiom, (topolo503727757_space @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Ot1__space_13, axiom, (topological_t1_space @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Ot0__space_14, axiom, (topological_t0_space @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Groups_Oab__semigroup__mult_15, axiom, (ab_semigroup_mult @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Orderings_Odense__order, axiom, (dense_order @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Groups_Osemigroup__mult_16, axiom, (semigroup_mult @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Orderings_Opreorder_17, axiom, (preorder @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Orderings_Olinorder_18, axiom, (linorder @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Orderings_Oorder_19, axiom, (order @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Orderings_Oord_20, axiom, (ord @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Groups_Ouminus_21, axiom, (uminus @ extended_ereal)).
% 2.43/1.48 thf(tcon_Extended__Real_Oereal___Groups_Ozero_22, axiom, (zero @ extended_ereal)).
% 2.43/1.48 thf(tfree_0, hypothesis, (real_V2090557954_space @ a)).
% 2.43/1.48 thf(conj_0, conjecture, (((((lower_582600101lsc_at @ a) @ extended_ereal) @ x0) @ f) != (~ ((! [C:extended_ereal]: (((((ord_less @ extended_ereal) @ C) @ (f @ x0)) => (? [T:(set @ a)]: ((((topolo1751647064n_open @ a) @ T) & ((((member @ a) @ x0) @ T) & (! [X:a]: (((((member @ a) @ X) @ T) => (((ord_less @ extended_ereal) @ C) @ (f @ X)))))))))))))))).
% 2.43/1.48 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2DTF16074.p
% 2.43/1.48 ------------------------
% 2.69/1.50 ---- Cleaned THF ---
% 2.69/1.50 thf(ty_t_Extended__Real_Oereal,type,
% 2.69/1.50 extended_ereal: $tType ).
% 2.69/1.50
% 2.69/1.50 thf(ty_t_Real_Oreal,type,
% 2.69/1.50 real: $tType ).
% 2.69/1.50
% 2.69/1.50 thf(ty_t_Set_Oset,type,
% 2.69/1.50 set: $tType > $tType ).
% 2.69/1.50
% 2.69/1.50 thf(ty_tf_a,type,
% 2.69/1.50 a: $tType ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 2.69/1.50 real_V2090557954_space:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_HOL_Otype,type,
% 2.69/1.50 type:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Oidom,type,
% 2.69/1.50 idom:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Oring,type,
% 2.69/1.50 ring:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Ozero,type,
% 2.69/1.50 zero:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Fields_Ofield,type,
% 2.69/1.50 field:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Ouminus,type,
% 2.69/1.50 uminus:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Oord,type,
% 2.69/1.50 ord:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Oorder,type,
% 2.69/1.50 order:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Omult__zero,type,
% 2.69/1.50 mult_zero:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Ogroup__add,type,
% 2.69/1.50 group_add:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Ono__bot,type,
% 2.69/1.50 no_bot:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Ono__top,type,
% 2.69/1.50 no_top:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Olinorder,type,
% 2.69/1.50 linorder:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Opreorder,type,
% 2.69/1.50 preorder:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Owellorder,type,
% 2.69/1.50 wellorder:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Fields_Odivision__ring,type,
% 2.69/1.50 division_ring:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Osemidom__divide,type,
% 2.69/1.50 semidom_divide:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Osemigroup__mult,type,
% 2.69/1.50 semigroup_mult:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Orderings_Odense__order,type,
% 2.69/1.50 dense_order:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.69/1.50 linordered_idom:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Olinordered__ring,type,
% 2.69/1.50 linordered_ring:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Fields_Olinordered__field,type,
% 2.69/1.50 linordered_field:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 2.69/1.50 ab_semigroup_mult:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 2.69/1.50 boolean_algebra:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.69/1.50 ordered_ab_group_add:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Topological__Spaces_Ot0__space,type,
% 2.69/1.50 topological_t0_space:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Topological__Spaces_Ot1__space,type,
% 2.69/1.50 topological_t1_space:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 2.69/1.50 linord581940658strict:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.69/1.50 linord219039673up_add:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 2.69/1.50 semiri1193490041visors:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Olinordered__semiring__strict,type,
% 2.69/1.50 linord20386208strict:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.69/1.50 linord1659791738miring:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Topological__Spaces_Odiscrete__topology,type,
% 2.69/1.50 topolo2133971006pology:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 2.69/1.50 topolo503727757_space:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.69/1.50 canoni770627133id_add:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Olinordered__comm__semiring__strict,type,
% 2.69/1.50 linord893533164strict:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 2.69/1.50 semiri1923998003cancel:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Euclidean__Division_Oeuclidean__ring__cancel,type,
% 2.69/1.50 euclid24285859cancel:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Euclidean__Division_Oeuclidean__semiring__cancel,type,
% 2.69/1.50 euclid191655569cancel:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 2.69/1.50 condit1656338222tinuum:
% 2.69/1.50 !>[A: $tType] : $o ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Extended__Nat_Oinfinity__class_Oinfinity,type,
% 2.69/1.50 extend1396239628finity:
% 2.69/1.50 !>[A: $tType] : A ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Extended__Real_Oereal_OMInfty,type,
% 2.69/1.50 extended_MInfty: extended_ereal ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Extended__Real_Oereal_OPInfty,type,
% 2.69/1.50 extended_PInfty: extended_ereal ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Extended__Real_Oereal_Orec__ereal,type,
% 2.69/1.50 extended_rec_ereal:
% 2.69/1.50 !>[A: $tType] : ( ( real > A ) > A > A > extended_ereal > A ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 2.69/1.50 times_times:
% 2.69/1.50 !>[A: $tType] : ( A > A > A ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.69/1.50 uminus_uminus:
% 2.69/1.50 !>[A: $tType] : ( A > A ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.69/1.50 zero_zero:
% 2.69/1.50 !>[A: $tType] : A ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Lower__Semicontinuous__Mirabelle__quczrylfpw_Olsc__at,type,
% 2.69/1.50 lower_582600101lsc_at:
% 2.69/1.50 !>[A: $tType,B: $tType] : ( A > ( A > B ) > $o ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.69/1.50 ord_less:
% 2.69/1.50 !>[A: $tType] : ( A > A > $o ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Rings_Odivide__class_Odivide,type,
% 2.69/1.50 divide_divide:
% 2.69/1.50 !>[A: $tType] : ( A > A > A ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Set_OCollect,type,
% 2.69/1.50 collect:
% 2.69/1.50 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_Topological__Spaces_Oopen__class_Oopen,type,
% 2.69/1.50 topolo1751647064n_open:
% 2.69/1.50 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_c_member,type,
% 2.69/1.50 member:
% 2.69/1.50 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.69/1.50
% 2.69/1.50 thf(sy_v_f,type,
% 2.69/1.50 f: a > extended_ereal ).
% 2.69/1.50
% 2.69/1.50 thf(sy_v_x0,type,
% 2.69/1.50 x0: a ).
% 2.69/1.50
% 2.69/1.50 thf(fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 2.69/1.50 ( ( ( f @ x0 )
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 => ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 2.69/1.50 = ( ! [C: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 2.69/1.50 => ? [T: set @ a] :
% 2.69/1.50 ( ( topolo1751647064n_open @ a @ T )
% 2.69/1.50 & ( member @ a @ x0 @ T )
% 2.69/1.50 & ! [X: a] :
% 2.69/1.50 ( ( member @ a @ X @ T )
% 2.69/1.50 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 2.69/1.50 ( ( ( f @ x0 )
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 => ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 2.69/1.50 = ( ! [C: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 2.69/1.50 => ? [T: set @ a] :
% 2.69/1.50 ( ( topolo1751647064n_open @ a @ T )
% 2.69/1.50 & ( member @ a @ x0 @ T )
% 2.69/1.50 & ! [X: a] :
% 2.69/1.50 ( ( member @ a @ X @ T )
% 2.69/1.50 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 2.69/1.50 ( ( ( f @ x0 )
% 2.69/1.50 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 => ( ( ( f @ x0 )
% 2.69/1.50 != ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 => ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 2.69/1.50 = ( ! [C: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 2.69/1.50 => ? [T: set @ a] :
% 2.69/1.50 ( ( topolo1751647064n_open @ a @ T )
% 2.69/1.50 & ( member @ a @ x0 @ T )
% 2.69/1.50 & ! [X: a] :
% 2.69/1.50 ( ( member @ a @ X @ T )
% 2.69/1.50 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_3_lsc__at__MInfty,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( topolo503727757_space @ A )
% 2.69/1.50 => ! [F: A > extended_ereal,X0: A] :
% 2.69/1.50 ( ( ( F @ X0 )
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 => ( lower_582600101lsc_at @ A @ extended_ereal @ X0 @ F ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_4_t0__space,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( topological_t0_space @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( X2 != Y )
% 2.69/1.50 => ? [U: set @ A] :
% 2.69/1.50 ( ( topolo1751647064n_open @ A @ U )
% 2.69/1.50 & ( ( member @ A @ X2 @ U )
% 2.69/1.50 != ( member @ A @ Y @ U ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_5_t1__space,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( topological_t1_space @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( X2 != Y )
% 2.69/1.50 => ? [U: set @ A] :
% 2.69/1.50 ( ( topolo1751647064n_open @ A @ U )
% 2.69/1.50 & ( member @ A @ X2 @ U )
% 2.69/1.50 & ~ ( member @ A @ Y @ U ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_6_separation__t0,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( topological_t0_space @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( X2 != Y )
% 2.69/1.50 = ( ? [U2: set @ A] :
% 2.69/1.50 ( ( topolo1751647064n_open @ A @ U2 )
% 2.69/1.50 & ( ( member @ A @ X2 @ U2 )
% 2.69/1.50 != ( member @ A @ Y @ U2 ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_7_separation__t1,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( topological_t1_space @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( X2 != Y )
% 2.69/1.50 = ( ? [U2: set @ A] :
% 2.69/1.50 ( ( topolo1751647064n_open @ A @ U2 )
% 2.69/1.50 & ( member @ A @ X2 @ U2 )
% 2.69/1.50 & ~ ( member @ A @ Y @ U2 ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_8_open__discrete,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( topolo2133971006pology @ A )
% 2.69/1.50 => ! [A2: set @ A] : ( topolo1751647064n_open @ A @ A2 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_9_minf_I11_J,axiom,
% 2.69/1.50 ! [C2: $tType,D: $tType] :
% 2.69/1.50 ( ( ord @ C2 )
% 2.69/1.50 => ! [F2: D] :
% 2.69/1.50 ? [Z: C2] :
% 2.69/1.50 ! [X3: C2] :
% 2.69/1.50 ( ( ord_less @ C2 @ X3 @ Z )
% 2.69/1.50 => ( F2 = F2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_10_minf_I7_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ X3 @ Z )
% 2.69/1.50 => ~ ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_11_minf_I5_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ X3 @ Z )
% 2.69/1.50 => ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_12_minf_I4_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ X3 @ Z )
% 2.69/1.50 => ( X3 != T2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_13_minf_I3_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ X3 @ Z )
% 2.69/1.50 => ( X3 != T2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_14_minf_I2_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.69/1.50 ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ X4 @ Z2 )
% 2.69/1.50 => ( ( P @ X4 )
% 2.69/1.50 = ( P2 @ X4 ) ) )
% 2.69/1.50 => ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ X4 @ Z2 )
% 2.69/1.50 => ( ( Q @ X4 )
% 2.69/1.50 = ( Q2 @ X4 ) ) )
% 2.69/1.50 => ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ X3 @ Z )
% 2.69/1.50 => ( ( ( P @ X3 )
% 2.69/1.50 | ( Q @ X3 ) )
% 2.69/1.50 = ( ( P2 @ X3 )
% 2.69/1.50 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_15_pinf_I1_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.69/1.50 ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z2 @ X4 )
% 2.69/1.50 => ( ( P @ X4 )
% 2.69/1.50 = ( P2 @ X4 ) ) )
% 2.69/1.50 => ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z2 @ X4 )
% 2.69/1.50 => ( ( Q @ X4 )
% 2.69/1.50 = ( Q2 @ X4 ) ) )
% 2.69/1.50 => ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z @ X3 )
% 2.69/1.50 => ( ( ( P @ X3 )
% 2.69/1.50 & ( Q @ X3 ) )
% 2.69/1.50 = ( ( P2 @ X3 )
% 2.69/1.50 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_16_pinf_I2_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.69/1.50 ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z2 @ X4 )
% 2.69/1.50 => ( ( P @ X4 )
% 2.69/1.50 = ( P2 @ X4 ) ) )
% 2.69/1.50 => ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z2 @ X4 )
% 2.69/1.50 => ( ( Q @ X4 )
% 2.69/1.50 = ( Q2 @ X4 ) ) )
% 2.69/1.50 => ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z @ X3 )
% 2.69/1.50 => ( ( ( P @ X3 )
% 2.69/1.50 | ( Q @ X3 ) )
% 2.69/1.50 = ( ( P2 @ X3 )
% 2.69/1.50 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_17_pinf_I3_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z @ X3 )
% 2.69/1.50 => ( X3 != T2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_18_pinf_I4_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z @ X3 )
% 2.69/1.50 => ( X3 != T2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_19_pinf_I5_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z @ X3 )
% 2.69/1.50 => ~ ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_20_pinf_I7_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [T2: A] :
% 2.69/1.50 ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ Z @ X3 )
% 2.69/1.50 => ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_21_pinf_I11_J,axiom,
% 2.69/1.50 ! [C2: $tType,D: $tType] :
% 2.69/1.50 ( ( ord @ C2 )
% 2.69/1.50 => ! [F2: D] :
% 2.69/1.50 ? [Z: C2] :
% 2.69/1.50 ! [X3: C2] :
% 2.69/1.50 ( ( ord_less @ C2 @ Z @ X3 )
% 2.69/1.50 => ( F2 = F2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_22_minf_I1_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.69/1.50 ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ X4 @ Z2 )
% 2.69/1.50 => ( ( P @ X4 )
% 2.69/1.50 = ( P2 @ X4 ) ) )
% 2.69/1.50 => ( ? [Z2: A] :
% 2.69/1.50 ! [X4: A] :
% 2.69/1.50 ( ( ord_less @ A @ X4 @ Z2 )
% 2.69/1.50 => ( ( Q @ X4 )
% 2.69/1.50 = ( Q2 @ X4 ) ) )
% 2.69/1.50 => ? [Z: A] :
% 2.69/1.50 ! [X3: A] :
% 2.69/1.50 ( ( ord_less @ A @ X3 @ Z )
% 2.69/1.50 => ( ( ( P @ X3 )
% 2.69/1.50 & ( Q @ X3 ) )
% 2.69/1.50 = ( ( P2 @ X3 )
% 2.69/1.50 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_23_ereal__MInfty__lessI,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ( ( A3
% 2.69/1.50 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 => ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ A3 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_24_ereal__infty__less_I2_J,axiom,
% 2.69/1.50 ! [X2: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ X2 )
% 2.69/1.50 = ( X2
% 2.69/1.50 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_25_ereal__minus__less__minus,axiom,
% 2.69/1.50 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) @ ( uminus_uminus @ extended_ereal @ B2 ) )
% 2.69/1.50 = ( ord_less @ extended_ereal @ B2 @ A3 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_26_ereal__less__PInfty,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ( ( A3
% 2.69/1.50 != ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 => ( ord_less @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_27_ereal__infty__less_I1_J,axiom,
% 2.69/1.50 ! [X2: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ X2 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 = ( X2
% 2.69/1.50 != ( extend1396239628finity @ extended_ereal ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_28_neg__less__iff__less,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ordered_ab_group_add @ A )
% 2.69/1.50 => ! [B2: A,A3: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) )
% 2.69/1.50 = ( ord_less @ A @ A3 @ B2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_29_less__ereal_Osimps_I3_J,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ~ ( ord_less @ extended_ereal @ A3 @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_30_less__ereal_Osimps_I6_J,axiom,
% 2.69/1.50 ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_31_ereal__uminus__eq__iff,axiom,
% 2.69/1.50 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.50 ( ( ( uminus_uminus @ extended_ereal @ A3 )
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ B2 ) )
% 2.69/1.50 = ( A3 = B2 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_32_ereal__uminus__uminus,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ( ( uminus_uminus @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) )
% 2.69/1.50 = A3 ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_33_neg__equal__iff__equal,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( group_add @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ( uminus_uminus @ A @ A3 )
% 2.69/1.50 = ( uminus_uminus @ A @ B2 ) )
% 2.69/1.50 = ( A3 = B2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_34_add_Oinverse__inverse,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( group_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A3 ) )
% 2.69/1.50 = A3 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_35_minus__equation__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( group_add @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ( uminus_uminus @ A @ A3 )
% 2.69/1.50 = B2 )
% 2.69/1.50 = ( ( uminus_uminus @ A @ B2 )
% 2.69/1.50 = A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_36_equation__minus__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( group_add @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( A3
% 2.69/1.50 = ( uminus_uminus @ A @ B2 ) )
% 2.69/1.50 = ( B2
% 2.69/1.50 = ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_37_ereal__uminus__eq__reorder,axiom,
% 2.69/1.50 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.50 ( ( ( uminus_uminus @ extended_ereal @ A3 )
% 2.69/1.50 = B2 )
% 2.69/1.50 = ( A3
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ B2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_38_less__minus__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ordered_ab_group_add @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 2.69/1.50 = ( ord_less @ A @ B2 @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_39_minus__less__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ordered_ab_group_add @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 2.69/1.50 = ( ord_less @ A @ ( uminus_uminus @ A @ B2 ) @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_40_MInfty__neq__PInfty_I1_J,axiom,
% 2.69/1.50 ( ( extend1396239628finity @ extended_ereal )
% 2.69/1.50 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_41_less__ereal_Osimps_I2_J,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ~ ( ord_less @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_42_ereal__less__uminus__reorder,axiom,
% 2.69/1.50 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ A3 @ ( uminus_uminus @ extended_ereal @ B2 ) )
% 2.69/1.50 = ( ord_less @ extended_ereal @ B2 @ ( uminus_uminus @ extended_ereal @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_43_ereal__uminus__less__reorder,axiom,
% 2.69/1.50 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) @ B2 )
% 2.69/1.50 = ( ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ B2 ) @ A3 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_44_compl__eq__compl__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( boolean_algebra @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ( uminus_uminus @ A @ X2 )
% 2.69/1.50 = ( uminus_uminus @ A @ Y ) )
% 2.69/1.50 = ( X2 = Y ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_45_mem__Collect__eq,axiom,
% 2.69/1.50 ! [A: $tType,A3: A,P: A > $o] :
% 2.69/1.50 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.69/1.50 = ( P @ A3 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_46_Collect__mem__eq,axiom,
% 2.69/1.50 ! [A: $tType,A2: set @ A] :
% 2.69/1.50 ( ( collect @ A
% 2.69/1.50 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 2.69/1.50 = A2 ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_47_Collect__cong,axiom,
% 2.69/1.50 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.69/1.50 ( ! [X4: A] :
% 2.69/1.50 ( ( P @ X4 )
% 2.69/1.50 = ( Q @ X4 ) )
% 2.69/1.50 => ( ( collect @ A @ P )
% 2.69/1.50 = ( collect @ A @ Q ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_48_ext,axiom,
% 2.69/1.50 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.69/1.50 ( ! [X4: A] :
% 2.69/1.50 ( ( F @ X4 )
% 2.69/1.50 = ( G @ X4 ) )
% 2.69/1.50 => ( F = G ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_49_double__compl,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( boolean_algebra @ A )
% 2.69/1.50 => ! [X2: A] :
% 2.69/1.50 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X2 ) )
% 2.69/1.50 = X2 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_50_uminus__apply,axiom,
% 2.69/1.50 ! [B: $tType,A: $tType] :
% 2.69/1.50 ( ( uminus @ B )
% 2.69/1.50 => ( ( uminus_uminus @ ( A > B ) )
% 2.69/1.50 = ( ^ [A4: A > B,X: A] : ( uminus_uminus @ B @ ( A4 @ X ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_51_verit__minus__simplify_I4_J,axiom,
% 2.69/1.50 ! [B: $tType] :
% 2.69/1.50 ( ( group_add @ B )
% 2.69/1.50 => ! [B2: B] :
% 2.69/1.50 ( ( uminus_uminus @ B @ ( uminus_uminus @ B @ B2 ) )
% 2.69/1.50 = B2 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_52_verit__negate__coefficient_I2_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ordered_ab_group_add @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ( ord_less @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_53_compl__less__swap1,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( boolean_algebra @ A )
% 2.69/1.50 => ! [Y: A,X2: A] :
% 2.69/1.50 ( ( ord_less @ A @ Y @ ( uminus_uminus @ A @ X2 ) )
% 2.69/1.50 => ( ord_less @ A @ X2 @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_54_compl__less__swap2,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( boolean_algebra @ A )
% 2.69/1.50 => ! [Y: A,X2: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ Y ) @ X2 )
% 2.69/1.50 => ( ord_less @ A @ ( uminus_uminus @ A @ X2 ) @ Y ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_55_compl__less__compl__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( boolean_algebra @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ X2 ) @ ( uminus_uminus @ A @ Y ) )
% 2.69/1.50 = ( ord_less @ A @ Y @ X2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_56_MInfty__eq__minfinity,axiom,
% 2.69/1.50 ( extended_MInfty
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_57_verit__comp__simplify1_I1_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_58_verit__negate__coefficient_I3_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ordered_ab_group_add @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( A3 = B2 )
% 2.69/1.50 => ( ( uminus_uminus @ A @ A3 )
% 2.69/1.50 = ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_59_fun__Compl__def,axiom,
% 2.69/1.50 ! [B: $tType,A: $tType] :
% 2.69/1.50 ( ( uminus @ B )
% 2.69/1.50 => ( ( uminus_uminus @ ( A > B ) )
% 2.69/1.50 = ( ^ [A4: A > B,X: A] : ( uminus_uminus @ B @ ( A4 @ X ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_60_uminus__ereal_Osimps_I2_J,axiom,
% 2.69/1.50 ( ( uminus_uminus @ extended_ereal @ extended_PInfty )
% 2.69/1.50 = extended_MInfty ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_61_uminus__ereal_Osimps_I3_J,axiom,
% 2.69/1.50 ( ( uminus_uminus @ extended_ereal @ extended_MInfty )
% 2.69/1.50 = extended_PInfty ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_62_ereal__less_I6_J,axiom,
% 2.69/1.50 ord_less @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( zero_zero @ extended_ereal ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_63_ereal_Osimps_I13_J,axiom,
% 2.69/1.50 ! [A: $tType,F1: real > A,F22: A,F3: A] :
% 2.69/1.50 ( ( extended_rec_ereal @ A @ F1 @ F22 @ F3 @ extended_MInfty )
% 2.69/1.50 = F3 ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_64_ex__gt__or__lt,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( condit1656338222tinuum @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ? [B3: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B3 )
% 2.69/1.50 | ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_65_linorder__neqE__linordered__idom,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linordered_idom @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( X2 != Y )
% 2.69/1.50 => ( ~ ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_66_dual__order_Ostrict__implies__not__eq,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [B2: A,A3: A] :
% 2.69/1.50 ( ( ord_less @ A @ B2 @ A3 )
% 2.69/1.50 => ( A3 != B2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_67_not__gr__zero,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( canoni770627133id_add @ A )
% 2.69/1.50 => ! [N: A] :
% 2.69/1.50 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.69/1.50 = ( N
% 2.69/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_68_neg__equal__zero,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linord219039673up_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( ( uminus_uminus @ A @ A3 )
% 2.69/1.50 = A3 )
% 2.69/1.50 = ( A3
% 2.69/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_69_equal__neg__zero,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linord219039673up_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( A3
% 2.69/1.50 = ( uminus_uminus @ A @ A3 ) )
% 2.69/1.50 = ( A3
% 2.69/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_70_neg__equal__0__iff__equal,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( group_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( ( uminus_uminus @ A @ A3 )
% 2.69/1.50 = ( zero_zero @ A ) )
% 2.69/1.50 = ( A3
% 2.69/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_71_neg__0__equal__iff__equal,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( group_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( ( zero_zero @ A )
% 2.69/1.50 = ( uminus_uminus @ A @ A3 ) )
% 2.69/1.50 = ( ( zero_zero @ A )
% 2.69/1.50 = A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_72_add_Oinverse__neutral,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( group_add @ A )
% 2.69/1.50 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 2.69/1.50 = ( zero_zero @ A ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_73_ereal__uminus__zero__iff,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ( ( ( uminus_uminus @ extended_ereal @ A3 )
% 2.69/1.50 = ( zero_zero @ extended_ereal ) )
% 2.69/1.50 = ( A3
% 2.69/1.50 = ( zero_zero @ extended_ereal ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_74_ereal__uminus__zero,axiom,
% 2.69/1.50 ( ( uminus_uminus @ extended_ereal @ ( zero_zero @ extended_ereal ) )
% 2.69/1.50 = ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_75_less__neg__neg,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linord219039673up_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ ( uminus_uminus @ A @ A3 ) )
% 2.69/1.50 = ( ord_less @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_76_neg__less__pos,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linord219039673up_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ A3 ) @ A3 )
% 2.69/1.50 = ( ord_less @ A @ ( zero_zero @ A ) @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_77_neg__0__less__iff__less,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ordered_ab_group_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A3 ) )
% 2.69/1.50 = ( ord_less @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_78_neg__less__0__iff__less,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ordered_ab_group_add @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ A3 ) @ ( zero_zero @ A ) )
% 2.69/1.50 = ( ord_less @ A @ ( zero_zero @ A ) @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_79_neg__0__less__iff__less__erea,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ A3 ) )
% 2.69/1.50 = ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_80_ereal_Osimps_I12_J,axiom,
% 2.69/1.50 ! [A: $tType,F1: real > A,F22: A,F3: A] :
% 2.69/1.50 ( ( extended_rec_ereal @ A @ F1 @ F22 @ F3 @ extended_PInfty )
% 2.69/1.50 = F22 ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_81_zero__reorient,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( zero @ A )
% 2.69/1.50 => ! [X2: A] :
% 2.69/1.50 ( ( ( zero_zero @ A )
% 2.69/1.50 = X2 )
% 2.69/1.50 = ( X2
% 2.69/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_82_gr__zeroI,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( canoni770627133id_add @ A )
% 2.69/1.50 => ! [N: A] :
% 2.69/1.50 ( ( N
% 2.69/1.50 != ( zero_zero @ A ) )
% 2.69/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_83_not__less__zero,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( canoni770627133id_add @ A )
% 2.69/1.50 => ! [N: A] :
% 2.69/1.50 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_84_gr__implies__not__zero,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( canoni770627133id_add @ A )
% 2.69/1.50 => ! [M: A,N: A] :
% 2.69/1.50 ( ( ord_less @ A @ M @ N )
% 2.69/1.50 => ( N
% 2.69/1.50 != ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_85_zero__less__iff__neq__zero,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( canoni770627133id_add @ A )
% 2.69/1.50 => ! [N: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.69/1.50 = ( N
% 2.69/1.50 != ( zero_zero @ A ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_86_Infty__neq__0_I1_J,axiom,
% 2.69/1.50 ( ( extend1396239628finity @ extended_ereal )
% 2.69/1.50 != ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_87_infinity__ereal__def,axiom,
% 2.69/1.50 ( ( extend1396239628finity @ extended_ereal )
% 2.69/1.50 = extended_PInfty ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_88_ereal_Odistinct_I5_J,axiom,
% 2.69/1.50 extended_PInfty != extended_MInfty ).
% 2.69/1.50
% 2.69/1.50 thf(fact_89_Infty__neq__0_I3_J,axiom,
% 2.69/1.50 ( ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 != ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_90_ereal__less_I5_J,axiom,
% 2.69/1.50 ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_91_ord__eq__less__subst,axiom,
% 2.69/1.50 ! [A: $tType,B: $tType] :
% 2.69/1.50 ( ( ( ord @ B )
% 2.69/1.50 & ( ord @ A ) )
% 2.69/1.50 => ! [A3: A,F: B > A,B2: B,C3: B] :
% 2.69/1.50 ( ( A3
% 2.69/1.50 = ( F @ B2 ) )
% 2.69/1.50 => ( ( ord_less @ B @ B2 @ C3 )
% 2.69/1.50 => ( ! [X4: B,Y2: B] :
% 2.69/1.50 ( ( ord_less @ B @ X4 @ Y2 )
% 2.69/1.50 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.69/1.50 => ( ord_less @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_92_ord__less__eq__subst,axiom,
% 2.69/1.50 ! [A: $tType,B: $tType] :
% 2.69/1.50 ( ( ( ord @ B )
% 2.69/1.50 & ( ord @ A ) )
% 2.69/1.50 => ! [A3: A,B2: A,F: A > B,C3: B] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ( ( ( F @ B2 )
% 2.69/1.50 = C3 )
% 2.69/1.50 => ( ! [X4: A,Y2: A] :
% 2.69/1.50 ( ( ord_less @ A @ X4 @ Y2 )
% 2.69/1.50 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.69/1.50 => ( ord_less @ B @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_93_order__less__subst1,axiom,
% 2.69/1.50 ! [A: $tType,B: $tType] :
% 2.69/1.50 ( ( ( order @ B )
% 2.69/1.50 & ( order @ A ) )
% 2.69/1.50 => ! [A3: A,F: B > A,B2: B,C3: B] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ ( F @ B2 ) )
% 2.69/1.50 => ( ( ord_less @ B @ B2 @ C3 )
% 2.69/1.50 => ( ! [X4: B,Y2: B] :
% 2.69/1.50 ( ( ord_less @ B @ X4 @ Y2 )
% 2.69/1.50 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.69/1.50 => ( ord_less @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_94_order__less__subst2,axiom,
% 2.69/1.50 ! [A: $tType,C2: $tType] :
% 2.69/1.50 ( ( ( order @ C2 )
% 2.69/1.50 & ( order @ A ) )
% 2.69/1.50 => ! [A3: A,B2: A,F: A > C2,C3: C2] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C3 )
% 2.69/1.50 => ( ! [X4: A,Y2: A] :
% 2.69/1.50 ( ( ord_less @ A @ X4 @ Y2 )
% 2.69/1.50 => ( ord_less @ C2 @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.69/1.50 => ( ord_less @ C2 @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_95_lt__ex,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( no_bot @ A )
% 2.69/1.50 => ! [X2: A] :
% 2.69/1.50 ? [Y2: A] : ( ord_less @ A @ Y2 @ X2 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_96_gt__ex,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( no_top @ A )
% 2.69/1.50 => ! [X2: A] :
% 2.69/1.50 ? [X_1: A] : ( ord_less @ A @ X2 @ X_1 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_97_neqE,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( X2 != Y )
% 2.69/1.50 => ( ~ ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_98_neq__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( X2 != Y )
% 2.69/1.50 = ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 | ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_99_order_Oasym,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ~ ( ord_less @ A @ B2 @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_100_dense,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( dense_order @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ? [Z: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Z )
% 2.69/1.50 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_101_less__imp__neq,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( X2 != Y ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_102_less__asym,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( preorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_103_less__asym_H,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( preorder @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ~ ( ord_less @ A @ B2 @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_104_less__trans,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( preorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A,Z3: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( ( ord_less @ A @ Y @ Z3 )
% 2.69/1.50 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_105_less__linear,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 | ( X2 = Y )
% 2.69/1.50 | ( ord_less @ A @ Y @ X2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_106_less__irrefl,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( preorder @ A )
% 2.69/1.50 => ! [X2: A] :
% 2.69/1.50 ~ ( ord_less @ A @ X2 @ X2 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_107_ord__eq__less__trans,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ord @ A )
% 2.69/1.50 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.50 ( ( A3 = B2 )
% 2.69/1.50 => ( ( ord_less @ A @ B2 @ C3 )
% 2.69/1.50 => ( ord_less @ A @ A3 @ C3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_108_ord__less__eq__trans,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ord @ A )
% 2.69/1.50 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ( ( B2 = C3 )
% 2.69/1.50 => ( ord_less @ A @ A3 @ C3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_109_dual__order_Oasym,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [B2: A,A3: A] :
% 2.69/1.50 ( ( ord_less @ A @ B2 @ A3 )
% 2.69/1.50 => ~ ( ord_less @ A @ A3 @ B2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_110_less__imp__not__eq,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( X2 != Y ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_111_less__not__sym,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( preorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_112_less__induct,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( wellorder @ A )
% 2.69/1.50 => ! [P: A > $o,A3: A] :
% 2.69/1.50 ( ! [X4: A] :
% 2.69/1.50 ( ! [Y3: A] :
% 2.69/1.50 ( ( ord_less @ A @ Y3 @ X4 )
% 2.69/1.50 => ( P @ Y3 ) )
% 2.69/1.50 => ( P @ X4 ) )
% 2.69/1.50 => ( P @ A3 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_113_antisym__conv3,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [Y: A,X2: A] :
% 2.69/1.50 ( ~ ( ord_less @ A @ Y @ X2 )
% 2.69/1.50 => ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 2.69/1.50 = ( X2 = Y ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_114_less__imp__not__eq2,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( Y != X2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_115_less__imp__triv,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( preorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A,P: $o] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( ( ord_less @ A @ Y @ X2 )
% 2.69/1.50 => P ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_116_linorder__cases,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ~ ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ( ( X2 != Y )
% 2.69/1.50 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_117_dual__order_Oirrefl,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_118_order_Ostrict__trans,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ( ( ord_less @ A @ B2 @ C3 )
% 2.69/1.50 => ( ord_less @ A @ A3 @ C3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_119_less__imp__not__less,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( preorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ord_less @ A @ X2 @ Y )
% 2.69/1.50 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_120_exists__least__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( wellorder @ A )
% 2.69/1.50 => ( ( ^ [P3: A > $o] :
% 2.69/1.50 ? [X5: A] : ( P3 @ X5 ) )
% 2.69/1.50 = ( ^ [P4: A > $o] :
% 2.69/1.50 ? [N2: A] :
% 2.69/1.50 ( ( P4 @ N2 )
% 2.69/1.50 & ! [M2: A] :
% 2.69/1.50 ( ( ord_less @ A @ M2 @ N2 )
% 2.69/1.50 => ~ ( P4 @ M2 ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_121_linorder__less__wlog,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [P: A > A > $o,A3: A,B2: A] :
% 2.69/1.50 ( ! [A5: A,B3: A] :
% 2.69/1.50 ( ( ord_less @ A @ A5 @ B3 )
% 2.69/1.50 => ( P @ A5 @ B3 ) )
% 2.69/1.50 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 2.69/1.50 => ( ! [A5: A,B3: A] :
% 2.69/1.50 ( ( P @ B3 @ A5 )
% 2.69/1.50 => ( P @ A5 @ B3 ) )
% 2.69/1.50 => ( P @ A3 @ B2 ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_122_dual__order_Ostrict__trans,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [B2: A,A3: A,C3: A] :
% 2.69/1.50 ( ( ord_less @ A @ B2 @ A3 )
% 2.69/1.50 => ( ( ord_less @ A @ C3 @ B2 )
% 2.69/1.50 => ( ord_less @ A @ C3 @ A3 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_123_not__less__iff__gr__or__eq,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linorder @ A )
% 2.69/1.50 => ! [X2: A,Y: A] :
% 2.69/1.50 ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 2.69/1.50 = ( ( ord_less @ A @ Y @ X2 )
% 2.69/1.50 | ( X2 = Y ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_124_order_Ostrict__implies__not__eq,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( order @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.50 => ( A3 != B2 ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_125_field__lbound__gt__zero,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linordered_field @ A )
% 2.69/1.50 => ! [D1: A,D2: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ D1 )
% 2.69/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ D2 )
% 2.69/1.50 => ? [E: A] :
% 2.69/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ E )
% 2.69/1.50 & ( ord_less @ A @ E @ D1 )
% 2.69/1.50 & ( ord_less @ A @ E @ D2 ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_126_less__numeral__extra_I3_J,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( linord1659791738miring @ A )
% 2.69/1.50 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_127_ereal__mult__eq__PInfty,axiom,
% 2.69/1.50 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.50 ( ( ( times_times @ extended_ereal @ A3 @ B2 )
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 = ( ( ( A3
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) )
% 2.69/1.50 | ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.50 & ( B2
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 | ( ( A3
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) )
% 2.69/1.50 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 2.69/1.50 & ( B2
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_128_ereal__mult__eq__MInfty,axiom,
% 2.69/1.50 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.50 ( ( ( times_times @ extended_ereal @ A3 @ B2 )
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 = ( ( ( A3
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) )
% 2.69/1.50 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 2.69/1.50 & ( B2
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 | ( ( A3
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) )
% 2.69/1.50 | ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.50 & ( B2
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_129_ereal__mult__infty,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ( ( ( A3
% 2.69/1.50 = ( zero_zero @ extended_ereal ) )
% 2.69/1.50 => ( ( times_times @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 = ( zero_zero @ extended_ereal ) ) )
% 2.69/1.50 & ( ( A3
% 2.69/1.50 != ( zero_zero @ extended_ereal ) )
% 2.69/1.50 => ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.50 => ( ( times_times @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 & ( ~ ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.50 => ( ( times_times @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_130_ereal__infty__mult,axiom,
% 2.69/1.50 ! [A3: extended_ereal] :
% 2.69/1.50 ( ( ( A3
% 2.69/1.50 = ( zero_zero @ extended_ereal ) )
% 2.69/1.50 => ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 )
% 2.69/1.50 = ( zero_zero @ extended_ereal ) ) )
% 2.69/1.50 & ( ( A3
% 2.69/1.50 != ( zero_zero @ extended_ereal ) )
% 2.69/1.50 => ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.50 => ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 )
% 2.69/1.50 = ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 & ( ~ ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.50 => ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A3 )
% 2.69/1.50 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_131_ereal__divide__Infty_I2_J,axiom,
% 2.69/1.50 ! [X2: extended_ereal] :
% 2.69/1.50 ( ( divide_divide @ extended_ereal @ X2 @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.50 = ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_132_mult__zero__left,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( mult_zero @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( times_times @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.50 = ( zero_zero @ A ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_133_mult__zero__right,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( mult_zero @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( times_times @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.50 = ( zero_zero @ A ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_134_mult__eq__0__iff,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( semiri1193490041visors @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( ( times_times @ A @ A3 @ B2 )
% 2.69/1.50 = ( zero_zero @ A ) )
% 2.69/1.50 = ( ( A3
% 2.69/1.50 = ( zero_zero @ A ) )
% 2.69/1.50 | ( B2
% 2.69/1.50 = ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_135_mult__cancel__left,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( semiri1923998003cancel @ A )
% 2.69/1.50 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.50 ( ( ( times_times @ A @ C3 @ A3 )
% 2.69/1.50 = ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.50 = ( ( C3
% 2.69/1.50 = ( zero_zero @ A ) )
% 2.69/1.50 | ( A3 = B2 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_136_mult__cancel__right,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( semiri1923998003cancel @ A )
% 2.69/1.50 => ! [A3: A,C3: A,B2: A] :
% 2.69/1.50 ( ( ( times_times @ A @ A3 @ C3 )
% 2.69/1.50 = ( times_times @ A @ B2 @ C3 ) )
% 2.69/1.50 = ( ( C3
% 2.69/1.50 = ( zero_zero @ A ) )
% 2.69/1.50 | ( A3 = B2 ) ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_137_div__0,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( semidom_divide @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.50 = ( zero_zero @ A ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_138_div__by__0,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( semidom_divide @ A )
% 2.69/1.50 => ! [A3: A] :
% 2.69/1.50 ( ( divide_divide @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.50 = ( zero_zero @ A ) ) ) ).
% 2.69/1.50
% 2.69/1.50 thf(fact_139_mult__minus__right,axiom,
% 2.69/1.50 ! [A: $tType] :
% 2.69/1.50 ( ( ring @ A )
% 2.69/1.50 => ! [A3: A,B2: A] :
% 2.69/1.50 ( ( times_times @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 2.69/1.50 = ( uminus_uminus @ A @ ( times_times @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_140_minus__mult__minus,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( ring @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( times_times @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 2.69/1.51 = ( times_times @ A @ A3 @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_141_mult__minus__left,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( ring @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( times_times @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 2.69/1.51 = ( uminus_uminus @ A @ ( times_times @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_142_ereal__mult__minus__left,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( times_times @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A3 ) @ B2 )
% 2.69/1.51 = ( uminus_uminus @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_143_ereal__mult__minus__right,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( times_times @ extended_ereal @ A3 @ ( uminus_uminus @ extended_ereal @ B2 ) )
% 2.69/1.51 = ( uminus_uminus @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_144_ereal__zero__times,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( ( times_times @ extended_ereal @ A3 @ B2 )
% 2.69/1.51 = ( zero_zero @ extended_ereal ) )
% 2.69/1.51 = ( ( A3
% 2.69/1.51 = ( zero_zero @ extended_ereal ) )
% 2.69/1.51 | ( B2
% 2.69/1.51 = ( zero_zero @ extended_ereal ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_145_ereal__zero__mult,axiom,
% 2.69/1.51 ! [A3: extended_ereal] :
% 2.69/1.51 ( ( times_times @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.51 = ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_146_ereal__mult__zero,axiom,
% 2.69/1.51 ! [A3: extended_ereal] :
% 2.69/1.51 ( ( times_times @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 2.69/1.51 = ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_147_ereal__uminus__divide,axiom,
% 2.69/1.51 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.69/1.51 ( ( divide_divide @ extended_ereal @ ( uminus_uminus @ extended_ereal @ X2 ) @ Y )
% 2.69/1.51 = ( uminus_uminus @ extended_ereal @ ( divide_divide @ extended_ereal @ X2 @ Y ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_148_ereal__divide__zero__left,axiom,
% 2.69/1.51 ! [A3: extended_ereal] :
% 2.69/1.51 ( ( divide_divide @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.51 = ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_149_ereal__times__divide__eq__left,axiom,
% 2.69/1.51 ! [B2: extended_ereal,C3: extended_ereal,A3: extended_ereal] :
% 2.69/1.51 ( ( times_times @ extended_ereal @ ( divide_divide @ extended_ereal @ B2 @ C3 ) @ A3 )
% 2.69/1.51 = ( divide_divide @ extended_ereal @ ( times_times @ extended_ereal @ B2 @ A3 ) @ C3 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_150_nonzero__mult__div__cancel__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( semidom_divide @ A )
% 2.69/1.51 => ! [B2: A,A3: A] :
% 2.69/1.51 ( ( B2
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ B2 ) @ B2 )
% 2.69/1.51 = A3 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_151_nonzero__mult__div__cancel__left,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( semidom_divide @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( A3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ B2 ) @ A3 )
% 2.69/1.51 = B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_152_ereal__divide__Infty_I1_J,axiom,
% 2.69/1.51 ! [X2: extended_ereal] :
% 2.69/1.51 ( ( divide_divide @ extended_ereal @ X2 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 = ( zero_zero @ extended_ereal ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_153_mult_Oleft__commute,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( ab_semigroup_mult @ A )
% 2.69/1.51 => ! [B2: A,A3: A,C3: A] :
% 2.69/1.51 ( ( times_times @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) )
% 2.69/1.51 = ( times_times @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_154_mult_Ocommute,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( ab_semigroup_mult @ A )
% 2.69/1.51 => ( ( times_times @ A )
% 2.69/1.51 = ( ^ [A6: A,B4: A] : ( times_times @ A @ B4 @ A6 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_155_mult_Oassoc,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( semigroup_mult @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( times_times @ A @ ( times_times @ A @ A3 @ B2 ) @ C3 )
% 2.69/1.51 = ( times_times @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_156_ereal__times__divide__eq,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal,C3: extended_ereal] :
% 2.69/1.51 ( ( times_times @ extended_ereal @ A3 @ ( divide_divide @ extended_ereal @ B2 @ C3 ) )
% 2.69/1.51 = ( divide_divide @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) @ C3 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_157_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( ab_semigroup_mult @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( times_times @ A @ ( times_times @ A @ A3 @ B2 ) @ C3 )
% 2.69/1.51 = ( times_times @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_158_mult__not__zero,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( mult_zero @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ( times_times @ A @ A3 @ B2 )
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( A3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 & ( B2
% 2.69/1.51 != ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_159_divisors__zero,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( semiri1193490041visors @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ( times_times @ A @ A3 @ B2 )
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 => ( ( A3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 | ( B2
% 2.69/1.51 = ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_160_no__zero__divisors,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( semiri1193490041visors @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( A3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( B2
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( times_times @ A @ A3 @ B2 )
% 2.69/1.51 != ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_161_mult__left__cancel,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( semiri1923998003cancel @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ( times_times @ A @ C3 @ A3 )
% 2.69/1.51 = ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( A3 = B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_162_mult__right__cancel,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( semiri1923998003cancel @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ( times_times @ A @ A3 @ C3 )
% 2.69/1.51 = ( times_times @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( A3 = B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_163_square__eq__iff,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( idom @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ( times_times @ A @ A3 @ A3 )
% 2.69/1.51 = ( times_times @ A @ B2 @ B2 ) )
% 2.69/1.51 = ( ( A3 = B2 )
% 2.69/1.51 | ( A3
% 2.69/1.51 = ( uminus_uminus @ A @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_164_minus__mult__commute,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( ring @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( times_times @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 2.69/1.51 = ( times_times @ A @ A3 @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_165_times__ereal_Osimps_I6_J,axiom,
% 2.69/1.51 ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 = ( extend1396239628finity @ extended_ereal ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_166_ereal__right__mult__cong,axiom,
% 2.69/1.51 ! [C3: extended_ereal,D3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( C3 = D3 )
% 2.69/1.51 => ( ( ( D3
% 2.69/1.51 != ( zero_zero @ extended_ereal ) )
% 2.69/1.51 => ( A3 = B2 ) )
% 2.69/1.51 => ( ( times_times @ extended_ereal @ C3 @ A3 )
% 2.69/1.51 = ( times_times @ extended_ereal @ D3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_167_ereal__left__mult__cong,axiom,
% 2.69/1.51 ! [C3: extended_ereal,D3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( C3 = D3 )
% 2.69/1.51 => ( ( ( D3
% 2.69/1.51 != ( zero_zero @ extended_ereal ) )
% 2.69/1.51 => ( A3 = B2 ) )
% 2.69/1.51 => ( ( times_times @ extended_ereal @ A3 @ C3 )
% 2.69/1.51 = ( times_times @ extended_ereal @ B2 @ D3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_168_ereal__mult__divide,axiom,
% 2.69/1.51 ! [B2: extended_ereal,A3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ B2 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ( times_times @ extended_ereal @ B2 @ ( divide_divide @ extended_ereal @ A3 @ B2 ) )
% 2.69/1.51 = A3 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_169_ereal__divide__less__iff,axiom,
% 2.69/1.51 ! [C3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ ( divide_divide @ extended_ereal @ A3 @ C3 ) @ B2 )
% 2.69/1.51 = ( ord_less @ extended_ereal @ A3 @ ( times_times @ extended_ereal @ B2 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_170_ereal__divide__less__pos,axiom,
% 2.69/1.51 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ X2 )
% 2.69/1.51 => ( ( X2
% 2.69/1.51 != ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ ( divide_divide @ extended_ereal @ Y @ X2 ) @ Z3 )
% 2.69/1.51 = ( ord_less @ extended_ereal @ Y @ ( times_times @ extended_ereal @ X2 @ Z3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_171_ereal__less__divide__iff,axiom,
% 2.69/1.51 ! [C3: extended_ereal,A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ A3 @ ( divide_divide @ extended_ereal @ B2 @ C3 ) )
% 2.69/1.51 = ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_172_ereal__less__divide__pos,axiom,
% 2.69/1.51 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ X2 )
% 2.69/1.51 => ( ( X2
% 2.69/1.51 != ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ Y @ ( divide_divide @ extended_ereal @ Z3 @ X2 ) )
% 2.69/1.51 = ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ X2 @ Y ) @ Z3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_173_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord893533164strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_174_mult__less__cancel__right__disj,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [A3: A,C3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 & ( ord_less @ A @ A3 @ B2 ) )
% 2.69/1.51 | ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 & ( ord_less @ A @ B2 @ A3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_175_mult__strict__right__mono,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_176_mult__strict__right__mono__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [B2: A,A3: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ B2 @ A3 )
% 2.69/1.51 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_177_mult__less__cancel__left__disj,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 & ( ord_less @ A @ A3 @ B2 ) )
% 2.69/1.51 | ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 & ( ord_less @ A @ B2 @ A3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_178_mult__strict__left__mono,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_179_mult__strict__left__mono__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [B2: A,A3: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ B2 @ A3 )
% 2.69/1.51 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_180_mult__less__cancel__left__pos,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( ord_less @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_181_mult__less__cancel__left__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( ord_less @ A @ B2 @ A3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_182_zero__less__mult__pos2,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [B2: A,A3: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B2 @ A3 ) )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_183_zero__less__mult__pos,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_184_zero__less__mult__iff,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.69/1.51 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.51 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_185_mult__pos__neg2,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ B2 @ A3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_186_mult__pos__pos,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 2.69/1.51 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_187_mult__pos__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ A3 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_188_mult__neg__pos,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord20386208strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ A3 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_189_mult__less__0__iff,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( times_times @ A @ A3 @ B2 ) @ ( zero_zero @ A ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.69/1.51 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.51 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_190_not__square__less__zero,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_ring @ A )
% 2.69/1.51 => ! [A3: A] :
% 2.69/1.51 ~ ( ord_less @ A @ ( times_times @ A @ A3 @ A3 ) @ ( zero_zero @ A ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_191_mult__neg__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linord581940658strict @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_192_times__ereal_Osimps_I9_J,axiom,
% 2.69/1.51 ( ( times_times @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.51 = ( extend1396239628finity @ extended_ereal ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_193_times__ereal_Osimps_I8_J,axiom,
% 2.69/1.51 ( ( times_times @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
% 2.69/1.51 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_194_times__ereal_Osimps_I7_J,axiom,
% 2.69/1.51 ( ( times_times @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_195_ereal__mult__less__0__iff,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ B2 ) @ ( zero_zero @ extended_ereal ) )
% 2.69/1.51 = ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.51 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) )
% 2.69/1.51 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 2.69/1.51 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_196_ereal__zero__less__0__iff,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( times_times @ extended_ereal @ A3 @ B2 ) )
% 2.69/1.51 = ( ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.51 & ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 ) )
% 2.69/1.51 | ( ( ord_less @ extended_ereal @ A3 @ ( zero_zero @ extended_ereal ) )
% 2.69/1.51 & ( ord_less @ extended_ereal @ B2 @ ( zero_zero @ extended_ereal ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_197_ereal__mult__mono__strict,axiom,
% 2.69/1.51 ! [B2: extended_ereal,C3: extended_ereal,A3: extended_ereal,D3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B2 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ C3 @ D3 )
% 2.69/1.51 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ ( times_times @ extended_ereal @ B2 @ D3 ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_198_ereal__mult__mono__strict_H,axiom,
% 2.69/1.51 ! [A3: extended_ereal,C3: extended_ereal,B2: extended_ereal,D3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ C3 @ D3 )
% 2.69/1.51 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ ( times_times @ extended_ereal @ B2 @ D3 ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_199_ereal__mult__less__right,axiom,
% 2.69/1.51 ! [B2: extended_ereal,A3: extended_ereal,C3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ B2 @ A3 ) @ ( times_times @ extended_ereal @ C3 @ A3 ) )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ A3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ord_less @ extended_ereal @ B2 @ C3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_200_ereal__mult__strict__left__mono,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal,C3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ C3 @ A3 ) @ ( times_times @ extended_ereal @ C3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_201_ereal__mult__strict__right__mono,axiom,
% 2.69/1.51 ! [A3: extended_ereal,B2: extended_ereal,C3: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ ( zero_zero @ extended_ereal ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ extended_ereal @ C3 @ ( extend1396239628finity @ extended_ereal ) )
% 2.69/1.51 => ( ord_less @ extended_ereal @ ( times_times @ extended_ereal @ A3 @ C3 ) @ ( times_times @ extended_ereal @ B2 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_202_div__mult__mult1__if,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( euclid191655569cancel @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ( C3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( zero_zero @ A ) ) )
% 2.69/1.51 & ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_203_div__mult__mult2,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( euclid191655569cancel @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_204_div__mult__mult1,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( euclid191655569cancel @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_205_nonzero__mult__divide__mult__cancel__right2,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_206_divide__eq__0__iff,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ( divide_divide @ A @ A3 @ B2 )
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 = ( ( A3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 | ( B2
% 2.69/1.51 = ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_207_divide__cancel__left,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ( divide_divide @ A @ C3 @ A3 )
% 2.69/1.51 = ( divide_divide @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( ( C3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 | ( A3 = B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_208_divide__cancel__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [A3: A,C3: A,B2: A] :
% 2.69/1.51 ( ( ( divide_divide @ A @ A3 @ C3 )
% 2.69/1.51 = ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ( C3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 | ( A3 = B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_209_division__ring__divide__zero,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [A3: A] :
% 2.69/1.51 ( ( divide_divide @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.51 = ( zero_zero @ A ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_210_times__divide__eq__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( times_times @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( divide_divide @ A @ ( times_times @ A @ A3 @ B2 ) @ C3 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_211_divide__divide__eq__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( divide_divide @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_212_divide__divide__eq__left,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( divide_divide @ A @ ( divide_divide @ A @ A3 @ B2 ) @ C3 )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ ( times_times @ A @ B2 @ C3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_213_times__divide__eq__left,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [B2: A,C3: A,A3: A] :
% 2.69/1.51 ( ( times_times @ A @ ( divide_divide @ A @ B2 @ C3 ) @ A3 )
% 2.69/1.51 = ( divide_divide @ A @ ( times_times @ A @ B2 @ A3 ) @ C3 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_214_div__minus__minus,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( euclid24285859cancel @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_215_mult__divide__mult__cancel__left__if,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ( C3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( zero_zero @ A ) ) )
% 2.69/1.51 & ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_216_nonzero__mult__divide__mult__cancel__left,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ C3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_217_nonzero__mult__divide__mult__cancel__left2,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ C3 @ A3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_218_nonzero__mult__divide__mult__cancel__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( times_times @ A @ A3 @ C3 ) @ ( times_times @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_219_linordered__field__no__lb,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [X3: A] :
% 2.69/1.51 ? [Y2: A] : ( ord_less @ A @ Y2 @ X3 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_220_linordered__field__no__ub,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [X3: A] :
% 2.69/1.51 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_221_divide__divide__eq__left_H,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( divide_divide @ A @ ( divide_divide @ A @ A3 @ B2 ) @ C3 )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ ( times_times @ A @ C3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_222_divide__divide__times__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [X2: A,Y: A,Z3: A,W: A] :
% 2.69/1.51 ( ( divide_divide @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( divide_divide @ A @ Z3 @ W ) )
% 2.69/1.51 = ( divide_divide @ A @ ( times_times @ A @ X2 @ W ) @ ( times_times @ A @ Y @ Z3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_223_times__divide__times__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [X2: A,Y: A,Z3: A,W: A] :
% 2.69/1.51 ( ( times_times @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( divide_divide @ A @ Z3 @ W ) )
% 2.69/1.51 = ( divide_divide @ A @ ( times_times @ A @ X2 @ Z3 ) @ ( times_times @ A @ Y @ W ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_224_div__minus__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( euclid24285859cancel @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( divide_divide @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_225_minus__divide__left,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( uminus_uminus @ A @ ( divide_divide @ A @ A3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_226_minus__divide__divide,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_227_minus__divide__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( uminus_uminus @ A @ ( divide_divide @ A @ A3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_228_divide__neg__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [X2: A,Y: A] :
% 2.69/1.51 ( ( ord_less @ A @ X2 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ Y @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X2 @ Y ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_229_divide__neg__pos,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [X2: A,Y: A] :
% 2.69/1.51 ( ( ord_less @ A @ X2 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 2.69/1.51 => ( ord_less @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_230_divide__pos__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [X2: A,Y: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ X2 )
% 2.69/1.51 => ( ( ord_less @ A @ Y @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( divide_divide @ A @ X2 @ Y ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_231_divide__pos__pos,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [X2: A,Y: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ X2 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 2.69/1.51 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X2 @ Y ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_232_divide__less__0__iff,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( divide_divide @ A @ A3 @ B2 ) @ ( zero_zero @ A ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.69/1.51 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.51 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_233_divide__less__cancel,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [A3: A,C3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( divide_divide @ A @ A3 @ C3 ) @ ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ord_less @ A @ A3 @ B2 ) )
% 2.69/1.51 & ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ B2 @ A3 ) )
% 2.69/1.51 & ( C3
% 2.69/1.51 != ( zero_zero @ A ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_234_zero__less__divide__iff,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ A3 @ B2 ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A3 )
% 2.69/1.51 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.69/1.51 | ( ( ord_less @ A @ A3 @ ( zero_zero @ A ) )
% 2.69/1.51 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_235_divide__strict__right__mono,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ord_less @ A @ ( divide_divide @ A @ A3 @ C3 ) @ ( divide_divide @ A @ B2 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_236_divide__strict__right__mono__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [B2: A,A3: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ B2 @ A3 )
% 2.69/1.51 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ ( divide_divide @ A @ A3 @ C3 ) @ ( divide_divide @ A @ B2 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_237_frac__eq__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( field @ A )
% 2.69/1.51 => ! [Y: A,Z3: A,X2: A,W: A] :
% 2.69/1.51 ( ( Y
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( Z3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ( divide_divide @ A @ X2 @ Y )
% 2.69/1.51 = ( divide_divide @ A @ W @ Z3 ) )
% 2.69/1.51 = ( ( times_times @ A @ X2 @ Z3 )
% 2.69/1.51 = ( times_times @ A @ W @ Y ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_238_divide__eq__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [B2: A,C3: A,A3: A] :
% 2.69/1.51 ( ( ( divide_divide @ A @ B2 @ C3 )
% 2.69/1.51 = A3 )
% 2.69/1.51 = ( ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( B2
% 2.69/1.51 = ( times_times @ A @ A3 @ C3 ) ) )
% 2.69/1.51 & ( ( C3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 => ( A3
% 2.69/1.51 = ( zero_zero @ A ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_239_eq__divide__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( A3
% 2.69/1.51 = ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( times_times @ A @ A3 @ C3 )
% 2.69/1.51 = B2 ) )
% 2.69/1.51 & ( ( C3
% 2.69/1.51 = ( zero_zero @ A ) )
% 2.69/1.51 => ( A3
% 2.69/1.51 = ( zero_zero @ A ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_240_divide__eq__imp,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [C3: A,B2: A,A3: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( B2
% 2.69/1.51 = ( times_times @ A @ A3 @ C3 ) )
% 2.69/1.51 => ( ( divide_divide @ A @ B2 @ C3 )
% 2.69/1.51 = A3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_241_eq__divide__imp,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ( times_times @ A @ A3 @ C3 )
% 2.69/1.51 = B2 )
% 2.69/1.51 => ( A3
% 2.69/1.51 = ( divide_divide @ A @ B2 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_242_nonzero__divide__eq__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [C3: A,B2: A,A3: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ( divide_divide @ A @ B2 @ C3 )
% 2.69/1.51 = A3 )
% 2.69/1.51 = ( B2
% 2.69/1.51 = ( times_times @ A @ A3 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_243_nonzero__eq__divide__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( C3
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( A3
% 2.69/1.51 = ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ( times_times @ A @ A3 @ C3 )
% 2.69/1.51 = B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_244_nonzero__minus__divide__right,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [B2: A,A3: A] :
% 2.69/1.51 ( ( B2
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( uminus_uminus @ A @ ( divide_divide @ A @ A3 @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ ( uminus_uminus @ A @ B2 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_245_nonzero__minus__divide__divide,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( division_ring @ A )
% 2.69/1.51 => ! [B2: A,A3: A] :
% 2.69/1.51 ( ( B2
% 2.69/1.51 != ( zero_zero @ A ) )
% 2.69/1.51 => ( ( divide_divide @ A @ ( uminus_uminus @ A @ A3 ) @ ( uminus_uminus @ A @ B2 ) )
% 2.69/1.51 = ( divide_divide @ A @ A3 @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_246_divide__strict__left__mono__neg,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ B2 )
% 2.69/1.51 => ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 2.69/1.51 => ( ord_less @ A @ ( divide_divide @ A @ C3 @ A3 ) @ ( divide_divide @ A @ C3 @ B2 ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_247_divide__strict__left__mono,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [B2: A,A3: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ B2 @ A3 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A3 @ B2 ) )
% 2.69/1.51 => ( ord_less @ A @ ( divide_divide @ A @ C3 @ A3 ) @ ( divide_divide @ A @ C3 @ B2 ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_248_mult__imp__less__div__pos,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [Y: A,Z3: A,X2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 2.69/1.51 => ( ( ord_less @ A @ ( times_times @ A @ Z3 @ Y ) @ X2 )
% 2.69/1.51 => ( ord_less @ A @ Z3 @ ( divide_divide @ A @ X2 @ Y ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_249_mult__imp__div__pos__less,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [Y: A,X2: A,Z3: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y )
% 2.69/1.51 => ( ( ord_less @ A @ X2 @ ( times_times @ A @ Z3 @ Y ) )
% 2.69/1.51 => ( ord_less @ A @ ( divide_divide @ A @ X2 @ Y ) @ Z3 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_250_pos__less__divide__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_251_pos__divide__less__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [C3: A,B2: A,A3: A] :
% 2.69/1.51 ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C3 ) @ A3 )
% 2.69/1.51 = ( ord_less @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_252_neg__less__divide__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [C3: A,A3: A,B2: A] :
% 2.69/1.51 ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ord_less @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_253_neg__divide__less__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [C3: A,B2: A,A3: A] :
% 2.69/1.51 ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C3 ) @ A3 )
% 2.69/1.51 = ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(fact_254_less__divide__eq,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( linordered_field @ A )
% 2.69/1.51 => ! [A3: A,B2: A,C3: A] :
% 2.69/1.51 ( ( ord_less @ A @ A3 @ ( divide_divide @ A @ B2 @ C3 ) )
% 2.69/1.51 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ord_less @ A @ ( times_times @ A @ A3 @ C3 ) @ B2 ) )
% 2.69/1.51 & ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ C3 )
% 2.69/1.51 => ( ( ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ B2 @ ( times_times @ A @ A3 @ C3 ) ) )
% 2.69/1.51 & ( ~ ( ord_less @ A @ C3 @ ( zero_zero @ A ) )
% 2.69/1.51 => ( ord_less @ A @ A3 @ ( zero_zero @ A ) ) ) ) ) ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( real_V2090557954_space @ A )
% 2.69/1.51 => ( type @ A ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Ot0__space,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( real_V2090557954_space @ A )
% 2.69/1.51 => ( topological_t0_space @ A ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Ot1__space,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( real_V2090557954_space @ A )
% 2.69/1.51 => ( topological_t1_space @ A ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space,axiom,
% 2.69/1.51 ! [A: $tType] :
% 2.69/1.51 ( ( real_V2090557954_space @ A )
% 2.69/1.51 => ( topolo503727757_space @ A ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 2.69/1.51 ! [A7: $tType,A8: $tType] :
% 2.69/1.51 ( ( topolo503727757_space @ A8 )
% 2.69/1.51 => ( topolo503727757_space @ ( A7 > A8 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 2.69/1.51 ! [A7: $tType,A8: $tType] :
% 2.69/1.51 ( ( boolean_algebra @ A8 )
% 2.69/1.51 => ( boolean_algebra @ ( A7 > A8 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.69/1.51 ! [A7: $tType,A8: $tType] :
% 2.69/1.51 ( ( preorder @ A8 )
% 2.69/1.51 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.69/1.51 ! [A7: $tType,A8: $tType] :
% 2.69/1.51 ( ( order @ A8 )
% 2.69/1.51 => ( order @ ( A7 > A8 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_fun___Orderings_Oord,axiom,
% 2.69/1.51 ! [A7: $tType,A8: $tType] :
% 2.69/1.51 ( ( ord @ A8 )
% 2.69/1.51 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_fun___Groups_Ouminus,axiom,
% 2.69/1.51 ! [A7: $tType,A8: $tType] :
% 2.69/1.51 ( ( uminus @ A8 )
% 2.69/1.51 => ( uminus @ ( A7 > A8 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_1,axiom,
% 2.69/1.51 ! [A7: $tType] : ( boolean_algebra @ ( set @ A7 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Groups_Oab__semigroup__mult,axiom,
% 2.69/1.51 ! [A7: $tType] :
% 2.69/1.51 ( ( ab_semigroup_mult @ A7 )
% 2.69/1.51 => ( ab_semigroup_mult @ ( set @ A7 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Groups_Osemigroup__mult,axiom,
% 2.69/1.51 ! [A7: $tType] :
% 2.69/1.51 ( ( semigroup_mult @ A7 )
% 2.69/1.51 => ( semigroup_mult @ ( set @ A7 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 2.69/1.51 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 2.69/1.51 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 2.69/1.51 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Groups_Ouminus_5,axiom,
% 2.69/1.51 ! [A7: $tType] : ( uminus @ ( set @ A7 ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Set_Oset___Groups_Ozero,axiom,
% 2.69/1.51 ! [A7: $tType] :
% 2.69/1.51 ( ( zero @ A7 )
% 2.69/1.51 => ( zero @ ( set @ A7 ) ) ) ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_6,axiom,
% 2.69/1.51 topolo503727757_space @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology,axiom,
% 2.69/1.51 topolo2133971006pology @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Topological__Spaces_Ot1__space,axiom,
% 2.69/1.51 topological_t1_space @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Topological__Spaces_Ot0__space,axiom,
% 2.69/1.51 topological_t0_space @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_7,axiom,
% 2.69/1.51 boolean_algebra @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 2.69/1.51 preorder @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.69/1.51 linorder @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 2.69/1.51 order @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 2.69/1.51 ord @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_HOL_Obool___Groups_Ouminus_11,axiom,
% 2.69/1.51 uminus @ $o ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Conditionally__Complete__Lattices_Olinear__continuum,axiom,
% 2.69/1.51 condit1656338222tinuum @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_12,axiom,
% 2.69/1.51 topolo503727757_space @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Ot1__space_13,axiom,
% 2.69/1.51 topological_t1_space @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Topological__Spaces_Ot0__space_14,axiom,
% 2.69/1.51 topological_t0_space @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Groups_Oab__semigroup__mult_15,axiom,
% 2.69/1.51 ab_semigroup_mult @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Orderings_Odense__order,axiom,
% 2.69/1.51 dense_order @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Groups_Osemigroup__mult_16,axiom,
% 2.69/1.51 semigroup_mult @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Orderings_Opreorder_17,axiom,
% 2.69/1.51 preorder @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Orderings_Olinorder_18,axiom,
% 2.69/1.51 linorder @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Orderings_Oorder_19,axiom,
% 2.69/1.51 order @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Orderings_Oord_20,axiom,
% 2.69/1.51 ord @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Groups_Ouminus_21,axiom,
% 2.69/1.51 uminus @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tcon_Extended__Real_Oereal___Groups_Ozero_22,axiom,
% 2.69/1.51 zero @ extended_ereal ).
% 2.69/1.51
% 2.69/1.51 thf(tfree_0,hypothesis,
% 2.69/1.51 real_V2090557954_space @ a ).
% 2.69/1.51
% 2.69/1.51 thf(conj_0,conjecture,
% 2.69/1.51 ( ( lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f )
% 2.69/1.51 != ( ~ ! [C: extended_ereal] :
% 2.69/1.51 ( ( ord_less @ extended_ereal @ C @ ( f @ x0 ) )
% 2.69/1.51 => ? [T: set @ a] :
% 2.69/1.51 ( ( topolo1751647064n_open @ a @ T )
% 2.69/1.51 & ( member @ a @ x0 @ T )
% 2.69/1.51 & ! [X: a] :
% 2.69/1.51 ( ( member @ a @ X @ T )
% 2.69/1.51 => ( ord_less @ extended_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ).
% 2.69/1.51 ------------------------
% 2.69/1.54 % (16295)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_16074 for (2999ds/4Mi)
% 2.69/1.54 % (16297)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/2Mi)
% 2.69/1.54 % (16296)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_16074 for (2999ds/27Mi)
% 2.69/1.54 % (16295)Instruction limit reached!
% 2.69/1.54 % (16295)------------------------------
% 2.69/1.54 % (16295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (16295)Termination reason: Unknown
% 2.69/1.54 % (16295)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (16295)Memory used [KB]: 1407
% 2.69/1.54 % (16295)Time elapsed: 0.003 s
% 2.69/1.54 % (16295)Instructions burned: 4 (million)
% 2.69/1.54 % (16295)------------------------------
% 2.69/1.54 % (16295)------------------------------
% 2.69/1.54 % (16297)Instruction limit reached!
% 2.69/1.54 % (16297)------------------------------
% 2.69/1.54 % (16297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (16297)Termination reason: Unknown
% 2.69/1.54 % (16297)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (16297)Memory used [KB]: 1407
% 2.69/1.54 % (16297)Time elapsed: 0.003 s
% 2.69/1.54 % (16297)Instructions burned: 4 (million)
% 2.69/1.54 % (16297)------------------------------
% 2.69/1.54 % (16297)------------------------------
% 2.69/1.54 % (16294)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/183Mi)
% 2.69/1.54 % (16298)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_16074 for (2999ds/2Mi)
% 2.69/1.54 % (16299)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_16074 for (2999ds/275Mi)
% 2.69/1.54 % (16300)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/18Mi)
% 2.69/1.54 % (16296)Instruction limit reached!
% 2.69/1.54 % (16296)------------------------------
% 2.69/1.54 % (16296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (16296)Termination reason: Unknown
% 2.69/1.54 % (16296)Termination phase: Property scanning
% 2.69/1.54
% 2.69/1.54 % (16296)Memory used [KB]: 1663
% 2.69/1.54 % (16296)Time elapsed: 0.010 s
% 2.69/1.54 % (16296)Instructions burned: 27 (million)
% 2.69/1.54 % (16296)------------------------------
% 2.69/1.54 % (16296)------------------------------
% 2.69/1.55 % (16298)Instruction limit reached!
% 2.69/1.55 % (16298)------------------------------
% 2.69/1.55 % (16298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (16298)Termination reason: Unknown
% 2.69/1.55 % (16298)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (16298)Memory used [KB]: 1407
% 2.69/1.55 % (16298)Time elapsed: 0.004 s
% 2.69/1.55 % (16298)Instructions burned: 3 (million)
% 2.69/1.55 % (16298)------------------------------
% 2.69/1.55 % (16298)------------------------------
% 2.69/1.55 % (16301)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/3Mi)
% 2.69/1.55 % (16302)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_16074 for (2999ds/37Mi)
% 2.69/1.55 % (16301)Instruction limit reached!
% 2.69/1.55 % (16301)------------------------------
% 2.69/1.55 % (16301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (16301)Termination reason: Unknown
% 2.69/1.55 % (16301)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (16301)Memory used [KB]: 1279
% 2.69/1.55 % (16301)Time elapsed: 0.002 s
% 2.69/1.55 % (16301)Instructions burned: 3 (million)
% 2.69/1.55 % (16301)------------------------------
% 2.69/1.55 % (16301)------------------------------
% 2.69/1.56 % (16300)Instruction limit reached!
% 2.69/1.56 % (16300)------------------------------
% 2.69/1.56 % (16300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (16300)Termination reason: Unknown
% 2.69/1.56 % (16300)Termination phase: Property scanning
% 2.69/1.56
% 2.69/1.56 % (16300)Memory used [KB]: 1663
% 2.69/1.56 % (16300)Time elapsed: 0.014 s
% 2.69/1.56 % (16300)Instructions burned: 19 (million)
% 2.69/1.56 % (16300)------------------------------
% 2.69/1.56 % (16300)------------------------------
% 2.69/1.56 % (16305)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_16074 for (2999ds/1041Mi)
% 2.69/1.56 % (16302)Instruction limit reached!
% 2.69/1.56 % (16302)------------------------------
% 2.69/1.56 % (16302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (16302)Termination reason: Unknown
% 2.69/1.56 % (16302)Termination phase: Property scanning
% 2.69/1.56
% 2.69/1.56 % (16302)Memory used [KB]: 2046
% 2.69/1.56 % (16302)Time elapsed: 0.012 s
% 2.69/1.56 % (16302)Instructions burned: 41 (million)
% 2.69/1.56 % (16302)------------------------------
% 2.69/1.56 % (16302)------------------------------
% 2.69/1.56 % (16304)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_16074 for (2999ds/3Mi)
% 2.69/1.56 % (16303)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_16074 for (2999ds/15Mi)
% 2.69/1.56 % (16304)Instruction limit reached!
% 2.69/1.56 % (16304)------------------------------
% 2.69/1.56 % (16304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (16304)Termination reason: Unknown
% 2.69/1.56 % (16304)Termination phase: shuffling
% 2.69/1.56
% 2.69/1.56 % (16304)Memory used [KB]: 1279
% 2.69/1.56 % (16304)Time elapsed: 0.004 s
% 2.69/1.56 % (16304)Instructions burned: 3 (million)
% 2.69/1.56 % (16304)------------------------------
% 2.69/1.56 % (16304)------------------------------
% 2.69/1.57 % (16307)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/16Mi)
% 2.69/1.57 % (16303)Instruction limit reached!
% 2.69/1.57 % (16303)------------------------------
% 2.69/1.57 % (16303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (16303)Termination reason: Unknown
% 2.69/1.57 % (16303)Termination phase: shuffling
% 2.69/1.57
% 2.69/1.57 % (16303)Memory used [KB]: 1663
% 2.69/1.57 % (16303)Time elapsed: 0.011 s
% 2.69/1.57 % (16303)Instructions burned: 15 (million)
% 2.69/1.57 % (16303)------------------------------
% 2.69/1.57 % (16303)------------------------------
% 2.69/1.57 % (16307)Instruction limit reached!
% 2.69/1.57 % (16307)------------------------------
% 2.69/1.57 % (16307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (16307)Termination reason: Unknown
% 2.69/1.57 % (16307)Termination phase: shuffling
% 2.69/1.57
% 2.69/1.57 % (16307)Memory used [KB]: 1663
% 2.69/1.57 % (16307)Time elapsed: 0.007 s
% 2.69/1.57 % (16307)Instructions burned: 18 (million)
% 2.69/1.57 % (16307)------------------------------
% 2.69/1.57 % (16307)------------------------------
% 2.69/1.57 % (16306)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/7Mi)
% 2.69/1.58 % (16306)Instruction limit reached!
% 2.69/1.58 % (16306)------------------------------
% 2.69/1.58 % (16306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (16306)Termination reason: Unknown
% 2.69/1.58 % (16306)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (16306)Memory used [KB]: 1407
% 2.69/1.58 % (16306)Time elapsed: 0.006 s
% 2.69/1.58 % (16306)Instructions burned: 7 (million)
% 2.69/1.58 % (16306)------------------------------
% 2.69/1.58 % (16306)------------------------------
% 2.69/1.58 % (16308)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_16074 for (2999ds/3Mi)
% 2.69/1.58 % (16308)Instruction limit reached!
% 2.69/1.58 % (16308)------------------------------
% 2.69/1.58 % (16308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (16308)Termination reason: Unknown
% 2.69/1.58 % (16308)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (16308)Memory used [KB]: 1407
% 2.69/1.58 % (16308)Time elapsed: 0.003 s
% 2.69/1.58 % (16308)Instructions burned: 5 (million)
% 2.69/1.58 % (16308)------------------------------
% 2.69/1.58 % (16308)------------------------------
% 2.69/1.58 % (16310)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/7Mi)
% 2.69/1.58 % (16309)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_16074 for (2999ds/3Mi)
% 2.69/1.58 % (16309)Instruction limit reached!
% 2.69/1.58 % (16309)------------------------------
% 2.69/1.58 % (16309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (16309)Termination reason: Unknown
% 2.69/1.58 % (16309)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (16309)Memory used [KB]: 1279
% 2.69/1.58 % (16309)Time elapsed: 0.003 s
% 2.69/1.58 % (16309)Instructions burned: 4 (million)
% 2.69/1.58 % (16309)------------------------------
% 2.69/1.58 % (16309)------------------------------
% 2.69/1.59 % (16310)Instruction limit reached!
% 2.69/1.59 % (16310)------------------------------
% 2.69/1.59 % (16310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (16310)Termination reason: Unknown
% 2.69/1.59 % (16310)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (16310)Memory used [KB]: 1535
% 2.69/1.59 % (16310)Time elapsed: 0.004 s
% 2.69/1.59 % (16310)Instructions burned: 9 (million)
% 2.69/1.59 % (16310)------------------------------
% 2.69/1.59 % (16310)------------------------------
% 2.69/1.59 % (16312)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/4Mi)
% 2.69/1.59 % (16312)Instruction limit reached!
% 2.69/1.59 % (16312)------------------------------
% 2.69/1.59 % (16312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (16312)Termination reason: Unknown
% 2.69/1.59 % (16312)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (16312)Memory used [KB]: 1407
% 2.69/1.59 % (16312)Time elapsed: 0.003 s
% 2.69/1.59 % (16312)Instructions burned: 6 (million)
% 2.69/1.59 % (16312)------------------------------
% 2.69/1.59 % (16312)------------------------------
% 2.69/1.59 % (16313)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/18Mi)
% 2.69/1.59 % (16311)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/3Mi)
% 2.69/1.59 % (16314)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/710Mi)
% 2.71/1.60 % (16311)Instruction limit reached!
% 2.71/1.60 % (16311)------------------------------
% 2.71/1.60 % (16311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (16311)Termination reason: Unknown
% 2.71/1.60 % (16311)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (16311)Memory used [KB]: 1407
% 2.71/1.60 % (16311)Time elapsed: 0.004 s
% 2.71/1.60 % (16311)Instructions burned: 3 (million)
% 2.71/1.60 % (16311)------------------------------
% 2.71/1.60 % (16311)------------------------------
% 2.71/1.60 % (16313)Instruction limit reached!
% 2.71/1.60 % (16313)------------------------------
% 2.71/1.60 % (16313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (16313)Termination reason: Unknown
% 2.71/1.60 % (16313)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (16313)Memory used [KB]: 1663
% 2.71/1.60 % (16313)Time elapsed: 0.008 s
% 2.71/1.60 % (16313)Instructions burned: 18 (million)
% 2.71/1.60 % (16313)------------------------------
% 2.71/1.60 % (16313)------------------------------
% 2.71/1.60 % (16315)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/6Mi)
% 2.71/1.61 % (16315)Instruction limit reached!
% 2.71/1.61 % (16315)------------------------------
% 2.71/1.61 % (16315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.61 % (16315)Termination reason: Unknown
% 2.71/1.61 % (16315)Termination phase: shuffling
% 2.71/1.61
% 2.71/1.61 % (16315)Memory used [KB]: 1407
% 2.71/1.61 % (16315)Time elapsed: 0.004 s
% 2.71/1.61 % (16315)Instructions burned: 7 (million)
% 2.71/1.61 % (16315)------------------------------
% 2.71/1.61 % (16315)------------------------------
% 2.71/1.61 % (16317)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_16074 for (2999ds/21Mi)
% 2.71/1.61 % (16316)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_16074 for (2999ds/902Mi)
% 2.71/1.62 % (16318)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/5Mi)
% 2.71/1.62 % (16317)Instruction limit reached!
% 2.71/1.62 % (16317)------------------------------
% 2.71/1.62 % (16317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (16317)Termination reason: Unknown
% 2.71/1.62 % (16317)Termination phase: Property scanning
% 2.71/1.62
% 2.71/1.62 % (16317)Memory used [KB]: 1663
% 2.71/1.62 % (16317)Time elapsed: 0.009 s
% 2.71/1.62 % (16317)Instructions burned: 21 (million)
% 2.71/1.62 % (16317)------------------------------
% 2.71/1.62 % (16317)------------------------------
% 2.71/1.62 % (16294)Instruction limit reached!
% 2.71/1.62 % (16294)------------------------------
% 2.71/1.62 % (16294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (16294)Termination reason: Unknown
% 2.71/1.62 % (16294)Termination phase: Saturation
% 2.71/1.62
% 2.71/1.62 % (16294)Memory used [KB]: 6908
% 2.71/1.62 % (16294)Time elapsed: 0.077 s
% 2.71/1.62 % (16294)Instructions burned: 186 (million)
% 2.71/1.62 % (16294)------------------------------
% 2.71/1.62 % (16294)------------------------------
% 2.71/1.62 % (16318)Instruction limit reached!
% 2.71/1.62 % (16318)------------------------------
% 2.71/1.62 % (16318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (16318)Termination reason: Unknown
% 2.71/1.62 % (16318)Termination phase: shuffling
% 2.71/1.62
% 2.71/1.62 % (16318)Memory used [KB]: 1407
% 2.71/1.62 % (16318)Time elapsed: 0.004 s
% 2.71/1.62 % (16318)Instructions burned: 7 (million)
% 2.71/1.62 % (16318)------------------------------
% 2.71/1.62 % (16318)------------------------------
% 2.71/1.63 % (16320)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/377Mi)
% 2.71/1.63 % (16321)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_16074 for (2999ds/779Mi)
% 2.71/1.64 % (16319)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_16074 for (2999ds/6Mi)
% 2.71/1.64 % (16319)Instruction limit reached!
% 2.71/1.64 % (16319)------------------------------
% 2.71/1.64 % (16319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.64 % (16319)Termination reason: Unknown
% 2.71/1.64 % (16319)Termination phase: shuffling
% 2.71/1.64
% 2.71/1.64 % (16319)Memory used [KB]: 1407
% 2.71/1.64 % (16319)Time elapsed: 0.006 s
% 2.71/1.64 % (16319)Instructions burned: 7 (million)
% 2.71/1.64 % (16319)------------------------------
% 2.71/1.64 % (16319)------------------------------
% 2.71/1.66 % (16322)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_16074 for (2998ds/19Mi)
% 2.71/1.67 % (16322)Instruction limit reached!
% 2.71/1.67 % (16322)------------------------------
% 2.71/1.67 % (16322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.67 % (16322)Termination reason: Unknown
% 2.71/1.67 % (16322)Termination phase: shuffling
% 2.71/1.67
% 2.71/1.67 % (16322)Memory used [KB]: 1663
% 2.71/1.67 % (16322)Time elapsed: 0.012 s
% 2.71/1.67 % (16322)Instructions burned: 19 (million)
% 2.71/1.67 % (16322)------------------------------
% 2.71/1.67 % (16322)------------------------------
% 2.71/1.68 % (16299)Instruction limit reached!
% 2.71/1.68 % (16299)------------------------------
% 2.71/1.68 % (16299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.68 % (16299)Termination reason: Unknown
% 2.71/1.68 % (16299)Termination phase: Saturation
% 2.71/1.68
% 2.71/1.68 % (16299)Memory used [KB]: 6908
% 2.71/1.68 % (16299)Time elapsed: 0.135 s
% 2.71/1.68 % (16299)Instructions burned: 275 (million)
% 2.71/1.68 % (16299)------------------------------
% 2.71/1.68 % (16299)------------------------------
% 2.71/1.68 % (16323)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16074 for (2998ds/879Mi)
% 2.71/1.69 % (16324)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16074 for (2998ds/17Mi)
% 2.71/1.69 % (16324)Instruction limit reached!
% 2.71/1.69 % (16324)------------------------------
% 2.71/1.69 % (16324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.69 % (16324)Termination reason: Unknown
% 2.71/1.69 % (16324)Termination phase: shuffling
% 2.71/1.69
% 2.71/1.69 % (16324)Memory used [KB]: 1663
% 2.71/1.69 % (16324)Time elapsed: 0.008 s
% 2.71/1.69 % (16324)Instructions burned: 18 (million)
% 2.71/1.69 % (16324)------------------------------
% 2.71/1.69 % (16324)------------------------------
% 2.71/1.70 % (16325)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16074 for (2998ds/3Mi)
% 2.71/1.70 % (16325)Instruction limit reached!
% 2.71/1.70 % (16325)------------------------------
% 2.71/1.70 % (16325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.70 % (16325)Termination reason: Unknown
% 2.71/1.70 % (16325)Termination phase: shuffling
% 2.71/1.70
% 2.71/1.70 % (16325)Memory used [KB]: 1279
% 2.71/1.70 % (16325)Time elapsed: 0.003 s
% 2.71/1.70 % (16325)Instructions burned: 4 (million)
% 2.71/1.70 % (16325)------------------------------
% 2.71/1.70 % (16325)------------------------------
% 2.71/1.71 % (16326)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16074 for (2998ds/30Mi)
% 2.71/1.72 % (16326)Instruction limit reached!
% 2.71/1.72 % (16326)------------------------------
% 2.71/1.72 % (16326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.72 % (16326)Termination reason: Unknown
% 2.71/1.72 % (16326)Termination phase: Preprocessing 1
% 2.71/1.72
% 2.71/1.72 % (16326)Memory used [KB]: 1663
% 2.71/1.72 % (16326)Time elapsed: 0.012 s
% 2.71/1.72 % (16326)Instructions burned: 32 (million)
% 2.71/1.72 % (16326)------------------------------
% 2.71/1.72 % (16326)------------------------------
% 2.71/1.73 % (16327)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16074 for (2997ds/127Mi)
% 2.71/1.75 % (16320)Instruction limit reached!
% 2.71/1.75 % (16320)------------------------------
% 2.71/1.75 % (16320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.75 % (16320)Termination reason: Unknown
% 2.71/1.75 % (16320)Termination phase: Saturation
% 2.71/1.75
% 2.71/1.75 % (16320)Memory used [KB]: 7419
% 2.71/1.75 % (16320)Time elapsed: 0.123 s
% 2.71/1.75 % (16320)Instructions burned: 377 (million)
% 2.71/1.75 % (16320)------------------------------
% 2.71/1.75 % (16320)------------------------------
% 2.71/1.76 % (16328)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16074 for (2997ds/100Mi)
% 2.71/1.77 % (16327)Instruction limit reached!
% 2.71/1.77 % (16327)------------------------------
% 2.71/1.77 % (16327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.77 % (16327)Termination reason: Unknown
% 2.71/1.77 % (16327)Termination phase: Saturation
% 2.71/1.77
% 2.71/1.77 % (16327)Memory used [KB]: 6780
% 2.71/1.77 % (16327)Time elapsed: 0.042 s
% 2.71/1.77 % (16327)Instructions burned: 129 (million)
% 2.71/1.77 % (16327)------------------------------
% 2.71/1.77 % (16327)------------------------------
% 2.71/1.79 % (16329)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_16074 for (2997ds/3Mi)
% 2.71/1.79 % (16328)Instruction limit reached!
% 2.71/1.79 % (16328)------------------------------
% 2.71/1.79 % (16328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.79 % (16328)Termination reason: Unknown
% 2.71/1.79 % (16328)Termination phase: Property scanning
% 2.71/1.79
% 2.71/1.79 % (16328)Memory used [KB]: 2174
% 2.71/1.79 % (16328)Time elapsed: 0.028 s
% 2.71/1.79 % (16328)Instructions burned: 102 (million)
% 2.71/1.79 % (16328)------------------------------
% 2.71/1.79 % (16328)------------------------------
% 2.71/1.79 % (16329)Instruction limit reached!
% 2.71/1.79 % (16329)------------------------------
% 2.71/1.79 % (16329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.79 % (16329)Termination reason: Unknown
% 2.71/1.79 % (16329)Termination phase: shuffling
% 2.71/1.79
% 2.71/1.79 % (16329)Memory used [KB]: 1407
% 2.71/1.79 % (16329)Time elapsed: 0.003 s
% 2.71/1.79 % (16329)Instructions burned: 4 (million)
% 2.71/1.79 % (16329)------------------------------
% 2.71/1.79 % (16329)------------------------------
% 2.71/1.80 % (16330)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_16074 for (2997ds/20Mi)
% 2.71/1.80 % (16331)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_16074 for (2997ds/86Mi)
% 2.71/1.80 % (16330)Instruction limit reached!
% 2.71/1.80 % (16330)------------------------------
% 2.71/1.80 % (16330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.80 % (16330)Termination reason: Unknown
% 2.71/1.80 % (16330)Termination phase: Property scanning
% 2.71/1.80
% 2.71/1.80 % (16330)Memory used [KB]: 1663
% 2.71/1.80 % (16330)Time elapsed: 0.008 s
% 2.71/1.80 % (16330)Instructions burned: 22 (million)
% 2.71/1.80 % (16330)------------------------------
% 2.71/1.80 % (16330)------------------------------
% 2.71/1.81 % (16314)Instruction limit reached!
% 2.71/1.81 % (16314)------------------------------
% 2.71/1.81 % (16314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.81 % (16314)Termination reason: Unknown
% 2.71/1.81 % (16314)Termination phase: Saturation
% 2.71/1.81
% 2.71/1.81 % (16314)Memory used [KB]: 7931
% 2.71/1.81 % (16314)Time elapsed: 0.218 s
% 2.71/1.81 % (16314)Instructions burned: 712 (million)
% 2.71/1.81 % (16314)------------------------------
% 2.71/1.81 % (16314)------------------------------
% 2.71/1.81 % (16332)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_16074 for (2997ds/107Mi)
% 2.71/1.82 % (16333)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_16074 for (2996ds/39Mi)
% 2.71/1.82 % (16331)Instruction limit reached!
% 2.71/1.82 % (16331)------------------------------
% 2.71/1.82 % (16331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.82 % (16331)Termination reason: Unknown
% 2.71/1.82 % (16331)Termination phase: Saturation
% 2.71/1.82
% 2.71/1.82 % (16331)Memory used [KB]: 6652
% 2.71/1.82 % (16331)Time elapsed: 0.029 s
% 2.71/1.82 % (16331)Instructions burned: 88 (million)
% 2.71/1.82 % (16331)------------------------------
% 2.71/1.82 % (16331)------------------------------
% 2.71/1.83 % (16333)Instruction limit reached!
% 2.71/1.83 % (16333)------------------------------
% 2.71/1.83 % (16333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.83 % (16333)Termination reason: Unknown
% 2.71/1.83 % (16333)Termination phase: Property scanning
% 2.71/1.83
% 2.71/1.83 % (16333)Memory used [KB]: 2046
% 2.71/1.83 % (16333)Time elapsed: 0.012 s
% 2.71/1.83 % (16333)Instructions burned: 40 (million)
% 2.71/1.83 % (16333)------------------------------
% 2.71/1.83 % (16333)------------------------------
% 2.71/1.83 % (16334)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_16074 for (2996ds/448Mi)
% 2.71/1.84 % (16335)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_16074 for (2996ds/46Mi)
% 2.71/1.84 % (16332)Instruction limit reached!
% 2.71/1.84 % (16332)------------------------------
% 2.71/1.84 % (16332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.84 % (16332)Termination reason: Unknown
% 2.71/1.84 % (16332)Termination phase: Saturation
% 2.71/1.84
% 2.71/1.84 % (16332)Memory used [KB]: 6780
% 2.71/1.84 % (16332)Time elapsed: 0.033 s
% 2.71/1.84 % (16332)Instructions burned: 110 (million)
% 2.71/1.84 % (16332)------------------------------
% 2.71/1.84 % (16332)------------------------------
% 2.71/1.85 % (16336)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_16074 for (2996ds/98Mi)
% 2.71/1.86 % (16335)Instruction limit reached!
% 2.71/1.86 % (16335)------------------------------
% 2.71/1.86 % (16335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.86 % (16335)Termination reason: Unknown
% 2.71/1.86 % (16335)Termination phase: Property scanning
% 2.71/1.86
% 2.71/1.86 % (16335)Memory used [KB]: 1918
% 2.71/1.86 % (16335)Time elapsed: 0.015 s
% 2.71/1.86 % (16335)Instructions burned: 47 (million)
% 2.71/1.86 % (16335)------------------------------
% 2.71/1.86 % (16335)------------------------------
% 2.71/1.86 % (16337)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_16074 for (2996ds/507Mi)
% 2.71/1.87 % (16305)Instruction limit reached!
% 2.71/1.87 % (16305)------------------------------
% 2.71/1.87 % (16305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.87 % (16305)Termination reason: Unknown
% 2.71/1.87 % (16305)Termination phase: Saturation
% 2.71/1.87
% 2.71/1.87 % (16305)Memory used [KB]: 9466
% 2.71/1.87 % (16305)Time elapsed: 0.313 s
% 2.71/1.87 % (16305)Instructions burned: 1041 (million)
% 2.71/1.87 % (16305)------------------------------
% 2.71/1.87 % (16305)------------------------------
% 2.71/1.88 % (16338)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_16074 for (2996ds/149Mi)
% 2.71/1.88 % (16336)Instruction limit reached!
% 2.71/1.88 % (16336)------------------------------
% 2.71/1.88 % (16336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.88 % (16336)Termination reason: Unknown
% 2.71/1.88 % (16336)Termination phase: Property scanning
% 2.71/1.88
% 2.71/1.88 % (16336)Memory used [KB]: 2174
% 2.71/1.88 % (16336)Time elapsed: 0.027 s
% 2.71/1.88 % (16336)Instructions burned: 99 (million)
% 2.71/1.88 % (16336)------------------------------
% 2.71/1.88 % (16336)------------------------------
% 2.71/1.89 % (16339)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_16074 for (2996ds/39Mi)
% 2.71/1.89 % (16321)Instruction limit reached!
% 2.71/1.89 % (16321)------------------------------
% 2.71/1.89 % (16321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.89 % (16321)Termination reason: Unknown
% 2.71/1.89 % (16321)Termination phase: Saturation
% 2.71/1.89
% 2.71/1.89 % (16321)Memory used [KB]: 7931
% 2.71/1.89 % (16321)Time elapsed: 0.267 s
% 2.71/1.89 % (16321)Instructions burned: 779 (million)
% 2.71/1.89 % (16321)------------------------------
% 2.71/1.89 % (16321)------------------------------
% 2.71/1.90 % (16316)Instruction limit reached!
% 2.71/1.90 % (16316)------------------------------
% 2.71/1.90 % (16316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.90 % (16316)Termination reason: Unknown
% 2.71/1.90 % (16316)Termination phase: Saturation
% 2.71/1.90
% 2.71/1.90 % (16316)Memory used [KB]: 8443
% 2.71/1.90 % (16316)Time elapsed: 0.290 s
% 2.71/1.90 % (16316)Instructions burned: 903 (million)
% 2.71/1.90 % (16316)------------------------------
% 2.71/1.90 % (16316)------------------------------
% 2.71/1.90 % (16339)Instruction limit reached!
% 2.71/1.90 % (16339)------------------------------
% 2.71/1.90 % (16339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.90 % (16339)Termination reason: Unknown
% 2.71/1.90 % (16339)Termination phase: Preprocessing 3
% 2.71/1.90
% 2.71/1.90 % (16339)Memory used [KB]: 1918
% 2.71/1.90 % (16339)Time elapsed: 0.014 s
% 2.71/1.90 % (16339)Instructions burned: 41 (million)
% 2.71/1.90 % (16339)------------------------------
% 2.71/1.90 % (16339)------------------------------
% 2.71/1.90 % (16340)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_16074 for (2996ds/6Mi)
% 2.71/1.91 % (16340)Instruction limit reached!
% 2.71/1.91 % (16340)------------------------------
% 2.71/1.91 % (16340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.91 % (16340)Termination reason: Unknown
% 2.71/1.91 % (16340)Termination phase: shuffling
% 2.71/1.91
% 2.71/1.91 % (16340)Memory used [KB]: 1407
% 2.71/1.91 % (16340)Time elapsed: 0.003 s
% 2.71/1.91 % (16340)Instructions burned: 7 (million)
% 2.71/1.91 % (16340)------------------------------
% 2.71/1.91 % (16340)------------------------------
% 2.71/1.91 % (16342)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_16074 for (2996ds/47Mi)
% 2.71/1.91 % (16341)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_16074 for (2996ds/1087Mi)
% 2.71/1.92 % (16343)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_16074 for (2996ds/44Mi)
% 2.71/1.92 % (16337)Refutation not found, incomplete strategy
% 2.71/1.92 % (16337)------------------------------
% 2.71/1.92 % (16337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.92 % (16337)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.92
% 2.71/1.92
% 2.71/1.92 % (16337)Memory used [KB]: 7291
% 2.71/1.92 % (16337)Time elapsed: 0.058 s
% 2.71/1.92 % (16337)Instructions burned: 193 (million)
% 2.71/1.92 % (16337)------------------------------
% 2.71/1.92 % (16337)------------------------------
% 2.71/1.92 % (16338)Instruction limit reached!
% 2.71/1.92 % (16338)------------------------------
% 2.71/1.92 % (16338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.92 % (16338)Termination reason: Unknown
% 2.71/1.92 % (16338)Termination phase: Saturation
% 2.71/1.92
% 2.71/1.92 % (16338)Memory used [KB]: 7036
% 2.71/1.92 % (16338)Time elapsed: 0.047 s
% 2.71/1.92 % (16338)Instructions burned: 150 (million)
% 2.71/1.92 % (16338)------------------------------
% 2.71/1.92 % (16338)------------------------------
% 2.71/1.92 % (16342)Instruction limit reached!
% 2.71/1.92 % (16342)------------------------------
% 2.71/1.92 % (16342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.92 % (16342)Termination reason: Unknown
% 2.71/1.92 % (16342)Termination phase: Property scanning
% 2.71/1.92
% 2.71/1.92 % (16342)Memory used [KB]: 2046
% 2.71/1.92 % (16342)Time elapsed: 0.015 s
% 2.71/1.92 % (16342)Instructions burned: 47 (million)
% 2.71/1.92 % (16342)------------------------------
% 2.71/1.92 % (16342)------------------------------
% 2.71/1.93 % (16343)Instruction limit reached!
% 2.71/1.93 % (16343)------------------------------
% 2.71/1.93 % (16343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.93 % (16343)Termination reason: Unknown
% 2.71/1.93 % (16343)Termination phase: Property scanning
% 2.71/1.93
% 2.71/1.93 % (16343)Memory used [KB]: 2046
% 2.71/1.93 % (16343)Time elapsed: 0.015 s
% 2.71/1.93 % (16343)Instructions burned: 46 (million)
% 2.71/1.93 % (16343)------------------------------
% 2.71/1.93 % (16343)------------------------------
% 2.71/1.93 % (16344)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_16074 for (2995ds/432Mi)
% 2.71/1.93 % (16346)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_16074 for (2995ds/31Mi)
% 2.71/1.94 % (16347)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_16074 for (2995ds/96Mi)
% 2.71/1.94 % (16345)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_16074 for (2995ds/62Mi)
% 2.71/1.94 % (16346)Instruction limit reached!
% 2.71/1.94 % (16346)------------------------------
% 2.71/1.94 % (16346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.94 % (16346)Termination reason: Unknown
% 2.71/1.94 % (16346)Termination phase: Preprocessing 2
% 2.71/1.94
% 2.71/1.94 % (16346)Memory used [KB]: 1791
% 2.71/1.94 % (16346)Time elapsed: 0.011 s
% 2.71/1.94 % (16346)Instructions burned: 33 (million)
% 2.71/1.94 % (16346)------------------------------
% 2.71/1.94 % (16346)------------------------------
% 2.71/1.95 % (16348)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_16074 for (2995ds/453Mi)
% 2.71/1.97 % (16347)Instruction limit reached!
% 2.71/1.97 % (16347)------------------------------
% 2.71/1.97 % (16347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.97 % (16347)Termination reason: Unknown
% 2.71/1.97 % (16347)Termination phase: Saturation
% 2.71/1.97
% 2.71/1.97 % (16347)Memory used [KB]: 6652
% 2.71/1.97 % (16347)Time elapsed: 0.029 s
% 2.71/1.97 % (16347)Instructions burned: 98 (million)
% 2.71/1.97 % (16347)------------------------------
% 2.71/1.97 % (16347)------------------------------
% 2.71/1.97 % (16345)Instruction limit reached!
% 2.71/1.97 % (16345)------------------------------
% 2.71/1.97 % (16345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.97 % (16345)Termination reason: Unknown
% 2.71/1.97 % (16345)Termination phase: Preprocessing 3
% 2.71/1.97
% 2.71/1.97 % (16345)Memory used [KB]: 2174
% 2.71/1.97 % (16345)Time elapsed: 0.034 s
% 2.71/1.97 % (16345)Instructions burned: 63 (million)
% 2.71/1.97 % (16345)------------------------------
% 2.71/1.97 % (16345)------------------------------
% 2.71/1.98 % (16349)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_16074 for (2995ds/71Mi)
% 2.71/1.98 % (16334)Instruction limit reached!
% 2.71/1.98 % (16334)------------------------------
% 2.71/1.98 % (16334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.98 % (16334)Termination reason: Unknown
% 2.71/1.98 % (16334)Termination phase: Saturation
% 2.71/1.98
% 2.71/1.98 % (16334)Memory used [KB]: 8059
% 2.71/1.98 % (16334)Time elapsed: 0.148 s
% 2.71/1.98 % (16334)Instructions burned: 449 (million)
% 2.71/1.98 % (16334)------------------------------
% 2.71/1.98 % (16334)------------------------------
% 2.71/1.99 % (16323)Instruction limit reached!
% 2.71/1.99 % (16323)------------------------------
% 2.71/1.99 % (16323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.99 % (16323)Termination reason: Unknown
% 2.71/1.99 % (16323)Termination phase: Saturation
% 2.71/1.99
% 2.71/1.99 % (16323)Memory used [KB]: 7931
% 2.71/1.99 % (16323)Time elapsed: 0.327 s
% 2.71/1.99 % (16323)Instructions burned: 879 (million)
% 2.71/1.99 % (16323)------------------------------
% 2.71/1.99 % (16323)------------------------------
% 2.71/1.99 % (16351)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_16074 for (2995ds/11Mi)
% 2.71/1.99 % (16350)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_16074 for (2995ds/83Mi)
% 2.71/1.99 % (16351)Instruction limit reached!
% 2.71/1.99 % (16351)------------------------------
% 2.71/1.99 % (16351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.99 % (16351)Termination reason: Unknown
% 2.71/1.99 % (16351)Termination phase: shuffling
% 2.71/1.99
% 2.71/1.99 % (16351)Memory used [KB]: 1535
% 2.71/1.99 % (16351)Time elapsed: 0.004 s
% 2.71/1.99 % (16351)Instructions burned: 11 (million)
% 2.71/1.99 % (16351)------------------------------
% 2.71/1.99 % (16351)------------------------------
% 2.71/2.00 % (16352)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_16074 for (2995ds/41Mi)
% 2.71/2.00 % (16349)Instruction limit reached!
% 2.71/2.00 % (16349)------------------------------
% 2.71/2.00 % (16349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/2.00 % (16349)Termination reason: Unknown
% 2.71/2.00 % (16349)Termination phase: Saturation
% 2.71/2.00
% 2.71/2.00 % (16349)Memory used [KB]: 6524
% 2.71/2.00 % (16349)Time elapsed: 0.022 s
% 2.71/2.00 % (16349)Instructions burned: 73 (million)
% 2.71/2.00 % (16349)------------------------------
% 2.71/2.00 % (16349)------------------------------
% 2.71/2.00 % (16353)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16074 for (2995ds/6Mi)
% 2.71/2.00 % (16353)Instruction limit reached!
% 2.71/2.00 % (16353)------------------------------
% 2.71/2.00 % (16353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/2.00 % (16353)Termination reason: Unknown
% 2.71/2.00 % (16353)Termination phase: shuffling
% 2.71/2.00
% 2.71/2.00 % (16353)Memory used [KB]: 1407
% 2.71/2.00 % (16353)Time elapsed: 0.003 s
% 2.71/2.00 % (16353)Instructions burned: 7 (million)
% 2.71/2.00 % (16353)------------------------------
% 2.71/2.00 % (16353)------------------------------
% 2.71/2.01 % (16354)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_16074 for (2995ds/150Mi)
% 2.71/2.01 % (16352)Instruction limit reached!
% 2.71/2.01 % (16352)------------------------------
% 2.71/2.01 % (16352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/2.01 % (16352)Termination reason: Unknown
% 2.71/2.01 % (16352)Termination phase: Property scanning
% 2.71/2.01
% 2.71/2.01 % (16352)Memory used [KB]: 2046
% 2.71/2.01 % (16352)Time elapsed: 0.014 s
% 2.71/2.01 % (16352)Instructions burned: 42 (million)
% 2.71/2.01 % (16352)------------------------------
% 2.71/2.01 % (16352)------------------------------
% 6.05/2.01 % (16355)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_16074 for (2995ds/343Mi)
% 6.05/2.02 % (16356)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_16074 for (2995ds/109Mi)
% 6.05/2.03 % (16350)Instruction limit reached!
% 6.05/2.03 % (16350)------------------------------
% 6.05/2.03 % (16350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.03 % (16350)Termination reason: Unknown
% 6.05/2.03 % (16350)Termination phase: Saturation
% 6.05/2.03
% 6.05/2.03 % (16350)Memory used [KB]: 6524
% 6.05/2.03 % (16350)Time elapsed: 0.039 s
% 6.05/2.03 % (16350)Instructions burned: 85 (million)
% 6.05/2.03 % (16350)------------------------------
% 6.05/2.03 % (16350)------------------------------
% 6.05/2.04 % (16357)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_16074 for (2994ds/253Mi)
% 6.05/2.05 % (16356)Instruction limit reached!
% 6.05/2.05 % (16356)------------------------------
% 6.05/2.05 % (16356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.05 % (16356)Termination reason: Unknown
% 6.05/2.05 % (16356)Termination phase: Saturation
% 6.05/2.05
% 6.05/2.05 % (16356)Memory used [KB]: 6652
% 6.05/2.05 % (16356)Time elapsed: 0.033 s
% 6.05/2.05 % (16356)Instructions burned: 109 (million)
% 6.05/2.05 % (16356)------------------------------
% 6.05/2.05 % (16356)------------------------------
% 6.05/2.05 % (16354)Instruction limit reached!
% 6.05/2.05 % (16354)------------------------------
% 6.05/2.05 % (16354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.05 % (16354)Termination reason: Unknown
% 6.05/2.05 % (16354)Termination phase: Saturation
% 6.05/2.05
% 6.05/2.05 % (16354)Memory used [KB]: 7036
% 6.05/2.05 % (16354)Time elapsed: 0.046 s
% 6.05/2.05 % (16354)Instructions burned: 150 (million)
% 6.05/2.05 % (16354)------------------------------
% 6.05/2.05 % (16354)------------------------------
% 6.05/2.06 % (16358)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_16074 for (2994ds/140Mi)
% 6.05/2.06 % (16359)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_16074 for (2994ds/614Mi)
% 6.05/2.06 % (16344)Instruction limit reached!
% 6.05/2.06 % (16344)------------------------------
% 6.05/2.06 % (16344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.06 % (16344)Termination reason: Unknown
% 6.05/2.06 % (16344)Termination phase: Saturation
% 6.05/2.06
% 6.05/2.06 % (16344)Memory used [KB]: 3582
% 6.05/2.06 % (16344)Time elapsed: 0.134 s
% 6.05/2.06 % (16344)Instructions burned: 433 (million)
% 6.05/2.06 % (16344)------------------------------
% 6.05/2.06 % (16344)------------------------------
% 6.05/2.07 % (16360)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_16074 for (2994ds/202Mi)
% 6.05/2.09 % (16348)Instruction limit reached!
% 6.05/2.09 % (16348)------------------------------
% 6.05/2.09 % (16348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.09 % (16348)Termination reason: Unknown
% 6.05/2.09 % (16348)Termination phase: Saturation
% 6.05/2.09
% 6.05/2.09 % (16348)Memory used [KB]: 7675
% 6.05/2.09 % (16348)Time elapsed: 0.134 s
% 6.05/2.09 % (16348)Instructions burned: 453 (million)
% 6.05/2.09 % (16348)------------------------------
% 6.05/2.09 % (16348)------------------------------
% 6.05/2.10 % (16361)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_16074 for (2994ds/339Mi)
% 6.05/2.10 % (16358)Instruction limit reached!
% 6.05/2.10 % (16358)------------------------------
% 6.05/2.10 % (16358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.10 % (16358)Termination reason: Unknown
% 6.05/2.10 % (16358)Termination phase: Saturation
% 6.05/2.10
% 6.05/2.10 % (16358)Memory used [KB]: 6780
% 6.05/2.10 % (16358)Time elapsed: 0.046 s
% 6.05/2.10 % (16358)Instructions burned: 142 (million)
% 6.05/2.10 % (16358)------------------------------
% 6.05/2.10 % (16358)------------------------------
% 6.48/2.11 % (16362)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_16074 for (2994ds/283Mi)
% 6.48/2.12 % (16355)Instruction limit reached!
% 6.48/2.12 % (16355)------------------------------
% 6.48/2.12 % (16355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.12 % (16355)Termination reason: Unknown
% 6.48/2.12 % (16355)Termination phase: Saturation
% 6.48/2.12
% 6.48/2.12 % (16355)Memory used [KB]: 7164
% 6.48/2.12 % (16355)Time elapsed: 0.103 s
% 6.48/2.12 % (16355)Instructions burned: 344 (million)
% 6.48/2.12 % (16355)------------------------------
% 6.48/2.12 % (16355)------------------------------
% 6.48/2.12 % (16363)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_16074 for (2994ds/134Mi)
% 6.48/2.13 % (16357)Instruction limit reached!
% 6.48/2.13 % (16357)------------------------------
% 6.48/2.13 % (16357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.13 % (16357)Termination reason: Unknown
% 6.48/2.13 % (16357)Termination phase: Saturation
% 6.48/2.13
% 6.48/2.13 % (16357)Memory used [KB]: 7291
% 6.48/2.13 % (16357)Time elapsed: 0.089 s
% 6.48/2.13 % (16357)Instructions burned: 255 (million)
% 6.48/2.13 % (16357)------------------------------
% 6.48/2.13 % (16357)------------------------------
% 6.48/2.14 % (16364)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_16074 for (2993ds/298Mi)
% 6.48/2.14 % (16360)Instruction limit reached!
% 6.48/2.14 % (16360)------------------------------
% 6.48/2.14 % (16360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.14 % (16360)Termination reason: Unknown
% 6.48/2.14 % (16360)Termination phase: Saturation
% 6.48/2.14
% 6.48/2.14 % (16360)Memory used [KB]: 6908
% 6.48/2.14 % (16360)Time elapsed: 0.067 s
% 6.48/2.14 % (16360)Instructions burned: 203 (million)
% 6.48/2.14 % (16360)------------------------------
% 6.48/2.14 % (16360)------------------------------
% 6.48/2.15 % (16365)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_16074 for (2993ds/192Mi)
% 6.48/2.16 % (16363)Instruction limit reached!
% 6.48/2.16 % (16363)------------------------------
% 6.48/2.16 % (16363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.16 % (16363)Termination reason: Unknown
% 6.48/2.16 % (16363)Termination phase: Saturation
% 6.48/2.16
% 6.48/2.16 % (16363)Memory used [KB]: 6908
% 6.48/2.16 % (16363)Time elapsed: 0.041 s
% 6.48/2.16 % (16363)Instructions burned: 136 (million)
% 6.48/2.16 % (16363)------------------------------
% 6.48/2.16 % (16363)------------------------------
% 6.48/2.17 % (16366)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_16074 for (2993ds/258Mi)
% 6.91/2.20 % (16361)Instruction limit reached!
% 6.91/2.20 % (16361)------------------------------
% 6.91/2.20 % (16361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.20 % (16361)Termination reason: Unknown
% 6.91/2.20 % (16361)Termination phase: Saturation
% 6.91/2.20
% 6.91/2.20 % (16361)Memory used [KB]: 7419
% 6.91/2.20 % (16361)Time elapsed: 0.102 s
% 6.91/2.20 % (16361)Instructions burned: 340 (million)
% 6.91/2.20 % (16361)------------------------------
% 6.91/2.20 % (16361)------------------------------
% 6.91/2.20 % (16362)Instruction limit reached!
% 6.91/2.20 % (16362)------------------------------
% 6.91/2.20 % (16362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.20 % (16362)Termination reason: Unknown
% 6.91/2.20 % (16362)Termination phase: Saturation
% 6.91/2.20
% 6.91/2.20 % (16362)Memory used [KB]: 7291
% 6.91/2.20 % (16362)Time elapsed: 0.110 s
% 6.91/2.20 % (16362)Instructions burned: 283 (million)
% 6.91/2.20 % (16362)------------------------------
% 6.91/2.20 % (16362)------------------------------
% 6.91/2.21 % (16367)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_16074 for (2993ds/90Mi)
% 6.91/2.21 % (16365)Instruction limit reached!
% 6.91/2.21 % (16365)------------------------------
% 6.91/2.21 % (16365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.21 % (16365)Termination reason: Unknown
% 6.91/2.21 % (16365)Termination phase: Saturation
% 6.91/2.21
% 6.91/2.21 % (16365)Memory used [KB]: 7675
% 6.91/2.21 % (16365)Time elapsed: 0.061 s
% 6.91/2.21 % (16365)Instructions burned: 192 (million)
% 6.91/2.21 % (16365)------------------------------
% 6.91/2.21 % (16365)------------------------------
% 6.91/2.21 % (16368)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_16074 for (2993ds/231Mi)
% 6.91/2.22 % (16369)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_16074 for (2992ds/458Mi)
% 6.91/2.23 % (16364)Instruction limit reached!
% 6.91/2.23 % (16364)------------------------------
% 6.91/2.23 % (16364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.23 % (16364)Termination reason: Unknown
% 6.91/2.23 % (16364)Termination phase: Saturation
% 6.91/2.23
% 6.91/2.23 % (16364)Memory used [KB]: 7675
% 6.91/2.23 % (16364)Time elapsed: 0.092 s
% 6.91/2.23 % (16364)Instructions burned: 298 (million)
% 6.91/2.23 % (16364)------------------------------
% 6.91/2.23 % (16364)------------------------------
% 6.91/2.23 % (16367)Instruction limit reached!
% 6.91/2.23 % (16367)------------------------------
% 6.91/2.23 % (16367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.23 % (16367)Termination reason: Unknown
% 6.91/2.23 % (16367)Termination phase: Saturation
% 6.91/2.23
% 6.91/2.23 % (16367)Memory used [KB]: 6652
% 6.91/2.23 % (16367)Time elapsed: 0.028 s
% 6.91/2.23 % (16367)Instructions burned: 93 (million)
% 6.91/2.23 % (16367)------------------------------
% 6.91/2.23 % (16367)------------------------------
% 6.91/2.24 % (16370)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_16074 for (2992ds/31Mi)
% 6.91/2.24 % (16371)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_16074 for (2992ds/297Mi)
% 6.91/2.25 % (16370)Instruction limit reached!
% 6.91/2.25 % (16370)------------------------------
% 6.91/2.25 % (16370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.25 % (16370)Termination reason: Unknown
% 6.91/2.25 % (16370)Termination phase: Preprocessing 1
% 6.91/2.25
% 6.91/2.25 % (16370)Memory used [KB]: 1663
% 6.91/2.25 % (16370)Time elapsed: 0.012 s
% 6.91/2.25 % (16370)Instructions burned: 32 (million)
% 6.91/2.25 % (16370)------------------------------
% 6.91/2.25 % (16370)------------------------------
% 6.91/2.25 % (16366)Instruction limit reached!
% 6.91/2.25 % (16366)------------------------------
% 6.91/2.25 % (16366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.25 % (16366)Termination reason: Unknown
% 6.91/2.25 % (16366)Termination phase: Saturation
% 6.91/2.25
% 6.91/2.25 % (16366)Memory used [KB]: 7291
% 6.91/2.25 % (16366)Time elapsed: 0.081 s
% 6.91/2.25 % (16366)Instructions burned: 260 (million)
% 6.91/2.25 % (16366)------------------------------
% 6.91/2.25 % (16366)------------------------------
% 6.91/2.26 % (16359)Instruction limit reached!
% 6.91/2.26 % (16359)------------------------------
% 6.91/2.26 % (16359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.26 % (16359)Termination reason: Unknown
% 6.91/2.26 % (16359)Termination phase: Saturation
% 6.91/2.26
% 6.91/2.26 % (16359)Memory used [KB]: 8443
% 6.91/2.26 % (16359)Time elapsed: 0.197 s
% 6.91/2.26 % (16359)Instructions burned: 615 (million)
% 6.91/2.26 % (16359)------------------------------
% 6.91/2.26 % (16359)------------------------------
% 6.91/2.26 % (16372)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_16074 for (2992ds/987Mi)
% 6.91/2.26 % (16373)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_16074 for (2992ds/182Mi)
% 6.91/2.27 % (16374)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_16074 for (2992ds/182Mi)
% 6.91/2.27 % (16341)Instruction limit reached!
% 6.91/2.27 % (16341)------------------------------
% 6.91/2.27 % (16341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.27 % (16341)Termination reason: Unknown
% 6.91/2.27 % (16341)Termination phase: Saturation
% 6.91/2.27
% 6.91/2.27 % (16341)Memory used [KB]: 8187
% 6.91/2.27 % (16341)Time elapsed: 0.358 s
% 6.91/2.27 % (16341)Instructions burned: 1089 (million)
% 6.91/2.27 % (16341)------------------------------
% 6.91/2.27 % (16341)------------------------------
% 6.91/2.27 % (16368)Instruction limit reached!
% 6.91/2.27 % (16368)------------------------------
% 6.91/2.27 % (16368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.27 % (16368)Termination reason: Unknown
% 6.91/2.27 % (16368)Termination phase: Saturation
% 6.91/2.27
% 6.91/2.27 % (16368)Memory used [KB]: 6908
% 6.91/2.27 % (16368)Time elapsed: 0.063 s
% 6.91/2.27 % (16368)Instructions burned: 233 (million)
% 6.91/2.27 % (16368)------------------------------
% 6.91/2.27 % (16368)------------------------------
% 6.91/2.28 % (16375)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_16074 for (2992ds/154Mi)
% 6.91/2.28 % (16376)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_16074 for (2992ds/79Mi)
% 7.78/2.31 % (16376)Instruction limit reached!
% 7.78/2.31 % (16376)------------------------------
% 7.78/2.31 % (16376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.31 % (16376)Termination reason: Unknown
% 7.78/2.31 % (16376)Termination phase: Saturation
% 7.78/2.31
% 7.78/2.31 % (16376)Memory used [KB]: 6524
% 7.78/2.31 % (16376)Time elapsed: 0.024 s
% 7.78/2.31 % (16376)Instructions burned: 81 (million)
% 7.78/2.31 % (16376)------------------------------
% 7.78/2.31 % (16376)------------------------------
% 7.78/2.32 % (16377)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_16074 for (2992ds/216Mi)
% 7.78/2.32 % (16373)Instruction limit reached!
% 7.78/2.32 % (16373)------------------------------
% 7.78/2.32 % (16373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.32 % (16373)Termination reason: Unknown
% 7.78/2.32 % (16373)Termination phase: Saturation
% 7.78/2.32
% 7.78/2.32 % (16373)Memory used [KB]: 7036
% 7.78/2.32 % (16373)Time elapsed: 0.056 s
% 7.78/2.32 % (16373)Instructions burned: 184 (million)
% 7.78/2.32 % (16373)------------------------------
% 7.78/2.32 % (16373)------------------------------
% 7.78/2.32 % (16375)Instruction limit reached!
% 7.78/2.32 % (16375)------------------------------
% 7.78/2.32 % (16375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.32 % (16375)Termination reason: Unknown
% 7.78/2.32 % (16375)Termination phase: Saturation
% 7.78/2.32
% 7.78/2.32 % (16375)Memory used [KB]: 2430
% 7.78/2.32 % (16375)Time elapsed: 0.042 s
% 7.78/2.32 % (16375)Instructions burned: 154 (million)
% 7.78/2.32 % (16375)------------------------------
% 7.78/2.32 % (16375)------------------------------
% 7.78/2.32 % (16374)Instruction limit reached!
% 7.78/2.32 % (16374)------------------------------
% 7.78/2.32 % (16374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.32 % (16374)Termination reason: Unknown
% 7.78/2.32 % (16374)Termination phase: Saturation
% 7.78/2.32
% 7.78/2.32 % (16374)Memory used [KB]: 7164
% 7.78/2.32 % (16374)Time elapsed: 0.058 s
% 7.78/2.32 % (16374)Instructions burned: 182 (million)
% 7.78/2.32 % (16374)------------------------------
% 7.78/2.32 % (16374)------------------------------
% 7.78/2.33 % (16378)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_16074 for (2991ds/114Mi)
% 7.78/2.33 % (16379)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_16074 for (2991ds/922Mi)
% 7.78/2.33 % (16380)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_16074 for (2991ds/182Mi)
% 7.78/2.33 % (16371)Instruction limit reached!
% 7.78/2.33 % (16371)------------------------------
% 7.78/2.33 % (16371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.33 % (16371)Termination reason: Unknown
% 7.78/2.33 % (16371)Termination phase: Saturation
% 7.78/2.33
% 7.78/2.33 % (16371)Memory used [KB]: 7036
% 7.78/2.33 % (16371)Time elapsed: 0.092 s
% 7.78/2.33 % (16371)Instructions burned: 297 (million)
% 7.78/2.33 % (16371)------------------------------
% 7.78/2.33 % (16371)------------------------------
% 7.78/2.34 % (16381)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_16074 for (2991ds/164Mi)
% 7.78/2.36 % (16369)Instruction limit reached!
% 7.78/2.36 % (16369)------------------------------
% 7.78/2.36 % (16369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.36 % (16369)Termination reason: Unknown
% 7.78/2.36 % (16369)Termination phase: Saturation
% 7.78/2.36
% 7.78/2.36 % (16369)Memory used [KB]: 7419
% 7.78/2.36 % (16369)Time elapsed: 0.142 s
% 7.78/2.36 % (16369)Instructions burned: 459 (million)
% 7.78/2.36 % (16369)------------------------------
% 7.78/2.36 % (16369)------------------------------
% 7.78/2.36 % (16378)Instruction limit reached!
% 7.78/2.36 % (16378)------------------------------
% 7.78/2.36 % (16378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.36 % (16378)Termination reason: Unknown
% 7.78/2.36 % (16378)Termination phase: Saturation
% 7.78/2.36
% 7.78/2.36 % (16378)Memory used [KB]: 6780
% 7.78/2.36 % (16378)Time elapsed: 0.035 s
% 7.78/2.36 % (16378)Instructions burned: 114 (million)
% 7.78/2.36 % (16378)------------------------------
% 7.78/2.36 % (16378)------------------------------
% 7.78/2.37 % (16382)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_16074 for (2991ds/50Mi)
% 7.78/2.37 % (16383)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_16074 for (2991ds/368Mi)
% 7.78/2.38 % (16377)Instruction limit reached!
% 7.78/2.38 % (16377)------------------------------
% 7.78/2.38 % (16377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.38 % (16377)Termination reason: Unknown
% 7.78/2.38 % (16377)Termination phase: Saturation
% 7.78/2.38
% 7.78/2.38 % (16377)Memory used [KB]: 7291
% 7.78/2.38 % (16377)Time elapsed: 0.064 s
% 7.78/2.38 % (16377)Instructions burned: 217 (million)
% 7.78/2.38 % (16377)------------------------------
% 7.78/2.38 % (16377)------------------------------
% 7.78/2.38 % (16380)Instruction limit reached!
% 7.78/2.38 % (16380)------------------------------
% 7.78/2.38 % (16380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.38 % (16380)Termination reason: Unknown
% 7.78/2.38 % (16380)Termination phase: Saturation
% 7.78/2.38
% 7.78/2.38 % (16380)Memory used [KB]: 6780
% 7.78/2.38 % (16380)Time elapsed: 0.051 s
% 7.78/2.38 % (16380)Instructions burned: 184 (million)
% 7.78/2.38 % (16380)------------------------------
% 7.78/2.38 % (16380)------------------------------
% 7.78/2.38 % (16382)Instruction limit reached!
% 7.78/2.38 % (16382)------------------------------
% 7.78/2.38 % (16382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.38 % (16382)Termination reason: Unknown
% 7.78/2.38 % (16382)Termination phase: Property scanning
% 7.78/2.38
% 7.78/2.38 % (16382)Memory used [KB]: 2046
% 7.78/2.38 % (16382)Time elapsed: 0.015 s
% 7.78/2.38 % (16382)Instructions burned: 53 (million)
% 7.78/2.38 % (16382)------------------------------
% 7.78/2.38 % (16382)------------------------------
% 7.78/2.39 % (16384)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_16074 for (2991ds/1021Mi)
% 7.78/2.39 % (16381)Instruction limit reached!
% 7.78/2.39 % (16381)------------------------------
% 7.78/2.39 % (16381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.39 % (16381)Termination reason: Unknown
% 7.78/2.39 % (16381)Termination phase: Saturation
% 7.78/2.39
% 7.78/2.39 % (16381)Memory used [KB]: 2430
% 7.78/2.39 % (16381)Time elapsed: 0.049 s
% 7.78/2.39 % (16381)Instructions burned: 165 (million)
% 7.78/2.39 % (16381)------------------------------
% 7.78/2.39 % (16381)------------------------------
% 7.78/2.39 % (16385)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_16074 for (2991ds/267Mi)
% 7.78/2.39 % (16386)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_16074 for (2991ds/204Mi)
% 8.50/2.40 % (16387)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_16074 for (2991ds/26Mi)
% 8.50/2.41 % (16387)Instruction limit reached!
% 8.50/2.41 % (16387)------------------------------
% 8.50/2.41 % (16387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.50/2.41 % (16387)Termination reason: Unknown
% 8.50/2.41 % (16387)Termination phase: shuffling
% 8.50/2.41
% 8.50/2.41 % (16387)Memory used [KB]: 1791
% 8.50/2.41 % (16387)Time elapsed: 0.008 s
% 8.50/2.41 % (16387)Instructions burned: 26 (million)
% 8.50/2.41 % (16387)------------------------------
% 8.50/2.41 % (16387)------------------------------
% 8.50/2.42 % (16388)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_16074 for (2991ds/53Mi)
% 8.50/2.43 % (16388)Instruction limit reached!
% 8.50/2.43 % (16388)------------------------------
% 8.50/2.43 % (16388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.50/2.43 % (16388)Termination reason: Unknown
% 8.50/2.43 % (16388)Termination phase: Property scanning
% 8.50/2.43
% 8.50/2.43 % (16388)Memory used [KB]: 2046
% 8.50/2.43 % (16388)Time elapsed: 0.016 s
% 8.50/2.43 % (16388)Instructions burned: 53 (million)
% 8.50/2.43 % (16388)------------------------------
% 8.50/2.43 % (16388)------------------------------
% 8.50/2.44 % (16389)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_16074 for (2990ds/4436Mi)
% 8.50/2.46 % (16386)Instruction limit reached!
% 8.50/2.46 % (16386)------------------------------
% 8.50/2.46 % (16386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.50/2.46 % (16386)Termination reason: Unknown
% 8.50/2.46 % (16386)Termination phase: Saturation
% 8.50/2.46
% 8.50/2.46 % (16386)Memory used [KB]: 7164
% 8.50/2.46 % (16386)Time elapsed: 0.064 s
% 8.50/2.46 % (16386)Instructions burned: 204 (million)
% 8.50/2.46 % (16386)------------------------------
% 8.50/2.46 % (16386)------------------------------
% 8.50/2.47 % (16390)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_16074 for (2990ds/1539Mi)
% 8.50/2.47 % (16385)Instruction limit reached!
% 8.50/2.47 % (16385)------------------------------
% 8.50/2.47 % (16385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.50/2.47 % (16385)Termination reason: Unknown
% 8.50/2.47 % (16385)Termination phase: Saturation
% 8.50/2.47
% 8.50/2.47 % (16385)Memory used [KB]: 7291
% 8.50/2.47 % (16385)Time elapsed: 0.082 s
% 8.50/2.47 % (16385)Instructions burned: 267 (million)
% 8.50/2.47 % (16385)------------------------------
% 8.50/2.47 % (16385)------------------------------
% 8.50/2.48 % (16391)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_16074 for (2990ds/408Mi)
% 8.50/2.49 % (16383)Instruction limit reached!
% 8.50/2.49 % (16383)------------------------------
% 8.50/2.49 % (16383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.50/2.49 % (16383)Termination reason: Unknown
% 8.50/2.49 % (16383)Termination phase: Saturation
% 8.50/2.49
% 8.50/2.49 % (16383)Memory used [KB]: 8059
% 8.50/2.49 % (16383)Time elapsed: 0.121 s
% 8.50/2.49 % (16383)Instructions burned: 370 (million)
% 8.50/2.49 % (16383)------------------------------
% 8.50/2.49 % (16383)------------------------------
% 8.83/2.50 % (16392)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_16074 for (2990ds/5205Mi)
% 8.83/2.57 % (16372)Instruction limit reached!
% 8.83/2.57 % (16372)------------------------------
% 8.83/2.57 % (16372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.57 % (16372)Termination reason: Unknown
% 8.83/2.57 % (16372)Termination phase: Saturation
% 8.83/2.57
% 8.83/2.57 % (16372)Memory used [KB]: 8827
% 8.83/2.57 % (16372)Time elapsed: 0.312 s
% 8.83/2.57 % (16372)Instructions burned: 988 (million)
% 8.83/2.57 % (16372)------------------------------
% 8.83/2.57 % (16372)------------------------------
% 8.83/2.58 % (16393)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_16074 for (2989ds/1913Mi)
% 9.18/2.61 % (16391)Instruction limit reached!
% 9.18/2.61 % (16391)------------------------------
% 9.18/2.61 % (16391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.61 % (16391)Termination reason: Unknown
% 9.18/2.61 % (16391)Termination phase: Saturation
% 9.18/2.61
% 9.18/2.61 % (16391)Memory used [KB]: 7803
% 9.18/2.61 % (16391)Time elapsed: 0.126 s
% 9.18/2.61 % (16391)Instructions burned: 409 (million)
% 9.18/2.61 % (16391)------------------------------
% 9.18/2.61 % (16391)------------------------------
% 9.18/2.62 % (16394)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_16074 for (2989ds/4350Mi)
% 9.18/2.63 % (16379)Instruction limit reached!
% 9.18/2.63 % (16379)------------------------------
% 9.18/2.63 % (16379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.63 % (16379)Termination reason: Unknown
% 9.18/2.63 % (16379)Termination phase: Saturation
% 9.18/2.63
% 9.18/2.63 % (16379)Memory used [KB]: 7931
% 9.18/2.63 % (16379)Time elapsed: 0.302 s
% 9.18/2.63 % (16379)Instructions burned: 922 (million)
% 9.18/2.63 % (16379)------------------------------
% 9.18/2.63 % (16379)------------------------------
% 9.18/2.64 % (16395)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_16074 for (2988ds/68Mi)
% 9.18/2.66 % (16395)Instruction limit reached!
% 9.18/2.66 % (16395)------------------------------
% 9.18/2.66 % (16395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.66 % (16395)Termination reason: Unknown
% 9.18/2.66 % (16395)Termination phase: Saturation
% 9.18/2.66
% 9.18/2.66 % (16395)Memory used [KB]: 1918
% 9.18/2.66 % (16395)Time elapsed: 0.022 s
% 9.18/2.66 % (16395)Instructions burned: 70 (million)
% 9.18/2.66 % (16395)------------------------------
% 9.18/2.66 % (16395)------------------------------
% 9.18/2.67 % (16396)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_16074 for (2988ds/358Mi)
% 9.66/2.72 % (16384)Instruction limit reached!
% 9.66/2.72 % (16384)------------------------------
% 9.66/2.72 % (16384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.72 % (16384)Termination reason: Unknown
% 9.66/2.72 % (16384)Termination phase: Saturation
% 9.66/2.72
% 9.66/2.72 % (16384)Memory used [KB]: 8699
% 9.66/2.72 % (16384)Time elapsed: 0.330 s
% 9.66/2.72 % (16384)Instructions burned: 1023 (million)
% 9.66/2.72 % (16384)------------------------------
% 9.66/2.72 % (16384)------------------------------
% 9.66/2.73 % (16397)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_16074 for (2988ds/31Mi)
% 9.66/2.74 % (16397)Instruction limit reached!
% 9.66/2.74 % (16397)------------------------------
% 9.66/2.74 % (16397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.74 % (16397)Termination reason: Unknown
% 9.66/2.74 % (16397)Termination phase: Unused predicate definition removal
% 9.66/2.74
% 9.66/2.74 % (16397)Memory used [KB]: 1791
% 9.66/2.74 % (16397)Time elapsed: 0.011 s
% 9.66/2.74 % (16397)Instructions burned: 33 (million)
% 9.66/2.74 % (16397)------------------------------
% 9.66/2.74 % (16397)------------------------------
% 9.66/2.75 % (16398)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_16074 for (2987ds/279Mi)
% 9.66/2.78 % (16396)Instruction limit reached!
% 9.66/2.78 % (16396)------------------------------
% 9.66/2.78 % (16396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.78 % (16396)Termination reason: Unknown
% 9.66/2.78 % (16396)Termination phase: Saturation
% 9.66/2.78
% 9.66/2.78 % (16396)Memory used [KB]: 7419
% 9.66/2.78 % (16396)Time elapsed: 0.116 s
% 9.66/2.78 % (16396)Instructions burned: 360 (million)
% 9.66/2.78 % (16396)------------------------------
% 9.66/2.78 % (16396)------------------------------
% 9.66/2.79 % (16399)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_16074 for (2987ds/258Mi)
% 10.13/2.83 % (16398)Instruction limit reached!
% 10.13/2.83 % (16398)------------------------------
% 10.13/2.83 % (16398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.83 % (16398)Termination reason: Unknown
% 10.13/2.83 % (16398)Termination phase: Saturation
% 10.13/2.83
% 10.13/2.83 % (16398)Memory used [KB]: 7547
% 10.13/2.83 % (16398)Time elapsed: 0.085 s
% 10.13/2.83 % (16398)Instructions burned: 280 (million)
% 10.13/2.83 % (16398)------------------------------
% 10.13/2.83 % (16398)------------------------------
% 10.13/2.84 % (16400)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_16074 for (2986ds/26Mi)
% 10.13/2.85 % (16400)Instruction limit reached!
% 10.13/2.85 % (16400)------------------------------
% 10.13/2.85 % (16400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.85 % (16400)Termination reason: Unknown
% 10.13/2.85 % (16400)Termination phase: shuffling
% 10.13/2.85
% 10.13/2.85 % (16400)Memory used [KB]: 1791
% 10.13/2.85 % (16400)Time elapsed: 0.009 s
% 10.13/2.85 % (16400)Instructions burned: 27 (million)
% 10.13/2.85 % (16400)------------------------------
% 10.13/2.85 % (16400)------------------------------
% 10.13/2.86 % (16401)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_16074 for (2986ds/995Mi)
% 10.13/2.87 % (16399)Instruction limit reached!
% 10.13/2.87 % (16399)------------------------------
% 10.13/2.87 % (16399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.87 % (16399)Termination reason: Unknown
% 10.13/2.87 % (16399)Termination phase: Saturation
% 10.13/2.87
% 10.13/2.87 % (16399)Memory used [KB]: 7291
% 10.13/2.87 % (16399)Time elapsed: 0.080 s
% 10.13/2.87 % (16399)Instructions burned: 260 (million)
% 10.13/2.87 % (16399)------------------------------
% 10.13/2.87 % (16399)------------------------------
% 10.13/2.88 % (16402)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_16074 for (2986ds/373Mi)
% 10.34/2.96 % (16390)Instruction limit reached!
% 10.34/2.96 % (16390)------------------------------
% 10.34/2.96 % (16390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.34/2.96 % (16390)Termination reason: Unknown
% 10.34/2.96 % (16390)Termination phase: Saturation
% 10.34/2.96
% 10.34/2.96 % (16390)Memory used [KB]: 10106
% 10.34/2.96 % (16390)Time elapsed: 0.491 s
% 10.34/2.96 % (16390)Instructions burned: 1542 (million)
% 10.34/2.96 % (16390)------------------------------
% 10.34/2.96 % (16390)------------------------------
% 10.34/2.97 % (16403)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_16074 for (2985ds/253Mi)
% 10.34/3.00 % (16402)Instruction limit reached!
% 10.34/3.00 % (16402)------------------------------
% 10.34/3.00 % (16402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.34/3.00 % (16402)Termination reason: Unknown
% 10.34/3.00 % (16402)Termination phase: Saturation
% 10.34/3.00
% 10.34/3.00 % (16402)Memory used [KB]: 7547
% 10.34/3.00 % (16402)Time elapsed: 0.119 s
% 10.34/3.00 % (16402)Instructions burned: 373 (million)
% 10.34/3.00 % (16402)------------------------------
% 10.34/3.00 % (16402)------------------------------
% 10.34/3.01 % (16404)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_16074 for (2985ds/832Mi)
% 13.14/3.04 % (16403)Instruction limit reached!
% 13.14/3.04 % (16403)------------------------------
% 13.14/3.04 % (16403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.14/3.04 % (16403)Termination reason: Unknown
% 13.14/3.04 % (16403)Termination phase: Saturation
% 13.14/3.04
% 13.14/3.04 % (16403)Memory used [KB]: 7164
% 13.14/3.04 % (16403)Time elapsed: 0.072 s
% 13.14/3.04 % (16403)Instructions burned: 254 (million)
% 13.14/3.04 % (16403)------------------------------
% 13.14/3.04 % (16403)------------------------------
% 13.14/3.05 % (16405)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_16074 for (2984ds/668Mi)
% 13.14/3.12 % (16393)Instruction limit reached!
% 13.14/3.12 % (16393)------------------------------
% 13.14/3.12 % (16393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.14/3.12 % (16393)Termination reason: Unknown
% 13.14/3.12 % (16393)Termination phase: Saturation
% 13.14/3.12
% 13.14/3.12 % (16393)Memory used [KB]: 3709
% 13.14/3.12 % (16393)Time elapsed: 0.544 s
% 13.14/3.12 % (16393)Instructions burned: 1917 (million)
% 13.14/3.12 % (16393)------------------------------
% 13.14/3.12 % (16393)------------------------------
% 13.68/3.13 % (16406)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_16074 for (2983ds/40Mi)
% 13.68/3.14 % (16406)Instruction limit reached!
% 13.68/3.14 % (16406)------------------------------
% 13.68/3.14 % (16406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.14 % (16406)Termination reason: Unknown
% 13.68/3.14 % (16406)Termination phase: Property scanning
% 13.68/3.14
% 13.68/3.14 % (16406)Memory used [KB]: 2046
% 13.68/3.14 % (16406)Time elapsed: 0.012 s
% 13.68/3.14 % (16406)Instructions burned: 40 (million)
% 13.68/3.14 % (16406)------------------------------
% 13.68/3.14 % (16406)------------------------------
% 13.68/3.15 % (16407)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_16074 for (2983ds/294Mi)
% 13.68/3.16 % (16401)Instruction limit reached!
% 13.68/3.16 % (16401)------------------------------
% 13.68/3.16 % (16401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.16 % (16401)Termination reason: Unknown
% 13.68/3.16 % (16401)Termination phase: Saturation
% 13.68/3.16
% 13.68/3.16 % (16401)Memory used [KB]: 9083
% 13.68/3.16 % (16401)Time elapsed: 0.304 s
% 13.68/3.16 % (16401)Instructions burned: 997 (million)
% 13.68/3.16 % (16401)------------------------------
% 13.68/3.16 % (16401)------------------------------
% 13.68/3.17 % (16408)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_16074 for (2983ds/187Mi)
% 13.98/3.23 % (16408)Instruction limit reached!
% 13.98/3.23 % (16408)------------------------------
% 13.98/3.23 % (16408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/3.23 % (16408)Termination reason: Unknown
% 13.98/3.23 % (16408)Termination phase: Saturation
% 13.98/3.23
% 13.98/3.23 % (16408)Memory used [KB]: 7164
% 13.98/3.23 % (16408)Time elapsed: 0.061 s
% 13.98/3.23 % (16408)Instructions burned: 188 (million)
% 13.98/3.23 % (16408)------------------------------
% 13.98/3.23 % (16408)------------------------------
% 13.98/3.24 % (16407)Instruction limit reached!
% 13.98/3.24 % (16407)------------------------------
% 13.98/3.24 % (16407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/3.24 % (16407)Termination reason: Unknown
% 13.98/3.24 % (16407)Termination phase: Saturation
% 13.98/3.24
% 13.98/3.24 % (16407)Memory used [KB]: 7164
% 13.98/3.24 % (16407)Time elapsed: 0.088 s
% 13.98/3.24 % (16407)Instructions burned: 294 (million)
% 13.98/3.24 % (16407)------------------------------
% 13.98/3.24 % (16407)------------------------------
% 13.98/3.24 % (16409)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_16074 for (2982ds/371Mi)
% 13.98/3.25 % (16410)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_16074 for (2982ds/1827Mi)
% 13.98/3.25 % (16405)Instruction limit reached!
% 13.98/3.25 % (16405)------------------------------
% 13.98/3.25 % (16405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/3.25 % (16405)Termination reason: Unknown
% 13.98/3.25 % (16405)Termination phase: Saturation
% 13.98/3.25
% 13.98/3.25 % (16405)Memory used [KB]: 13176
% 13.98/3.25 % (16405)Time elapsed: 0.206 s
% 13.98/3.25 % (16405)Instructions burned: 668 (million)
% 13.98/3.25 % (16405)------------------------------
% 13.98/3.25 % (16405)------------------------------
% 13.98/3.26 % (16411)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_16074 for (2982ds/70Mi)
% 13.98/3.27 % (16404)Instruction limit reached!
% 13.98/3.27 % (16404)------------------------------
% 13.98/3.27 % (16404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/3.27 % (16404)Termination reason: Unknown
% 13.98/3.27 % (16404)Termination phase: Saturation
% 13.98/3.27
% 13.98/3.27 % (16404)Memory used [KB]: 7675
% 13.98/3.27 % (16404)Time elapsed: 0.259 s
% 13.98/3.27 % (16404)Instructions burned: 834 (million)
% 13.98/3.27 % (16404)------------------------------
% 13.98/3.27 % (16404)------------------------------
% 13.98/3.28 % (16412)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_16074 for (2982ds/316Mi)
% 13.98/3.28 % (16411)Instruction limit reached!
% 13.98/3.28 % (16411)------------------------------
% 13.98/3.28 % (16411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/3.28 % (16411)Termination reason: Unknown
% 13.98/3.28 % (16411)Termination phase: Property scanning
% 13.98/3.28
% 13.98/3.28 % (16411)Memory used [KB]: 2174
% 13.98/3.28 % (16411)Time elapsed: 0.020 s
% 13.98/3.28 % (16411)Instructions burned: 72 (million)
% 13.98/3.28 % (16411)------------------------------
% 13.98/3.28 % (16411)------------------------------
% 13.98/3.29 % (16413)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_16074 for (2982ds/932Mi)
% 14.96/3.35 % (16409)Instruction limit reached!
% 14.96/3.35 % (16409)------------------------------
% 14.96/3.35 % (16409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.96/3.35 % (16409)Termination reason: Unknown
% 14.96/3.35 % (16409)Termination phase: Saturation
% 14.96/3.35
% 14.96/3.35 % (16409)Memory used [KB]: 7164
% 14.96/3.35 % (16409)Time elapsed: 0.116 s
% 14.96/3.35 % (16409)Instructions burned: 373 (million)
% 14.96/3.35 % (16409)------------------------------
% 14.96/3.35 % (16409)------------------------------
% 14.96/3.36 % (16414)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_16074 for (2981ds/4714Mi)
% 14.96/3.37 % (16412)Instruction limit reached!
% 14.96/3.37 % (16412)------------------------------
% 14.96/3.37 % (16412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.96/3.37 % (16412)Termination reason: Unknown
% 14.96/3.37 % (16412)Termination phase: Saturation
% 14.96/3.37
% 14.96/3.37 % (16412)Memory used [KB]: 7675
% 14.96/3.37 % (16412)Time elapsed: 0.094 s
% 14.96/3.37 % (16412)Instructions burned: 317 (million)
% 14.96/3.37 % (16412)------------------------------
% 14.96/3.37 % (16412)------------------------------
% 14.96/3.38 % (16415)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_16074 for (2981ds/8250Mi)
% 15.48/3.48 % (16415)First to succeed.
% 15.48/3.49 % (16415)Refutation found. Thanks to Tanya!
% 15.48/3.49 % SZS status Theorem for DTF2THF_16074
% 15.48/3.49 % SZS output start Proof for DTF2THF_16074
% 15.48/3.49 thf(type_def_5, type, extended_ereal: $tType).
% 15.48/3.49 thf(type_def_6, type, real: $tType).
% 15.48/3.49 thf(type_def_8, type, set: ($tType) > $tType).
% 15.48/3.49 thf(type_def_9, type, a: $tType).
% 15.48/3.49 thf(func_def_0, type, extended_ereal: $tType).
% 15.48/3.49 thf(func_def_1, type, real: $tType).
% 15.48/3.49 thf(func_def_2, type, set: ($tType) > $tType).
% 15.48/3.49 thf(func_def_3, type, a: $tType).
% 15.48/3.49 thf(func_def_4, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_5, type, type: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_6, type, idom: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_7, type, ring: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_8, type, zero: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_9, type, field: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_10, type, uminus: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_11, type, ord: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_12, type, order: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_13, type, mult_zero: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_14, type, group_add: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_15, type, no_bot: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_16, type, no_top: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_17, type, linorder: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_18, type, preorder: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_19, type, wellorder: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_20, type, division_ring: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_21, type, semidom_divide: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_22, type, semigroup_mult: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_23, type, dense_order: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_24, type, linordered_idom: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_25, type, linordered_ring: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_26, type, linordered_field: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_27, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_28, type, boolean_algebra: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_29, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_30, type, topological_t0_space: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_31, type, topological_t1_space: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_32, type, linord581940658strict: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_33, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_34, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_35, type, linord20386208strict: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_36, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_37, type, topolo2133971006pology: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_38, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_39, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_40, type, linord893533164strict: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_41, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_42, type, euclid24285859cancel: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_43, type, euclid191655569cancel: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_44, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 15.48/3.49 thf(func_def_45, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 15.48/3.49 thf(func_def_46, type, extended_MInfty: extended_ereal).
% 15.48/3.49 thf(func_def_47, type, extended_PInfty: extended_ereal).
% 15.48/3.49 thf(func_def_48, type, extended_rec_ereal: !>[X0: $tType]:((real > X0) > X0 > X0 > extended_ereal > X0)).
% 15.48/3.49 thf(func_def_49, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.48/3.49 thf(func_def_50, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_51, type, zero_zero: !>[X0: $tType]:(X0)).
% 15.48/3.49 thf(func_def_52, type, lower_582600101lsc_at: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1) > $o)).
% 15.48/3.49 thf(func_def_53, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 15.48/3.49 thf(func_def_54, type, divide_divide: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.48/3.49 thf(func_def_55, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 15.48/3.49 thf(func_def_56, type, topolo1751647064n_open: !>[X0: $tType]:(set @ X0 > $o)).
% 15.48/3.49 thf(func_def_57, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 15.48/3.49 thf(func_def_58, type, f: a > extended_ereal).
% 15.48/3.49 thf(func_def_59, type, x0: a).
% 15.48/3.49 thf(func_def_72, type, sP0: extended_ereal > extended_ereal > $o).
% 15.48/3.49 thf(func_def_73, type, sP1: extended_ereal > extended_ereal > $o).
% 15.48/3.49 thf(func_def_74, type, sP2: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 15.48/3.49 thf(func_def_75, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 15.48/3.49 thf(func_def_76, type, sP4: extended_ereal > extended_ereal > $o).
% 15.48/3.49 thf(func_def_77, type, sP5: extended_ereal > extended_ereal > $o).
% 15.48/3.49 thf(func_def_78, type, sP6: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 15.48/3.49 thf(func_def_79, type, sP7: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 15.48/3.49 thf(func_def_80, type, sP8: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 15.48/3.49 thf(func_def_81, type, sK9: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_82, type, sK10: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.48/3.49 thf(func_def_83, type, sK11: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.48/3.49 thf(func_def_84, type, sK12: extended_ereal).
% 15.48/3.49 thf(func_def_85, type, sK13: set @ a > a).
% 15.48/3.49 thf(func_def_86, type, sK14: extended_ereal > set @ a).
% 15.48/3.49 thf(func_def_87, type, sK15: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_88, type, sK16: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 15.48/3.49 thf(func_def_89, type, sK17: extended_ereal > set @ a).
% 15.48/3.49 thf(func_def_90, type, sK18: extended_ereal).
% 15.48/3.49 thf(func_def_91, type, sK19: set @ a > a).
% 15.48/3.49 thf(func_def_92, type, sK20: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_93, type, sK21: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_94, type, sK22: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_95, type, sK23: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_96, type, sK24: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_97, type, sK25: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_98, type, sK26: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_99, type, sK27: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_100, type, sK28: !>[X0: $tType, X1: $tType]:(X1 > X0)).
% 15.48/3.49 thf(func_def_101, type, sK29: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 15.48/3.49 thf(func_def_102, type, sK30: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_103, type, sK31: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_104, type, sK32: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 15.48/3.49 thf(func_def_105, type, sK33: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_106, type, sK34: extended_ereal > set @ a).
% 15.48/3.49 thf(func_def_107, type, sK35: extended_ereal).
% 15.48/3.49 thf(func_def_108, type, sK36: set @ a > a).
% 15.48/3.49 thf(func_def_109, type, sK37: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_110, type, sK38: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_111, type, sK39: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_112, type, sK40: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.48/3.49 thf(func_def_113, type, sK41: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.48/3.49 thf(func_def_114, type, sK42: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_115, type, sK43: !>[X0: $tType, X1: $tType]:(X1 > X0)).
% 15.48/3.49 thf(func_def_116, type, sK44: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_117, type, sK45: !>[X0: $tType]:((X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_118, type, sK46: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_119, type, sK47: extended_ereal).
% 15.48/3.49 thf(func_def_120, type, sK48: set @ a > a).
% 15.48/3.49 thf(func_def_121, type, sK49: extended_ereal > set @ a).
% 15.48/3.49 thf(func_def_122, type, sK50: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.48/3.49 thf(func_def_123, type, sK51: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.48/3.49 thf(func_def_124, type, sK52: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_125, type, sK53: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.48/3.49 thf(func_def_126, type, sK54: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.48/3.49 thf(func_def_127, type, sK55: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.48/3.49 thf(func_def_128, type, sK56: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_129, type, sK57: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_130, type, sK58: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_131, type, sK59: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_132, type, sK60: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_133, type, sK61: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_134, type, sK62: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 15.48/3.49 thf(func_def_135, type, sK63: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.48/3.49 thf(func_def_136, type, sK64: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_137, type, sK65: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_138, type, sK66: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_139, type, sK67: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 15.48/3.49 thf(func_def_140, type, sK68: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.48/3.49 thf(func_def_141, type, sK69: !>[X0: $tType]:(X0 > X0)).
% 15.48/3.49 thf(func_def_143, type, ph71: !>[X0: $tType]:(X0)).
% 15.48/3.49 thf(f2952,plain,(
% 15.48/3.49 $false),
% 15.48/3.49 inference(avatar_sat_refutation,[status(thm)],[f2107,f2115,f2119,f2123,f2127,f2131,f2136,f2140,f2144,f2148,f2152,f2157,f2161,f2165,f2177,f2181,f2185,f2199,f2203,f2207,f2212,f2476,f2489,f2703,f2718,f2824,f2951])).
% 15.48/3.49 thf(f2951,plain,(
% 15.48/3.49 ~spl70_1 | ~spl70_7 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18),
% 15.48/3.49 inference(avatar_contradiction_clause,[status(thm)],[f2950])).
% 15.48/3.49 thf(f2950,plain,(
% 15.48/3.49 $false | (~spl70_1 | ~spl70_7 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2949,f2864])).
% 15.48/3.49 thf(f2864,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK17 @ sK47)) = $true) | (~spl70_1 | ~spl70_8 | ~spl70_11)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2854])).
% 15.48/3.49 thf(f2854,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK17 @ sK47)) = $true) | ($true != $true) | (~spl70_1 | ~spl70_8 | ~spl70_11)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2740,f2826])).
% 15.48/3.49 thf(f2826,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK47 @ extended_PInfty) = $true) | (~spl70_1 | ~spl70_11)),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2135,f2728])).
% 15.48/3.49 thf(f2728,plain,(
% 15.48/3.49 ((f @ x0) = extended_PInfty) | ~spl70_1),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2095,f1414])).
% 15.48/3.49 thf(f1414,plain,(
% 15.48/3.49 (extend1396239628finity @ extended_ereal = extended_PInfty)),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f88])).
% 15.48/3.49 thf(f88,axiom,(
% 15.48/3.49 (extend1396239628finity @ extended_ereal = extended_PInfty)),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',fact_87_infinity__ereal__def)).
% 15.48/3.49 thf(f2095,plain,(
% 15.48/3.49 ((f @ x0) = extend1396239628finity @ extended_ereal) | ~spl70_1),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2093])).
% 15.48/3.49 thf(f2093,definition,(
% 15.48/3.49 spl70_1 <=> ((f @ x0) = extend1396239628finity @ extended_ereal)),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_1])],[avatar_definition])).
% 15.48/3.49 thf(f2135,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK47 @ (f @ x0)) = $true) | ~spl70_11),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2133])).
% 15.48/3.49 thf(f2133,definition,(
% 15.48/3.49 spl70_11 <=> ((ord_less @ extended_ereal @ sK47 @ (f @ x0)) = $true)),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_11])],[avatar_definition])).
% 15.48/3.49 thf(f2740,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ extended_PInfty) != $true) | ((member @ a @ x0 @ (sK17 @ X0)) = $true)) ) | (~spl70_1 | ~spl70_8)),
% 15.48/3.49 inference(backward_demodulation,[status(thm)],[f2122,f2728])).
% 15.48/3.49 thf(f2122,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((member @ a @ x0 @ (sK17 @ X0)) = $true)) ) | ~spl70_8),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2121])).
% 15.48/3.49 thf(f2121,definition,(
% 15.48/3.49 spl70_8 <=> ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((member @ a @ x0 @ (sK17 @ X0)) = $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_8])],[avatar_definition])).
% 15.48/3.49 thf(f2949,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK17 @ sK47)) != $true) | (~spl70_1 | ~spl70_7 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2948,f2862])).
% 15.48/3.49 thf(f2862,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK17 @ sK47)) = $true) | (~spl70_1 | ~spl70_11 | ~spl70_18)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2856])).
% 15.48/3.49 thf(f2856,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK17 @ sK47)) = $true) | ($true != $true) | (~spl70_1 | ~spl70_11 | ~spl70_18)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2743,f2826])).
% 15.48/3.49 thf(f2743,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ extended_PInfty) != $true) | ((topolo1751647064n_open @ a @ (sK17 @ X0)) = $true)) ) | (~spl70_1 | ~spl70_18)),
% 15.48/3.49 inference(backward_demodulation,[status(thm)],[f2164,f2728])).
% 15.48/3.49 thf(f2164,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((topolo1751647064n_open @ a @ (sK17 @ X0)) = $true)) ) | ~spl70_18),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2163])).
% 15.48/3.49 thf(f2163,definition,(
% 15.48/3.49 spl70_18 <=> ! [X0 : extended_ereal] : (((topolo1751647064n_open @ a @ (sK17 @ X0)) = $true) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_18])],[avatar_definition])).
% 15.48/3.49 thf(f2948,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK17 @ sK47)) != $true) | ((member @ a @ x0 @ (sK17 @ sK47)) != $true) | (~spl70_1 | ~spl70_7 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2947])).
% 15.48/3.49 thf(f2947,plain,(
% 15.48/3.49 ($true != $true) | ((topolo1751647064n_open @ a @ (sK17 @ sK47)) != $true) | ((member @ a @ x0 @ (sK17 @ sK47)) != $true) | (~spl70_1 | ~spl70_7 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2118,f2946])).
% 15.48/3.49 thf(f2946,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ (sK17 @ sK47)))) = $true) | (~spl70_1 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2945,f2826])).
% 15.48/3.49 thf(f2945,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ (sK17 @ sK47)))) = $true) | ((ord_less @ extended_ereal @ sK47 @ extended_PInfty) != $true) | (~spl70_1 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2944])).
% 15.48/3.49 thf(f2944,plain,(
% 15.48/3.49 ($true != $true) | ((ord_less @ extended_ereal @ sK47 @ extended_PInfty) != $true) | ((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ (sK17 @ sK47)))) = $true) | (~spl70_1 | ~spl70_8 | ~spl70_11 | ~spl70_12 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2825,f2889])).
% 15.48/3.49 thf(f2889,plain,(
% 15.48/3.49 ((member @ a @ (sK48 @ (sK17 @ sK47)) @ (sK17 @ sK47)) = $true) | (~spl70_1 | ~spl70_8 | ~spl70_11 | ~spl70_13 | ~spl70_18)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2886,f2862])).
% 15.48/3.49 thf(f2886,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK17 @ sK47)) != $true) | ((member @ a @ (sK48 @ (sK17 @ sK47)) @ (sK17 @ sK47)) = $true) | (~spl70_1 | ~spl70_8 | ~spl70_11 | ~spl70_13)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2881])).
% 15.48/3.49 thf(f2881,plain,(
% 15.48/3.49 ($true != $true) | ((member @ a @ (sK48 @ (sK17 @ sK47)) @ (sK17 @ sK47)) = $true) | ((topolo1751647064n_open @ a @ (sK17 @ sK47)) != $true) | (~spl70_1 | ~spl70_8 | ~spl70_11 | ~spl70_13)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2143,f2864])).
% 15.48/3.49 thf(f2143,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((member @ a @ x0 @ X1) != $true) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ (sK48 @ X1) @ X1) = $true)) ) | ~spl70_13),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2142])).
% 15.48/3.49 thf(f2142,definition,(
% 15.48/3.49 spl70_13 <=> ! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ (sK48 @ X1) @ X1) = $true) | ((member @ a @ x0 @ X1) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_13])],[avatar_definition])).
% 15.48/3.49 thf(f2825,plain,(
% 15.48/3.49 ( ! [X2 : a,X0 : extended_ereal] : (((member @ a @ X2 @ (sK17 @ X0)) != $true) | ((ord_less @ extended_ereal @ X0 @ extended_PInfty) != $true) | ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true)) ) | (~spl70_1 | ~spl70_12)),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2139,f2728])).
% 15.48/3.49 thf(f2139,plain,(
% 15.48/3.49 ( ! [X2 : a,X0 : extended_ereal] : (((member @ a @ X2 @ (sK17 @ X0)) != $true) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true)) ) | ~spl70_12),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2138])).
% 15.48/3.49 thf(f2138,definition,(
% 15.48/3.49 spl70_12 <=> ! [X2 : a,X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((member @ a @ X2 @ (sK17 @ X0)) != $true) | ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_12])],[avatar_definition])).
% 15.48/3.49 thf(f2118,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ X1))) != $true) | ((member @ a @ x0 @ X1) != $true) | ((topolo1751647064n_open @ a @ X1) != $true)) ) | ~spl70_7),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2117])).
% 15.48/3.49 thf(f2117,definition,(
% 15.48/3.49 spl70_7 <=> ! [X1 : set @ a] : (((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ X1))) != $true) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_7])],[avatar_definition])).
% 15.48/3.49 thf(f2824,plain,(
% 15.48/3.49 ~spl70_1 | ~spl70_9 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26),
% 15.48/3.49 inference(avatar_contradiction_clause,[status(thm)],[f2823])).
% 15.48/3.49 thf(f2823,plain,(
% 15.48/3.49 $false | (~spl70_1 | ~spl70_9 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2822,f2795])).
% 15.48/3.49 thf(f2795,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK49 @ sK18)) = $true) | (~spl70_1 | ~spl70_15 | ~spl70_16)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2792])).
% 15.48/3.49 thf(f2792,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK49 @ sK18)) = $true) | ($true != $true) | (~spl70_1 | ~spl70_15 | ~spl70_16)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2789,f2741])).
% 15.48/3.49 thf(f2741,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ extended_PInfty) = $true) | (~spl70_1 | ~spl70_16)),
% 15.48/3.49 inference(backward_demodulation,[status(thm)],[f2156,f2728])).
% 15.48/3.49 thf(f2156,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) = $true) | ~spl70_16),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2154])).
% 15.48/3.49 thf(f2154,definition,(
% 15.48/3.49 spl70_16 <=> ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) = $true)),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_16])],[avatar_definition])).
% 15.48/3.49 thf(f2789,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ extended_PInfty) != $true) | ((member @ a @ x0 @ (sK49 @ X3)) = $true)) ) | (~spl70_1 | ~spl70_15)),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2151,f2728])).
% 15.48/3.49 thf(f2151,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((member @ a @ x0 @ (sK49 @ X3)) = $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) ) | ~spl70_15),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2150])).
% 15.48/3.49 thf(f2150,definition,(
% 15.48/3.49 spl70_15 <=> ! [X3 : extended_ereal] : (((member @ a @ x0 @ (sK49 @ X3)) = $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_15])],[avatar_definition])).
% 15.48/3.49 thf(f2822,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK49 @ sK18)) != $true) | (~spl70_1 | ~spl70_9 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2821,f2776])).
% 15.48/3.49 thf(f2776,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK49 @ sK18)) = $true) | (~spl70_1 | ~spl70_16 | ~spl70_26)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2773])).
% 15.48/3.49 thf(f2773,plain,(
% 15.48/3.49 ($true != $true) | ((topolo1751647064n_open @ a @ (sK49 @ sK18)) = $true) | (~spl70_1 | ~spl70_16 | ~spl70_26)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2770,f2741])).
% 15.48/3.49 thf(f2770,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ extended_PInfty) != $true) | ((topolo1751647064n_open @ a @ (sK49 @ X3)) = $true)) ) | (~spl70_1 | ~spl70_26)),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2198,f2728])).
% 15.48/3.49 thf(f2198,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((topolo1751647064n_open @ a @ (sK49 @ X3)) = $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) ) | ~spl70_26),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2197])).
% 15.48/3.49 thf(f2197,definition,(
% 15.48/3.49 spl70_26 <=> ! [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((topolo1751647064n_open @ a @ (sK49 @ X3)) = $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_26])],[avatar_definition])).
% 15.48/3.49 thf(f2821,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK49 @ sK18)) != $true) | ((member @ a @ x0 @ (sK49 @ sK18)) != $true) | (~spl70_1 | ~spl70_9 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2820])).
% 15.48/3.49 thf(f2820,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK49 @ sK18)) != $true) | ((member @ a @ x0 @ (sK49 @ sK18)) != $true) | ($true != $true) | (~spl70_1 | ~spl70_9 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2126,f2819])).
% 15.48/3.49 thf(f2819,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK49 @ sK18)))) = $true) | (~spl70_1 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2813,f2741])).
% 15.48/3.49 thf(f2813,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK49 @ sK18)))) = $true) | ((ord_less @ extended_ereal @ sK18 @ extended_PInfty) != $true) | (~spl70_1 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2812])).
% 15.48/3.49 thf(f2812,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ extended_PInfty) != $true) | ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK49 @ sK18)))) = $true) | ($true != $true) | (~spl70_1 | ~spl70_14 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2809,f2803])).
% 15.48/3.49 thf(f2803,plain,(
% 15.48/3.49 ((member @ a @ (sK19 @ (sK49 @ sK18)) @ (sK49 @ sK18)) = $true) | (~spl70_1 | ~spl70_15 | ~spl70_16 | ~spl70_23 | ~spl70_26)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2800,f2776])).
% 15.48/3.49 thf(f2800,plain,(
% 15.48/3.49 ((member @ a @ (sK19 @ (sK49 @ sK18)) @ (sK49 @ sK18)) = $true) | ((topolo1751647064n_open @ a @ (sK49 @ sK18)) != $true) | (~spl70_1 | ~spl70_15 | ~spl70_16 | ~spl70_23)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2797])).
% 15.48/3.49 thf(f2797,plain,(
% 15.48/3.49 ((member @ a @ (sK19 @ (sK49 @ sK18)) @ (sK49 @ sK18)) = $true) | ($true != $true) | ((topolo1751647064n_open @ a @ (sK49 @ sK18)) != $true) | (~spl70_1 | ~spl70_15 | ~spl70_16 | ~spl70_23)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2184,f2795])).
% 15.48/3.49 thf(f2184,plain,(
% 15.48/3.49 ( ! [X4 : set @ a] : (((member @ a @ x0 @ X4) != $true) | ((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ (sK19 @ X4) @ X4) = $true)) ) | ~spl70_23),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2183])).
% 15.48/3.49 thf(f2183,definition,(
% 15.48/3.49 spl70_23 <=> ! [X4 : set @ a] : (((member @ a @ x0 @ X4) != $true) | ((member @ a @ (sK19 @ X4) @ X4) = $true) | ((topolo1751647064n_open @ a @ X4) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_23])],[avatar_definition])).
% 15.48/3.49 thf(f2809,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal,X5 : a] : (((member @ a @ X5 @ (sK49 @ X3)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((ord_less @ extended_ereal @ X3 @ extended_PInfty) != $true)) ) | (~spl70_1 | ~spl70_14)),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2147,f2728])).
% 15.48/3.49 thf(f2147,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal,X5 : a] : (((member @ a @ X5 @ (sK49 @ X3)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true)) ) | ~spl70_14),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2146])).
% 15.48/3.49 thf(f2146,definition,(
% 15.48/3.49 spl70_14 <=> ! [X5 : a,X3 : extended_ereal] : (((member @ a @ X5 @ (sK49 @ X3)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_14])],[avatar_definition])).
% 15.48/3.49 thf(f2126,plain,(
% 15.48/3.49 ( ! [X4 : set @ a] : (((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ X4))) != $true) | ((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ x0 @ X4) != $true)) ) | ~spl70_9),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2125])).
% 15.48/3.49 thf(f2125,definition,(
% 15.48/3.49 spl70_9 <=> ! [X4 : set @ a] : (((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ X4))) != $true) | ((member @ a @ x0 @ X4) != $true) | ((topolo1751647064n_open @ a @ X4) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_9])],[avatar_definition])).
% 15.48/3.49 thf(f2718,plain,(
% 15.48/3.49 ~spl70_2 | ~spl70_6 | ~spl70_9 | ~spl70_16 | ~spl70_23 | ~spl70_29),
% 15.48/3.49 inference(avatar_contradiction_clause,[status(thm)],[f2717])).
% 15.48/3.49 thf(f2717,plain,(
% 15.48/3.49 $false | (~spl70_2 | ~spl70_6 | ~spl70_9 | ~spl70_16 | ~spl70_23 | ~spl70_29)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2716,f2599])).
% 15.48/3.49 thf(f2599,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK14 @ sK18)) = $true) | (~spl70_2 | ~spl70_16)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2597])).
% 15.48/3.49 thf(f2597,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK14 @ sK18)) = $true) | ($true != $true) | (~spl70_2 | ~spl70_16)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2098,f2156])).
% 15.48/3.49 thf(f2098,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((member @ a @ x0 @ (sK14 @ X3)) = $true)) ) | ~spl70_2),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2097])).
% 15.48/3.49 thf(f2097,definition,(
% 15.48/3.49 spl70_2 <=> ! [X3 : extended_ereal] : (((member @ a @ x0 @ (sK14 @ X3)) = $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_2])],[avatar_definition])).
% 15.48/3.49 thf(f2716,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK14 @ sK18)) != $true) | (~spl70_2 | ~spl70_6 | ~spl70_9 | ~spl70_16 | ~spl70_23 | ~spl70_29)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2715,f2592])).
% 15.48/3.49 thf(f2592,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK14 @ sK18)) = $true) | (~spl70_6 | ~spl70_16)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2589])).
% 15.48/3.49 thf(f2589,plain,(
% 15.48/3.49 ($true != $true) | ((topolo1751647064n_open @ a @ (sK14 @ sK18)) = $true) | (~spl70_6 | ~spl70_16)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2114,f2156])).
% 15.48/3.49 thf(f2114,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((topolo1751647064n_open @ a @ (sK14 @ X3)) = $true)) ) | ~spl70_6),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2113])).
% 15.48/3.49 thf(f2113,definition,(
% 15.48/3.49 spl70_6 <=> ! [X3 : extended_ereal] : (((topolo1751647064n_open @ a @ (sK14 @ X3)) = $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_6])],[avatar_definition])).
% 15.48/3.49 thf(f2715,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK14 @ sK18)) != $true) | ((member @ a @ x0 @ (sK14 @ sK18)) != $true) | (~spl70_2 | ~spl70_6 | ~spl70_9 | ~spl70_16 | ~spl70_23 | ~spl70_29)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2714])).
% 15.48/3.49 thf(f2714,plain,(
% 15.48/3.49 ($true != $true) | ((member @ a @ x0 @ (sK14 @ sK18)) != $true) | ((topolo1751647064n_open @ a @ (sK14 @ sK18)) != $true) | (~spl70_2 | ~spl70_6 | ~spl70_9 | ~spl70_16 | ~spl70_23 | ~spl70_29)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2126,f2711])).
% 15.48/3.49 thf(f2711,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK14 @ sK18)))) = $true) | (~spl70_2 | ~spl70_6 | ~spl70_16 | ~spl70_23 | ~spl70_29)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2710,f2156])).
% 15.48/3.49 thf(f2710,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK14 @ sK18)))) = $true) | ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) != $true) | (~spl70_2 | ~spl70_6 | ~spl70_16 | ~spl70_23 | ~spl70_29)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2706])).
% 15.48/3.49 thf(f2706,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK14 @ sK18)))) = $true) | ($true != $true) | ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) != $true) | (~spl70_2 | ~spl70_6 | ~spl70_16 | ~spl70_23 | ~spl70_29)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2211,f2621])).
% 15.48/3.49 thf(f2621,plain,(
% 15.48/3.49 ((member @ a @ (sK19 @ (sK14 @ sK18)) @ (sK14 @ sK18)) = $true) | (~spl70_2 | ~spl70_6 | ~spl70_16 | ~spl70_23)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2618,f2592])).
% 15.48/3.49 thf(f2618,plain,(
% 15.48/3.49 ((member @ a @ (sK19 @ (sK14 @ sK18)) @ (sK14 @ sK18)) = $true) | ((topolo1751647064n_open @ a @ (sK14 @ sK18)) != $true) | (~spl70_2 | ~spl70_16 | ~spl70_23)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2615])).
% 15.48/3.49 thf(f2615,plain,(
% 15.48/3.49 ((member @ a @ (sK19 @ (sK14 @ sK18)) @ (sK14 @ sK18)) = $true) | ($true != $true) | ((topolo1751647064n_open @ a @ (sK14 @ sK18)) != $true) | (~spl70_2 | ~spl70_16 | ~spl70_23)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2184,f2599])).
% 15.48/3.49 thf(f2211,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal,X5 : a] : (((member @ a @ X5 @ (sK14 @ X3)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true)) ) | ~spl70_29),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2210])).
% 15.48/3.49 thf(f2210,definition,(
% 15.48/3.49 spl70_29 <=> ! [X5 : a,X3 : extended_ereal] : (((member @ a @ X5 @ (sK14 @ X3)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_29])],[avatar_definition])).
% 15.48/3.49 thf(f2703,plain,(
% 15.48/3.49 ~spl70_9 | ~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28),
% 15.48/3.49 inference(avatar_contradiction_clause,[status(thm)],[f2702])).
% 15.48/3.49 thf(f2702,plain,(
% 15.48/3.49 $false | (~spl70_9 | ~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2701,f2612])).
% 15.48/3.49 thf(f2612,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK34 @ sK18)) = $true) | (~spl70_16 | ~spl70_17)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2610])).
% 15.48/3.49 thf(f2610,plain,(
% 15.48/3.49 ($true != $true) | ((member @ a @ x0 @ (sK34 @ sK18)) = $true) | (~spl70_16 | ~spl70_17)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2160,f2156])).
% 15.48/3.49 thf(f2160,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((member @ a @ x0 @ (sK34 @ X0)) = $true)) ) | ~spl70_17),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2159])).
% 15.48/3.49 thf(f2159,definition,(
% 15.48/3.49 spl70_17 <=> ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((member @ a @ x0 @ (sK34 @ X0)) = $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_17])],[avatar_definition])).
% 15.48/3.49 thf(f2701,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK34 @ sK18)) != $true) | (~spl70_9 | ~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2700,f2596])).
% 15.48/3.49 thf(f2596,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK34 @ sK18)) = $true) | (~spl70_16 | ~spl70_28)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2593])).
% 15.48/3.49 thf(f2593,plain,(
% 15.48/3.49 ($true != $true) | ((topolo1751647064n_open @ a @ (sK34 @ sK18)) = $true) | (~spl70_16 | ~spl70_28)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2206,f2156])).
% 15.48/3.49 thf(f2206,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((topolo1751647064n_open @ a @ (sK34 @ X0)) = $true)) ) | ~spl70_28),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2205])).
% 15.48/3.49 thf(f2205,definition,(
% 15.48/3.49 spl70_28 <=> ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((topolo1751647064n_open @ a @ (sK34 @ X0)) = $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_28])],[avatar_definition])).
% 15.48/3.49 thf(f2700,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK34 @ sK18)) != $true) | ((member @ a @ x0 @ (sK34 @ sK18)) != $true) | (~spl70_9 | ~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2699])).
% 15.48/3.49 thf(f2699,plain,(
% 15.48/3.49 ($true != $true) | ((topolo1751647064n_open @ a @ (sK34 @ sK18)) != $true) | ((member @ a @ x0 @ (sK34 @ sK18)) != $true) | (~spl70_9 | ~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2126,f2696])).
% 15.48/3.49 thf(f2696,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK34 @ sK18)))) = $true) | (~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2695,f2156])).
% 15.48/3.49 thf(f2695,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK34 @ sK18)))) = $true) | (~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2691])).
% 15.48/3.49 thf(f2691,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ (sK34 @ sK18)))) = $true) | ($true != $true) | (~spl70_16 | ~spl70_17 | ~spl70_22 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2180,f2630])).
% 15.48/3.49 thf(f2630,plain,(
% 15.48/3.49 ((member @ a @ (sK19 @ (sK34 @ sK18)) @ (sK34 @ sK18)) = $true) | (~spl70_16 | ~spl70_17 | ~spl70_23 | ~spl70_28)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2627,f2596])).
% 15.48/3.49 thf(f2627,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK34 @ sK18)) != $true) | ((member @ a @ (sK19 @ (sK34 @ sK18)) @ (sK34 @ sK18)) = $true) | (~spl70_16 | ~spl70_17 | ~spl70_23)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2624])).
% 15.48/3.49 thf(f2624,plain,(
% 15.48/3.49 ($true != $true) | ((member @ a @ (sK19 @ (sK34 @ sK18)) @ (sK34 @ sK18)) = $true) | ((topolo1751647064n_open @ a @ (sK34 @ sK18)) != $true) | (~spl70_16 | ~spl70_17 | ~spl70_23)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2184,f2612])).
% 15.48/3.49 thf(f2180,plain,(
% 15.48/3.49 ( ! [X2 : a,X0 : extended_ereal] : (((member @ a @ X2 @ (sK34 @ X0)) != $true) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true)) ) | ~spl70_22),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2179])).
% 15.48/3.49 thf(f2179,definition,(
% 15.48/3.49 spl70_22 <=> ! [X2 : a,X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((member @ a @ X2 @ (sK34 @ X0)) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_22])],[avatar_definition])).
% 15.48/3.49 thf(f2489,plain,(
% 15.48/3.49 spl70_3 | ~spl70_4),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f2488,f2104,f2100])).
% 15.48/3.49 thf(f2100,definition,(
% 15.48/3.49 spl70_3 <=> ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true)),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_3])],[avatar_definition])).
% 15.48/3.49 thf(f2104,definition,(
% 15.48/3.49 spl70_4 <=> ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_4])],[avatar_definition])).
% 15.48/3.49 thf(f2488,plain,(
% 15.48/3.49 ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ~spl70_4),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2484,f2214])).
% 15.48/3.49 thf(f2214,plain,(
% 15.48/3.49 (topolo503727757_space @ a = $true)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2213])).
% 15.48/3.49 thf(f2213,plain,(
% 15.48/3.49 ($true != $true) | (topolo503727757_space @ a = $true)),
% 15.48/3.49 inference(superposition,[status(thm)],[f1407,f1486])).
% 15.48/3.49 thf(f1486,plain,(
% 15.48/3.49 (real_V2090557954_space @ a = $true)),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f794])).
% 15.48/3.49 thf(f794,plain,(
% 15.48/3.49 (real_V2090557954_space @ a = $true)),
% 15.48/3.49 inference(fool_elimination,[status(thm)],[f793])).
% 15.48/3.49 thf(f793,plain,(
% 15.48/3.49 real_V2090557954_space @ a),
% 15.48/3.49 inference(rectify,[status(thm)],[f297])).
% 15.48/3.49 thf(f297,axiom,(
% 15.48/3.49 real_V2090557954_space @ a),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',tfree_0)).
% 15.48/3.49 thf(f1407,plain,(
% 15.48/3.49 ( ! [X0 : $tType] : ((real_V2090557954_space @ X0 != $true) | (topolo503727757_space @ X0 = $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f892])).
% 15.48/3.49 thf(f892,plain,(
% 15.48/3.49 ! [X0 : $tType] : ((topolo503727757_space @ X0 = $true) | (real_V2090557954_space @ X0 != $true))),
% 15.48/3.49 inference(ennf_transformation,[status(thm)],[f338])).
% 15.48/3.49 thf(f338,plain,(
% 15.48/3.49 ! [X0 : $tType] : ((real_V2090557954_space @ X0 = $true) => (topolo503727757_space @ X0 = $true))),
% 15.48/3.49 inference(fool_elimination,[status(thm)],[f337])).
% 15.48/3.49 thf(f337,plain,(
% 15.48/3.49 ! [X0 : $tType] : (real_V2090557954_space @ X0 => topolo503727757_space @ X0)),
% 15.48/3.49 inference(rectify,[status(thm)],[f259])).
% 15.48/3.49 thf(f259,axiom,(
% 15.48/3.49 ! [X0 : $tType] : (real_V2090557954_space @ X0 => topolo503727757_space @ X0)),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space)).
% 15.48/3.49 thf(f2484,plain,(
% 15.48/3.49 ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | (topolo503727757_space @ a != $true) | ~spl70_4),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2483])).
% 15.48/3.49 thf(f2483,plain,(
% 15.48/3.49 (topolo503727757_space @ a != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | (extended_MInfty != extended_MInfty) | ~spl70_4),
% 15.48/3.49 inference(superposition,[status(thm)],[f2350,f2478])).
% 15.48/3.49 thf(f2478,plain,(
% 15.48/3.49 ((f @ x0) = extended_MInfty) | ~spl70_4),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2477,f1832])).
% 15.48/3.49 thf(f1832,plain,(
% 15.48/3.49 (extended_MInfty = (uminus_uminus @ extended_ereal @ extended_PInfty))),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f61])).
% 15.48/3.49 thf(f61,axiom,(
% 15.48/3.49 (extended_MInfty = (uminus_uminus @ extended_ereal @ extended_PInfty))),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',fact_60_uminus__ereal_Osimps_I2_J)).
% 15.48/3.49 thf(f2477,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extended_PInfty)) | ~spl70_4),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f2106,f1414])).
% 15.48/3.49 thf(f2106,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ~spl70_4),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2104])).
% 15.48/3.49 thf(f2350,plain,(
% 15.48/3.49 ( ! [X0 : $tType,X2 : X0,X1 : X0 > extended_ereal] : ((extended_MInfty != (X1 @ X2)) | (topolo503727757_space @ X0 != $true) | ((lower_582600101lsc_at @ X0 @ extended_ereal @ X2 @ X1) = $true)) )),
% 15.48/3.49 inference(backward_demodulation,[status(thm)],[f2310,f1832])).
% 15.48/3.49 thf(f2310,plain,(
% 15.48/3.49 ( ! [X0 : $tType,X2 : X0,X1 : X0 > extended_ereal] : (((uminus_uminus @ extended_ereal @ extended_PInfty) != (X1 @ X2)) | ((lower_582600101lsc_at @ X0 @ extended_ereal @ X2 @ X1) = $true) | (topolo503727757_space @ X0 != $true)) )),
% 15.48/3.49 inference(forward_demodulation,[status(thm)],[f1478,f1414])).
% 15.48/3.49 thf(f1478,plain,(
% 15.48/3.49 ( ! [X0 : $tType,X2 : X0,X1 : X0 > extended_ereal] : ((topolo503727757_space @ X0 != $true) | ((uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal) != (X1 @ X2)) | ((lower_582600101lsc_at @ X0 @ extended_ereal @ X2 @ X1) = $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f928])).
% 15.48/3.49 thf(f928,plain,(
% 15.48/3.49 ! [X0 : $tType] : ((topolo503727757_space @ X0 != $true) | ! [X1 : X0 > extended_ereal,X2 : X0] : (((lower_582600101lsc_at @ X0 @ extended_ereal @ X2 @ X1) = $true) | ((uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal) != (X1 @ X2))))),
% 15.48/3.49 inference(ennf_transformation,[status(thm)],[f604])).
% 15.48/3.49 thf(f604,plain,(
% 15.48/3.49 ! [X0 : $tType] : ((topolo503727757_space @ X0 = $true) => ! [X1 : X0 > extended_ereal,X2 : X0] : (((uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal) = (X1 @ X2)) => ((lower_582600101lsc_at @ X0 @ extended_ereal @ X2 @ X1) = $true)))),
% 15.48/3.49 inference(fool_elimination,[status(thm)],[f603])).
% 15.48/3.49 thf(f603,plain,(
% 15.48/3.49 ! [X0 : $tType] : (topolo503727757_space @ X0 => ! [X1 : X0 > extended_ereal,X2 : X0] : (((uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal) = (X1 @ X2)) => (lower_582600101lsc_at @ X0 @ extended_ereal @ X2 @ X1)))),
% 15.48/3.49 inference(rectify,[status(thm)],[f4])).
% 15.48/3.49 thf(f4,axiom,(
% 15.48/3.49 ! [X0 : $tType] : (topolo503727757_space @ X0 => ! [X5 : X0 > extended_ereal,X6 : X0] : (((uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal) = (X5 @ X6)) => (lower_582600101lsc_at @ X0 @ extended_ereal @ X6 @ X5)))),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',fact_3_lsc__at__MInfty)).
% 15.48/3.49 thf(f2476,plain,(
% 15.48/3.49 ~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21 | ~spl70_27),
% 15.48/3.49 inference(avatar_contradiction_clause,[status(thm)],[f2475])).
% 15.48/3.49 thf(f2475,plain,(
% 15.48/3.49 $false | (~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21 | ~spl70_27)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2474,f2232])).
% 15.48/3.49 thf(f2232,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK17 @ sK12)) = $true) | (~spl70_18 | ~spl70_21)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2230])).
% 15.48/3.49 thf(f2230,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK17 @ sK12)) = $true) | ($true != $true) | (~spl70_18 | ~spl70_21)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2164,f2176])).
% 15.48/3.49 thf(f2176,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK12 @ (f @ x0)) = $true) | ~spl70_21),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2174])).
% 15.48/3.49 thf(f2174,definition,(
% 15.48/3.49 spl70_21 <=> ((ord_less @ extended_ereal @ sK12 @ (f @ x0)) = $true)),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_21])],[avatar_definition])).
% 15.48/3.49 thf(f2474,plain,(
% 15.48/3.49 ((topolo1751647064n_open @ a @ (sK17 @ sK12)) != $true) | (~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21 | ~spl70_27)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2473,f2231])).
% 15.48/3.49 thf(f2231,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK17 @ sK12)) = $true) | (~spl70_8 | ~spl70_21)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2229])).
% 15.48/3.49 thf(f2229,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK17 @ sK12)) = $true) | ($true != $true) | (~spl70_8 | ~spl70_21)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2122,f2176])).
% 15.48/3.49 thf(f2473,plain,(
% 15.48/3.49 ((member @ a @ x0 @ (sK17 @ sK12)) != $true) | ((topolo1751647064n_open @ a @ (sK17 @ sK12)) != $true) | (~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21 | ~spl70_27)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2472])).
% 15.48/3.49 thf(f2472,plain,(
% 15.48/3.49 ($true != $true) | ((member @ a @ x0 @ (sK17 @ sK12)) != $true) | ((topolo1751647064n_open @ a @ (sK17 @ sK12)) != $true) | (~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21 | ~spl70_27)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2202,f2404])).
% 15.48/3.49 thf(f2404,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ (sK17 @ sK12)))) = $true) | (~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2403,f2176])).
% 15.48/3.49 thf(f2403,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK12 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ (sK17 @ sK12)))) = $true) | (~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2402])).
% 15.48/3.49 thf(f2402,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK12 @ (f @ x0)) != $true) | ((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ (sK17 @ sK12)))) = $true) | ($true != $true) | (~spl70_8 | ~spl70_10 | ~spl70_12 | ~spl70_18 | ~spl70_21)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2139,f2401])).
% 15.48/3.49 thf(f2401,plain,(
% 15.48/3.49 ((member @ a @ (sK13 @ (sK17 @ sK12)) @ (sK17 @ sK12)) = $true) | (~spl70_8 | ~spl70_10 | ~spl70_18 | ~spl70_21)),
% 15.48/3.49 inference(subsumption_resolution,[status(thm)],[f2400,f2232])).
% 15.48/3.49 thf(f2400,plain,(
% 15.48/3.49 ((member @ a @ (sK13 @ (sK17 @ sK12)) @ (sK17 @ sK12)) = $true) | ((topolo1751647064n_open @ a @ (sK17 @ sK12)) != $true) | (~spl70_8 | ~spl70_10 | ~spl70_21)),
% 15.48/3.49 inference(trivial_inequality_removal,[status(thm)],[f2399])).
% 15.48/3.49 thf(f2399,plain,(
% 15.48/3.49 ((member @ a @ (sK13 @ (sK17 @ sK12)) @ (sK17 @ sK12)) = $true) | ((topolo1751647064n_open @ a @ (sK17 @ sK12)) != $true) | ($true != $true) | (~spl70_8 | ~spl70_10 | ~spl70_21)),
% 15.48/3.49 inference(superposition,[status(thm)],[f2130,f2231])).
% 15.48/3.49 thf(f2130,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((member @ a @ x0 @ X1) != $true) | ((member @ a @ (sK13 @ X1) @ X1) = $true) | ((topolo1751647064n_open @ a @ X1) != $true)) ) | ~spl70_10),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2129])).
% 15.48/3.49 thf(f2129,definition,(
% 15.48/3.49 spl70_10 <=> ! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true) | ((member @ a @ (sK13 @ X1) @ X1) = $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_10])],[avatar_definition])).
% 15.48/3.49 thf(f2202,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ X1))) != $true) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true)) ) | ~spl70_27),
% 15.48/3.49 inference(avatar_component_clause,[status(thm)],[f2201])).
% 15.48/3.49 thf(f2201,definition,(
% 15.48/3.49 spl70_27 <=> ! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true) | ((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ X1))) != $true))),
% 15.48/3.49 introduced(definition,[new_symbols(naming,[spl70_27])],[avatar_definition])).
% 15.48/3.49 thf(f2212,plain,(
% 15.48/3.49 ~spl70_3 | spl70_29 | spl70_1 | spl70_4),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1469,f2104,f2093,f2210,f2100])).
% 15.48/3.49 thf(f1469,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal,X5 : a] : (((f @ x0) = extend1396239628finity @ extended_ereal) | ((member @ a @ X5 @ (sK14 @ X3)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1200])).
% 15.48/3.49 thf(f1200,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | (! [X1 : set @ a] : (((member @ a @ x0 @ X1) != $true) | (((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ X1))) != $true) & ((member @ a @ (sK13 @ X1) @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true)) & ((ord_less @ extended_ereal @ sK12 @ (f @ x0)) = $true))) & (! [X3 : extended_ereal] : ((((member @ a @ x0 @ (sK14 @ X3)) = $true) & ! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ (sK14 @ X3)) != $true)) & ((topolo1751647064n_open @ a @ (sK14 @ X3)) = $true)) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)))),
% 15.48/3.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f1196,f1199,f1198,f1197])).
% 15.48/3.49 thf(f1197,plain,(
% 15.48/3.49 ? [X0 : extended_ereal] : (! [X1 : set @ a] : (((member @ a @ x0 @ X1) != $true) | ? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true)) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true)) => (! [X1 : set @ a] : (((member @ a @ x0 @ X1) != $true) | ? [X2 : a] : (((ord_less @ extended_ereal @ sK12 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true)) & ((ord_less @ extended_ereal @ sK12 @ (f @ x0)) = $true))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1198,plain,(
% 15.48/3.49 ! [X1 : set @ a] : (? [X2 : a] : (((ord_less @ extended_ereal @ sK12 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) => (((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ X1))) != $true) & ((member @ a @ (sK13 @ X1) @ X1) = $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1199,plain,(
% 15.48/3.49 ! [X3 : extended_ereal] : (? [X4 : set @ a] : (((member @ a @ x0 @ X4) = $true) & ! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ X4) != $true)) & ((topolo1751647064n_open @ a @ X4) = $true)) => (((member @ a @ x0 @ (sK14 @ X3)) = $true) & ! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ (sK14 @ X3)) != $true)) & ((topolo1751647064n_open @ a @ (sK14 @ X3)) = $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1196,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ? [X0 : extended_ereal] : (! [X1 : set @ a] : (((member @ a @ x0 @ X1) != $true) | ? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true)) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true))) & (! [X3 : extended_ereal] : (? [X4 : set @ a] : (((member @ a @ x0 @ X4) = $true) & ! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ X4) != $true)) & ((topolo1751647064n_open @ a @ X4) = $true)) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)))),
% 15.48/3.49 inference(rectify,[status(thm)],[f1195])).
% 15.48/3.49 thf(f1195,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ? [X0 : extended_ereal] : (! [X1 : set @ a] : (((member @ a @ x0 @ X1) != $true) | ? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true)) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true))) & (! [X0 : extended_ereal] : (? [X1 : set @ a] : (((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((topolo1751647064n_open @ a @ X1) = $true)) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)))),
% 15.48/3.49 inference(nnf_transformation,[status(thm)],[f1144])).
% 15.48/3.49 thf(f1144,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((f @ x0) = extend1396239628finity @ extended_ereal) | (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) <=> ! [X0 : extended_ereal] : (? [X1 : set @ a] : (((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((topolo1751647064n_open @ a @ X1) = $true)) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true)))),
% 15.48/3.49 inference(flattening,[status(thm)],[f1143])).
% 15.48/3.49 thf(f1143,plain,(
% 15.48/3.49 ((((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) <=> ! [X0 : extended_ereal] : (? [X1 : set @ a] : (((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((topolo1751647064n_open @ a @ X1) = $true)) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true))) | ((f @ x0) = extend1396239628finity @ extended_ereal)) | ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))),
% 15.48/3.49 inference(ennf_transformation,[status(thm)],[f516])).
% 15.48/3.49 thf(f516,plain,(
% 15.48/3.49 ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) => (((f @ x0) != extend1396239628finity @ extended_ereal) => (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) <=> ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true) => ? [X1 : set @ a] : (((member @ a @ x0 @ X1) = $true) & ((topolo1751647064n_open @ a @ X1) = $true) & ! [X2 : a] : (((member @ a @ X2 @ X1) = $true) => ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true))))))),
% 15.48/3.49 inference(fool_elimination,[status(thm)],[f515])).
% 15.48/3.49 thf(f515,plain,(
% 15.48/3.49 ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) => (((f @ x0) != extend1396239628finity @ extended_ereal) => ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = ! [X0 : extended_ereal] : ((ord_less @ extended_ereal @ X0 @ (f @ x0)) => ? [X1 : set @ a] : ((topolo1751647064n_open @ a @ X1) & ! [X2 : a] : ((member @ a @ X2 @ X1) => (ord_less @ extended_ereal @ X0 @ (f @ X2))) & (member @ a @ x0 @ X1)))))),
% 15.48/3.49 inference(rectify,[status(thm)],[f3])).
% 15.48/3.49 thf(f3,axiom,(
% 15.48/3.49 ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) => (((f @ x0) != extend1396239628finity @ extended_ereal) => ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = ! [X2 : extended_ereal] : ((ord_less @ extended_ereal @ X2 @ (f @ x0)) => ? [X3 : set @ a] : ((topolo1751647064n_open @ a @ X3) & ! [X4 : a] : ((member @ a @ X4 @ X3) => (ord_less @ extended_ereal @ X2 @ (f @ X4))) & (member @ a @ x0 @ X3)))))),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062)).
% 15.48/3.49 thf(f2207,plain,(
% 15.48/3.49 ~spl70_4 | ~spl70_3 | spl70_28),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1663,f2205,f2100,f2104])).
% 15.48/3.49 thf(f1663,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((topolo1751647064n_open @ a @ (sK34 @ X0)) = $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1281])).
% 15.48/3.49 thf(f1281,plain,(
% 15.48/3.49 ((! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | (((topolo1751647064n_open @ a @ (sK34 @ X0)) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ (sK34 @ X0)) != $true)) & ((member @ a @ x0 @ (sK34 @ X0)) = $true))) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)) & (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | (((ord_less @ extended_ereal @ sK35 @ (f @ x0)) = $true) & ! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | (((ord_less @ extended_ereal @ sK35 @ (f @ (sK36 @ X4))) != $true) & ((member @ a @ (sK36 @ X4) @ X4) = $true)) | ((member @ a @ x0 @ X4) != $true))))) | ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))),
% 15.48/3.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36])],[f1277,f1280,f1279,f1278])).
% 15.48/3.49 thf(f1278,plain,(
% 15.48/3.49 ! [X0 : extended_ereal] : (? [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((member @ a @ x0 @ X1) = $true)) => (((topolo1751647064n_open @ a @ (sK34 @ X0)) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ (sK34 @ X0)) != $true)) & ((member @ a @ x0 @ (sK34 @ X0)) = $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1279,plain,(
% 15.48/3.49 ? [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ (f @ x0)) = $true) & ! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | ? [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true)) | ((member @ a @ x0 @ X4) != $true))) => (((ord_less @ extended_ereal @ sK35 @ (f @ x0)) = $true) & ! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | ? [X5 : a] : (((ord_less @ extended_ereal @ sK35 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true)) | ((member @ a @ x0 @ X4) != $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1280,plain,(
% 15.48/3.49 ! [X4 : set @ a] : (? [X5 : a] : (((ord_less @ extended_ereal @ sK35 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true)) => (((ord_less @ extended_ereal @ sK35 @ (f @ (sK36 @ X4))) != $true) & ((member @ a @ (sK36 @ X4) @ X4) = $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1277,plain,(
% 15.48/3.49 ((! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ? [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((member @ a @ x0 @ X1) = $true))) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)) & (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ? [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ (f @ x0)) = $true) & ! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | ? [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true)) | ((member @ a @ x0 @ X4) != $true))))) | ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))),
% 15.48/3.49 inference(rectify,[status(thm)],[f1276])).
% 15.48/3.49 thf(f1276,plain,(
% 15.48/3.49 ((! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ? [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((member @ a @ x0 @ X1) = $true))) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)) & (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ? [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true) & ! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((member @ a @ x0 @ X1) != $true))))) | ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))),
% 15.48/3.49 inference(nnf_transformation,[status(thm)],[f1074])).
% 15.48/3.49 thf(f1074,plain,(
% 15.48/3.49 (! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ? [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((member @ a @ x0 @ X1) = $true))) <=> ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true)) | ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))),
% 15.48/3.49 inference(ennf_transformation,[status(thm)],[f474])).
% 15.48/3.49 thf(f474,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) => (! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true) => ? [X1 : set @ a] : (! [X2 : a] : (((member @ a @ X2 @ X1) = $true) => ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true)) & ((member @ a @ x0 @ X1) = $true) & ((topolo1751647064n_open @ a @ X1) = $true))) <=> ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true))),
% 15.48/3.49 inference(fool_elimination,[status(thm)],[f473])).
% 15.48/3.49 thf(f473,plain,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) => ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = ! [X0 : extended_ereal] : ((ord_less @ extended_ereal @ X0 @ (f @ x0)) => ? [X1 : set @ a] : (! [X2 : a] : ((member @ a @ X2 @ X1) => (ord_less @ extended_ereal @ X0 @ (f @ X2))) & (member @ a @ x0 @ X1) & (topolo1751647064n_open @ a @ X1))))),
% 15.48/3.49 inference(rectify,[status(thm)],[f2])).
% 15.48/3.49 thf(f2,axiom,(
% 15.48/3.49 ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) => ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = ! [X2 : extended_ereal] : ((ord_less @ extended_ereal @ X2 @ (f @ x0)) => ? [X3 : set @ a] : (! [X4 : a] : ((member @ a @ X4 @ X3) => (ord_less @ extended_ereal @ X2 @ (f @ X4))) & (member @ a @ x0 @ X3) & (topolo1751647064n_open @ a @ X3))))),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062)).
% 15.48/3.49 thf(f2203,plain,(
% 15.48/3.49 spl70_1 | spl70_4 | spl70_3 | spl70_27),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1473,f2201,f2100,f2104,f2093])).
% 15.48/3.49 thf(f1473,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((ord_less @ extended_ereal @ sK12 @ (f @ (sK13 @ X1))) != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((member @ a @ x0 @ X1) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1200])).
% 15.48/3.49 thf(f2199,plain,(
% 15.48/3.49 ~spl70_1 | ~spl70_3 | spl70_26),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1731,f2197,f2100,f2093])).
% 15.48/3.49 thf(f1731,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((f @ x0) != extend1396239628finity @ extended_ereal) | ((topolo1751647064n_open @ a @ (sK49 @ X3)) = $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1313])).
% 15.48/3.49 thf(f1313,plain,(
% 15.48/3.49 ((f @ x0) != extend1396239628finity @ extended_ereal) | ((((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | (! [X1 : set @ a] : ((((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ X1))) != $true) & ((member @ a @ (sK48 @ X1) @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true)) & ((ord_less @ extended_ereal @ sK47 @ (f @ x0)) = $true))) & (! [X3 : extended_ereal] : ((! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ (sK49 @ X3)) != $true)) & ((topolo1751647064n_open @ a @ (sK49 @ X3)) = $true) & ((member @ a @ x0 @ (sK49 @ X3)) = $true)) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)))),
% 15.48/3.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49])],[f1309,f1312,f1311,f1310])).
% 15.48/3.49 thf(f1310,plain,(
% 15.48/3.49 ? [X0 : extended_ereal] : (! [X1 : set @ a] : (? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true)) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true)) => (! [X1 : set @ a] : (? [X2 : a] : (((ord_less @ extended_ereal @ sK47 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true)) & ((ord_less @ extended_ereal @ sK47 @ (f @ x0)) = $true))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1311,plain,(
% 15.48/3.49 ! [X1 : set @ a] : (? [X2 : a] : (((ord_less @ extended_ereal @ sK47 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) => (((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ X1))) != $true) & ((member @ a @ (sK48 @ X1) @ X1) = $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1312,plain,(
% 15.48/3.49 ! [X3 : extended_ereal] : (? [X4 : set @ a] : (! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ X4) != $true)) & ((topolo1751647064n_open @ a @ X4) = $true) & ((member @ a @ x0 @ X4) = $true)) => (! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ (sK49 @ X3)) != $true)) & ((topolo1751647064n_open @ a @ (sK49 @ X3)) = $true) & ((member @ a @ x0 @ (sK49 @ X3)) = $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1309,plain,(
% 15.48/3.49 ((f @ x0) != extend1396239628finity @ extended_ereal) | ((((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ? [X0 : extended_ereal] : (! [X1 : set @ a] : (? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true)) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true))) & (! [X3 : extended_ereal] : (? [X4 : set @ a] : (! [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true) | ((member @ a @ X5 @ X4) != $true)) & ((topolo1751647064n_open @ a @ X4) = $true) & ((member @ a @ x0 @ X4) = $true)) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)))),
% 15.48/3.49 inference(rectify,[status(thm)],[f1308])).
% 15.48/3.49 thf(f1308,plain,(
% 15.48/3.49 ((f @ x0) != extend1396239628finity @ extended_ereal) | ((((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ? [X0 : extended_ereal] : (! [X1 : set @ a] : (? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true)) | ((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true)) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true))) & (! [X0 : extended_ereal] : (? [X1 : set @ a] : (! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((topolo1751647064n_open @ a @ X1) = $true) & ((member @ a @ x0 @ X1) = $true)) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)))),
% 15.48/3.49 inference(nnf_transformation,[status(thm)],[f1017])).
% 15.48/3.49 thf(f1017,plain,(
% 15.48/3.49 ((f @ x0) != extend1396239628finity @ extended_ereal) | (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) <=> ! [X0 : extended_ereal] : (? [X1 : set @ a] : (! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true)) & ((topolo1751647064n_open @ a @ X1) = $true) & ((member @ a @ x0 @ X1) = $true)) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true)))),
% 15.48/3.49 inference(ennf_transformation,[status(thm)],[f704])).
% 15.48/3.49 thf(f704,plain,(
% 15.48/3.49 ((f @ x0) = extend1396239628finity @ extended_ereal) => (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) <=> ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true) => ? [X1 : set @ a] : (((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((member @ a @ X2 @ X1) = $true) => ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true)) & ((topolo1751647064n_open @ a @ X1) = $true))))),
% 15.48/3.49 inference(fool_elimination,[status(thm)],[f703])).
% 15.48/3.49 thf(f703,plain,(
% 15.48/3.49 ((f @ x0) = extend1396239628finity @ extended_ereal) => ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = ! [X0 : extended_ereal] : ((ord_less @ extended_ereal @ X0 @ (f @ x0)) => ? [X1 : set @ a] : ((member @ a @ x0 @ X1) & ! [X2 : a] : ((member @ a @ X2 @ X1) => (ord_less @ extended_ereal @ X0 @ (f @ X2))) & (topolo1751647064n_open @ a @ X1))))),
% 15.48/3.49 inference(rectify,[status(thm)],[f1])).
% 15.48/3.49 thf(f1,axiom,(
% 15.48/3.49 ((f @ x0) = extend1396239628finity @ extended_ereal) => ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = ! [X2 : extended_ereal] : ((ord_less @ extended_ereal @ X2 @ (f @ x0)) => ? [X3 : set @ a] : ((member @ a @ x0 @ X3) & ! [X4 : a] : ((member @ a @ X4 @ X3) => (ord_less @ extended_ereal @ X2 @ (f @ X4))) & (topolo1751647064n_open @ a @ X3))))),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062)).
% 15.48/3.49 thf(f2185,plain,(
% 15.48/3.49 spl70_23 | ~spl70_3),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1514,f2100,f2183])).
% 15.48/3.49 thf(f1514,plain,(
% 15.48/3.49 ( ! [X4 : set @ a] : (((member @ a @ x0 @ X4) != $true) | ((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ (sK19 @ X4) @ X4) = $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1220])).
% 15.48/3.49 thf(f1220,plain,(
% 15.48/3.49 (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ! [X0 : extended_ereal] : ((((topolo1751647064n_open @ a @ (sK17 @ X0)) = $true) & ((member @ a @ x0 @ (sK17 @ X0)) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ (sK17 @ X0)) != $true))) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true))) & ((! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ x0 @ X4) != $true) | (((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ X4))) != $true) & ((member @ a @ (sK19 @ X4) @ X4) = $true))) & ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) = $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true))),
% 15.48/3.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f1216,f1219,f1218,f1217])).
% 15.48/3.49 thf(f1217,plain,(
% 15.48/3.49 ! [X0 : extended_ereal] : (? [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) = $true) & ((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true))) => (((topolo1751647064n_open @ a @ (sK17 @ X0)) = $true) & ((member @ a @ x0 @ (sK17 @ X0)) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ (sK17 @ X0)) != $true))))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1218,plain,(
% 15.48/3.49 ? [X3 : extended_ereal] : (! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ x0 @ X4) != $true) | ? [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true))) & ((ord_less @ extended_ereal @ X3 @ (f @ x0)) = $true)) => (! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ x0 @ X4) != $true) | ? [X5 : a] : (((ord_less @ extended_ereal @ sK18 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true))) & ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) = $true))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1219,plain,(
% 15.48/3.49 ! [X4 : set @ a] : (? [X5 : a] : (((ord_less @ extended_ereal @ sK18 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true)) => (((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ X4))) != $true) & ((member @ a @ (sK19 @ X4) @ X4) = $true)))),
% 15.48/3.49 introduced(definition,[],[choice_axiom])).
% 15.48/3.49 thf(f1216,plain,(
% 15.48/3.49 (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ! [X0 : extended_ereal] : (? [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) = $true) & ((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true))) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true))) & (? [X3 : extended_ereal] : (! [X4 : set @ a] : (((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ x0 @ X4) != $true) | ? [X5 : a] : (((ord_less @ extended_ereal @ X3 @ (f @ X5)) != $true) & ((member @ a @ X5 @ X4) = $true))) & ((ord_less @ extended_ereal @ X3 @ (f @ x0)) = $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true))),
% 15.48/3.49 inference(rectify,[status(thm)],[f1215])).
% 15.48/3.49 thf(f1215,plain,(
% 15.48/3.49 (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ! [X0 : extended_ereal] : (? [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) = $true) & ((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ X1) != $true))) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true))) & (? [X0 : extended_ereal] : (! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true) | ? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true))) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true)) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true))),
% 15.48/3.49 inference(nnf_transformation,[status(thm)],[f922])).
% 15.48/3.49 thf(f922,plain,(
% 15.48/3.49 ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) <=> ? [X0 : extended_ereal] : (! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ x0 @ X1) != $true) | ? [X2 : a] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) != $true) & ((member @ a @ X2 @ X1) = $true))) & ((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true))),
% 15.48/3.49 inference(ennf_transformation,[status(thm)],[f380])).
% 15.48/3.49 thf(f380,plain,(
% 15.48/3.49 ~(~! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) = $true) => ? [X1 : set @ a] : (((member @ a @ x0 @ X1) = $true) & ! [X2 : a] : (((member @ a @ X2 @ X1) = $true) => ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true)) & ((topolo1751647064n_open @ a @ X1) = $true))) <~> ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true))),
% 15.48/3.49 inference(fool_elimination,[status(thm)],[f379])).
% 15.48/3.49 thf(f379,plain,(
% 15.48/3.49 ~(~! [X0 : extended_ereal] : ((ord_less @ extended_ereal @ X0 @ (f @ x0)) => ? [X1 : set @ a] : ((member @ a @ x0 @ X1) & (topolo1751647064n_open @ a @ X1) & ! [X2 : a] : ((member @ a @ X2 @ X1) => (ord_less @ extended_ereal @ X0 @ (f @ X2))))) != (lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f))),
% 15.48/3.49 inference(rectify,[status(thm)],[f299])).
% 15.48/3.49 thf(f299,negated_conjecture,(
% 15.48/3.49 ~(~! [X2 : extended_ereal] : ((ord_less @ extended_ereal @ X2 @ (f @ x0)) => ? [X3 : set @ a] : ((member @ a @ x0 @ X3) & (topolo1751647064n_open @ a @ X3) & ! [X4 : a] : ((member @ a @ X4 @ X3) => (ord_less @ extended_ereal @ X2 @ (f @ X4))))) != (lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f))),
% 15.48/3.49 inference(negated_conjecture,[status(cth)],[f298])).
% 15.48/3.49 thf(f298,conjecture,(
% 15.48/3.49 (~! [X2 : extended_ereal] : ((ord_less @ extended_ereal @ X2 @ (f @ x0)) => ? [X3 : set @ a] : ((member @ a @ x0 @ X3) & (topolo1751647064n_open @ a @ X3) & ! [X4 : a] : ((member @ a @ X4 @ X3) => (ord_less @ extended_ereal @ X2 @ (f @ X4))))) != (lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f))),
% 15.48/3.49 file('/export/starexec/sandbox2/tmp/tmp.IzC8eXDzJt/DTF2THF_16074.p',conj_0)).
% 15.48/3.49 thf(f2181,plain,(
% 15.48/3.49 ~spl70_3 | spl70_22 | ~spl70_4),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1662,f2104,f2179,f2100])).
% 15.48/3.49 thf(f1662,plain,(
% 15.48/3.49 ( ! [X2 : a,X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((member @ a @ X2 @ (sK34 @ X0)) != $true) | ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1281])).
% 15.48/3.49 thf(f2177,plain,(
% 15.48/3.49 spl70_3 | spl70_21 | spl70_4 | spl70_1),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1471,f2093,f2104,f2174,f2100])).
% 15.48/3.49 thf(f1471,plain,(
% 15.48/3.49 ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((ord_less @ extended_ereal @ sK12 @ (f @ x0)) = $true)),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1200])).
% 15.48/3.49 thf(f2165,plain,(
% 15.48/3.49 spl70_18 | spl70_3),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1518,f2100,f2163])).
% 15.48/3.49 thf(f1518,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((topolo1751647064n_open @ a @ (sK17 @ X0)) = $true) | ((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1220])).
% 15.48/3.49 thf(f2161,plain,(
% 15.48/3.49 ~spl70_4 | ~spl70_3 | spl70_17),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1661,f2159,f2100,f2104])).
% 15.48/3.49 thf(f1661,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((member @ a @ x0 @ (sK34 @ X0)) = $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((f @ x0) != (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1281])).
% 15.48/3.49 thf(f2157,plain,(
% 15.48/3.49 ~spl70_3 | spl70_16),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1513,f2154,f2100])).
% 15.48/3.49 thf(f1513,plain,(
% 15.48/3.49 ((ord_less @ extended_ereal @ sK18 @ (f @ x0)) = $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true)),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1220])).
% 15.48/3.49 thf(f2152,plain,(
% 15.48/3.49 ~spl70_1 | spl70_15 | ~spl70_3),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1730,f2100,f2150,f2093])).
% 15.48/3.49 thf(f1730,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((member @ a @ x0 @ (sK49 @ X3)) = $true) | ((f @ x0) != extend1396239628finity @ extended_ereal) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1313])).
% 15.48/3.49 thf(f2148,plain,(
% 15.48/3.49 spl70_14 | ~spl70_1 | ~spl70_3),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1732,f2100,f2093,f2146])).
% 15.48/3.49 thf(f1732,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal,X5 : a] : (((member @ a @ X5 @ (sK49 @ X3)) != $true) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((f @ x0) != extend1396239628finity @ extended_ereal) | ((ord_less @ extended_ereal @ X3 @ (f @ X5)) = $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1313])).
% 15.48/3.49 thf(f2144,plain,(
% 15.48/3.49 ~spl70_1 | spl70_3 | spl70_13),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1734,f2142,f2100,f2093])).
% 15.48/3.49 thf(f1734,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((member @ a @ x0 @ X1) != $true) | ((member @ a @ (sK48 @ X1) @ X1) = $true) | ((f @ x0) != extend1396239628finity @ extended_ereal)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1313])).
% 15.48/3.49 thf(f2140,plain,(
% 15.48/3.49 spl70_3 | spl70_12),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1516,f2138,f2100])).
% 15.48/3.49 thf(f1516,plain,(
% 15.48/3.49 ( ! [X2 : a,X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((ord_less @ extended_ereal @ X0 @ (f @ X2)) = $true) | ((member @ a @ X2 @ (sK17 @ X0)) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1220])).
% 15.48/3.49 thf(f2136,plain,(
% 15.48/3.49 ~spl70_1 | spl70_3 | spl70_11),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1733,f2133,f2100,f2093])).
% 15.48/3.49 thf(f1733,plain,(
% 15.48/3.49 ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((f @ x0) != extend1396239628finity @ extended_ereal) | ((ord_less @ extended_ereal @ sK47 @ (f @ x0)) = $true)),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1313])).
% 15.48/3.49 thf(f2131,plain,(
% 15.48/3.49 spl70_4 | spl70_10 | spl70_1 | spl70_3),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1472,f2100,f2093,f2129,f2104])).
% 15.48/3.49 thf(f1472,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((topolo1751647064n_open @ a @ X1) != $true) | ((member @ a @ (sK13 @ X1) @ X1) = $true) | ((member @ a @ x0 @ X1) != $true) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1200])).
% 15.48/3.49 thf(f2127,plain,(
% 15.48/3.49 spl70_9 | ~spl70_3),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1515,f2100,f2125])).
% 15.48/3.49 thf(f1515,plain,(
% 15.48/3.49 ( ! [X4 : set @ a] : (((ord_less @ extended_ereal @ sK18 @ (f @ (sK19 @ X4))) != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((topolo1751647064n_open @ a @ X4) != $true) | ((member @ a @ x0 @ X4) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1220])).
% 15.48/3.49 thf(f2123,plain,(
% 15.48/3.49 spl70_3 | spl70_8),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1517,f2121,f2100])).
% 15.48/3.49 thf(f1517,plain,(
% 15.48/3.49 ( ! [X0 : extended_ereal] : (((ord_less @ extended_ereal @ X0 @ (f @ x0)) != $true) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((member @ a @ x0 @ (sK17 @ X0)) = $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1220])).
% 15.48/3.49 thf(f2119,plain,(
% 15.48/3.49 spl70_3 | spl70_7 | ~spl70_1),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1735,f2093,f2117,f2100])).
% 15.48/3.49 thf(f1735,plain,(
% 15.48/3.49 ( ! [X1 : set @ a] : (((ord_less @ extended_ereal @ sK47 @ (f @ (sK48 @ X1))) != $true) | ((f @ x0) != extend1396239628finity @ extended_ereal) | ((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) = $true) | ((member @ a @ x0 @ X1) != $true) | ((topolo1751647064n_open @ a @ X1) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1313])).
% 15.48/3.49 thf(f2115,plain,(
% 15.48/3.49 spl70_6 | ~spl70_3 | spl70_4 | spl70_1),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1468,f2093,f2104,f2100,f2113])).
% 15.48/3.49 thf(f1468,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((topolo1751647064n_open @ a @ (sK14 @ X3)) = $true) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true) | ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal))) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1200])).
% 15.48/3.49 thf(f2107,plain,(
% 15.48/3.49 spl70_1 | spl70_2 | ~spl70_3 | spl70_4),
% 15.48/3.49 inference(avatar_split_clause,[status(thm)],[f1470,f2104,f2100,f2097,f2093])).
% 15.48/3.49 thf(f1470,plain,(
% 15.48/3.49 ( ! [X3 : extended_ereal] : (((lower_582600101lsc_at @ a @ extended_ereal @ x0 @ f) != $true) | ((f @ x0) = extend1396239628finity @ extended_ereal) | ((member @ a @ x0 @ (sK14 @ X3)) = $true) | ((f @ x0) = (uminus_uminus @ extended_ereal @ extend1396239628finity @ extended_ereal)) | ((ord_less @ extended_ereal @ X3 @ (f @ x0)) != $true)) )),
% 15.48/3.49 inference(cnf_transformation,[status(thm)],[f1200])).
% 15.48/3.49 % SZS output end Proof for DTF2THF_16074
% 15.48/3.49 % (16415)------------------------------
% 15.48/3.49 % (16415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.48/3.49 % (16415)Termination reason: Refutation
% 15.48/3.49
% 15.48/3.49 % (16415)Memory used [KB]: 7675
% 15.48/3.49 % (16415)Time elapsed: 0.109 s
% 15.48/3.49 % (16415)Instructions burned: 310 (million)
% 15.48/3.49 % (16415)------------------------------
% 15.48/3.49 % (16415)------------------------------
% 15.48/3.49 % (16293)Success in time 1.983 s
%------------------------------------------------------------------------------