%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP133^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 08:55:49 AM UTC 2026
% Result : Theorem 106.67s 16.60s
% Output : Refutation 106.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP133^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n020.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:27:42 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : ITP133^2 : TPTP v9.2.1. Released v7.5.0.
% 0.26/0.47 % Domain : Interactive Theorem Proving
% 0.26/0.47 % Problem : Sledgehammer Number_Partition problem prob_28__5323650_1
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English :
% 0.26/0.47
% 0.26/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.47 % Source : [Des21]
% 0.26/0.47 % Names : Number_Partition/prob_28__5323650_1 [Des21]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % Rating : 0.33 v8.1.0, 0.75 v7.5.0
% 0.26/0.47 % Syntax : Number of formulae : 336 ( 83 unt; 48 typ; 0 def)
% 0.26/0.47 % Number of atoms : 938 ( 252 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 13 ( 3 avg)
% 0.26/0.47 % Number of connectives : 3288 ( 83 ~; 28 |; 59 &;2641 @)
% 0.26/0.47 % ( 0 <=>; 477 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 22 ( 8 avg)
% 0.26/0.47 % Number of types : 2 ( 1 usr)
% 0.26/0.47 % Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 48 ( 47 usr; 0 con; 1-4 aty)
% 0.26/0.47 % Number of variables : 955 ( 79 ^; 822 !; 9 ?; 955 :)
% 0.26/0.47 % ( 45 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.47 % SPC : TH1_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:26:56.647
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % Could-be-implicit typings (2)
% 0.26/0.47 thf(ty_t_Set_Oset,type,
% 0.26/0.47 set: $tType > $tType ).
% 0.26/0.47
% 0.26/0.47 thf(ty_t_Nat_Onat,type,
% 0.26/0.47 nat: $tType ).
% 0.26/0.47
% 0.26/0.47 % Explicit typings (46)
% 0.26/0.47 thf(sy_cl_HOL_Otype,type,
% 0.26/0.47 type:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Oone,type,
% 0.26/0.47 one:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Ozero,type,
% 0.26/0.47 zero:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.26/0.47 ord:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Num_Oneg__numeral,type,
% 0.26/0.47 neg_numeral:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.26/0.47 order:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Omult__zero,type,
% 0.26/0.47 mult_zero:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Ono__bot,type,
% 0.26/0.47 no_bot:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Ono__top,type,
% 0.26/0.47 no_top:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Osemiring__0,type,
% 0.26/0.47 semiring_0:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.26/0.47 monoid_mult:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.26/0.47 linorder:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.26/0.47 preorder:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Oordered__ring,type,
% 0.26/0.47 ordered_ring:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.26/0.47 zero_neq_one:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Owellorder,type,
% 0.26/0.47 wellorder:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.26/0.47 semigroup_mult:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Odense__order,type,
% 0.26/0.47 dense_order:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.26/0.47 linordered_idom:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Olinordered__ring,type,
% 0.26/0.47 linordered_ring:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.26/0.47 comm_monoid_add:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Oordered__semiring,type,
% 0.26/0.47 ordered_semiring:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.26/0.47 comm_monoid_mult:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.26/0.47 ab_semigroup_mult:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.26/0.47 dense_linorder:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Oordered__semiring__0,type,
% 0.26/0.47 ordered_semiring_0:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Oordered__comm__semiring,type,
% 0.26/0.47 ordere1490568538miring:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 0.26/0.47 linord581940658strict:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 0.26/0.47 ring_11004092258visors:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.26/0.47 ordere216010020id_add:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 0.26/0.47 semiri1193490041visors:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.26/0.47 linord1659791738miring:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.26/0.47 canoni770627133id_add:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 0.26/0.47 semiri1923998003cancel:
% 0.26/0.47 !>[A: $tType] : $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.26/0.47 one_one:
% 0.26/0.47 !>[A: $tType] : A ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.26/0.47 times_times:
% 0.26/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.26/0.47 zero_zero:
% 0.26/0.47 !>[A: $tType] : A ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum,type,
% 0.26/0.47 groups1340683514dd_sum:
% 0.26/0.47 !>[B: $tType,A: $tType] : ( ( B > A ) > ( set @ B ) > A ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 0.26/0.47 neg_numeral_dbl_inc:
% 0.26/0.47 !>[A: $tType] : ( A > A ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Number__Partition__Mirabelle__ihnzjotehb_Opartitions,type,
% 0.26/0.47 number2016821345itions: ( nat > nat ) > nat > $o ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.26/0.47 ord_less:
% 0.26/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.26/0.47 ord_less_eq:
% 0.26/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Set_OCollect,type,
% 0.26/0.47 collect:
% 0.26/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_Set__Interval_Oord__class_OatMost,type,
% 0.26/0.47 set_ord_atMost:
% 0.26/0.47 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_c_member,type,
% 0.26/0.47 member:
% 0.26/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf(sy_v_p,type,
% 0.26/0.47 p: nat > nat ).
% 0.26/0.47
% 0.26/0.47 % Relevant facts (253)
% 0.26/0.47 thf(fact_0_mult__cancel__left1,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ring_11004092258visors @ A )
% 0.26/0.47 => ! [C: A,B2: A] :
% 0.26/0.47 ( ( C
% 0.26/0.47 = ( times_times @ A @ C @ B2 ) )
% 0.26/0.47 = ( ( C
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( B2
% 0.26/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel_left1
% 0.26/0.47 thf(fact_1_mult__cancel__left2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ring_11004092258visors @ A )
% 0.26/0.47 => ! [C: A,A2: A] :
% 0.26/0.47 ( ( ( times_times @ A @ C @ A2 )
% 0.26/0.47 = C )
% 0.26/0.47 = ( ( C
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( A2
% 0.26/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel_left2
% 0.26/0.47 thf(fact_2_mult__cancel__right1,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ring_11004092258visors @ A )
% 0.26/0.47 => ! [C: A,B2: A] :
% 0.26/0.47 ( ( C
% 0.26/0.47 = ( times_times @ A @ B2 @ C ) )
% 0.26/0.47 = ( ( C
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( B2
% 0.26/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel_right1
% 0.26/0.47 thf(fact_3_mult__cancel__right2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ring_11004092258visors @ A )
% 0.26/0.47 => ! [A2: A,C: A] :
% 0.26/0.47 ( ( ( times_times @ A @ A2 @ C )
% 0.26/0.47 = C )
% 0.26/0.47 = ( ( C
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( A2
% 0.26/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel_right2
% 0.26/0.47 thf(fact_4_sum_Oneutral__const,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [A3: set @ B] :
% 0.26/0.47 ( ( groups1340683514dd_sum @ B @ A
% 0.26/0.47 @ ^ [Uu: B] : ( zero_zero @ A )
% 0.26/0.47 @ A3 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.neutral_const
% 0.26/0.47 thf(fact_5_partitionsE,axiom,
% 0.26/0.47 ! [P: nat > nat,N: nat] :
% 0.26/0.47 ( ( number2016821345itions @ P @ N )
% 0.26/0.47 => ~ ( ! [I: nat] :
% 0.26/0.47 ( ( ( P @ I )
% 0.26/0.47 != ( zero_zero @ nat ) )
% 0.26/0.47 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I )
% 0.26/0.47 & ( ord_less_eq @ nat @ I @ N ) ) )
% 0.26/0.47 => ( ( groups1340683514dd_sum @ nat @ nat
% 0.26/0.47 @ ^ [I2: nat] : ( times_times @ nat @ ( P @ I2 ) @ I2 )
% 0.26/0.47 @ ( set_ord_atMost @ nat @ N ) )
% 0.26/0.47 != N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % partitionsE
% 0.26/0.47 thf(fact_6_partitionsI,axiom,
% 0.26/0.47 ! [P: nat > nat,N: nat] :
% 0.26/0.47 ( ! [I3: nat] :
% 0.26/0.47 ( ( ( P @ I3 )
% 0.26/0.47 != ( zero_zero @ nat ) )
% 0.26/0.47 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I3 )
% 0.26/0.47 & ( ord_less_eq @ nat @ I3 @ N ) ) )
% 0.26/0.47 => ( ( ( groups1340683514dd_sum @ nat @ nat
% 0.26/0.47 @ ^ [I2: nat] : ( times_times @ nat @ ( P @ I2 ) @ I2 )
% 0.26/0.47 @ ( set_ord_atMost @ nat @ N ) )
% 0.26/0.47 = N )
% 0.26/0.47 => ( number2016821345itions @ P @ N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % partitionsI
% 0.26/0.47 thf(fact_7_partitions__def,axiom,
% 0.26/0.47 ( number2016821345itions
% 0.26/0.47 = ( ^ [P2: nat > nat,N2: nat] :
% 0.26/0.47 ( ! [I2: nat] :
% 0.26/0.47 ( ( ( P2 @ I2 )
% 0.26/0.47 != ( zero_zero @ nat ) )
% 0.26/0.47 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I2 )
% 0.26/0.47 & ( ord_less_eq @ nat @ I2 @ N2 ) ) )
% 0.26/0.47 & ( ( groups1340683514dd_sum @ nat @ nat
% 0.26/0.47 @ ^ [I2: nat] : ( times_times @ nat @ ( P2 @ I2 ) @ I2 )
% 0.26/0.47 @ ( set_ord_atMost @ nat @ N2 ) )
% 0.26/0.47 = N2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % partitions_def
% 0.26/0.47 thf(fact_8_nat__1__eq__mult__iff,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( ( one_one @ nat )
% 0.26/0.47 = ( times_times @ nat @ M @ N ) )
% 0.26/0.47 = ( ( M
% 0.26/0.47 = ( one_one @ nat ) )
% 0.26/0.47 & ( N
% 0.26/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_1_eq_mult_iff
% 0.26/0.47 thf(fact_9_nat__mult__eq__1__iff,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( ( times_times @ nat @ M @ N )
% 0.26/0.47 = ( one_one @ nat ) )
% 0.26/0.47 = ( ( M
% 0.26/0.47 = ( one_one @ nat ) )
% 0.26/0.47 & ( N
% 0.26/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_mult_eq_1_iff
% 0.26/0.47 thf(fact_10_atMost__subset__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( preorder @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ X ) @ ( set_ord_atMost @ A @ Y ) )
% 0.26/0.47 = ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % atMost_subset_iff
% 0.26/0.47 thf(fact_11_atMost__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ord @ A )
% 0.26/0.47 => ! [I4: A,K: A] :
% 0.26/0.47 ( ( member @ A @ I4 @ ( set_ord_atMost @ A @ K ) )
% 0.26/0.47 = ( ord_less_eq @ A @ I4 @ K ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % atMost_iff
% 0.26/0.47 thf(fact_12_atMost__eq__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ( set_ord_atMost @ A @ X )
% 0.26/0.47 = ( set_ord_atMost @ A @ Y ) )
% 0.26/0.47 = ( X = Y ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % atMost_eq_iff
% 0.26/0.47 thf(fact_13_mult__cancel__right,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semiri1923998003cancel @ A )
% 0.26/0.47 => ! [A2: A,C: A,B2: A] :
% 0.26/0.47 ( ( ( times_times @ A @ A2 @ C )
% 0.26/0.47 = ( times_times @ A @ B2 @ C ) )
% 0.26/0.47 = ( ( C
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel_right
% 0.26/0.47 thf(fact_14_mult__cancel__left,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semiri1923998003cancel @ A )
% 0.26/0.47 => ! [C: A,A2: A,B2: A] :
% 0.26/0.47 ( ( ( times_times @ A @ C @ A2 )
% 0.26/0.47 = ( times_times @ A @ C @ B2 ) )
% 0.26/0.47 = ( ( C
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel_left
% 0.26/0.47 thf(fact_15_mult__eq__0__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semiri1193490041visors @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ( times_times @ A @ A2 @ B2 )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 = ( ( A2
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( B2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_eq_0_iff
% 0.26/0.47 thf(fact_16_mult__zero__right,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( mult_zero @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_zero_right
% 0.26/0.47 thf(fact_17_mult__zero__left,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( mult_zero @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_zero_left
% 0.26/0.47 thf(fact_18_bot__nat__0_Oextremum,axiom,
% 0.26/0.47 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.26/0.47
% 0.26/0.47 % bot_nat_0.extremum
% 0.26/0.47 thf(fact_19_le0,axiom,
% 0.26/0.47 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.26/0.47
% 0.26/0.47 % le0
% 0.26/0.47 thf(fact_20_mult__cancel2,axiom,
% 0.26/0.47 ! [M: nat,K: nat,N: nat] :
% 0.26/0.47 ( ( ( times_times @ nat @ M @ K )
% 0.26/0.47 = ( times_times @ nat @ N @ K ) )
% 0.26/0.47 = ( ( M = N )
% 0.26/0.47 | ( K
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel2
% 0.26/0.47 thf(fact_21_mult__cancel1,axiom,
% 0.26/0.47 ! [K: nat,M: nat,N: nat] :
% 0.26/0.47 ( ( ( times_times @ nat @ K @ M )
% 0.26/0.47 = ( times_times @ nat @ K @ N ) )
% 0.26/0.47 = ( ( M = N )
% 0.26/0.47 | ( K
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_cancel1
% 0.26/0.47 thf(fact_22_mult__0__right,axiom,
% 0.26/0.47 ! [M: nat] :
% 0.26/0.47 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 0.26/0.47 = ( zero_zero @ nat ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_0_right
% 0.26/0.47 thf(fact_23_mult__is__0,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( ( times_times @ nat @ M @ N )
% 0.26/0.47 = ( zero_zero @ nat ) )
% 0.26/0.47 = ( ( M
% 0.26/0.47 = ( zero_zero @ nat ) )
% 0.26/0.47 | ( N
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_is_0
% 0.26/0.47 thf(fact_24_bounded__Max__nat,axiom,
% 0.26/0.47 ! [P3: nat > $o,X: nat,M2: nat] :
% 0.26/0.47 ( ( P3 @ X )
% 0.26/0.47 => ( ! [X2: nat] :
% 0.26/0.47 ( ( P3 @ X2 )
% 0.26/0.47 => ( ord_less_eq @ nat @ X2 @ M2 ) )
% 0.26/0.47 => ~ ! [M3: nat] :
% 0.26/0.47 ( ( P3 @ M3 )
% 0.26/0.47 => ~ ! [X3: nat] :
% 0.26/0.47 ( ( P3 @ X3 )
% 0.26/0.47 => ( ord_less_eq @ nat @ X3 @ M3 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % bounded_Max_nat
% 0.26/0.47 thf(fact_25_Nat_Oex__has__greatest__nat,axiom,
% 0.26/0.47 ! [P3: nat > $o,K: nat,B2: nat] :
% 0.26/0.47 ( ( P3 @ K )
% 0.26/0.47 => ( ! [Y2: nat] :
% 0.26/0.47 ( ( P3 @ Y2 )
% 0.26/0.47 => ( ord_less_eq @ nat @ Y2 @ B2 ) )
% 0.26/0.47 => ? [X2: nat] :
% 0.26/0.47 ( ( P3 @ X2 )
% 0.26/0.47 & ! [Y3: nat] :
% 0.26/0.47 ( ( P3 @ Y3 )
% 0.26/0.47 => ( ord_less_eq @ nat @ Y3 @ X2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % Nat.ex_has_greatest_nat
% 0.26/0.47 thf(fact_26_nat__le__linear,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.47 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_le_linear
% 0.26/0.47 thf(fact_27_le__antisym,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.47 => ( ( ord_less_eq @ nat @ N @ M )
% 0.26/0.47 => ( M = N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_antisym
% 0.26/0.47 thf(fact_28_eq__imp__le,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( M = N )
% 0.26/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.26/0.47
% 0.26/0.47 % eq_imp_le
% 0.26/0.47 thf(fact_29_le__trans,axiom,
% 0.26/0.47 ! [I4: nat,J: nat,K: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I4 @ J )
% 0.26/0.47 => ( ( ord_less_eq @ nat @ J @ K )
% 0.26/0.47 => ( ord_less_eq @ nat @ I4 @ K ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_trans
% 0.26/0.47 thf(fact_30_le__refl,axiom,
% 0.26/0.47 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.26/0.47
% 0.26/0.47 % le_refl
% 0.26/0.47 thf(fact_31_sum_Oreindex__bij__witness,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType,C2: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [S: set @ B,I4: C2 > B,J: B > C2,T: set @ C2,H: C2 > A,G: B > A] :
% 0.26/0.47 ( ! [A4: B] :
% 0.26/0.47 ( ( member @ B @ A4 @ S )
% 0.26/0.47 => ( ( I4 @ ( J @ A4 ) )
% 0.26/0.47 = A4 ) )
% 0.26/0.47 => ( ! [A4: B] :
% 0.26/0.47 ( ( member @ B @ A4 @ S )
% 0.26/0.47 => ( member @ C2 @ ( J @ A4 ) @ T ) )
% 0.26/0.47 => ( ! [B3: C2] :
% 0.26/0.47 ( ( member @ C2 @ B3 @ T )
% 0.26/0.47 => ( ( J @ ( I4 @ B3 ) )
% 0.26/0.47 = B3 ) )
% 0.26/0.47 => ( ! [B3: C2] :
% 0.26/0.47 ( ( member @ C2 @ B3 @ T )
% 0.26/0.47 => ( member @ B @ ( I4 @ B3 ) @ S ) )
% 0.26/0.47 => ( ! [A4: B] :
% 0.26/0.47 ( ( member @ B @ A4 @ S )
% 0.26/0.47 => ( ( H @ ( J @ A4 ) )
% 0.26/0.47 = ( G @ A4 ) ) )
% 0.26/0.47 => ( ( groups1340683514dd_sum @ B @ A @ G @ S )
% 0.26/0.47 = ( groups1340683514dd_sum @ C2 @ A @ H @ T ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.reindex_bij_witness
% 0.26/0.47 thf(fact_32_sum_Oeq__general__inverses,axiom,
% 0.26/0.47 ! [C2: $tType,A: $tType,B: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [B4: set @ B,K: B > C2,A3: set @ C2,H: C2 > B,Gamma: B > A,Phi: C2 > A] :
% 0.26/0.47 ( ! [Y2: B] :
% 0.26/0.47 ( ( member @ B @ Y2 @ B4 )
% 0.26/0.47 => ( ( member @ C2 @ ( K @ Y2 ) @ A3 )
% 0.26/0.47 & ( ( H @ ( K @ Y2 ) )
% 0.26/0.47 = Y2 ) ) )
% 0.26/0.47 => ( ! [X2: C2] :
% 0.26/0.47 ( ( member @ C2 @ X2 @ A3 )
% 0.26/0.47 => ( ( member @ B @ ( H @ X2 ) @ B4 )
% 0.26/0.47 & ( ( K @ ( H @ X2 ) )
% 0.26/0.47 = X2 )
% 0.26/0.47 & ( ( Gamma @ ( H @ X2 ) )
% 0.26/0.47 = ( Phi @ X2 ) ) ) )
% 0.26/0.47 => ( ( groups1340683514dd_sum @ C2 @ A @ Phi @ A3 )
% 0.26/0.47 = ( groups1340683514dd_sum @ B @ A @ Gamma @ B4 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.eq_general_inverses
% 0.26/0.47 thf(fact_33_sum_Oeq__general,axiom,
% 0.26/0.47 ! [C2: $tType,A: $tType,B: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [B4: set @ B,A3: set @ C2,H: C2 > B,Gamma: B > A,Phi: C2 > A] :
% 0.26/0.47 ( ! [Y2: B] :
% 0.26/0.47 ( ( member @ B @ Y2 @ B4 )
% 0.26/0.47 => ? [X3: C2] :
% 0.26/0.47 ( ( member @ C2 @ X3 @ A3 )
% 0.26/0.47 & ( ( H @ X3 )
% 0.26/0.47 = Y2 )
% 0.26/0.47 & ! [Ya: C2] :
% 0.26/0.47 ( ( ( member @ C2 @ Ya @ A3 )
% 0.26/0.47 & ( ( H @ Ya )
% 0.26/0.47 = Y2 ) )
% 0.26/0.47 => ( Ya = X3 ) ) ) )
% 0.26/0.47 => ( ! [X2: C2] :
% 0.26/0.47 ( ( member @ C2 @ X2 @ A3 )
% 0.26/0.47 => ( ( member @ B @ ( H @ X2 ) @ B4 )
% 0.26/0.47 & ( ( Gamma @ ( H @ X2 ) )
% 0.26/0.47 = ( Phi @ X2 ) ) ) )
% 0.26/0.47 => ( ( groups1340683514dd_sum @ C2 @ A @ Phi @ A3 )
% 0.26/0.47 = ( groups1340683514dd_sum @ B @ A @ Gamma @ B4 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.eq_general
% 0.26/0.47 thf(fact_34_sum_Ocong,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [A3: set @ B,B4: set @ B,G: B > A,H: B > A] :
% 0.26/0.47 ( ( A3 = B4 )
% 0.26/0.47 => ( ! [X2: B] :
% 0.26/0.47 ( ( member @ B @ X2 @ B4 )
% 0.26/0.47 => ( ( G @ X2 )
% 0.26/0.47 = ( H @ X2 ) ) )
% 0.26/0.47 => ( ( groups1340683514dd_sum @ B @ A @ G @ A3 )
% 0.26/0.47 = ( groups1340683514dd_sum @ B @ A @ H @ B4 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.cong
% 0.26/0.47 thf(fact_35_sum_Oswap,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType,C2: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [G: B > C2 > A,B4: set @ C2,A3: set @ B] :
% 0.26/0.47 ( ( groups1340683514dd_sum @ B @ A
% 0.26/0.47 @ ^ [I2: B] : ( groups1340683514dd_sum @ C2 @ A @ ( G @ I2 ) @ B4 )
% 0.26/0.47 @ A3 )
% 0.26/0.47 = ( groups1340683514dd_sum @ C2 @ A
% 0.26/0.47 @ ^ [J2: C2] :
% 0.26/0.47 ( groups1340683514dd_sum @ B @ A
% 0.26/0.47 @ ^ [I2: B] : ( G @ I2 @ J2 )
% 0.26/0.47 @ A3 )
% 0.26/0.47 @ B4 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.swap
% 0.26/0.47 thf(fact_36_mult__right__cancel,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semiri1923998003cancel @ A )
% 0.26/0.47 => ! [C: A,A2: A,B2: A] :
% 0.26/0.47 ( ( C
% 0.26/0.47 != ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ( times_times @ A @ A2 @ C )
% 0.26/0.47 = ( times_times @ A @ B2 @ C ) )
% 0.26/0.47 = ( A2 = B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_right_cancel
% 0.26/0.47 thf(fact_37_mult__left__cancel,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semiri1923998003cancel @ A )
% 0.26/0.47 => ! [C: A,A2: A,B2: A] :
% 0.26/0.47 ( ( C
% 0.26/0.47 != ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ( times_times @ A @ C @ A2 )
% 0.26/0.47 = ( times_times @ A @ C @ B2 ) )
% 0.26/0.47 = ( A2 = B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_left_cancel
% 0.26/0.47 thf(fact_38_no__zero__divisors,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semiri1193490041visors @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( A2
% 0.26/0.47 != ( zero_zero @ A ) )
% 0.26/0.47 => ( ( B2
% 0.26/0.47 != ( zero_zero @ A ) )
% 0.26/0.47 => ( ( times_times @ A @ A2 @ B2 )
% 0.26/0.47 != ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % no_zero_divisors
% 0.26/0.47 thf(fact_39_divisors__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semiri1193490041visors @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ( times_times @ A @ A2 @ B2 )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 => ( ( A2
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 | ( B2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % divisors_zero
% 0.26/0.47 thf(fact_40_mult__not__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( mult_zero @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ( times_times @ A @ A2 @ B2 )
% 0.26/0.47 != ( zero_zero @ A ) )
% 0.26/0.47 => ( ( A2
% 0.26/0.47 != ( zero_zero @ A ) )
% 0.26/0.47 & ( B2
% 0.26/0.47 != ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_not_zero
% 0.26/0.47 thf(fact_41_zero__neq__one,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( zero_neq_one @ A )
% 0.26/0.47 => ( ( zero_zero @ A )
% 0.26/0.47 != ( one_one @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_neq_one
% 0.26/0.47 thf(fact_42_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [G: B > A,A3: set @ B] :
% 0.26/0.47 ( ( ( groups1340683514dd_sum @ B @ A @ G @ A3 )
% 0.26/0.47 != ( zero_zero @ A ) )
% 0.26/0.47 => ~ ! [A4: B] :
% 0.26/0.47 ( ( member @ B @ A4 @ A3 )
% 0.26/0.47 => ( ( G @ A4 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.not_neutral_contains_not_neutral
% 0.26/0.47 thf(fact_43_sum_Oneutral,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [A3: set @ B,G: B > A] :
% 0.26/0.47 ( ! [X2: B] :
% 0.26/0.47 ( ( member @ B @ X2 @ A3 )
% 0.26/0.47 => ( ( G @ X2 )
% 0.26/0.47 = ( zero_zero @ A ) ) )
% 0.26/0.47 => ( ( groups1340683514dd_sum @ B @ A @ G @ A3 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum.neutral
% 0.26/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.26/0.47 ! [A: $tType,A2: A,P3: A > $o] :
% 0.26/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 0.26/0.47 = ( P3 @ A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % mem_Collect_eq
% 0.26/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A] :
% 0.26/0.47 ( ( collect @ A
% 0.26/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.26/0.47 = A3 ) ).
% 0.26/0.47
% 0.26/0.47 % Collect_mem_eq
% 0.26/0.47 thf(fact_46_Collect__cong,axiom,
% 0.26/0.47 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.26/0.47 ( ! [X2: A] :
% 0.26/0.47 ( ( P3 @ X2 )
% 0.26/0.47 = ( Q @ X2 ) )
% 0.26/0.47 => ( ( collect @ A @ P3 )
% 0.26/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % Collect_cong
% 0.26/0.47 thf(fact_47_ext,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.26/0.47 ( ! [X2: A] :
% 0.26/0.47 ( ( F @ X2 )
% 0.26/0.47 = ( G @ X2 ) )
% 0.26/0.47 => ( F = G ) ) ).
% 0.26/0.47
% 0.26/0.47 % ext
% 0.26/0.47 thf(fact_48_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.26/0.47 ! [A2: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.26/0.47 => ( A2
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % bot_nat_0.extremum_uniqueI
% 0.26/0.47 thf(fact_49_bot__nat__0_Oextremum__unique,axiom,
% 0.26/0.47 ! [A2: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.26/0.47 = ( A2
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % bot_nat_0.extremum_unique
% 0.26/0.47 thf(fact_50_le__0__eq,axiom,
% 0.26/0.47 ! [N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 0.26/0.47 = ( N
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_0_eq
% 0.26/0.47 thf(fact_51_less__eq__nat_Osimps_I1_J,axiom,
% 0.26/0.47 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.26/0.47
% 0.26/0.47 % less_eq_nat.simps(1)
% 0.26/0.47 thf(fact_52_mult__0,axiom,
% 0.26/0.47 ! [N: nat] :
% 0.26/0.47 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 0.26/0.47 = ( zero_zero @ nat ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_0
% 0.26/0.47 thf(fact_53_mult__le__mono2,axiom,
% 0.26/0.47 ! [I4: nat,J: nat,K: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I4 @ J )
% 0.26/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ K @ I4 ) @ ( times_times @ nat @ K @ J ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_mono2
% 0.26/0.47 thf(fact_54_mult__le__mono1,axiom,
% 0.26/0.47 ! [I4: nat,J: nat,K: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I4 @ J )
% 0.26/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ I4 @ K ) @ ( times_times @ nat @ J @ K ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_mono1
% 0.26/0.47 thf(fact_55_mult__le__mono,axiom,
% 0.26/0.47 ! [I4: nat,J: nat,K: nat,L: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I4 @ J )
% 0.26/0.47 => ( ( ord_less_eq @ nat @ K @ L )
% 0.26/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ I4 @ K ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_mono
% 0.26/0.47 thf(fact_56_le__square,axiom,
% 0.26/0.47 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_square
% 0.26/0.47 thf(fact_57_le__cube,axiom,
% 0.26/0.47 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_cube
% 0.26/0.47 thf(fact_58_nat__mult__1__right,axiom,
% 0.26/0.47 ! [N: nat] :
% 0.26/0.47 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 0.26/0.47 = N ) ).
% 0.26/0.47
% 0.26/0.47 % nat_mult_1_right
% 0.26/0.47 thf(fact_59_nat__mult__1,axiom,
% 0.26/0.47 ! [N: nat] :
% 0.26/0.47 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 0.26/0.47 = N ) ).
% 0.26/0.47
% 0.26/0.47 % nat_mult_1
% 0.26/0.47 thf(fact_60_lambda__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( mult_zero @ A )
% 0.26/0.47 => ( ( ^ [H2: A] : ( zero_zero @ A ) )
% 0.26/0.47 = ( times_times @ A @ ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % lambda_zero
% 0.26/0.47 thf(fact_61_lambda__one,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( monoid_mult @ A )
% 0.26/0.47 => ( ( ^ [X4: A] : X4 )
% 0.26/0.47 = ( times_times @ A @ ( one_one @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % lambda_one
% 0.26/0.47 thf(fact_62_sum__mono,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [K2: set @ B,F: B > A,G: B > A] :
% 0.26/0.47 ( ! [I3: B] :
% 0.26/0.47 ( ( member @ B @ I3 @ K2 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F @ K2 ) @ ( groups1340683514dd_sum @ B @ A @ G @ K2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum_mono
% 0.26/0.47 thf(fact_63_sum__distrib__right,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( semiring_0 @ A )
% 0.26/0.47 => ! [F: B > A,A3: set @ B,R: A] :
% 0.26/0.47 ( ( times_times @ A @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) @ R )
% 0.26/0.47 = ( groups1340683514dd_sum @ B @ A
% 0.26/0.47 @ ^ [N2: B] : ( times_times @ A @ ( F @ N2 ) @ R )
% 0.26/0.47 @ A3 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum_distrib_right
% 0.26/0.47 thf(fact_64_sum__distrib__left,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( semiring_0 @ A )
% 0.26/0.47 => ! [R: A,F: B > A,A3: set @ B] :
% 0.26/0.47 ( ( times_times @ A @ R @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) )
% 0.26/0.47 = ( groups1340683514dd_sum @ B @ A
% 0.26/0.47 @ ^ [N2: B] : ( times_times @ A @ R @ ( F @ N2 ) )
% 0.26/0.47 @ A3 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum_distrib_left
% 0.26/0.47 thf(fact_65_sum__product,axiom,
% 0.26/0.47 ! [B: $tType,C2: $tType,A: $tType] :
% 0.26/0.47 ( ( semiring_0 @ B )
% 0.26/0.47 => ! [F: A > B,A3: set @ A,G: C2 > B,B4: set @ C2] :
% 0.26/0.47 ( ( times_times @ B @ ( groups1340683514dd_sum @ A @ B @ F @ A3 ) @ ( groups1340683514dd_sum @ C2 @ B @ G @ B4 ) )
% 0.26/0.47 = ( groups1340683514dd_sum @ A @ B
% 0.26/0.47 @ ^ [I2: A] :
% 0.26/0.47 ( groups1340683514dd_sum @ C2 @ B
% 0.26/0.47 @ ^ [J2: C2] : ( times_times @ B @ ( F @ I2 ) @ ( G @ J2 ) )
% 0.26/0.47 @ B4 )
% 0.26/0.47 @ A3 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum_product
% 0.26/0.47 thf(fact_66_atMost__def,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ord @ A )
% 0.26/0.47 => ( ( set_ord_atMost @ A )
% 0.26/0.47 = ( ^ [U: A] :
% 0.26/0.47 ( collect @ A
% 0.26/0.47 @ ^ [X4: A] : ( ord_less_eq @ A @ X4 @ U ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % atMost_def
% 0.26/0.47 thf(fact_67_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere1490568538miring @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.26/0.47 thf(fact_68_zero__le__mult__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord581940658strict @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 0.26/0.47 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.26/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_le_mult_iff
% 0.26/0.47 thf(fact_69_mult__nonneg__nonpos2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring_0 @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_nonneg_nonpos2
% 0.26/0.47 thf(fact_70_mult__nonpos__nonneg,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring_0 @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_nonpos_nonneg
% 0.26/0.47 thf(fact_71_mult__nonneg__nonpos,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring_0 @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_nonneg_nonpos
% 0.26/0.47 thf(fact_72_mult__nonneg__nonneg,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring_0 @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_nonneg_nonneg
% 0.26/0.47 thf(fact_73_split__mult__neg__le,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring_0 @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.26/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % split_mult_neg_le
% 0.26/0.47 thf(fact_74_mult__le__0__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord581940658strict @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.26/0.47 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.26/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_0_iff
% 0.26/0.47 thf(fact_75_mult__right__mono,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_right_mono
% 0.26/0.47 thf(fact_76_mult__right__mono__neg,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_ring @ A )
% 0.26/0.47 => ! [B2: A,A2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_right_mono_neg
% 0.26/0.47 thf(fact_77_mult__left__mono,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_left_mono
% 0.26/0.47 thf(fact_78_mult__nonpos__nonpos,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_ring @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_nonpos_nonpos
% 0.26/0.47 thf(fact_79_mult__left__mono__neg,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_ring @ A )
% 0.26/0.47 => ! [B2: A,A2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_left_mono_neg
% 0.26/0.47 thf(fact_80_split__mult__pos__le,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_ring @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.26/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % split_mult_pos_le
% 0.26/0.47 thf(fact_81_zero__le__square,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linordered_ring @ A )
% 0.26/0.47 => ! [A2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ A2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_le_square
% 0.26/0.47 thf(fact_82_mult__mono_H,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A,D: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_mono'
% 0.26/0.47 thf(fact_83_mult__mono,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_semiring @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A,D: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_mono
% 0.26/0.47 thf(fact_84_not__one__le__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % not_one_le_zero
% 0.26/0.47 thf(fact_85_zero__le__one,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_le_one
% 0.26/0.47 thf(fact_86_sum__nonpos,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [A3: set @ B,F: B > A] :
% 0.26/0.47 ( ! [X2: B] :
% 0.26/0.47 ( ( member @ B @ X2 @ A3 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( zero_zero @ A ) ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) @ ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum_nonpos
% 0.26/0.47 thf(fact_87_sum__nonneg,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [A3: set @ B,F: B > A] :
% 0.26/0.47 ( ! [X2: B] :
% 0.26/0.47 ( ( member @ B @ X2 @ A3 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F @ X2 ) ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % sum_nonneg
% 0.26/0.47 thf(fact_88_mult__eq__self__implies__10,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( M
% 0.26/0.47 = ( times_times @ nat @ M @ N ) )
% 0.26/0.47 => ( ( N
% 0.26/0.47 = ( one_one @ nat ) )
% 0.26/0.47 | ( M
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_eq_self_implies_10
% 0.26/0.47 thf(fact_89_mult__left__le,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ! [C: A,A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ C @ ( one_one @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ A2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_left_le
% 0.26/0.47 thf(fact_90_mult__le__one,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( one_one @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B2 @ ( one_one @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( one_one @ A ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_one
% 0.26/0.47 thf(fact_91_mult__right__le__one__le,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linordered_idom @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.26/0.47 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ X @ Y ) @ X ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_right_le_one_le
% 0.26/0.47 thf(fact_92_mult__left__le__one__le,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linordered_idom @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.26/0.47 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ Y @ X ) @ X ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_left_le_one_le
% 0.26/0.47 thf(fact_93_mult_Oright__neutral,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( monoid_mult @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult.right_neutral
% 0.26/0.47 thf(fact_94_mult_Oleft__neutral,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( monoid_mult @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult.left_neutral
% 0.26/0.47 thf(fact_95_le__zero__eq,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( canoni770627133id_add @ A )
% 0.26/0.47 => ! [N: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.26/0.47 = ( N
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_zero_eq
% 0.26/0.47 thf(fact_96_subsetI,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.47 ( ! [X2: A] :
% 0.26/0.47 ( ( member @ A @ X2 @ A3 )
% 0.26/0.47 => ( member @ A @ X2 @ B4 ) )
% 0.26/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.26/0.47
% 0.26/0.47 % subsetI
% 0.26/0.47 thf(fact_97_subset__antisym,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 0.26/0.47 => ( A3 = B4 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % subset_antisym
% 0.26/0.47 thf(fact_98_order__refl,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( preorder @ A )
% 0.26/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.26/0.47
% 0.26/0.47 % order_refl
% 0.26/0.47 thf(fact_99_nat__mult__eq__cancel__disj,axiom,
% 0.26/0.47 ! [K: nat,M: nat,N: nat] :
% 0.26/0.47 ( ( ( times_times @ nat @ K @ M )
% 0.26/0.47 = ( times_times @ nat @ K @ N ) )
% 0.26/0.47 = ( ( K
% 0.26/0.47 = ( zero_zero @ nat ) )
% 0.26/0.47 | ( M = N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_mult_eq_cancel_disj
% 0.26/0.47 thf(fact_100_mult_Ocomm__neutral,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( comm_monoid_mult @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult.comm_neutral
% 0.26/0.47 thf(fact_101_comm__monoid__mult__class_Omult__1,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( comm_monoid_mult @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % comm_monoid_mult_class.mult_1
% 0.26/0.47 thf(fact_102_le__funD,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( ord @ B )
% 0.26/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.26/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.26/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_funD
% 0.26/0.47 thf(fact_103_le__funE,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( ord @ B )
% 0.26/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.26/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.26/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_funE
% 0.26/0.47 thf(fact_104_le__funI,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( ord @ B )
% 0.26/0.47 => ! [F: A > B,G: A > B] :
% 0.26/0.47 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.26/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_funI
% 0.26/0.47 thf(fact_105_le__fun__def,axiom,
% 0.26/0.47 ! [B: $tType,A: $tType] :
% 0.26/0.47 ( ( ord @ B )
% 0.26/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.26/0.47 = ( ^ [F2: A > B,G2: A > B] :
% 0.26/0.47 ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_fun_def
% 0.26/0.47 thf(fact_106_order__subst1,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( ( order @ B )
% 0.26/0.47 & ( order @ A ) )
% 0.26/0.47 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.26/0.47 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.26/0.47 => ( ! [X2: B,Y2: B] :
% 0.26/0.47 ( ( ord_less_eq @ B @ X2 @ Y2 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % order_subst1
% 0.26/0.47 thf(fact_107_order__subst2,axiom,
% 0.26/0.47 ! [A: $tType,C2: $tType] :
% 0.26/0.47 ( ( ( order @ C2 )
% 0.26/0.47 & ( order @ A ) )
% 0.26/0.47 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.26/0.47 => ( ! [X2: A,Y2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.26/0.47 => ( ord_less_eq @ C2 @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.47 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % order_subst2
% 0.26/0.47 thf(fact_108_ord__eq__le__subst,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( ( ord @ B )
% 0.26/0.47 & ( ord @ A ) )
% 0.26/0.47 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.26/0.47 ( ( A2
% 0.26/0.47 = ( F @ B2 ) )
% 0.26/0.47 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.26/0.47 => ( ! [X2: B,Y2: B] :
% 0.26/0.47 ( ( ord_less_eq @ B @ X2 @ Y2 )
% 0.26/0.47 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % ord_eq_le_subst
% 0.26/0.47 thf(fact_109_ord__le__eq__subst,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType] :
% 0.26/0.47 ( ( ( ord @ B )
% 0.26/0.47 & ( ord @ A ) )
% 0.26/0.47 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ( F @ B2 )
% 0.26/0.47 = C )
% 0.26/0.47 => ( ! [X2: A,Y2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.26/0.47 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.47 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % ord_le_eq_subst
% 0.26/0.47 thf(fact_110_eq__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.26/0.47 = ( ^ [X4: A,Y5: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.26/0.47 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % eq_iff
% 0.26/0.47 thf(fact_111_antisym,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.47 => ( ( ord_less_eq @ A @ Y @ X )
% 0.26/0.47 => ( X = Y ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % antisym
% 0.26/0.47 thf(fact_112_linear,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linorder @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.47 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % linear
% 0.26/0.47 thf(fact_113_eq__refl,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( preorder @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( X = Y )
% 0.26/0.47 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % eq_refl
% 0.26/0.47 thf(fact_114_le__cases,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linorder @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.26/0.47 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_cases
% 0.26/0.47 thf(fact_115_order_Otrans,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % order.trans
% 0.26/0.47 thf(fact_116_le__cases3,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linorder @ A )
% 0.26/0.47 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.47 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.26/0.47 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.26/0.47 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.26/0.47 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.26/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.26/0.47 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_cases3
% 0.26/0.47 thf(fact_117_antisym__conv,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [Y: A,X: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ Y @ X )
% 0.26/0.47 => ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.47 = ( X = Y ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % antisym_conv
% 0.26/0.47 thf(fact_118_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.26/0.47 = ( ^ [A5: A,B5: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.26/0.47 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % order_class.order.eq_iff
% 0.26/0.47 thf(fact_119_ord__eq__le__trans,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ord @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( A2 = B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % ord_eq_le_trans
% 0.26/0.47 thf(fact_120_ord__le__eq__trans,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ord @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( B2 = C )
% 0.26/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % ord_le_eq_trans
% 0.26/0.47 thf(fact_121_order__class_Oorder_Oantisym,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.26/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % order_class.order.antisym
% 0.26/0.47 thf(fact_122_order__trans,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( preorder @ A )
% 0.26/0.47 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.47 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.26/0.47 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % order_trans
% 0.26/0.47 thf(fact_123_dual__order_Orefl,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % dual_order.refl
% 0.26/0.47 thf(fact_124_linorder__wlog,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linorder @ A )
% 0.26/0.47 => ! [P3: A > A > $o,A2: A,B2: A] :
% 0.26/0.47 ( ! [A4: A,B3: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.26/0.47 => ( P3 @ A4 @ B3 ) )
% 0.26/0.47 => ( ! [A4: A,B3: A] :
% 0.26/0.47 ( ( P3 @ B3 @ A4 )
% 0.26/0.47 => ( P3 @ A4 @ B3 ) )
% 0.26/0.47 => ( P3 @ A2 @ B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % linorder_wlog
% 0.26/0.47 thf(fact_125_dual__order_Otrans,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [B2: A,A2: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.26/0.47 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % dual_order.trans
% 0.26/0.47 thf(fact_126_dual__order_Oeq__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.26/0.47 = ( ^ [A5: A,B5: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.26/0.47 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % dual_order.eq_iff
% 0.26/0.47 thf(fact_127_dual__order_Oantisym,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [B2: A,A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % dual_order.antisym
% 0.26/0.47 thf(fact_128_zero__reorient,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( zero @ A )
% 0.26/0.47 => ! [X: A] :
% 0.26/0.47 ( ( ( zero_zero @ A )
% 0.26/0.47 = X )
% 0.26/0.47 = ( X
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_reorient
% 0.26/0.47 thf(fact_129_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ab_semigroup_mult @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.26/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % ab_semigroup_mult_class.mult_ac(1)
% 0.26/0.47 thf(fact_130_mult_Oassoc,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( semigroup_mult @ A )
% 0.26/0.47 => ! [A2: A,B2: A,C: A] :
% 0.26/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.26/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult.assoc
% 0.26/0.47 thf(fact_131_mult_Ocommute,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ab_semigroup_mult @ A )
% 0.26/0.47 => ( ( times_times @ A )
% 0.26/0.47 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult.commute
% 0.26/0.47 thf(fact_132_mult_Oleft__commute,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ab_semigroup_mult @ A )
% 0.26/0.47 => ! [B2: A,A2: A,C: A] :
% 0.26/0.47 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C ) )
% 0.26/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult.left_commute
% 0.26/0.47 thf(fact_133_one__reorient,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( one @ A )
% 0.26/0.47 => ! [X: A] :
% 0.26/0.47 ( ( ( one_one @ A )
% 0.26/0.47 = X )
% 0.26/0.47 = ( X
% 0.26/0.47 = ( one_one @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % one_reorient
% 0.26/0.47 thf(fact_134_Collect__mono__iff,axiom,
% 0.26/0.47 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) )
% 0.26/0.47 = ( ! [X4: A] :
% 0.26/0.47 ( ( P3 @ X4 )
% 0.26/0.47 => ( Q @ X4 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % Collect_mono_iff
% 0.26/0.47 thf(fact_135_set__eq__subset,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 0.26/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.26/0.47 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % set_eq_subset
% 0.26/0.47 thf(fact_136_subset__trans,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 0.26/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % subset_trans
% 0.26/0.47 thf(fact_137_Collect__mono,axiom,
% 0.26/0.47 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.26/0.47 ( ! [X2: A] :
% 0.26/0.47 ( ( P3 @ X2 )
% 0.26/0.47 => ( Q @ X2 ) )
% 0.26/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % Collect_mono
% 0.26/0.47 thf(fact_138_subset__refl,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.26/0.47
% 0.26/0.47 % subset_refl
% 0.26/0.47 thf(fact_139_subset__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.26/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.26/0.47 ! [T2: A] :
% 0.26/0.47 ( ( member @ A @ T2 @ A6 )
% 0.26/0.47 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % subset_iff
% 0.26/0.47 thf(fact_140_equalityD2,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.47 ( ( A3 = B4 )
% 0.26/0.47 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 0.26/0.47
% 0.26/0.47 % equalityD2
% 0.26/0.47 thf(fact_141_equalityD1,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.47 ( ( A3 = B4 )
% 0.26/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.26/0.47
% 0.26/0.47 % equalityD1
% 0.26/0.47 thf(fact_142_subset__eq,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.26/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.26/0.47 ! [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ A6 )
% 0.26/0.47 => ( member @ A @ X4 @ B6 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % subset_eq
% 0.26/0.47 thf(fact_143_equalityE,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.47 ( ( A3 = B4 )
% 0.26/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % equalityE
% 0.26/0.47 thf(fact_144_subsetD,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.47 => ( ( member @ A @ C @ A3 )
% 0.26/0.47 => ( member @ A @ C @ B4 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % subsetD
% 0.26/0.47 thf(fact_145_in__mono,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,X: A] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.47 => ( ( member @ A @ X @ A3 )
% 0.26/0.47 => ( member @ A @ X @ B4 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % in_mono
% 0.26/0.47 thf(fact_146_less__eq__set__def,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.26/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.26/0.47 ( ord_less_eq @ ( A > $o )
% 0.26/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 0.26/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ B6 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % less_eq_set_def
% 0.26/0.47 thf(fact_147_Collect__subset,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,P3: A > $o] :
% 0.26/0.47 ( ord_less_eq @ ( set @ A )
% 0.26/0.47 @ ( collect @ A
% 0.26/0.47 @ ^ [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ A3 )
% 0.26/0.47 & ( P3 @ X4 ) ) )
% 0.26/0.47 @ A3 ) ).
% 0.26/0.47
% 0.26/0.47 % Collect_subset
% 0.26/0.47 thf(fact_148_zero__le,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( canoni770627133id_add @ A )
% 0.26/0.47 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_le
% 0.26/0.47 thf(fact_149_le__numeral__extra_I4_J,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_numeral_extra(4)
% 0.26/0.47 thf(fact_150_le__numeral__extra_I3_J,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_numeral_extra(3)
% 0.26/0.47 thf(fact_151_subset__Collect__iff,axiom,
% 0.26/0.47 ! [A: $tType,B4: set @ A,A3: set @ A,P3: A > $o] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 0.26/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4
% 0.26/0.47 @ ( collect @ A
% 0.26/0.47 @ ^ [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ A3 )
% 0.26/0.47 & ( P3 @ X4 ) ) ) )
% 0.26/0.47 = ( ! [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ B4 )
% 0.26/0.47 => ( P3 @ X4 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % subset_Collect_iff
% 0.26/0.47 thf(fact_152_subset__CollectI,axiom,
% 0.26/0.47 ! [A: $tType,B4: set @ A,A3: set @ A,Q: A > $o,P3: A > $o] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 0.26/0.47 => ( ! [X2: A] :
% 0.26/0.47 ( ( member @ A @ X2 @ B4 )
% 0.26/0.47 => ( ( Q @ X2 )
% 0.26/0.47 => ( P3 @ X2 ) ) )
% 0.26/0.47 => ( ord_less_eq @ ( set @ A )
% 0.26/0.47 @ ( collect @ A
% 0.26/0.47 @ ^ [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ B4 )
% 0.26/0.47 & ( Q @ X4 ) ) )
% 0.26/0.47 @ ( collect @ A
% 0.26/0.47 @ ^ [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ A3 )
% 0.26/0.47 & ( P3 @ X4 ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % subset_CollectI
% 0.26/0.47 thf(fact_153_Collect__restrict,axiom,
% 0.26/0.47 ! [A: $tType,X5: set @ A,P3: A > $o] :
% 0.26/0.47 ( ord_less_eq @ ( set @ A )
% 0.26/0.47 @ ( collect @ A
% 0.26/0.47 @ ^ [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ X5 )
% 0.26/0.47 & ( P3 @ X4 ) ) )
% 0.26/0.47 @ X5 ) ).
% 0.26/0.47
% 0.26/0.47 % Collect_restrict
% 0.26/0.47 thf(fact_154_predicate1I,axiom,
% 0.26/0.47 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.26/0.47 ( ! [X2: A] :
% 0.26/0.47 ( ( P3 @ X2 )
% 0.26/0.47 => ( Q @ X2 ) )
% 0.26/0.47 => ( ord_less_eq @ ( A > $o ) @ P3 @ Q ) ) ).
% 0.26/0.47
% 0.26/0.47 % predicate1I
% 0.26/0.47 thf(fact_155_predicate1D,axiom,
% 0.26/0.47 ! [A: $tType,P3: A > $o,Q: A > $o,X: A] :
% 0.26/0.47 ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 0.26/0.47 => ( ( P3 @ X )
% 0.26/0.47 => ( Q @ X ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % predicate1D
% 0.26/0.47 thf(fact_156_rev__predicate1D,axiom,
% 0.26/0.47 ! [A: $tType,P3: A > $o,X: A,Q: A > $o] :
% 0.26/0.47 ( ( P3 @ X )
% 0.26/0.47 => ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 0.26/0.47 => ( Q @ X ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % rev_predicate1D
% 0.26/0.47 thf(fact_157_prop__restrict,axiom,
% 0.26/0.47 ! [A: $tType,X: A,Z3: set @ A,X5: set @ A,P3: A > $o] :
% 0.26/0.47 ( ( member @ A @ X @ Z3 )
% 0.26/0.47 => ( ( ord_less_eq @ ( set @ A ) @ Z3
% 0.26/0.47 @ ( collect @ A
% 0.26/0.47 @ ^ [X4: A] :
% 0.26/0.47 ( ( member @ A @ X4 @ X5 )
% 0.26/0.47 & ( P3 @ X4 ) ) ) )
% 0.26/0.47 => ( P3 @ X ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % prop_restrict
% 0.26/0.47 thf(fact_158_pred__subset__eq,axiom,
% 0.26/0.47 ! [A: $tType,R2: set @ A,S: set @ A] :
% 0.26/0.47 ( ( ord_less_eq @ ( A > $o )
% 0.26/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ R2 )
% 0.26/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 0.26/0.47 = ( ord_less_eq @ ( set @ A ) @ R2 @ S ) ) ).
% 0.26/0.47
% 0.26/0.47 % pred_subset_eq
% 0.26/0.47 thf(fact_159_dbl__inc__simps_I2_J,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( neg_numeral @ A )
% 0.26/0.47 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 0.26/0.47 = ( one_one @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % dbl_inc_simps(2)
% 0.26/0.47 thf(fact_160_conj__subset__def,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,P3: A > $o,Q: A > $o] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3
% 0.26/0.47 @ ( collect @ A
% 0.26/0.47 @ ^ [X4: A] :
% 0.26/0.47 ( ( P3 @ X4 )
% 0.26/0.47 & ( Q @ X4 ) ) ) )
% 0.26/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ P3 ) )
% 0.26/0.47 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ Q ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % conj_subset_def
% 0.26/0.47 thf(fact_161_fun__cong__unused__0,axiom,
% 0.26/0.47 ! [A: $tType,B: $tType,C2: $tType] :
% 0.26/0.47 ( ( zero @ B )
% 0.26/0.47 => ! [F: ( A > B ) > C2,G: C2] :
% 0.26/0.47 ( ( F
% 0.26/0.47 = ( ^ [X4: A > B] : G ) )
% 0.26/0.47 => ( ( F
% 0.26/0.47 @ ^ [X4: A] : ( zero_zero @ B ) )
% 0.26/0.47 = G ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % fun_cong_unused_0
% 0.26/0.47 thf(fact_162_mult__le__cancel__left1,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linordered_idom @ A )
% 0.26/0.47 => ! [C: A,B2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ C @ ( times_times @ A @ C @ B2 ) )
% 0.26/0.47 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ B2 ) )
% 0.26/0.47 & ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ B2 @ ( one_one @ A ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_cancel_left1
% 0.26/0.47 thf(fact_163_mult__le__cancel__left2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linordered_idom @ A )
% 0.26/0.47 => ! [C: A,A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ C )
% 0.26/0.47 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ A2 @ ( one_one @ A ) ) )
% 0.26/0.47 & ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ A2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_cancel_left2
% 0.26/0.47 thf(fact_164_neq0__conv,axiom,
% 0.26/0.47 ! [N: nat] :
% 0.26/0.47 ( ( N
% 0.26/0.47 != ( zero_zero @ nat ) )
% 0.26/0.47 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.26/0.47
% 0.26/0.47 % neq0_conv
% 0.26/0.47 thf(fact_165_less__nat__zero__code,axiom,
% 0.26/0.47 ! [N: nat] :
% 0.26/0.47 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.26/0.47
% 0.26/0.47 % less_nat_zero_code
% 0.26/0.47 thf(fact_166_bot__nat__0_Onot__eq__extremum,axiom,
% 0.26/0.47 ! [A2: nat] :
% 0.26/0.47 ( ( A2
% 0.26/0.47 != ( zero_zero @ nat ) )
% 0.26/0.47 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % bot_nat_0.not_eq_extremum
% 0.26/0.47 thf(fact_167_psubsetI,axiom,
% 0.26/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.47 => ( ( A3 != B4 )
% 0.26/0.47 => ( ord_less @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % psubsetI
% 0.26/0.47 thf(fact_168_not__gr__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( canoni770627133id_add @ A )
% 0.26/0.47 => ! [N: A] :
% 0.26/0.47 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.26/0.47 = ( N
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % not_gr_zero
% 0.26/0.47 thf(fact_169_nat__0__less__mult__iff,axiom,
% 0.26/0.47 ! [M: nat,N: nat] :
% 0.26/0.47 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ M @ N ) )
% 0.26/0.47 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.26/0.47 & ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_0_less_mult_iff
% 0.26/0.47 thf(fact_170_mult__less__cancel2,axiom,
% 0.26/0.47 ! [M: nat,K: nat,N: nat] :
% 0.26/0.47 ( ( ord_less @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 0.26/0.47 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.26/0.47 & ( ord_less @ nat @ M @ N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_less_cancel2
% 0.26/0.47 thf(fact_171_nat__mult__less__cancel__disj,axiom,
% 0.26/0.47 ! [K: nat,M: nat,N: nat] :
% 0.26/0.47 ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.26/0.47 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.26/0.47 & ( ord_less @ nat @ M @ N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_mult_less_cancel_disj
% 0.26/0.47 thf(fact_172_less__one,axiom,
% 0.26/0.47 ! [N: nat] :
% 0.26/0.47 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 0.26/0.47 = ( N
% 0.26/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % less_one
% 0.26/0.47 thf(fact_173_mult__le__cancel2,axiom,
% 0.26/0.47 ! [M: nat,K: nat,N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 0.26/0.47 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.26/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % mult_le_cancel2
% 0.26/0.47 thf(fact_174_nat__mult__le__cancel__disj,axiom,
% 0.26/0.47 ! [K: nat,M: nat,N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.26/0.47 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.26/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_mult_le_cancel_disj
% 0.26/0.47 thf(fact_175_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [B2: A,A2: A] :
% 0.26/0.47 ( ( ord_less @ A @ B2 @ A2 )
% 0.26/0.47 => ( A2 != B2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % dual_order.strict_implies_not_eq
% 0.26/0.47 thf(fact_176_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [A2: A,B2: A] :
% 0.26/0.47 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.47 => ( A2 != B2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % order.strict_implies_not_eq
% 0.26/0.47 thf(fact_177_not__less__iff__gr__or__eq,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linorder @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.26/0.47 = ( ( ord_less @ A @ Y @ X )
% 0.26/0.47 | ( X = Y ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % not_less_iff_gr_or_eq
% 0.26/0.47 thf(fact_178_dual__order_Ostrict__trans,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( order @ A )
% 0.26/0.47 => ! [B2: A,A2: A,C: A] :
% 0.26/0.47 ( ( ord_less @ A @ B2 @ A2 )
% 0.26/0.47 => ( ( ord_less @ A @ C @ B2 )
% 0.26/0.47 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % dual_order.strict_trans
% 0.26/0.47 thf(fact_179_linorder__less__wlog,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linorder @ A )
% 0.26/0.47 => ! [P3: A > A > $o,A2: A,B2: A] :
% 0.26/0.47 ( ! [A4: A,B3: A] :
% 0.26/0.47 ( ( ord_less @ A @ A4 @ B3 )
% 0.26/0.47 => ( P3 @ A4 @ B3 ) )
% 0.26/0.47 => ( ! [A4: A] : ( P3 @ A4 @ A4 )
% 0.26/0.47 => ( ! [A4: A,B3: A] :
% 0.26/0.47 ( ( P3 @ B3 @ A4 )
% 0.26/0.47 => ( P3 @ A4 @ B3 ) )
% 0.26/0.47 => ( P3 @ A2 @ B2 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % linorder_less_wlog
% 0.26/0.47 thf(fact_180_exists__least__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( wellorder @ A )
% 0.26/0.47 => ( ( ^ [P4: A > $o] :
% 0.26/0.47 ? [X6: A] : ( P4 @ X6 ) )
% 0.26/0.47 = ( ^ [P5: A > $o] :
% 0.26/0.47 ? [N2: A] :
% 0.26/0.47 ( ( P5 @ N2 )
% 0.26/0.47 & ! [M4: A] :
% 0.26/0.47 ( ( ord_less @ A @ M4 @ N2 )
% 0.26/0.47 => ~ ( P5 @ M4 ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % exists_least_iff
% 0.26/0.47 thf(fact_181_less__imp__not__less,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( preorder @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_imp_not_less
% 0.26/0.48 thf(fact_182_order_Ostrict__trans,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [A2: A,B2: A,C: A] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ( ( ord_less @ A @ B2 @ C )
% 0.26/0.48 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.strict_trans
% 0.26/0.48 thf(fact_183_dual__order_Oirrefl,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [A2: A] :
% 0.26/0.48 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.26/0.48
% 0.26/0.48 % dual_order.irrefl
% 0.26/0.48 thf(fact_184_linorder__cases,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linorder @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ~ ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( ( X != Y )
% 0.26/0.48 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % linorder_cases
% 0.26/0.48 thf(fact_185_less__imp__triv,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( preorder @ A )
% 0.26/0.48 => ! [X: A,Y: A,P3: $o] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( ( ord_less @ A @ Y @ X )
% 0.26/0.48 => P3 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_imp_triv
% 0.26/0.48 thf(fact_186_less__imp__not__eq2,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( Y != X ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_imp_not_eq2
% 0.26/0.48 thf(fact_187_antisym__conv3,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linorder @ A )
% 0.26/0.48 => ! [Y: A,X: A] :
% 0.26/0.48 ( ~ ( ord_less @ A @ Y @ X )
% 0.26/0.48 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.26/0.48 = ( X = Y ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % antisym_conv3
% 0.26/0.48 thf(fact_188_less__induct,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( wellorder @ A )
% 0.26/0.48 => ! [P3: A > $o,A2: A] :
% 0.26/0.48 ( ! [X2: A] :
% 0.26/0.48 ( ! [Y3: A] :
% 0.26/0.48 ( ( ord_less @ A @ Y3 @ X2 )
% 0.26/0.48 => ( P3 @ Y3 ) )
% 0.26/0.48 => ( P3 @ X2 ) )
% 0.26/0.48 => ( P3 @ A2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_induct
% 0.26/0.48 thf(fact_189_less__not__sym,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( preorder @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_not_sym
% 0.26/0.48 thf(fact_190_less__imp__not__eq,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( X != Y ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_imp_not_eq
% 0.26/0.48 thf(fact_191_dual__order_Oasym,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [B2: A,A2: A] :
% 0.26/0.48 ( ( ord_less @ A @ B2 @ A2 )
% 0.26/0.48 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dual_order.asym
% 0.26/0.48 thf(fact_192_ord__less__eq__trans,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( ord @ A )
% 0.26/0.48 => ! [A2: A,B2: A,C: A] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ( ( B2 = C )
% 0.26/0.48 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % ord_less_eq_trans
% 0.26/0.48 thf(fact_193_ord__eq__less__trans,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( ord @ A )
% 0.26/0.48 => ! [A2: A,B2: A,C: A] :
% 0.26/0.48 ( ( A2 = B2 )
% 0.26/0.48 => ( ( ord_less @ A @ B2 @ C )
% 0.26/0.48 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % ord_eq_less_trans
% 0.26/0.48 thf(fact_194_less__irrefl,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( preorder @ A )
% 0.26/0.48 => ! [X: A] :
% 0.26/0.48 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_irrefl
% 0.26/0.48 thf(fact_195_less__linear,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linorder @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 | ( X = Y )
% 0.26/0.48 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_linear
% 0.26/0.48 thf(fact_196_less__trans,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( preorder @ A )
% 0.26/0.48 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( ( ord_less @ A @ Y @ Z2 )
% 0.26/0.48 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_trans
% 0.26/0.48 thf(fact_197_less__asym_H,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( preorder @ A )
% 0.26/0.48 => ! [A2: A,B2: A] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_asym'
% 0.26/0.48 thf(fact_198_less__asym,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( preorder @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_asym
% 0.26/0.48 thf(fact_199_less__imp__neq,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( X != Y ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_imp_neq
% 0.26/0.48 thf(fact_200_dense,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( dense_order @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ? [Z4: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Z4 )
% 0.26/0.48 & ( ord_less @ A @ Z4 @ Y ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dense
% 0.26/0.48 thf(fact_201_order_Oasym,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [A2: A,B2: A] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.asym
% 0.26/0.48 thf(fact_202_neq__iff,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linorder @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( X != Y )
% 0.26/0.48 = ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % neq_iff
% 0.26/0.48 thf(fact_203_neqE,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linorder @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( X != Y )
% 0.26/0.48 => ( ~ ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % neqE
% 0.26/0.48 thf(fact_204_gt__ex,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( no_top @ A )
% 0.26/0.48 => ! [X: A] :
% 0.26/0.48 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 0.26/0.48
% 0.26/0.48 % gt_ex
% 0.26/0.48 thf(fact_205_lt__ex,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( no_bot @ A )
% 0.26/0.48 => ! [X: A] :
% 0.26/0.48 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.26/0.48
% 0.26/0.48 % lt_ex
% 0.26/0.48 thf(fact_206_order__less__subst2,axiom,
% 0.26/0.48 ! [A: $tType,C2: $tType] :
% 0.26/0.48 ( ( ( order @ C2 )
% 0.26/0.48 & ( order @ A ) )
% 0.26/0.48 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C )
% 0.26/0.48 => ( ! [X2: A,Y2: A] :
% 0.26/0.48 ( ( ord_less @ A @ X2 @ Y2 )
% 0.26/0.48 => ( ord_less @ C2 @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.48 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order_less_subst2
% 0.26/0.48 thf(fact_207_order__less__subst1,axiom,
% 0.26/0.48 ! [A: $tType,B: $tType] :
% 0.26/0.48 ( ( ( order @ B )
% 0.26/0.48 & ( order @ A ) )
% 0.26/0.48 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.26/0.48 => ( ( ord_less @ B @ B2 @ C )
% 0.26/0.48 => ( ! [X2: B,Y2: B] :
% 0.26/0.48 ( ( ord_less @ B @ X2 @ Y2 )
% 0.26/0.48 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.48 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order_less_subst1
% 0.26/0.48 thf(fact_208_ord__less__eq__subst,axiom,
% 0.26/0.48 ! [A: $tType,B: $tType] :
% 0.26/0.48 ( ( ( ord @ B )
% 0.26/0.48 & ( ord @ A ) )
% 0.26/0.48 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ( ( ( F @ B2 )
% 0.26/0.48 = C )
% 0.26/0.48 => ( ! [X2: A,Y2: A] :
% 0.26/0.48 ( ( ord_less @ A @ X2 @ Y2 )
% 0.26/0.48 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.48 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % ord_less_eq_subst
% 0.26/0.48 thf(fact_209_ord__eq__less__subst,axiom,
% 0.26/0.48 ! [A: $tType,B: $tType] :
% 0.26/0.48 ( ( ( ord @ B )
% 0.26/0.48 & ( ord @ A ) )
% 0.26/0.48 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.26/0.48 ( ( A2
% 0.26/0.48 = ( F @ B2 ) )
% 0.26/0.48 => ( ( ord_less @ B @ B2 @ C )
% 0.26/0.48 => ( ! [X2: B,Y2: B] :
% 0.26/0.48 ( ( ord_less @ B @ X2 @ Y2 )
% 0.26/0.48 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.26/0.48 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % ord_eq_less_subst
% 0.26/0.48 thf(fact_210_gr__zeroI,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( canoni770627133id_add @ A )
% 0.26/0.48 => ! [N: A] :
% 0.26/0.48 ( ( N
% 0.26/0.48 != ( zero_zero @ A ) )
% 0.26/0.48 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % gr_zeroI
% 0.26/0.48 thf(fact_211_not__less__zero,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( canoni770627133id_add @ A )
% 0.26/0.48 => ! [N: A] :
% 0.26/0.48 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % not_less_zero
% 0.26/0.48 thf(fact_212_gr__implies__not__zero,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( canoni770627133id_add @ A )
% 0.26/0.48 => ! [M: A,N: A] :
% 0.26/0.48 ( ( ord_less @ A @ M @ N )
% 0.26/0.48 => ( N
% 0.26/0.48 != ( zero_zero @ A ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % gr_implies_not_zero
% 0.26/0.48 thf(fact_213_zero__less__iff__neq__zero,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( canoni770627133id_add @ A )
% 0.26/0.48 => ! [N: A] :
% 0.26/0.48 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.26/0.48 = ( N
% 0.26/0.48 != ( zero_zero @ A ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % zero_less_iff_neq_zero
% 0.26/0.48 thf(fact_214_linorder__neqE__linordered__idom,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linordered_idom @ A )
% 0.26/0.48 => ! [X: A,Y: A] :
% 0.26/0.48 ( ( X != Y )
% 0.26/0.48 => ( ~ ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % linorder_neqE_linordered_idom
% 0.26/0.48 thf(fact_215_measure__induct__rule,axiom,
% 0.26/0.48 ! [B: $tType,A: $tType] :
% 0.26/0.48 ( ( wellorder @ B )
% 0.26/0.48 => ! [F: A > B,P3: A > $o,A2: A] :
% 0.26/0.48 ( ! [X2: A] :
% 0.26/0.48 ( ! [Y3: A] :
% 0.26/0.48 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X2 ) )
% 0.26/0.48 => ( P3 @ Y3 ) )
% 0.26/0.48 => ( P3 @ X2 ) )
% 0.26/0.48 => ( P3 @ A2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % measure_induct_rule
% 0.26/0.48 thf(fact_216_measure__induct,axiom,
% 0.26/0.48 ! [B: $tType,A: $tType] :
% 0.26/0.48 ( ( wellorder @ B )
% 0.26/0.48 => ! [F: A > B,P3: A > $o,A2: A] :
% 0.26/0.48 ( ! [X2: A] :
% 0.26/0.48 ( ! [Y3: A] :
% 0.26/0.48 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X2 ) )
% 0.26/0.48 => ( P3 @ Y3 ) )
% 0.26/0.48 => ( P3 @ X2 ) )
% 0.26/0.48 => ( P3 @ A2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % measure_induct
% 0.26/0.48 thf(fact_217_nat__less__le,axiom,
% 0.26/0.48 ( ( ord_less @ nat )
% 0.26/0.48 = ( ^ [M4: nat,N2: nat] :
% 0.26/0.48 ( ( ord_less_eq @ nat @ M4 @ N2 )
% 0.26/0.48 & ( M4 != N2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % nat_less_le
% 0.26/0.48 thf(fact_218_less__imp__le__nat,axiom,
% 0.26/0.48 ! [M: nat,N: nat] :
% 0.26/0.48 ( ( ord_less @ nat @ M @ N )
% 0.26/0.48 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_imp_le_nat
% 0.26/0.48 thf(fact_219_le__eq__less__or__eq,axiom,
% 0.26/0.48 ( ( ord_less_eq @ nat )
% 0.26/0.48 = ( ^ [M4: nat,N2: nat] :
% 0.26/0.48 ( ( ord_less @ nat @ M4 @ N2 )
% 0.26/0.48 | ( M4 = N2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % le_eq_less_or_eq
% 0.26/0.48 thf(fact_220_less__or__eq__imp__le,axiom,
% 0.26/0.48 ! [M: nat,N: nat] :
% 0.26/0.48 ( ( ( ord_less @ nat @ M @ N )
% 0.26/0.48 | ( M = N ) )
% 0.26/0.48 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_or_eq_imp_le
% 0.26/0.48 thf(fact_221_le__neq__implies__less,axiom,
% 0.26/0.48 ! [M: nat,N: nat] :
% 0.26/0.48 ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.48 => ( ( M != N )
% 0.26/0.48 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % le_neq_implies_less
% 0.26/0.48 thf(fact_222_less__mono__imp__le__mono,axiom,
% 0.26/0.48 ! [F: nat > nat,I4: nat,J: nat] :
% 0.26/0.48 ( ! [I3: nat,J3: nat] :
% 0.26/0.48 ( ( ord_less @ nat @ I3 @ J3 )
% 0.26/0.48 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
% 0.26/0.48 => ( ( ord_less_eq @ nat @ I4 @ J )
% 0.26/0.48 => ( ord_less_eq @ nat @ ( F @ I4 ) @ ( F @ J ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_mono_imp_le_mono
% 0.26/0.48 thf(fact_223_gr0I,axiom,
% 0.26/0.48 ! [N: nat] :
% 0.26/0.48 ( ( N
% 0.26/0.48 != ( zero_zero @ nat ) )
% 0.26/0.48 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.26/0.48
% 0.26/0.48 % gr0I
% 0.26/0.48 thf(fact_224_not__gr0,axiom,
% 0.26/0.48 ! [N: nat] :
% 0.26/0.48 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.26/0.48 = ( N
% 0.26/0.48 = ( zero_zero @ nat ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % not_gr0
% 0.26/0.48 thf(fact_225_not__less0,axiom,
% 0.26/0.48 ! [N: nat] :
% 0.26/0.48 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.26/0.48
% 0.26/0.48 % not_less0
% 0.26/0.48 thf(fact_226_less__zeroE,axiom,
% 0.26/0.48 ! [N: nat] :
% 0.26/0.48 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_zeroE
% 0.26/0.48 thf(fact_227_gr__implies__not0,axiom,
% 0.26/0.48 ! [M: nat,N: nat] :
% 0.26/0.48 ( ( ord_less @ nat @ M @ N )
% 0.26/0.48 => ( N
% 0.26/0.48 != ( zero_zero @ nat ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % gr_implies_not0
% 0.26/0.48 thf(fact_228_infinite__descent0,axiom,
% 0.26/0.48 ! [P3: nat > $o,N: nat] :
% 0.26/0.48 ( ( P3 @ ( zero_zero @ nat ) )
% 0.26/0.48 => ( ! [N3: nat] :
% 0.26/0.48 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 )
% 0.26/0.48 => ( ~ ( P3 @ N3 )
% 0.26/0.48 => ? [M5: nat] :
% 0.26/0.48 ( ( ord_less @ nat @ M5 @ N3 )
% 0.26/0.48 & ~ ( P3 @ M5 ) ) ) )
% 0.26/0.48 => ( P3 @ N ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % infinite_descent0
% 0.26/0.48 thf(fact_229_bot__nat__0_Oextremum__strict,axiom,
% 0.26/0.48 ! [A2: nat] :
% 0.26/0.48 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 0.26/0.48
% 0.26/0.48 % bot_nat_0.extremum_strict
% 0.26/0.48 thf(fact_230_infinite__descent0__measure,axiom,
% 0.26/0.48 ! [A: $tType,V: A > nat,P3: A > $o,X: A] :
% 0.26/0.48 ( ! [X2: A] :
% 0.26/0.48 ( ( ( V @ X2 )
% 0.26/0.48 = ( zero_zero @ nat ) )
% 0.26/0.48 => ( P3 @ X2 ) )
% 0.26/0.48 => ( ! [X2: A] :
% 0.26/0.48 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V @ X2 ) )
% 0.26/0.48 => ( ~ ( P3 @ X2 )
% 0.26/0.48 => ? [Y3: A] :
% 0.26/0.48 ( ( ord_less @ nat @ ( V @ Y3 ) @ ( V @ X2 ) )
% 0.26/0.48 & ~ ( P3 @ Y3 ) ) ) )
% 0.26/0.48 => ( P3 @ X ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % infinite_descent0_measure
% 0.26/0.48 thf(fact_231_psubsetE,axiom,
% 0.26/0.48 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.48 ( ( ord_less @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.48 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.48 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % psubsetE
% 0.26/0.48 thf(fact_232_psubset__eq,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( ord_less @ ( set @ A ) )
% 0.26/0.48 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.26/0.48 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.26/0.48 & ( A6 != B6 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % psubset_eq
% 0.26/0.48 thf(fact_233_psubset__imp__subset,axiom,
% 0.26/0.48 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.26/0.48 ( ( ord_less @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.48 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.26/0.48
% 0.26/0.48 % psubset_imp_subset
% 0.26/0.48 thf(fact_234_psubset__subset__trans,axiom,
% 0.26/0.48 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.26/0.48 ( ( ord_less @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.48 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 0.26/0.48 => ( ord_less @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % psubset_subset_trans
% 0.26/0.48 thf(fact_235_subset__not__subset__eq,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( ord_less @ ( set @ A ) )
% 0.26/0.48 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.26/0.48 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.26/0.48 & ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % subset_not_subset_eq
% 0.26/0.48 thf(fact_236_subset__psubset__trans,axiom,
% 0.26/0.48 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.26/0.48 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.26/0.48 => ( ( ord_less @ ( set @ A ) @ B4 @ C3 )
% 0.26/0.48 => ( ord_less @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % subset_psubset_trans
% 0.26/0.48 thf(fact_237_subset__iff__psubset__eq,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( ord_less_eq @ ( set @ A ) )
% 0.26/0.48 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.26/0.48 ( ( ord_less @ ( set @ A ) @ A6 @ B6 )
% 0.26/0.48 | ( A6 = B6 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % subset_iff_psubset_eq
% 0.26/0.48 thf(fact_238_less__numeral__extra_I4_J,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linord1659791738miring @ A )
% 0.26/0.48 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_numeral_extra(4)
% 0.26/0.48 thf(fact_239_less__numeral__extra_I3_J,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( linord1659791738miring @ A )
% 0.26/0.48 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % less_numeral_extra(3)
% 0.26/0.48 thf(fact_240_order_Onot__eq__order__implies__strict,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [A2: A,B2: A] :
% 0.26/0.48 ( ( A2 != B2 )
% 0.26/0.48 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.48 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.not_eq_order_implies_strict
% 0.26/0.48 thf(fact_241_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [B2: A,A2: A] :
% 0.26/0.48 ( ( ord_less @ A @ B2 @ A2 )
% 0.26/0.48 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dual_order.strict_implies_order
% 0.26/0.48 thf(fact_242_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ( ( ord_less @ A )
% 0.26/0.48 = ( ^ [B5: A,A5: A] :
% 0.26/0.48 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.26/0.48 & ( A5 != B5 ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dual_order.strict_iff_order
% 0.26/0.48 thf(fact_243_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ( ( ord_less_eq @ A )
% 0.26/0.48 = ( ^ [B5: A,A5: A] :
% 0.26/0.48 ( ( ord_less @ A @ B5 @ A5 )
% 0.26/0.48 | ( A5 = B5 ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dual_order.order_iff_strict
% 0.26/0.48 thf(fact_244_order_Ostrict__implies__order,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [A2: A,B2: A] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.strict_implies_order
% 0.26/0.48 thf(fact_245_dense__le__bounded,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( dense_linorder @ A )
% 0.26/0.48 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ Y )
% 0.26/0.48 => ( ! [W: A] :
% 0.26/0.48 ( ( ord_less @ A @ X @ W )
% 0.26/0.48 => ( ( ord_less @ A @ W @ Y )
% 0.26/0.48 => ( ord_less_eq @ A @ W @ Z2 ) ) )
% 0.26/0.48 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dense_le_bounded
% 0.26/0.48 thf(fact_246_dense__ge__bounded,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( dense_linorder @ A )
% 0.26/0.48 => ! [Z2: A,X: A,Y: A] :
% 0.26/0.48 ( ( ord_less @ A @ Z2 @ X )
% 0.26/0.48 => ( ! [W: A] :
% 0.26/0.48 ( ( ord_less @ A @ Z2 @ W )
% 0.26/0.48 => ( ( ord_less @ A @ W @ X )
% 0.26/0.48 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.26/0.48 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dense_ge_bounded
% 0.26/0.48 thf(fact_247_dual__order_Ostrict__trans2,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [B2: A,A2: A,C: A] :
% 0.26/0.48 ( ( ord_less @ A @ B2 @ A2 )
% 0.26/0.48 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.26/0.48 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dual_order.strict_trans2
% 0.26/0.48 thf(fact_248_dual__order_Ostrict__trans1,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [B2: A,A2: A,C: A] :
% 0.26/0.48 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.26/0.48 => ( ( ord_less @ A @ C @ B2 )
% 0.26/0.48 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % dual_order.strict_trans1
% 0.26/0.48 thf(fact_249_order_Ostrict__iff__order,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ( ( ord_less @ A )
% 0.26/0.48 = ( ^ [A5: A,B5: A] :
% 0.26/0.48 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.26/0.48 & ( A5 != B5 ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.strict_iff_order
% 0.26/0.48 thf(fact_250_order_Oorder__iff__strict,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ( ( ord_less_eq @ A )
% 0.26/0.48 = ( ^ [A5: A,B5: A] :
% 0.26/0.48 ( ( ord_less @ A @ A5 @ B5 )
% 0.26/0.48 | ( A5 = B5 ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.order_iff_strict
% 0.26/0.48 thf(fact_251_order_Ostrict__trans2,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [A2: A,B2: A,C: A] :
% 0.26/0.48 ( ( ord_less @ A @ A2 @ B2 )
% 0.26/0.48 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.26/0.48 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.strict_trans2
% 0.26/0.48 thf(fact_252_order_Ostrict__trans1,axiom,
% 0.26/0.48 ! [A: $tType] :
% 0.26/0.48 ( ( order @ A )
% 0.26/0.48 => ! [A2: A,B2: A,C: A] :
% 0.26/0.48 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.26/0.48 => ( ( ord_less @ A @ B2 @ C )
% 0.26/0.48 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 % order.strict_trans1
% 0.26/0.48
% 0.26/0.48 % Type constructors (34)
% 0.26/0.48 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.26/0.48 ! [A7: $tType,A8: $tType] :
% 0.26/0.48 ( ( preorder @ A8 )
% 0.26/0.48 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.26/0.48 ! [A7: $tType,A8: $tType] :
% 0.26/0.48 ( ( order @ A8 )
% 0.26/0.48 => ( order @ ( A7 > A8 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_fun___Orderings_Oord,axiom,
% 0.26/0.48 ! [A7: $tType,A8: $tType] :
% 0.26/0.48 ( ( ord @ A8 )
% 0.26/0.48 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 0.26/0.48 semiri1923998003cancel @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.26/0.48 canoni770627133id_add @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.26/0.48 linord1659791738miring @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 0.26/0.48 semiri1193490041visors @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 0.26/0.48 ordere216010020id_add @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
% 0.26/0.48 ordere1490568538miring @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0,axiom,
% 0.26/0.48 ordered_semiring_0 @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.26/0.48 ab_semigroup_mult @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.26/0.48 comm_monoid_mult @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Oordered__semiring,axiom,
% 0.26/0.48 ordered_semiring @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.26/0.48 comm_monoid_add @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.26/0.48 semigroup_mult @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.26/0.48 wellorder @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.26/0.48 zero_neq_one @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.26/0.48 preorder @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.26/0.48 linorder @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.26/0.48 monoid_mult @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Osemiring__0,axiom,
% 0.26/0.48 semiring_0 @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.26/0.48 no_top @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 0.26/0.48 mult_zero @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.26/0.48 order @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.26/0.48 ord @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.26/0.48 zero @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.26/0.48 one @ nat ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.26/0.48 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.26/0.48 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.26/0.48 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.26/0.48 preorder @ $o ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 0.26/0.48 linorder @ $o ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.26/0.48 order @ $o ).
% 0.26/0.48
% 0.26/0.48 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.26/0.48 ord @ $o ).
% 0.26/0.48
% 0.26/0.48 % Conjectures (1)
% 0.26/0.48 thf(conj_0,conjecture,
% 0.26/0.48 ( ( ! [I2: nat] :
% 0.26/0.48 ( ( ( p @ I2 )
% 0.26/0.48 != ( zero_zero @ nat ) )
% 0.26/0.48 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I2 )
% 0.26/0.48 & ( ord_less_eq @ nat @ I2 @ ( zero_zero @ nat ) ) ) )
% 0.26/0.48 & ( ( groups1340683514dd_sum @ nat @ nat
% 0.26/0.48 @ ^ [I2: nat] : ( times_times @ nat @ ( p @ I2 ) @ I2 )
% 0.26/0.48 @ ( set_ord_atMost @ nat @ ( zero_zero @ nat ) ) )
% 0.26/0.48 = ( zero_zero @ nat ) ) )
% 0.26/0.48 = ( p
% 0.26/0.48 = ( ^ [I2: nat] : ( zero_zero @ nat ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 2.76/1.55 ---- Embedded in THF ---
% 2.76/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.76/1.55 %%% Generated on Tue Feb 24 08:27:43 EST 2026
% 2.76/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.76/1.55 %%% Logic specification used:
% 2.76/1.55 %%% thf(spec, logic, $$dhol).
% 2.76/1.55
% 2.76/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2DTF11076.p
% 2.76/1.55 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.76/1.55 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.76/1.55 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Omult__zero, type, mult_zero: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Osemiring__0, type, semiring_0: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Omonoid__mult, type, monoid_mult: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Oordered__ring, type, ordered_ring: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Olinordered__ring, type, linordered_ring: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Oordered__semiring, type, ordered_semiring: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Ocomm__monoid__mult, type, comm_monoid_mult: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Oordered__semiring__0, type, ordered_semiring_0: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Oordered__comm__semiring, type, ordere1490568538miring: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Olinordered__ring__strict, type, linord581940658strict: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Oring__1__no__zero__divisors, type, ring_11004092258visors: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Osemiring__no__zero__divisors, type, semiri1193490041visors: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel, type, semiri1923998003cancel: (!> [A:$tType]: ($o))).
% 2.76/1.55 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.76/1.55 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 2.76/1.55 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.76/1.55 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum, type, groups1340683514dd_sum: (!> [B:$tType,A:$tType]: (((B > A) > ((set @ B) > A))))).
% 2.76/1.55 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc, type, neg_numeral_dbl_inc: (!> [A:$tType]: ((A > A)))).
% 2.76/1.55 thf(sy_c_Number__Partition__Mirabelle__ihnzjotehb_Opartitions, type, number2016821345itions: ((nat > nat) > (nat > $o))).
% 2.76/1.55 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.76/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.76/1.55 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.76/1.55 thf(sy_c_Set__Interval_Oord__class_OatMost, type, set_ord_atMost: (!> [A:$tType]: ((A > (set @ A))))).
% 2.76/1.55 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.76/1.55 thf(sy_v_p, type, p: (nat > nat)).
% 2.76/1.55 thf(fact_0_mult__cancel__left1, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C:A,B2:A]: (((C = (((times_times @ A) @ C) @ B2)) = ((C = (zero_zero @ A)) | (B2 = (one_one @ A)))))))))).
% 2.76/1.55 thf(fact_1_mult__cancel__left2, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C:A,A2:A]: ((((((times_times @ A) @ C) @ A2) = C) = ((C = (zero_zero @ A)) | (A2 = (one_one @ A)))))))))).
% 2.76/1.55 thf(fact_2_mult__cancel__right1, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C:A,B2:A]: (((C = (((times_times @ A) @ B2) @ C)) = ((C = (zero_zero @ A)) | (B2 = (one_one @ A)))))))))).
% 2.76/1.55 thf(fact_3_mult__cancel__right2, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [A2:A,C:A]: ((((((times_times @ A) @ A2) @ C) = C) = ((C = (zero_zero @ A)) | (A2 = (one_one @ A)))))))))).
% 2.76/1.55 thf(fact_4_sum_Oneutral__const, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [A3:(set @ B)]: ((((((groups1340683514dd_sum @ B) @ A) @ (^ [Uu:B]: ((zero_zero @ A)))) @ A3) = (zero_zero @ A)))))))).
% 2.76/1.55 thf(fact_5_partitionsE, axiom, (! [P:(nat > nat),N:nat]: ((((number2016821345itions @ P) @ N) => (~ (((! [I:nat]: ((((P @ I) != (zero_zero @ nat)) => ((((ord_less_eq @ nat) @ (one_one @ nat)) @ I) & (((ord_less_eq @ nat) @ I) @ N))))) => (((((groups1340683514dd_sum @ nat) @ nat) @ (^ [I2:nat]: ((((times_times @ nat) @ (P @ I2)) @ I2)))) @ ((set_ord_atMost @ nat) @ N)) != N)))))))).
% 2.76/1.55 thf(fact_6_partitionsI, axiom, (! [P:(nat > nat),N:nat]: (((! [I3:nat]: ((((P @ I3) != (zero_zero @ nat)) => ((((ord_less_eq @ nat) @ (one_one @ nat)) @ I3) & (((ord_less_eq @ nat) @ I3) @ N))))) => ((((((groups1340683514dd_sum @ nat) @ nat) @ (^ [I2:nat]: ((((times_times @ nat) @ (P @ I2)) @ I2)))) @ ((set_ord_atMost @ nat) @ N)) = N) => ((number2016821345itions @ P) @ N)))))).
% 2.76/1.55 thf(fact_7_partitions__def, axiom, (number2016821345itions = (^ [P2:(nat > nat),N2:nat]: (((! [I2:nat]: ((((P2 @ I2) != (zero_zero @ nat)) => ((((ord_less_eq @ nat) @ (one_one @ nat)) @ I2) & (((ord_less_eq @ nat) @ I2) @ N2))))) & (((((groups1340683514dd_sum @ nat) @ nat) @ (^ [I2:nat]: ((((times_times @ nat) @ (P2 @ I2)) @ I2)))) @ ((set_ord_atMost @ nat) @ N2)) = N2)))))).
% 2.76/1.55 thf(fact_8_nat__1__eq__mult__iff, axiom, (! [M:nat,N:nat]: ((((one_one @ nat) = (((times_times @ nat) @ M) @ N)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 2.76/1.55 thf(fact_9_nat__mult__eq__1__iff, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (one_one @ nat)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 2.76/1.55 thf(fact_10_atMost__subset__iff, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ (set @ A)) @ ((set_ord_atMost @ A) @ X)) @ ((set_ord_atMost @ A) @ Y)) = (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.76/1.55 thf(fact_11_atMost__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I4:A,K:A]: (((((member @ A) @ I4) @ ((set_ord_atMost @ A) @ K)) = (((ord_less_eq @ A) @ I4) @ K)))))))).
% 2.76/1.55 thf(fact_12_atMost__eq__iff, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((set_ord_atMost @ A) @ X) = ((set_ord_atMost @ A) @ Y)) = (X = Y)))))))).
% 2.76/1.55 thf(fact_13_mult__cancel__right, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [A2:A,C:A,B2:A]: ((((((times_times @ A) @ A2) @ C) = (((times_times @ A) @ B2) @ C)) = ((C = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.76/1.55 thf(fact_14_mult__cancel__left, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B2:A]: ((((((times_times @ A) @ C) @ A2) = (((times_times @ A) @ C) @ B2)) = ((C = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.76/1.55 thf(fact_15_mult__eq__0__iff, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) = (zero_zero @ A)) = ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_16_mult__zero__right, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.76/1.55 thf(fact_17_mult__zero__left, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.76/1.55 thf(fact_18_bot__nat__0_Oextremum, axiom, (! [A2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A2)))).
% 2.76/1.55 thf(fact_19_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.76/1.55 thf(fact_20_mult__cancel2, axiom, (! [M:nat,K:nat,N:nat]: ((((((times_times @ nat) @ M) @ K) = (((times_times @ nat) @ N) @ K)) = ((M = N) | (K = (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_21_mult__cancel1, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = ((M = N) | (K = (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_22_mult__0__right, axiom, (! [M:nat]: (((((times_times @ nat) @ M) @ (zero_zero @ nat)) = (zero_zero @ nat))))).
% 2.76/1.55 thf(fact_23_mult__is__0, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) | (N = (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_24_bounded__Max__nat, axiom, (! [P3:(nat > $o),X:nat,M2:nat]: (((P3 @ X) => ((! [X2:nat]: (((P3 @ X2) => (((ord_less_eq @ nat) @ X2) @ M2)))) => (~ ((! [M3:nat]: (((P3 @ M3) => (~ ((! [X3:nat]: (((P3 @ X3) => (((ord_less_eq @ nat) @ X3) @ M3)))))))))))))))).
% 2.76/1.55 thf(fact_25_Nat_Oex__has__greatest__nat, axiom, (! [P3:(nat > $o),K:nat,B2:nat]: (((P3 @ K) => ((! [Y2:nat]: (((P3 @ Y2) => (((ord_less_eq @ nat) @ Y2) @ B2)))) => (? [X2:nat]: (((P3 @ X2) & (! [Y3:nat]: (((P3 @ Y3) => (((ord_less_eq @ nat) @ Y3) @ X2)))))))))))).
% 2.76/1.55 thf(fact_26_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.76/1.55 thf(fact_27_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.76/1.55 thf(fact_28_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.76/1.55 thf(fact_29_le__trans, axiom, (! [I4:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I4) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I4) @ K)))))).
% 2.76/1.55 thf(fact_30_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.76/1.55 thf(fact_31_sum_Oreindex__bij__witness, axiom, (! [B:$tType,A:$tType,C2:$tType]: (((comm_monoid_add @ A) => (! [S:(set @ B),I4:(C2 > B),J:(B > C2),T:(set @ C2),H:(C2 > A),G:(B > A)]: (((! [A4:B]: (((((member @ B) @ A4) @ S) => ((I4 @ (J @ A4)) = A4)))) => ((! [A4:B]: (((((member @ B) @ A4) @ S) => (((member @ C2) @ (J @ A4)) @ T)))) => ((! [B3:C2]: (((((member @ C2) @ B3) @ T) => ((J @ (I4 @ B3)) = B3)))) => ((! [B3:C2]: (((((member @ C2) @ B3) @ T) => (((member @ B) @ (I4 @ B3)) @ S)))) => ((! [A4:B]: (((((member @ B) @ A4) @ S) => ((H @ (J @ A4)) = (G @ A4))))) => (((((groups1340683514dd_sum @ B) @ A) @ G) @ S) = ((((groups1340683514dd_sum @ C2) @ A) @ H) @ T))))))))))))).
% 2.76/1.55 thf(fact_32_sum_Oeq__general__inverses, axiom, (! [C2:$tType,A:$tType,B:$tType]: (((comm_monoid_add @ A) => (! [B4:(set @ B),K:(B > C2),A3:(set @ C2),H:(C2 > B),Gamma:(B > A),Phi:(C2 > A)]: (((! [Y2:B]: (((((member @ B) @ Y2) @ B4) => ((((member @ C2) @ (K @ Y2)) @ A3) & ((H @ (K @ Y2)) = Y2))))) => ((! [X2:C2]: (((((member @ C2) @ X2) @ A3) => ((((member @ B) @ (H @ X2)) @ B4) & (((K @ (H @ X2)) = X2) & ((Gamma @ (H @ X2)) = (Phi @ X2))))))) => (((((groups1340683514dd_sum @ C2) @ A) @ Phi) @ A3) = ((((groups1340683514dd_sum @ B) @ A) @ Gamma) @ B4)))))))))).
% 2.76/1.55 thf(fact_33_sum_Oeq__general, axiom, (! [C2:$tType,A:$tType,B:$tType]: (((comm_monoid_add @ A) => (! [B4:(set @ B),A3:(set @ C2),H:(C2 > B),Gamma:(B > A),Phi:(C2 > A)]: (((! [Y2:B]: (((((member @ B) @ Y2) @ B4) => (? [X3:C2]: (((((member @ C2) @ X3) @ A3) & (((H @ X3) = Y2) & (! [Ya:C2]: ((((((member @ C2) @ Ya) @ A3) & ((H @ Ya) = Y2)) => (Ya = X3))))))))))) => ((! [X2:C2]: (((((member @ C2) @ X2) @ A3) => ((((member @ B) @ (H @ X2)) @ B4) & ((Gamma @ (H @ X2)) = (Phi @ X2)))))) => (((((groups1340683514dd_sum @ C2) @ A) @ Phi) @ A3) = ((((groups1340683514dd_sum @ B) @ A) @ Gamma) @ B4)))))))))).
% 2.76/1.55 thf(fact_34_sum_Ocong, axiom, (! [A:$tType,B:$tType]: (((comm_monoid_add @ A) => (! [A3:(set @ B),B4:(set @ B),G:(B > A),H:(B > A)]: (((A3 = B4) => ((! [X2:B]: (((((member @ B) @ X2) @ B4) => ((G @ X2) = (H @ X2))))) => (((((groups1340683514dd_sum @ B) @ A) @ G) @ A3) = ((((groups1340683514dd_sum @ B) @ A) @ H) @ B4)))))))))).
% 2.76/1.55 thf(fact_35_sum_Oswap, axiom, (! [A:$tType,B:$tType,C2:$tType]: (((comm_monoid_add @ A) => (! [G:(B > (C2 > A)),B4:(set @ C2),A3:(set @ B)]: ((((((groups1340683514dd_sum @ B) @ A) @ (^ [I2:B]: (((((groups1340683514dd_sum @ C2) @ A) @ (G @ I2)) @ B4)))) @ A3) = ((((groups1340683514dd_sum @ C2) @ A) @ (^ [J2:C2]: (((((groups1340683514dd_sum @ B) @ A) @ (^ [I2:B]: (((G @ I2) @ J2)))) @ A3)))) @ B4)))))))).
% 2.76/1.55 thf(fact_36_mult__right__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => (((((times_times @ A) @ A2) @ C) = (((times_times @ A) @ B2) @ C)) = (A2 = B2))))))))).
% 2.76/1.55 thf(fact_37_mult__left__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => (((((times_times @ A) @ C) @ A2) = (((times_times @ A) @ C) @ B2)) = (A2 = B2))))))))).
% 2.76/1.55 thf(fact_38_no__zero__divisors, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: (((A2 != (zero_zero @ A)) => ((B2 != (zero_zero @ A)) => ((((times_times @ A) @ A2) @ B2) != (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_39_divisors__zero, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) = (zero_zero @ A)) => ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_40_mult__not__zero, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) != (zero_zero @ A)) => ((A2 != (zero_zero @ A)) & (B2 != (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_41_zero__neq__one, axiom, (! [A:$tType]: (((zero_neq_one @ A) => ((zero_zero @ A) != (one_one @ A)))))).
% 2.76/1.55 thf(fact_42_sum_Onot__neutral__contains__not__neutral, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [G:(B > A),A3:(set @ B)]: (((((((groups1340683514dd_sum @ B) @ A) @ G) @ A3) != (zero_zero @ A)) => (~ ((! [A4:B]: (((((member @ B) @ A4) @ A3) => ((G @ A4) = (zero_zero @ A)))))))))))))).
% 2.76/1.55 thf(fact_43_sum_Oneutral, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [A3:(set @ B),G:(B > A)]: (((! [X2:B]: (((((member @ B) @ X2) @ A3) => ((G @ X2) = (zero_zero @ A))))) => (((((groups1340683514dd_sum @ B) @ A) @ G) @ A3) = (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P3:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P3)) = (P3 @ A2))))).
% 2.76/1.55 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 2.76/1.55 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P3 @ X2) = (Q @ X2)))) => (((collect @ A) @ P3) = ((collect @ A) @ Q)))))).
% 2.76/1.55 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.76/1.55 thf(fact_48_bot__nat__0_Oextremum__uniqueI, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) => (A2 = (zero_zero @ nat)))))).
% 2.76/1.55 thf(fact_49_bot__nat__0_Oextremum__unique, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) = (A2 = (zero_zero @ nat)))))).
% 2.76/1.55 thf(fact_50_le__0__eq, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ N) @ (zero_zero @ nat)) = (N = (zero_zero @ nat)))))).
% 2.76/1.55 thf(fact_51_less__eq__nat_Osimps_I1_J, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.76/1.55 thf(fact_52_mult__0, axiom, (! [N:nat]: (((((times_times @ nat) @ (zero_zero @ nat)) @ N) = (zero_zero @ nat))))).
% 2.76/1.55 thf(fact_53_mult__le__mono2, axiom, (! [I4:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I4) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ K) @ I4)) @ (((times_times @ nat) @ K) @ J)))))).
% 2.76/1.55 thf(fact_54_mult__le__mono1, axiom, (! [I4:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I4) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I4) @ K)) @ (((times_times @ nat) @ J) @ K)))))).
% 2.76/1.55 thf(fact_55_mult__le__mono, axiom, (! [I4:nat,J:nat,K:nat,L:nat]: (((((ord_less_eq @ nat) @ I4) @ J) => ((((ord_less_eq @ nat) @ K) @ L) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I4) @ K)) @ (((times_times @ nat) @ J) @ L))))))).
% 2.76/1.55 thf(fact_56_le__square, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ M))))).
% 2.76/1.55 thf(fact_57_le__cube, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ (((times_times @ nat) @ M) @ M)))))).
% 2.76/1.55 thf(fact_58_nat__mult__1__right, axiom, (! [N:nat]: (((((times_times @ nat) @ N) @ (one_one @ nat)) = N)))).
% 2.76/1.55 thf(fact_59_nat__mult__1, axiom, (! [N:nat]: (((((times_times @ nat) @ (one_one @ nat)) @ N) = N)))).
% 2.76/1.55 thf(fact_60_lambda__zero, axiom, (! [A:$tType]: (((mult_zero @ A) => ((^ [H2:A]: ((zero_zero @ A))) = ((times_times @ A) @ (zero_zero @ A))))))).
% 2.76/1.55 thf(fact_61_lambda__one, axiom, (! [A:$tType]: (((monoid_mult @ A) => ((^ [X4:A]: (X4)) = ((times_times @ A) @ (one_one @ A))))))).
% 2.76/1.55 thf(fact_62_sum__mono, axiom, (! [A:$tType,B:$tType]: (((ordere216010020id_add @ A) => (! [K2:(set @ B),F:(B > A),G:(B > A)]: (((! [I3:B]: (((((member @ B) @ I3) @ K2) => (((ord_less_eq @ A) @ (F @ I3)) @ (G @ I3))))) => (((ord_less_eq @ A) @ ((((groups1340683514dd_sum @ B) @ A) @ F) @ K2)) @ ((((groups1340683514dd_sum @ B) @ A) @ G) @ K2))))))))).
% 2.76/1.55 thf(fact_63_sum__distrib__right, axiom, (! [A:$tType,B:$tType]: (((semiring_0 @ A) => (! [F:(B > A),A3:(set @ B),R:A]: (((((times_times @ A) @ ((((groups1340683514dd_sum @ B) @ A) @ F) @ A3)) @ R) = ((((groups1340683514dd_sum @ B) @ A) @ (^ [N2:B]: ((((times_times @ A) @ (F @ N2)) @ R)))) @ A3)))))))).
% 2.76/1.55 thf(fact_64_sum__distrib__left, axiom, (! [A:$tType,B:$tType]: (((semiring_0 @ A) => (! [R:A,F:(B > A),A3:(set @ B)]: (((((times_times @ A) @ R) @ ((((groups1340683514dd_sum @ B) @ A) @ F) @ A3)) = ((((groups1340683514dd_sum @ B) @ A) @ (^ [N2:B]: ((((times_times @ A) @ R) @ (F @ N2))))) @ A3)))))))).
% 2.76/1.55 thf(fact_65_sum__product, axiom, (! [B:$tType,C2:$tType,A:$tType]: (((semiring_0 @ B) => (! [F:(A > B),A3:(set @ A),G:(C2 > B),B4:(set @ C2)]: (((((times_times @ B) @ ((((groups1340683514dd_sum @ A) @ B) @ F) @ A3)) @ ((((groups1340683514dd_sum @ C2) @ B) @ G) @ B4)) = ((((groups1340683514dd_sum @ A) @ B) @ (^ [I2:A]: (((((groups1340683514dd_sum @ C2) @ B) @ (^ [J2:C2]: ((((times_times @ B) @ (F @ I2)) @ (G @ J2))))) @ B4)))) @ A3)))))))).
% 2.76/1.55 thf(fact_66_atMost__def, axiom, (! [A:$tType]: (((ord @ A) => ((set_ord_atMost @ A) = (^ [U:A]: (((collect @ A) @ (^ [X4:A]: ((((ord_less_eq @ A) @ X4) @ U))))))))))).
% 2.76/1.55 thf(fact_67_ordered__comm__semiring__class_Ocomm__mult__left__mono, axiom, (! [A:$tType]: (((ordere1490568538miring @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.76/1.55 thf(fact_68_zero__le__mult__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.76/1.55 thf(fact_69_mult__nonneg__nonpos2, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ B2) @ A2)) @ (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_70_mult__nonpos__nonneg, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_71_mult__nonneg__nonpos, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_72_mult__nonneg__nonneg, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.76/1.55 thf(fact_73_split__mult__neg__le, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2))) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_74_mult__le__0__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.76/1.55 thf(fact_75_mult__right__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)))))))))).
% 2.76/1.55 thf(fact_76_mult__right__mono__neg, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)))))))))).
% 2.76/1.55 thf(fact_77_mult__left__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.76/1.55 thf(fact_78_mult__nonpos__nonpos, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.76/1.55 thf(fact_79_mult__left__mono__neg, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.76/1.55 thf(fact_80_split__mult__pos__le, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,B2:A]: (((((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A)))) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2))))))))).
% 2.76/1.55 thf(fact_81_zero__le__square, axiom, (! [A:$tType]: (((linordered_ring @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ A2)))))))).
% 2.76/1.55 thf(fact_82_mult__mono_H, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ D)))))))))))).
% 2.76/1.55 thf(fact_83_mult__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ D)))))))))))).
% 2.76/1.55 thf(fact_84_not__one__le__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less_eq @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.76/1.55 thf(fact_85_zero__le__one, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.76/1.55 thf(fact_86_sum__nonpos, axiom, (! [B:$tType,A:$tType]: (((ordere216010020id_add @ A) => (! [A3:(set @ B),F:(B > A)]: (((! [X2:B]: (((((member @ B) @ X2) @ A3) => (((ord_less_eq @ A) @ (F @ X2)) @ (zero_zero @ A))))) => (((ord_less_eq @ A) @ ((((groups1340683514dd_sum @ B) @ A) @ F) @ A3)) @ (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_87_sum__nonneg, axiom, (! [A:$tType,B:$tType]: (((ordere216010020id_add @ A) => (! [A3:(set @ B),F:(B > A)]: (((! [X2:B]: (((((member @ B) @ X2) @ A3) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (F @ X2))))) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ ((((groups1340683514dd_sum @ B) @ A) @ F) @ A3))))))))).
% 2.76/1.55 thf(fact_88_mult__eq__self__implies__10, axiom, (! [M:nat,N:nat]: (((M = (((times_times @ nat) @ M) @ N)) => ((N = (one_one @ nat)) | (M = (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_89_mult__left__le, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [C:A,A2:A]: (((((ord_less_eq @ A) @ C) @ (one_one @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ A2))))))))).
% 2.76/1.55 thf(fact_90_mult__le__one, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (one_one @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => ((((ord_less_eq @ A) @ B2) @ (one_one @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (one_one @ A))))))))))).
% 2.76/1.55 thf(fact_91_mult__right__le__one__le, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y) => ((((ord_less_eq @ A) @ Y) @ (one_one @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ X) @ Y)) @ X)))))))))).
% 2.76/1.55 thf(fact_92_mult__left__le__one__le, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y) => ((((ord_less_eq @ A) @ Y) @ (one_one @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ Y) @ X)) @ X)))))))))).
% 2.76/1.55 thf(fact_93_mult_Oright__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 2.76/1.55 thf(fact_94_mult_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 2.76/1.55 thf(fact_95_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_96_subsetI, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.76/1.55 thf(fact_97_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A3) => (A3 = B4)))))).
% 2.76/1.55 thf(fact_98_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.76/1.55 thf(fact_99_nat__mult__eq__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = ((K = (zero_zero @ nat)) | (M = N)))))).
% 2.76/1.55 thf(fact_100_mult_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 2.76/1.55 thf(fact_101_comm__monoid__mult__class_Omult__1, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 2.76/1.55 thf(fact_102_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.76/1.55 thf(fact_103_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.76/1.55 thf(fact_104_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.76/1.55 thf(fact_105_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F2 @ X4)) @ (G2 @ X4))))))))))).
% 2.76/1.55 thf(fact_106_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X2:B,Y2:B]: (((((ord_less_eq @ B) @ X2) @ Y2) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.76/1.55 thf(fact_107_order__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C2) @ (F @ B2)) @ C) => ((! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => (((ord_less_eq @ C2) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less_eq @ C2) @ (F @ A2)) @ C)))))))))).
% 2.76/1.55 thf(fact_108_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X2:B,Y2:B]: (((((ord_less_eq @ B) @ X2) @ Y2) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.76/1.55 thf(fact_109_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C)))))))))).
% 2.76/1.55 thf(fact_110_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X4))))))))).
% 2.76/1.55 thf(fact_111_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.76/1.55 thf(fact_112_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.76/1.55 thf(fact_113_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.76/1.55 thf(fact_114_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.76/1.55 thf(fact_115_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(fact_116_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.76/1.55 thf(fact_117_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.76/1.55 thf(fact_118_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) & (((ord_less_eq @ A) @ B5) @ A5))))))))).
% 2.76/1.55 thf(fact_119_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(fact_120_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(fact_121_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.76/1.55 thf(fact_122_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.76/1.55 thf(fact_123_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.76/1.55 thf(fact_124_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P3:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((P3 @ A4) @ B3)))) => ((! [A4:A,B3:A]: ((((P3 @ B3) @ A4) => ((P3 @ A4) @ B3)))) => ((P3 @ A2) @ B2))))))))).
% 2.76/1.55 thf(fact_125_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 2.76/1.55 thf(fact_126_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A5) & (((ord_less_eq @ A) @ A5) @ B5))))))))).
% 2.76/1.55 thf(fact_127_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.76/1.55 thf(fact_128_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_129_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [A2:A,B2:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 2.76/1.55 thf(fact_130_mult_Oassoc, axiom, (! [A:$tType]: (((semigroup_mult @ A) => (! [A2:A,B2:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 2.76/1.55 thf(fact_131_mult_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => ((times_times @ A) = (^ [A5:A,B5:A]: ((((times_times @ A) @ B5) @ A5)))))))).
% 2.76/1.55 thf(fact_132_mult_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [B2:A,A2:A,C:A]: (((((times_times @ A) @ B2) @ (((times_times @ A) @ A2) @ C)) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 2.76/1.55 thf(fact_133_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.76/1.55 thf(fact_134_Collect__mono__iff, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q)) = (! [X4:A]: (((P3 @ X4) => (Q @ X4)))))))).
% 2.76/1.55 thf(fact_135_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z:(set @ A)]: ((Y4 = Z))) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))).
% 2.76/1.55 thf(fact_136_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C3) => (((ord_less_eq @ (set @ A)) @ A3) @ C3)))))).
% 2.76/1.55 thf(fact_137_Collect__mono, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P3 @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q)))))).
% 2.76/1.55 thf(fact_138_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 2.76/1.55 thf(fact_139_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A6) => (((member @ A) @ T2) @ B6)))))))))).
% 2.76/1.55 thf(fact_140_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A3))))).
% 2.76/1.55 thf(fact_141_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.76/1.55 thf(fact_142_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ A6) => (((member @ A) @ X4) @ B6)))))))))).
% 2.76/1.55 thf(fact_143_equalityE, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (~ ((((ord_less_eq @ (set @ A)) @ B4) @ A3)))))))))).
% 2.76/1.55 thf(fact_144_subsetD, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ C) @ A3) => (((member @ A) @ C) @ B4)))))).
% 2.76/1.55 thf(fact_145_in__mono, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ X) @ A3) => (((member @ A) @ X) @ B4)))))).
% 2.76/1.55 thf(fact_146_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A6)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B6)))))))))).
% 2.76/1.55 thf(fact_147_Collect__subset, axiom, (! [A:$tType,A3:(set @ A),P3:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A3) & (P3 @ X4)))))) @ A3)))).
% 2.76/1.55 thf(fact_148_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 2.76/1.55 thf(fact_149_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 2.76/1.55 thf(fact_150_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.76/1.55 thf(fact_151_subset__Collect__iff, axiom, (! [A:$tType,B4:(set @ A),A3:(set @ A),P3:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B4) @ A3) => ((((ord_less_eq @ (set @ A)) @ B4) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A3) & (P3 @ X4)))))) = (! [X4:A]: (((((member @ A) @ X4) @ B4) => (P3 @ X4))))))))).
% 2.76/1.55 thf(fact_152_subset__CollectI, axiom, (! [A:$tType,B4:(set @ A),A3:(set @ A),Q:(A > $o),P3:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B4) @ A3) => ((! [X2:A]: (((((member @ A) @ X2) @ B4) => ((Q @ X2) => (P3 @ X2))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ B4) & (Q @ X4)))))) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A3) & (P3 @ X4))))))))))).
% 2.76/1.55 thf(fact_153_Collect__restrict, axiom, (! [A:$tType,X5:(set @ A),P3:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ X5) & (P3 @ X4)))))) @ X5)))).
% 2.76/1.55 thf(fact_154_predicate1I, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P3 @ X2) => (Q @ X2)))) => (((ord_less_eq @ (A > $o)) @ P3) @ Q))))).
% 2.76/1.55 thf(fact_155_predicate1D, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o),X:A]: (((((ord_less_eq @ (A > $o)) @ P3) @ Q) => ((P3 @ X) => (Q @ X)))))).
% 2.76/1.55 thf(fact_156_rev__predicate1D, axiom, (! [A:$tType,P3:(A > $o),X:A,Q:(A > $o)]: (((P3 @ X) => ((((ord_less_eq @ (A > $o)) @ P3) @ Q) => (Q @ X)))))).
% 2.76/1.55 thf(fact_157_prop__restrict, axiom, (! [A:$tType,X:A,Z3:(set @ A),X5:(set @ A),P3:(A > $o)]: (((((member @ A) @ X) @ Z3) => ((((ord_less_eq @ (set @ A)) @ Z3) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ X5) & (P3 @ X4)))))) => (P3 @ X)))))).
% 2.76/1.55 thf(fact_158_pred__subset__eq, axiom, (! [A:$tType,R2:(set @ A),S:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ R2)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ S)))) = (((ord_less_eq @ (set @ A)) @ R2) @ S))))).
% 2.76/1.55 thf(fact_159_dbl__inc__simps_I2_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (((neg_numeral_dbl_inc @ A) @ (zero_zero @ A)) = (one_one @ A)))))).
% 2.76/1.55 thf(fact_160_conj__subset__def, axiom, (! [A:$tType,A3:(set @ A),P3:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A3) @ ((collect @ A) @ (^ [X4:A]: (((P3 @ X4) & (Q @ X4)))))) = ((((ord_less_eq @ (set @ A)) @ A3) @ ((collect @ A) @ P3)) & (((ord_less_eq @ (set @ A)) @ A3) @ ((collect @ A) @ Q))))))).
% 2.76/1.55 thf(fact_161_fun__cong__unused__0, axiom, (! [A:$tType,B:$tType,C2:$tType]: (((zero @ B) => (! [F:((A > B) > C2),G:C2]: (((F = (^ [X4:(A > B)]: (G))) => ((F @ (^ [X4:A]: ((zero_zero @ B)))) = G)))))))).
% 2.76/1.55 thf(fact_162_mult__le__cancel__left1, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [C:A,B2:A]: (((((ord_less_eq @ A) @ C) @ (((times_times @ A) @ C) @ B2)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (one_one @ A)) @ B2)) & ((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ B2) @ (one_one @ A))))))))))).
% 2.76/1.55 thf(fact_163_mult__le__cancel__left2, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [C:A,A2:A]: (((((ord_less_eq @ A) @ (((times_times @ A) @ C) @ A2)) @ C) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ A2) @ (one_one @ A))) & ((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (one_one @ A)) @ A2)))))))))).
% 2.76/1.55 thf(fact_164_neq0__conv, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.76/1.55 thf(fact_165_less__nat__zero__code, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_166_bot__nat__0_Onot__eq__extremum, axiom, (! [A2:nat]: (((A2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A2))))).
% 2.76/1.55 thf(fact_167_psubsetI, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((A3 != B4) => (((ord_less @ (set @ A)) @ A3) @ B4)))))).
% 2.76/1.55 thf(fact_168_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_169_nat__0__less__mult__iff, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (((times_times @ nat) @ M) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ M) & (((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))).
% 2.76/1.55 thf(fact_170_mult__less__cancel2, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less @ nat) @ (((times_times @ nat) @ M) @ K)) @ (((times_times @ nat) @ N) @ K)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) & (((ord_less @ nat) @ M) @ N)))))).
% 2.76/1.55 thf(fact_171_nat__mult__less__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) & (((ord_less @ nat) @ M) @ N)))))).
% 2.76/1.55 thf(fact_172_less__one, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (one_one @ nat)) = (N = (zero_zero @ nat)))))).
% 2.76/1.55 thf(fact_173_mult__le__cancel2, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((times_times @ nat) @ M) @ K)) @ (((times_times @ nat) @ N) @ K)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less_eq @ nat) @ M) @ N)))))).
% 2.76/1.55 thf(fact_174_nat__mult__le__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less_eq @ nat) @ M) @ N)))))).
% 2.76/1.55 thf(fact_175_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (A2 != B2)))))))).
% 2.76/1.55 thf(fact_176_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (A2 != B2)))))))).
% 2.76/1.55 thf(fact_177_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 2.76/1.55 thf(fact_178_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ B2) => (((ord_less @ A) @ C) @ A2))))))))).
% 2.76/1.55 thf(fact_179_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P3:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => ((P3 @ A4) @ B3)))) => ((! [A4:A]: (((P3 @ A4) @ A4))) => ((! [A4:A,B3:A]: ((((P3 @ B3) @ A4) => ((P3 @ A4) @ B3)))) => ((P3 @ A2) @ B2)))))))))).
% 2.76/1.55 thf(fact_180_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P4:(A > $o)]: ((? [X6:A]: ((P4 @ X6))))) = (^ [P5:(A > $o)]: ((? [N2:A]: (((P5 @ N2) & (! [M4:A]: (((((ord_less @ A) @ M4) @ N2) => (~ ((P5 @ M4)))))))))))))))).
% 2.76/1.55 thf(fact_181_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.76/1.55 thf(fact_182_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(fact_183_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 2.76/1.55 thf(fact_184_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.76/1.55 thf(fact_185_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,P3:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P3)))))))).
% 2.76/1.55 thf(fact_186_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 2.76/1.55 thf(fact_187_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 2.76/1.55 thf(fact_188_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P3:(A > $o),A2:A]: (((! [X2:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X2) => (P3 @ Y3)))) => (P3 @ X2)))) => (P3 @ A2)))))))).
% 2.76/1.55 thf(fact_189_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.76/1.55 thf(fact_190_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.76/1.55 thf(fact_191_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (~ ((((ord_less @ A) @ A2) @ B2)))))))))).
% 2.76/1.55 thf(fact_192_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(fact_193_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(fact_194_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 2.76/1.55 thf(fact_195_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.76/1.55 thf(fact_196_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z2) => (((ord_less @ A) @ X) @ Z2))))))))).
% 2.76/1.55 thf(fact_197_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 2.76/1.55 thf(fact_198_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.76/1.55 thf(fact_199_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.76/1.55 thf(fact_200_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z4:A]: (((((ord_less @ A) @ X) @ Z4) & (((ord_less @ A) @ Z4) @ Y))))))))))).
% 2.76/1.55 thf(fact_201_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 2.76/1.55 thf(fact_202_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.76/1.55 thf(fact_203_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.76/1.55 thf(fact_204_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X:A]: ((? [X_1:A]: ((((ord_less @ A) @ X) @ X_1))))))))).
% 2.76/1.55 thf(fact_205_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X))))))))).
% 2.76/1.55 thf(fact_206_order__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ C2) @ (F @ B2)) @ C) => ((! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less @ C2) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less @ C2) @ (F @ A2)) @ C)))))))))).
% 2.76/1.55 thf(fact_207_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X2:B,Y2:B]: (((((ord_less @ B) @ X2) @ Y2) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.76/1.55 thf(fact_208_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less @ B) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less @ B) @ (F @ A2)) @ C)))))))))).
% 2.76/1.55 thf(fact_209_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X2:B,Y2:B]: (((((ord_less @ B) @ X2) @ Y2) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y2))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.76/1.55 thf(fact_210_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.76/1.55 thf(fact_211_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.76/1.55 thf(fact_212_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_213_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.76/1.55 thf(fact_214_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.76/1.55 thf(fact_215_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P3:(A > $o),A2:A]: (((! [X2:A]: (((! [Y3:A]: (((((ord_less @ B) @ (F @ Y3)) @ (F @ X2)) => (P3 @ Y3)))) => (P3 @ X2)))) => (P3 @ A2)))))))).
% 2.76/1.55 thf(fact_216_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P3:(A > $o),A2:A]: (((! [X2:A]: (((! [Y3:A]: (((((ord_less @ B) @ (F @ Y3)) @ (F @ X2)) => (P3 @ Y3)))) => (P3 @ X2)))) => (P3 @ A2)))))))).
% 2.76/1.55 thf(fact_217_nat__less__le, axiom, ((ord_less @ nat) = (^ [M4:nat,N2:nat]: (((((ord_less_eq @ nat) @ M4) @ N2) & (M4 != N2)))))).
% 2.76/1.55 thf(fact_218_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.76/1.55 thf(fact_219_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M4:nat,N2:nat]: (((((ord_less @ nat) @ M4) @ N2) | (M4 = N2)))))).
% 2.76/1.55 thf(fact_220_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.76/1.55 thf(fact_221_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 2.76/1.55 thf(fact_222_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I4:nat,J:nat]: (((! [I3:nat,J3:nat]: (((((ord_less @ nat) @ I3) @ J3) => (((ord_less @ nat) @ (F @ I3)) @ (F @ J3))))) => ((((ord_less_eq @ nat) @ I4) @ J) => (((ord_less_eq @ nat) @ (F @ I4)) @ (F @ J))))))).
% 2.76/1.55 thf(fact_223_gr0I, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.76/1.55 thf(fact_224_not__gr0, axiom, (! [N:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))) = (N = (zero_zero @ nat)))))).
% 2.76/1.55 thf(fact_225_not__less0, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_226_less__zeroE, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_227_gr__implies__not0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (N != (zero_zero @ nat)))))).
% 2.76/1.55 thf(fact_228_infinite__descent0, axiom, (! [P3:(nat > $o),N:nat]: (((P3 @ (zero_zero @ nat)) => ((! [N3:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N3) => ((~ ((P3 @ N3))) => (? [M5:nat]: (((((ord_less @ nat) @ M5) @ N3) & (~ ((P3 @ M5)))))))))) => (P3 @ N)))))).
% 2.76/1.55 thf(fact_229_bot__nat__0_Oextremum__strict, axiom, (! [A2:nat]: ((~ ((((ord_less @ nat) @ A2) @ (zero_zero @ nat))))))).
% 2.76/1.55 thf(fact_230_infinite__descent0__measure, axiom, (! [A:$tType,V:(A > nat),P3:(A > $o),X:A]: (((! [X2:A]: ((((V @ X2) = (zero_zero @ nat)) => (P3 @ X2)))) => ((! [X2:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V @ X2)) => ((~ ((P3 @ X2))) => (? [Y3:A]: (((((ord_less @ nat) @ (V @ Y3)) @ (V @ X2)) & (~ ((P3 @ Y3)))))))))) => (P3 @ X)))))).
% 2.76/1.55 thf(fact_231_psubsetE, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less @ (set @ A)) @ A3) @ B4) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A3)))))))).
% 2.76/1.55 thf(fact_232_psubset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (A6 != B6)))))))).
% 2.76/1.55 thf(fact_233_psubset__imp__subset, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less @ (set @ A)) @ A3) @ B4) => (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.76/1.55 thf(fact_234_psubset__subset__trans, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C3) => (((ord_less @ (set @ A)) @ A3) @ C3)))))).
% 2.76/1.55 thf(fact_235_subset__not__subset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (~ ((((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))))).
% 2.76/1.55 thf(fact_236_subset__psubset__trans, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less @ (set @ A)) @ B4) @ C3) => (((ord_less @ (set @ A)) @ A3) @ C3)))))).
% 2.76/1.55 thf(fact_237_subset__iff__psubset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less @ (set @ A)) @ A6) @ B6) | (A6 = B6)))))))).
% 2.76/1.55 thf(fact_238_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.76/1.55 thf(fact_239_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.76/1.55 thf(fact_240_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((A2 != B2) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 2.76/1.55 thf(fact_241_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 2.76/1.55 thf(fact_242_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B5:A,A5:A]: (((((ord_less_eq @ A) @ B5) @ A5) & (A5 != B5))))))))).
% 2.76/1.55 thf(fact_243_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: (((((ord_less @ A) @ B5) @ A5) | (A5 = B5))))))))).
% 2.76/1.55 thf(fact_244_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.76/1.55 thf(fact_245_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less @ A) @ X) @ Y) => ((! [W:A]: (((((ord_less @ A) @ X) @ W) => ((((ord_less @ A) @ W) @ Y) => (((ord_less_eq @ A) @ W) @ Z2))))) => (((ord_less_eq @ A) @ Y) @ Z2))))))))).
% 2.76/1.55 thf(fact_246_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z2:A,X:A,Y:A]: (((((ord_less @ A) @ Z2) @ X) => ((! [W:A]: (((((ord_less @ A) @ Z2) @ W) => ((((ord_less @ A) @ W) @ X) => (((ord_less_eq @ A) @ Y) @ W))))) => (((ord_less_eq @ A) @ Y) @ Z2))))))))).
% 2.76/1.55 thf(fact_247_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less @ A) @ C) @ A2))))))))).
% 2.76/1.55 thf(fact_248_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ B2) => (((ord_less @ A) @ C) @ A2))))))))).
% 2.76/1.55 thf(fact_249_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) & (A5 != B5))))))))).
% 2.76/1.55 thf(fact_250_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A5:A,B5:A]: (((((ord_less @ A) @ A5) @ B5) | (A5 = B5))))))))).
% 2.76/1.55 thf(fact_251_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(fact_252_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.76/1.55 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.76/1.55 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.76/1.55 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, axiom, (semiri1923998003cancel @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, axiom, (semiri1193490041visors @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add, axiom, (ordere216010020id_add @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring, axiom, (ordere1490568538miring @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0, axiom, (ordered_semiring_0 @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult, axiom, (ab_semigroup_mult @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult, axiom, (comm_monoid_mult @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Oordered__semiring, axiom, (ordered_semiring @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Osemigroup__mult, axiom, (semigroup_mult @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Ozero__neq__one, axiom, (zero_neq_one @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, (preorder @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Omonoid__mult, axiom, (monoid_mult @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Osemiring__0, axiom, (semiring_0 @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, (no_top @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Rings_Omult__zero, axiom, (mult_zero @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, (order @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, (ord @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.76/1.55 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 2.76/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_4, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.76/1.55 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.76/1.55 thf(tcon_Set_Oset___Orderings_Oord_6, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.76/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, (preorder @ $o)).
% 2.76/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder_8, axiom, (linorder @ $o)).
% 2.76/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, (order @ $o)).
% 2.76/1.55 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, (ord @ $o)).
% 2.76/1.55 thf(conj_0, conjecture, (((! [I2:nat]: ((((p @ I2) != (zero_zero @ nat)) => ((((ord_less_eq @ nat) @ (one_one @ nat)) @ I2) & (((ord_less_eq @ nat) @ I2) @ (zero_zero @ nat)))))) & (((((groups1340683514dd_sum @ nat) @ nat) @ (^ [I2:nat]: ((((times_times @ nat) @ (p @ I2)) @ I2)))) @ ((set_ord_atMost @ nat) @ (zero_zero @ nat))) = (zero_zero @ nat))) = (p = (^ [I2:nat]: ((zero_zero @ nat)))))).
% 2.76/1.55 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2DTF11076.p
% 2.76/1.55 ------------------------
% 2.76/1.58 ---- Cleaned THF ---
% 2.76/1.58 thf(ty_t_Set_Oset,type,
% 2.76/1.58 set: $tType > $tType ).
% 2.76/1.58
% 2.76/1.58 thf(ty_t_Nat_Onat,type,
% 2.76/1.58 nat: $tType ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_HOL_Otype,type,
% 2.76/1.58 type:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Oone,type,
% 2.76/1.58 one:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Ozero,type,
% 2.76/1.58 zero:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Oord,type,
% 2.76/1.58 ord:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Num_Oneg__numeral,type,
% 2.76/1.58 neg_numeral:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Oorder,type,
% 2.76/1.58 order:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Omult__zero,type,
% 2.76/1.58 mult_zero:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Ono__bot,type,
% 2.76/1.58 no_bot:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Ono__top,type,
% 2.76/1.58 no_top:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Osemiring__0,type,
% 2.76/1.58 semiring_0:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Omonoid__mult,type,
% 2.76/1.58 monoid_mult:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Olinorder,type,
% 2.76/1.58 linorder:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Opreorder,type,
% 2.76/1.58 preorder:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Oordered__ring,type,
% 2.76/1.58 ordered_ring:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.76/1.58 zero_neq_one:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Owellorder,type,
% 2.76/1.58 wellorder:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Osemigroup__mult,type,
% 2.76/1.58 semigroup_mult:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Odense__order,type,
% 2.76/1.58 dense_order:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.76/1.58 linordered_idom:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Olinordered__ring,type,
% 2.76/1.58 linordered_ring:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.76/1.58 comm_monoid_add:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Oordered__semiring,type,
% 2.76/1.58 ordered_semiring:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 2.76/1.58 comm_monoid_mult:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 2.76/1.58 ab_semigroup_mult:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Orderings_Odense__linorder,type,
% 2.76/1.58 dense_linorder:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Oordered__semiring__0,type,
% 2.76/1.58 ordered_semiring_0:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Oordered__comm__semiring,type,
% 2.76/1.58 ordere1490568538miring:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 2.76/1.58 linord581940658strict:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 2.76/1.58 ring_11004092258visors:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 2.76/1.58 ordere216010020id_add:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 2.76/1.58 semiri1193490041visors:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.76/1.58 linord1659791738miring:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.76/1.58 canoni770627133id_add:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 2.76/1.58 semiri1923998003cancel:
% 2.76/1.58 !>[A: $tType] : $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.76/1.58 one_one:
% 2.76/1.58 !>[A: $tType] : A ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 2.76/1.58 times_times:
% 2.76/1.58 !>[A: $tType] : ( A > A > A ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.76/1.58 zero_zero:
% 2.76/1.58 !>[A: $tType] : A ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum,type,
% 2.76/1.58 groups1340683514dd_sum:
% 2.76/1.58 !>[B: $tType,A: $tType] : ( ( B > A ) > ( set @ B ) > A ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 2.76/1.58 neg_numeral_dbl_inc:
% 2.76/1.58 !>[A: $tType] : ( A > A ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Number__Partition__Mirabelle__ihnzjotehb_Opartitions,type,
% 2.76/1.58 number2016821345itions: ( nat > nat ) > nat > $o ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.76/1.58 ord_less:
% 2.76/1.58 !>[A: $tType] : ( A > A > $o ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.76/1.58 ord_less_eq:
% 2.76/1.58 !>[A: $tType] : ( A > A > $o ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Set_OCollect,type,
% 2.76/1.58 collect:
% 2.76/1.58 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_Set__Interval_Oord__class_OatMost,type,
% 2.76/1.58 set_ord_atMost:
% 2.76/1.58 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_c_member,type,
% 2.76/1.58 member:
% 2.76/1.58 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.76/1.58
% 2.76/1.58 thf(sy_v_p,type,
% 2.76/1.58 p: nat > nat ).
% 2.76/1.58
% 2.76/1.58 thf(fact_0_mult__cancel__left1,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ring_11004092258visors @ A )
% 2.76/1.58 => ! [C: A,B2: A] :
% 2.76/1.58 ( ( C
% 2.76/1.58 = ( times_times @ A @ C @ B2 ) )
% 2.76/1.58 = ( ( C
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( B2
% 2.76/1.58 = ( one_one @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_1_mult__cancel__left2,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ring_11004092258visors @ A )
% 2.76/1.58 => ! [C: A,A2: A] :
% 2.76/1.58 ( ( ( times_times @ A @ C @ A2 )
% 2.76/1.58 = C )
% 2.76/1.58 = ( ( C
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( A2
% 2.76/1.58 = ( one_one @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_2_mult__cancel__right1,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ring_11004092258visors @ A )
% 2.76/1.58 => ! [C: A,B2: A] :
% 2.76/1.58 ( ( C
% 2.76/1.58 = ( times_times @ A @ B2 @ C ) )
% 2.76/1.58 = ( ( C
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( B2
% 2.76/1.58 = ( one_one @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_3_mult__cancel__right2,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ring_11004092258visors @ A )
% 2.76/1.58 => ! [A2: A,C: A] :
% 2.76/1.58 ( ( ( times_times @ A @ A2 @ C )
% 2.76/1.58 = C )
% 2.76/1.58 = ( ( C
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( A2
% 2.76/1.58 = ( one_one @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_4_sum_Oneutral__const,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [A3: set @ B] :
% 2.76/1.58 ( ( groups1340683514dd_sum @ B @ A
% 2.76/1.58 @ ^ [Uu: B] : ( zero_zero @ A )
% 2.76/1.58 @ A3 )
% 2.76/1.58 = ( zero_zero @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_5_partitionsE,axiom,
% 2.76/1.58 ! [P: nat > nat,N: nat] :
% 2.76/1.58 ( ( number2016821345itions @ P @ N )
% 2.76/1.58 => ~ ( ! [I: nat] :
% 2.76/1.58 ( ( ( P @ I )
% 2.76/1.58 != ( zero_zero @ nat ) )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I )
% 2.76/1.58 & ( ord_less_eq @ nat @ I @ N ) ) )
% 2.76/1.58 => ( ( groups1340683514dd_sum @ nat @ nat
% 2.76/1.58 @ ^ [I2: nat] : ( times_times @ nat @ ( P @ I2 ) @ I2 )
% 2.76/1.58 @ ( set_ord_atMost @ nat @ N ) )
% 2.76/1.58 != N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_6_partitionsI,axiom,
% 2.76/1.58 ! [P: nat > nat,N: nat] :
% 2.76/1.58 ( ! [I3: nat] :
% 2.76/1.58 ( ( ( P @ I3 )
% 2.76/1.58 != ( zero_zero @ nat ) )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I3 )
% 2.76/1.58 & ( ord_less_eq @ nat @ I3 @ N ) ) )
% 2.76/1.58 => ( ( ( groups1340683514dd_sum @ nat @ nat
% 2.76/1.58 @ ^ [I2: nat] : ( times_times @ nat @ ( P @ I2 ) @ I2 )
% 2.76/1.58 @ ( set_ord_atMost @ nat @ N ) )
% 2.76/1.58 = N )
% 2.76/1.58 => ( number2016821345itions @ P @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_7_partitions__def,axiom,
% 2.76/1.58 ( number2016821345itions
% 2.76/1.58 = ( ^ [P2: nat > nat,N2: nat] :
% 2.76/1.58 ( ! [I2: nat] :
% 2.76/1.58 ( ( ( P2 @ I2 )
% 2.76/1.58 != ( zero_zero @ nat ) )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I2 )
% 2.76/1.58 & ( ord_less_eq @ nat @ I2 @ N2 ) ) )
% 2.76/1.58 & ( ( groups1340683514dd_sum @ nat @ nat
% 2.76/1.58 @ ^ [I2: nat] : ( times_times @ nat @ ( P2 @ I2 ) @ I2 )
% 2.76/1.58 @ ( set_ord_atMost @ nat @ N2 ) )
% 2.76/1.58 = N2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_8_nat__1__eq__mult__iff,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ( one_one @ nat )
% 2.76/1.58 = ( times_times @ nat @ M @ N ) )
% 2.76/1.58 = ( ( M
% 2.76/1.58 = ( one_one @ nat ) )
% 2.76/1.58 & ( N
% 2.76/1.58 = ( one_one @ nat ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_9_nat__mult__eq__1__iff,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ( times_times @ nat @ M @ N )
% 2.76/1.58 = ( one_one @ nat ) )
% 2.76/1.58 = ( ( M
% 2.76/1.58 = ( one_one @ nat ) )
% 2.76/1.58 & ( N
% 2.76/1.58 = ( one_one @ nat ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_10_atMost__subset__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ X ) @ ( set_ord_atMost @ A @ Y ) )
% 2.76/1.58 = ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_11_atMost__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord @ A )
% 2.76/1.58 => ! [I4: A,K: A] :
% 2.76/1.58 ( ( member @ A @ I4 @ ( set_ord_atMost @ A @ K ) )
% 2.76/1.58 = ( ord_less_eq @ A @ I4 @ K ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_12_atMost__eq__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ( set_ord_atMost @ A @ X )
% 2.76/1.58 = ( set_ord_atMost @ A @ Y ) )
% 2.76/1.58 = ( X = Y ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_13_mult__cancel__right,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semiri1923998003cancel @ A )
% 2.76/1.58 => ! [A2: A,C: A,B2: A] :
% 2.76/1.58 ( ( ( times_times @ A @ A2 @ C )
% 2.76/1.58 = ( times_times @ A @ B2 @ C ) )
% 2.76/1.58 = ( ( C
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( A2 = B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_14_mult__cancel__left,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semiri1923998003cancel @ A )
% 2.76/1.58 => ! [C: A,A2: A,B2: A] :
% 2.76/1.58 ( ( ( times_times @ A @ C @ A2 )
% 2.76/1.58 = ( times_times @ A @ C @ B2 ) )
% 2.76/1.58 = ( ( C
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( A2 = B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_15_mult__eq__0__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semiri1193490041visors @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ( times_times @ A @ A2 @ B2 )
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 = ( ( A2
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( B2
% 2.76/1.58 = ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_16_mult__zero__right,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( mult_zero @ A )
% 2.76/1.58 => ! [A2: A] :
% 2.76/1.58 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.58 = ( zero_zero @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_17_mult__zero__left,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( mult_zero @ A )
% 2.76/1.58 => ! [A2: A] :
% 2.76/1.58 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 = ( zero_zero @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_18_bot__nat__0_Oextremum,axiom,
% 2.76/1.58 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_19_le0,axiom,
% 2.76/1.58 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_20_mult__cancel2,axiom,
% 2.76/1.58 ! [M: nat,K: nat,N: nat] :
% 2.76/1.58 ( ( ( times_times @ nat @ M @ K )
% 2.76/1.58 = ( times_times @ nat @ N @ K ) )
% 2.76/1.58 = ( ( M = N )
% 2.76/1.58 | ( K
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_21_mult__cancel1,axiom,
% 2.76/1.58 ! [K: nat,M: nat,N: nat] :
% 2.76/1.58 ( ( ( times_times @ nat @ K @ M )
% 2.76/1.58 = ( times_times @ nat @ K @ N ) )
% 2.76/1.58 = ( ( M = N )
% 2.76/1.58 | ( K
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_22_mult__0__right,axiom,
% 2.76/1.58 ! [M: nat] :
% 2.76/1.58 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 2.76/1.58 = ( zero_zero @ nat ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_23_mult__is__0,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ( times_times @ nat @ M @ N )
% 2.76/1.58 = ( zero_zero @ nat ) )
% 2.76/1.58 = ( ( M
% 2.76/1.58 = ( zero_zero @ nat ) )
% 2.76/1.58 | ( N
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_24_bounded__Max__nat,axiom,
% 2.76/1.58 ! [P3: nat > $o,X: nat,M2: nat] :
% 2.76/1.58 ( ( P3 @ X )
% 2.76/1.58 => ( ! [X2: nat] :
% 2.76/1.58 ( ( P3 @ X2 )
% 2.76/1.58 => ( ord_less_eq @ nat @ X2 @ M2 ) )
% 2.76/1.58 => ~ ! [M3: nat] :
% 2.76/1.58 ( ( P3 @ M3 )
% 2.76/1.58 => ~ ! [X3: nat] :
% 2.76/1.58 ( ( P3 @ X3 )
% 2.76/1.58 => ( ord_less_eq @ nat @ X3 @ M3 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_25_Nat_Oex__has__greatest__nat,axiom,
% 2.76/1.58 ! [P3: nat > $o,K: nat,B2: nat] :
% 2.76/1.58 ( ( P3 @ K )
% 2.76/1.58 => ( ! [Y2: nat] :
% 2.76/1.58 ( ( P3 @ Y2 )
% 2.76/1.58 => ( ord_less_eq @ nat @ Y2 @ B2 ) )
% 2.76/1.58 => ? [X2: nat] :
% 2.76/1.58 ( ( P3 @ X2 )
% 2.76/1.58 & ! [Y3: nat] :
% 2.76/1.58 ( ( P3 @ Y3 )
% 2.76/1.58 => ( ord_less_eq @ nat @ Y3 @ X2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_26_nat__le__linear,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ M @ N )
% 2.76/1.58 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_27_le__antisym,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ M @ N )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ N @ M )
% 2.76/1.58 => ( M = N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_28_eq__imp__le,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( M = N )
% 2.76/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_29_le__trans,axiom,
% 2.76/1.58 ! [I4: nat,J: nat,K: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ I4 @ J )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ J @ K )
% 2.76/1.58 => ( ord_less_eq @ nat @ I4 @ K ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_30_le__refl,axiom,
% 2.76/1.58 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_31_sum_Oreindex__bij__witness,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType,C2: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [S: set @ B,I4: C2 > B,J: B > C2,T: set @ C2,H: C2 > A,G: B > A] :
% 2.76/1.58 ( ! [A4: B] :
% 2.76/1.58 ( ( member @ B @ A4 @ S )
% 2.76/1.58 => ( ( I4 @ ( J @ A4 ) )
% 2.76/1.58 = A4 ) )
% 2.76/1.58 => ( ! [A4: B] :
% 2.76/1.58 ( ( member @ B @ A4 @ S )
% 2.76/1.58 => ( member @ C2 @ ( J @ A4 ) @ T ) )
% 2.76/1.58 => ( ! [B3: C2] :
% 2.76/1.58 ( ( member @ C2 @ B3 @ T )
% 2.76/1.58 => ( ( J @ ( I4 @ B3 ) )
% 2.76/1.58 = B3 ) )
% 2.76/1.58 => ( ! [B3: C2] :
% 2.76/1.58 ( ( member @ C2 @ B3 @ T )
% 2.76/1.58 => ( member @ B @ ( I4 @ B3 ) @ S ) )
% 2.76/1.58 => ( ! [A4: B] :
% 2.76/1.58 ( ( member @ B @ A4 @ S )
% 2.76/1.58 => ( ( H @ ( J @ A4 ) )
% 2.76/1.58 = ( G @ A4 ) ) )
% 2.76/1.58 => ( ( groups1340683514dd_sum @ B @ A @ G @ S )
% 2.76/1.58 = ( groups1340683514dd_sum @ C2 @ A @ H @ T ) ) ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_32_sum_Oeq__general__inverses,axiom,
% 2.76/1.58 ! [C2: $tType,A: $tType,B: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [B4: set @ B,K: B > C2,A3: set @ C2,H: C2 > B,Gamma: B > A,Phi: C2 > A] :
% 2.76/1.58 ( ! [Y2: B] :
% 2.76/1.58 ( ( member @ B @ Y2 @ B4 )
% 2.76/1.58 => ( ( member @ C2 @ ( K @ Y2 ) @ A3 )
% 2.76/1.58 & ( ( H @ ( K @ Y2 ) )
% 2.76/1.58 = Y2 ) ) )
% 2.76/1.58 => ( ! [X2: C2] :
% 2.76/1.58 ( ( member @ C2 @ X2 @ A3 )
% 2.76/1.58 => ( ( member @ B @ ( H @ X2 ) @ B4 )
% 2.76/1.58 & ( ( K @ ( H @ X2 ) )
% 2.76/1.58 = X2 )
% 2.76/1.58 & ( ( Gamma @ ( H @ X2 ) )
% 2.76/1.58 = ( Phi @ X2 ) ) ) )
% 2.76/1.58 => ( ( groups1340683514dd_sum @ C2 @ A @ Phi @ A3 )
% 2.76/1.58 = ( groups1340683514dd_sum @ B @ A @ Gamma @ B4 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_33_sum_Oeq__general,axiom,
% 2.76/1.58 ! [C2: $tType,A: $tType,B: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [B4: set @ B,A3: set @ C2,H: C2 > B,Gamma: B > A,Phi: C2 > A] :
% 2.76/1.58 ( ! [Y2: B] :
% 2.76/1.58 ( ( member @ B @ Y2 @ B4 )
% 2.76/1.58 => ? [X3: C2] :
% 2.76/1.58 ( ( member @ C2 @ X3 @ A3 )
% 2.76/1.58 & ( ( H @ X3 )
% 2.76/1.58 = Y2 )
% 2.76/1.58 & ! [Ya: C2] :
% 2.76/1.58 ( ( ( member @ C2 @ Ya @ A3 )
% 2.76/1.58 & ( ( H @ Ya )
% 2.76/1.58 = Y2 ) )
% 2.76/1.58 => ( Ya = X3 ) ) ) )
% 2.76/1.58 => ( ! [X2: C2] :
% 2.76/1.58 ( ( member @ C2 @ X2 @ A3 )
% 2.76/1.58 => ( ( member @ B @ ( H @ X2 ) @ B4 )
% 2.76/1.58 & ( ( Gamma @ ( H @ X2 ) )
% 2.76/1.58 = ( Phi @ X2 ) ) ) )
% 2.76/1.58 => ( ( groups1340683514dd_sum @ C2 @ A @ Phi @ A3 )
% 2.76/1.58 = ( groups1340683514dd_sum @ B @ A @ Gamma @ B4 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_34_sum_Ocong,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [A3: set @ B,B4: set @ B,G: B > A,H: B > A] :
% 2.76/1.58 ( ( A3 = B4 )
% 2.76/1.58 => ( ! [X2: B] :
% 2.76/1.58 ( ( member @ B @ X2 @ B4 )
% 2.76/1.58 => ( ( G @ X2 )
% 2.76/1.58 = ( H @ X2 ) ) )
% 2.76/1.58 => ( ( groups1340683514dd_sum @ B @ A @ G @ A3 )
% 2.76/1.58 = ( groups1340683514dd_sum @ B @ A @ H @ B4 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_35_sum_Oswap,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType,C2: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [G: B > C2 > A,B4: set @ C2,A3: set @ B] :
% 2.76/1.58 ( ( groups1340683514dd_sum @ B @ A
% 2.76/1.58 @ ^ [I2: B] : ( groups1340683514dd_sum @ C2 @ A @ ( G @ I2 ) @ B4 )
% 2.76/1.58 @ A3 )
% 2.76/1.58 = ( groups1340683514dd_sum @ C2 @ A
% 2.76/1.58 @ ^ [J2: C2] :
% 2.76/1.58 ( groups1340683514dd_sum @ B @ A
% 2.76/1.58 @ ^ [I2: B] : ( G @ I2 @ J2 )
% 2.76/1.58 @ A3 )
% 2.76/1.58 @ B4 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_36_mult__right__cancel,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semiri1923998003cancel @ A )
% 2.76/1.58 => ! [C: A,A2: A,B2: A] :
% 2.76/1.58 ( ( C
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 => ( ( ( times_times @ A @ A2 @ C )
% 2.76/1.58 = ( times_times @ A @ B2 @ C ) )
% 2.76/1.58 = ( A2 = B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_37_mult__left__cancel,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semiri1923998003cancel @ A )
% 2.76/1.58 => ! [C: A,A2: A,B2: A] :
% 2.76/1.58 ( ( C
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 => ( ( ( times_times @ A @ C @ A2 )
% 2.76/1.58 = ( times_times @ A @ C @ B2 ) )
% 2.76/1.58 = ( A2 = B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_38_no__zero__divisors,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semiri1193490041visors @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( A2
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 => ( ( B2
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 => ( ( times_times @ A @ A2 @ B2 )
% 2.76/1.58 != ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_39_divisors__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semiri1193490041visors @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ( times_times @ A @ A2 @ B2 )
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 => ( ( A2
% 2.76/1.58 = ( zero_zero @ A ) )
% 2.76/1.58 | ( B2
% 2.76/1.58 = ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_40_mult__not__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( mult_zero @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ( times_times @ A @ A2 @ B2 )
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 => ( ( A2
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 & ( B2
% 2.76/1.58 != ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_41_zero__neq__one,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( zero_neq_one @ A )
% 2.76/1.58 => ( ( zero_zero @ A )
% 2.76/1.58 != ( one_one @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_42_sum_Onot__neutral__contains__not__neutral,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [G: B > A,A3: set @ B] :
% 2.76/1.58 ( ( ( groups1340683514dd_sum @ B @ A @ G @ A3 )
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 => ~ ! [A4: B] :
% 2.76/1.58 ( ( member @ B @ A4 @ A3 )
% 2.76/1.58 => ( ( G @ A4 )
% 2.76/1.58 = ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_43_sum_Oneutral,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( comm_monoid_add @ A )
% 2.76/1.58 => ! [A3: set @ B,G: B > A] :
% 2.76/1.58 ( ! [X2: B] :
% 2.76/1.58 ( ( member @ B @ X2 @ A3 )
% 2.76/1.58 => ( ( G @ X2 )
% 2.76/1.58 = ( zero_zero @ A ) ) )
% 2.76/1.58 => ( ( groups1340683514dd_sum @ B @ A @ G @ A3 )
% 2.76/1.58 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_44_mem__Collect__eq,axiom,
% 2.76/1.58 ! [A: $tType,A2: A,P3: A > $o] :
% 2.76/1.58 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 2.76/1.58 = ( P3 @ A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_45_Collect__mem__eq,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A] :
% 2.76/1.58 ( ( collect @ A
% 2.76/1.58 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 2.76/1.58 = A3 ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_46_Collect__cong,axiom,
% 2.76/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ( P3 @ X2 )
% 2.76/1.58 = ( Q @ X2 ) )
% 2.76/1.58 => ( ( collect @ A @ P3 )
% 2.76/1.58 = ( collect @ A @ Q ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_47_ext,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ( F @ X2 )
% 2.76/1.58 = ( G @ X2 ) )
% 2.76/1.58 => ( F = G ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_48_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.76/1.58 ! [A2: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.76/1.58 => ( A2
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_49_bot__nat__0_Oextremum__unique,axiom,
% 2.76/1.58 ! [A2: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.76/1.58 = ( A2
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_50_le__0__eq,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 2.76/1.58 = ( N
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_51_less__eq__nat_Osimps_I1_J,axiom,
% 2.76/1.58 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_52_mult__0,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 2.76/1.58 = ( zero_zero @ nat ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_53_mult__le__mono2,axiom,
% 2.76/1.58 ! [I4: nat,J: nat,K: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ I4 @ J )
% 2.76/1.58 => ( ord_less_eq @ nat @ ( times_times @ nat @ K @ I4 ) @ ( times_times @ nat @ K @ J ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_54_mult__le__mono1,axiom,
% 2.76/1.58 ! [I4: nat,J: nat,K: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ I4 @ J )
% 2.76/1.58 => ( ord_less_eq @ nat @ ( times_times @ nat @ I4 @ K ) @ ( times_times @ nat @ J @ K ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_55_mult__le__mono,axiom,
% 2.76/1.58 ! [I4: nat,J: nat,K: nat,L: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ I4 @ J )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ K @ L )
% 2.76/1.58 => ( ord_less_eq @ nat @ ( times_times @ nat @ I4 @ K ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_56_le__square,axiom,
% 2.76/1.58 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_57_le__cube,axiom,
% 2.76/1.58 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_58_nat__mult__1__right,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 2.76/1.58 = N ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_59_nat__mult__1,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 2.76/1.58 = N ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_60_lambda__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( mult_zero @ A )
% 2.76/1.58 => ( ( ^ [H2: A] : ( zero_zero @ A ) )
% 2.76/1.58 = ( times_times @ A @ ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_61_lambda__one,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( monoid_mult @ A )
% 2.76/1.58 => ( ( ^ [X4: A] : X4 )
% 2.76/1.58 = ( times_times @ A @ ( one_one @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_62_sum__mono,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ordere216010020id_add @ A )
% 2.76/1.58 => ! [K2: set @ B,F: B > A,G: B > A] :
% 2.76/1.58 ( ! [I3: B] :
% 2.76/1.58 ( ( member @ B @ I3 @ K2 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F @ K2 ) @ ( groups1340683514dd_sum @ B @ A @ G @ K2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_63_sum__distrib__right,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( semiring_0 @ A )
% 2.76/1.58 => ! [F: B > A,A3: set @ B,R: A] :
% 2.76/1.58 ( ( times_times @ A @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) @ R )
% 2.76/1.58 = ( groups1340683514dd_sum @ B @ A
% 2.76/1.58 @ ^ [N2: B] : ( times_times @ A @ ( F @ N2 ) @ R )
% 2.76/1.58 @ A3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_64_sum__distrib__left,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( semiring_0 @ A )
% 2.76/1.58 => ! [R: A,F: B > A,A3: set @ B] :
% 2.76/1.58 ( ( times_times @ A @ R @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) )
% 2.76/1.58 = ( groups1340683514dd_sum @ B @ A
% 2.76/1.58 @ ^ [N2: B] : ( times_times @ A @ R @ ( F @ N2 ) )
% 2.76/1.58 @ A3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_65_sum__product,axiom,
% 2.76/1.58 ! [B: $tType,C2: $tType,A: $tType] :
% 2.76/1.58 ( ( semiring_0 @ B )
% 2.76/1.58 => ! [F: A > B,A3: set @ A,G: C2 > B,B4: set @ C2] :
% 2.76/1.58 ( ( times_times @ B @ ( groups1340683514dd_sum @ A @ B @ F @ A3 ) @ ( groups1340683514dd_sum @ C2 @ B @ G @ B4 ) )
% 2.76/1.58 = ( groups1340683514dd_sum @ A @ B
% 2.76/1.58 @ ^ [I2: A] :
% 2.76/1.58 ( groups1340683514dd_sum @ C2 @ B
% 2.76/1.58 @ ^ [J2: C2] : ( times_times @ B @ ( F @ I2 ) @ ( G @ J2 ) )
% 2.76/1.58 @ B4 )
% 2.76/1.58 @ A3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_66_atMost__def,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord @ A )
% 2.76/1.58 => ( ( set_ord_atMost @ A )
% 2.76/1.58 = ( ^ [U: A] :
% 2.76/1.58 ( collect @ A
% 2.76/1.58 @ ^ [X4: A] : ( ord_less_eq @ A @ X4 @ U ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_67_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordere1490568538miring @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_68_zero__le__mult__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord581940658strict @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 2.76/1.58 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.76/1.58 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.58 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_69_mult__nonneg__nonpos2,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring_0 @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_70_mult__nonpos__nonneg,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring_0 @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_71_mult__nonneg__nonpos,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring_0 @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_72_mult__nonneg__nonneg,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring_0 @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_73_split__mult__neg__le,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring_0 @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.76/1.58 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.58 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_74_mult__le__0__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord581940658strict @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 2.76/1.58 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.76/1.58 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.58 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_75_mult__right__mono,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_76_mult__right__mono__neg,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_ring @ A )
% 2.76/1.58 => ! [B2: A,A2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_77_mult__left__mono,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_78_mult__nonpos__nonpos,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_ring @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_79_mult__left__mono__neg,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_ring @ A )
% 2.76/1.58 => ! [B2: A,A2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_80_split__mult__pos__le,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_ring @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.76/1.58 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.58 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_81_zero__le__square,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linordered_ring @ A )
% 2.76/1.58 => ! [A2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ A2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_82_mult__mono_H,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A,D: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ C @ D )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_83_mult__mono,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ordered_semiring @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A,D: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ C @ D )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_84_not__one__le__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_85_zero__le__one,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_86_sum__nonpos,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( ordere216010020id_add @ A )
% 2.76/1.58 => ! [A3: set @ B,F: B > A] :
% 2.76/1.58 ( ! [X2: B] :
% 2.76/1.58 ( ( member @ B @ X2 @ A3 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( zero_zero @ A ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) @ ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_87_sum__nonneg,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ordere216010020id_add @ A )
% 2.76/1.58 => ! [A3: set @ B,F: B > A] :
% 2.76/1.58 ( ! [X2: B] :
% 2.76/1.58 ( ( member @ B @ X2 @ A3 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F @ X2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( groups1340683514dd_sum @ B @ A @ F @ A3 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_88_mult__eq__self__implies__10,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( M
% 2.76/1.58 = ( times_times @ nat @ M @ N ) )
% 2.76/1.58 => ( ( N
% 2.76/1.58 = ( one_one @ nat ) )
% 2.76/1.58 | ( M
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_89_mult__left__le,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ! [C: A,A2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ C @ ( one_one @ A ) )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ A2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_90_mult__le__one,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ ( one_one @ A ) )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ ( one_one @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( one_one @ A ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_91_mult__right__le__one__le,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linordered_idom @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 2.76/1.58 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ X @ Y ) @ X ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_92_mult__left__le__one__le,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linordered_idom @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 2.76/1.58 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 2.76/1.58 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( times_times @ A @ Y @ X ) @ X ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_93_mult_Oright__neutral,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( monoid_mult @ A )
% 2.76/1.58 => ! [A2: A] :
% 2.76/1.58 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 2.76/1.58 = A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_94_mult_Oleft__neutral,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( monoid_mult @ A )
% 2.76/1.58 => ! [A2: A] :
% 2.76/1.58 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 2.76/1.58 = A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_95_le__zero__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( canoni770627133id_add @ A )
% 2.76/1.58 => ! [N: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.76/1.58 = ( N
% 2.76/1.58 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_96_subsetI,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ( member @ A @ X2 @ A3 )
% 2.76/1.58 => ( member @ A @ X2 @ B4 ) )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_97_subset__antisym,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 2.76/1.58 => ( A3 = B4 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_98_order__refl,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_99_nat__mult__eq__cancel__disj,axiom,
% 2.76/1.58 ! [K: nat,M: nat,N: nat] :
% 2.76/1.58 ( ( ( times_times @ nat @ K @ M )
% 2.76/1.58 = ( times_times @ nat @ K @ N ) )
% 2.76/1.58 = ( ( K
% 2.76/1.58 = ( zero_zero @ nat ) )
% 2.76/1.58 | ( M = N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_100_mult_Ocomm__neutral,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( comm_monoid_mult @ A )
% 2.76/1.58 => ! [A2: A] :
% 2.76/1.58 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 2.76/1.58 = A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_101_comm__monoid__mult__class_Omult__1,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( comm_monoid_mult @ A )
% 2.76/1.58 => ! [A2: A] :
% 2.76/1.58 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 2.76/1.58 = A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_102_le__funD,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( ord @ B )
% 2.76/1.58 => ! [F: A > B,G: A > B,X: A] :
% 2.76/1.58 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.76/1.58 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_103_le__funE,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( ord @ B )
% 2.76/1.58 => ! [F: A > B,G: A > B,X: A] :
% 2.76/1.58 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.76/1.58 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_104_le__funI,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( ord @ B )
% 2.76/1.58 => ! [F: A > B,G: A > B] :
% 2.76/1.58 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 2.76/1.58 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_105_le__fun__def,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( ord @ B )
% 2.76/1.58 => ( ( ord_less_eq @ ( A > B ) )
% 2.76/1.58 = ( ^ [F2: A > B,G2: A > B] :
% 2.76/1.58 ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_106_order__subst1,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ( order @ B )
% 2.76/1.58 & ( order @ A ) )
% 2.76/1.58 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.76/1.58 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.76/1.58 => ( ! [X2: B,Y2: B] :
% 2.76/1.58 ( ( ord_less_eq @ B @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_107_order__subst2,axiom,
% 2.76/1.58 ! [A: $tType,C2: $tType] :
% 2.76/1.58 ( ( ( order @ C2 )
% 2.76/1.58 & ( order @ A ) )
% 2.76/1.58 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 2.76/1.58 => ( ! [X2: A,Y2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less_eq @ C2 @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_108_ord__eq__le__subst,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ( ord @ B )
% 2.76/1.58 & ( ord @ A ) )
% 2.76/1.58 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.76/1.58 ( ( A2
% 2.76/1.58 = ( F @ B2 ) )
% 2.76/1.58 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.76/1.58 => ( ! [X2: B,Y2: B] :
% 2.76/1.58 ( ( ord_less_eq @ B @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_109_ord__le__eq__subst,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ( ord @ B )
% 2.76/1.58 & ( ord @ A ) )
% 2.76/1.58 => ! [A2: A,B2: A,F: A > B,C: B] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ( F @ B2 )
% 2.76/1.58 = C )
% 2.76/1.58 => ( ! [X2: A,Y2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_110_eq__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.76/1.58 = ( ^ [X4: A,Y5: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 2.76/1.58 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_111_antisym,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ X @ Y )
% 2.76/1.58 => ( ( ord_less_eq @ A @ Y @ X )
% 2.76/1.58 => ( X = Y ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_112_linear,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ X @ Y )
% 2.76/1.58 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_113_eq__refl,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( X = Y )
% 2.76/1.58 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_114_le__cases,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.76/1.58 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_115_order_Otrans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_116_le__cases3,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A,Z2: A] :
% 2.76/1.58 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.76/1.58 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.76/1.58 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.76/1.58 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 2.76/1.58 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 2.76/1.58 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.76/1.58 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.76/1.58 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.76/1.58 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.76/1.58 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 2.76/1.58 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 2.76/1.58 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_117_antisym__conv,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [Y: A,X: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ Y @ X )
% 2.76/1.58 => ( ( ord_less_eq @ A @ X @ Y )
% 2.76/1.58 = ( X = Y ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_118_order__class_Oorder_Oeq__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.76/1.58 = ( ^ [A5: A,B5: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A5 @ B5 )
% 2.76/1.58 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_119_ord__eq__le__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( A2 = B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_120_ord__le__eq__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( B2 = C )
% 2.76/1.58 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_121_order__class_Oorder_Oantisym,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.76/1.58 => ( A2 = B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_122_order__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A,Z2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ X @ Y )
% 2.76/1.58 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.76/1.58 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_123_dual__order_Orefl,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_124_linorder__wlog,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [P3: A > A > $o,A2: A,B2: A] :
% 2.76/1.58 ( ! [A4: A,B3: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.76/1.58 => ( P3 @ A4 @ B3 ) )
% 2.76/1.58 => ( ! [A4: A,B3: A] :
% 2.76/1.58 ( ( P3 @ B3 @ A4 )
% 2.76/1.58 => ( P3 @ A4 @ B3 ) )
% 2.76/1.58 => ( P3 @ A2 @ B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_125_dual__order_Otrans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ C @ B2 )
% 2.76/1.58 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_126_dual__order_Oeq__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.76/1.58 = ( ^ [A5: A,B5: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ B5 @ A5 )
% 2.76/1.58 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_127_dual__order_Oantisym,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( A2 = B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_128_zero__reorient,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( zero @ A )
% 2.76/1.58 => ! [X: A] :
% 2.76/1.58 ( ( ( zero_zero @ A )
% 2.76/1.58 = X )
% 2.76/1.58 = ( X
% 2.76/1.58 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_129_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ab_semigroup_mult @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 2.76/1.58 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_130_mult_Oassoc,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( semigroup_mult @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 2.76/1.58 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_131_mult_Ocommute,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ab_semigroup_mult @ A )
% 2.76/1.58 => ( ( times_times @ A )
% 2.76/1.58 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_132_mult_Oleft__commute,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ab_semigroup_mult @ A )
% 2.76/1.58 => ! [B2: A,A2: A,C: A] :
% 2.76/1.58 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C ) )
% 2.76/1.58 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_133_one__reorient,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( one @ A )
% 2.76/1.58 => ! [X: A] :
% 2.76/1.58 ( ( ( one_one @ A )
% 2.76/1.58 = X )
% 2.76/1.58 = ( X
% 2.76/1.58 = ( one_one @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_134_Collect__mono__iff,axiom,
% 2.76/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) )
% 2.76/1.58 = ( ! [X4: A] :
% 2.76/1.58 ( ( P3 @ X4 )
% 2.76/1.58 => ( Q @ X4 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_135_set__eq__subset,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 2.76/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.76/1.58 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_136_subset__trans,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_137_Collect__mono,axiom,
% 2.76/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ( P3 @ X2 )
% 2.76/1.58 => ( Q @ X2 ) )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_138_subset__refl,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_139_subset__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.76/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.76/1.58 ! [T2: A] :
% 2.76/1.58 ( ( member @ A @ T2 @ A6 )
% 2.76/1.58 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_140_equalityD2,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ( A3 = B4 )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_141_equalityD1,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ( A3 = B4 )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_142_subset__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.76/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.76/1.58 ! [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ A6 )
% 2.76/1.58 => ( member @ A @ X4 @ B6 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_143_equalityE,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ( A3 = B4 )
% 2.76/1.58 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_144_subsetD,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ( member @ A @ C @ A3 )
% 2.76/1.58 => ( member @ A @ C @ B4 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_145_in__mono,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A,X: A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ( member @ A @ X @ A3 )
% 2.76/1.58 => ( member @ A @ X @ B4 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_146_less__eq__set__def,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.76/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.76/1.58 ( ord_less_eq @ ( A > $o )
% 2.76/1.58 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 2.76/1.58 @ ^ [X4: A] : ( member @ A @ X4 @ B6 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_147_Collect__subset,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,P3: A > $o] :
% 2.76/1.58 ( ord_less_eq @ ( set @ A )
% 2.76/1.58 @ ( collect @ A
% 2.76/1.58 @ ^ [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ A3 )
% 2.76/1.58 & ( P3 @ X4 ) ) )
% 2.76/1.58 @ A3 ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_148_zero__le,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( canoni770627133id_add @ A )
% 2.76/1.58 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_149_le__numeral__extra_I4_J,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_150_le__numeral__extra_I3_J,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_151_subset__Collect__iff,axiom,
% 2.76/1.58 ! [A: $tType,B4: set @ A,A3: set @ A,P3: A > $o] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 2.76/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B4
% 2.76/1.58 @ ( collect @ A
% 2.76/1.58 @ ^ [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ A3 )
% 2.76/1.58 & ( P3 @ X4 ) ) ) )
% 2.76/1.58 = ( ! [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ B4 )
% 2.76/1.58 => ( P3 @ X4 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_152_subset__CollectI,axiom,
% 2.76/1.58 ! [A: $tType,B4: set @ A,A3: set @ A,Q: A > $o,P3: A > $o] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 2.76/1.58 => ( ! [X2: A] :
% 2.76/1.58 ( ( member @ A @ X2 @ B4 )
% 2.76/1.58 => ( ( Q @ X2 )
% 2.76/1.58 => ( P3 @ X2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A )
% 2.76/1.58 @ ( collect @ A
% 2.76/1.58 @ ^ [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ B4 )
% 2.76/1.58 & ( Q @ X4 ) ) )
% 2.76/1.58 @ ( collect @ A
% 2.76/1.58 @ ^ [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ A3 )
% 2.76/1.58 & ( P3 @ X4 ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_153_Collect__restrict,axiom,
% 2.76/1.58 ! [A: $tType,X5: set @ A,P3: A > $o] :
% 2.76/1.58 ( ord_less_eq @ ( set @ A )
% 2.76/1.58 @ ( collect @ A
% 2.76/1.58 @ ^ [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ X5 )
% 2.76/1.58 & ( P3 @ X4 ) ) )
% 2.76/1.58 @ X5 ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_154_predicate1I,axiom,
% 2.76/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ( P3 @ X2 )
% 2.76/1.58 => ( Q @ X2 ) )
% 2.76/1.58 => ( ord_less_eq @ ( A > $o ) @ P3 @ Q ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_155_predicate1D,axiom,
% 2.76/1.58 ! [A: $tType,P3: A > $o,Q: A > $o,X: A] :
% 2.76/1.58 ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 2.76/1.58 => ( ( P3 @ X )
% 2.76/1.58 => ( Q @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_156_rev__predicate1D,axiom,
% 2.76/1.58 ! [A: $tType,P3: A > $o,X: A,Q: A > $o] :
% 2.76/1.58 ( ( P3 @ X )
% 2.76/1.58 => ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 2.76/1.58 => ( Q @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_157_prop__restrict,axiom,
% 2.76/1.58 ! [A: $tType,X: A,Z3: set @ A,X5: set @ A,P3: A > $o] :
% 2.76/1.58 ( ( member @ A @ X @ Z3 )
% 2.76/1.58 => ( ( ord_less_eq @ ( set @ A ) @ Z3
% 2.76/1.58 @ ( collect @ A
% 2.76/1.58 @ ^ [X4: A] :
% 2.76/1.58 ( ( member @ A @ X4 @ X5 )
% 2.76/1.58 & ( P3 @ X4 ) ) ) )
% 2.76/1.58 => ( P3 @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_158_pred__subset__eq,axiom,
% 2.76/1.58 ! [A: $tType,R2: set @ A,S: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( A > $o )
% 2.76/1.58 @ ^ [X4: A] : ( member @ A @ X4 @ R2 )
% 2.76/1.58 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 2.76/1.58 = ( ord_less_eq @ ( set @ A ) @ R2 @ S ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_159_dbl__inc__simps_I2_J,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( neg_numeral @ A )
% 2.76/1.58 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 2.76/1.58 = ( one_one @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_160_conj__subset__def,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,P3: A > $o,Q: A > $o] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A3
% 2.76/1.58 @ ( collect @ A
% 2.76/1.58 @ ^ [X4: A] :
% 2.76/1.58 ( ( P3 @ X4 )
% 2.76/1.58 & ( Q @ X4 ) ) ) )
% 2.76/1.58 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ P3 ) )
% 2.76/1.58 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ Q ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_161_fun__cong__unused__0,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType,C2: $tType] :
% 2.76/1.58 ( ( zero @ B )
% 2.76/1.58 => ! [F: ( A > B ) > C2,G: C2] :
% 2.76/1.58 ( ( F
% 2.76/1.58 = ( ^ [X4: A > B] : G ) )
% 2.76/1.58 => ( ( F
% 2.76/1.58 @ ^ [X4: A] : ( zero_zero @ B ) )
% 2.76/1.58 = G ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_162_mult__le__cancel__left1,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linordered_idom @ A )
% 2.76/1.58 => ! [C: A,B2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ C @ ( times_times @ A @ C @ B2 ) )
% 2.76/1.58 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ ( one_one @ A ) @ B2 ) )
% 2.76/1.58 & ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ B2 @ ( one_one @ A ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_163_mult__le__cancel__left2,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linordered_idom @ A )
% 2.76/1.58 => ! [C: A,A2: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ C )
% 2.76/1.58 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.76/1.58 => ( ord_less_eq @ A @ A2 @ ( one_one @ A ) ) )
% 2.76/1.58 & ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less_eq @ A @ ( one_one @ A ) @ A2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_164_neq0__conv,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( N
% 2.76/1.58 != ( zero_zero @ nat ) )
% 2.76/1.58 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_165_less__nat__zero__code,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_166_bot__nat__0_Onot__eq__extremum,axiom,
% 2.76/1.58 ! [A2: nat] :
% 2.76/1.58 ( ( A2
% 2.76/1.58 != ( zero_zero @ nat ) )
% 2.76/1.58 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_167_psubsetI,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ( A3 != B4 )
% 2.76/1.58 => ( ord_less @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_168_not__gr__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( canoni770627133id_add @ A )
% 2.76/1.58 => ! [N: A] :
% 2.76/1.58 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.76/1.58 = ( N
% 2.76/1.58 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_169_nat__0__less__mult__iff,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ M @ N ) )
% 2.76/1.58 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.76/1.58 & ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_170_mult__less__cancel2,axiom,
% 2.76/1.58 ! [M: nat,K: nat,N: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 2.76/1.58 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.76/1.58 & ( ord_less @ nat @ M @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_171_nat__mult__less__cancel__disj,axiom,
% 2.76/1.58 ! [K: nat,M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.76/1.58 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.76/1.58 & ( ord_less @ nat @ M @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_172_less__one,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 2.76/1.58 = ( N
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_173_mult__le__cancel2,axiom,
% 2.76/1.58 ! [M: nat,K: nat,N: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 2.76/1.58 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.76/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_174_nat__mult__le__cancel__disj,axiom,
% 2.76/1.58 ! [K: nat,M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.76/1.58 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.76/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_175_dual__order_Ostrict__implies__not__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A] :
% 2.76/1.58 ( ( ord_less @ A @ B2 @ A2 )
% 2.76/1.58 => ( A2 != B2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_176_order_Ostrict__implies__not__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ( A2 != B2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_177_not__less__iff__gr__or__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.76/1.58 = ( ( ord_less @ A @ Y @ X )
% 2.76/1.58 | ( X = Y ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_178_dual__order_Ostrict__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A,C: A] :
% 2.76/1.58 ( ( ord_less @ A @ B2 @ A2 )
% 2.76/1.58 => ( ( ord_less @ A @ C @ B2 )
% 2.76/1.58 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_179_linorder__less__wlog,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [P3: A > A > $o,A2: A,B2: A] :
% 2.76/1.58 ( ! [A4: A,B3: A] :
% 2.76/1.58 ( ( ord_less @ A @ A4 @ B3 )
% 2.76/1.58 => ( P3 @ A4 @ B3 ) )
% 2.76/1.58 => ( ! [A4: A] : ( P3 @ A4 @ A4 )
% 2.76/1.58 => ( ! [A4: A,B3: A] :
% 2.76/1.58 ( ( P3 @ B3 @ A4 )
% 2.76/1.58 => ( P3 @ A4 @ B3 ) )
% 2.76/1.58 => ( P3 @ A2 @ B2 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_180_exists__least__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( wellorder @ A )
% 2.76/1.58 => ( ( ^ [P4: A > $o] :
% 2.76/1.58 ? [X6: A] : ( P4 @ X6 ) )
% 2.76/1.58 = ( ^ [P5: A > $o] :
% 2.76/1.58 ? [N2: A] :
% 2.76/1.58 ( ( P5 @ N2 )
% 2.76/1.58 & ! [M4: A] :
% 2.76/1.58 ( ( ord_less @ A @ M4 @ N2 )
% 2.76/1.58 => ~ ( P5 @ M4 ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_181_less__imp__not__less,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_182_order_Ostrict__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less @ A @ B2 @ C )
% 2.76/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_183_dual__order_Oirrefl,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A] :
% 2.76/1.58 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_184_linorder__cases,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ~ ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( ( X != Y )
% 2.76/1.58 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_185_less__imp__triv,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A,P3: $o] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( ( ord_less @ A @ Y @ X )
% 2.76/1.58 => P3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_186_less__imp__not__eq2,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( Y != X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_187_antisym__conv3,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [Y: A,X: A] :
% 2.76/1.58 ( ~ ( ord_less @ A @ Y @ X )
% 2.76/1.58 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.76/1.58 = ( X = Y ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_188_less__induct,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( wellorder @ A )
% 2.76/1.58 => ! [P3: A > $o,A2: A] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ! [Y3: A] :
% 2.76/1.58 ( ( ord_less @ A @ Y3 @ X2 )
% 2.76/1.58 => ( P3 @ Y3 ) )
% 2.76/1.58 => ( P3 @ X2 ) )
% 2.76/1.58 => ( P3 @ A2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_189_less__not__sym,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_190_less__imp__not__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( X != Y ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_191_dual__order_Oasym,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A] :
% 2.76/1.58 ( ( ord_less @ A @ B2 @ A2 )
% 2.76/1.58 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_192_ord__less__eq__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( B2 = C )
% 2.76/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_193_ord__eq__less__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( A2 = B2 )
% 2.76/1.58 => ( ( ord_less @ A @ B2 @ C )
% 2.76/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_194_less__irrefl,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A] :
% 2.76/1.58 ~ ( ord_less @ A @ X @ X ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_195_less__linear,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 | ( X = Y )
% 2.76/1.58 | ( ord_less @ A @ Y @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_196_less__trans,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A,Z2: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( ( ord_less @ A @ Y @ Z2 )
% 2.76/1.58 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_197_less__asym_H,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_198_less__asym,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( preorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_199_less__imp__neq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( X != Y ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_200_dense,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( dense_order @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ? [Z4: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Z4 )
% 2.76/1.58 & ( ord_less @ A @ Z4 @ Y ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_201_order_Oasym,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_202_neq__iff,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( X != Y )
% 2.76/1.58 = ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_203_neqE,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( X != Y )
% 2.76/1.58 => ( ~ ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_204_gt__ex,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( no_top @ A )
% 2.76/1.58 => ! [X: A] :
% 2.76/1.58 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_205_lt__ex,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( no_bot @ A )
% 2.76/1.58 => ! [X: A] :
% 2.76/1.58 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_206_order__less__subst2,axiom,
% 2.76/1.58 ! [A: $tType,C2: $tType] :
% 2.76/1.58 ( ( ( order @ C2 )
% 2.76/1.58 & ( order @ A ) )
% 2.76/1.58 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C )
% 2.76/1.58 => ( ! [X2: A,Y2: A] :
% 2.76/1.58 ( ( ord_less @ A @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less @ C2 @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_207_order__less__subst1,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ( order @ B )
% 2.76/1.58 & ( order @ A ) )
% 2.76/1.58 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 2.76/1.58 => ( ( ord_less @ B @ B2 @ C )
% 2.76/1.58 => ( ! [X2: B,Y2: B] :
% 2.76/1.58 ( ( ord_less @ B @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_208_ord__less__eq__subst,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ( ord @ B )
% 2.76/1.58 & ( ord @ A ) )
% 2.76/1.58 => ! [A2: A,B2: A,F: A > B,C: B] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ( F @ B2 )
% 2.76/1.58 = C )
% 2.76/1.58 => ( ! [X2: A,Y2: A] :
% 2.76/1.58 ( ( ord_less @ A @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_209_ord__eq__less__subst,axiom,
% 2.76/1.58 ! [A: $tType,B: $tType] :
% 2.76/1.58 ( ( ( ord @ B )
% 2.76/1.58 & ( ord @ A ) )
% 2.76/1.58 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.76/1.58 ( ( A2
% 2.76/1.58 = ( F @ B2 ) )
% 2.76/1.58 => ( ( ord_less @ B @ B2 @ C )
% 2.76/1.58 => ( ! [X2: B,Y2: B] :
% 2.76/1.58 ( ( ord_less @ B @ X2 @ Y2 )
% 2.76/1.58 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.76/1.58 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_210_gr__zeroI,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( canoni770627133id_add @ A )
% 2.76/1.58 => ! [N: A] :
% 2.76/1.58 ( ( N
% 2.76/1.58 != ( zero_zero @ A ) )
% 2.76/1.58 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_211_not__less__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( canoni770627133id_add @ A )
% 2.76/1.58 => ! [N: A] :
% 2.76/1.58 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_212_gr__implies__not__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( canoni770627133id_add @ A )
% 2.76/1.58 => ! [M: A,N: A] :
% 2.76/1.58 ( ( ord_less @ A @ M @ N )
% 2.76/1.58 => ( N
% 2.76/1.58 != ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_213_zero__less__iff__neq__zero,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( canoni770627133id_add @ A )
% 2.76/1.58 => ! [N: A] :
% 2.76/1.58 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.76/1.58 = ( N
% 2.76/1.58 != ( zero_zero @ A ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_214_linorder__neqE__linordered__idom,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linordered_idom @ A )
% 2.76/1.58 => ! [X: A,Y: A] :
% 2.76/1.58 ( ( X != Y )
% 2.76/1.58 => ( ~ ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_215_measure__induct__rule,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( wellorder @ B )
% 2.76/1.58 => ! [F: A > B,P3: A > $o,A2: A] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ! [Y3: A] :
% 2.76/1.58 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X2 ) )
% 2.76/1.58 => ( P3 @ Y3 ) )
% 2.76/1.58 => ( P3 @ X2 ) )
% 2.76/1.58 => ( P3 @ A2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_216_measure__induct,axiom,
% 2.76/1.58 ! [B: $tType,A: $tType] :
% 2.76/1.58 ( ( wellorder @ B )
% 2.76/1.58 => ! [F: A > B,P3: A > $o,A2: A] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ! [Y3: A] :
% 2.76/1.58 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X2 ) )
% 2.76/1.58 => ( P3 @ Y3 ) )
% 2.76/1.58 => ( P3 @ X2 ) )
% 2.76/1.58 => ( P3 @ A2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_217_nat__less__le,axiom,
% 2.76/1.58 ( ( ord_less @ nat )
% 2.76/1.58 = ( ^ [M4: nat,N2: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ M4 @ N2 )
% 2.76/1.58 & ( M4 != N2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_218_less__imp__le__nat,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ M @ N )
% 2.76/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_219_le__eq__less__or__eq,axiom,
% 2.76/1.58 ( ( ord_less_eq @ nat )
% 2.76/1.58 = ( ^ [M4: nat,N2: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ M4 @ N2 )
% 2.76/1.58 | ( M4 = N2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_220_less__or__eq__imp__le,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ( ord_less @ nat @ M @ N )
% 2.76/1.58 | ( M = N ) )
% 2.76/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_221_le__neq__implies__less,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less_eq @ nat @ M @ N )
% 2.76/1.58 => ( ( M != N )
% 2.76/1.58 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_222_less__mono__imp__le__mono,axiom,
% 2.76/1.58 ! [F: nat > nat,I4: nat,J: nat] :
% 2.76/1.58 ( ! [I3: nat,J3: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ I3 @ J3 )
% 2.76/1.58 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ I4 @ J )
% 2.76/1.58 => ( ord_less_eq @ nat @ ( F @ I4 ) @ ( F @ J ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_223_gr0I,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( N
% 2.76/1.58 != ( zero_zero @ nat ) )
% 2.76/1.58 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_224_not__gr0,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.76/1.58 = ( N
% 2.76/1.58 = ( zero_zero @ nat ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_225_not__less0,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_226_less__zeroE,axiom,
% 2.76/1.58 ! [N: nat] :
% 2.76/1.58 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_227_gr__implies__not0,axiom,
% 2.76/1.58 ! [M: nat,N: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ M @ N )
% 2.76/1.58 => ( N
% 2.76/1.58 != ( zero_zero @ nat ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_228_infinite__descent0,axiom,
% 2.76/1.58 ! [P3: nat > $o,N: nat] :
% 2.76/1.58 ( ( P3 @ ( zero_zero @ nat ) )
% 2.76/1.58 => ( ! [N3: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 )
% 2.76/1.58 => ( ~ ( P3 @ N3 )
% 2.76/1.58 => ? [M5: nat] :
% 2.76/1.58 ( ( ord_less @ nat @ M5 @ N3 )
% 2.76/1.58 & ~ ( P3 @ M5 ) ) ) )
% 2.76/1.58 => ( P3 @ N ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_229_bot__nat__0_Oextremum__strict,axiom,
% 2.76/1.58 ! [A2: nat] :
% 2.76/1.58 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_230_infinite__descent0__measure,axiom,
% 2.76/1.58 ! [A: $tType,V: A > nat,P3: A > $o,X: A] :
% 2.76/1.58 ( ! [X2: A] :
% 2.76/1.58 ( ( ( V @ X2 )
% 2.76/1.58 = ( zero_zero @ nat ) )
% 2.76/1.58 => ( P3 @ X2 ) )
% 2.76/1.58 => ( ! [X2: A] :
% 2.76/1.58 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V @ X2 ) )
% 2.76/1.58 => ( ~ ( P3 @ X2 )
% 2.76/1.58 => ? [Y3: A] :
% 2.76/1.58 ( ( ord_less @ nat @ ( V @ Y3 ) @ ( V @ X2 ) )
% 2.76/1.58 & ~ ( P3 @ Y3 ) ) ) )
% 2.76/1.58 => ( P3 @ X ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_231_psubsetE,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ( ord_less @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_232_psubset__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord_less @ ( set @ A ) )
% 2.76/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.76/1.58 & ( A6 != B6 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_233_psubset__imp__subset,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.76/1.58 ( ( ord_less @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_234_psubset__subset__trans,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 2.76/1.58 ( ( ord_less @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 2.76/1.58 => ( ord_less @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_235_subset__not__subset__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord_less @ ( set @ A ) )
% 2.76/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.76/1.58 & ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_236_subset__psubset__trans,axiom,
% 2.76/1.58 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.76/1.58 => ( ( ord_less @ ( set @ A ) @ B4 @ C3 )
% 2.76/1.58 => ( ord_less @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_237_subset__iff__psubset__eq,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.76/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.76/1.58 ( ( ord_less @ ( set @ A ) @ A6 @ B6 )
% 2.76/1.58 | ( A6 = B6 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_238_less__numeral__extra_I4_J,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_239_less__numeral__extra_I3_J,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( linord1659791738miring @ A )
% 2.76/1.58 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_240_order_Onot__eq__order__implies__strict,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( A2 != B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_241_dual__order_Ostrict__implies__order,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A] :
% 2.76/1.58 ( ( ord_less @ A @ B2 @ A2 )
% 2.76/1.58 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_242_dual__order_Ostrict__iff__order,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ( ( ord_less @ A )
% 2.76/1.58 = ( ^ [B5: A,A5: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ B5 @ A5 )
% 2.76/1.58 & ( A5 != B5 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_243_dual__order_Oorder__iff__strict,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ( ( ord_less_eq @ A )
% 2.76/1.58 = ( ^ [B5: A,A5: A] :
% 2.76/1.58 ( ( ord_less @ A @ B5 @ A5 )
% 2.76/1.58 | ( A5 = B5 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_244_order_Ostrict__implies__order,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_245_dense__le__bounded,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( dense_linorder @ A )
% 2.76/1.58 => ! [X: A,Y: A,Z2: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ Y )
% 2.76/1.58 => ( ! [W: A] :
% 2.76/1.58 ( ( ord_less @ A @ X @ W )
% 2.76/1.58 => ( ( ord_less @ A @ W @ Y )
% 2.76/1.58 => ( ord_less_eq @ A @ W @ Z2 ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_246_dense__ge__bounded,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( dense_linorder @ A )
% 2.76/1.58 => ! [Z2: A,X: A,Y: A] :
% 2.76/1.58 ( ( ord_less @ A @ Z2 @ X )
% 2.76/1.58 => ( ! [W: A] :
% 2.76/1.58 ( ( ord_less @ A @ Z2 @ W )
% 2.76/1.58 => ( ( ord_less @ A @ W @ X )
% 2.76/1.58 => ( ord_less_eq @ A @ Y @ W ) ) )
% 2.76/1.58 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_247_dual__order_Ostrict__trans2,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A,C: A] :
% 2.76/1.58 ( ( ord_less @ A @ B2 @ A2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ C @ B2 )
% 2.76/1.58 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_248_dual__order_Ostrict__trans1,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [B2: A,A2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.76/1.58 => ( ( ord_less @ A @ C @ B2 )
% 2.76/1.58 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_249_order_Ostrict__iff__order,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ( ( ord_less @ A )
% 2.76/1.58 = ( ^ [A5: A,B5: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A5 @ B5 )
% 2.76/1.58 & ( A5 != B5 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_250_order_Oorder__iff__strict,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ( ( ord_less_eq @ A )
% 2.76/1.58 = ( ^ [A5: A,B5: A] :
% 2.76/1.58 ( ( ord_less @ A @ A5 @ B5 )
% 2.76/1.58 | ( A5 = B5 ) ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_251_order_Ostrict__trans2,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.76/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(fact_252_order_Ostrict__trans1,axiom,
% 2.76/1.58 ! [A: $tType] :
% 2.76/1.58 ( ( order @ A )
% 2.76/1.58 => ! [A2: A,B2: A,C: A] :
% 2.76/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.58 => ( ( ord_less @ A @ B2 @ C )
% 2.76/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.76/1.58 ! [A7: $tType,A8: $tType] :
% 2.76/1.58 ( ( preorder @ A8 )
% 2.76/1.58 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.76/1.58 ! [A7: $tType,A8: $tType] :
% 2.76/1.58 ( ( order @ A8 )
% 2.76/1.58 => ( order @ ( A7 > A8 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_fun___Orderings_Oord,axiom,
% 2.76/1.58 ! [A7: $tType,A8: $tType] :
% 2.76/1.58 ( ( ord @ A8 )
% 2.76/1.58 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 2.76/1.58 semiri1923998003cancel @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.76/1.58 canoni770627133id_add @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.76/1.58 linord1659791738miring @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 2.76/1.58 semiri1193490041visors @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 2.76/1.58 ordere216010020id_add @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
% 2.76/1.58 ordere1490568538miring @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0,axiom,
% 2.76/1.58 ordered_semiring_0 @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 2.76/1.58 ab_semigroup_mult @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 2.76/1.58 comm_monoid_mult @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Oordered__semiring,axiom,
% 2.76/1.58 ordered_semiring @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 2.76/1.58 comm_monoid_add @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 2.76/1.58 semigroup_mult @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.76/1.58 wellorder @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 2.76/1.58 zero_neq_one @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.76/1.58 preorder @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.76/1.58 linorder @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 2.76/1.58 monoid_mult @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Osemiring__0,axiom,
% 2.76/1.58 semiring_0 @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.76/1.58 no_top @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 2.76/1.58 mult_zero @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 2.76/1.58 order @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 2.76/1.58 ord @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.76/1.58 zero @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.76/1.58 one @ nat ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 2.76/1.58 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.76/1.58 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 2.76/1.58 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 2.76/1.58 preorder @ $o ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 2.76/1.58 linorder @ $o ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 2.76/1.58 order @ $o ).
% 2.76/1.58
% 2.76/1.58 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 2.76/1.58 ord @ $o ).
% 2.76/1.58
% 2.76/1.58 thf(conj_0,conjecture,
% 2.76/1.58 ( ( ! [I2: nat] :
% 2.76/1.58 ( ( ( p @ I2 )
% 2.76/1.58 != ( zero_zero @ nat ) )
% 2.76/1.58 => ( ( ord_less_eq @ nat @ ( one_one @ nat ) @ I2 )
% 2.76/1.58 & ( ord_less_eq @ nat @ I2 @ ( zero_zero @ nat ) ) ) )
% 2.76/1.58 & ( ( groups1340683514dd_sum @ nat @ nat
% 2.76/1.58 @ ^ [I2: nat] : ( times_times @ nat @ ( p @ I2 ) @ I2 )
% 2.76/1.58 @ ( set_ord_atMost @ nat @ ( zero_zero @ nat ) ) )
% 2.76/1.58 = ( zero_zero @ nat ) ) )
% 2.76/1.58 = ( p
% 2.76/1.58 = ( ^ [I2: nat] : ( zero_zero @ nat ) ) ) ) ).
% 2.76/1.58 ------------------------
% 2.88/1.60 % (11269)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_11076 for (2999ds/4Mi)
% 2.88/1.60 % (11271)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/2Mi)
% 2.88/1.60 % (11270)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_11076 for (2999ds/27Mi)
% 2.88/1.60 % (11272)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_11076 for (2999ds/2Mi)
% 2.88/1.60 % (11274)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/18Mi)
% 2.88/1.60 % (11269)Instruction limit reached!
% 2.88/1.60 % (11269)------------------------------
% 2.88/1.60 % (11269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.60 % (11269)Termination reason: Unknown
% 2.88/1.60 % (11269)Termination phase: shuffling
% 2.88/1.60
% 2.88/1.60 % (11269)Memory used [KB]: 1407
% 2.88/1.60 % (11269)Time elapsed: 0.003 s
% 2.88/1.60 % (11269)Instructions burned: 5 (million)
% 2.88/1.60 % (11269)------------------------------
% 2.88/1.60 % (11269)------------------------------
% 2.88/1.60 % (11268)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/183Mi)
% 2.88/1.60 % (11271)Instruction limit reached!
% 2.88/1.60 % (11271)------------------------------
% 2.88/1.60 % (11271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.60 % (11271)Termination reason: Unknown
% 2.88/1.60 % (11271)Termination phase: shuffling
% 2.88/1.60
% 2.88/1.60 % (11271)Memory used [KB]: 1407
% 2.88/1.60 % (11271)Time elapsed: 0.003 s
% 2.88/1.60 % (11271)Instructions burned: 4 (million)
% 2.88/1.60 % (11271)------------------------------
% 2.88/1.60 % (11271)------------------------------
% 2.88/1.60 % (11272)Instruction limit reached!
% 2.88/1.60 % (11272)------------------------------
% 2.88/1.60 % (11272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.60 % (11272)Termination reason: Unknown
% 2.88/1.60 % (11272)Termination phase: shuffling
% 2.88/1.60
% 2.88/1.60 % (11272)Memory used [KB]: 1407
% 2.88/1.60 % (11272)Time elapsed: 0.002 s
% 2.88/1.60 % (11272)Instructions burned: 3 (million)
% 2.88/1.60 % (11272)------------------------------
% 2.88/1.60 % (11272)------------------------------
% 2.88/1.61 % (11273)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_11076 for (2999ds/275Mi)
% 2.88/1.61 % (11274)Instruction limit reached!
% 2.88/1.61 % (11274)------------------------------
% 2.88/1.61 % (11274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.61 % (11274)Termination reason: Unknown
% 2.88/1.61 % (11274)Termination phase: shuffling
% 2.88/1.61
% 2.88/1.61 % (11274)Memory used [KB]: 1791
% 2.88/1.61 % (11274)Time elapsed: 0.008 s
% 2.88/1.61 % (11274)Instructions burned: 19 (million)
% 2.88/1.61 % (11274)------------------------------
% 2.88/1.61 % (11274)------------------------------
% 2.88/1.61 % (11270)Instruction limit reached!
% 2.88/1.61 % (11270)------------------------------
% 2.88/1.61 % (11270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.61 % (11270)Termination reason: Unknown
% 2.88/1.61 % (11270)Termination phase: Property scanning
% 2.88/1.61
% 2.88/1.61 % (11270)Memory used [KB]: 1791
% 2.88/1.61 % (11270)Time elapsed: 0.011 s
% 2.88/1.61 % (11270)Instructions burned: 30 (million)
% 2.88/1.61 % (11270)------------------------------
% 2.88/1.61 % (11270)------------------------------
% 2.88/1.61 % (11280)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/3Mi)
% 2.88/1.61 % (11281)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_11076 for (2999ds/37Mi)
% 2.88/1.61 % (11282)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_11076 for (2999ds/15Mi)
% 2.88/1.61 % (11280)Instruction limit reached!
% 2.88/1.61 % (11280)------------------------------
% 2.88/1.61 % (11280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.61 % (11280)Termination reason: Unknown
% 2.88/1.61 % (11280)Termination phase: shuffling
% 2.88/1.61
% 2.88/1.61 % (11280)Memory used [KB]: 1279
% 2.88/1.61 % (11280)Time elapsed: 0.002 s
% 2.88/1.61 % (11280)Instructions burned: 3 (million)
% 2.88/1.61 % (11280)------------------------------
% 2.88/1.61 % (11280)------------------------------
% 2.88/1.62 % (11282)Instruction limit reached!
% 2.88/1.62 % (11282)------------------------------
% 2.88/1.62 % (11282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.62 % (11282)Termination reason: Unknown
% 2.88/1.62 % (11282)Termination phase: shuffling
% 2.88/1.62
% 2.88/1.62 % (11282)Memory used [KB]: 1663
% 2.88/1.62 % (11282)Time elapsed: 0.007 s
% 2.88/1.62 % (11282)Instructions burned: 16 (million)
% 2.88/1.62 % (11282)------------------------------
% 2.88/1.62 % (11282)------------------------------
% 2.88/1.62 % (11283)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_11076 for (2999ds/3Mi)
% 2.88/1.62 % (11283)Instruction limit reached!
% 2.88/1.62 % (11283)------------------------------
% 2.88/1.62 % (11283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.62 % (11283)Termination reason: Unknown
% 2.88/1.62 % (11283)Termination phase: shuffling
% 2.88/1.62
% 2.88/1.62 % (11283)Memory used [KB]: 1407
% 2.88/1.62 % (11283)Time elapsed: 0.003 s
% 2.88/1.62 % (11283)Instructions burned: 4 (million)
% 2.88/1.62 % (11283)------------------------------
% 2.88/1.62 % (11283)------------------------------
% 2.88/1.62 % (11284)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_11076 for (2999ds/1041Mi)
% 2.88/1.62 % (11285)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/7Mi)
% 2.88/1.62 % (11281)Instruction limit reached!
% 2.88/1.62 % (11281)------------------------------
% 2.88/1.62 % (11281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.62 % (11281)Termination reason: Unknown
% 2.88/1.62 % (11281)Termination phase: Property scanning
% 2.88/1.62
% 2.88/1.62 % (11281)Memory used [KB]: 2046
% 2.88/1.62 % (11281)Time elapsed: 0.012 s
% 2.88/1.62 % (11281)Instructions burned: 40 (million)
% 2.88/1.62 % (11281)------------------------------
% 2.88/1.62 % (11281)------------------------------
% 2.88/1.63 % (11285)Instruction limit reached!
% 2.88/1.63 % (11285)------------------------------
% 2.88/1.63 % (11285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.63 % (11285)Termination reason: Unknown
% 2.88/1.63 % (11285)Termination phase: shuffling
% 2.88/1.63
% 2.88/1.63 % (11285)Memory used [KB]: 1535
% 2.88/1.63 % (11285)Time elapsed: 0.004 s
% 2.88/1.63 % (11285)Instructions burned: 9 (million)
% 2.88/1.63 % (11285)------------------------------
% 2.88/1.63 % (11285)------------------------------
% 2.88/1.63 % (11286)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/16Mi)
% 2.88/1.63 % (11287)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_11076 for (2999ds/3Mi)
% 2.88/1.63 % (11287)Instruction limit reached!
% 2.88/1.63 % (11287)------------------------------
% 2.88/1.63 % (11287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.63 % (11287)Termination reason: Unknown
% 2.88/1.63 % (11287)Termination phase: shuffling
% 2.88/1.63
% 2.88/1.63 % (11287)Memory used [KB]: 1407
% 2.88/1.63 % (11287)Time elapsed: 0.003 s
% 2.88/1.63 % (11287)Instructions burned: 4 (million)
% 2.88/1.63 % (11287)------------------------------
% 2.88/1.63 % (11287)------------------------------
% 2.88/1.63 % (11288)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_11076 for (2999ds/3Mi)
% 2.88/1.63 % (11286)Instruction limit reached!
% 2.88/1.63 % (11286)------------------------------
% 2.88/1.63 % (11286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.63 % (11286)Termination reason: Unknown
% 2.88/1.63 % (11286)Termination phase: shuffling
% 2.88/1.63
% 2.88/1.63 % (11286)Memory used [KB]: 1663
% 2.88/1.63 % (11286)Time elapsed: 0.006 s
% 2.88/1.63 % (11286)Instructions burned: 16 (million)
% 2.88/1.63 % (11286)------------------------------
% 2.88/1.63 % (11286)------------------------------
% 2.88/1.63 % (11288)Instruction limit reached!
% 2.88/1.63 % (11288)------------------------------
% 2.88/1.63 % (11288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.63 % (11288)Termination reason: Unknown
% 2.88/1.63 % (11288)Termination phase: shuffling
% 2.88/1.63
% 2.88/1.63 % (11288)Memory used [KB]: 1407
% 2.88/1.63 % (11288)Time elapsed: 0.002 s
% 2.88/1.63 % (11288)Instructions burned: 3 (million)
% 2.88/1.63 % (11288)------------------------------
% 2.88/1.63 % (11288)------------------------------
% 2.88/1.63 % (11289)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/7Mi)
% 2.88/1.64 % (11289)Instruction limit reached!
% 2.88/1.64 % (11289)------------------------------
% 2.88/1.64 % (11289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.64 % (11289)Termination reason: Unknown
% 2.88/1.64 % (11289)Termination phase: shuffling
% 2.88/1.64
% 2.88/1.64 % (11289)Memory used [KB]: 1535
% 2.88/1.64 % (11289)Time elapsed: 0.004 s
% 2.88/1.64 % (11289)Instructions burned: 10 (million)
% 2.88/1.64 % (11289)------------------------------
% 2.88/1.64 % (11289)------------------------------
% 2.88/1.64 % (11290)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/3Mi)
% 2.88/1.64 % (11291)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/4Mi)
% 2.88/1.64 % (11292)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/18Mi)
% 2.88/1.64 % (11290)Instruction limit reached!
% 2.88/1.64 % (11290)------------------------------
% 2.88/1.64 % (11290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.64 % (11290)Termination reason: Unknown
% 2.88/1.64 % (11290)Termination phase: shuffling
% 2.88/1.64
% 2.88/1.64 % (11290)Memory used [KB]: 1407
% 2.88/1.64 % (11290)Time elapsed: 0.003 s
% 2.88/1.64 % (11290)Instructions burned: 4 (million)
% 2.88/1.64 % (11290)------------------------------
% 2.88/1.64 % (11290)------------------------------
% 2.88/1.64 % (11291)Instruction limit reached!
% 2.88/1.64 % (11291)------------------------------
% 2.88/1.64 % (11291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.64 % (11291)Termination reason: Unknown
% 2.88/1.64 % (11291)Termination phase: shuffling
% 2.88/1.64
% 2.88/1.64 % (11291)Memory used [KB]: 1407
% 2.88/1.64 % (11291)Time elapsed: 0.003 s
% 2.88/1.64 % (11291)Instructions burned: 6 (million)
% 2.88/1.64 % (11291)------------------------------
% 2.88/1.64 % (11291)------------------------------
% 2.88/1.65 % (11293)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/710Mi)
% 2.88/1.65 % (11292)Instruction limit reached!
% 2.88/1.65 % (11292)------------------------------
% 2.88/1.65 % (11292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.65 % (11292)Termination reason: Unknown
% 2.88/1.65 % (11292)Termination phase: shuffling
% 2.88/1.65
% 2.88/1.65 % (11292)Memory used [KB]: 1663
% 2.88/1.65 % (11292)Time elapsed: 0.007 s
% 2.88/1.65 % (11292)Instructions burned: 18 (million)
% 2.88/1.65 % (11292)------------------------------
% 2.88/1.65 % (11292)------------------------------
% 2.88/1.65 % (11294)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/6Mi)
% 2.88/1.65 % (11295)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_11076 for (2999ds/902Mi)
% 2.88/1.66 % (11294)Instruction limit reached!
% 2.88/1.66 % (11294)------------------------------
% 2.88/1.66 % (11294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.66 % (11294)Termination reason: Unknown
% 2.88/1.66 % (11294)Termination phase: shuffling
% 2.88/1.66
% 2.88/1.66 % (11294)Memory used [KB]: 1407
% 2.88/1.66 % (11294)Time elapsed: 0.004 s
% 2.88/1.66 % (11294)Instructions burned: 6 (million)
% 2.88/1.66 % (11294)------------------------------
% 2.88/1.66 % (11294)------------------------------
% 2.88/1.66 % (11296)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_11076 for (2999ds/21Mi)
% 2.88/1.67 % (11297)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/5Mi)
% 2.88/1.67 % (11268)Instruction limit reached!
% 2.88/1.67 % (11268)------------------------------
% 2.88/1.67 % (11268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.67 % (11268)Termination reason: Unknown
% 2.88/1.67 % (11268)Termination phase: Saturation
% 2.88/1.67
% 2.88/1.67 % (11268)Memory used [KB]: 7036
% 2.88/1.67 % (11268)Time elapsed: 0.064 s
% 2.88/1.67 % (11268)Instructions burned: 184 (million)
% 2.88/1.67 % (11268)------------------------------
% 2.88/1.67 % (11268)------------------------------
% 2.88/1.67 % (11296)Instruction limit reached!
% 2.88/1.67 % (11296)------------------------------
% 2.88/1.67 % (11296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.67 % (11296)Termination reason: Unknown
% 2.88/1.67 % (11296)Termination phase: Property scanning
% 2.88/1.67
% 2.88/1.67 % (11296)Memory used [KB]: 1791
% 2.88/1.67 % (11296)Time elapsed: 0.009 s
% 2.88/1.67 % (11296)Instructions burned: 24 (million)
% 2.88/1.67 % (11296)------------------------------
% 2.88/1.67 % (11296)------------------------------
% 2.88/1.67 % (11297)Instruction limit reached!
% 2.88/1.67 % (11297)------------------------------
% 2.88/1.67 % (11297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.67 % (11297)Termination reason: Unknown
% 2.88/1.67 % (11297)Termination phase: shuffling
% 2.88/1.67
% 2.88/1.67 % (11297)Memory used [KB]: 1407
% 2.88/1.67 % (11297)Time elapsed: 0.004 s
% 2.88/1.67 % (11297)Instructions burned: 7 (million)
% 2.88/1.67 % (11297)------------------------------
% 2.88/1.67 % (11297)------------------------------
% 2.88/1.68 % (11301)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11076 for (2999ds/377Mi)
% 2.88/1.68 % (11300)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_11076 for (2999ds/6Mi)
% 2.88/1.68 % (11302)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_11076 for (2999ds/779Mi)
% 2.88/1.68 % (11300)Instruction limit reached!
% 2.88/1.68 % (11300)------------------------------
% 2.88/1.68 % (11300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.68 % (11300)Termination reason: Unknown
% 2.88/1.68 % (11300)Termination phase: shuffling
% 2.88/1.68
% 2.88/1.68 % (11300)Memory used [KB]: 1407
% 2.88/1.68 % (11300)Time elapsed: 0.004 s
% 2.88/1.68 % (11300)Instructions burned: 7 (million)
% 2.88/1.68 % (11300)------------------------------
% 2.88/1.68 % (11300)------------------------------
% 2.88/1.70 % (11309)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_11076 for (2999ds/19Mi)
% 2.88/1.71 % (11309)Instruction limit reached!
% 2.88/1.71 % (11309)------------------------------
% 2.88/1.71 % (11309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (11309)Termination reason: Unknown
% 2.88/1.71 % (11309)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (11309)Memory used [KB]: 1663
% 2.88/1.71 % (11309)Time elapsed: 0.011 s
% 2.88/1.71 % (11309)Instructions burned: 19 (million)
% 2.88/1.71 % (11309)------------------------------
% 2.88/1.71 % (11309)------------------------------
% 2.88/1.72 % (11315)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11076 for (2998ds/879Mi)
% 2.88/1.74 % (11273)Instruction limit reached!
% 2.88/1.74 % (11273)------------------------------
% 2.88/1.74 % (11273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.74 % (11273)Termination reason: Unknown
% 2.88/1.74 % (11273)Termination phase: Saturation
% 2.88/1.74
% 2.88/1.74 % (11273)Memory used [KB]: 7036
% 2.88/1.74 % (11273)Time elapsed: 0.136 s
% 2.88/1.74 % (11273)Instructions burned: 276 (million)
% 2.88/1.74 % (11273)------------------------------
% 2.88/1.74 % (11273)------------------------------
% 2.88/1.76 % (11323)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11076 for (2998ds/17Mi)
% 2.88/1.76 % (11323)Instruction limit reached!
% 2.88/1.76 % (11323)------------------------------
% 2.88/1.76 % (11323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.76 % (11323)Termination reason: Unknown
% 2.88/1.76 % (11323)Termination phase: shuffling
% 2.88/1.76
% 2.88/1.76 % (11323)Memory used [KB]: 1791
% 2.88/1.76 % (11323)Time elapsed: 0.008 s
% 2.88/1.76 % (11323)Instructions burned: 18 (million)
% 2.88/1.76 % (11323)------------------------------
% 2.88/1.76 % (11323)------------------------------
% 2.88/1.77 % (11331)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11076 for (2998ds/3Mi)
% 2.88/1.77 % (11331)Instruction limit reached!
% 2.88/1.77 % (11331)------------------------------
% 2.88/1.77 % (11331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.77 % (11331)Termination reason: Unknown
% 2.88/1.77 % (11331)Termination phase: shuffling
% 2.88/1.77
% 2.88/1.77 % (11331)Memory used [KB]: 1407
% 2.88/1.77 % (11331)Time elapsed: 0.003 s
% 2.88/1.77 % (11331)Instructions burned: 5 (million)
% 2.88/1.77 % (11331)------------------------------
% 2.88/1.77 % (11331)------------------------------
% 2.88/1.78 % (11334)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11076 for (2998ds/30Mi)
% 2.88/1.80 % (11334)Instruction limit reached!
% 2.88/1.80 % (11334)------------------------------
% 2.88/1.80 % (11334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.80 % (11334)Termination reason: Unknown
% 2.88/1.80 % (11334)Termination phase: Property scanning
% 2.88/1.80
% 2.88/1.80 % (11334)Memory used [KB]: 1791
% 2.88/1.80 % (11334)Time elapsed: 0.016 s
% 2.88/1.80 % (11334)Instructions burned: 30 (million)
% 2.88/1.80 % (11334)------------------------------
% 2.88/1.80 % (11334)------------------------------
% 2.88/1.82 % (11339)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11076 for (2997ds/127Mi)
% 2.88/1.82 % (11301)Instruction limit reached!
% 2.88/1.82 % (11301)------------------------------
% 2.88/1.82 % (11301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.82 % (11301)Termination reason: Unknown
% 2.88/1.82 % (11301)Termination phase: Saturation
% 2.88/1.82
% 2.88/1.82 % (11301)Memory used [KB]: 7675
% 2.88/1.82 % (11301)Time elapsed: 0.149 s
% 2.88/1.82 % (11301)Instructions burned: 378 (million)
% 2.88/1.82 % (11301)------------------------------
% 2.88/1.82 % (11301)------------------------------
% 2.88/1.83 % (11341)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11076 for (2997ds/100Mi)
% 2.88/1.87 % (11341)Instruction limit reached!
% 2.88/1.87 % (11341)------------------------------
% 2.88/1.87 % (11341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.87 % (11341)Termination reason: Unknown
% 2.88/1.87 % (11341)Termination phase: Property scanning
% 2.88/1.87
% 2.88/1.87 % (11341)Memory used [KB]: 2302
% 2.88/1.87 % (11341)Time elapsed: 0.039 s
% 2.88/1.87 % (11341)Instructions burned: 100 (million)
% 2.88/1.87 % (11341)------------------------------
% 2.88/1.87 % (11341)------------------------------
% 2.88/1.88 % (11339)Instruction limit reached!
% 2.88/1.88 % (11339)------------------------------
% 2.88/1.88 % (11339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.88 % (11339)Termination reason: Unknown
% 2.88/1.88 % (11339)Termination phase: Saturation
% 2.88/1.88
% 2.88/1.88 % (11339)Memory used [KB]: 6908
% 2.88/1.88 % (11339)Time elapsed: 0.064 s
% 2.88/1.88 % (11339)Instructions burned: 128 (million)
% 2.88/1.88 % (11339)------------------------------
% 2.88/1.88 % (11339)------------------------------
% 2.88/1.89 % (11344)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_11076 for (2997ds/3Mi)
% 2.88/1.89 % (11344)Instruction limit reached!
% 2.88/1.89 % (11344)------------------------------
% 2.88/1.89 % (11344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.89 % (11344)Termination reason: Unknown
% 2.88/1.89 % (11344)Termination phase: shuffling
% 2.88/1.89
% 2.88/1.89 % (11344)Memory used [KB]: 1407
% 2.88/1.89 % (11344)Time elapsed: 0.004 s
% 2.88/1.89 % (11344)Instructions burned: 4 (million)
% 2.88/1.89 % (11344)------------------------------
% 2.88/1.89 % (11344)------------------------------
% 2.88/1.89 % (11345)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_11076 for (2997ds/20Mi)
% 2.88/1.91 % (11345)Instruction limit reached!
% 2.88/1.91 % (11345)------------------------------
% 2.88/1.91 % (11345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.91 % (11345)Termination reason: Unknown
% 2.88/1.91 % (11345)Termination phase: Property scanning
% 2.88/1.91
% 2.88/1.91 % (11345)Memory used [KB]: 1791
% 2.88/1.91 % (11345)Time elapsed: 0.013 s
% 2.88/1.91 % (11345)Instructions burned: 22 (million)
% 2.88/1.91 % (11345)------------------------------
% 2.88/1.91 % (11345)------------------------------
% 2.88/1.91 % (11346)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_11076 for (2997ds/86Mi)
% 2.88/1.92 % (11347)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_11076 for (2996ds/107Mi)
% 2.88/1.95 % (11346)Instruction limit reached!
% 2.88/1.95 % (11346)------------------------------
% 2.88/1.95 % (11346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.95 % (11346)Termination reason: Unknown
% 2.88/1.95 % (11346)Termination phase: Saturation
% 2.88/1.95
% 2.88/1.95 % (11346)Memory used [KB]: 6780
% 2.88/1.95 % (11346)Time elapsed: 0.043 s
% 2.88/1.95 % (11346)Instructions burned: 87 (million)
% 2.88/1.95 % (11346)------------------------------
% 2.88/1.95 % (11346)------------------------------
% 2.88/1.97 % (11349)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_11076 for (2996ds/39Mi)
% 2.88/1.97 % (11347)Instruction limit reached!
% 2.88/1.97 % (11347)------------------------------
% 2.88/1.97 % (11347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.97 % (11347)Termination reason: Unknown
% 2.88/1.97 % (11347)Termination phase: Saturation
% 2.88/1.97
% 2.88/1.97 % (11347)Memory used [KB]: 6908
% 2.88/1.97 % (11347)Time elapsed: 0.050 s
% 2.88/1.97 % (11347)Instructions burned: 107 (million)
% 2.88/1.97 % (11347)------------------------------
% 2.88/1.97 % (11347)------------------------------
% 2.88/1.98 % (11351)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_11076 for (2996ds/448Mi)
% 2.88/1.98 % (11293)Instruction limit reached!
% 2.88/1.98 % (11293)------------------------------
% 2.88/1.98 % (11293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.98 % (11293)Termination reason: Unknown
% 2.88/1.98 % (11293)Termination phase: Saturation
% 2.88/1.98
% 2.88/1.98 % (11293)Memory used [KB]: 7547
% 2.88/1.98 % (11293)Time elapsed: 0.336 s
% 2.88/1.98 % (11293)Instructions burned: 712 (million)
% 2.88/1.98 % (11293)------------------------------
% 2.88/1.98 % (11293)------------------------------
% 2.88/1.98 % (11349)Instruction limit reached!
% 2.88/1.98 % (11349)------------------------------
% 2.88/1.98 % (11349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.98 % (11349)Termination reason: Unknown
% 2.88/1.98 % (11349)Termination phase: Property scanning
% 2.88/1.98
% 2.88/1.98 % (11349)Memory used [KB]: 2046
% 2.88/1.98 % (11349)Time elapsed: 0.020 s
% 2.88/1.98 % (11349)Instructions burned: 39 (million)
% 2.88/1.98 % (11349)------------------------------
% 2.88/1.98 % (11349)------------------------------
% 2.88/1.99 % (11295)Instruction limit reached!
% 2.88/1.99 % (11295)------------------------------
% 2.88/1.99 % (11295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.99 % (11295)Termination reason: Unknown
% 2.88/1.99 % (11295)Termination phase: Saturation
% 2.88/1.99
% 2.88/1.99 % (11295)Memory used [KB]: 9466
% 2.88/1.99 % (11295)Time elapsed: 0.341 s
% 2.88/1.99 % (11295)Instructions burned: 902 (million)
% 2.88/1.99 % (11295)------------------------------
% 2.88/1.99 % (11295)------------------------------
% 2.88/2.00 % (11352)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_11076 for (2996ds/46Mi)
% 2.88/2.00 % (11353)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_11076 for (2996ds/98Mi)
% 2.88/2.00 % (11356)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_11076 for (2996ds/507Mi)
% 5.75/2.02 % (11352)Instruction limit reached!
% 5.75/2.02 % (11352)------------------------------
% 5.75/2.02 % (11352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.02 % (11352)Termination reason: Unknown
% 5.75/2.02 % (11352)Termination phase: Clausification
% 5.75/2.02
% 5.75/2.02 % (11352)Memory used [KB]: 2174
% 5.75/2.02 % (11352)Time elapsed: 0.018 s
% 5.75/2.02 % (11352)Instructions burned: 47 (million)
% 5.75/2.02 % (11352)------------------------------
% 5.75/2.02 % (11352)------------------------------
% 5.75/2.02 % (11302)Instruction limit reached!
% 5.75/2.02 % (11302)------------------------------
% 5.75/2.02 % (11302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.02 % (11302)Termination reason: Unknown
% 5.75/2.02 % (11302)Termination phase: Saturation
% 5.75/2.02
% 5.75/2.02 % (11302)Memory used [KB]: 7675
% 5.75/2.02 % (11302)Time elapsed: 0.344 s
% 5.75/2.02 % (11302)Instructions burned: 779 (million)
% 5.75/2.02 % (11302)------------------------------
% 5.75/2.02 % (11302)------------------------------
% 5.75/2.03 % (11358)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_11076 for (2995ds/149Mi)
% 5.75/2.03 % (11353)Instruction limit reached!
% 5.75/2.03 % (11353)------------------------------
% 5.75/2.03 % (11353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.03 % (11353)Termination reason: Unknown
% 5.75/2.03 % (11353)Termination phase: Function definition elimination
% 5.75/2.03
% 5.75/2.03 % (11353)Memory used [KB]: 2174
% 5.75/2.03 % (11353)Time elapsed: 0.029 s
% 5.75/2.03 % (11353)Instructions burned: 99 (million)
% 5.75/2.03 % (11353)------------------------------
% 5.75/2.03 % (11353)------------------------------
% 5.75/2.03 % (11359)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_11076 for (2995ds/39Mi)
% 5.75/2.04 % (11360)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_11076 for (2995ds/6Mi)
% 5.75/2.04 % (11360)Instruction limit reached!
% 5.75/2.04 % (11360)------------------------------
% 5.75/2.04 % (11360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.04 % (11360)Termination reason: Unknown
% 5.75/2.04 % (11360)Termination phase: shuffling
% 5.75/2.04
% 5.75/2.04 % (11360)Memory used [KB]: 1407
% 5.75/2.04 % (11360)Time elapsed: 0.003 s
% 5.75/2.04 % (11360)Instructions burned: 6 (million)
% 5.75/2.04 % (11360)------------------------------
% 5.75/2.04 % (11360)------------------------------
% 5.75/2.04 % (11359)Instruction limit reached!
% 5.75/2.04 % (11359)------------------------------
% 5.75/2.04 % (11359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.04 % (11359)Termination reason: Unknown
% 5.75/2.04 % (11359)Termination phase: Preprocessing 3
% 5.75/2.04
% 5.75/2.04 % (11359)Memory used [KB]: 2046
% 5.75/2.04 % (11359)Time elapsed: 0.014 s
% 5.75/2.04 % (11359)Instructions burned: 40 (million)
% 5.75/2.04 % (11359)------------------------------
% 5.75/2.04 % (11359)------------------------------
% 5.75/2.05 % (11361)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_11076 for (2995ds/1087Mi)
% 5.75/2.05 % (11362)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_11076 for (2995ds/47Mi)
% 5.75/2.06 % (11284)Instruction limit reached!
% 5.75/2.06 % (11284)------------------------------
% 5.75/2.06 % (11284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.06 % (11284)Termination reason: Unknown
% 5.75/2.06 % (11284)Termination phase: Saturation
% 5.75/2.06
% 5.75/2.06 % (11284)Memory used [KB]: 9594
% 5.75/2.06 % (11284)Time elapsed: 0.440 s
% 5.75/2.06 % (11284)Instructions burned: 1041 (million)
% 5.75/2.06 % (11284)------------------------------
% 5.75/2.06 % (11284)------------------------------
% 5.75/2.07 % (11362)Instruction limit reached!
% 5.75/2.07 % (11362)------------------------------
% 5.75/2.07 % (11362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.07 % (11362)Termination reason: Unknown
% 5.75/2.07 % (11362)Termination phase: Property scanning
% 5.75/2.07
% 5.75/2.07 % (11362)Memory used [KB]: 2174
% 5.75/2.07 % (11362)Time elapsed: 0.016 s
% 5.75/2.07 % (11362)Instructions burned: 50 (million)
% 5.75/2.07 % (11362)------------------------------
% 5.75/2.07 % (11362)------------------------------
% 5.75/2.07 % (11358)Instruction limit reached!
% 5.75/2.07 % (11358)------------------------------
% 5.75/2.07 % (11358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.07 % (11358)Termination reason: Unknown
% 5.75/2.07 % (11358)Termination phase: Saturation
% 5.75/2.07
% 5.75/2.07 % (11358)Memory used [KB]: 6908
% 5.75/2.07 % (11358)Time elapsed: 0.046 s
% 5.75/2.07 % (11358)Instructions burned: 151 (million)
% 5.75/2.07 % (11358)------------------------------
% 5.75/2.07 % (11358)------------------------------
% 5.75/2.07 % (11363)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_11076 for (2995ds/44Mi)
% 5.75/2.08 % (11364)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_11076 for (2995ds/432Mi)
% 5.75/2.08 % (11365)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_11076 for (2995ds/62Mi)
% 5.75/2.08 % (11363)Instruction limit reached!
% 5.75/2.08 % (11363)------------------------------
% 5.75/2.08 % (11363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.08 % (11363)Termination reason: Unknown
% 5.75/2.08 % (11363)Termination phase: Property scanning
% 5.75/2.08
% 5.75/2.08 % (11363)Memory used [KB]: 2046
% 5.75/2.08 % (11363)Time elapsed: 0.013 s
% 5.75/2.08 % (11363)Instructions burned: 45 (million)
% 5.75/2.08 % (11363)------------------------------
% 5.75/2.08 % (11363)------------------------------
% 5.75/2.09 % (11366)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_11076 for (2995ds/31Mi)
% 5.75/2.09 % (11365)Instruction limit reached!
% 5.75/2.09 % (11365)------------------------------
% 5.75/2.09 % (11365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.09 % (11365)Termination reason: Unknown
% 5.75/2.09 % (11365)Termination phase: Preprocessing 1
% 5.75/2.09
% 5.75/2.09 % (11365)Memory used [KB]: 2174
% 5.75/2.09 % (11365)Time elapsed: 0.017 s
% 5.75/2.09 % (11365)Instructions burned: 62 (million)
% 5.75/2.09 % (11365)------------------------------
% 5.75/2.09 % (11365)------------------------------
% 5.75/2.10 % (11366)Instruction limit reached!
% 5.75/2.10 % (11366)------------------------------
% 5.75/2.10 % (11366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.10 % (11366)Termination reason: Unknown
% 5.75/2.10 % (11366)Termination phase: shuffling
% 5.75/2.10
% 5.75/2.10 % (11366)Memory used [KB]: 1791
% 5.75/2.10 % (11366)Time elapsed: 0.011 s
% 5.75/2.10 % (11366)Instructions burned: 33 (million)
% 5.75/2.10 % (11366)------------------------------
% 5.75/2.10 % (11366)------------------------------
% 5.75/2.10 % (11315)Instruction limit reached!
% 5.75/2.10 % (11315)------------------------------
% 5.75/2.10 % (11315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.10 % (11315)Termination reason: Unknown
% 5.75/2.10 % (11315)Termination phase: Saturation
% 5.75/2.10
% 5.75/2.10 % (11315)Memory used [KB]: 7547
% 5.75/2.10 % (11315)Time elapsed: 0.377 s
% 5.75/2.10 % (11315)Instructions burned: 882 (million)
% 5.75/2.10 % (11315)------------------------------
% 5.75/2.10 % (11315)------------------------------
% 5.75/2.10 % (11367)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_11076 for (2994ds/96Mi)
% 5.75/2.11 % (11370)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_11076 for (2994ds/453Mi)
% 5.75/2.11 % (11371)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_11076 for (2994ds/71Mi)
% 6.34/2.12 % (11351)Instruction limit reached!
% 6.34/2.12 % (11351)------------------------------
% 6.34/2.12 % (11351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.12 % (11351)Termination reason: Unknown
% 6.34/2.12 % (11351)Termination phase: Saturation
% 6.34/2.12
% 6.34/2.12 % (11351)Memory used [KB]: 7675
% 6.34/2.12 % (11351)Time elapsed: 0.144 s
% 6.34/2.12 % (11351)Instructions burned: 450 (million)
% 6.34/2.12 % (11351)------------------------------
% 6.34/2.12 % (11351)------------------------------
% 6.34/2.13 % (11371)Instruction limit reached!
% 6.34/2.13 % (11371)------------------------------
% 6.34/2.13 % (11371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.13 % (11371)Termination reason: Unknown
% 6.34/2.13 % (11371)Termination phase: Property scanning
% 6.34/2.13
% 6.34/2.13 % (11371)Memory used [KB]: 2174
% 6.34/2.13 % (11371)Time elapsed: 0.022 s
% 6.34/2.13 % (11371)Instructions burned: 72 (million)
% 6.34/2.13 % (11371)------------------------------
% 6.34/2.13 % (11371)------------------------------
% 6.34/2.13 % (11367)Instruction limit reached!
% 6.34/2.13 % (11367)------------------------------
% 6.34/2.13 % (11367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.13 % (11367)Termination reason: Unknown
% 6.34/2.13 % (11367)Termination phase: Saturation
% 6.34/2.13
% 6.34/2.13 % (11367)Memory used [KB]: 6780
% 6.34/2.13 % (11367)Time elapsed: 0.029 s
% 6.34/2.13 % (11367)Instructions burned: 97 (million)
% 6.34/2.13 % (11367)------------------------------
% 6.34/2.13 % (11367)------------------------------
% 6.34/2.13 % (11380)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_11076 for (2994ds/83Mi)
% 6.34/2.14 % (11385)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_11076 for (2994ds/11Mi)
% 6.34/2.14 % (11386)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_11076 for (2994ds/41Mi)
% 6.34/2.14 % (11385)Instruction limit reached!
% 6.34/2.14 % (11385)------------------------------
% 6.34/2.14 % (11385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.14 % (11385)Termination reason: Unknown
% 6.34/2.14 % (11385)Termination phase: shuffling
% 6.34/2.14
% 6.34/2.14 % (11385)Memory used [KB]: 1535
% 6.34/2.14 % (11385)Time elapsed: 0.004 s
% 6.34/2.14 % (11385)Instructions burned: 11 (million)
% 6.34/2.14 % (11385)------------------------------
% 6.34/2.14 % (11385)------------------------------
% 6.34/2.15 % (11392)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11076 for (2994ds/6Mi)
% 6.34/2.15 % (11386)Instruction limit reached!
% 6.34/2.15 % (11386)------------------------------
% 6.34/2.15 % (11386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.15 % (11386)Termination reason: Unknown
% 6.34/2.15 % (11386)Termination phase: Property scanning
% 6.34/2.15
% 6.34/2.15 % (11386)Memory used [KB]: 2046
% 6.34/2.15 % (11386)Time elapsed: 0.013 s
% 6.34/2.15 % (11386)Instructions burned: 44 (million)
% 6.34/2.15 % (11386)------------------------------
% 6.34/2.15 % (11386)------------------------------
% 6.34/2.16 % (11392)Instruction limit reached!
% 6.34/2.16 % (11392)------------------------------
% 6.34/2.16 % (11392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.16 % (11392)Termination reason: Unknown
% 6.34/2.16 % (11392)Termination phase: shuffling
% 6.34/2.16
% 6.34/2.16 % (11392)Memory used [KB]: 1407
% 6.34/2.16 % (11392)Time elapsed: 0.003 s
% 6.34/2.16 % (11392)Instructions burned: 6 (million)
% 6.34/2.16 % (11392)------------------------------
% 6.34/2.16 % (11392)------------------------------
% 6.34/2.16 % (11380)Instruction limit reached!
% 6.34/2.16 % (11380)------------------------------
% 6.34/2.16 % (11380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.16 % (11380)Termination reason: Unknown
% 6.34/2.16 % (11380)Termination phase: Saturation
% 6.34/2.16
% 6.34/2.16 % (11380)Memory used [KB]: 6652
% 6.34/2.16 % (11380)Time elapsed: 0.027 s
% 6.34/2.16 % (11380)Instructions burned: 85 (million)
% 6.34/2.16 % (11380)------------------------------
% 6.34/2.16 % (11380)------------------------------
% 6.34/2.16 % (11356)Instruction limit reached!
% 6.34/2.16 % (11356)------------------------------
% 6.34/2.16 % (11356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.16 % (11356)Termination reason: Unknown
% 6.34/2.16 % (11356)Termination phase: Saturation
% 6.34/2.16
% 6.34/2.16 % (11356)Memory used [KB]: 7931
% 6.34/2.16 % (11356)Time elapsed: 0.179 s
% 6.34/2.16 % (11356)Instructions burned: 508 (million)
% 6.34/2.16 % (11356)------------------------------
% 6.34/2.16 % (11356)------------------------------
% 6.34/2.16 % (11396)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_11076 for (2994ds/150Mi)
% 6.34/2.16 % (11398)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_11076 for (2994ds/343Mi)
% 6.34/2.17 % (11400)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_11076 for (2994ds/109Mi)
% 6.34/2.17 % (11402)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_11076 for (2994ds/253Mi)
% 6.56/2.20 % (11400)Instruction limit reached!
% 6.56/2.20 % (11400)------------------------------
% 6.56/2.20 % (11400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.20 % (11400)Termination reason: Unknown
% 6.56/2.20 % (11400)Termination phase: Saturation
% 6.56/2.20
% 6.56/2.20 % (11400)Memory used [KB]: 6780
% 6.56/2.20 % (11400)Time elapsed: 0.033 s
% 6.56/2.20 % (11400)Instructions burned: 109 (million)
% 6.56/2.20 % (11400)------------------------------
% 6.56/2.20 % (11400)------------------------------
% 6.56/2.21 % (11396)Instruction limit reached!
% 6.56/2.21 % (11396)------------------------------
% 6.56/2.21 % (11396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.21 % (11396)Termination reason: Unknown
% 6.56/2.21 % (11396)Termination phase: Saturation
% 6.56/2.21
% 6.56/2.21 % (11396)Memory used [KB]: 7036
% 6.56/2.21 % (11396)Time elapsed: 0.046 s
% 6.56/2.21 % (11396)Instructions burned: 151 (million)
% 6.56/2.21 % (11396)------------------------------
% 6.56/2.21 % (11396)------------------------------
% 6.56/2.21 % (11364)Instruction limit reached!
% 6.56/2.21 % (11364)------------------------------
% 6.56/2.21 % (11364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.21 % (11364)Termination reason: Unknown
% 6.56/2.21 % (11364)Termination phase: Saturation
% 6.56/2.21
% 6.56/2.21 % (11364)Memory used [KB]: 3709
% 6.56/2.21 % (11364)Time elapsed: 0.133 s
% 6.56/2.21 % (11364)Instructions burned: 433 (million)
% 6.56/2.21 % (11364)------------------------------
% 6.56/2.21 % (11364)------------------------------
% 6.56/2.21 % (11419)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_11076 for (2993ds/140Mi)
% 6.56/2.22 % (11423)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_11076 for (2993ds/614Mi)
% 6.56/2.22 % (11425)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_11076 for (2993ds/202Mi)
% 6.56/2.24 % (11370)Instruction limit reached!
% 6.56/2.24 % (11370)------------------------------
% 6.56/2.24 % (11370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.24 % (11370)Termination reason: Unknown
% 6.56/2.24 % (11370)Termination phase: Saturation
% 6.56/2.24
% 6.56/2.24 % (11370)Memory used [KB]: 7547
% 6.56/2.24 % (11370)Time elapsed: 0.132 s
% 6.56/2.24 % (11370)Instructions burned: 454 (million)
% 6.56/2.24 % (11370)------------------------------
% 6.56/2.24 % (11370)------------------------------
% 6.56/2.25 % (11438)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_11076 for (2993ds/339Mi)
% 6.56/2.25 % (11402)Instruction limit reached!
% 6.56/2.25 % (11402)------------------------------
% 6.56/2.25 % (11402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.25 % (11402)Termination reason: Unknown
% 6.56/2.25 % (11402)Termination phase: Saturation
% 6.56/2.25
% 6.56/2.25 % (11402)Memory used [KB]: 7291
% 6.56/2.25 % (11402)Time elapsed: 0.083 s
% 6.56/2.25 % (11402)Instructions burned: 253 (million)
% 6.56/2.25 % (11402)------------------------------
% 6.56/2.25 % (11402)------------------------------
% 6.56/2.25 % (11419)Instruction limit reached!
% 6.56/2.25 % (11419)------------------------------
% 6.56/2.25 % (11419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.25 % (11419)Termination reason: Unknown
% 6.56/2.25 % (11419)Termination phase: Saturation
% 6.56/2.25
% 6.56/2.25 % (11419)Memory used [KB]: 6780
% 6.56/2.25 % (11419)Time elapsed: 0.046 s
% 6.56/2.25 % (11419)Instructions burned: 141 (million)
% 6.56/2.25 % (11419)------------------------------
% 6.56/2.25 % (11419)------------------------------
% 6.56/2.26 % (11440)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_11076 for (2993ds/283Mi)
% 6.56/2.26 % (11443)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_11076 for (2993ds/134Mi)
% 6.56/2.27 % (11398)Instruction limit reached!
% 6.56/2.27 % (11398)------------------------------
% 6.56/2.27 % (11398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.27 % (11398)Termination reason: Unknown
% 6.56/2.27 % (11398)Termination phase: Saturation
% 6.56/2.27
% 6.56/2.27 % (11398)Memory used [KB]: 7291
% 6.56/2.27 % (11398)Time elapsed: 0.110 s
% 6.56/2.27 % (11398)Instructions burned: 343 (million)
% 6.56/2.27 % (11398)------------------------------
% 6.56/2.27 % (11398)------------------------------
% 6.56/2.28 % (11425)Instruction limit reached!
% 6.56/2.28 % (11425)------------------------------
% 6.56/2.28 % (11425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.28 % (11425)Termination reason: Unknown
% 6.56/2.28 % (11425)Termination phase: Saturation
% 6.56/2.28
% 6.56/2.28 % (11425)Memory used [KB]: 7419
% 6.56/2.28 % (11425)Time elapsed: 0.062 s
% 6.56/2.28 % (11425)Instructions burned: 202 (million)
% 6.56/2.28 % (11425)------------------------------
% 6.56/2.28 % (11425)------------------------------
% 6.56/2.28 % (11450)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_11076 for (2993ds/298Mi)
% 6.56/2.29 % (11451)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_11076 for (2993ds/192Mi)
% 7.28/2.30 % (11443)Instruction limit reached!
% 7.28/2.30 % (11443)------------------------------
% 7.28/2.30 % (11443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.30 % (11443)Termination reason: Unknown
% 7.28/2.30 % (11443)Termination phase: Saturation
% 7.28/2.30
% 7.28/2.30 % (11443)Memory used [KB]: 7036
% 7.28/2.30 % (11443)Time elapsed: 0.042 s
% 7.28/2.30 % (11443)Instructions burned: 136 (million)
% 7.28/2.30 % (11443)------------------------------
% 7.28/2.30 % (11443)------------------------------
% 7.28/2.31 % (11469)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_11076 for (2992ds/258Mi)
% 7.28/2.35 % (11440)Instruction limit reached!
% 7.28/2.35 % (11440)------------------------------
% 7.28/2.35 % (11440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.35 % (11440)Termination reason: Unknown
% 7.28/2.35 % (11440)Termination phase: Saturation
% 7.28/2.35
% 7.28/2.35 % (11440)Memory used [KB]: 7547
% 7.28/2.35 % (11440)Time elapsed: 0.088 s
% 7.28/2.35 % (11440)Instructions burned: 283 (million)
% 7.28/2.35 % (11440)------------------------------
% 7.28/2.35 % (11440)------------------------------
% 7.28/2.35 % (11451)Instruction limit reached!
% 7.28/2.35 % (11451)------------------------------
% 7.28/2.35 % (11451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.35 % (11451)Termination reason: Unknown
% 7.28/2.35 % (11451)Termination phase: Saturation
% 7.28/2.35
% 7.28/2.35 % (11451)Memory used [KB]: 7803
% 7.28/2.35 % (11451)Time elapsed: 0.061 s
% 7.28/2.35 % (11451)Instructions burned: 193 (million)
% 7.28/2.35 % (11451)------------------------------
% 7.28/2.35 % (11451)------------------------------
% 7.28/2.35 % (11438)Instruction limit reached!
% 7.28/2.35 % (11438)------------------------------
% 7.28/2.35 % (11438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.35 % (11438)Termination reason: Unknown
% 7.28/2.35 % (11438)Termination phase: Saturation
% 7.28/2.35
% 7.28/2.35 % (11438)Memory used [KB]: 7675
% 7.28/2.35 % (11438)Time elapsed: 0.103 s
% 7.28/2.35 % (11438)Instructions burned: 342 (million)
% 7.28/2.35 % (11438)------------------------------
% 7.28/2.35 % (11438)------------------------------
% 7.28/2.36 % (11491)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_11076 for (2992ds/231Mi)
% 7.28/2.36 % (11494)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_11076 for (2992ds/458Mi)
% 7.28/2.37 % (11489)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_11076 for (2992ds/90Mi)
% 7.28/2.37 % (11450)Instruction limit reached!
% 7.28/2.37 % (11450)------------------------------
% 7.28/2.37 % (11450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.37 % (11450)Termination reason: Unknown
% 7.28/2.37 % (11450)Termination phase: Saturation
% 7.28/2.37
% 7.28/2.37 % (11450)Memory used [KB]: 7675
% 7.28/2.37 % (11450)Time elapsed: 0.086 s
% 7.28/2.37 % (11450)Instructions burned: 299 (million)
% 7.28/2.37 % (11450)------------------------------
% 7.28/2.37 % (11450)------------------------------
% 7.28/2.38 % (11500)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_11076 for (2992ds/31Mi)
% 7.28/2.39 % (11500)Instruction limit reached!
% 7.28/2.39 % (11500)------------------------------
% 7.28/2.39 % (11500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.39 % (11500)Termination reason: Unknown
% 7.28/2.39 % (11500)Termination phase: Preprocessing 2
% 7.28/2.39
% 7.28/2.39 % (11500)Memory used [KB]: 1791
% 7.28/2.39 % (11500)Time elapsed: 0.011 s
% 7.28/2.39 % (11500)Instructions burned: 33 (million)
% 7.28/2.39 % (11500)------------------------------
% 7.28/2.39 % (11500)------------------------------
% 7.28/2.39 % (11469)Instruction limit reached!
% 7.28/2.39 % (11469)------------------------------
% 7.28/2.39 % (11469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.39 % (11469)Termination reason: Unknown
% 7.28/2.39 % (11469)Termination phase: Saturation
% 7.28/2.39
% 7.28/2.39 % (11469)Memory used [KB]: 7547
% 7.28/2.39 % (11469)Time elapsed: 0.078 s
% 7.28/2.39 % (11469)Instructions burned: 261 (million)
% 7.28/2.39 % (11469)------------------------------
% 7.28/2.39 % (11469)------------------------------
% 7.81/2.40 % (11512)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_11076 for (2992ds/297Mi)
% 7.81/2.40 % (11361)Instruction limit reached!
% 7.81/2.40 % (11361)------------------------------
% 7.81/2.40 % (11361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.40 % (11361)Termination reason: Unknown
% 7.81/2.40 % (11361)Termination phase: Saturation
% 7.81/2.40
% 7.81/2.40 % (11361)Memory used [KB]: 8443
% 7.81/2.40 % (11361)Time elapsed: 0.374 s
% 7.81/2.40 % (11361)Instructions burned: 1089 (million)
% 7.81/2.40 % (11361)------------------------------
% 7.81/2.40 % (11361)------------------------------
% 7.81/2.40 % (11517)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_11076 for (2992ds/987Mi)
% 7.81/2.40 % (11423)Instruction limit reached!
% 7.81/2.40 % (11423)------------------------------
% 7.81/2.40 % (11423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.40 % (11423)Termination reason: Unknown
% 7.81/2.40 % (11423)Termination phase: Saturation
% 7.81/2.40
% 7.81/2.40 % (11423)Memory used [KB]: 8059
% 7.81/2.40 % (11423)Time elapsed: 0.188 s
% 7.81/2.40 % (11423)Instructions burned: 617 (million)
% 7.81/2.40 % (11423)------------------------------
% 7.81/2.40 % (11423)------------------------------
% 7.81/2.41 % (11518)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_11076 for (2992ds/182Mi)
% 7.81/2.41 % (11521)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_11076 for (2991ds/182Mi)
% 7.81/2.42 % (11489)Instruction limit reached!
% 7.81/2.42 % (11489)------------------------------
% 7.81/2.42 % (11489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.42 % (11489)Termination reason: Unknown
% 7.81/2.42 % (11489)Termination phase: Saturation
% 7.81/2.42
% 7.81/2.42 % (11489)Memory used [KB]: 6780
% 7.81/2.42 % (11489)Time elapsed: 0.052 s
% 7.81/2.42 % (11489)Instructions burned: 90 (million)
% 7.81/2.42 % (11489)------------------------------
% 7.81/2.42 % (11489)------------------------------
% 7.81/2.42 % (11491)Instruction limit reached!
% 7.81/2.42 % (11491)------------------------------
% 7.81/2.42 % (11491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.42 % (11491)Termination reason: Unknown
% 7.81/2.42 % (11491)Termination phase: Saturation
% 7.81/2.42
% 7.81/2.42 % (11491)Memory used [KB]: 6908
% 7.81/2.42 % (11491)Time elapsed: 0.062 s
% 7.81/2.42 % (11491)Instructions burned: 234 (million)
% 7.81/2.42 % (11491)------------------------------
% 7.81/2.42 % (11491)------------------------------
% 7.81/2.43 % (11530)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_11076 for (2991ds/79Mi)
% 7.81/2.43 % (11527)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_11076 for (2991ds/154Mi)
% 7.81/2.45 % (11530)Instruction limit reached!
% 7.81/2.45 % (11530)------------------------------
% 7.81/2.45 % (11530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.45 % (11530)Termination reason: Unknown
% 7.81/2.45 % (11530)Termination phase: Property scanning
% 7.81/2.45
% 7.81/2.45 % (11530)Memory used [KB]: 2174
% 7.81/2.45 % (11530)Time elapsed: 0.025 s
% 7.81/2.45 % (11530)Instructions burned: 80 (million)
% 7.81/2.45 % (11530)------------------------------
% 7.81/2.45 % (11530)------------------------------
% 7.81/2.46 % (11518)Instruction limit reached!
% 7.81/2.46 % (11518)------------------------------
% 7.81/2.46 % (11518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.46 % (11518)Termination reason: Unknown
% 7.81/2.46 % (11518)Termination phase: Saturation
% 7.81/2.46
% 7.81/2.46 % (11518)Memory used [KB]: 7036
% 7.81/2.46 % (11518)Time elapsed: 0.056 s
% 7.81/2.46 % (11518)Instructions burned: 182 (million)
% 7.81/2.46 % (11518)------------------------------
% 7.81/2.46 % (11518)------------------------------
% 7.81/2.46 % (11544)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_11076 for (2991ds/216Mi)
% 7.81/2.47 % (11547)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_11076 for (2991ds/114Mi)
% 7.81/2.47 % (11521)Instruction limit reached!
% 7.81/2.47 % (11521)------------------------------
% 7.81/2.47 % (11521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.47 % (11521)Termination reason: Unknown
% 7.81/2.47 % (11521)Termination phase: Saturation
% 7.81/2.47
% 7.81/2.47 % (11521)Memory used [KB]: 7164
% 7.81/2.47 % (11521)Time elapsed: 0.080 s
% 7.81/2.47 % (11521)Instructions burned: 182 (million)
% 7.81/2.47 % (11521)------------------------------
% 7.81/2.47 % (11521)------------------------------
% 7.81/2.47 % (11527)Instruction limit reached!
% 7.81/2.47 % (11527)------------------------------
% 7.81/2.47 % (11527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.47 % (11527)Termination reason: Unknown
% 7.81/2.47 % (11527)Termination phase: Saturation
% 7.81/2.47
% 7.81/2.47 % (11527)Memory used [KB]: 2558
% 7.81/2.47 % (11527)Time elapsed: 0.045 s
% 7.81/2.47 % (11527)Instructions burned: 157 (million)
% 7.81/2.47 % (11527)------------------------------
% 7.81/2.47 % (11527)------------------------------
% 7.81/2.48 % (11552)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_11076 for (2991ds/922Mi)
% 7.81/2.48 % (11554)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_11076 for (2991ds/182Mi)
% 7.81/2.49 % (11512)Instruction limit reached!
% 7.81/2.49 % (11512)------------------------------
% 7.81/2.49 % (11512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.49 % (11512)Termination reason: Unknown
% 7.81/2.49 % (11512)Termination phase: Saturation
% 7.81/2.49
% 7.81/2.49 % (11512)Memory used [KB]: 7291
% 7.81/2.49 % (11512)Time elapsed: 0.092 s
% 7.81/2.49 % (11512)Instructions burned: 299 (million)
% 7.81/2.49 % (11512)------------------------------
% 7.81/2.49 % (11512)------------------------------
% 8.82/2.50 % (11557)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_11076 for (2990ds/164Mi)
% 8.82/2.50 % (11547)Instruction limit reached!
% 8.82/2.50 % (11547)------------------------------
% 8.82/2.50 % (11547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.50 % (11547)Termination reason: Unknown
% 8.82/2.50 % (11547)Termination phase: Saturation
% 8.82/2.50
% 8.82/2.50 % (11547)Memory used [KB]: 6908
% 8.82/2.50 % (11547)Time elapsed: 0.034 s
% 8.82/2.50 % (11547)Instructions burned: 114 (million)
% 8.82/2.50 % (11547)------------------------------
% 8.82/2.50 % (11547)------------------------------
% 8.82/2.51 % (11494)Instruction limit reached!
% 8.82/2.51 % (11494)------------------------------
% 8.82/2.51 % (11494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.51 % (11494)Termination reason: Unknown
% 8.82/2.51 % (11494)Termination phase: Saturation
% 8.82/2.51
% 8.82/2.51 % (11494)Memory used [KB]: 7675
% 8.82/2.51 % (11494)Time elapsed: 0.146 s
% 8.82/2.51 % (11494)Instructions burned: 458 (million)
% 8.82/2.51 % (11494)------------------------------
% 8.82/2.51 % (11494)------------------------------
% 8.82/2.51 % (11565)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_11076 for (2990ds/50Mi)
% 8.82/2.52 % (11568)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_11076 for (2990ds/368Mi)
% 8.82/2.53 % (11544)Instruction limit reached!
% 8.82/2.53 % (11544)------------------------------
% 8.82/2.53 % (11544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.53 % (11544)Termination reason: Unknown
% 8.82/2.53 % (11544)Termination phase: Saturation
% 8.82/2.53
% 8.82/2.53 % (11544)Memory used [KB]: 7291
% 8.82/2.53 % (11544)Time elapsed: 0.085 s
% 8.82/2.53 % (11544)Instructions burned: 216 (million)
% 8.82/2.53 % (11544)------------------------------
% 8.82/2.53 % (11544)------------------------------
% 8.82/2.53 % (11565)Instruction limit reached!
% 8.82/2.53 % (11565)------------------------------
% 8.82/2.53 % (11565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.53 % (11565)Termination reason: Unknown
% 8.82/2.53 % (11565)Termination phase: Property scanning
% 8.82/2.53
% 8.82/2.53 % (11565)Memory used [KB]: 2046
% 8.82/2.53 % (11565)Time elapsed: 0.015 s
% 8.82/2.53 % (11565)Instructions burned: 50 (million)
% 8.82/2.53 % (11565)------------------------------
% 8.82/2.53 % (11565)------------------------------
% 8.82/2.54 % (11554)Instruction limit reached!
% 8.82/2.54 % (11554)------------------------------
% 8.82/2.54 % (11554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.54 % (11554)Termination reason: Unknown
% 8.82/2.54 % (11554)Termination phase: Saturation
% 8.82/2.54
% 8.82/2.54 % (11554)Memory used [KB]: 6780
% 8.82/2.54 % (11554)Time elapsed: 0.053 s
% 8.82/2.54 % (11554)Instructions burned: 183 (million)
% 8.82/2.54 % (11554)------------------------------
% 8.82/2.54 % (11554)------------------------------
% 8.82/2.54 % (11574)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_11076 for (2990ds/1021Mi)
% 8.82/2.54 % (11576)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_11076 for (2990ds/267Mi)
% 8.82/2.54 % (11557)Instruction limit reached!
% 8.82/2.54 % (11557)------------------------------
% 8.82/2.54 % (11557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.54 % (11557)Termination reason: Unknown
% 8.82/2.54 % (11557)Termination phase: Saturation
% 8.82/2.54
% 8.82/2.54 % (11557)Memory used [KB]: 2430
% 8.82/2.54 % (11557)Time elapsed: 0.048 s
% 8.82/2.54 % (11557)Instructions burned: 164 (million)
% 8.82/2.54 % (11557)------------------------------
% 8.82/2.54 % (11557)------------------------------
% 8.82/2.55 % (11578)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_11076 for (2990ds/204Mi)
% 8.82/2.55 % (11582)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_11076 for (2990ds/26Mi)
% 8.82/2.56 % (11582)Instruction limit reached!
% 8.82/2.56 % (11582)------------------------------
% 8.82/2.56 % (11582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.56 % (11582)Termination reason: Unknown
% 8.82/2.56 % (11582)Termination phase: shuffling
% 8.82/2.56
% 8.82/2.56 % (11582)Memory used [KB]: 1791
% 8.82/2.56 % (11582)Time elapsed: 0.009 s
% 8.82/2.56 % (11582)Instructions burned: 27 (million)
% 8.82/2.56 % (11582)------------------------------
% 8.82/2.56 % (11582)------------------------------
% 8.82/2.57 % (11586)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_11076 for (2990ds/53Mi)
% 8.82/2.59 % (11586)Instruction limit reached!
% 8.82/2.59 % (11586)------------------------------
% 8.82/2.59 % (11586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.59 % (11586)Termination reason: Unknown
% 8.82/2.59 % (11586)Termination phase: Property scanning
% 8.82/2.59
% 8.82/2.59 % (11586)Memory used [KB]: 2046
% 8.82/2.59 % (11586)Time elapsed: 0.016 s
% 8.82/2.59 % (11586)Instructions burned: 56 (million)
% 8.82/2.59 % (11586)------------------------------
% 8.82/2.59 % (11586)------------------------------
% 9.28/2.60 % (11596)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_11076 for (2989ds/4436Mi)
% 9.28/2.61 % (11578)Instruction limit reached!
% 9.28/2.61 % (11578)------------------------------
% 9.28/2.61 % (11578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.61 % (11578)Termination reason: Unknown
% 9.28/2.61 % (11578)Termination phase: Saturation
% 9.28/2.61
% 9.28/2.61 % (11578)Memory used [KB]: 7036
% 9.28/2.61 % (11578)Time elapsed: 0.066 s
% 9.28/2.61 % (11578)Instructions burned: 205 (million)
% 9.28/2.61 % (11578)------------------------------
% 9.28/2.61 % (11578)------------------------------
% 9.28/2.62 % (11576)Instruction limit reached!
% 9.28/2.62 % (11576)------------------------------
% 9.28/2.62 % (11576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.62 % (11576)Termination reason: Unknown
% 9.28/2.62 % (11576)Termination phase: Saturation
% 9.28/2.62
% 9.28/2.62 % (11576)Memory used [KB]: 7419
% 9.28/2.62 % (11576)Time elapsed: 0.082 s
% 9.28/2.62 % (11576)Instructions burned: 269 (million)
% 9.28/2.62 % (11576)------------------------------
% 9.28/2.62 % (11576)------------------------------
% 9.28/2.62 % (11603)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_11076 for (2989ds/1539Mi)
% 9.28/2.62 % (11568)Instruction limit reached!
% 9.28/2.62 % (11568)------------------------------
% 9.28/2.62 % (11568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.62 % (11568)Termination reason: Unknown
% 9.28/2.62 % (11568)Termination phase: Saturation
% 9.28/2.62
% 9.28/2.62 % (11568)Memory used [KB]: 7931
% 9.28/2.62 % (11568)Time elapsed: 0.106 s
% 9.28/2.62 % (11568)Instructions burned: 368 (million)
% 9.28/2.62 % (11568)------------------------------
% 9.28/2.62 % (11568)------------------------------
% 9.28/2.63 % (11605)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_11076 for (2989ds/408Mi)
% 9.28/2.63 % (11608)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_11076 for (2989ds/5205Mi)
% 9.56/2.70 % (11517)Instruction limit reached!
% 9.56/2.70 % (11517)------------------------------
% 9.56/2.70 % (11517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.70 % (11517)Termination reason: Unknown
% 9.56/2.70 % (11517)Termination phase: Saturation
% 9.56/2.70
% 9.56/2.70 % (11517)Memory used [KB]: 9466
% 9.56/2.70 % (11517)Time elapsed: 0.297 s
% 9.56/2.70 % (11517)Instructions burned: 987 (million)
% 9.56/2.70 % (11517)------------------------------
% 9.56/2.70 % (11517)------------------------------
% 9.56/2.71 % (11646)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_11076 for (2988ds/1913Mi)
% 9.56/2.75 % (11605)Instruction limit reached!
% 9.56/2.75 % (11605)------------------------------
% 9.56/2.75 % (11605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.75 % (11605)Termination reason: Unknown
% 9.56/2.75 % (11605)Termination phase: Saturation
% 9.56/2.75
% 9.56/2.75 % (11605)Memory used [KB]: 8315
% 9.56/2.75 % (11605)Time elapsed: 0.127 s
% 9.56/2.75 % (11605)Instructions burned: 408 (million)
% 9.56/2.75 % (11605)------------------------------
% 9.56/2.75 % (11605)------------------------------
% 9.56/2.76 % (11647)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_11076 for (2988ds/4350Mi)
% 9.56/2.78 % (11552)Instruction limit reached!
% 9.56/2.78 % (11552)------------------------------
% 9.56/2.78 % (11552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.78 % (11552)Termination reason: Unknown
% 9.56/2.78 % (11552)Termination phase: Saturation
% 9.56/2.78
% 9.56/2.78 % (11552)Memory used [KB]: 8187
% 9.56/2.78 % (11552)Time elapsed: 0.296 s
% 9.56/2.78 % (11552)Instructions burned: 922 (million)
% 9.56/2.78 % (11552)------------------------------
% 9.56/2.78 % (11552)------------------------------
% 9.56/2.79 % (11648)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_11076 for (2988ds/68Mi)
% 10.31/2.81 % (11648)Instruction limit reached!
% 10.31/2.81 % (11648)------------------------------
% 10.31/2.81 % (11648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/2.81 % (11648)Termination reason: Unknown
% 10.31/2.81 % (11648)Termination phase: Property scanning
% 10.31/2.81
% 10.31/2.81 % (11648)Memory used [KB]: 2174
% 10.31/2.81 % (11648)Time elapsed: 0.022 s
% 10.31/2.81 % (11648)Instructions burned: 69 (million)
% 10.31/2.81 % (11648)------------------------------
% 10.31/2.81 % (11648)------------------------------
% 10.31/2.82 % (11649)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_11076 for (2987ds/358Mi)
% 10.31/2.86 % (11574)Instruction limit reached!
% 10.31/2.86 % (11574)------------------------------
% 10.31/2.86 % (11574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/2.86 % (11574)Termination reason: Unknown
% 10.31/2.86 % (11574)Termination phase: Saturation
% 10.31/2.86
% 10.31/2.86 % (11574)Memory used [KB]: 8827
% 10.31/2.86 % (11574)Time elapsed: 0.321 s
% 10.31/2.86 % (11574)Instructions burned: 1023 (million)
% 10.31/2.86 % (11574)------------------------------
% 10.31/2.86 % (11574)------------------------------
% 10.31/2.87 % (11650)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_11076 for (2987ds/31Mi)
% 10.31/2.88 % (11650)Instruction limit reached!
% 10.31/2.88 % (11650)------------------------------
% 10.31/2.88 % (11650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/2.88 % (11650)Termination reason: Unknown
% 10.31/2.88 % (11650)Termination phase: Preprocessing 1
% 10.31/2.88
% 10.31/2.88 % (11650)Memory used [KB]: 1791
% 10.31/2.88 % (11650)Time elapsed: 0.011 s
% 10.31/2.88 % (11650)Instructions burned: 33 (million)
% 10.31/2.88 % (11650)------------------------------
% 10.31/2.88 % (11650)------------------------------
% 10.31/2.88 % (11651)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_11076 for (2987ds/279Mi)
% 10.69/2.92 % (11651)Refutation not found, incomplete strategy
% 10.69/2.92 % (11651)------------------------------
% 10.69/2.92 % (11651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/2.92 % (11651)Termination reason: Refutation not found, incomplete strategy
% 10.69/2.92
% 10.69/2.92
% 10.69/2.92 % (11651)Memory used [KB]: 6908
% 10.69/2.92 % (11651)Time elapsed: 0.036 s
% 10.69/2.92 % (11651)Instructions burned: 123 (million)
% 10.69/2.92 % (11651)------------------------------
% 10.69/2.92 % (11651)------------------------------
% 10.69/2.93 % (11649)Instruction limit reached!
% 10.69/2.93 % (11649)------------------------------
% 10.69/2.93 % (11649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/2.93 % (11649)Termination reason: Unknown
% 10.69/2.93 % (11649)Termination phase: Saturation
% 10.69/2.93
% 10.69/2.93 % (11649)Memory used [KB]: 7547
% 10.69/2.93 % (11649)Time elapsed: 0.113 s
% 10.69/2.93 % (11649)Instructions burned: 360 (million)
% 10.69/2.93 % (11649)------------------------------
% 10.69/2.93 % (11649)------------------------------
% 10.69/2.93 % (11652)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_11076 for (2986ds/258Mi)
% 10.69/2.94 % (11653)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_11076 for (2986ds/26Mi)
% 10.69/2.95 % (11653)Instruction limit reached!
% 10.69/2.95 % (11653)------------------------------
% 10.69/2.95 % (11653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/2.95 % (11653)Termination reason: Unknown
% 10.69/2.95 % (11653)Termination phase: shuffling
% 10.69/2.95
% 10.69/2.95 % (11653)Memory used [KB]: 1791
% 10.69/2.95 % (11653)Time elapsed: 0.009 s
% 10.69/2.95 % (11653)Instructions burned: 27 (million)
% 10.69/2.95 % (11653)------------------------------
% 10.69/2.95 % (11653)------------------------------
% 10.69/2.96 % (11654)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_11076 for (2986ds/995Mi)
% 10.69/3.01 % (11652)Instruction limit reached!
% 10.69/3.01 % (11652)------------------------------
% 10.69/3.01 % (11652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/3.01 % (11652)Termination reason: Unknown
% 10.69/3.01 % (11652)Termination phase: Saturation
% 10.69/3.01
% 10.69/3.01 % (11652)Memory used [KB]: 7419
% 10.69/3.01 % (11652)Time elapsed: 0.081 s
% 10.69/3.01 % (11652)Instructions burned: 259 (million)
% 10.69/3.01 % (11652)------------------------------
% 10.69/3.01 % (11652)------------------------------
% 12.74/3.02 % (11655)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_11076 for (2985ds/373Mi)
% 13.36/3.14 % (11655)Instruction limit reached!
% 13.36/3.14 % (11655)------------------------------
% 13.36/3.14 % (11655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.14 % (11655)Termination reason: Unknown
% 13.36/3.14 % (11655)Termination phase: Saturation
% 13.36/3.14
% 13.36/3.14 % (11655)Memory used [KB]: 7803
% 13.36/3.14 % (11655)Time elapsed: 0.140 s
% 13.36/3.14 % (11655)Instructions burned: 374 (million)
% 13.36/3.14 % (11655)------------------------------
% 13.36/3.14 % (11655)------------------------------
% 13.36/3.15 % (11656)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_11076 for (2984ds/253Mi)
% 13.36/3.15 % (11603)Instruction limit reached!
% 13.36/3.15 % (11603)------------------------------
% 13.36/3.15 % (11603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.15 % (11603)Termination reason: Unknown
% 13.36/3.15 % (11603)Termination phase: Saturation
% 13.36/3.15
% 13.36/3.15 % (11603)Memory used [KB]: 11257
% 13.36/3.15 % (11603)Time elapsed: 0.531 s
% 13.36/3.15 % (11603)Instructions burned: 1541 (million)
% 13.36/3.15 % (11603)------------------------------
% 13.36/3.15 % (11603)------------------------------
% 13.36/3.15 % (11646)Instruction limit reached!
% 13.36/3.15 % (11646)------------------------------
% 13.36/3.15 % (11646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.15 % (11646)Termination reason: Unknown
% 13.36/3.15 % (11646)Termination phase: Saturation
% 13.36/3.15
% 13.36/3.15 % (11646)Memory used [KB]: 3965
% 13.36/3.15 % (11646)Time elapsed: 0.447 s
% 13.36/3.15 % (11646)Instructions burned: 1917 (million)
% 13.36/3.15 % (11646)------------------------------
% 13.36/3.15 % (11646)------------------------------
% 13.36/3.16 % (11657)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_11076 for (2984ds/832Mi)
% 13.36/3.16 % (11658)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_11076 for (2984ds/668Mi)
% 13.92/3.22 % (11656)Instruction limit reached!
% 13.92/3.22 % (11656)------------------------------
% 13.92/3.22 % (11656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.22 % (11656)Termination reason: Unknown
% 13.92/3.22 % (11656)Termination phase: Saturation
% 13.92/3.22
% 13.92/3.22 % (11656)Memory used [KB]: 7291
% 13.92/3.22 % (11656)Time elapsed: 0.074 s
% 13.92/3.22 % (11656)Instructions burned: 253 (million)
% 13.92/3.22 % (11656)------------------------------
% 13.92/3.22 % (11656)------------------------------
% 13.92/3.23 % (11659)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_11076 for (2983ds/40Mi)
% 13.92/3.24 % (11659)Instruction limit reached!
% 13.92/3.24 % (11659)------------------------------
% 13.92/3.24 % (11659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.24 % (11659)Termination reason: Unknown
% 13.92/3.24 % (11659)Termination phase: Property scanning
% 13.92/3.24
% 13.92/3.24 % (11659)Memory used [KB]: 2046
% 13.92/3.24 % (11659)Time elapsed: 0.013 s
% 13.92/3.24 % (11659)Instructions burned: 42 (million)
% 13.92/3.24 % (11659)------------------------------
% 13.92/3.24 % (11659)------------------------------
% 13.92/3.25 % (11660)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_11076 for (2983ds/294Mi)
% 13.92/3.26 % (11654)Instruction limit reached!
% 13.92/3.26 % (11654)------------------------------
% 13.92/3.26 % (11654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.26 % (11654)Termination reason: Unknown
% 13.92/3.26 % (11654)Termination phase: Saturation
% 13.92/3.26
% 13.92/3.26 % (11654)Memory used [KB]: 8699
% 13.92/3.26 % (11654)Time elapsed: 0.302 s
% 13.92/3.26 % (11654)Instructions burned: 996 (million)
% 13.92/3.26 % (11654)------------------------------
% 13.92/3.26 % (11654)------------------------------
% 13.92/3.27 % (11661)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_11076 for (2983ds/187Mi)
% 14.39/3.30 % (11660)Refutation not found, incomplete strategy
% 14.39/3.30 % (11660)------------------------------
% 14.39/3.30 % (11660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.39/3.30 % (11660)Termination reason: Refutation not found, incomplete strategy
% 14.39/3.30
% 14.39/3.30
% 14.39/3.30 % (11660)Memory used [KB]: 7164
% 14.39/3.30 % (11660)Time elapsed: 0.053 s
% 14.39/3.30 % (11660)Instructions burned: 182 (million)
% 14.39/3.30 % (11660)------------------------------
% 14.39/3.30 % (11660)------------------------------
% 14.39/3.31 % (11662)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_11076 for (2982ds/371Mi)
% 14.39/3.33 % (11661)Instruction limit reached!
% 14.39/3.33 % (11661)------------------------------
% 14.39/3.33 % (11661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.39/3.33 % (11661)Termination reason: Unknown
% 14.39/3.33 % (11661)Termination phase: Saturation
% 14.39/3.33
% 14.39/3.33 % (11661)Memory used [KB]: 7291
% 14.39/3.33 % (11661)Time elapsed: 0.062 s
% 14.39/3.33 % (11661)Instructions burned: 187 (million)
% 14.39/3.33 % (11661)------------------------------
% 14.39/3.33 % (11661)------------------------------
% 14.39/3.34 % (11663)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_11076 for (2982ds/1827Mi)
% 14.39/3.37 % (11658)Instruction limit reached!
% 14.39/3.37 % (11658)------------------------------
% 14.39/3.37 % (11658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.39/3.37 % (11658)Termination reason: Unknown
% 14.39/3.37 % (11658)Termination phase: Saturation
% 14.39/3.37
% 14.39/3.37 % (11658)Memory used [KB]: 13688
% 14.39/3.37 % (11658)Time elapsed: 0.206 s
% 14.39/3.37 % (11658)Instructions burned: 669 (million)
% 14.39/3.37 % (11658)------------------------------
% 14.39/3.37 % (11658)------------------------------
% 14.39/3.38 % (11664)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_11076 for (2982ds/70Mi)
% 14.39/3.40 % (11664)Instruction limit reached!
% 14.39/3.40 % (11664)------------------------------
% 14.39/3.40 % (11664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.39/3.40 % (11664)Termination reason: Unknown
% 14.39/3.40 % (11664)Termination phase: Preprocessing 3
% 14.39/3.40
% 14.39/3.40 % (11664)Memory used [KB]: 2174
% 14.39/3.40 % (11664)Time elapsed: 0.020 s
% 14.39/3.40 % (11664)Instructions burned: 71 (million)
% 14.39/3.40 % (11664)------------------------------
% 14.39/3.40 % (11664)------------------------------
% 15.07/3.41 % (11665)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_11076 for (2981ds/316Mi)
% 15.07/3.42 % (11657)Instruction limit reached!
% 15.07/3.42 % (11657)------------------------------
% 15.07/3.42 % (11657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.07/3.42 % (11657)Termination reason: Unknown
% 15.07/3.42 % (11657)Termination phase: Saturation
% 15.07/3.42
% 15.07/3.42 % (11657)Memory used [KB]: 8187
% 15.07/3.42 % (11657)Time elapsed: 0.263 s
% 15.07/3.42 % (11657)Instructions burned: 834 (million)
% 15.07/3.42 % (11657)------------------------------
% 15.07/3.42 % (11657)------------------------------
% 15.07/3.43 % (11666)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_11076 for (2981ds/932Mi)
% 15.07/3.43 % (11662)Instruction limit reached!
% 15.07/3.43 % (11662)------------------------------
% 15.07/3.43 % (11662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.07/3.43 % (11662)Termination reason: Unknown
% 15.07/3.43 % (11662)Termination phase: Saturation
% 15.07/3.43
% 15.07/3.43 % (11662)Memory used [KB]: 7547
% 15.07/3.43 % (11662)Time elapsed: 0.122 s
% 15.07/3.43 % (11662)Instructions burned: 371 (million)
% 15.07/3.43 % (11662)------------------------------
% 15.07/3.43 % (11662)------------------------------
% 15.07/3.44 % (11667)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_11076 for (2981ds/4714Mi)
% 15.07/3.46 % (11665)Refutation not found, incomplete strategy
% 15.07/3.46 % (11665)------------------------------
% 15.07/3.46 % (11665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.07/3.46 % (11665)Termination reason: Refutation not found, incomplete strategy
% 15.07/3.46
% 15.07/3.46
% 15.07/3.46 % (11665)Memory used [KB]: 7419
% 15.07/3.46 % (11665)Time elapsed: 0.057 s
% 15.07/3.46 % (11665)Instructions burned: 198 (million)
% 15.07/3.46 % (11665)------------------------------
% 15.07/3.46 % (11665)------------------------------
% 15.07/3.47 % (11668)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_11076 for (2981ds/8250Mi)
% 15.84/3.50 % (11667)Refutation not found, incomplete strategy
% 15.84/3.50 % (11667)------------------------------
% 15.84/3.50 % (11667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.84/3.50 % (11667)Termination reason: Refutation not found, incomplete strategy
% 15.84/3.50
% 15.84/3.50
% 15.84/3.50 % (11667)Memory used [KB]: 7547
% 15.84/3.50 % (11667)Time elapsed: 0.060 s
% 15.84/3.50 % (11667)Instructions burned: 210 (million)
% 15.84/3.50 % (11667)------------------------------
% 15.84/3.50 % (11667)------------------------------
% 15.84/3.51 % (11669)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_11076 for (2980ds/770Mi)
% 15.84/3.54 % (11669)Refutation not found, incomplete strategy
% 15.84/3.54 % (11669)------------------------------
% 15.84/3.54 % (11669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.84/3.54 % (11669)Termination reason: Refutation not found, incomplete strategy
% 15.84/3.54
% 15.84/3.54
% 15.84/3.54 % (11669)Memory used [KB]: 6652
% 15.84/3.54 % (11669)Time elapsed: 0.026 s
% 15.84/3.54 % (11669)Instructions burned: 77 (million)
% 15.84/3.54 % (11669)------------------------------
% 15.84/3.54 % (11669)------------------------------
% 15.84/3.55 % (11670)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_11076 for (2980ds/794Mi)
% 16.56/3.70 % (11666)Instruction limit reached!
% 16.56/3.70 % (11666)------------------------------
% 16.56/3.70 % (11666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.56/3.70 % (11666)Termination reason: Unknown
% 16.56/3.70 % (11666)Termination phase: Saturation
% 16.56/3.70
% 16.56/3.70 % (11666)Memory used [KB]: 9722
% 16.56/3.70 % (11666)Time elapsed: 0.273 s
% 16.56/3.70 % (11666)Instructions burned: 934 (million)
% 16.56/3.70 % (11666)------------------------------
% 16.56/3.70 % (11666)------------------------------
% 16.56/3.71 % (11671)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_11076 for (2978ds/464Mi)
% 16.56/3.79 % (11670)Instruction limit reached!
% 16.56/3.79 % (11670)------------------------------
% 16.56/3.79 % (11670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.56/3.79 % (11670)Termination reason: Unknown
% 16.56/3.79 % (11670)Termination phase: Saturation
% 16.56/3.79
% 16.56/3.79 % (11670)Memory used [KB]: 6140
% 16.56/3.79 % (11670)Time elapsed: 0.245 s
% 16.56/3.79 % (11670)Instructions burned: 795 (million)
% 16.56/3.79 % (11670)------------------------------
% 16.56/3.79 % (11670)------------------------------
% 17.39/3.80 % (11672)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_11076 for (2977ds/1376Mi)
% 17.39/3.82 % (11663)Instruction limit reached!
% 17.39/3.82 % (11663)------------------------------
% 17.39/3.82 % (11663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.39/3.82 % (11663)Termination reason: Unknown
% 17.39/3.82 % (11663)Termination phase: Saturation
% 17.39/3.82
% 17.39/3.82 % (11663)Memory used [KB]: 9083
% 17.39/3.82 % (11663)Time elapsed: 0.488 s
% 17.39/3.82 % (11663)Instructions burned: 1829 (million)
% 17.39/3.82 % (11663)------------------------------
% 17.39/3.82 % (11663)------------------------------
% 17.39/3.83 % (11673)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_11076 for (2977ds/906Mi)
% 17.39/3.86 % (11671)Instruction limit reached!
% 17.39/3.86 % (11671)------------------------------
% 17.39/3.86 % (11671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.39/3.86 % (11671)Termination reason: Unknown
% 17.39/3.86 % (11671)Termination phase: Saturation
% 17.39/3.86
% 17.39/3.86 % (11671)Memory used [KB]: 7547
% 17.39/3.86 % (11671)Time elapsed: 0.148 s
% 17.39/3.86 % (11671)Instructions burned: 465 (million)
% 17.39/3.86 % (11671)------------------------------
% 17.39/3.86 % (11671)------------------------------
% 17.39/3.87 % (11674)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_11076 for (2977ds/434Mi)
% 18.35/3.97 % (11596)Instruction limit reached!
% 18.35/3.97 % (11596)------------------------------
% 18.35/3.97 % (11596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.35/3.97 % (11596)Termination reason: Unknown
% 18.35/3.97 % (11596)Termination phase: Saturation
% 18.35/3.97
% 18.35/3.97 % (11596)Memory used [KB]: 12920
% 18.35/3.97 % (11596)Time elapsed: 1.376 s
% 18.35/3.97 % (11596)Instructions burned: 4436 (million)
% 18.35/3.97 % (11596)------------------------------
% 18.35/3.97 % (11596)------------------------------
% 18.35/3.98 % (11675)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_11076 for (2976ds/865Mi)
% 18.35/4.01 % (11674)Instruction limit reached!
% 18.35/4.01 % (11674)------------------------------
% 18.35/4.01 % (11674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.35/4.01 % (11674)Termination reason: Unknown
% 18.35/4.01 % (11674)Termination phase: Saturation
% 18.35/4.01
% 18.35/4.01 % (11674)Memory used [KB]: 7419
% 18.35/4.01 % (11674)Time elapsed: 0.136 s
% 18.35/4.01 % (11674)Instructions burned: 434 (million)
% 18.35/4.01 % (11674)------------------------------
% 18.35/4.01 % (11674)------------------------------
% 18.35/4.02 % (11676)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_11076 for (2975ds/593Mi)
% 19.83/4.11 % (11647)Instruction limit reached!
% 19.83/4.11 % (11647)------------------------------
% 19.83/4.11 % (11647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.83/4.11 % (11647)Termination reason: Unknown
% 19.83/4.11 % (11647)Termination phase: Saturation
% 19.83/4.11
% 19.83/4.11 % (11647)Memory used [KB]: 13304
% 19.83/4.11 % (11647)Time elapsed: 1.345 s
% 19.83/4.11 % (11647)Instructions burned: 4352 (million)
% 19.83/4.11 % (11647)------------------------------
% 19.83/4.11 % (11647)------------------------------
% 19.83/4.12 % (11677)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_11076 for (2974ds/443Mi)
% 20.44/4.12 % (11608)Instruction limit reached!
% 20.44/4.12 % (11608)------------------------------
% 20.44/4.12 % (11608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.44/4.12 % (11608)Termination reason: Unknown
% 20.44/4.12 % (11608)Termination phase: Saturation
% 20.44/4.12
% 20.44/4.12 % (11608)Memory used [KB]: 15351
% 20.44/4.12 % (11608)Time elapsed: 1.493 s
% 20.44/4.12 % (11608)Instructions burned: 5205 (million)
% 20.44/4.12 % (11608)------------------------------
% 20.44/4.12 % (11608)------------------------------
% 20.44/4.13 % (11678)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_11076 for (2974ds/594Mi)
% 20.44/4.15 % (11673)Instruction limit reached!
% 20.44/4.15 % (11673)------------------------------
% 20.44/4.15 % (11673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.44/4.15 % (11673)Termination reason: Unknown
% 20.44/4.15 % (11673)Termination phase: Saturation
% 20.44/4.15
% 20.44/4.15 % (11673)Memory used [KB]: 10618
% 20.44/4.15 % (11673)Time elapsed: 0.316 s
% 20.44/4.15 % (11673)Instructions burned: 906 (million)
% 20.44/4.15 % (11673)------------------------------
% 20.44/4.15 % (11673)------------------------------
% 20.44/4.16 % (11679)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_11076 for (2974ds/327Mi)
% 20.44/4.19 % (11676)Instruction limit reached!
% 20.44/4.19 % (11676)------------------------------
% 20.44/4.19 % (11676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.44/4.19 % (11676)Termination reason: Unknown
% 20.44/4.19 % (11676)Termination phase: Saturation
% 20.44/4.19
% 20.44/4.19 % (11676)Memory used [KB]: 9083
% 20.44/4.19 % (11676)Time elapsed: 0.178 s
% 20.44/4.19 % (11676)Instructions burned: 594 (million)
% 20.44/4.19 % (11676)------------------------------
% 20.44/4.19 % (11676)------------------------------
% 20.89/4.20 % (11680)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_11076 for (2974ds/5411Mi)
% 20.89/4.21 % (11672)Instruction limit reached!
% 20.89/4.21 % (11672)------------------------------
% 20.89/4.21 % (11672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.21 % (11672)Termination reason: Unknown
% 20.89/4.21 % (11672)Termination phase: Saturation
% 20.89/4.21
% 20.89/4.21 % (11672)Memory used [KB]: 12025
% 20.89/4.21 % (11672)Time elapsed: 0.407 s
% 20.89/4.21 % (11672)Instructions burned: 1377 (million)
% 20.89/4.21 % (11672)------------------------------
% 20.89/4.21 % (11672)------------------------------
% 20.89/4.22 % (11681)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_11076 for (2973ds/1762Mi)
% 20.89/4.24 % (11675)Instruction limit reached!
% 20.89/4.24 % (11675)------------------------------
% 20.89/4.24 % (11675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.24 % (11675)Termination reason: Unknown
% 20.89/4.24 % (11675)Termination phase: Saturation
% 20.89/4.24
% 20.89/4.24 % (11675)Memory used [KB]: 7803
% 20.89/4.24 % (11675)Time elapsed: 0.260 s
% 20.89/4.24 % (11675)Instructions burned: 865 (million)
% 20.89/4.24 % (11675)------------------------------
% 20.89/4.24 % (11675)------------------------------
% 20.89/4.25 % (11682)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_11076 for (2973ds/96Mi)
% 20.89/4.26 % (11677)Instruction limit reached!
% 20.89/4.26 % (11677)------------------------------
% 20.89/4.26 % (11677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.26 % (11677)Termination reason: Unknown
% 20.89/4.26 % (11677)Termination phase: Saturation
% 20.89/4.26
% 20.89/4.26 % (11677)Memory used [KB]: 7931
% 20.89/4.26 % (11677)Time elapsed: 0.167 s
% 20.89/4.26 % (11677)Instructions burned: 444 (million)
% 20.89/4.26 % (11677)------------------------------
% 20.89/4.26 % (11677)------------------------------
% 20.89/4.26 % (11679)Instruction limit reached!
% 20.89/4.26 % (11679)------------------------------
% 20.89/4.26 % (11679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.26 % (11679)Termination reason: Unknown
% 20.89/4.26 % (11679)Termination phase: Saturation
% 20.89/4.26
% 20.89/4.26 % (11679)Memory used [KB]: 7675
% 20.89/4.26 % (11679)Time elapsed: 0.128 s
% 20.89/4.26 % (11679)Instructions burned: 329 (million)
% 20.89/4.26 % (11679)------------------------------
% 20.89/4.26 % (11679)------------------------------
% 20.89/4.27 % (11683)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_11076 for (2973ds/503Mi)
% 20.89/4.27 % (11684)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_11076 for (2973ds/90Mi)
% 20.89/4.28 % (11682)Instruction limit reached!
% 20.89/4.28 % (11682)------------------------------
% 20.89/4.28 % (11682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.28 % (11682)Termination reason: Unknown
% 20.89/4.28 % (11682)Termination phase: Function definition elimination
% 20.89/4.28
% 20.89/4.28 % (11682)Memory used [KB]: 2174
% 20.89/4.28 % (11682)Time elapsed: 0.026 s
% 20.89/4.28 % (11682)Instructions burned: 96 (million)
% 20.89/4.28 % (11682)------------------------------
% 20.89/4.28 % (11682)------------------------------
% 20.89/4.28 % (11685)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_11076 for (2973ds/593Mi)
% 21.38/4.30 % (11684)Instruction limit reached!
% 21.38/4.30 % (11684)------------------------------
% 21.38/4.30 % (11684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.38/4.30 % (11684)Termination reason: Unknown
% 21.38/4.30 % (11684)Termination phase: Saturation
% 21.38/4.30
% 21.38/4.30 % (11684)Memory used [KB]: 6780
% 21.38/4.30 % (11684)Time elapsed: 0.027 s
% 21.38/4.30 % (11684)Instructions burned: 90 (million)
% 21.38/4.30 % (11684)------------------------------
% 21.38/4.30 % (11684)------------------------------
% 21.38/4.31 % (11686)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_11076 for (2972ds/1512Mi)
% 21.38/4.32 % (11678)Instruction limit reached!
% 21.38/4.32 % (11678)------------------------------
% 21.38/4.32 % (11678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.38/4.32 % (11678)Termination reason: Unknown
% 21.38/4.32 % (11678)Termination phase: Saturation
% 21.38/4.32
% 21.38/4.32 % (11678)Memory used [KB]: 8443
% 21.38/4.32 % (11678)Time elapsed: 0.207 s
% 21.38/4.32 % (11678)Instructions burned: 595 (million)
% 21.38/4.32 % (11678)------------------------------
% 21.38/4.32 % (11678)------------------------------
% 21.38/4.33 % (11687)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_11076 for (2972ds/569Mi)
% 21.71/4.43 % (11683)Instruction limit reached!
% 21.71/4.43 % (11683)------------------------------
% 21.71/4.43 % (11683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.71/4.43 % (11683)Termination reason: Unknown
% 21.71/4.43 % (11683)Termination phase: Saturation
% 21.71/4.43
% 21.71/4.43 % (11683)Memory used [KB]: 8059
% 21.71/4.43 % (11683)Time elapsed: 0.159 s
% 21.71/4.43 % (11683)Instructions burned: 506 (million)
% 21.71/4.43 % (11683)------------------------------
% 21.71/4.43 % (11683)------------------------------
% 21.71/4.44 % (11688)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_11076 for (2971ds/501Mi)
% 21.71/4.48 % (11685)Instruction limit reached!
% 21.71/4.48 % (11685)------------------------------
% 21.71/4.48 % (11685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.71/4.48 % (11685)Termination reason: Unknown
% 21.71/4.48 % (11685)Termination phase: Saturation
% 21.71/4.48
% 21.71/4.48 % (11685)Memory used [KB]: 8443
% 21.71/4.48 % (11685)Time elapsed: 0.195 s
% 21.71/4.48 % (11685)Instructions burned: 594 (million)
% 21.71/4.48 % (11685)------------------------------
% 21.71/4.48 % (11685)------------------------------
% 21.71/4.49 % (11689)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_11076 for (2971ds/562Mi)
% 21.71/4.49 % (11687)Instruction limit reached!
% 21.71/4.49 % (11687)------------------------------
% 21.71/4.49 % (11687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.71/4.49 % (11687)Termination reason: Unknown
% 21.71/4.49 % (11687)Termination phase: Saturation
% 21.71/4.49
% 21.71/4.49 % (11687)Memory used [KB]: 7803
% 21.71/4.49 % (11687)Time elapsed: 0.167 s
% 21.71/4.49 % (11687)Instructions burned: 570 (million)
% 21.71/4.49 % (11687)------------------------------
% 21.71/4.49 % (11687)------------------------------
% 22.35/4.50 % (11690)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_11076 for (2970ds/406Mi)
% 22.45/4.60 % (11688)Instruction limit reached!
% 22.45/4.60 % (11688)------------------------------
% 22.45/4.60 % (11688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.45/4.60 % (11688)Termination reason: Unknown
% 22.45/4.60 % (11688)Termination phase: Saturation
% 22.45/4.60
% 22.45/4.60 % (11688)Memory used [KB]: 8571
% 22.45/4.60 % (11688)Time elapsed: 0.160 s
% 22.45/4.60 % (11688)Instructions burned: 502 (million)
% 22.45/4.60 % (11688)------------------------------
% 22.45/4.60 % (11688)------------------------------
% 22.45/4.61 % (11691)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_11076 for (2969ds/582Mi)
% 22.45/4.63 % (11690)Refutation not found, non-redundant clauses discarded% (11690)------------------------------
% 22.45/4.63 % (11690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.45/4.63 % (11690)Termination reason: Refutation not found, non-redundant clauses discarded
% 22.45/4.63
% 22.45/4.63 % (11690)Memory used [KB]: 7675
% 22.45/4.63 % (11690)Time elapsed: 0.129 s
% 22.45/4.63 % (11690)Instructions burned: 401 (million)
% 22.45/4.63 % (11690)------------------------------
% 22.45/4.63 % (11690)------------------------------
% 22.45/4.64 % (11692)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_11076 for (2969ds/456Mi)
% 22.45/4.66 % (11689)Instruction limit reached!
% 22.45/4.66 % (11689)------------------------------
% 22.45/4.66 % (11689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.45/4.66 % (11689)Termination reason: Unknown
% 22.45/4.66 % (11689)Termination phase: Saturation
% 22.45/4.66
% 22.45/4.66 % (11689)Memory used [KB]: 7675
% 22.45/4.66 % (11689)Time elapsed: 0.176 s
% 22.45/4.66 % (11689)Instructions burned: 562 (million)
% 22.45/4.66 % (11689)------------------------------
% 22.45/4.66 % (11689)------------------------------
% 22.45/4.67 % (11693)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_11076 for (2969ds/393Mi)
% 23.05/4.73 % (11681)Instruction limit reached!
% 23.05/4.73 % (11681)------------------------------
% 23.05/4.73 % (11681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.05/4.73 % (11681)Termination reason: Unknown
% 23.05/4.73 % (11681)Termination phase: Saturation
% 23.05/4.73
% 23.05/4.73 % (11681)Memory used [KB]: 9850
% 23.05/4.73 % (11681)Time elapsed: 0.533 s
% 23.05/4.73 % (11681)Instructions burned: 1763 (million)
% 23.05/4.73 % (11681)------------------------------
% 23.05/4.73 % (11681)------------------------------
% 23.05/4.74 % (11694)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_11076 for (2968ds/1335Mi)
% 23.05/4.78 % (11692)Instruction limit reached!
% 23.05/4.78 % (11692)------------------------------
% 23.05/4.78 % (11692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.05/4.78 % (11692)Termination reason: Unknown
% 23.05/4.78 % (11692)Termination phase: Saturation
% 23.05/4.78
% 23.05/4.78 % (11692)Memory used [KB]: 7931
% 23.05/4.78 % (11692)Time elapsed: 0.140 s
% 23.05/4.78 % (11692)Instructions burned: 458 (million)
% 23.05/4.78 % (11692)------------------------------
% 23.05/4.78 % (11692)------------------------------
% 23.05/4.78 % (11693)Instruction limit reached!
% 23.05/4.78 % (11693)------------------------------
% 23.05/4.78 % (11693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.05/4.78 % (11693)Termination reason: Unknown
% 23.05/4.78 % (11693)Termination phase: Saturation
% 23.05/4.78
% 23.05/4.78 % (11693)Memory used [KB]: 7547
% 23.05/4.78 % (11693)Time elapsed: 0.113 s
% 23.05/4.78 % (11693)Instructions burned: 395 (million)
% 23.05/4.78 % (11693)------------------------------
% 23.05/4.78 % (11693)------------------------------
% 23.05/4.79 % (11686)Instruction limit reached!
% 23.05/4.79 % (11686)------------------------------
% 23.05/4.79 % (11686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.05/4.79 % (11686)Termination reason: Unknown
% 23.05/4.79 % (11686)Termination phase: Saturation
% 23.05/4.79
% 23.05/4.79 % (11686)Memory used [KB]: 8699
% 23.05/4.79 % (11686)Time elapsed: 0.477 s
% 23.05/4.79 % (11686)Instructions burned: 1514 (million)
% 23.05/4.79 % (11686)------------------------------
% 23.05/4.79 % (11686)------------------------------
% 23.05/4.79 % (11691)Instruction limit reached!
% 23.05/4.79 % (11691)------------------------------
% 23.05/4.79 % (11691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.05/4.79 % (11691)Termination reason: Unknown
% 23.05/4.79 % (11691)Termination phase: Saturation
% 23.05/4.79
% 23.05/4.79 % (11691)Memory used [KB]: 8059
% 23.05/4.79 % (11691)Time elapsed: 0.181 s
% 23.05/4.79 % (11691)Instructions burned: 582 (million)
% 23.05/4.79 % (11691)------------------------------
% 23.05/4.79 % (11691)------------------------------
% 23.05/4.79 % (11695)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_11076 for (2968ds/3373Mi)
% 23.05/4.79 % (11696)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_11076 for (2968ds/474Mi)
% 23.05/4.80 % (11697)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_11076 for (2968ds/157Mi)
% 24.62/4.80 % (11698)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_11076 for (2968ds/590Mi)
% 24.62/4.84 % (11697)Instruction limit reached!
% 24.62/4.84 % (11697)------------------------------
% 24.62/4.84 % (11697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.62/4.84 % (11697)Termination reason: Unknown
% 24.62/4.84 % (11697)Termination phase: Saturation
% 24.62/4.84
% 24.62/4.84 % (11697)Memory used [KB]: 6780
% 24.62/4.84 % (11697)Time elapsed: 0.043 s
% 24.62/4.84 % (11697)Instructions burned: 158 (million)
% 24.62/4.84 % (11697)------------------------------
% 24.62/4.84 % (11697)------------------------------
% 24.62/4.85 % (11699)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_11076 for (2967ds/104Mi)
% 24.62/4.88 % (11699)Instruction limit reached!
% 24.62/4.88 % (11699)------------------------------
% 24.62/4.88 % (11699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.62/4.88 % (11699)Termination reason: Unknown
% 24.62/4.88 % (11699)Termination phase: Saturation
% 24.62/4.88
% 24.62/4.88 % (11699)Memory used [KB]: 2558
% 24.62/4.88 % (11699)Time elapsed: 0.032 s
% 24.62/4.88 % (11699)Instructions burned: 106 (million)
% 24.62/4.88 % (11699)------------------------------
% 24.62/4.88 % (11699)------------------------------
% 24.62/4.89 % (11700)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_11076 for (2967ds/414Mi)
% 24.82/4.93 % (11696)Instruction limit reached!
% 24.82/4.93 % (11696)------------------------------
% 24.82/4.93 % (11696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.82/4.93 % (11696)Termination reason: Unknown
% 24.82/4.93 % (11696)Termination phase: Saturation
% 24.82/4.93
% 24.82/4.93 % (11696)Memory used [KB]: 7931
% 24.82/4.93 % (11696)Time elapsed: 0.141 s
% 24.82/4.93 % (11696)Instructions burned: 477 (million)
% 24.82/4.93 % (11696)------------------------------
% 24.82/4.93 % (11696)------------------------------
% 24.82/4.94 % (11701)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_11076 for (2966ds/715Mi)
% 24.82/4.97 % (11698)Instruction limit reached!
% 24.82/4.97 % (11698)------------------------------
% 24.82/4.97 % (11698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.82/4.97 % (11698)Termination reason: Unknown
% 24.82/4.97 % (11698)Termination phase: Saturation
% 24.82/4.97
% 24.82/4.97 % (11698)Memory used [KB]: 8315
% 24.82/4.97 % (11698)Time elapsed: 0.176 s
% 24.82/4.97 % (11698)Instructions burned: 590 (million)
% 24.82/4.97 % (11698)------------------------------
% 24.82/4.97 % (11698)------------------------------
% 24.82/4.98 % (11702)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_11076 for (2966ds/961Mi)
% 24.82/5.01 % (11700)Instruction limit reached!
% 24.82/5.01 % (11700)------------------------------
% 24.82/5.01 % (11700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.82/5.01 % (11700)Termination reason: Unknown
% 24.82/5.01 % (11700)Termination phase: Saturation
% 24.82/5.01
% 24.82/5.01 % (11700)Memory used [KB]: 7419
% 24.82/5.01 % (11700)Time elapsed: 0.120 s
% 24.82/5.01 % (11700)Instructions burned: 414 (million)
% 24.82/5.01 % (11700)------------------------------
% 24.82/5.01 % (11700)------------------------------
% 24.82/5.02 % (11703)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_11076 for (2965ds/1213Mi)
% 26.84/5.07 % (11694)Instruction limit reached!
% 26.84/5.07 % (11694)------------------------------
% 26.84/5.07 % (11694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.84/5.07 % (11694)Termination reason: Unknown
% 26.84/5.07 % (11694)Termination phase: Saturation
% 26.84/5.07
% 26.84/5.07 % (11694)Memory used [KB]: 7931
% 26.84/5.07 % (11694)Time elapsed: 0.329 s
% 26.84/5.07 % (11694)Instructions burned: 1337 (million)
% 26.84/5.07 % (11694)------------------------------
% 26.84/5.07 % (11694)------------------------------
% 26.84/5.08 % (11704)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_11076 for (2965ds/1979Mi)
% 27.42/5.17 % (11701)Instruction limit reached!
% 27.42/5.17 % (11701)------------------------------
% 27.42/5.17 % (11701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.42/5.17 % (11701)Termination reason: Unknown
% 27.42/5.17 % (11701)Termination phase: Saturation
% 27.42/5.17
% 27.42/5.17 % (11701)Memory used [KB]: 4861
% 27.42/5.17 % (11701)Time elapsed: 0.226 s
% 27.42/5.17 % (11701)Instructions burned: 716 (million)
% 27.42/5.17 % (11701)------------------------------
% 27.42/5.17 % (11701)------------------------------
% 27.42/5.18 % (11705)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_11076 for (2964ds/481Mi)
% 27.79/5.25 % (11702)Instruction limit reached!
% 27.79/5.25 % (11702)------------------------------
% 27.79/5.25 % (11702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.79/5.25 % (11702)Termination reason: Unknown
% 27.79/5.25 % (11702)Termination phase: Saturation
% 27.79/5.25
% 27.79/5.25 % (11702)Memory used [KB]: 7675
% 27.79/5.25 % (11702)Time elapsed: 0.267 s
% 27.79/5.25 % (11702)Instructions burned: 961 (million)
% 27.79/5.25 % (11702)------------------------------
% 27.79/5.25 % (11702)------------------------------
% 27.79/5.26 % (11706)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_11076 for (2963ds/783Mi)
% 28.14/5.33 % (11705)Instruction limit reached!
% 28.14/5.33 % (11705)------------------------------
% 28.14/5.33 % (11705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.14/5.33 % (11705)Termination reason: Unknown
% 28.14/5.33 % (11705)Termination phase: Saturation
% 28.14/5.33
% 28.14/5.33 % (11705)Memory used [KB]: 7547
% 28.14/5.33 % (11705)Time elapsed: 0.172 s
% 28.14/5.33 % (11705)Instructions burned: 483 (million)
% 28.14/5.33 % (11705)------------------------------
% 28.14/5.33 % (11705)------------------------------
% 28.14/5.34 % (11707)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_11076 for (2962ds/432Mi)
% 28.58/5.41 % (11703)Instruction limit reached!
% 28.58/5.41 % (11703)------------------------------
% 28.58/5.41 % (11703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.58/5.41 % (11703)Termination reason: Unknown
% 28.58/5.41 % (11703)Termination phase: Saturation
% 28.58/5.41
% 28.58/5.41 % (11703)Memory used [KB]: 8955
% 28.58/5.41 % (11703)Time elapsed: 0.414 s
% 28.58/5.41 % (11703)Instructions burned: 1214 (million)
% 28.58/5.41 % (11703)------------------------------
% 28.58/5.41 % (11703)------------------------------
% 28.58/5.42 % (11708)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_11076 for (2961ds/1670Mi)
% 28.58/5.47 % (11707)Instruction limit reached!
% 28.58/5.47 % (11707)------------------------------
% 28.58/5.47 % (11707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.58/5.47 % (11707)Termination reason: Unknown
% 28.58/5.47 % (11707)Termination phase: Saturation
% 28.58/5.47
% 28.58/5.47 % (11707)Memory used [KB]: 7291
% 28.58/5.47 % (11707)Time elapsed: 0.163 s
% 28.58/5.47 % (11707)Instructions burned: 432 (million)
% 28.58/5.47 % (11707)------------------------------
% 28.58/5.47 % (11707)------------------------------
% 28.58/5.48 % (11709)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_11076 for (2961ds/90Mi)
% 29.44/5.51 % (11706)Instruction limit reached!
% 29.44/5.51 % (11706)------------------------------
% 29.44/5.51 % (11706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.51 % (11706)Termination reason: Unknown
% 29.44/5.51 % (11706)Termination phase: Saturation
% 29.44/5.51
% 29.44/5.51 % (11706)Memory used [KB]: 8315
% 29.44/5.51 % (11706)Time elapsed: 0.272 s
% 29.44/5.51 % (11706)Instructions burned: 784 (million)
% 29.44/5.51 % (11706)------------------------------
% 29.44/5.51 % (11706)------------------------------
% 29.44/5.51 % (11709)Instruction limit reached!
% 29.44/5.51 % (11709)------------------------------
% 29.44/5.51 % (11709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.51 % (11709)Termination reason: Unknown
% 29.44/5.51 % (11709)Termination phase: Saturation
% 29.44/5.51
% 29.44/5.51 % (11709)Memory used [KB]: 6780
% 29.44/5.51 % (11709)Time elapsed: 0.027 s
% 29.44/5.51 % (11709)Instructions burned: 91 (million)
% 29.44/5.51 % (11709)------------------------------
% 29.44/5.51 % (11709)------------------------------
% 29.44/5.51 % (11710)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_11076 for (2960ds/346Mi)
% 29.44/5.52 % (11711)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_11076 for (2960ds/401Mi)
% 30.03/5.62 % (11710)Instruction limit reached!
% 30.03/5.62 % (11710)------------------------------
% 30.03/5.62 % (11710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.03/5.62 % (11710)Termination reason: Unknown
% 30.03/5.62 % (11710)Termination phase: Saturation
% 30.03/5.62
% 30.03/5.62 % (11710)Memory used [KB]: 7547
% 30.03/5.62 % (11710)Time elapsed: 0.105 s
% 30.03/5.62 % (11710)Instructions burned: 348 (million)
% 30.03/5.62 % (11710)------------------------------
% 30.03/5.62 % (11710)------------------------------
% 30.03/5.63 % (11712)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_11076 for (2959ds/6454Mi)
% 30.03/5.63 % (11711)Instruction limit reached!
% 30.03/5.63 % (11711)------------------------------
% 30.03/5.63 % (11711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.03/5.63 % (11711)Termination reason: Unknown
% 30.03/5.63 % (11711)Termination phase: Saturation
% 30.03/5.63
% 30.03/5.63 % (11711)Memory used [KB]: 8059
% 30.03/5.63 % (11711)Time elapsed: 0.116 s
% 30.03/5.63 % (11711)Instructions burned: 401 (million)
% 30.03/5.63 % (11711)------------------------------
% 30.03/5.63 % (11711)------------------------------
% 30.03/5.64 % (11713)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_11076 for (2959ds/283Mi)
% 30.57/5.71 % (11704)Instruction limit reached!
% 30.57/5.71 % (11704)------------------------------
% 30.57/5.71 % (11704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.57/5.71 % (11704)Termination reason: Unknown
% 30.57/5.71 % (11704)Termination phase: Saturation
% 30.57/5.71
% 30.57/5.71 % (11704)Memory used [KB]: 8443
% 30.57/5.71 % (11704)Time elapsed: 0.655 s
% 30.57/5.71 % (11704)Instructions burned: 1981 (million)
% 30.57/5.71 % (11704)------------------------------
% 30.57/5.71 % (11704)------------------------------
% 30.57/5.72 % (11714)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_11076 for (2958ds/865Mi)
% 30.57/5.73 % (11713)Instruction limit reached!
% 30.57/5.73 % (11713)------------------------------
% 30.57/5.73 % (11713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.57/5.73 % (11713)Termination reason: Unknown
% 30.57/5.73 % (11713)Termination phase: Saturation
% 30.57/5.73
% 30.57/5.73 % (11713)Memory used [KB]: 7675
% 30.57/5.73 % (11713)Time elapsed: 0.089 s
% 30.57/5.73 % (11713)Instructions burned: 284 (million)
% 30.57/5.73 % (11713)------------------------------
% 30.57/5.73 % (11713)------------------------------
% 30.57/5.74 % (11715)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_11076 for (2958ds/4528Mi)
% 30.57/5.76 % (11715)Refutation not found, incomplete strategy
% 30.57/5.76 % (11715)------------------------------
% 30.57/5.76 % (11715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.57/5.76 % (11715)Termination reason: Refutation not found, incomplete strategy
% 30.57/5.76
% 30.57/5.76
% 30.57/5.76 % (11715)Memory used [KB]: 2046
% 30.57/5.76 % (11715)Time elapsed: 0.018 s
% 30.57/5.76 % (11715)Instructions burned: 54 (million)
% 30.57/5.76 % (11715)------------------------------
% 30.57/5.76 % (11715)------------------------------
% 30.57/5.77 % (11716)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_11076 for (2958ds/1001Mi)
% 31.64/5.84 % (11695)Instruction limit reached!
% 31.64/5.84 % (11695)------------------------------
% 31.64/5.84 % (11695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.64/5.84 % (11695)Termination reason: Unknown
% 31.64/5.84 % (11695)Termination phase: Saturation
% 31.64/5.84
% 31.64/5.84 % (11695)Memory used [KB]: 10746
% 31.64/5.84 % (11695)Time elapsed: 1.046 s
% 31.64/5.84 % (11695)Instructions burned: 3376 (million)
% 31.64/5.84 % (11695)------------------------------
% 31.64/5.84 % (11695)------------------------------
% 31.64/5.85 % (11717)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_11076 for (2957ds/102Mi)
% 31.64/5.87 % (11717)Instruction limit reached!
% 31.64/5.87 % (11717)------------------------------
% 31.64/5.87 % (11717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.64/5.87 % (11717)Termination reason: Unknown
% 31.64/5.87 % (11717)Termination phase: Property scanning
% 31.64/5.87
% 31.64/5.87 % (11717)Memory used [KB]: 2302
% 31.64/5.87 % (11717)Time elapsed: 0.028 s
% 31.64/5.87 % (11717)Instructions burned: 103 (million)
% 31.64/5.87 % (11717)------------------------------
% 31.64/5.87 % (11717)------------------------------
% 31.64/5.88 % (11718)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_11076 for (2957ds/952Mi)
% 31.94/5.92 % (11708)Instruction limit reached!
% 31.94/5.92 % (11708)------------------------------
% 31.94/5.92 % (11708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.92 % (11708)Termination reason: Unknown
% 31.94/5.92 % (11708)Termination phase: Saturation
% 31.94/5.92
% 31.94/5.92 % (11708)Memory used [KB]: 9594
% 31.94/5.92 % (11708)Time elapsed: 0.525 s
% 31.94/5.92 % (11708)Instructions burned: 1671 (million)
% 31.94/5.92 % (11708)------------------------------
% 31.94/5.92 % (11708)------------------------------
% 31.94/5.93 % (11680)Instruction limit reached!
% 31.94/5.93 % (11680)------------------------------
% 31.94/5.93 % (11680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.93 % (11680)Termination reason: Unknown
% 31.94/5.93 % (11680)Termination phase: Saturation
% 31.94/5.93
% 31.94/5.93 % (11680)Memory used [KB]: 11513
% 31.94/5.93 % (11680)Time elapsed: 1.748 s
% 31.94/5.93 % (11680)Instructions burned: 5412 (million)
% 31.94/5.93 % (11680)------------------------------
% 31.94/5.93 % (11680)------------------------------
% 31.94/5.93 % (11719)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_11076 for (2956ds/578Mi)
% 31.94/5.94 % (11720)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_11076 for (2956ds/643Mi)
% 31.94/5.99 % (11714)Instruction limit reached!
% 31.94/5.99 % (11714)------------------------------
% 31.94/5.99 % (11714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.99 % (11714)Termination reason: Unknown
% 31.94/5.99 % (11714)Termination phase: Saturation
% 31.94/5.99
% 31.94/5.99 % (11714)Memory used [KB]: 9338
% 31.94/5.99 % (11714)Time elapsed: 0.275 s
% 31.94/5.99 % (11714)Instructions burned: 866 (million)
% 31.94/5.99 % (11714)------------------------------
% 31.94/5.99 % (11714)------------------------------
% 31.94/6.00 % (11721)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_11076 for (2956ds/865Mi)
% 33.88/6.06 % (11668)Instruction limit reached!
% 33.88/6.06 % (11668)------------------------------
% 33.88/6.06 % (11668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.88/6.06 % (11668)Termination reason: Unknown
% 33.88/6.06 % (11668)Termination phase: Saturation
% 33.88/6.06
% 33.88/6.06 % (11668)Memory used [KB]: 14967
% 33.88/6.06 % (11668)Time elapsed: 2.590 s
% 33.88/6.06 % (11668)Instructions burned: 8252 (million)
% 33.88/6.06 % (11668)------------------------------
% 33.88/6.06 % (11668)------------------------------
% 33.88/6.07 % (11722)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_11076 for (2955ds/1174Mi)
% 33.88/6.08 % (11716)Instruction limit reached!
% 33.88/6.08 % (11716)------------------------------
% 33.88/6.08 % (11716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.88/6.08 % (11716)Termination reason: Unknown
% 33.88/6.08 % (11716)Termination phase: Saturation
% 33.88/6.08
% 33.88/6.08 % (11716)Memory used [KB]: 9978
% 33.88/6.08 % (11716)Time elapsed: 0.307 s
% 33.88/6.08 % (11716)Instructions burned: 1002 (million)
% 33.88/6.08 % (11716)------------------------------
% 33.88/6.08 % (11716)------------------------------
% 33.88/6.08 % (11723)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_11076 for (2955ds/644Mi)
% 33.88/6.10 % (11719)Instruction limit reached!
% 33.88/6.10 % (11719)------------------------------
% 33.88/6.10 % (11719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.88/6.10 % (11719)Termination reason: Unknown
% 33.88/6.10 % (11719)Termination phase: Saturation
% 33.88/6.10
% 33.88/6.10 % (11719)Memory used [KB]: 8315
% 33.88/6.10 % (11719)Time elapsed: 0.173 s
% 33.88/6.10 % (11719)Instructions burned: 580 (million)
% 33.88/6.10 % (11719)------------------------------
% 33.88/6.10 % (11719)------------------------------
% 33.88/6.11 % (11724)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_11076 for (2954ds/1201Mi)
% 34.51/6.13 % (11720)Instruction limit reached!
% 34.51/6.13 % (11720)------------------------------
% 34.51/6.13 % (11720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.51/6.13 % (11720)Termination reason: Unknown
% 34.51/6.13 % (11720)Termination phase: Saturation
% 34.51/6.13
% 34.51/6.13 % (11720)Memory used [KB]: 8443
% 34.51/6.13 % (11720)Time elapsed: 0.194 s
% 34.51/6.13 % (11720)Instructions burned: 644 (million)
% 34.51/6.13 % (11720)------------------------------
% 34.51/6.13 % (11720)------------------------------
% 34.51/6.14 % (11725)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_11076 for (2954ds/1046Mi)
% 34.51/6.18 % (11718)Instruction limit reached!
% 34.51/6.18 % (11718)------------------------------
% 34.51/6.18 % (11718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.51/6.18 % (11718)Termination reason: Unknown
% 34.51/6.18 % (11718)Termination phase: Saturation
% 34.51/6.18
% 34.51/6.18 % (11718)Memory used [KB]: 9083
% 34.51/6.18 % (11718)Time elapsed: 0.300 s
% 34.51/6.18 % (11718)Instructions burned: 954 (million)
% 34.51/6.18 % (11718)------------------------------
% 34.51/6.18 % (11718)------------------------------
% 34.51/6.19 % (11726)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_11076 for (2954ds/222Mi)
% 34.73/6.25 % (11721)Refutation not found, non-redundant clauses discarded% (11721)------------------------------
% 34.73/6.25 % (11721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.73/6.25 % (11721)Termination reason: Refutation not found, non-redundant clauses discarded
% 34.73/6.25
% 34.73/6.25 % (11721)Memory used [KB]: 8443
% 34.73/6.25 % (11721)Time elapsed: 0.250 s
% 34.73/6.25 % (11721)Instructions burned: 803 (million)
% 34.73/6.25 % (11721)------------------------------
% 34.73/6.25 % (11721)------------------------------
% 34.73/6.25 % (11726)Instruction limit reached!
% 34.73/6.25 % (11726)------------------------------
% 34.73/6.25 % (11726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.73/6.25 % (11726)Termination reason: Unknown
% 34.73/6.25 % (11726)Termination phase: Saturation
% 34.73/6.25
% 34.73/6.25 % (11726)Memory used [KB]: 7291
% 34.73/6.25 % (11726)Time elapsed: 0.063 s
% 34.73/6.25 % (11726)Instructions burned: 223 (million)
% 34.73/6.25 % (11726)------------------------------
% 34.73/6.25 % (11726)------------------------------
% 34.73/6.26 % (11727)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_11076 for (2953ds/68Mi)
% 34.73/6.26 % (11728)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_11076 for (2953ds/454Mi)
% 34.73/6.28 % (11727)Instruction limit reached!
% 34.73/6.28 % (11727)------------------------------
% 34.73/6.28 % (11727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.73/6.28 % (11727)Termination reason: Unknown
% 34.73/6.28 % (11727)Termination phase: Property scanning
% 34.73/6.28
% 34.73/6.28 % (11727)Memory used [KB]: 2174
% 34.73/6.28 % (11727)Time elapsed: 0.022 s
% 34.73/6.28 % (11727)Instructions burned: 69 (million)
% 34.73/6.28 % (11727)------------------------------
% 34.73/6.28 % (11727)------------------------------
% 34.73/6.29 % (11723)Instruction limit reached!
% 34.73/6.29 % (11723)------------------------------
% 34.73/6.29 % (11723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.73/6.29 % (11723)Termination reason: Unknown
% 34.73/6.29 % (11723)Termination phase: Saturation
% 34.73/6.29
% 34.73/6.29 % (11723)Memory used [KB]: 8955
% 34.73/6.29 % (11723)Time elapsed: 0.203 s
% 34.73/6.29 % (11723)Instructions burned: 644 (million)
% 34.73/6.29 % (11723)------------------------------
% 34.73/6.29 % (11723)------------------------------
% 34.73/6.29 % (11729)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_11076 for (2953ds/360Mi)
% 35.21/6.30 % (11730)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_11076 for (2953ds/157Mi)
% 35.21/6.34 % (11730)Instruction limit reached!
% 35.21/6.34 % (11730)------------------------------
% 35.21/6.34 % (11730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.21/6.34 % (11730)Termination reason: Unknown
% 35.21/6.34 % (11730)Termination phase: Saturation
% 35.21/6.34
% 35.21/6.34 % (11730)Memory used [KB]: 6780
% 35.21/6.34 % (11730)Time elapsed: 0.044 s
% 35.21/6.34 % (11730)Instructions burned: 157 (million)
% 35.21/6.34 % (11730)------------------------------
% 35.21/6.34 % (11730)------------------------------
% 35.21/6.35 % (11731)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_11076 for (2952ds/5061Mi)
% 35.21/6.39 % (11729)Instruction limit reached!
% 35.21/6.39 % (11729)------------------------------
% 35.21/6.39 % (11729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.21/6.39 % (11729)Termination reason: Unknown
% 35.21/6.39 % (11729)Termination phase: Saturation
% 35.21/6.39
% 35.21/6.39 % (11729)Memory used [KB]: 7931
% 35.21/6.39 % (11729)Time elapsed: 0.104 s
% 35.21/6.39 % (11729)Instructions burned: 361 (million)
% 35.21/6.39 % (11729)------------------------------
% 35.21/6.39 % (11729)------------------------------
% 35.48/6.40 % (11728)Instruction limit reached!
% 35.48/6.40 % (11728)------------------------------
% 35.48/6.40 % (11728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.40 % (11728)Termination reason: Unknown
% 35.48/6.40 % (11728)Termination phase: Saturation
% 35.48/6.40
% 35.48/6.40 % (11728)Memory used [KB]: 12537
% 35.48/6.40 % (11728)Time elapsed: 0.137 s
% 35.48/6.40 % (11728)Instructions burned: 454 (million)
% 35.48/6.40 % (11728)------------------------------
% 35.48/6.40 % (11728)------------------------------
% 35.48/6.40 % (11732)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_11076 for (2951ds/2401Mi)
% 35.48/6.41 % (11733)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_11076 for (2951ds/5798Mi)
% 35.48/6.44 % (11722)Instruction limit reached!
% 35.48/6.44 % (11722)------------------------------
% 35.48/6.44 % (11722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.44 % (11722)Termination reason: Unknown
% 35.48/6.44 % (11722)Termination phase: Saturation
% 35.48/6.44
% 35.48/6.44 % (11722)Memory used [KB]: 8955
% 35.48/6.44 % (11722)Time elapsed: 0.367 s
% 35.48/6.44 % (11722)Instructions burned: 1174 (million)
% 35.48/6.44 % (11722)------------------------------
% 35.48/6.44 % (11722)------------------------------
% 35.48/6.45 % (11734)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_11076 for (2951ds/346Mi)
% 35.48/6.45 % (11725)Instruction limit reached!
% 35.48/6.45 % (11725)------------------------------
% 35.48/6.45 % (11725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.45 % (11725)Termination reason: Unknown
% 35.48/6.45 % (11725)Termination phase: Saturation
% 35.48/6.45
% 35.48/6.45 % (11725)Memory used [KB]: 8827
% 35.48/6.45 % (11725)Time elapsed: 0.312 s
% 35.48/6.45 % (11725)Instructions burned: 1046 (million)
% 35.48/6.45 % (11725)------------------------------
% 35.48/6.45 % (11725)------------------------------
% 35.48/6.46 % (11735)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_11076 for (2951ds/1321Mi)
% 35.48/6.47 % (11724)Instruction limit reached!
% 35.48/6.47 % (11724)------------------------------
% 35.48/6.47 % (11724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.47 % (11724)Termination reason: Unknown
% 35.48/6.47 % (11724)Termination phase: Saturation
% 35.48/6.47
% 35.48/6.47 % (11724)Memory used [KB]: 8571
% 35.48/6.47 % (11724)Time elapsed: 0.365 s
% 35.48/6.47 % (11724)Instructions burned: 1202 (million)
% 35.48/6.47 % (11724)------------------------------
% 35.48/6.47 % (11724)------------------------------
% 35.48/6.48 % (11736)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_11076 for (2951ds/1312Mi)
% 36.80/6.55 % (11734)Instruction limit reached!
% 36.80/6.55 % (11734)------------------------------
% 36.80/6.55 % (11734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.80/6.55 % (11734)Termination reason: Unknown
% 36.80/6.55 % (11734)Termination phase: Saturation
% 36.80/6.55
% 36.80/6.55 % (11734)Memory used [KB]: 7547
% 36.80/6.55 % (11734)Time elapsed: 0.106 s
% 36.80/6.55 % (11734)Instructions burned: 349 (million)
% 36.80/6.55 % (11734)------------------------------
% 36.80/6.55 % (11734)------------------------------
% 36.80/6.56 % (11737)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_11076 for (2950ds/672Mi)
% 37.12/6.77 % (11737)Instruction limit reached!
% 37.12/6.77 % (11737)------------------------------
% 37.12/6.77 % (11737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.12/6.77 % (11737)Termination reason: Unknown
% 37.12/6.77 % (11737)Termination phase: Saturation
% 37.12/6.77
% 37.12/6.77 % (11737)Memory used [KB]: 8699
% 37.12/6.77 % (11737)Time elapsed: 0.212 s
% 37.12/6.77 % (11737)Instructions burned: 673 (million)
% 37.12/6.77 % (11737)------------------------------
% 37.12/6.77 % (11737)------------------------------
% 37.12/6.78 % (11738)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_11076 for (2948ds/1897Mi)
% 37.44/6.87 % (11735)Instruction limit reached!
% 37.44/6.87 % (11735)------------------------------
% 37.44/6.87 % (11735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.44/6.87 % (11735)Termination reason: Unknown
% 37.44/6.87 % (11735)Termination phase: Saturation
% 37.44/6.87
% 37.44/6.87 % (11735)Memory used [KB]: 5117
% 37.44/6.87 % (11735)Time elapsed: 0.409 s
% 37.44/6.87 % (11735)Instructions burned: 1323 (million)
% 37.44/6.87 % (11735)------------------------------
% 37.44/6.87 % (11735)------------------------------
% 37.44/6.88 % (11739)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_11076 for (2947ds/1202Mi)
% 37.44/6.89 % (11736)Instruction limit reached!
% 37.44/6.89 % (11736)------------------------------
% 37.44/6.89 % (11736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.44/6.89 % (11736)Termination reason: Unknown
% 37.44/6.89 % (11736)Termination phase: Saturation
% 37.44/6.89
% 37.44/6.89 % (11736)Memory used [KB]: 8827
% 37.44/6.89 % (11736)Time elapsed: 0.408 s
% 37.44/6.89 % (11736)Instructions burned: 1314 (million)
% 37.44/6.89 % (11736)------------------------------
% 37.44/6.89 % (11736)------------------------------
% 38.38/6.90 % (11740)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_11076 for (2947ds/1493Mi)
% 38.38/6.93 % (11740)Refutation not found, incomplete strategy
% 38.38/6.93 % (11740)------------------------------
% 38.38/6.93 % (11740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.38/6.93 % (11740)Termination reason: Refutation not found, incomplete strategy
% 38.38/6.93
% 38.38/6.93
% 38.38/6.93 % (11740)Memory used [KB]: 6908
% 38.38/6.93 % (11740)Time elapsed: 0.034 s
% 38.38/6.93 % (11740)Instructions burned: 117 (million)
% 38.38/6.93 % (11740)------------------------------
% 38.38/6.93 % (11740)------------------------------
% 38.38/6.94 % (11741)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_11076 for (2946ds/7679Mi)
% 41.64/7.16 % (11732)Instruction limit reached!
% 41.64/7.16 % (11732)------------------------------
% 41.64/7.16 % (11732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.64/7.16 % (11732)Termination reason: Unknown
% 41.64/7.16 % (11732)Termination phase: Saturation
% 41.64/7.16
% 41.64/7.16 % (11732)Memory used [KB]: 7164
% 41.64/7.16 % (11732)Time elapsed: 0.756 s
% 41.64/7.16 % (11732)Instructions burned: 2402 (million)
% 41.64/7.16 % (11732)------------------------------
% 41.64/7.16 % (11732)------------------------------
% 41.64/7.17 % (11742)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_11076 for (2944ds/340Mi)
% 42.13/7.25 % (11739)Instruction limit reached!
% 42.13/7.25 % (11739)------------------------------
% 42.13/7.25 % (11739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.13/7.25 % (11739)Termination reason: Unknown
% 42.13/7.25 % (11739)Termination phase: Saturation
% 42.13/7.25
% 42.13/7.25 % (11739)Memory used [KB]: 4349
% 42.13/7.25 % (11739)Time elapsed: 0.371 s
% 42.13/7.25 % (11739)Instructions burned: 1202 (million)
% 42.13/7.25 % (11739)------------------------------
% 42.13/7.25 % (11739)------------------------------
% 42.13/7.26 % (11743)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_11076 for (2943ds/3672Mi)
% 42.13/7.27 % (11742)Instruction limit reached!
% 42.13/7.27 % (11742)------------------------------
% 42.13/7.27 % (11742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.13/7.27 % (11742)Termination reason: Unknown
% 42.13/7.27 % (11742)Termination phase: Saturation
% 42.13/7.27
% 42.13/7.27 % (11742)Memory used [KB]: 8571
% 42.13/7.27 % (11742)Time elapsed: 0.105 s
% 42.13/7.27 % (11742)Instructions burned: 341 (million)
% 42.13/7.27 % (11742)------------------------------
% 42.13/7.27 % (11742)------------------------------
% 42.13/7.28 % (11744)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_11076 for (2943ds/1535Mi)
% 42.79/7.38 % (11738)Instruction limit reached!
% 42.79/7.38 % (11738)------------------------------
% 42.79/7.38 % (11738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.79/7.38 % (11738)Termination reason: Unknown
% 42.79/7.38 % (11738)Termination phase: Saturation
% 42.79/7.38
% 42.79/7.38 % (11738)Memory used [KB]: 9850
% 42.79/7.38 % (11738)Time elapsed: 0.601 s
% 42.79/7.38 % (11738)Instructions burned: 1898 (million)
% 42.79/7.38 % (11738)------------------------------
% 42.79/7.38 % (11738)------------------------------
% 42.79/7.39 % (11745)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_11076 for (2941ds/4637Mi)
% 44.09/7.67 % (11712)Instruction limit reached!
% 44.09/7.67 % (11712)------------------------------
% 44.09/7.67 % (11712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.09/7.67 % (11712)Termination reason: Unknown
% 44.09/7.67 % (11712)Termination phase: Saturation
% 44.09/7.67
% 44.09/7.67 % (11712)Memory used [KB]: 11641
% 44.09/7.67 % (11712)Time elapsed: 2.038 s
% 44.09/7.67 % (11712)Instructions burned: 6454 (million)
% 44.09/7.67 % (11712)------------------------------
% 44.09/7.67 % (11712)------------------------------
% 44.09/7.68 % (11746)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_11076 for (2939ds/3174Mi)
% 44.47/7.73 % (11744)Instruction limit reached!
% 44.47/7.73 % (11744)------------------------------
% 44.47/7.73 % (11744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.47/7.73 % (11744)Termination reason: Unknown
% 44.47/7.73 % (11744)Termination phase: Saturation
% 44.47/7.73
% 44.47/7.73 % (11744)Memory used [KB]: 10490
% 44.47/7.73 % (11744)Time elapsed: 0.451 s
% 44.47/7.73 % (11744)Instructions burned: 1537 (million)
% 44.47/7.73 % (11744)------------------------------
% 44.47/7.73 % (11744)------------------------------
% 44.47/7.74 % (11747)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_11076 for (2938ds/307Mi)
% 45.24/7.83 % (11747)Instruction limit reached!
% 45.24/7.83 % (11747)------------------------------
% 45.24/7.83 % (11747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.24/7.83 % (11747)Termination reason: Unknown
% 45.24/7.83 % (11747)Termination phase: Saturation
% 45.24/7.83
% 45.24/7.83 % (11747)Memory used [KB]: 7291
% 45.24/7.83 % (11747)Time elapsed: 0.091 s
% 45.24/7.83 % (11747)Instructions burned: 309 (million)
% 45.24/7.83 % (11747)------------------------------
% 45.24/7.83 % (11747)------------------------------
% 45.24/7.84 % (11748)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_11076 for (2937ds/3619Mi)
% 45.24/7.89 % (11731)Instruction limit reached!
% 45.24/7.89 % (11731)------------------------------
% 45.24/7.89 % (11731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.24/7.89 % (11731)Termination reason: Unknown
% 45.24/7.89 % (11731)Termination phase: Saturation
% 45.24/7.89
% 45.24/7.89 % (11731)Memory used [KB]: 11769
% 45.24/7.89 % (11731)Time elapsed: 1.545 s
% 45.24/7.89 % (11731)Instructions burned: 5064 (million)
% 45.24/7.89 % (11731)------------------------------
% 45.24/7.89 % (11731)------------------------------
% 45.65/7.90 % (11749)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_11076 for (2936ds/2325Mi)
% 49.17/8.20 % (11733)Instruction limit reached!
% 49.17/8.20 % (11733)------------------------------
% 49.17/8.20 % (11733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.17/8.20 % (11733)Termination reason: Unknown
% 49.17/8.20 % (11733)Termination phase: Saturation
% 49.17/8.20
% 49.17/8.20 % (11733)Memory used [KB]: 10746
% 49.17/8.20 % (11733)Time elapsed: 1.796 s
% 49.17/8.20 % (11733)Instructions burned: 5800 (million)
% 49.17/8.20 % (11733)------------------------------
% 49.17/8.20 % (11733)------------------------------
% 49.17/8.22 % (11750)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_11076 for (2933ds/2341Mi)
% 50.39/8.41 % (11743)Instruction limit reached!
% 50.39/8.41 % (11743)------------------------------
% 50.39/8.41 % (11743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.39/8.41 % (11743)Termination reason: Unknown
% 50.39/8.41 % (11743)Termination phase: Saturation
% 50.39/8.41
% 50.39/8.41 % (11743)Memory used [KB]: 12025
% 50.39/8.41 % (11743)Time elapsed: 1.182 s
% 50.39/8.41 % (11743)Instructions burned: 3674 (million)
% 50.39/8.41 % (11743)------------------------------
% 50.39/8.41 % (11743)------------------------------
% 50.39/8.43 % (11751)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_11076 for (2931ds/7257Mi)
% 51.40/8.63 % (11749)Instruction limit reached!
% 51.40/8.63 % (11749)------------------------------
% 51.40/8.63 % (11749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.40/8.63 % (11749)Termination reason: Unknown
% 51.40/8.63 % (11749)Termination phase: Saturation
% 51.40/8.63
% 51.40/8.63 % (11749)Memory used [KB]: 10874
% 51.40/8.63 % (11749)Time elapsed: 0.732 s
% 51.40/8.63 % (11749)Instructions burned: 2326 (million)
% 51.40/8.63 % (11749)------------------------------
% 51.40/8.63 % (11749)------------------------------
% 51.40/8.64 % (11752)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_11076 for (2929ds/3710Mi)
% 51.40/8.68 % (11746)Instruction limit reached!
% 51.40/8.68 % (11746)------------------------------
% 51.40/8.68 % (11746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.40/8.68 % (11746)Termination reason: Unknown
% 51.40/8.68 % (11746)Termination phase: Saturation
% 51.40/8.68
% 51.40/8.68 % (11746)Memory used [KB]: 12409
% 51.40/8.68 % (11746)Time elapsed: 1.009 s
% 51.40/8.68 % (11746)Instructions burned: 3174 (million)
% 51.40/8.68 % (11746)------------------------------
% 51.40/8.68 % (11746)------------------------------
% 51.40/8.69 % (11753)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_11076 for (2929ds/326Mi)
% 52.16/8.80 % (11753)Instruction limit reached!
% 52.16/8.80 % (11753)------------------------------
% 52.16/8.80 % (11753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.16/8.80 % (11753)Termination reason: Unknown
% 52.16/8.80 % (11753)Termination phase: Saturation
% 52.16/8.80
% 52.16/8.80 % (11753)Memory used [KB]: 7164
% 52.16/8.80 % (11753)Time elapsed: 0.110 s
% 52.16/8.80 % (11753)Instructions burned: 327 (million)
% 52.16/8.80 % (11753)------------------------------
% 52.16/8.80 % (11753)------------------------------
% 52.16/8.81 % (11754)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_11076 for (2927ds/1100Mi)
% 52.16/8.82 % (11745)Instruction limit reached!
% 52.16/8.82 % (11745)------------------------------
% 52.16/8.82 % (11745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.16/8.82 % (11745)Termination reason: Unknown
% 52.16/8.82 % (11745)Termination phase: Saturation
% 52.16/8.82
% 52.16/8.82 % (11745)Memory used [KB]: 13432
% 52.16/8.82 % (11745)Time elapsed: 1.430 s
% 52.16/8.82 % (11745)Instructions burned: 4637 (million)
% 52.16/8.82 % (11745)------------------------------
% 52.16/8.82 % (11745)------------------------------
% 52.16/8.83 % (11755)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_11076 for (2927ds/406Mi)
% 52.51/8.93 % (11748)Instruction limit reached!
% 52.51/8.93 % (11748)------------------------------
% 52.51/8.93 % (11748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.51/8.93 % (11748)Termination reason: Unknown
% 52.51/8.93 % (11748)Termination phase: Saturation
% 52.51/8.93
% 52.51/8.93 % (11748)Memory used [KB]: 15863
% 52.51/8.93 % (11748)Time elapsed: 1.092 s
% 52.51/8.93 % (11748)Instructions burned: 3620 (million)
% 52.51/8.93 % (11748)------------------------------
% 52.51/8.93 % (11748)------------------------------
% 52.51/8.94 % (11756)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_11076 for (2926ds/1871Mi)
% 52.51/8.96 % (11755)Instruction limit reached!
% 52.51/8.96 % (11755)------------------------------
% 52.51/8.96 % (11755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.51/8.96 % (11755)Termination reason: Unknown
% 52.51/8.96 % (11755)Termination phase: Saturation
% 52.51/8.96
% 52.51/8.96 % (11755)Memory used [KB]: 7803
% 52.51/8.96 % (11755)Time elapsed: 0.129 s
% 52.51/8.96 % (11755)Instructions burned: 408 (million)
% 52.51/8.96 % (11755)------------------------------
% 52.51/8.96 % (11755)------------------------------
% 52.51/8.96 % (11750)Instruction limit reached!
% 52.51/8.96 % (11750)------------------------------
% 52.51/8.96 % (11750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.51/8.96 % (11750)Termination reason: Unknown
% 52.51/8.96 % (11750)Termination phase: Saturation
% 52.51/8.96
% 52.51/8.96 % (11750)Memory used [KB]: 9338
% 52.51/8.96 % (11750)Time elapsed: 0.746 s
% 52.51/8.96 % (11750)Instructions burned: 2341 (million)
% 52.51/8.96 % (11750)------------------------------
% 52.51/8.96 % (11750)------------------------------
% 52.51/8.97 % (11757)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_11076 for (2926ds/1194Mi)
% 52.51/8.97 % (11758)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_11076 for (2926ds/474Mi)
% 54.94/9.11 % (11758)Instruction limit reached!
% 54.94/9.11 % (11758)------------------------------
% 54.94/9.11 % (11758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.94/9.11 % (11758)Termination reason: Unknown
% 54.94/9.11 % (11758)Termination phase: Saturation
% 54.94/9.11
% 54.94/9.11 % (11758)Memory used [KB]: 7931
% 54.94/9.11 % (11758)Time elapsed: 0.167 s
% 54.94/9.11 % (11758)Instructions burned: 475 (million)
% 54.94/9.11 % (11758)------------------------------
% 54.94/9.11 % (11758)------------------------------
% 54.94/9.12 % (11759)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_11076 for (2924ds/3115Mi)
% 55.67/9.16 % (11754)Instruction limit reached!
% 55.67/9.16 % (11754)------------------------------
% 55.67/9.16 % (11754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.67/9.16 % (11754)Termination reason: Unknown
% 55.67/9.16 % (11754)Termination phase: Saturation
% 55.67/9.16
% 55.67/9.16 % (11754)Memory used [KB]: 10234
% 55.67/9.16 % (11754)Time elapsed: 0.351 s
% 55.67/9.16 % (11754)Instructions burned: 1102 (million)
% 55.67/9.16 % (11754)------------------------------
% 55.67/9.16 % (11754)------------------------------
% 55.67/9.17 % (11760)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_11076 for (2924ds/831Mi)
% 56.09/9.23 % (11741)Instruction limit reached!
% 56.09/9.23 % (11741)------------------------------
% 56.09/9.23 % (11741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.09/9.23 % (11741)Termination reason: Unknown
% 56.09/9.23 % (11741)Termination phase: Saturation
% 56.09/9.23
% 56.09/9.23 % (11741)Memory used [KB]: 15479
% 56.09/9.23 % (11741)Time elapsed: 2.291 s
% 56.09/9.23 % (11741)Instructions burned: 7679 (million)
% 56.09/9.23 % (11741)------------------------------
% 56.09/9.23 % (11741)------------------------------
% 56.09/9.25 % (11761)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_11076 for (2923ds/1188Mi)
% 56.54/9.35 % (11757)Instruction limit reached!
% 56.54/9.35 % (11757)------------------------------
% 56.54/9.35 % (11757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.54/9.35 % (11757)Termination reason: Unknown
% 56.54/9.35 % (11757)Termination phase: Saturation
% 56.54/9.35
% 56.54/9.35 % (11757)Memory used [KB]: 8827
% 56.54/9.35 % (11757)Time elapsed: 0.401 s
% 56.54/9.35 % (11757)Instructions burned: 1195 (million)
% 56.54/9.35 % (11757)------------------------------
% 56.54/9.35 % (11757)------------------------------
% 56.54/9.36 % (11762)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_11076 for (2922ds/2868Mi)
% 56.89/9.43 % (11762)Refutation not found, incomplete strategy
% 56.89/9.43 % (11762)------------------------------
% 56.89/9.43 % (11762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.89/9.43 % (11762)Termination reason: Refutation not found, incomplete strategy
% 56.89/9.43
% 56.89/9.43
% 56.89/9.43 % (11762)Memory used [KB]: 7803
% 56.89/9.43 % (11762)Time elapsed: 0.070 s
% 56.89/9.43 % (11762)Instructions burned: 239 (million)
% 56.89/9.43 % (11762)------------------------------
% 56.89/9.43 % (11762)------------------------------
% 56.89/9.43 % (11760)Instruction limit reached!
% 56.89/9.43 % (11760)------------------------------
% 56.89/9.43 % (11760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.89/9.43 % (11760)Termination reason: Unknown
% 56.89/9.43 % (11760)Termination phase: Saturation
% 56.89/9.43
% 56.89/9.43 % (11760)Memory used [KB]: 8955
% 56.89/9.43 % (11760)Time elapsed: 0.261 s
% 56.89/9.43 % (11760)Instructions burned: 832 (million)
% 56.89/9.43 % (11760)------------------------------
% 56.89/9.43 % (11760)------------------------------
% 56.89/9.44 % (11763)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_11076 for (2921ds/1516Mi)
% 56.89/9.44 % (11764)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_11076 for (2921ds/2321Mi)
% 57.56/9.50 % (11764)Refutation not found, incomplete strategy
% 57.56/9.50 % (11764)------------------------------
% 57.56/9.50 % (11764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.56/9.50 % (11764)Termination reason: Refutation not found, incomplete strategy
% 57.56/9.50
% 57.56/9.50
% 57.56/9.50 % (11764)Memory used [KB]: 7547
% 57.56/9.50 % (11764)Time elapsed: 0.061 s
% 57.56/9.50 % (11764)Instructions burned: 218 (million)
% 57.56/9.50 % (11764)------------------------------
% 57.56/9.50 % (11764)------------------------------
% 57.56/9.51 % (11765)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_11076 for (2920ds/2812Mi)
% 57.56/9.53 % (11756)Instruction limit reached!
% 57.56/9.53 % (11756)------------------------------
% 57.56/9.53 % (11756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.56/9.53 % (11756)Termination reason: Unknown
% 57.56/9.53 % (11756)Termination phase: Saturation
% 57.56/9.53
% 57.56/9.53 % (11756)Memory used [KB]: 11513
% 57.56/9.53 % (11756)Time elapsed: 0.609 s
% 57.56/9.53 % (11756)Instructions burned: 1871 (million)
% 57.56/9.53 % (11756)------------------------------
% 57.56/9.53 % (11756)------------------------------
% 57.56/9.54 % (11766)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_11076 for (2920ds/4604Mi)
% 57.86/9.61 % (11761)Instruction limit reached!
% 57.86/9.61 % (11761)------------------------------
% 57.86/9.61 % (11761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.86/9.61 % (11761)Termination reason: Unknown
% 57.86/9.61 % (11761)Termination phase: Saturation
% 57.86/9.61
% 57.86/9.61 % (11761)Memory used [KB]: 9466
% 57.86/9.61 % (11761)Time elapsed: 0.371 s
% 57.86/9.61 % (11761)Instructions burned: 1189 (million)
% 57.86/9.61 % (11761)------------------------------
% 57.86/9.61 % (11761)------------------------------
% 57.86/9.63 % (11767)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_11076 for (2919ds/2678Mi)
% 58.44/9.75 % (11752)Instruction limit reached!
% 58.44/9.75 % (11752)------------------------------
% 58.44/9.75 % (11752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.44/9.75 % (11752)Termination reason: Unknown
% 58.44/9.75 % (11752)Termination phase: Saturation
% 58.44/9.75
% 58.44/9.75 % (11752)Memory used [KB]: 13944
% 58.44/9.75 % (11752)Time elapsed: 1.111 s
% 58.44/9.75 % (11752)Instructions burned: 3712 (million)
% 58.44/9.75 % (11752)------------------------------
% 58.44/9.75 % (11752)------------------------------
% 58.44/9.77 % (11768)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_11076 for (2918ds/643Mi)
% 58.72/9.91 % (11763)Instruction limit reached!
% 58.72/9.91 % (11763)------------------------------
% 58.72/9.91 % (11763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.72/9.91 % (11763)Termination reason: Unknown
% 58.72/9.91 % (11763)Termination phase: Saturation
% 58.72/9.91
% 58.72/9.91 % (11763)Memory used [KB]: 8955
% 58.72/9.91 % (11763)Time elapsed: 0.480 s
% 58.72/9.91 % (11763)Instructions burned: 1518 (million)
% 58.72/9.91 % (11763)------------------------------
% 58.72/9.91 % (11763)------------------------------
% 58.72/9.92 % (11769)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_11076 for (2916ds/458Mi)
% 58.72/9.97 % (11768)Instruction limit reached!
% 58.72/9.97 % (11768)------------------------------
% 58.72/9.97 % (11768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.72/9.97 % (11768)Termination reason: Unknown
% 58.72/9.97 % (11768)Termination phase: Saturation
% 58.72/9.97
% 58.72/9.97 % (11768)Memory used [KB]: 8443
% 58.72/9.97 % (11768)Time elapsed: 0.202 s
% 58.72/9.97 % (11768)Instructions burned: 645 (million)
% 58.72/9.97 % (11768)------------------------------
% 58.72/9.97 % (11768)------------------------------
% 58.72/9.98 % (11770)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_11076 for (2916ds/2546Mi)
% 58.72/10.01 % (11759)Instruction limit reached!
% 58.72/10.01 % (11759)------------------------------
% 58.72/10.01 % (11759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.72/10.01 % (11759)Termination reason: Unknown
% 58.72/10.01 % (11759)Termination phase: Saturation
% 58.72/10.01
% 58.72/10.01 % (11759)Memory used [KB]: 12792
% 58.72/10.01 % (11759)Time elapsed: 0.891 s
% 58.72/10.01 % (11759)Instructions burned: 3117 (million)
% 58.72/10.01 % (11759)------------------------------
% 58.72/10.01 % (11759)------------------------------
% 58.72/10.02 % (11771)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_11076 for (2915ds/1432Mi)
% 61.97/10.06 % (11769)Instruction limit reached!
% 61.97/10.06 % (11769)------------------------------
% 61.97/10.06 % (11769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.97/10.06 % (11769)Termination reason: Unknown
% 61.97/10.06 % (11769)Termination phase: Saturation
% 61.97/10.06
% 61.97/10.06 % (11769)Memory used [KB]: 7547
% 61.97/10.06 % (11769)Time elapsed: 0.134 s
% 61.97/10.06 % (11769)Instructions burned: 458 (million)
% 61.97/10.06 % (11769)------------------------------
% 61.97/10.06 % (11769)------------------------------
% 61.97/10.07 % (11772)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_11076 for (2915ds/386Mi)
% 62.53/10.18 % (11772)Instruction limit reached!
% 62.53/10.18 % (11772)------------------------------
% 62.53/10.18 % (11772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.53/10.18 % (11772)Termination reason: Unknown
% 62.53/10.18 % (11772)Termination phase: Saturation
% 62.53/10.18
% 62.53/10.18 % (11772)Memory used [KB]: 7931
% 62.53/10.18 % (11772)Time elapsed: 0.111 s
% 62.53/10.18 % (11772)Instructions burned: 387 (million)
% 62.53/10.18 % (11772)------------------------------
% 62.53/10.18 % (11772)------------------------------
% 62.53/10.19 % (11773)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_11076 for (2914ds/360Mi)
% 63.02/10.29 % (11773)Instruction limit reached!
% 63.02/10.29 % (11773)------------------------------
% 63.02/10.29 % (11773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.02/10.29 % (11773)Termination reason: Unknown
% 63.02/10.29 % (11773)Termination phase: Saturation
% 63.02/10.29
% 63.02/10.29 % (11773)Memory used [KB]: 7931
% 63.02/10.29 % (11773)Time elapsed: 0.104 s
% 63.02/10.29 % (11773)Instructions burned: 360 (million)
% 63.02/10.29 % (11773)------------------------------
% 63.02/10.29 % (11773)------------------------------
% 63.63/10.30 % (11774)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_11076 for (2912ds/5446Mi)
% 63.63/10.39 % (11771)Instruction limit reached!
% 63.63/10.39 % (11771)------------------------------
% 63.63/10.39 % (11771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.63/10.39 % (11771)Termination reason: Unknown
% 63.63/10.39 % (11771)Termination phase: Saturation
% 63.63/10.39
% 63.63/10.39 % (11771)Memory used [KB]: 10618
% 63.63/10.39 % (11771)Time elapsed: 0.367 s
% 63.63/10.39 % (11771)Instructions burned: 1433 (million)
% 63.63/10.39 % (11771)------------------------------
% 63.63/10.39 % (11771)------------------------------
% 64.52/10.40 % (11775)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_11076 for (2911ds/2573Mi)
% 64.52/10.43 % (11765)Instruction limit reached!
% 64.52/10.43 % (11765)------------------------------
% 64.52/10.43 % (11765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.52/10.43 % (11765)Termination reason: Unknown
% 64.52/10.43 % (11765)Termination phase: Saturation
% 64.52/10.43
% 64.52/10.43 % (11765)Memory used [KB]: 11513
% 64.52/10.43 % (11765)Time elapsed: 0.915 s
% 64.52/10.43 % (11765)Instructions burned: 2813 (million)
% 64.52/10.43 % (11765)------------------------------
% 64.52/10.43 % (11765)------------------------------
% 64.52/10.44 % (11776)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_11076 for (2911ds/2655Mi)
% 64.52/10.46 % (11767)Instruction limit reached!
% 64.52/10.46 % (11767)------------------------------
% 64.52/10.46 % (11767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.52/10.46 % (11767)Termination reason: Unknown
% 64.52/10.46 % (11767)Termination phase: Saturation
% 64.52/10.46
% 64.52/10.46 % (11767)Memory used [KB]: 10746
% 64.52/10.46 % (11767)Time elapsed: 0.832 s
% 64.52/10.46 % (11767)Instructions burned: 2678 (million)
% 64.52/10.46 % (11767)------------------------------
% 64.52/10.46 % (11767)------------------------------
% 64.52/10.47 % (11777)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_11076 for (2911ds/2781Mi)
% 65.53/10.75 % (11751)Instruction limit reached!
% 65.53/10.75 % (11751)------------------------------
% 65.53/10.75 % (11751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.53/10.75 % (11751)Termination reason: Unknown
% 65.53/10.75 % (11751)Termination phase: Saturation
% 65.53/10.75
% 65.53/10.75 % (11751)Memory used [KB]: 16119
% 65.53/10.75 % (11751)Time elapsed: 2.327 s
% 65.53/10.75 % (11751)Instructions burned: 7257 (million)
% 65.53/10.75 % (11751)------------------------------
% 65.53/10.75 % (11751)------------------------------
% 65.53/10.76 % (11778)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_11076 for (2908ds/307Mi)
% 65.80/10.80 % (11770)Instruction limit reached!
% 65.80/10.80 % (11770)------------------------------
% 65.80/10.80 % (11770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.80/10.80 % (11770)Termination reason: Unknown
% 65.80/10.80 % (11770)Termination phase: Saturation
% 65.80/10.80
% 65.80/10.80 % (11770)Memory used [KB]: 11129
% 65.80/10.80 % (11770)Time elapsed: 0.825 s
% 65.80/10.80 % (11770)Instructions burned: 2548 (million)
% 65.80/10.80 % (11770)------------------------------
% 65.80/10.80 % (11770)------------------------------
% 65.80/10.81 % (11779)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_11076 for (2907ds/1548Mi)
% 65.80/10.85 % (11778)Instruction limit reached!
% 65.80/10.85 % (11778)------------------------------
% 65.80/10.85 % (11778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.80/10.85 % (11778)Termination reason: Unknown
% 65.80/10.85 % (11778)Termination phase: Saturation
% 65.80/10.85
% 65.80/10.85 % (11778)Memory used [KB]: 7291
% 65.80/10.85 % (11778)Time elapsed: 0.087 s
% 65.80/10.85 % (11778)Instructions burned: 308 (million)
% 65.80/10.85 % (11778)------------------------------
% 65.80/10.85 % (11778)------------------------------
% 65.80/10.86 % (11780)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_11076 for (2907ds/5214Mi)
% 66.01/10.97 % (11766)Instruction limit reached!
% 66.01/10.97 % (11766)------------------------------
% 66.01/10.97 % (11766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.01/10.97 % (11766)Termination reason: Unknown
% 66.01/10.97 % (11766)Termination phase: Saturation
% 66.01/10.97
% 66.01/10.97 % (11766)Memory used [KB]: 13560
% 66.01/10.97 % (11766)Time elapsed: 1.430 s
% 66.01/10.97 % (11766)Instructions burned: 4604 (million)
% 66.01/10.97 % (11766)------------------------------
% 66.01/10.97 % (11766)------------------------------
% 66.01/10.98 % (11781)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_11076 for (2906ds/3201Mi)
% 69.71/11.15 % (11775)Instruction limit reached!
% 69.71/11.15 % (11775)------------------------------
% 69.71/11.15 % (11775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.71/11.15 % (11775)Termination reason: Unknown
% 69.71/11.15 % (11775)Termination phase: Saturation
% 69.71/11.15
% 69.71/11.15 % (11775)Memory used [KB]: 12025
% 69.71/11.15 % (11775)Time elapsed: 0.752 s
% 69.71/11.15 % (11775)Instructions burned: 2573 (million)
% 69.71/11.15 % (11775)------------------------------
% 69.71/11.15 % (11775)------------------------------
% 69.71/11.16 % (11782)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_11076 for (2904ds/454Mi)
% 70.20/11.22 % (11776)Instruction limit reached!
% 70.20/11.22 % (11776)------------------------------
% 70.20/11.22 % (11776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.20/11.22 % (11776)Termination reason: Unknown
% 70.20/11.22 % (11776)Termination phase: Saturation
% 70.20/11.22
% 70.20/11.22 % (11776)Memory used [KB]: 11129
% 70.20/11.22 % (11776)Time elapsed: 0.784 s
% 70.20/11.22 % (11776)Instructions burned: 2655 (million)
% 70.20/11.22 % (11776)------------------------------
% 70.20/11.22 % (11776)------------------------------
% 70.20/11.23 % (11783)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_11076 for (2903ds/3049Mi)
% 70.74/11.30 % (11782)Instruction limit reached!
% 70.74/11.30 % (11782)------------------------------
% 70.74/11.30 % (11782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.74/11.30 % (11782)Termination reason: Unknown
% 70.74/11.30 % (11782)Termination phase: Saturation
% 70.74/11.30
% 70.74/11.30 % (11782)Memory used [KB]: 12665
% 70.74/11.30 % (11782)Time elapsed: 0.142 s
% 70.74/11.30 % (11782)Instructions burned: 457 (million)
% 70.74/11.30 % (11782)------------------------------
% 70.74/11.30 % (11782)------------------------------
% 70.74/11.31 % (11779)Instruction limit reached!
% 70.74/11.31 % (11779)------------------------------
% 70.74/11.31 % (11779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.74/11.31 % (11779)Termination reason: Unknown
% 70.74/11.31 % (11779)Termination phase: Saturation
% 70.74/11.31
% 70.74/11.31 % (11779)Memory used [KB]: 8955
% 70.74/11.31 % (11779)Time elapsed: 0.499 s
% 70.74/11.31 % (11779)Instructions burned: 1550 (million)
% 70.74/11.31 % (11779)------------------------------
% 70.74/11.31 % (11779)------------------------------
% 70.74/11.31 % (11784)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_11076 for (2902ds/7311Mi)
% 70.74/11.32 % (11785)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_11076 for (2902ds/6804Mi)
% 70.74/11.35 % (11777)Instruction limit reached!
% 70.74/11.35 % (11777)------------------------------
% 70.74/11.35 % (11777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.74/11.35 % (11777)Termination reason: Unknown
% 70.74/11.35 % (11777)Termination phase: Saturation
% 70.74/11.35
% 70.74/11.35 % (11777)Memory used [KB]: 5373
% 70.74/11.35 % (11777)Time elapsed: 0.885 s
% 70.74/11.35 % (11777)Instructions burned: 2783 (million)
% 70.74/11.35 % (11777)------------------------------
% 70.74/11.35 % (11777)------------------------------
% 70.74/11.36 % (11786)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_11076 for (2902ds/1683Mi)
% 72.47/11.90 % (11786)Instruction limit reached!
% 72.47/11.90 % (11786)------------------------------
% 72.47/11.90 % (11786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.47/11.90 % (11786)Termination reason: Unknown
% 72.47/11.90 % (11786)Termination phase: Saturation
% 72.47/11.90
% 72.47/11.90 % (11786)Memory used [KB]: 9338
% 72.47/11.90 % (11786)Time elapsed: 0.559 s
% 72.47/11.90 % (11786)Instructions burned: 1684 (million)
% 72.47/11.90 % (11786)------------------------------
% 72.47/11.90 % (11786)------------------------------
% 72.76/11.91 % (11787)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_11076 for (2897ds/4688Mi)
% 72.76/11.99 % (11781)Instruction limit reached!
% 72.76/11.99 % (11781)------------------------------
% 72.76/11.99 % (11781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.76/11.99 % (11781)Termination reason: Unknown
% 72.76/11.99 % (11781)Termination phase: Saturation
% 72.76/11.99
% 72.76/11.99 % (11781)Memory used [KB]: 13688
% 72.76/11.99 % (11781)Time elapsed: 1.017 s
% 72.76/11.99 % (11781)Instructions burned: 3203 (million)
% 72.76/11.99 % (11781)------------------------------
% 72.76/11.99 % (11781)------------------------------
% 72.76/12.00 % (11788)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_11076 for (2896ds/2207Mi)
% 76.02/12.07 % (11774)Instruction limit reached!
% 76.02/12.07 % (11774)------------------------------
% 76.02/12.07 % (11774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.02/12.07 % (11774)Termination reason: Unknown
% 76.02/12.07 % (11774)Termination phase: Saturation
% 76.02/12.07
% 76.02/12.07 % (11774)Memory used [KB]: 17398
% 76.02/12.07 % (11774)Time elapsed: 1.774 s
% 76.02/12.07 % (11774)Instructions burned: 5446 (million)
% 76.02/12.07 % (11774)------------------------------
% 76.02/12.07 % (11774)------------------------------
% 76.02/12.08 % (11789)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_11076 for (2895ds/8216Mi)
% 76.71/12.18 % (11783)Instruction limit reached!
% 76.71/12.18 % (11783)------------------------------
% 76.71/12.18 % (11783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.71/12.18 % (11783)Termination reason: Unknown
% 76.71/12.18 % (11783)Termination phase: Saturation
% 76.71/12.18
% 76.71/12.18 % (11783)Memory used [KB]: 9594
% 76.71/12.18 % (11783)Time elapsed: 0.956 s
% 76.71/12.18 % (11783)Instructions burned: 3051 (million)
% 76.71/12.18 % (11783)------------------------------
% 76.71/12.18 % (11783)------------------------------
% 76.71/12.19 % (11790)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_11076 for (2893ds/430Mi)
% 77.64/12.32 % (11790)Instruction limit reached!
% 77.64/12.32 % (11790)------------------------------
% 77.64/12.32 % (11790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.64/12.32 % (11790)Termination reason: Unknown
% 77.64/12.32 % (11790)Termination phase: Saturation
% 77.64/12.32
% 77.64/12.32 % (11790)Memory used [KB]: 7675
% 77.64/12.32 % (11790)Time elapsed: 0.125 s
% 77.64/12.32 % (11790)Instructions burned: 432 (million)
% 77.64/12.32 % (11790)------------------------------
% 77.64/12.32 % (11790)------------------------------
% 77.64/12.33 % (11791)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_11076 for (2892ds/2012Mi)
% 78.28/12.47 % (11780)Instruction limit reached!
% 78.28/12.47 % (11780)------------------------------
% 78.28/12.47 % (11780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.28/12.47 % (11780)Termination reason: Unknown
% 78.28/12.47 % (11780)Termination phase: Saturation
% 78.28/12.47
% 78.28/12.47 % (11780)Memory used [KB]: 15607
% 78.28/12.47 % (11780)Time elapsed: 1.615 s
% 78.28/12.47 % (11780)Instructions burned: 5214 (million)
% 78.28/12.47 % (11780)------------------------------
% 78.28/12.47 % (11780)------------------------------
% 78.28/12.48 % (11792)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_11076 for (2891ds/631Mi)
% 79.17/12.68 % (11792)Instruction limit reached!
% 79.17/12.68 % (11792)------------------------------
% 79.17/12.68 % (11792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.17/12.68 % (11792)Termination reason: Unknown
% 79.17/12.68 % (11792)Termination phase: Saturation
% 79.17/12.68
% 79.17/12.68 % (11792)Memory used [KB]: 9083
% 79.17/12.68 % (11792)Time elapsed: 0.199 s
% 79.17/12.68 % (11792)Instructions burned: 633 (million)
% 79.17/12.68 % (11792)------------------------------
% 79.17/12.68 % (11792)------------------------------
% 79.17/12.69 % (11793)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_11076 for (2889ds/8785Mi)
% 79.77/12.70 % (11788)Instruction limit reached!
% 79.77/12.70 % (11788)------------------------------
% 79.77/12.70 % (11788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.77/12.70 % (11788)Termination reason: Unknown
% 79.77/12.70 % (11788)Termination phase: Saturation
% 79.77/12.70
% 79.77/12.70 % (11788)Memory used [KB]: 10362
% 79.77/12.70 % (11788)Time elapsed: 0.719 s
% 79.77/12.70 % (11788)Instructions burned: 2209 (million)
% 79.77/12.70 % (11788)------------------------------
% 79.77/12.70 % (11788)------------------------------
% 79.77/12.71 % (11794)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_11076 for (2888ds/739Mi)
% 80.39/12.93 % (11791)Instruction limit reached!
% 80.39/12.93 % (11791)------------------------------
% 80.39/12.93 % (11791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.39/12.93 % (11791)Termination reason: Unknown
% 80.39/12.93 % (11791)Termination phase: Saturation
% 80.39/12.93
% 80.39/12.93 % (11791)Memory used [KB]: 16502
% 80.39/12.93 % (11791)Time elapsed: 0.603 s
% 80.39/12.93 % (11791)Instructions burned: 2014 (million)
% 80.39/12.93 % (11791)------------------------------
% 80.39/12.93 % (11791)------------------------------
% 80.39/12.94 % (11795)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_11076 for (2886ds/5473Mi)
% 80.39/12.94 % (11794)Instruction limit reached!
% 80.39/12.94 % (11794)------------------------------
% 80.39/12.94 % (11794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.39/12.94 % (11794)Termination reason: Unknown
% 80.39/12.94 % (11794)Termination phase: Saturation
% 80.39/12.94
% 80.39/12.94 % (11794)Memory used [KB]: 8571
% 80.39/12.94 % (11794)Time elapsed: 0.234 s
% 80.39/12.94 % (11794)Instructions burned: 740 (million)
% 80.39/12.94 % (11794)------------------------------
% 80.39/12.94 % (11794)------------------------------
% 80.39/12.95 % (11796)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_11076 for (2886ds/43570Mi)
% 84.99/13.34 % (11787)Instruction limit reached!
% 84.99/13.34 % (11787)------------------------------
% 84.99/13.34 % (11787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.99/13.34 % (11787)Termination reason: Unknown
% 84.99/13.34 % (11787)Termination phase: Saturation
% 84.99/13.34
% 84.99/13.34 % (11787)Memory used [KB]: 7036
% 84.99/13.34 % (11787)Time elapsed: 1.455 s
% 84.99/13.34 % (11787)Instructions burned: 4690 (million)
% 84.99/13.34 % (11787)------------------------------
% 84.99/13.34 % (11787)------------------------------
% 84.99/13.35 % (11797)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_11076 for (2882ds/8382Mi)
% 85.64/13.42 % (11784)Refutation not found, non-redundant clauses discarded% (11784)------------------------------
% 85.64/13.42 % (11784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.64/13.42 % (11784)Termination reason: Refutation not found, non-redundant clauses discarded
% 85.64/13.42
% 85.64/13.42 % (11784)Memory used [KB]: 18421
% 85.64/13.42 % (11784)Time elapsed: 2.106 s
% 85.64/13.42 % (11784)Instructions burned: 6797 (million)
% 85.64/13.42 % (11784)------------------------------
% 85.64/13.42 % (11784)------------------------------
% 85.64/13.42 % (11785)Instruction limit reached!
% 85.64/13.42 % (11785)------------------------------
% 85.64/13.42 % (11785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.64/13.42 % (11785)Termination reason: Unknown
% 85.64/13.42 % (11785)Termination phase: Saturation
% 85.64/13.42
% 85.64/13.42 % (11785)Memory used [KB]: 13176
% 85.64/13.42 % (11785)Time elapsed: 2.102 s
% 85.64/13.42 % (11785)Instructions burned: 6804 (million)
% 85.64/13.42 % (11785)------------------------------
% 85.64/13.42 % (11785)------------------------------
% 85.64/13.43 % (11798)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_11076 for (2881ds/407Mi)
% 85.64/13.43 % (11799)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_11076 for (2881ds/2971Mi)
% 85.64/13.49 % (11799)Refutation not found, incomplete strategy
% 85.64/13.49 % (11799)------------------------------
% 85.64/13.49 % (11799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.64/13.49 % (11799)Termination reason: Refutation not found, incomplete strategy
% 85.64/13.49
% 85.64/13.49
% 85.64/13.49 % (11799)Memory used [KB]: 7803
% 85.64/13.49 % (11799)Time elapsed: 0.087 s
% 85.64/13.49 % (11799)Instructions burned: 238 (million)
% 85.64/13.49 % (11799)------------------------------
% 85.64/13.49 % (11799)------------------------------
% 86.17/13.50 % (11800)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_11076 for (2880ds/9822Mi)
% 86.17/13.56 % (11798)Instruction limit reached!
% 86.17/13.56 % (11798)------------------------------
% 86.17/13.56 % (11798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.17/13.56 % (11798)Termination reason: Unknown
% 86.17/13.56 % (11798)Termination phase: Saturation
% 86.17/13.56
% 86.17/13.56 % (11798)Memory used [KB]: 8187
% 86.17/13.56 % (11798)Time elapsed: 0.157 s
% 86.17/13.56 % (11798)Instructions burned: 408 (million)
% 86.17/13.56 % (11798)------------------------------
% 86.17/13.56 % (11798)------------------------------
% 86.17/13.57 % (11801)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_11076 for (2880ds/8425Mi)
% 93.39/14.59 % (11789)Instruction limit reached!
% 93.39/14.59 % (11789)------------------------------
% 93.39/14.59 % (11789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.39/14.59 % (11789)Termination reason: Unknown
% 93.39/14.59 % (11789)Termination phase: Saturation
% 93.39/14.59
% 93.39/14.59 % (11789)Memory used [KB]: 9594
% 93.39/14.59 % (11789)Time elapsed: 2.512 s
% 93.39/14.59 % (11789)Instructions burned: 8218 (million)
% 93.39/14.59 % (11789)------------------------------
% 93.39/14.59 % (11789)------------------------------
% 94.09/14.60 % (11953)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_11076 for (2870ds/3107Mi)
% 94.09/14.67 % (11795)Instruction limit reached!
% 94.09/14.67 % (11795)------------------------------
% 94.09/14.67 % (11795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.09/14.67 % (11795)Termination reason: Unknown
% 94.09/14.67 % (11795)Termination phase: Saturation
% 94.09/14.67
% 94.09/14.67 % (11795)Memory used [KB]: 11001
% 94.09/14.67 % (11795)Time elapsed: 1.732 s
% 94.09/14.67 % (11795)Instructions burned: 5474 (million)
% 94.09/14.67 % (11795)------------------------------
% 94.09/14.67 % (11795)------------------------------
% 94.09/14.68 % (11992)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_11076 for (2869ds/7967Mi)
% 94.67/14.74 % (11992)Refutation not found, incomplete strategy
% 94.67/14.74 % (11992)------------------------------
% 94.67/14.74 % (11992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.67/14.74 % (11992)Termination reason: Refutation not found, incomplete strategy
% 94.67/14.74
% 94.67/14.74
% 94.67/14.74 % (11992)Memory used [KB]: 7547
% 94.67/14.74 % (11992)Time elapsed: 0.058 s
% 94.67/14.74 % (11992)Instructions burned: 208 (million)
% 94.67/14.74 % (11992)------------------------------
% 94.67/14.74 % (11992)------------------------------
% 94.67/14.75 % (12028)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_11076 for (2868ds/3629Mi)
% 99.70/15.47 % (11793)Instruction limit reached!
% 99.70/15.47 % (11793)------------------------------
% 99.70/15.47 % (11793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.70/15.47 % (11793)Termination reason: Unknown
% 99.70/15.47 % (11793)Termination phase: Saturation
% 99.70/15.47
% 99.70/15.47 % (11793)Memory used [KB]: 16758
% 99.70/15.47 % (11793)Time elapsed: 2.785 s
% 99.70/15.47 % (11793)Instructions burned: 8787 (million)
% 99.70/15.47 % (11793)------------------------------
% 99.70/15.47 % (11793)------------------------------
% 99.70/15.48 % (12336)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_11076 for (2861ds/939Mi)
% 100.40/15.57 % (11953)Instruction limit reached!
% 100.40/15.57 % (11953)------------------------------
% 100.40/15.57 % (11953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.40/15.57 % (11953)Termination reason: Unknown
% 100.40/15.57 % (11953)Termination phase: Saturation
% 100.40/15.57
% 100.40/15.57 % (11953)Memory used [KB]: 12537
% 100.40/15.57 % (11953)Time elapsed: 0.963 s
% 100.40/15.57 % (11953)Instructions burned: 3109 (million)
% 100.40/15.57 % (11953)------------------------------
% 100.40/15.57 % (11953)------------------------------
% 100.40/15.58 % (12384)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_11076 for (2860ds/1188Mi)
% 101.48/15.74 % (12336)Instruction limit reached!
% 101.48/15.74 % (12336)------------------------------
% 101.48/15.74 % (12336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.48/15.74 % (12336)Termination reason: Unknown
% 101.48/15.74 % (12336)Termination phase: Saturation
% 101.48/15.74
% 101.48/15.74 % (12336)Memory used [KB]: 8315
% 101.48/15.74 % (12336)Time elapsed: 0.259 s
% 101.48/15.74 % (12336)Instructions burned: 939 (million)
% 101.48/15.74 % (12336)------------------------------
% 101.48/15.74 % (12336)------------------------------
% 101.48/15.75 % (12398)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_11076 for (2858ds/3205Mi)
% 102.26/15.87 % (12028)Instruction limit reached!
% 102.26/15.87 % (12028)------------------------------
% 102.26/15.87 % (12028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.26/15.87 % (12028)Termination reason: Unknown
% 102.26/15.87 % (12028)Termination phase: Saturation
% 102.26/15.87
% 102.26/15.87 % (12028)Memory used [KB]: 10106
% 102.26/15.87 % (12028)Time elapsed: 1.143 s
% 102.26/15.87 % (12028)Instructions burned: 3630 (million)
% 102.26/15.87 % (12028)------------------------------
% 102.26/15.87 % (12028)------------------------------
% 102.26/15.88 % (12399)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_11076 for (2857ds/865Mi)
% 102.74/15.94 % (12384)Instruction limit reached!
% 102.74/15.94 % (12384)------------------------------
% 102.74/15.94 % (12384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.74/15.94 % (12384)Termination reason: Unknown
% 102.74/15.94 % (12384)Termination phase: Saturation
% 102.74/15.94
% 102.74/15.94 % (12384)Memory used [KB]: 9466
% 102.74/15.94 % (12384)Time elapsed: 0.366 s
% 102.74/15.94 % (12384)Instructions burned: 1190 (million)
% 102.74/15.94 % (12384)------------------------------
% 102.74/15.94 % (12384)------------------------------
% 102.74/15.95 % (12400)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_11076 for (2856ds/7469Mi)
% 102.74/16.00 % (11797)Instruction limit reached!
% 102.74/16.00 % (11797)------------------------------
% 102.74/16.00 % (11797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.74/16.00 % (11797)Termination reason: Unknown
% 102.74/16.00 % (11797)Termination phase: Saturation
% 102.74/16.00
% 102.74/16.00 % (11797)Memory used [KB]: 20724
% 102.74/16.00 % (11797)Time elapsed: 2.678 s
% 102.74/16.00 % (11797)Instructions burned: 8385 (million)
% 102.74/16.00 % (11797)------------------------------
% 102.74/16.00 % (11797)------------------------------
% 102.74/16.01 % (12401)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_11076 for (2855ds/4165Mi)
% 104.70/16.15 % (12399)Instruction limit reached!
% 104.70/16.15 % (12399)------------------------------
% 104.70/16.15 % (12399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.70/16.15 % (12399)Termination reason: Unknown
% 104.70/16.15 % (12399)Termination phase: Saturation
% 104.70/16.15
% 104.70/16.15 % (12399)Memory used [KB]: 9466
% 104.70/16.15 % (12399)Time elapsed: 0.270 s
% 104.70/16.15 % (12399)Instructions burned: 867 (million)
% 104.70/16.15 % (12399)------------------------------
% 104.70/16.15 % (12399)------------------------------
% 104.70/16.15 % (11801)Instruction limit reached!
% 104.70/16.15 % (11801)------------------------------
% 104.70/16.15 % (11801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.70/16.15 % (11801)Termination reason: Unknown
% 104.70/16.15 % (11801)Termination phase: Saturation
% 104.70/16.15
% 104.70/16.15 % (11801)Memory used [KB]: 15479
% 104.70/16.15 % (11801)Time elapsed: 2.584 s
% 104.70/16.15 % (11801)Instructions burned: 8426 (million)
% 104.70/16.15 % (11801)------------------------------
% 104.70/16.15 % (11801)------------------------------
% 104.70/16.16 % (12402)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_11076 for (2854ds/13468Mi)
% 104.70/16.16 % (12403)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_11076 for (2854ds/2635Mi)
% 106.67/16.60 % (11800)First to succeed.
% 106.67/16.60 % (11800)Refutation found. Thanks to Tanya!
% 106.67/16.60 % SZS status Theorem for DTF2THF_11076
% 106.67/16.60 % SZS output start Proof for DTF2THF_11076
% 106.67/16.60 thf(type_def_6, type, set: ($tType) > $tType).
% 106.67/16.60 thf(type_def_7, type, nat: $tType).
% 106.67/16.60 thf(func_def_0, type, set: ($tType) > $tType).
% 106.67/16.60 thf(func_def_1, type, nat: $tType).
% 106.67/16.60 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_3, type, one: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_6, type, neg_numeral: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_8, type, mult_zero: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_9, type, no_bot: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_10, type, no_top: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_11, type, semiring_0: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_12, type, monoid_mult: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_13, type, linorder: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_14, type, preorder: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_15, type, ordered_ring: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_16, type, zero_neq_one: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_17, type, wellorder: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_18, type, semigroup_mult: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_19, type, dense_order: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_20, type, linordered_idom: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_21, type, linordered_ring: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_22, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_23, type, ordered_semiring: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_24, type, comm_monoid_mult: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_25, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_26, type, dense_linorder: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_27, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_28, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_29, type, linord581940658strict: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_30, type, ring_11004092258visors: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_31, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_32, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_33, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_34, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_35, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 106.67/16.60 thf(func_def_36, type, one_one: !>[X0: $tType]:(X0)).
% 106.67/16.60 thf(func_def_37, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 106.67/16.60 thf(func_def_38, type, zero_zero: !>[X0: $tType]:(X0)).
% 106.67/16.60 thf(func_def_39, type, groups1340683514dd_sum: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > X1)).
% 106.67/16.60 thf(func_def_40, type, neg_numeral_dbl_inc: !>[X0: $tType]:(X0 > X0)).
% 106.67/16.60 thf(func_def_41, type, number2016821345itions: (nat > nat) > nat > $o).
% 106.67/16.60 thf(func_def_42, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 106.67/16.60 thf(func_def_43, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 106.67/16.60 thf(func_def_44, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 106.67/16.60 thf(func_def_45, type, set_ord_atMost: !>[X0: $tType]:(X0 > set @ X0)).
% 106.67/16.60 thf(func_def_46, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 106.67/16.60 thf(func_def_47, type, p: nat > nat).
% 106.67/16.60 thf(func_def_62, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 106.67/16.60 thf(func_def_63, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 106.67/16.60 thf(func_def_64, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 106.67/16.60 thf(func_def_65, type, sP3: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > set @ X0 > $o)).
% 106.67/16.60 thf(func_def_66, type, sP4: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > set @ X0 > $o)).
% 106.67/16.60 thf(func_def_67, type, sK5: (nat > nat) > nat).
% 106.67/16.60 thf(func_def_68, type, sK6: (nat > nat) > nat).
% 106.67/16.60 thf(func_def_69, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_70, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_71, type, sK9: !>[X0: $tType]:(X0 > X0 > X0 > X0)).
% 106.67/16.60 thf(func_def_72, type, sK10: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_73, type, sK11: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 106.67/16.60 thf(func_def_74, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_75, type, sK13: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_76, type, sK14: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_77, type, sK15: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_78, type, sK16: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_79, type, sK17: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_80, type, sK18: nat > (nat > nat) > nat).
% 106.67/16.60 thf(func_def_81, type, sK19: nat > (nat > $o) > nat).
% 106.67/16.60 thf(func_def_82, type, sK20: (nat > $o) > nat).
% 106.67/16.60 thf(func_def_83, type, sK21: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_84, type, sK22: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_85, type, sK23: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_86, type, sK24: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 106.67/16.60 thf(func_def_87, type, sK25: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > X1)).
% 106.67/16.60 thf(func_def_88, type, sK26: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 106.67/16.60 thf(func_def_89, type, sK27: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 106.67/16.60 thf(func_def_90, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_91, type, sK29: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_92, type, sK30: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_93, type, sK31: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_94, type, sK32: !>[X0: $tType]:(X0 > X0 > X0 > X0)).
% 106.67/16.60 thf(func_def_95, type, sK33: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_96, type, sK34: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_97, type, sK35: nat > (nat > $o) > nat).
% 106.67/16.60 thf(func_def_98, type, sK36: (nat > $o) > nat).
% 106.67/16.60 thf(func_def_99, type, sK37: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_100, type, sK38: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_101, type, sK39: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_102, type, sK40: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > (X1 > X0) > set @ X1 > X1)).
% 106.67/16.60 thf(func_def_103, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > (X0 > X2) > set @ X0 > (X2 > X0) > set @ X2 > X0)).
% 106.67/16.60 thf(func_def_104, type, sK42: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_105, type, sK43: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_106, type, sK44: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_107, type, sK45: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_108, type, sK46: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_109, type, sK47: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_110, type, sK48: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_111, type, sK49: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > set @ X0 > X1)).
% 106.67/16.60 thf(func_def_112, type, sK50: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > set @ X0 > X1)).
% 106.67/16.60 thf(func_def_113, type, sK51: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_114, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > (X0 > X2) > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_115, type, sK53: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_116, type, sK54: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_117, type, sK55: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_118, type, sK56: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_119, type, sK57: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_120, type, sK58: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_121, type, sK59: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_122, type, sK60: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_123, type, sK61: !>[X0: $tType]:((X0 > $o) > X0)).
% 106.67/16.60 thf(func_def_124, type, sK62: !>[X0: $tType]:(X0 > X0)).
% 106.67/16.60 thf(func_def_125, type, sK63: !>[X0: $tType]:(X0 > X0)).
% 106.67/16.60 thf(func_def_126, type, sK64: !>[X0: $tType]:(X0 > X0 > X0)).
% 106.67/16.60 thf(func_def_127, type, sK65: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1 > X1)).
% 106.67/16.60 thf(func_def_128, type, sK66: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1) > set @ X0 > set @ X1 > X0)).
% 106.67/16.60 thf(func_def_129, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > (X0 > X2) > set @ X0 > set @ X2 > X0)).
% 106.67/16.60 thf(func_def_130, type, sK68: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 106.67/16.60 thf(func_def_131, type, sK69: nat).
% 106.67/16.60 thf(func_def_132, type, sK70: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_133, type, sK71: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 106.67/16.60 thf(func_def_134, type, sK72: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 106.67/16.60 thf(func_def_135, type, sK73: (nat > $o) > nat).
% 106.67/16.60 thf(func_def_137, type, ph75: !>[X0: $tType]:(X0)).
% 106.67/16.60 thf(func_def_138, type, sK76: nat).
% 106.67/16.60 thf(func_def_139, type, sK77: nat).
% 106.67/16.60 thf(func_def_140, type, sK78: nat).
% 106.67/16.60 thf(func_def_142, type, sK79: nat).
% 106.67/16.60 thf(f16031,plain,(
% 106.67/16.60 $false),
% 106.67/16.60 inference(avatar_sat_refutation,[status(thm)],[f1927,f1935,f1939,f15155,f15850,f15880,f15906,f15994,f16030])).
% 106.67/16.60 thf(f16030,plain,(
% 106.67/16.60 spl74_4 | ~spl74_369),
% 106.67/16.60 inference(avatar_contradiction_clause,[status(thm)],[f16029])).
% 106.67/16.60 thf(f16029,plain,(
% 106.67/16.60 $false | (spl74_4 | ~spl74_369)),
% 106.67/16.60 inference(trivial_inequality_removal,[status(thm)],[f16028])).
% 106.67/16.60 thf(f16028,plain,(
% 106.67/16.60 (zero_zero @ nat != zero_zero @ nat) | (spl74_4 | ~spl74_369)),
% 106.67/16.60 inference(superposition,[status(thm)],[f1934,f15269])).
% 106.67/16.60 thf(f15269,plain,(
% 106.67/16.60 ( ! [X8 : nat] : ((zero_zero @ nat = (p @ X8))) ) | ~spl74_369),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f15268])).
% 106.67/16.60 thf(f15268,definition,(
% 106.67/16.60 spl74_369 <=> ! [X8 : nat] : (zero_zero @ nat = (p @ X8))),
% 106.67/16.60 introduced(definition,[new_symbols(naming,[spl74_369])],[avatar_definition])).
% 106.67/16.60 thf(f1934,plain,(
% 106.67/16.60 (zero_zero @ nat != (p @ sK69)) | spl74_4),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f1933])).
% 106.67/16.60 thf(f1933,definition,(
% 106.67/16.60 spl74_4 <=> (zero_zero @ nat = (p @ sK69))),
% 106.67/16.60 introduced(definition,[new_symbols(naming,[spl74_4])],[avatar_definition])).
% 106.67/16.60 thf(f15994,plain,(
% 106.67/16.60 spl74_369 | ~spl74_1),
% 106.67/16.60 inference(avatar_split_clause,[status(thm)],[f15991,f1922,f15268])).
% 106.67/16.60 thf(f1922,definition,(
% 106.67/16.60 spl74_1 <=> (p = (^[Y0 : nat]: (zero_zero @ nat)))),
% 106.67/16.60 introduced(definition,[new_symbols(naming,[spl74_1])],[avatar_definition])).
% 106.67/16.60 thf(f15991,plain,(
% 106.67/16.60 ( ! [X1 : nat] : ((zero_zero @ nat = (p @ X1))) ) | ~spl74_1),
% 106.67/16.60 inference(beta_eta_normalization,[status(thm)],[f15910])).
% 106.67/16.60 thf(f15910,plain,(
% 106.67/16.60 ( ! [X1 : nat] : (((p @ X1) = ((^[Y0 : nat]: (zero_zero @ nat)) @ X1))) ) | ~spl74_1),
% 106.67/16.60 inference(argument_congruence,[status(thm)],[f1923])).
% 106.67/16.60 thf(f1923,plain,(
% 106.67/16.60 (p = (^[Y0 : nat]: (zero_zero @ nat))) | ~spl74_1),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f1922])).
% 106.67/16.60 thf(f15906,plain,(
% 106.67/16.60 ~spl74_364),
% 106.67/16.60 inference(avatar_contradiction_clause,[status(thm)],[f15905])).
% 106.67/16.60 thf(f15905,plain,(
% 106.67/16.60 $false | ~spl74_364),
% 106.67/16.60 inference(trivial_inequality_removal,[status(thm)],[f15904])).
% 106.67/16.60 thf(f15904,plain,(
% 106.67/16.60 ($true != $true) | ~spl74_364),
% 106.67/16.60 inference(superposition,[status(thm)],[f15216,f1693])).
% 106.67/16.60 thf(f1693,plain,(
% 106.67/16.60 (wellorder @ nat = $true)),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f476])).
% 106.67/16.60 thf(f476,plain,(
% 106.67/16.60 (wellorder @ nat = $true)),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f475])).
% 106.67/16.60 thf(f475,plain,(
% 106.67/16.60 wellorder @ nat),
% 106.67/16.60 inference(rectify,[status(thm)],[f269])).
% 106.67/16.60 thf(f269,axiom,(
% 106.67/16.60 wellorder @ nat),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',tcon_Nat_Onat___Orderings_Owellorder)).
% 106.67/16.60 thf(f15216,plain,(
% 106.67/16.60 ( ! [X2 : $tType] : (($true != wellorder @ X2)) ) | ~spl74_364),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f15215])).
% 106.67/16.60 thf(f15215,definition,(
% 106.67/16.60 spl74_364 <=> ! [X2 : $tType] : ($true != wellorder @ X2)),
% 106.67/16.60 introduced(definition,[new_symbols(naming,[spl74_364])],[avatar_definition])).
% 106.67/16.60 thf(f15880,plain,(
% 106.67/16.60 spl74_1 | ~spl74_369),
% 106.67/16.60 inference(avatar_contradiction_clause,[status(thm)],[f15879])).
% 106.67/16.60 thf(f15879,plain,(
% 106.67/16.60 $false | (spl74_1 | ~spl74_369)),
% 106.67/16.60 inference(subsumption_resolution,[status(thm)],[f15878,f15269])).
% 106.67/16.60 thf(f15878,plain,(
% 106.67/16.60 (zero_zero @ nat != (p @ sK79)) | spl74_1),
% 106.67/16.60 inference(beta_eta_normalization,[status(thm)],[f15877])).
% 106.67/16.60 thf(f15877,plain,(
% 106.67/16.60 (((^[Y0 : nat]: (zero_zero @ nat)) @ sK79) != (p @ sK79)) | spl74_1),
% 106.67/16.60 inference(negative_extensionality,[status(thm)],[f1931])).
% 106.67/16.60 thf(f1931,plain,(
% 106.67/16.60 (p != (^[Y0 : nat]: (zero_zero @ nat))) | spl74_1),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f1922])).
% 106.67/16.60 thf(f15850,plain,(
% 106.67/16.60 spl74_364 | spl74_369 | ~spl74_2 | ~spl74_5),
% 106.67/16.60 inference(avatar_split_clause,[status(thm)],[f15849,f1937,f1925,f15268,f15215])).
% 106.67/16.60 thf(f1925,definition,(
% 106.67/16.60 spl74_2 <=> ! [X1 : nat] : ((zero_zero @ nat = (p @ X1)) | ($true = (ord_less_eq @ nat @ X1 @ zero_zero @ nat)))),
% 106.67/16.60 introduced(definition,[new_symbols(naming,[spl74_2])],[avatar_definition])).
% 106.67/16.60 thf(f1937,definition,(
% 106.67/16.60 spl74_5 <=> ! [X1 : nat] : ((zero_zero @ nat = (p @ X1)) | ($true = (ord_less_eq @ nat @ one_one @ nat @ X1)))),
% 106.67/16.60 introduced(definition,[new_symbols(naming,[spl74_5])],[avatar_definition])).
% 106.67/16.60 thf(f15849,plain,(
% 106.67/16.60 ( ! [X0 : $tType,X2 : nat] : ((wellorder @ X0 != $true) | (zero_zero @ nat = (p @ X2))) ) | (~spl74_2 | ~spl74_5)),
% 106.67/16.60 inference(subsumption_resolution,[status(thm)],[f15848,f2152])).
% 106.67/16.60 thf(f2152,plain,(
% 106.67/16.60 ( ! [X0 : nat] : ((zero_zero @ nat = (p @ X0)) | (zero_zero @ nat = X0)) ) | ~spl74_2),
% 106.67/16.60 inference(trivial_inequality_removal,[status(thm)],[f1953])).
% 106.67/16.60 thf(f1953,plain,(
% 106.67/16.60 ( ! [X0 : nat] : ((zero_zero @ nat = X0) | ($true != $true) | (zero_zero @ nat = (p @ X0))) ) | ~spl74_2),
% 106.67/16.60 inference(superposition,[status(thm)],[f1643,f1926])).
% 106.67/16.60 thf(f1926,plain,(
% 106.67/16.60 ( ! [X1 : nat] : (($true = (ord_less_eq @ nat @ X1 @ zero_zero @ nat)) | (zero_zero @ nat = (p @ X1))) ) | ~spl74_2),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f1925])).
% 106.67/16.60 thf(f1643,plain,(
% 106.67/16.60 ( ! [X0 : nat] : (($true != (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) | (zero_zero @ nat = X0)) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1295])).
% 106.67/16.60 thf(f1295,plain,(
% 106.67/16.60 ! [X0 : nat] : ((($true = (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) | (zero_zero @ nat != X0)) & ((zero_zero @ nat = X0) | ($true != (ord_less_eq @ nat @ X0 @ zero_zero @ nat))))),
% 106.67/16.60 inference(nnf_transformation,[status(thm)],[f680])).
% 106.67/16.60 thf(f680,plain,(
% 106.67/16.60 ! [X0 : nat] : (($true = (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) <=> (zero_zero @ nat = X0))),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f679])).
% 106.67/16.60 thf(f679,plain,(
% 106.67/16.60 ! [X0 : nat] : ((ord_less_eq @ nat @ X0 @ zero_zero @ nat) = (zero_zero @ nat = X0))),
% 106.67/16.60 inference(rectify,[status(thm)],[f51])).
% 106.67/16.60 thf(f51,axiom,(
% 106.67/16.60 ! [X8 : nat] : ((ord_less_eq @ nat @ X8 @ zero_zero @ nat) = (zero_zero @ nat = X8))),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',fact_50_le__0__eq)).
% 106.67/16.60 thf(f15848,plain,(
% 106.67/16.60 ( ! [X0 : $tType,X2 : nat] : ((zero_zero @ nat = (p @ X2)) | (wellorder @ X0 != $true) | (zero_zero @ nat != X2)) ) | ~spl74_5),
% 106.67/16.60 inference(subsumption_resolution,[status(thm)],[f12092,f1611])).
% 106.67/16.60 thf(f1611,plain,(
% 106.67/16.60 (linord1659791738miring @ nat = $true)),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f696])).
% 106.67/16.60 thf(f696,plain,(
% 106.67/16.60 (linord1659791738miring @ nat = $true)),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f695])).
% 106.67/16.60 thf(f695,plain,(
% 106.67/16.60 linord1659791738miring @ nat),
% 106.67/16.60 inference(rectify,[status(thm)],[f259])).
% 106.67/16.60 thf(f259,axiom,(
% 106.67/16.60 linord1659791738miring @ nat),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring)).
% 106.67/16.60 thf(f12092,plain,(
% 106.67/16.60 ( ! [X0 : $tType,X2 : nat] : ((zero_zero @ nat != X2) | (linord1659791738miring @ nat != $true) | (wellorder @ X0 != $true) | (zero_zero @ nat = (p @ X2))) ) | ~spl74_5),
% 106.67/16.60 inference(beta_eta_normalization,[status(thm)],[f12091])).
% 106.67/16.60 thf(f12091,plain,(
% 106.67/16.60 ( ! [X0 : $tType,X2 : nat] : ((zero_zero @ nat = (p @ X2)) | (((^[Y0 : X0]: (zero_zero @ nat)) @ (sK61 @ X0 @ (^[Y0 : X0]: (ord_less_eq @ nat @ one_one @ nat @ ((^[Y1 : X0]: (zero_zero @ nat)) @ Y0))))) != X2) | (wellorder @ X0 != $true) | (linord1659791738miring @ nat != $true)) ) | ~spl74_5),
% 106.67/16.60 inference(trivial_inequality_removal,[status(thm)],[f12053])).
% 106.67/16.60 thf(f12053,plain,(
% 106.67/16.60 ( ! [X0 : $tType,X2 : nat] : ((((^[Y0 : X0]: (zero_zero @ nat)) @ (sK61 @ X0 @ (^[Y0 : X0]: (ord_less_eq @ nat @ one_one @ nat @ ((^[Y1 : X0]: (zero_zero @ nat)) @ Y0))))) != X2) | (zero_zero @ nat = (p @ X2)) | (wellorder @ X0 != $true) | ($true != $true) | (linord1659791738miring @ nat != $true)) ) | ~spl74_5),
% 106.67/16.60 inference(superposition,[status(thm)],[f1478,f3094])).
% 106.67/16.60 thf(f3094,plain,(
% 106.67/16.60 ( ! [X1 : $tType,X2 : X1 > nat,X3 : X1,X0 : nat] : (($true = (ord_less_eq @ nat @ one_one @ nat @ (X2 @ X3))) | (zero_zero @ nat = (p @ X0)) | (wellorder @ X1 != $true) | ((X2 @ (sK61 @ X1 @ (^[Y0 : X1]: (ord_less_eq @ nat @ one_one @ nat @ (X2 @ Y0))))) != X0)) ) | ~spl74_5),
% 106.67/16.60 inference(beta_eta_normalization,[status(thm)],[f3093])).
% 106.67/16.60 thf(f3093,plain,(
% 106.67/16.60 ( ! [X1 : $tType,X2 : X1 > nat,X3 : X1,X0 : nat] : ((wellorder @ X1 != $true) | (zero_zero @ nat = (p @ X0)) | ($true = ((^[Y0 : X1]: (ord_less_eq @ nat @ ((^[Y1 : X1]: (one_one @ nat)) @ Y0) @ (X2 @ Y0))) @ X3)) | ((X2 @ (sK61 @ X1 @ (^[Y0 : X1]: (ord_less_eq @ nat @ ((^[Y1 : X1]: (one_one @ nat)) @ Y0) @ (X2 @ Y0))))) != X0)) ) | ~spl74_5),
% 106.67/16.60 inference(trivial_inequality_removal,[status(thm)],[f2949])).
% 106.67/16.60 thf(f2949,plain,(
% 106.67/16.60 ( ! [X1 : $tType,X2 : X1 > nat,X3 : X1,X0 : nat] : (($true != $true) | (wellorder @ X1 != $true) | ($true = ((^[Y0 : X1]: (ord_less_eq @ nat @ ((^[Y1 : X1]: (one_one @ nat)) @ Y0) @ (X2 @ Y0))) @ X3)) | (zero_zero @ nat = (p @ X0)) | ((X2 @ (sK61 @ X1 @ (^[Y0 : X1]: (ord_less_eq @ nat @ ((^[Y1 : X1]: (one_one @ nat)) @ Y0) @ (X2 @ Y0))))) != X0)) ) | ~spl74_5),
% 106.67/16.60 inference(constrained_superposition,[status(thm)],[f1744,f1938])).
% 106.67/16.60 thf(f1938,plain,(
% 106.67/16.60 ( ! [X1 : nat] : (($true = (ord_less_eq @ nat @ one_one @ nat @ X1)) | (zero_zero @ nat = (p @ X1))) ) | ~spl74_5),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f1937])).
% 106.67/16.60 thf(f1744,plain,(
% 106.67/16.60 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != (X1 @ (sK61 @ X0 @ X1))) | (wellorder @ X0 != $true) | ($true = (X1 @ X2))) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1333])).
% 106.67/16.60 thf(f1333,plain,(
% 106.67/16.60 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0] : ((! [X4 : X0] : (($true = (X1 @ X4)) | ($true != (ord_less @ X0 @ X4 @ (sK61 @ X0 @ X1)))) & ($true != (X1 @ (sK61 @ X0 @ X1)))) | ($true = (X1 @ X2))) | (wellorder @ X0 != $true))),
% 106.67/16.60 inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f975,f1332])).
% 106.67/16.60 thf(f1332,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : (! [X4 : X0] : (($true = (X1 @ X4)) | ((ord_less @ X0 @ X4 @ X3) != $true)) & ($true != (X1 @ X3))) => (! [X4 : X0] : (($true = (X1 @ X4)) | ($true != (ord_less @ X0 @ X4 @ (sK61 @ X0 @ X1)))) & ($true != (X1 @ (sK61 @ X0 @ X1)))))),
% 106.67/16.60 introduced(definition,[],[choice_axiom])).
% 106.67/16.60 thf(f975,plain,(
% 106.67/16.60 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (! [X4 : X0] : (($true = (X1 @ X4)) | ((ord_less @ X0 @ X4 @ X3) != $true)) & ($true != (X1 @ X3))) | ($true = (X1 @ X2))) | (wellorder @ X0 != $true))),
% 106.67/16.60 inference(ennf_transformation,[status(thm)],[f760])).
% 106.67/16.60 thf(f760,plain,(
% 106.67/16.60 ! [X0 : $tType] : ((wellorder @ X0 = $true) => ! [X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (! [X4 : X0] : (((ord_less @ X0 @ X4 @ X3) = $true) => ($true = (X1 @ X4))) => ($true = (X1 @ X3))) => ($true = (X1 @ X2))))),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f759])).
% 106.67/16.60 thf(f759,plain,(
% 106.67/16.60 ! [X0 : $tType] : (wellorder @ X0 => ! [X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (! [X4 : X0] : ((ord_less @ X0 @ X4 @ X3) => (X1 @ X4)) => (X1 @ X3)) => (X1 @ X2)))),
% 106.67/16.60 inference(rectify,[status(thm)],[f189])).
% 106.67/16.60 thf(f189,axiom,(
% 106.67/16.60 ! [X0 : $tType] : (wellorder @ X0 => ! [X19 : X0 > $o,X4 : X0] : (! [X21 : X0] : (! [X25 : X0] : ((ord_less @ X0 @ X25 @ X21) => (X19 @ X25)) => (X19 @ X21)) => (X19 @ X4)))),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',fact_188_less__induct)).
% 106.67/16.60 thf(f1478,plain,(
% 106.67/16.60 ( ! [X0 : $tType] : (((ord_less_eq @ X0 @ one_one @ X0 @ zero_zero @ X0) != $true) | (linord1659791738miring @ X0 != $true)) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f982])).
% 106.67/16.60 thf(f982,plain,(
% 106.67/16.60 ! [X0 : $tType] : (((ord_less_eq @ X0 @ one_one @ X0 @ zero_zero @ X0) != $true) | (linord1659791738miring @ X0 != $true))),
% 106.67/16.60 inference(ennf_transformation,[status(thm)],[f863])).
% 106.67/16.60 thf(f863,plain,(
% 106.67/16.60 ! [X0 : $tType] : ((linord1659791738miring @ X0 = $true) => ((ord_less_eq @ X0 @ one_one @ X0 @ zero_zero @ X0) != $true))),
% 106.67/16.60 inference(flattening,[status(thm)],[f452])).
% 106.67/16.60 thf(f452,plain,(
% 106.67/16.60 ! [X0 : $tType] : ((linord1659791738miring @ X0 = $true) => ~((ord_less_eq @ X0 @ one_one @ X0 @ zero_zero @ X0) = $true))),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f451])).
% 106.67/16.60 thf(f451,plain,(
% 106.67/16.60 ! [X0 : $tType] : (linord1659791738miring @ X0 => ~(ord_less_eq @ X0 @ one_one @ X0 @ zero_zero @ X0))),
% 106.67/16.60 inference(rectify,[status(thm)],[f85])).
% 106.67/16.60 thf(f85,axiom,(
% 106.67/16.60 ! [X0 : $tType] : (linord1659791738miring @ X0 => ~(ord_less_eq @ X0 @ one_one @ X0 @ zero_zero @ X0))),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',fact_84_not__one__le__zero)).
% 106.67/16.60 thf(f15155,plain,(
% 106.67/16.60 ~spl74_1 | spl74_3),
% 106.67/16.60 inference(avatar_contradiction_clause,[status(thm)],[f15154])).
% 106.67/16.60 thf(f15154,plain,(
% 106.67/16.60 $false | (~spl74_1 | spl74_3)),
% 106.67/16.60 inference(subsumption_resolution,[status(thm)],[f15153,f3961])).
% 106.67/16.60 thf(f3961,plain,(
% 106.67/16.60 ( ! [X0 : set @ nat] : ((zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ p @ X0))) ) | ~spl74_1),
% 106.67/16.60 inference(subsumption_resolution,[status(thm)],[f3873,f1439])).
% 106.67/16.60 thf(f1439,plain,(
% 106.67/16.60 (comm_monoid_add @ nat = $true)),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f332])).
% 106.67/16.60 thf(f332,plain,(
% 106.67/16.60 (comm_monoid_add @ nat = $true)),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f331])).
% 106.67/16.60 thf(f331,plain,(
% 106.67/16.60 comm_monoid_add @ nat),
% 106.67/16.60 inference(rectify,[status(thm)],[f267])).
% 106.67/16.60 thf(f267,axiom,(
% 106.67/16.60 comm_monoid_add @ nat),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add)).
% 106.67/16.60 thf(f3873,plain,(
% 106.67/16.60 ( ! [X0 : set @ nat] : ((zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ p @ X0)) | (comm_monoid_add @ nat != $true)) ) | ~spl74_1),
% 106.67/16.60 inference(superposition,[status(thm)],[f1627,f1923])).
% 106.67/16.60 thf(f1627,plain,(
% 106.67/16.60 ( ! [X1 : $tType,X0 : $tType,X2 : set @ X0] : ((zero_zero @ X1 = (groups1340683514dd_sum @ X0 @ X1 @ (^[Y0 : X0]: (zero_zero @ X1)) @ X2)) | ($true != comm_monoid_add @ X1)) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1164])).
% 106.67/16.60 thf(f1164,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : (($true != comm_monoid_add @ X1) | ! [X2 : set @ X0] : (zero_zero @ X1 = (groups1340683514dd_sum @ X0 @ X1 @ (^[Y0 : X0]: (zero_zero @ X1)) @ X2)))),
% 106.67/16.60 inference(ennf_transformation,[status(thm)],[f850])).
% 106.67/16.60 thf(f850,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : (($true = comm_monoid_add @ X1) => ! [X2 : set @ X0] : (zero_zero @ X1 = (groups1340683514dd_sum @ X0 @ X1 @ (^[Y0 : X0]: (zero_zero @ X1)) @ X2)))),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f849])).
% 106.67/16.60 thf(f849,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : (comm_monoid_add @ X1 => ! [X2 : set @ X0] : ((groups1340683514dd_sum @ X0 @ X1 @ (^[X3 : X0] : (zero_zero @ X1)) @ X2) = zero_zero @ X1))),
% 106.67/16.60 inference(rectify,[status(thm)],[f5])).
% 106.67/16.60 thf(f5,axiom,(
% 106.67/16.60 ! [X1 : $tType,X0 : $tType] : (comm_monoid_add @ X0 => ! [X5 : set @ X1] : ((groups1340683514dd_sum @ X1 @ X0 @ (^[X6 : X1] : (zero_zero @ X0)) @ X5) = zero_zero @ X0))),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',fact_4_sum_Oneutral__const)).
% 106.67/16.60 thf(f15153,plain,(
% 106.67/16.60 (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ p @ (set_ord_atMost @ nat @ zero_zero @ nat))) | (~spl74_1 | spl74_3)),
% 106.67/16.60 inference(forward_demodulation,[status(thm)],[f15051,f1923])).
% 106.67/16.60 thf(f15051,plain,(
% 106.67/16.60 (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (zero_zero @ nat)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) | (~spl74_1 | spl74_3)),
% 106.67/16.60 inference(equality_resolution,[status(thm)],[f4267])).
% 106.67/16.60 thf(f4267,plain,(
% 106.67/16.60 ( ! [X0 : nat > nat] : ((zero_zero @ nat != (X0 @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ X0 @ (set_ord_atMost @ nat @ zero_zero @ nat)))) ) | (~spl74_1 | spl74_3)),
% 106.67/16.60 inference(forward_demodulation,[status(thm)],[f4266,f1902])).
% 106.67/16.60 thf(f1902,plain,(
% 106.67/16.60 ( ! [X1 : nat] : ((zero_zero @ nat = (times_times @ nat @ zero_zero @ nat @ X1))) )),
% 106.67/16.60 inference(equality_resolution,[status(thm)],[f1779])).
% 106.67/16.60 thf(f1779,plain,(
% 106.67/16.60 ( ! [X0 : nat,X1 : nat] : ((zero_zero @ nat = (times_times @ nat @ X0 @ X1)) | (zero_zero @ nat != X0)) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1348])).
% 106.67/16.60 thf(f1348,plain,(
% 106.67/16.60 ! [X0 : nat,X1 : nat] : (((zero_zero @ nat = X1) | (zero_zero @ nat = X0) | (zero_zero @ nat != (times_times @ nat @ X0 @ X1))) & ((zero_zero @ nat = (times_times @ nat @ X0 @ X1)) | ((zero_zero @ nat != X1) & (zero_zero @ nat != X0))))),
% 106.67/16.60 inference(flattening,[status(thm)],[f1347])).
% 106.67/16.60 thf(f1347,plain,(
% 106.67/16.60 ! [X0 : nat,X1 : nat] : ((((zero_zero @ nat = X1) | (zero_zero @ nat = X0)) | (zero_zero @ nat != (times_times @ nat @ X0 @ X1))) & ((zero_zero @ nat = (times_times @ nat @ X0 @ X1)) | ((zero_zero @ nat != X1) & (zero_zero @ nat != X0))))),
% 106.67/16.60 inference(nnf_transformation,[status(thm)],[f488])).
% 106.67/16.60 thf(f488,plain,(
% 106.67/16.60 ! [X0 : nat,X1 : nat] : (((zero_zero @ nat = X1) | (zero_zero @ nat = X0)) <=> (zero_zero @ nat = (times_times @ nat @ X0 @ X1)))),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f487])).
% 106.67/16.60 thf(f487,plain,(
% 106.67/16.60 ! [X0 : nat,X1 : nat] : ((zero_zero @ nat = (times_times @ nat @ X0 @ X1)) = (zero_zero @ nat = X0) | (zero_zero @ nat = X1))),
% 106.67/16.60 inference(rectify,[status(thm)],[f24])).
% 106.67/16.60 thf(f24,axiom,(
% 106.67/16.60 ! [X14 : nat,X8 : nat] : ((zero_zero @ nat = (times_times @ nat @ X14 @ X8)) = (zero_zero @ nat = X14) | (zero_zero @ nat = X8))),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',fact_23_mult__is__0)).
% 106.67/16.60 thf(f4266,plain,(
% 106.67/16.60 ( ! [X0 : nat > nat] : (((times_times @ nat @ zero_zero @ nat @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) != (X0 @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ X0 @ (set_ord_atMost @ nat @ zero_zero @ nat)))) ) | (~spl74_1 | spl74_3)),
% 106.67/16.60 inference(forward_demodulation,[status(thm)],[f4265,f3955])).
% 106.67/16.60 thf(f3955,plain,(
% 106.67/16.60 ( ! [X1 : nat] : ((zero_zero @ nat = (p @ X1))) ) | ~spl74_1),
% 106.67/16.60 inference(beta_eta_normalization,[status(thm)],[f3872])).
% 106.67/16.60 thf(f3872,plain,(
% 106.67/16.60 ( ! [X1 : nat] : (((p @ X1) = ((^[Y0 : nat]: (zero_zero @ nat)) @ X1))) ) | ~spl74_1),
% 106.67/16.60 inference(argument_congruence,[status(thm)],[f1923])).
% 106.67/16.60 thf(f4265,plain,(
% 106.67/16.60 ( ! [X0 : nat > nat] : (((times_times @ nat @ (p @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) != (X0 @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ X0 @ (set_ord_atMost @ nat @ zero_zero @ nat)))) ) | spl74_3),
% 106.67/16.60 inference(subsumption_resolution,[status(thm)],[f4264,f1439])).
% 106.67/16.60 thf(f4264,plain,(
% 106.67/16.60 ( ! [X0 : nat > nat] : ((comm_monoid_add @ nat != $true) | ((times_times @ nat @ (p @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) != (X0 @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ X0 @ (set_ord_atMost @ nat @ zero_zero @ nat)))) ) | spl74_3),
% 106.67/16.60 inference(beta_eta_normalization,[status(thm)],[f4260])).
% 106.67/16.60 thf(f4260,plain,(
% 106.67/16.60 ( ! [X0 : nat > nat] : ((comm_monoid_add @ nat != $true) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ X0 @ (set_ord_atMost @ nat @ zero_zero @ nat))) | (((^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) != (X0 @ (sK24 @ nat @ nat @ X0 @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))))) ) | spl74_3),
% 106.67/16.60 inference(superposition,[status(thm)],[f1930,f1860])).
% 106.67/16.60 thf(f1860,plain,(
% 106.67/16.60 ( ! [X1 : $tType,X0 : $tType,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : (((groups1340683514dd_sum @ X1 @ X0 @ X4 @ X3) = (groups1340683514dd_sum @ X1 @ X0 @ X5 @ X3)) | (comm_monoid_add @ X0 != $true) | ((X5 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3)) != (X4 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3)))) )),
% 106.67/16.60 inference(equality_resolution,[status(thm)],[f1484])).
% 106.67/16.60 thf(f1484,plain,(
% 106.67/16.60 ( ! [X1 : $tType,X0 : $tType,X2 : set @ X1,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : ((comm_monoid_add @ X0 != $true) | ((X5 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3)) != (X4 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3))) | ((groups1340683514dd_sum @ X1 @ X0 @ X5 @ X3) = (groups1340683514dd_sum @ X1 @ X0 @ X4 @ X2)) | (X2 != X3)) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1234])).
% 106.67/16.60 thf(f1234,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : ((comm_monoid_add @ X0 != $true) | ! [X2 : set @ X1,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : ((($true = (member @ X1 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3) @ X3)) & ((X5 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3)) != (X4 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3)))) | ((groups1340683514dd_sum @ X1 @ X0 @ X5 @ X3) = (groups1340683514dd_sum @ X1 @ X0 @ X4 @ X2)) | (X2 != X3)))),
% 106.67/16.60 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1044,f1233])).
% 106.67/16.60 thf(f1233,plain,(
% 106.67/16.60 ! [X1 : $tType,X0 : $tType,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : (? [X6 : X1] : (($true = (member @ X1 @ X6 @ X3)) & ((X4 @ X6) != (X5 @ X6))) => (($true = (member @ X1 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3) @ X3)) & ((X5 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3)) != (X4 @ (sK24 @ X0 @ X1 @ X5 @ X4 @ X3)))))),
% 106.67/16.60 introduced(definition,[],[choice_axiom])).
% 106.67/16.60 thf(f1044,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : ((comm_monoid_add @ X0 != $true) | ! [X2 : set @ X1,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : (? [X6 : X1] : (($true = (member @ X1 @ X6 @ X3)) & ((X4 @ X6) != (X5 @ X6))) | ((groups1340683514dd_sum @ X1 @ X0 @ X5 @ X3) = (groups1340683514dd_sum @ X1 @ X0 @ X4 @ X2)) | (X2 != X3)))),
% 106.67/16.60 inference(flattening,[status(thm)],[f1043])).
% 106.67/16.60 thf(f1043,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : (! [X2 : set @ X1,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : ((((groups1340683514dd_sum @ X1 @ X0 @ X5 @ X3) = (groups1340683514dd_sum @ X1 @ X0 @ X4 @ X2)) | ? [X6 : X1] : (($true = (member @ X1 @ X6 @ X3)) & ((X4 @ X6) != (X5 @ X6)))) | (X2 != X3)) | (comm_monoid_add @ X0 != $true))),
% 106.67/16.60 inference(ennf_transformation,[status(thm)],[f682])).
% 106.67/16.60 thf(f682,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : ((comm_monoid_add @ X0 = $true) => ! [X2 : set @ X1,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : ((X2 = X3) => (! [X6 : X1] : (($true = (member @ X1 @ X6 @ X3)) => ((X4 @ X6) = (X5 @ X6))) => ((groups1340683514dd_sum @ X1 @ X0 @ X5 @ X3) = (groups1340683514dd_sum @ X1 @ X0 @ X4 @ X2)))))),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f681])).
% 106.67/16.60 thf(f681,plain,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : (comm_monoid_add @ X0 => ! [X2 : set @ X1,X3 : set @ X1,X4 : X1 > X0,X5 : X1 > X0] : ((X2 = X3) => (! [X6 : X1] : ((member @ X1 @ X6 @ X3) => ((X4 @ X6) = (X5 @ X6))) => ((groups1340683514dd_sum @ X1 @ X0 @ X5 @ X3) = (groups1340683514dd_sum @ X1 @ X0 @ X4 @ X2)))))),
% 106.67/16.60 inference(rectify,[status(thm)],[f35])).
% 106.67/16.60 thf(f35,axiom,(
% 106.67/16.60 ! [X0 : $tType,X1 : $tType] : (comm_monoid_add @ X0 => ! [X5 : set @ X1,X34 : set @ X1,X31 : X1 > X0,X30 : X1 > X0] : ((X5 = X34) => (! [X21 : X1] : ((member @ X1 @ X21 @ X34) => ((X31 @ X21) = (X30 @ X21))) => ((groups1340683514dd_sum @ X1 @ X0 @ X31 @ X5) = (groups1340683514dd_sum @ X1 @ X0 @ X30 @ X34)))))),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',fact_34_sum_Ocong)).
% 106.67/16.60 thf(f1930,plain,(
% 106.67/16.60 (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) | spl74_3),
% 106.67/16.60 inference(avatar_component_clause,[status(thm)],[f1929])).
% 106.67/16.60 thf(f1929,definition,(
% 106.67/16.60 spl74_3 <=> (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))),
% 106.67/16.60 introduced(definition,[new_symbols(naming,[spl74_3])],[avatar_definition])).
% 106.67/16.60 thf(f1939,plain,(
% 106.67/16.60 spl74_5 | spl74_1),
% 106.67/16.60 inference(avatar_split_clause,[status(thm)],[f1802,f1922,f1937])).
% 106.67/16.60 thf(f1802,plain,(
% 106.67/16.60 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero @ nat))) | (zero_zero @ nat = (p @ X1)) | ($true = (ord_less_eq @ nat @ one_one @ nat @ X1))) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1360])).
% 106.67/16.60 thf(f1360,plain,(
% 106.67/16.60 (((zero_zero @ nat != (p @ sK69)) & (($true != (ord_less_eq @ nat @ sK69 @ zero_zero @ nat)) | ($true != (ord_less_eq @ nat @ one_one @ nat @ sK69)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) | (p != (^[Y0 : nat]: (zero_zero @ nat)))) & ((! [X1 : nat] : ((zero_zero @ nat = (p @ X1)) | (($true = (ord_less_eq @ nat @ X1 @ zero_zero @ nat)) & ($true = (ord_less_eq @ nat @ one_one @ nat @ X1)))) & (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (p = (^[Y0 : nat]: (zero_zero @ nat))))),
% 106.67/16.60 inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f1358,f1359])).
% 106.67/16.60 thf(f1359,plain,(
% 106.67/16.60 ? [X0 : nat] : ((zero_zero @ nat != (p @ X0)) & (($true != (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) | ($true != (ord_less_eq @ nat @ one_one @ nat @ X0)))) => ((zero_zero @ nat != (p @ sK69)) & (($true != (ord_less_eq @ nat @ sK69 @ zero_zero @ nat)) | ($true != (ord_less_eq @ nat @ one_one @ nat @ sK69))))),
% 106.67/16.60 introduced(definition,[],[choice_axiom])).
% 106.67/16.60 thf(f1358,plain,(
% 106.67/16.60 (? [X0 : nat] : ((zero_zero @ nat != (p @ X0)) & (($true != (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) | ($true != (ord_less_eq @ nat @ one_one @ nat @ X0)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) | (p != (^[Y0 : nat]: (zero_zero @ nat)))) & ((! [X1 : nat] : ((zero_zero @ nat = (p @ X1)) | (($true = (ord_less_eq @ nat @ X1 @ zero_zero @ nat)) & ($true = (ord_less_eq @ nat @ one_one @ nat @ X1)))) & (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (p = (^[Y0 : nat]: (zero_zero @ nat))))),
% 106.67/16.60 inference(rectify,[status(thm)],[f1357])).
% 106.67/16.60 thf(f1357,plain,(
% 106.67/16.60 (? [X0 : nat] : ((zero_zero @ nat != (p @ X0)) & (($true != (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) | ($true != (ord_less_eq @ nat @ one_one @ nat @ X0)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) | (p != (^[Y0 : nat]: (zero_zero @ nat)))) & ((! [X0 : nat] : ((zero_zero @ nat = (p @ X0)) | (($true = (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) & ($true = (ord_less_eq @ nat @ one_one @ nat @ X0)))) & (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (p = (^[Y0 : nat]: (zero_zero @ nat))))),
% 106.67/16.60 inference(flattening,[status(thm)],[f1356])).
% 106.67/16.60 thf(f1356,plain,(
% 106.67/16.60 ((? [X0 : nat] : ((zero_zero @ nat != (p @ X0)) & (($true != (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) | ($true != (ord_less_eq @ nat @ one_one @ nat @ X0)))) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (p != (^[Y0 : nat]: (zero_zero @ nat)))) & ((! [X0 : nat] : ((zero_zero @ nat = (p @ X0)) | (($true = (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) & ($true = (ord_less_eq @ nat @ one_one @ nat @ X0)))) & (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat)))) | (p = (^[Y0 : nat]: (zero_zero @ nat))))),
% 106.67/16.60 inference(nnf_transformation,[status(thm)],[f899])).
% 106.67/16.60 thf(f899,plain,(
% 106.67/16.60 (p = (^[Y0 : nat]: (zero_zero @ nat))) <~> (! [X0 : nat] : ((zero_zero @ nat = (p @ X0)) | (($true = (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) & ($true = (ord_less_eq @ nat @ one_one @ nat @ X0)))) & (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))))),
% 106.67/16.60 inference(ennf_transformation,[status(thm)],[f880])).
% 106.67/16.60 thf(f880,plain,(
% 106.67/16.60 ~((p = (^[Y0 : nat]: (zero_zero @ nat))) <=> ((zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) & ! [X0 : nat] : ((zero_zero @ nat != (p @ X0)) => (($true = (ord_less_eq @ nat @ X0 @ zero_zero @ nat)) & ($true = (ord_less_eq @ nat @ one_one @ nat @ X0))))))),
% 106.67/16.60 inference(rectify,[status(thm)],[f702])).
% 106.67/16.60 thf(f702,plain,(
% 106.67/16.60 ~((p = (^[Y0 : nat]: (zero_zero @ nat))) <=> ((zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) & ! [X2 : nat] : ((zero_zero @ nat != (p @ X2)) => (($true = (ord_less_eq @ nat @ one_one @ nat @ X2)) & ($true = (ord_less_eq @ nat @ X2 @ zero_zero @ nat))))))),
% 106.67/16.60 inference(fool_elimination,[status(thm)],[f701])).
% 106.67/16.60 thf(f701,plain,(
% 106.67/16.60 ~(((^[X0 : nat] : (zero_zero @ nat)) = p) = (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[X1 : nat] : (times_times @ nat @ (p @ X1) @ X1)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) & ! [X2 : nat] : ((zero_zero @ nat != (p @ X2)) => ((ord_less_eq @ nat @ one_one @ nat @ X2) & (ord_less_eq @ nat @ X2 @ zero_zero @ nat))))),
% 106.67/16.60 inference(rectify,[status(thm)],[f289])).
% 106.67/16.60 thf(f289,negated_conjecture,(
% 106.67/16.60 ~(((^[X10 : nat] : (zero_zero @ nat)) = p) = (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[X10 : nat] : (times_times @ nat @ (p @ X10) @ X10)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) & ! [X10 : nat] : ((zero_zero @ nat != (p @ X10)) => ((ord_less_eq @ nat @ one_one @ nat @ X10) & (ord_less_eq @ nat @ X10 @ zero_zero @ nat))))),
% 106.67/16.60 inference(negated_conjecture,[status(cth)],[f288])).
% 106.67/16.60 thf(f288,conjecture,(
% 106.67/16.60 (((^[X10 : nat] : (zero_zero @ nat)) = p) = (zero_zero @ nat = (groups1340683514dd_sum @ nat @ nat @ (^[X10 : nat] : (times_times @ nat @ (p @ X10) @ X10)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) & ! [X10 : nat] : ((zero_zero @ nat != (p @ X10)) => ((ord_less_eq @ nat @ one_one @ nat @ X10) & (ord_less_eq @ nat @ X10 @ zero_zero @ nat))))),
% 106.67/16.60 file('/export/starexec/sandbox/tmp/tmp.lUH4F7drhZ/DTF2THF_11076.p',conj_0)).
% 106.67/16.60 thf(f1935,plain,(
% 106.67/16.60 ~spl74_3 | ~spl74_1 | ~spl74_4),
% 106.67/16.60 inference(avatar_split_clause,[status(thm)],[f1805,f1933,f1922,f1929])).
% 106.67/16.60 thf(f1805,plain,(
% 106.67/16.60 (zero_zero @ nat != (p @ sK69)) | (zero_zero @ nat != (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ zero_zero @ nat))) | (p != (^[Y0 : nat]: (zero_zero @ nat)))),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1360])).
% 106.67/16.60 thf(f1927,plain,(
% 106.67/16.60 spl74_1 | spl74_2),
% 106.67/16.60 inference(avatar_split_clause,[status(thm)],[f1803,f1925,f1922])).
% 106.67/16.60 thf(f1803,plain,(
% 106.67/16.60 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero @ nat))) | (zero_zero @ nat = (p @ X1)) | ($true = (ord_less_eq @ nat @ X1 @ zero_zero @ nat))) )),
% 106.67/16.60 inference(cnf_transformation,[status(thm)],[f1360])).
% 106.67/16.60 % SZS output end Proof for DTF2THF_11076
% 106.67/16.60 % (11800)------------------------------
% 106.67/16.60 % (11800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.67/16.60 % (11800)Termination reason: Refutation
% 106.67/16.60
% 106.67/16.60 % (11800)Memory used [KB]: 21236
% 106.67/16.60 % (11800)Time elapsed: 3.098 s
% 106.67/16.60 % (11800)Instructions burned: 9800 (million)
% 106.67/16.60 % (11800)------------------------------
% 106.67/16.60 % (11800)------------------------------
% 106.67/16.60 % (11267)Success in time 15.011 s
%------------------------------------------------------------------------------