%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP145^2 : 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 : n010.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 08:55:55 AM UTC 2026
% Result : Theorem 98.84s 15.70s
% Output : Refutation 98.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP145^2 : 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
% 0.17/0.33 % Computer : n010.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 08:27:33 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ITP145^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.45 % Domain : Interactive Theorem Proving
% 0.30/0.45 % Problem : Sledgehammer PHoareTotal problem prob_632__3264706_1
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Des21]
% 0.30/0.45 % Names : PHoareTotal/prob_632__3264706_1 [Des21]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.75 v7.5.0
% 0.30/0.45 % Syntax : Number of formulae : 312 ( 113 unt; 48 typ; 0 def)
% 0.30/0.45 % Number of atoms : 641 ( 311 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.30/0.45 % Number of connectives : 7312 ( 153 ~; 18 |; 67 &;6680 @)
% 0.30/0.45 % ( 0 <=>; 394 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 28 ( 11 avg)
% 0.30/0.45 % Number of types : 4 ( 3 usr)
% 0.30/0.45 % Number of type conns : 244 ( 244 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 46 ( 45 usr; 4 con; 0-5 aty)
% 0.30/0.45 % Number of variables : 1353 ( 6 ^;1262 !; 52 ?;1353 :)
% 0.30/0.45 % ( 33 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.45 % SPC : TH1_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:50.622
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % Could-be-implicit typings (6)
% 0.30/0.45 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.45 product_prod: $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_PLang_Ostate,type,
% 0.30/0.45 state: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_PLang_Ocom,type,
% 0.30/0.45 com: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_List_Olist,type,
% 0.30/0.45 list: $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Set_Oset,type,
% 0.30/0.45 set: $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Nat_Onat,type,
% 0.30/0.45 nat: $tType ).
% 0.30/0.45
% 0.30/0.45 % Explicit typings (42)
% 0.30/0.45 thf(sy_cl_HOL_Otype,type,
% 0.30/0.45 type:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Groups_Ozero,type,
% 0.30/0.45 zero:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.45 ord:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.45 linorder:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.30/0.45 zero_zero:
% 0.30/0.45 !>[A: $tType] : A ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_List_Oappend,type,
% 0.30/0.45 append:
% 0.30/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_List_Obind,type,
% 0.30/0.45 bind:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_List_Oconcat,type,
% 0.30/0.45 concat:
% 0.30/0.45 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_List_Ogen__length,type,
% 0.30/0.45 gen_length:
% 0.30/0.45 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_List_Oinsert,type,
% 0.30/0.45 insert:
% 0.30/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_List_Olexord,type,
% 0.30/0.45 lexord:
% 0.30/0.45 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_List_Olist_OCons,type,
% 0.30/0.45 cons:
% 0.30/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.30/0.46 nil:
% 0.30/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olistrel,type,
% 0.30/0.46 listrel:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olistrel1,type,
% 0.30/0.46 listrel1:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Omaps,type,
% 0.30/0.46 maps:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_On__lists,type,
% 0.30/0.46 n_lists:
% 0.30/0.46 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onths,type,
% 0.30/0.46 nths:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( set @ nat ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Oproduct__lists,type,
% 0.30/0.46 product_lists:
% 0.30/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Osubseqs,type,
% 0.30/0.46 subseqs:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_OSuc,type,
% 0.30/0.46 suc: nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oexec1,type,
% 0.30/0.46 pHoare1053570893_exec1: set @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oexecs,type,
% 0.30/0.46 pHoare1053570959_execs: state > ( list @ com ) > state > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oinf,type,
% 0.30/0.46 pHoare1838713294le_inf: ( list @ com ) > state > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Otermis,type,
% 0.30/0.46 pHoare1335526537termis: ( list @ com ) > state > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PLang_Ocom_OCond,type,
% 0.30/0.46 cond: ( state > $o ) > com > com > com ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PLang_Ocom_ODo,type,
% 0.30/0.46 do: ( state > ( set @ state ) ) > com ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PLang_Ocom_OSemi,type,
% 0.30/0.46 semi: com > com > com ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PLang_Ocom_OWhile,type,
% 0.30/0.46 while: ( state > $o ) > com > com ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PLang_Oexec,type,
% 0.30/0.46 exec: state > com > state > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_PTermi_Otermi,type,
% 0.30/0.46 termi: com > state > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.46 product_Pair:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.46 product_rec_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_Oirrefl,type,
% 0.30/0.46 irrefl:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Transitive__Closure_Ortrancl,type,
% 0.30/0.46 transitive_rtrancl:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Transitive__Closure_Otrancl,type,
% 0.30/0.46 transitive_trancl:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_c,type,
% 0.30/0.46 c: com ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_f,type,
% 0.30/0.46 f: nat > ( product_prod @ ( list @ com ) @ state ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_n,type,
% 0.30/0.46 n: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_s,type,
% 0.30/0.46 s: state ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (252)
% 0.30/0.46 thf(fact_0_exec1E_I1_J,axiom,
% 0.30/0.46 ! [S: state,Cs: list @ com,S2: state] :
% 0.30/0.46 ~ ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 ) ).
% 0.30/0.46
% 0.30/0.46 % exec1E(1)
% 0.30/0.46 thf(fact_1_renumber,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,F: nat > A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ! [I: nat] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ ( F @ I ) ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 0.30/0.46 => ? [F2: nat > A] :
% 0.30/0.46 ( ( ( F2 @ ( zero_zero @ nat ) )
% 0.30/0.46 = A2 )
% 0.30/0.46 & ! [I2: nat] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % renumber
% 0.30/0.46 thf(fact_2_renumber__aux,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,F: nat > A,R: set @ ( product_prod @ A @ A ),B2: A] :
% 0.30/0.46 ( ! [I: nat] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ ( F @ I ) ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( B2
% 0.30/0.46 = ( F @ ( zero_zero @ nat ) ) )
% 0.30/0.46 => ? [F2: nat > A] :
% 0.30/0.46 ( ( ( F2 @ ( zero_zero @ nat ) )
% 0.30/0.46 = A2 )
% 0.30/0.46 & ! [I2: nat] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % renumber_aux
% 0.30/0.46 thf(fact_3_execs__pres__termi,axiom,
% 0.30/0.46 ! [C: com,S: state,C2: com,Cs: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( nil @ com ) ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C2 @ Cs ) @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 0.30/0.46 => ( ( termi @ C @ S )
% 0.30/0.46 => ( termi @ C2 @ S2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % execs_pres_termi
% 0.30/0.46 thf(fact_4_rtrancl__trancl__absorb,axiom,
% 0.30/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( transitive_trancl @ A @ ( transitive_rtrancl @ A @ R2 ) )
% 0.30/0.46 = ( transitive_rtrancl @ A @ R2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_trancl_absorb
% 0.30/0.46 thf(fact_5_trancl__rtrancl__absorb,axiom,
% 0.30/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( transitive_rtrancl @ A @ ( transitive_trancl @ A @ R2 ) )
% 0.30/0.46 = ( transitive_rtrancl @ A @ R2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_rtrancl_absorb
% 0.30/0.46 thf(fact_6_trancl__induct2,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Ax: A,Ay: B,Bx: A,By: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ),P: A > B > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_trancl @ ( product_prod @ A @ B ) @ R ) )
% 0.30/0.46 => ( ! [A3: A,B3: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ R )
% 0.30/0.46 => ( P @ A3 @ B3 ) )
% 0.30/0.46 => ( ! [A3: A,B3: B,Aa: A,Ba: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ ( transitive_trancl @ ( product_prod @ A @ B ) @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Aa @ Ba ) ) @ R )
% 0.30/0.46 => ( ( P @ A3 @ B3 )
% 0.30/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.30/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_induct2
% 0.30/0.46 thf(fact_7_inf__def,axiom,
% 0.30/0.46 ( pHoare1838713294le_inf
% 0.30/0.46 = ( ^ [Cs2: list @ com,S3: state] :
% 0.30/0.46 ? [F3: nat > ( product_prod @ ( list @ com ) @ state )] :
% 0.30/0.46 ( ( ( F3 @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( product_Pair @ ( list @ com ) @ state @ Cs2 @ S3 ) )
% 0.30/0.46 & ! [I3: nat] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ pHoare1053570893_exec1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_def
% 0.30/0.46 thf(fact_8_rtrancl__induct2,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Ax: A,Ay: B,Bx: A,By: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ),P: A > B > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 0.30/0.46 => ( ( P @ Ax @ Ay )
% 0.30/0.46 => ( ! [A3: A,B3: B,Aa: A,Ba: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Aa @ Ba ) ) @ R )
% 0.30/0.46 => ( ( P @ A3 @ B3 )
% 0.30/0.46 => ( P @ Aa @ Ba ) ) ) )
% 0.30/0.46 => ( P @ Bx @ By ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_induct2
% 0.30/0.46 thf(fact_9_converse__rtranclE2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Xa: A,Xb: B,Za: A,Zb: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Xa @ Xb ) @ ( product_Pair @ A @ B @ Za @ Zb ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ Xa @ Xb )
% 0.30/0.46 != ( product_Pair @ A @ B @ Za @ Zb ) )
% 0.30/0.46 => ~ ! [A3: A,B3: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Xa @ Xb ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ R )
% 0.30/0.46 => ~ ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Za @ Zb ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % converse_rtranclE2
% 0.30/0.46 thf(fact_10_converse__rtrancl__induct2,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Ax: A,Ay: B,Bx: A,By: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ),P: A > B > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 0.30/0.46 => ( ( P @ Bx @ By )
% 0.30/0.46 => ( ! [A3: A,B3: B,Aa: A,Ba: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Aa @ Ba ) ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Aa @ Ba ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 0.30/0.46 => ( ( P @ Aa @ Ba )
% 0.30/0.46 => ( P @ A3 @ B3 ) ) ) )
% 0.30/0.46 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % converse_rtrancl_induct2
% 0.30/0.46 thf(fact_11_tranclD,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R2: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R2 ) )
% 0.30/0.46 => ? [Z: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R2 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ Y ) @ ( transitive_rtrancl @ A @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % tranclD
% 0.30/0.46 thf(fact_12_rtranclD,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R2: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R2 ) )
% 0.30/0.46 => ( ( A2 = B2 )
% 0.30/0.46 | ( ( A2 != B2 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtranclD
% 0.30/0.46 thf(fact_13_tranclD2,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R2: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R2 ) )
% 0.30/0.46 => ? [Z: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ ( transitive_rtrancl @ A @ R2 ) )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ Y ) @ R2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % tranclD2
% 0.30/0.46 thf(fact_14_trancl__into__rtrancl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_into_rtrancl
% 0.30/0.46 thf(fact_15_rtrancl__eq__or__trancl,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R2: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R2 ) )
% 0.30/0.46 = ( ( X = Y )
% 0.30/0.46 | ( ( X != Y )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_eq_or_trancl
% 0.30/0.46 thf(fact_16_r__into__rtrancl,axiom,
% 0.30/0.46 ! [A: $tType,P2: product_prod @ A @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ P2 @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ P2 @ ( transitive_rtrancl @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % r_into_rtrancl
% 0.30/0.46 thf(fact_17_rtrancl__idemp,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( transitive_rtrancl @ A @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 = ( transitive_rtrancl @ A @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_idemp
% 0.30/0.46 thf(fact_18_r__into__trancl_H,axiom,
% 0.30/0.46 ! [A: $tType,P2: product_prod @ A @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ P2 @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ P2 @ ( transitive_trancl @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % r_into_trancl'
% 0.30/0.46 thf(fact_19_converse__rtrancl__into__rtrancl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % converse_rtrancl_into_rtrancl
% 0.30/0.46 thf(fact_20_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl.rtrancl_into_rtrancl
% 0.30/0.46 thf(fact_21_converse__rtrancl__induct,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ B2 )
% 0.30/0.46 => ( ! [Y2: A,Z: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ Z )
% 0.30/0.46 => ( P @ Y2 ) ) ) )
% 0.30/0.46 => ( P @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % converse_rtrancl_induct
% 0.30/0.46 thf(fact_22_rtrancl_Ortrancl__refl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,R: set @ ( product_prod @ A @ A )] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( transitive_rtrancl @ A @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl.rtrancl_refl
% 0.30/0.46 thf(fact_23_converse__rtranclE,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Z2: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( X != Z2 )
% 0.30/0.46 => ~ ! [Y2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z2 ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % converse_rtranclE
% 0.30/0.46 thf(fact_24_rtrancl_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,X1: A,X2: A,R: set @ ( product_prod @ A @ A ),P: A > A > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X1 @ X2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ! [A3: A] : ( P @ A3 @ A3 )
% 0.30/0.46 => ( ! [A3: A,B3: A,C3: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ A3 @ B3 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ C3 ) @ R )
% 0.30/0.46 => ( P @ A3 @ C3 ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl.inducts
% 0.30/0.46 thf(fact_25_rtrancl__induct,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ A2 )
% 0.30/0.46 => ( ! [Y2: A,Z: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 0.30/0.46 => ( ( P @ Y2 )
% 0.30/0.46 => ( P @ Z ) ) ) )
% 0.30/0.46 => ( P @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_induct
% 0.30/0.46 thf(fact_26_rtrancl__trans,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Z2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_trans
% 0.30/0.46 thf(fact_27_rtrancl_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 = ( ? [A4: A] :
% 0.30/0.46 ( ( A1 = A4 )
% 0.30/0.46 & ( A22 = A4 ) )
% 0.30/0.46 | ? [A4: A,B4: A,C4: A] :
% 0.30/0.46 ( ( A1 = A4 )
% 0.30/0.46 & ( A22 = C4 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ C4 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl.simps
% 0.30/0.46 thf(fact_28_rtrancl_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( A22 != A1 )
% 0.30/0.46 => ~ ! [B3: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ B3 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ A22 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl.cases
% 0.30/0.46 thf(fact_29_rtranclE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ~ ! [Y2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ B2 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtranclE
% 0.30/0.46 thf(fact_30_trancl_Otrancl__into__trancl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl.trancl_into_trancl
% 0.30/0.46 thf(fact_31_converse__trancl__induct,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ! [Y2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ B2 ) @ R )
% 0.30/0.46 => ( P @ Y2 ) )
% 0.30/0.46 => ( ! [Y2: A,Z: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ Z )
% 0.30/0.46 => ( P @ Y2 ) ) ) )
% 0.30/0.46 => ( P @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % converse_trancl_induct
% 0.30/0.46 thf(fact_32_trancl_Or__into__trancl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl.r_into_trancl
% 0.30/0.46 thf(fact_33_trancl__trans__induct,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),P: A > A > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ! [X3: A,Y2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y2 ) @ R )
% 0.30/0.46 => ( P @ X3 @ Y2 ) )
% 0.30/0.46 => ( ! [X3: A,Y2: A,Z: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ X3 @ Y2 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ Y2 @ Z )
% 0.30/0.46 => ( P @ X3 @ Z ) ) ) ) )
% 0.30/0.46 => ( P @ X @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_trans_induct
% 0.30/0.46 thf(fact_34_trancl__into__trancl2,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_into_trancl2
% 0.30/0.46 thf(fact_35_irrefl__trancl__rD,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ X3 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.30/0.46 => ( X != Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % irrefl_trancl_rD
% 0.30/0.46 thf(fact_36_converse__tranclE,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Z2: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ R )
% 0.30/0.46 => ~ ! [Y2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z2 ) @ ( transitive_trancl @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % converse_tranclE
% 0.30/0.46 thf(fact_37_r__r__into__trancl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R2: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R2 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R2 )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % r_r_into_trancl
% 0.30/0.46 thf(fact_38_trancl_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,X1: A,X2: A,R: set @ ( product_prod @ A @ A ),P: A > A > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X1 @ X2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ! [A3: A,B3: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ R )
% 0.30/0.46 => ( P @ A3 @ B3 ) )
% 0.30/0.46 => ( ! [A3: A,B3: A,C3: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( P @ A3 @ B3 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ C3 ) @ R )
% 0.30/0.46 => ( P @ A3 @ C3 ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl.inducts
% 0.30/0.46 thf(fact_39_trancl__induct,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ! [Y2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ R )
% 0.30/0.46 => ( P @ Y2 ) )
% 0.30/0.46 => ( ! [Y2: A,Z: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 0.30/0.46 => ( ( P @ Y2 )
% 0.30/0.46 => ( P @ Z ) ) ) )
% 0.30/0.46 => ( P @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_induct
% 0.30/0.46 thf(fact_40_trancl__trans,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Z2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_trans
% 0.30/0.46 thf(fact_41_trancl_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 = ( ? [A4: A,B4: A] :
% 0.30/0.46 ( ( A1 = A4 )
% 0.30/0.46 & ( A22 = B4 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ R ) )
% 0.30/0.46 | ? [A4: A,B4: A,C4: A] :
% 0.30/0.46 ( ( A1 = A4 )
% 0.30/0.46 & ( A22 = C4 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ C4 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl.simps
% 0.30/0.46 thf(fact_42_trancl_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ R )
% 0.30/0.46 => ~ ! [B3: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ B3 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ A22 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl.cases
% 0.30/0.46 thf(fact_43_tranclE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.30/0.46 => ~ ! [C3: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C3 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ C3 @ B2 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % tranclE
% 0.30/0.46 thf(fact_44_termi__impl__not__inf,axiom,
% 0.30/0.46 ! [C: com,S: state] :
% 0.30/0.46 ( ( termi @ C @ S )
% 0.30/0.46 => ~ ( pHoare1838713294le_inf @ ( cons @ com @ C @ ( nil @ com ) ) @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi_impl_not_inf
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 = ( Q @ X3 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_trancl__rtrancl__trancl,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trancl_rtrancl_trancl
% 0.30/0.46 thf(fact_49_rtrancl__trancl__trancl,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Z2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( transitive_trancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_trancl_trancl
% 0.30/0.46 thf(fact_50_rtrancl__into__trancl2,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_into_trancl2
% 0.30/0.46 thf(fact_51_rtrancl__into__trancl1,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_into_trancl1
% 0.30/0.46 thf(fact_52_exec1s__impl__execs,axiom,
% 0.30/0.46 ! [Cs3: list @ com,S: state,T2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ T2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 0.30/0.46 => ( pHoare1053570959_execs @ S @ Cs3 @ T2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1s_impl_execs
% 0.30/0.46 thf(fact_53_execs__pres__termis,axiom,
% 0.30/0.46 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 0.30/0.46 => ( ( pHoare1335526537termis @ Cs3 @ S )
% 0.30/0.46 => ( pHoare1335526537termis @ Cs @ S2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % execs_pres_termis
% 0.30/0.46 thf(fact_54_old_Onat_Oinject,axiom,
% 0.30/0.46 ! [Nat: nat,Nat2: nat] :
% 0.30/0.46 ( ( ( suc @ Nat )
% 0.30/0.46 = ( suc @ Nat2 ) )
% 0.30/0.46 = ( Nat = Nat2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.inject
% 0.30/0.46 thf(fact_55_nat_Oinject,axiom,
% 0.30/0.46 ! [X2: nat,Y22: nat] :
% 0.30/0.46 ( ( ( suc @ X2 )
% 0.30/0.46 = ( suc @ Y22 ) )
% 0.30/0.46 = ( X2 = Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.inject
% 0.30/0.46 thf(fact_56_list_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y222: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X21 @ X22 )
% 0.30/0.46 = ( cons @ A @ Y21 @ Y222 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X22 = Y222 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inject
% 0.30/0.46 thf(fact_57_exec1s__impl__exec,axiom,
% 0.30/0.46 ! [C: com,S: state,T2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( nil @ com ) ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ T2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 0.30/0.46 => ( exec @ S @ C @ T2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1s_impl_exec
% 0.30/0.46 thf(fact_58_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.30/0.46 = ( ( A2 = A6 )
% 0.30/0.46 & ( B2 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_59_prod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y22: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X2 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_60_execs_Ointros_I2_J,axiom,
% 0.30/0.46 ! [S: state,C: com,T2: state,Cs3: list @ com,U: state] :
% 0.30/0.46 ( ( exec @ S @ C @ T2 )
% 0.30/0.46 => ( ( pHoare1053570959_execs @ T2 @ Cs3 @ U )
% 0.30/0.46 => ( pHoare1053570959_execs @ S @ ( cons @ com @ C @ Cs3 ) @ U ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % execs.intros(2)
% 0.30/0.46 thf(fact_61_execs_Ocases,axiom,
% 0.30/0.46 ! [A1: state,A22: list @ com,A32: state] :
% 0.30/0.46 ( ( pHoare1053570959_execs @ A1 @ A22 @ A32 )
% 0.30/0.46 => ( ( ( A22
% 0.30/0.46 = ( nil @ com ) )
% 0.30/0.46 => ( A32 != A1 ) )
% 0.30/0.46 => ~ ! [C3: com,T3: state,Cs4: list @ com] :
% 0.30/0.46 ( ( A22
% 0.30/0.46 = ( cons @ com @ C3 @ Cs4 ) )
% 0.30/0.46 => ( ( exec @ A1 @ C3 @ T3 )
% 0.30/0.46 => ~ ( pHoare1053570959_execs @ T3 @ Cs4 @ A32 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % execs.cases
% 0.30/0.46 thf(fact_62_execs_Osimps,axiom,
% 0.30/0.46 ( pHoare1053570959_execs
% 0.30/0.46 = ( ^ [A12: state,A23: list @ com,A33: state] :
% 0.30/0.46 ( ? [S3: state] :
% 0.30/0.46 ( ( A12 = S3 )
% 0.30/0.46 & ( A23
% 0.30/0.46 = ( nil @ com ) )
% 0.30/0.46 & ( A33 = S3 ) )
% 0.30/0.46 | ? [S3: state,C4: com,T4: state,Cs2: list @ com,U2: state] :
% 0.30/0.46 ( ( A12 = S3 )
% 0.30/0.46 & ( A23
% 0.30/0.46 = ( cons @ com @ C4 @ Cs2 ) )
% 0.30/0.46 & ( A33 = U2 )
% 0.30/0.46 & ( exec @ S3 @ C4 @ T4 )
% 0.30/0.46 & ( pHoare1053570959_execs @ T4 @ Cs2 @ U2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % execs.simps
% 0.30/0.46 thf(fact_63_execs_Oinducts,axiom,
% 0.30/0.46 ! [X1: state,X2: list @ com,X32: state,P: state > ( list @ com ) > state > $o] :
% 0.30/0.46 ( ( pHoare1053570959_execs @ X1 @ X2 @ X32 )
% 0.30/0.46 => ( ! [S4: state] : ( P @ S4 @ ( nil @ com ) @ S4 )
% 0.30/0.46 => ( ! [S4: state,C3: com,T3: state,Cs4: list @ com,U3: state] :
% 0.30/0.46 ( ( exec @ S4 @ C3 @ T3 )
% 0.30/0.46 => ( ( pHoare1053570959_execs @ T3 @ Cs4 @ U3 )
% 0.30/0.46 => ( ( P @ T3 @ Cs4 @ U3 )
% 0.30/0.46 => ( P @ S4 @ ( cons @ com @ C3 @ Cs4 ) @ U3 ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 @ X32 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % execs.inducts
% 0.30/0.46 thf(fact_64_termis_Osimps_I2_J,axiom,
% 0.30/0.46 ! [C: com,Cs3: list @ com,S: state] :
% 0.30/0.46 ( ( pHoare1335526537termis @ ( cons @ com @ C @ Cs3 ) @ S )
% 0.30/0.46 = ( ( termi @ C @ S )
% 0.30/0.46 & ! [T4: state] :
% 0.30/0.46 ( ( exec @ S @ C @ T4 )
% 0.30/0.46 => ( pHoare1335526537termis @ Cs3 @ T4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % termis.simps(2)
% 0.30/0.46 thf(fact_65_execs_Ointros_I1_J,axiom,
% 0.30/0.46 ! [S: state] : ( pHoare1053570959_execs @ S @ ( nil @ com ) @ S ) ).
% 0.30/0.46
% 0.30/0.46 % execs.intros(1)
% 0.30/0.46 thf(fact_66_termis_Osimps_I1_J,axiom,
% 0.30/0.46 ! [S: state] : ( pHoare1335526537termis @ ( nil @ com ) @ S ) ).
% 0.30/0.46
% 0.30/0.46 % termis.simps(1)
% 0.30/0.46 thf(fact_67_zero__reorient,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( zero @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( ( zero_zero @ A )
% 0.30/0.46 = X )
% 0.30/0.46 = ( X
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_reorient
% 0.30/0.46 thf(fact_68_surj__pair,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.30/0.46 ? [X3: A,Y2: B] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( product_Pair @ A @ B @ X3 @ Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_69_prod__cases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A3: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_70_Pair__inject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.30/0.46 => ~ ( ( A2 = A6 )
% 0.30/0.46 => ( B2 != B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_71_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.30/0.46 ~ ! [A3: A,B3: B] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ B @ A3 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_72_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A3: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_73_not__Cons__self2,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( cons @ A @ X @ Xs )
% 0.30/0.46 != Xs ) ).
% 0.30/0.46
% 0.30/0.46 % not_Cons_self2
% 0.30/0.46 thf(fact_74_Suc__inject,axiom,
% 0.30/0.46 ! [X: nat,Y: nat] :
% 0.30/0.46 ( ( ( suc @ X )
% 0.30/0.46 = ( suc @ Y ) )
% 0.30/0.46 => ( X = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_inject
% 0.30/0.46 thf(fact_75_n__not__Suc__n,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( N
% 0.30/0.46 != ( suc @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % n_not_Suc_n
% 0.30/0.46 thf(fact_76_inf__cases,axiom,
% 0.30/0.46 ! [C: com,Cs3: list @ com,S: state] :
% 0.30/0.46 ( ( pHoare1838713294le_inf @ ( cons @ com @ C @ Cs3 ) @ S )
% 0.30/0.46 => ( ( pHoare1838713294le_inf @ ( cons @ com @ C @ ( nil @ com ) ) @ S )
% 0.30/0.46 | ? [T3: state] :
% 0.30/0.46 ( ( exec @ S @ C @ T3 )
% 0.30/0.46 & ( pHoare1838713294le_inf @ Cs3 @ T3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_cases
% 0.30/0.46 thf(fact_77_nat_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X2: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.distinct(1)
% 0.30/0.46 thf(fact_78_old_Onat_Odistinct_I2_J,axiom,
% 0.30/0.46 ! [Nat3: nat] :
% 0.30/0.46 ( ( suc @ Nat3 )
% 0.30/0.46 != ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.distinct(2)
% 0.30/0.46 thf(fact_79_old_Onat_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [Nat2: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ Nat2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.distinct(1)
% 0.30/0.46 thf(fact_80_nat_OdiscI,axiom,
% 0.30/0.46 ! [Nat: nat,X2: nat] :
% 0.30/0.46 ( ( Nat
% 0.30/0.46 = ( suc @ X2 ) )
% 0.30/0.46 => ( Nat
% 0.30/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.discI
% 0.30/0.46 thf(fact_81_nat__induct,axiom,
% 0.30/0.46 ! [P: nat > $o,N: nat] :
% 0.30/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [N2: nat] :
% 0.30/0.46 ( ( P @ N2 )
% 0.30/0.46 => ( P @ ( suc @ N2 ) ) )
% 0.30/0.46 => ( P @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_induct
% 0.30/0.46 thf(fact_82_diff__induct,axiom,
% 0.30/0.46 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.30/0.46 ( ! [X3: nat] : ( P @ X3 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [Y2: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y2 ) )
% 0.30/0.46 => ( ! [X3: nat,Y2: nat] :
% 0.30/0.46 ( ( P @ X3 @ Y2 )
% 0.30/0.46 => ( P @ ( suc @ X3 ) @ ( suc @ Y2 ) ) )
% 0.30/0.46 => ( P @ M @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_induct
% 0.30/0.46 thf(fact_83_zero__induct,axiom,
% 0.30/0.46 ! [P: nat > $o,K: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [N2: nat] :
% 0.30/0.46 ( ( P @ ( suc @ N2 ) )
% 0.30/0.46 => ( P @ N2 ) )
% 0.30/0.46 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_induct
% 0.30/0.46 thf(fact_84_Suc__neq__Zero,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( suc @ M )
% 0.30/0.46 != ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_neq_Zero
% 0.30/0.46 thf(fact_85_Zero__neq__Suc,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Zero_neq_Suc
% 0.30/0.46 thf(fact_86_Zero__not__Suc,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Zero_not_Suc
% 0.30/0.46 thf(fact_87_old_Onat_Oexhaust,axiom,
% 0.30/0.46 ! [Y: nat] :
% 0.30/0.46 ( ( Y
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ~ ! [Nat4: nat] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( suc @ Nat4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.exhaust
% 0.30/0.46 thf(fact_88_old_Onat_Oinducts,axiom,
% 0.30/0.46 ! [P: nat > $o,Nat: nat] :
% 0.30/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [Nat4: nat] :
% 0.30/0.46 ( ( P @ Nat4 )
% 0.30/0.46 => ( P @ ( suc @ Nat4 ) ) )
% 0.30/0.46 => ( P @ Nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.inducts
% 0.30/0.46 thf(fact_89_not0__implies__Suc,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( N
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( N
% 0.30/0.46 = ( suc @ M2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not0_implies_Suc
% 0.30/0.46 thf(fact_90_list_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.30/0.46 ( ( nil @ A )
% 0.30/0.46 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.distinct(1)
% 0.30/0.46 thf(fact_91_list_OdiscI,axiom,
% 0.30/0.46 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.30/0.46 ( ( List
% 0.30/0.46 = ( cons @ A @ X21 @ X22 ) )
% 0.30/0.46 => ( List
% 0.30/0.46 != ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.discI
% 0.30/0.46 thf(fact_92_list_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y: list @ A] :
% 0.30/0.46 ( ( Y
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [X212: A,X222: list @ A] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.exhaust
% 0.30/0.46 thf(fact_93_list_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X12: A,X23: list @ A] :
% 0.30/0.46 ( ( P @ X23 )
% 0.30/0.46 => ( P @ ( cons @ A @ X12 @ X23 ) ) )
% 0.30/0.46 => ( P @ List ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inducts
% 0.30/0.46 thf(fact_94_neq__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 = ( ? [Y3: A,Ys: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( cons @ A @ Y3 @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_Nil_conv
% 0.30/0.46 thf(fact_95_list__induct2_H,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 0.30/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.30/0.46 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 0.30/0.46 => ( ! [Y2: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys3 ) )
% 0.30/0.46 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys3: list @ B] :
% 0.30/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys3 ) ) )
% 0.30/0.46 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_induct2'
% 0.30/0.46 thf(fact_96_splice_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.30/0.46 => ( ! [X3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.30/0.46 ( ( P @ Ys3 @ Xs2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ Ys3 ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % splice.induct
% 0.30/0.46 thf(fact_97_induct__list012,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X3: A,Y2: A,Zs: list @ A] :
% 0.30/0.46 ( ( P @ Zs )
% 0.30/0.46 => ( ( P @ ( cons @ A @ Y2 @ Zs ) )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Zs ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % induct_list012
% 0.30/0.46 thf(fact_98_min__list_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [X: list @ A] :
% 0.30/0.46 ( ! [X3: A,Xs2: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ A @ X3 @ Xs2 ) )
% 0.30/0.46 => ( X
% 0.30/0.46 = ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % min_list.cases
% 0.30/0.46 thf(fact_99_min__list_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ! [X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ! [X213: A,X223: list @ A] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 = ( cons @ A @ X213 @ X223 ) )
% 0.30/0.46 => ( P @ Xs2 ) )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 0.30/0.46 => ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( P @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % min_list.induct
% 0.30/0.46 thf(fact_100_shuffles_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.30/0.46 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 0.30/0.46 ( ( P @ Xs2 @ ( cons @ A @ Y2 @ Ys3 ) )
% 0.30/0.46 => ( ( P @ ( cons @ A @ X3 @ Xs2 ) @ Ys3 )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % shuffles.induct
% 0.30/0.46 thf(fact_101_transpose_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ ( list @ A )] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( nil @ ( list @ A ) ) )
% 0.30/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.30/0.46 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % transpose.cases
% 0.30/0.46 thf(fact_102_remdups__adj_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.30/0.46 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.cases
% 0.30/0.46 thf(fact_103_sorted__wrt_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.30/0.46 ( ! [P3: A > A > $o] : ( P @ P3 @ ( nil @ A ) )
% 0.30/0.46 => ( ! [P3: A > A > $o,X3: A,Ys3: list @ A] :
% 0.30/0.46 ( ( P @ P3 @ Ys3 )
% 0.30/0.46 => ( P @ P3 @ ( cons @ A @ X3 @ Ys3 ) ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sorted_wrt.induct
% 0.30/0.46 thf(fact_104_remdups__adj_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( ( X3 = Y2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 0.30/0.46 => ( ( ( X3 != Y2 )
% 0.30/0.46 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.30/0.46 => ( P @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.induct
% 0.30/0.46 thf(fact_105_arg__min__list_Oinduct,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( linorder @ B )
% 0.30/0.46 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.30/0.46 ( ! [F2: A > B,X3: A] : ( P @ F2 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [F2: A > B,X3: A,Y2: A,Zs: list @ A] :
% 0.30/0.46 ( ( P @ F2 @ ( cons @ A @ Y2 @ Zs ) )
% 0.30/0.46 => ( P @ F2 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 0.30/0.46 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_min_list.induct
% 0.30/0.46 thf(fact_106_successively_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.30/0.46 ( ! [P3: A > A > $o] : ( P @ P3 @ ( nil @ A ) )
% 0.30/0.46 => ( ! [P3: A > A > $o,X3: A] : ( P @ P3 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [P3: A > A > $o,X3: A,Y2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( P @ P3 @ ( cons @ A @ Y2 @ Xs2 ) )
% 0.30/0.46 => ( P @ P3 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % successively.induct
% 0.30/0.46 thf(fact_107_list__nonempty__induct,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_nonempty_induct
% 0.30/0.46 thf(fact_108_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.30/0.46 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 0.30/0.46 => ( ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.30/0.46 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A3 ) @ Bs ) )
% 0.30/0.46 => ( P @ F2 @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 0.30/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.induct
% 0.30/0.46 thf(fact_109_strict__sorted_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: list @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [X3: A,Ys3: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ A @ X3 @ Ys3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_sorted.cases
% 0.30/0.46 thf(fact_110_strict__sorted_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A,Ys3: list @ A] :
% 0.30/0.46 ( ( P @ Ys3 )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Ys3 ) ) )
% 0.30/0.46 => ( P @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_sorted.induct
% 0.30/0.46 thf(fact_111_splice_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.30/0.46 ( ! [Ys3: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 0.30/0.46 => ~ ! [X3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % splice.cases
% 0.30/0.46 thf(fact_112_shuffles_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.30/0.46 ( ! [Ys3: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 0.30/0.46 => ( ! [Xs2: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 0.30/0.46 => ~ ! [X3: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % shuffles.cases
% 0.30/0.46 thf(fact_113_sorted__wrt_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.30/0.46 ( ! [P3: A > A > $o] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( nil @ A ) ) )
% 0.30/0.46 => ~ ! [P3: A > A > $o,X3: A,Ys3: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( cons @ A @ X3 @ Ys3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sorted_wrt.cases
% 0.30/0.46 thf(fact_114_successively_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.30/0.46 ( ! [P3: A > A > $o] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [P3: A > A > $o,X3: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.30/0.46 => ~ ! [P3: A > A > $o,X3: A,Y2: A,Xs2: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % successively.cases
% 0.30/0.46 thf(fact_115_arg__min__list_Ocases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( linorder @ B )
% 0.30/0.46 => ! [X: product_prod @ ( A > B ) @ ( list @ A )] :
% 0.30/0.46 ( ! [F2: A > B,X3: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.30/0.46 => ( ! [F2: A > B,X3: A,Y2: A,Zs: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 0.30/0.46 => ~ ! [A3: A > B] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A3 @ ( nil @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_min_list.cases
% 0.30/0.46 thf(fact_116_map__tailrec__rev_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.30/0.46 ( ! [F2: A > B,Bs: list @ B] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.30/0.46 => ~ ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A3 @ As ) @ Bs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.cases
% 0.30/0.46 thf(fact_117_exec__impl__execs,axiom,
% 0.30/0.46 ! [S: state,C: com,S2: state,Cs3: list @ com] :
% 0.30/0.46 ( ( exec @ S @ C @ S2 )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec_impl_execs
% 0.30/0.46 thf(fact_118_prod__cases3,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C5: $tType,Y: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 0.30/0.46 ~ ! [A3: A,B3: B,C3: C5] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A3 @ ( product_Pair @ B @ C5 @ B3 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases3
% 0.30/0.46 thf(fact_119_prod__cases4,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C5: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) )] :
% 0.30/0.46 ~ ! [A3: A,B3: B,C3: C5,D2: D] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ D ) @ B3 @ ( product_Pair @ C5 @ D @ C3 @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases4
% 0.30/0.46 thf(fact_120_prod__cases5,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C5: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.46 ~ ! [A3: A,B3: B,C3: C5,D2: D,E2: E] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases5
% 0.30/0.46 thf(fact_121_prod__cases6,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C5: $tType,D: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.30/0.46 ~ ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases6
% 0.30/0.46 thf(fact_122_prod__cases7,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C5: $tType,D: $tType,E: $tType,F4: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) )] :
% 0.30/0.46 ~ ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4,G2: G] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G ) @ E2 @ ( product_Pair @ F4 @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases7
% 0.30/0.46 thf(fact_123_prod__induct3,axiom,
% 0.30/0.46 ! [C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C5 ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 0.30/0.46 ( ! [A3: A,B3: B,C3: C5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A3 @ ( product_Pair @ B @ C5 @ B3 @ C3 ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct3
% 0.30/0.46 thf(fact_124_prod__induct4,axiom,
% 0.30/0.46 ! [D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) )] :
% 0.30/0.46 ( ! [A3: A,B3: B,C3: C5,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ D ) @ B3 @ ( product_Pair @ C5 @ D @ C3 @ D2 ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct4
% 0.30/0.46 thf(fact_125_prod__induct5,axiom,
% 0.30/0.46 ! [E: $tType,D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.46 ( ! [A3: A,B3: B,C3: C5,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct5
% 0.30/0.46 thf(fact_126_prod__induct6,axiom,
% 0.30/0.46 ! [F4: $tType,E: $tType,D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.30/0.46 ( ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct6
% 0.30/0.46 thf(fact_127_prod__induct7,axiom,
% 0.30/0.46 ! [G: $tType,F4: $tType,E: $tType,D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) )] :
% 0.30/0.46 ( ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G ) @ E2 @ ( product_Pair @ F4 @ G @ F2 @ G2 ) ) ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct7
% 0.30/0.46 thf(fact_128_exec1__pres__termis,axiom,
% 0.30/0.46 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ( ( pHoare1335526537termis @ Cs3 @ S )
% 0.30/0.46 => ( pHoare1335526537termis @ Cs @ S2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1_pres_termis
% 0.30/0.46 thf(fact_129_old_Oprod_Orec,axiom,
% 0.30/0.46 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.46 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.46 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.rec
% 0.30/0.46 thf(fact_130_dependent__nat__choice,axiom,
% 0.30/0.46 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 0.30/0.46 ( ? [X_12: A] : ( P @ ( zero_zero @ nat ) @ X_12 )
% 0.30/0.46 => ( ! [X3: A,N2: nat] :
% 0.30/0.46 ( ( P @ N2 @ X3 )
% 0.30/0.46 => ? [Y4: A] :
% 0.30/0.46 ( ( P @ ( suc @ N2 ) @ Y4 )
% 0.30/0.46 & ( Q @ N2 @ X3 @ Y4 ) ) )
% 0.30/0.46 => ? [F2: nat > A] :
% 0.30/0.46 ! [N3: nat] :
% 0.30/0.46 ( ( P @ N3 @ ( F2 @ N3 ) )
% 0.30/0.46 & ( Q @ N3 @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dependent_nat_choice
% 0.30/0.46 thf(fact_131_exec1E_I3_J,axiom,
% 0.30/0.46 ! [C1: com,C22: com,Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ~ ( ( Cs
% 0.30/0.46 = ( cons @ com @ C1 @ ( cons @ com @ C22 @ Cs3 ) ) )
% 0.30/0.46 => ( S2 != S ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1E(3)
% 0.30/0.46 thf(fact_132_exec1_OSemi,axiom,
% 0.30/0.46 ! [C1: com,C22: com,Cs3: list @ com,S: state] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C1 @ ( cons @ com @ C22 @ Cs3 ) ) @ S ) ) @ pHoare1053570893_exec1 ) ).
% 0.30/0.46
% 0.30/0.46 % exec1.Semi
% 0.30/0.46 thf(fact_133_n__lists__Nil,axiom,
% 0.30/0.46 ! [A: $tType,N: nat] :
% 0.30/0.46 ( ( ( N
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.30/0.46 & ( ( N
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.30/0.46 = ( nil @ ( list @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % n_lists_Nil
% 0.30/0.46 thf(fact_134_exec1E_I2_J,axiom,
% 0.30/0.46 ! [F: state > ( set @ state ),Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ F ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ~ ( ( Cs = Cs3 )
% 0.30/0.46 => ~ ( member @ state @ S2 @ ( F @ S ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1E(2)
% 0.30/0.46 thf(fact_135_exec1_ODo,axiom,
% 0.30/0.46 ! [T2: state,F: state > ( set @ state ),S: state,Cs3: list @ com] :
% 0.30/0.46 ( ( member @ state @ T2 @ ( F @ S ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ F ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ T2 ) ) @ pHoare1053570893_exec1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1.Do
% 0.30/0.46 thf(fact_136_n__lists_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % n_lists.simps(1)
% 0.30/0.46 thf(fact_137_termi_OSemi,axiom,
% 0.30/0.46 ! [C1: com,S0: state,C22: com] :
% 0.30/0.46 ( ( termi @ C1 @ S0 )
% 0.30/0.46 => ( ! [S1: state] :
% 0.30/0.46 ( ( exec @ S0 @ C1 @ S1 )
% 0.30/0.46 => ( termi @ C22 @ S1 ) )
% 0.30/0.46 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi.Semi
% 0.30/0.46 thf(fact_138_com_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X21: com,X22: com,Y21: com,Y222: com] :
% 0.30/0.46 ( ( ( semi @ X21 @ X22 )
% 0.30/0.46 = ( semi @ Y21 @ Y222 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X22 = Y222 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.inject(2)
% 0.30/0.46 thf(fact_139_com_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X1: state > ( set @ state ),Y1: state > ( set @ state )] :
% 0.30/0.46 ( ( ( do @ X1 )
% 0.30/0.46 = ( do @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.inject(1)
% 0.30/0.46 thf(fact_140_com_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X1: state > ( set @ state ),X21: com,X22: com] :
% 0.30/0.46 ( ( do @ X1 )
% 0.30/0.46 != ( semi @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.distinct(1)
% 0.30/0.46 thf(fact_141_exec_ODo,axiom,
% 0.30/0.46 ! [T2: state,F: state > ( set @ state ),S: state] :
% 0.30/0.46 ( ( member @ state @ T2 @ ( F @ S ) )
% 0.30/0.46 => ( exec @ S @ ( do @ F ) @ T2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec.Do
% 0.30/0.46 thf(fact_142_exec_OSemi,axiom,
% 0.30/0.46 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 0.30/0.46 ( ( exec @ S0 @ C1 @ S12 )
% 0.30/0.46 => ( ( exec @ S12 @ C22 @ S22 )
% 0.30/0.46 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec.Semi
% 0.30/0.46 thf(fact_143_product__lists_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % product_lists.simps(1)
% 0.30/0.46 thf(fact_144_subseqs_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( subseqs @ A @ ( nil @ A ) )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subseqs.simps(1)
% 0.30/0.46 thf(fact_145_exec1E_I4_J,axiom,
% 0.30/0.46 ! [B2: state > $o,C1: com,C22: com,Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ B2 @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ( ( ( Cs
% 0.30/0.46 = ( cons @ com @ C1 @ Cs3 ) )
% 0.30/0.46 => ( ( S2 = S )
% 0.30/0.46 => ~ ( B2 @ S ) ) )
% 0.30/0.46 => ~ ( ( Cs
% 0.30/0.46 = ( cons @ com @ C22 @ Cs3 ) )
% 0.30/0.46 => ( ( S2 = S )
% 0.30/0.46 => ( B2 @ S ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1E(4)
% 0.30/0.46 thf(fact_146_com_Oinject_I3_J,axiom,
% 0.30/0.46 ! [X31: state > $o,X322: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 0.30/0.46 ( ( ( cond @ X31 @ X322 @ X33 )
% 0.30/0.46 = ( cond @ Y31 @ Y32 @ Y33 ) )
% 0.30/0.46 = ( ( X31 = Y31 )
% 0.30/0.46 & ( X322 = Y32 )
% 0.30/0.46 & ( X33 = Y33 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.inject(3)
% 0.30/0.46 thf(fact_147_exec_OIfTrue,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C1: com,T2: state,C22: com] :
% 0.30/0.46 ( ( B2 @ S )
% 0.30/0.46 => ( ( exec @ S @ C1 @ T2 )
% 0.30/0.46 => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec.IfTrue
% 0.30/0.46 thf(fact_148_exec_OIfFalse,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C22: com,T2: state,C1: com] :
% 0.30/0.46 ( ~ ( B2 @ S )
% 0.30/0.46 => ( ( exec @ S @ C22 @ T2 )
% 0.30/0.46 => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec.IfFalse
% 0.30/0.46 thf(fact_149_termi_OIfTrue,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C1: com,C22: com] :
% 0.30/0.46 ( ( B2 @ S )
% 0.30/0.46 => ( ( termi @ C1 @ S )
% 0.30/0.46 => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi.IfTrue
% 0.30/0.46 thf(fact_150_termi_OIfFalse,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C22: com,C1: com] :
% 0.30/0.46 ( ~ ( B2 @ S )
% 0.30/0.46 => ( ( termi @ C22 @ S )
% 0.30/0.46 => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi.IfFalse
% 0.30/0.46 thf(fact_151_com_Odistinct_I3_J,axiom,
% 0.30/0.46 ! [X1: state > ( set @ state ),X31: state > $o,X322: com,X33: com] :
% 0.30/0.46 ( ( do @ X1 )
% 0.30/0.46 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.distinct(3)
% 0.30/0.46 thf(fact_152_com_Odistinct_I11_J,axiom,
% 0.30/0.46 ! [X21: com,X22: com,X31: state > $o,X322: com,X33: com] :
% 0.30/0.46 ( ( semi @ X21 @ X22 )
% 0.30/0.46 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.distinct(11)
% 0.30/0.46 thf(fact_153_exec1_OIfFalse,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C1: com,C22: com,Cs3: list @ com] :
% 0.30/0.46 ( ~ ( B2 @ S )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ B2 @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C22 @ Cs3 ) @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1.IfFalse
% 0.30/0.46 thf(fact_154_exec1_OIfTrue,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C1: com,C22: com,Cs3: list @ com] :
% 0.30/0.46 ( ( B2 @ S )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ B2 @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C1 @ Cs3 ) @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1.IfTrue
% 0.30/0.46 thf(fact_155_gen__length__code_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,N: nat,X: B,Xs: list @ B] :
% 0.30/0.46 ( ( gen_length @ B @ N @ ( cons @ B @ X @ Xs ) )
% 0.30/0.46 = ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % gen_length_code(2)
% 0.30/0.46 thf(fact_156_insert__Nil,axiom,
% 0.30/0.46 ! [A: $tType,X: A] :
% 0.30/0.46 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.30/0.46 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_Nil
% 0.30/0.46 thf(fact_157_exec1_OWhileFalse,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C: com,Cs3: list @ com] :
% 0.30/0.46 ( ~ ( B2 @ S )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1.WhileFalse
% 0.30/0.46 thf(fact_158_com_Oinject_I4_J,axiom,
% 0.30/0.46 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.30/0.46 ( ( ( while @ X41 @ X42 )
% 0.30/0.46 = ( while @ Y41 @ Y42 ) )
% 0.30/0.46 = ( ( X41 = Y41 )
% 0.30/0.46 & ( X42 = Y42 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.inject(4)
% 0.30/0.46 thf(fact_159_com_Odistinct_I19_J,axiom,
% 0.30/0.46 ! [X31: state > $o,X322: com,X33: com,X41: state > $o,X42: com] :
% 0.30/0.46 ( ( cond @ X31 @ X322 @ X33 )
% 0.30/0.46 != ( while @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.distinct(19)
% 0.30/0.46 thf(fact_160_while__termiE,axiom,
% 0.30/0.46 ! [B2: state > $o,C: com,S: state] :
% 0.30/0.46 ( ( termi @ ( while @ B2 @ C ) @ S )
% 0.30/0.46 => ( ( B2 @ S )
% 0.30/0.46 => ( termi @ C @ S ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % while_termiE
% 0.30/0.46 thf(fact_161_exec_OWhileFalse,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C: com] :
% 0.30/0.46 ( ~ ( B2 @ S )
% 0.30/0.46 => ( exec @ S @ ( while @ B2 @ C ) @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec.WhileFalse
% 0.30/0.46 thf(fact_162_exec_OWhileTrue,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C: com,T2: state,U: state] :
% 0.30/0.46 ( ( B2 @ S )
% 0.30/0.46 => ( ( exec @ S @ C @ T2 )
% 0.30/0.46 => ( ( exec @ T2 @ ( while @ B2 @ C ) @ U )
% 0.30/0.46 => ( exec @ S @ ( while @ B2 @ C ) @ U ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec.WhileTrue
% 0.30/0.46 thf(fact_163_termi_OWhileFalse,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C: com] :
% 0.30/0.46 ( ~ ( B2 @ S )
% 0.30/0.46 => ( termi @ ( while @ B2 @ C ) @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi.WhileFalse
% 0.30/0.46 thf(fact_164_com_Odistinct_I5_J,axiom,
% 0.30/0.46 ! [X1: state > ( set @ state ),X41: state > $o,X42: com] :
% 0.30/0.46 ( ( do @ X1 )
% 0.30/0.46 != ( while @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.distinct(5)
% 0.30/0.46 thf(fact_165_com_Odistinct_I13_J,axiom,
% 0.30/0.46 ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 0.30/0.46 ( ( semi @ X21 @ X22 )
% 0.30/0.46 != ( while @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % com.distinct(13)
% 0.30/0.46 thf(fact_166_termi_OWhileTrue,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C: com] :
% 0.30/0.46 ( ( B2 @ S )
% 0.30/0.46 => ( ( termi @ C @ S )
% 0.30/0.46 => ( ! [T3: state] :
% 0.30/0.46 ( ( exec @ S @ C @ T3 )
% 0.30/0.46 => ( termi @ ( while @ B2 @ C ) @ T3 ) )
% 0.30/0.46 => ( termi @ ( while @ B2 @ C ) @ S ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi.WhileTrue
% 0.30/0.46 thf(fact_167_while__termiE2,axiom,
% 0.30/0.46 ! [B2: state > $o,C: com,S: state,T2: state] :
% 0.30/0.46 ( ( termi @ ( while @ B2 @ C ) @ S )
% 0.30/0.46 => ( ( B2 @ S )
% 0.30/0.46 => ( ( exec @ S @ C @ T2 )
% 0.30/0.46 => ( termi @ ( while @ B2 @ C ) @ T2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % while_termiE2
% 0.30/0.46 thf(fact_168_gen__length__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,N: nat] :
% 0.30/0.46 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 0.30/0.46 = N ) ).
% 0.30/0.46
% 0.30/0.46 % gen_length_code(1)
% 0.30/0.46 thf(fact_169_termi__while,axiom,
% 0.30/0.46 ! [B2: state > $o,C: com,F: nat > state,K: nat] :
% 0.30/0.46 ( ( termi @ ( while @ B2 @ C ) @ ( F @ K ) )
% 0.30/0.46 => ( ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) )
% 0.30/0.46 => ? [I: nat] :
% 0.30/0.46 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi_while
% 0.30/0.46 thf(fact_170_termi__while__lemma,axiom,
% 0.30/0.46 ! [W: com,Fk: state,F: nat > state,K: nat,B2: state > $o,C: com] :
% 0.30/0.46 ( ( termi @ W @ Fk )
% 0.30/0.46 => ( ( ( Fk
% 0.30/0.46 = ( F @ K ) )
% 0.30/0.46 & ( W
% 0.30/0.46 = ( while @ B2 @ C ) )
% 0.30/0.46 & ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) ) )
% 0.30/0.46 => ? [I: nat] :
% 0.30/0.46 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % termi_while_lemma
% 0.30/0.46 thf(fact_171_exec1E_I5_J,axiom,
% 0.30/0.46 ! [B2: state > $o,C: com,Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ( ( ( Cs = Cs3 )
% 0.30/0.46 => ( ( S2 = S )
% 0.30/0.46 => ( B2 @ S ) ) )
% 0.30/0.46 => ~ ( ( Cs
% 0.30/0.46 = ( cons @ com @ C @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) ) )
% 0.30/0.46 => ( ( S2 = S )
% 0.30/0.46 => ~ ( B2 @ S ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1E(5)
% 0.30/0.46 thf(fact_172_exec1_OWhileTrue,axiom,
% 0.30/0.46 ! [B2: state > $o,S: state,C: com,Cs3: list @ com] :
% 0.30/0.46 ( ( B2 @ S )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) ) @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1.WhileTrue
% 0.30/0.46 thf(fact_173_nths__singleton,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ nat,X: A] :
% 0.30/0.46 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A5 )
% 0.30/0.46 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A5 )
% 0.30/0.46 = ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.30/0.46 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A5 )
% 0.30/0.46 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A5 )
% 0.30/0.46 = ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nths_singleton
% 0.30/0.46 thf(fact_174_app__execs,axiom,
% 0.30/0.46 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state,Cs22: list @ com] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs3 @ Cs22 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs @ Cs22 ) @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % app_execs
% 0.30/0.46 thf(fact_175_listrel_Ocases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ( ( ( A1
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( A22
% 0.30/0.46 != ( nil @ B ) ) )
% 0.30/0.46 => ~ ! [X3: A,Y2: B,Xs2: list @ A] :
% 0.30/0.46 ( ( A1
% 0.30/0.46 = ( cons @ A @ X3 @ Xs2 ) )
% 0.30/0.46 => ! [Ys3: list @ B] :
% 0.30/0.46 ( ( A22
% 0.30/0.46 = ( cons @ B @ Y2 @ Ys3 ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R )
% 0.30/0.46 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys3 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel.cases
% 0.30/0.46 thf(fact_176_same__append__eq,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys2 )
% 0.30/0.46 = ( append @ A @ Xs @ Zs2 ) )
% 0.30/0.46 = ( Ys2 = Zs2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % same_append_eq
% 0.30/0.46 thf(fact_177_append__same__eq,axiom,
% 0.30/0.46 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Ys2 @ Xs )
% 0.30/0.46 = ( append @ A @ Zs2 @ Xs ) )
% 0.30/0.46 = ( Ys2 = Zs2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_same_eq
% 0.30/0.46 thf(fact_178_append__assoc,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs2 )
% 0.30/0.46 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_assoc
% 0.30/0.46 thf(fact_179_append_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C )
% 0.30/0.46 = ( append @ A @ A2 @ ( append @ A @ B2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append.assoc
% 0.30/0.46 thf(fact_180_append__Nil2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % append_Nil2
% 0.30/0.46 thf(fact_181_append__self__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys2 )
% 0.30/0.46 = Xs )
% 0.30/0.46 = ( Ys2
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_self_conv
% 0.30/0.46 thf(fact_182_self__append__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Xs @ Ys2 ) )
% 0.30/0.46 = ( Ys2
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % self_append_conv
% 0.30/0.46 thf(fact_183_append__self__conv2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys2 )
% 0.30/0.46 = Ys2 )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_self_conv2
% 0.30/0.46 thf(fact_184_self__append__conv2,axiom,
% 0.30/0.46 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.30/0.46 ( ( Ys2
% 0.30/0.46 = ( append @ A @ Xs @ Ys2 ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % self_append_conv2
% 0.30/0.46 thf(fact_185_Nil__is__append__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( ( nil @ A )
% 0.30/0.46 = ( append @ A @ Xs @ Ys2 ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Ys2
% 0.30/0.46 = ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nil_is_append_conv
% 0.30/0.46 thf(fact_186_append__is__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys2 )
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Ys2
% 0.30/0.46 = ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_is_Nil_conv
% 0.30/0.46 thf(fact_187_append_Oright__neutral,axiom,
% 0.30/0.46 ! [A: $tType,A2: list @ A] :
% 0.30/0.46 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % append.right_neutral
% 0.30/0.46 thf(fact_188_nths__nil,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ nat] :
% 0.30/0.46 ( ( nths @ A @ ( nil @ A ) @ A5 )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % nths_nil
% 0.30/0.46 thf(fact_189_append1__eq__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y: A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.30/0.46 = ( ( Xs = Ys2 )
% 0.30/0.46 & ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append1_eq_conv
% 0.30/0.46 thf(fact_190_listrel__rtrancl__refl,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] : ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_rtrancl_refl
% 0.30/0.46 thf(fact_191_append__eq__append__conv2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys2 )
% 0.30/0.46 = ( append @ A @ Zs2 @ Ts ) )
% 0.30/0.46 = ( ? [Us: list @ A] :
% 0.30/0.46 ( ( ( Xs
% 0.30/0.46 = ( append @ A @ Zs2 @ Us ) )
% 0.30/0.46 & ( ( append @ A @ Us @ Ys2 )
% 0.30/0.46 = Ts ) )
% 0.30/0.46 | ( ( ( append @ A @ Xs @ Us )
% 0.30/0.46 = Zs2 )
% 0.30/0.46 & ( Ys2
% 0.30/0.46 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_eq_append_conv2
% 0.30/0.46 thf(fact_192_append__eq__appendI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys2: list @ A,Us2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Xs1 )
% 0.30/0.46 = Zs2 )
% 0.30/0.46 => ( ( Ys2
% 0.30/0.46 = ( append @ A @ Xs1 @ Us2 ) )
% 0.30/0.46 => ( ( append @ A @ Xs @ Ys2 )
% 0.30/0.46 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_eq_appendI
% 0.30/0.46 thf(fact_193_eq__Nil__appendI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( Xs = Ys2 )
% 0.30/0.46 => ( Xs
% 0.30/0.46 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_Nil_appendI
% 0.30/0.46 thf(fact_194_append__Nil,axiom,
% 0.30/0.46 ! [A: $tType,Ys2: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 0.30/0.46 = Ys2 ) ).
% 0.30/0.46
% 0.30/0.46 % append_Nil
% 0.30/0.46 thf(fact_195_append_Oleft__neutral,axiom,
% 0.30/0.46 ! [A: $tType,A2: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % append.left_neutral
% 0.30/0.46 thf(fact_196_Cons__eq__appendI,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Xs1 )
% 0.30/0.46 = Ys2 )
% 0.30/0.46 => ( ( Xs
% 0.30/0.46 = ( append @ A @ Xs1 @ Zs2 ) )
% 0.30/0.46 => ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_eq_appendI
% 0.30/0.46 thf(fact_197_append__Cons,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys2 )
% 0.30/0.46 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_Cons
% 0.30/0.46 thf(fact_198_rev__nonempty__induct,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_nonempty_induct
% 0.30/0.46 thf(fact_199_append__eq__Cons__conv,axiom,
% 0.30/0.46 ! [A: $tType,Ys2: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Ys2 @ Zs2 )
% 0.30/0.46 = ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( ( ( Ys2
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Zs2
% 0.30/0.46 = ( cons @ A @ X @ Xs ) ) )
% 0.30/0.46 | ? [Ys4: list @ A] :
% 0.30/0.46 ( ( Ys2
% 0.30/0.46 = ( cons @ A @ X @ Ys4 ) )
% 0.30/0.46 & ( ( append @ A @ Ys4 @ Zs2 )
% 0.30/0.46 = Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_eq_Cons_conv
% 0.30/0.46 thf(fact_200_Cons__eq__append__conv,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.30/0.46 = ( ( ( Ys2
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = Zs2 ) )
% 0.30/0.46 | ? [Ys4: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Ys4 )
% 0.30/0.46 = Ys2 )
% 0.30/0.46 & ( Xs
% 0.30/0.46 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_eq_append_conv
% 0.30/0.46 thf(fact_201_rev__exhaust,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [Ys3: list @ A,Y2: A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 != ( append @ A @ Ys3 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_exhaust
% 0.30/0.46 thf(fact_202_rev__induct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_induct
% 0.30/0.46 thf(fact_203_listrel_ONil,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] : ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel.Nil
% 0.30/0.46 thf(fact_204_listrel__Nil1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ( Xs
% 0.30/0.46 = ( nil @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_Nil1
% 0.30/0.46 thf(fact_205_listrel__Nil2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_Nil2
% 0.30/0.46 thf(fact_206_listrel__rtrancl__trans,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Zs2: list @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_rtrancl_trans
% 0.30/0.46 thf(fact_207_app__exec,axiom,
% 0.30/0.46 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state,Cs22: list @ com] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs3 @ Cs22 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs @ Cs22 ) @ S2 ) ) @ pHoare1053570893_exec1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % app_exec
% 0.30/0.46 thf(fact_208_listrel__Cons2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Xs: list @ A,Y: B,Ys2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( cons @ B @ Y @ Ys2 ) ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ~ ! [X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ A @ X3 @ Xs2 ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ R )
% 0.30/0.46 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_Cons2
% 0.30/0.46 thf(fact_209_listrel__Cons1,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Y: A,Ys2: list @ A,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ Y @ Ys2 ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ~ ! [Y2: B,Ys3: list @ B] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ B @ Y2 @ Ys3 ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y @ Y2 ) @ R )
% 0.30/0.46 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Ys2 @ Ys3 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_Cons1
% 0.30/0.46 thf(fact_210_listrel_OCons,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X: A,Y: B,R: set @ ( product_prod @ A @ B ),Xs: list @ A,Ys2: list @ B] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ X @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) @ ( listrel @ A @ B @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel.Cons
% 0.30/0.46 thf(fact_211_exec1__only1__aux,axiom,
% 0.30/0.46 ! [Ccs: list @ com,S: state,Cs: list @ com,T2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Ccs @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ T2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ! [C6: com,Cs5: list @ com] :
% 0.30/0.46 ( ( Ccs
% 0.30/0.46 = ( cons @ com @ C6 @ Cs5 ) )
% 0.30/0.46 => ? [Cs1: list @ com] :
% 0.30/0.46 ( Cs
% 0.30/0.46 = ( append @ com @ Cs1 @ Cs5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1_only1_aux
% 0.30/0.46 thf(fact_212_exec1__only1,axiom,
% 0.30/0.46 ! [C: com,Cs3: list @ com,S: state,Cs: list @ com,T2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ T2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ? [Cs1: list @ com] :
% 0.30/0.46 ( Cs
% 0.30/0.46 = ( append @ com @ Cs1 @ Cs3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1_only1
% 0.30/0.46 thf(fact_213_exec1__drop__suffix__aux,axiom,
% 0.30/0.46 ! [Cs12: list @ com,S: state,Cs1_2: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs12 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs1_2 @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ! [Cs13: list @ com,Cs23: list @ com,Cs14: list @ com] :
% 0.30/0.46 ( ( ( Cs12
% 0.30/0.46 = ( append @ com @ Cs13 @ Cs23 ) )
% 0.30/0.46 & ( Cs1_2
% 0.30/0.46 = ( append @ com @ Cs14 @ Cs23 ) )
% 0.30/0.46 & ( Cs13
% 0.30/0.46 != ( nil @ com ) ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs13 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs14 @ S2 ) ) @ pHoare1053570893_exec1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1_drop_suffix_aux
% 0.30/0.46 thf(fact_214_exec1__drop__suffix,axiom,
% 0.30/0.46 ! [Cs15: list @ com,Cs22: list @ com,S: state,Cs16: list @ com,S2: state] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs15 @ Cs22 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs16 @ Cs22 ) @ S2 ) ) @ pHoare1053570893_exec1 )
% 0.30/0.46 => ( ( Cs15
% 0.30/0.46 != ( nil @ com ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs15 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs16 @ S2 ) ) @ pHoare1053570893_exec1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exec1_drop_suffix
% 0.30/0.46 thf(fact_215_listrel_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X1: list @ A,X2: list @ B,R: set @ ( product_prod @ A @ B ),P: ( list @ A ) > ( list @ B ) > $o] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ X1 @ X2 ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.30/0.46 => ( ! [X3: A,Y2: B,Xs2: list @ A,Ys3: list @ B] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys3 ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.30/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys3 ) ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel.inducts
% 0.30/0.46 thf(fact_216_listrel_Osimps,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.30/0.46 = ( ( ( A1
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( A22
% 0.30/0.46 = ( nil @ B ) ) )
% 0.30/0.46 | ? [X4: A,Y3: B,Xs3: list @ A,Ys: list @ B] :
% 0.30/0.46 ( ( A1
% 0.30/0.46 = ( cons @ A @ X4 @ Xs3 ) )
% 0.30/0.46 & ( A22
% 0.30/0.46 = ( cons @ B @ Y3 @ Ys ) )
% 0.30/0.46 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ R )
% 0.30/0.46 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs3 @ Ys ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel.simps
% 0.30/0.46 thf(fact_217_bind__simps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 0.30/0.46 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 0.30/0.46 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_simps(2)
% 0.30/0.46 thf(fact_218_snoc__listrel1__snoc__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y: A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 = ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 & ( X = Y ) )
% 0.30/0.46 | ( ( Xs = Ys2 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % snoc_listrel1_snoc_iff
% 0.30/0.46 thf(fact_219_maps__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 0.30/0.46 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 0.30/0.46 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % maps_simps(1)
% 0.30/0.46 thf(fact_220_bind__simps_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.30/0.46 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_simps(1)
% 0.30/0.46 thf(fact_221_Cons__listrel1__Cons,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.30/0.46 & ( Xs = Ys2 ) )
% 0.30/0.46 | ( ( X = Y )
% 0.30/0.46 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_listrel1_Cons
% 0.30/0.46 thf(fact_222_rtrancl__listrel1__ConsI1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),X: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ X @ Ys2 ) ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_listrel1_ConsI1
% 0.30/0.46 thf(fact_223_listrel1I2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),X: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ X @ Ys2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel1I2
% 0.30/0.46 thf(fact_224_not__listrel1__Nil,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_listrel1_Nil
% 0.30/0.46 thf(fact_225_not__Nil__listrel1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Xs ) @ ( listrel1 @ A @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_Nil_listrel1
% 0.30/0.46 thf(fact_226_append__listrel1I,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Us2: list @ A,Vs: list @ A] :
% 0.30/0.46 ( ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 & ( Us2 = Vs ) )
% 0.30/0.46 | ( ( Xs = Ys2 )
% 0.30/0.46 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Vs ) @ ( listrel1 @ A @ R ) ) ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys2 @ Vs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_listrel1I
% 0.30/0.46 thf(fact_227_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 = ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_rtrancl_eq_rtrancl_listrel1
% 0.30/0.46 thf(fact_228_rtrancl__listrel1__if__listrel,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel @ A @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_listrel1_if_listrel
% 0.30/0.46 thf(fact_229_maps__simps_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.30/0.46 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % maps_simps(2)
% 0.30/0.46 thf(fact_230_listrel1I1,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Xs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel1I1
% 0.30/0.46 thf(fact_231_Cons__listrel1E1,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 => ( ! [Y2: A] :
% 0.30/0.46 ( ( Ys2
% 0.30/0.46 = ( cons @ A @ Y2 @ Xs ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R ) )
% 0.30/0.46 => ~ ! [Zs: list @ A] :
% 0.30/0.46 ( ( Ys2
% 0.30/0.46 = ( cons @ A @ X @ Zs ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_listrel1E1
% 0.30/0.46 thf(fact_232_Cons__listrel1E2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( cons @ A @ Y @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ A @ X3 @ Ys2 ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y ) @ R ) )
% 0.30/0.46 => ~ ! [Zs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ A @ Y @ Zs ) )
% 0.30/0.46 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Zs @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_listrel1E2
% 0.30/0.46 thf(fact_233_listrel__reflcl__if__listrel1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel_reflcl_if_listrel1
% 0.30/0.46 thf(fact_234_listrel1I,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Us2: list @ A,Vs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.30/0.46 => ( ( Xs
% 0.30/0.46 = ( append @ A @ Us2 @ ( cons @ A @ X @ Vs ) ) )
% 0.30/0.46 => ( ( Ys2
% 0.30/0.46 = ( append @ A @ Us2 @ ( cons @ A @ Y @ Vs ) ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel1I
% 0.30/0.46 thf(fact_235_listrel1E,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.30/0.46 => ~ ! [X3: A,Y2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y2 ) @ R )
% 0.30/0.46 => ! [Us3: list @ A,Vs2: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Us3 @ ( cons @ A @ X3 @ Vs2 ) ) )
% 0.30/0.46 => ( Ys2
% 0.30/0.46 != ( append @ A @ Us3 @ ( cons @ A @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % listrel1E
% 0.30/0.46 thf(fact_236_rtrancl__listrel1__ConsI2,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rtrancl_listrel1_ConsI2
% 0.30/0.46 thf(fact_237_concat__eq__append__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( concat @ A @ Xss2 )
% 0.30/0.46 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.30/0.46 = ( ( ( Xss2
% 0.30/0.46 = ( nil @ ( list @ A ) ) )
% 0.30/0.46 => ( ( Ys2
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Zs2
% 0.30/0.46 = ( nil @ A ) ) ) )
% 0.30/0.46 & ( ( Xss2
% 0.30/0.46 != ( nil @ ( list @ A ) ) )
% 0.30/0.46 => ? [Xss1: list @ ( list @ A ),Xs3: list @ A,Xs4: list @ A,Xss22: list @ ( list @ A )] :
% 0.30/0.46 ( ( Xss2
% 0.30/0.46 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.30/0.46 & ( Ys2
% 0.30/0.46 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs3 ) )
% 0.30/0.46 & ( Zs2
% 0.30/0.46 = ( append @ A @ Xs4 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % concat_eq_append_conv
% 0.30/0.46 thf(fact_238_lexord__append__left__rightI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),U: list @ A,X: list @ A,Y: list @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ U @ ( cons @ A @ A2 @ X ) ) @ ( append @ A @ U @ ( cons @ A @ B2 @ Y ) ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_append_left_rightI
% 0.30/0.46 thf(fact_239_concat__append,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 0.30/0.46 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys2 ) )
% 0.30/0.46 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % concat_append
% 0.30/0.46 thf(fact_240_lexord__cons__cons,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,X: list @ A,B2: A,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ A2 @ X ) @ ( cons @ A @ B2 @ Y ) ) @ ( lexord @ A @ R ) )
% 0.30/0.46 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.30/0.46 | ( ( A2 = B2 )
% 0.30/0.46 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ Y ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_cons_cons
% 0.30/0.46 thf(fact_241_lexord__Nil__left,axiom,
% 0.30/0.46 ! [A: $tType,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Y ) @ ( lexord @ A @ R ) )
% 0.30/0.46 = ( ? [A4: A,X4: list @ A] :
% 0.30/0.46 ( Y
% 0.30/0.46 = ( cons @ A @ A4 @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_Nil_left
% 0.30/0.46 thf(fact_242_lexord__linear,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: list @ A,Y: list @ A] :
% 0.30/0.46 ( ! [A3: A,B3: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ R )
% 0.30/0.46 | ( A3 = B3 )
% 0.30/0.46 | ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ A3 ) @ R ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ Y ) @ ( lexord @ A @ R ) )
% 0.30/0.46 | ( X = Y )
% 0.30/0.46 | ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Y @ X ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_linear
% 0.30/0.46 thf(fact_243_lexord__irreflexive,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ X3 ) @ R )
% 0.30/0.46 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( lexord @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_irreflexive
% 0.30/0.46 thf(fact_244_concat_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % concat.simps(1)
% 0.30/0.46 thf(fact_245_lexord__Nil__right,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ ( nil @ A ) ) @ ( lexord @ A @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_Nil_right
% 0.30/0.46 thf(fact_246_concat_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A,Xs: list @ ( list @ A )] :
% 0.30/0.46 ( ( concat @ A @ ( cons @ ( list @ A ) @ X @ Xs ) )
% 0.30/0.46 = ( append @ A @ X @ ( concat @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % concat.simps(2)
% 0.30/0.46 thf(fact_247_lexord__append__leftI,axiom,
% 0.30/0.46 ! [A: $tType,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A ),X: list @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X @ U ) @ ( append @ A @ X @ V ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_append_leftI
% 0.30/0.46 thf(fact_248_lexord__append__leftD,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X @ U ) @ ( append @ A @ X @ V ) ) @ ( lexord @ A @ R ) )
% 0.30/0.46 => ( ! [A3: A] :
% 0.30/0.46 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ A3 ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_append_leftD
% 0.30/0.46 thf(fact_249_lexord__append__rightI,axiom,
% 0.30/0.46 ! [A: $tType,Y: list @ A,X: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ? [B6: A,Z3: list @ A] :
% 0.30/0.46 ( Y
% 0.30/0.46 = ( cons @ A @ B6 @ Z3 ) )
% 0.30/0.46 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ ( append @ A @ X @ Y ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_append_rightI
% 0.30/0.46 thf(fact_250_concat__eq__appendD,axiom,
% 0.30/0.46 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( concat @ A @ Xss2 )
% 0.30/0.46 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.30/0.46 => ( ( Xss2
% 0.30/0.46 != ( nil @ ( list @ A ) ) )
% 0.30/0.46 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs5: list @ A,Xss23: list @ ( list @ A )] :
% 0.30/0.46 ( ( Xss2
% 0.30/0.46 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.30/0.46 & ( Ys2
% 0.30/0.46 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 0.30/0.46 & ( Zs2
% 0.30/0.46 = ( append @ A @ Xs5 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % concat_eq_appendD
% 0.30/0.46 thf(fact_251_lexord__same__pref__if__irrefl,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( irrefl @ A @ R )
% 0.30/0.46 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys2 ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lexord @ A @ R ) )
% 0.30/0.46 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lexord_same_pref_if_irrefl
% 0.30/0.46
% 0.30/0.46 % Type constructors (7)
% 0.30/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ord @ A8 )
% 0.30/0.46 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 0.30/0.46 ord @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.30/0.46 zero @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.30/0.46 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.30/0.46 ord @ $o ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (5)
% 0.30/0.46 thf(conj_0,hypothesis,
% 0.30/0.46 termi @ c @ s ).
% 0.30/0.46
% 0.30/0.46 thf(conj_1,hypothesis,
% 0.30/0.46 ( ( f @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj_2,hypothesis,
% 0.30/0.46 ! [I2: nat] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( f @ I2 ) @ ( f @ ( suc @ I2 ) ) ) @ ( transitive_trancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj_3,hypothesis,
% 0.30/0.46 member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) @ ( f @ n ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj_4,conjecture,
% 0.30/0.46 member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.78/1.47 ---- Embedded in THF ---
% 2.78/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.78/1.47 %%% Generated on Tue Feb 24 08:27:34 EST 2026
% 2.78/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 2.78/1.47 %%% Logic specification used:
% 2.78/1.47 %%% thf(spec, logic, $$dhol).
% 2.78/1.47
% 2.78/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2DTF24138.p
% 2.78/1.47 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.78/1.47 thf(ty_t_PLang_Ostate, type, state: $tType).
% 2.78/1.47 thf(ty_t_PLang_Ocom, type, com: $tType).
% 2.78/1.47 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.78/1.47 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.78/1.47 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.78/1.47 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.78/1.47 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.78/1.47 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.78/1.47 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.78/1.47 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.78/1.47 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.78/1.47 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.78/1.47 thf(sy_c_List_Oconcat, type, concat: (!> [A:$tType]: (((list @ (list @ A)) > (list @ A))))).
% 2.78/1.47 thf(sy_c_List_Ogen__length, type, gen_length: (!> [A:$tType]: ((nat > ((list @ A) > nat))))).
% 2.78/1.47 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.78/1.47 thf(sy_c_List_Olexord, type, lexord: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 2.78/1.47 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.78/1.47 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.78/1.47 thf(sy_c_List_Olistrel, type, listrel: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ B)) > (set @ ((product_prod @ (list @ A)) @ (list @ B))))))).
% 2.78/1.47 thf(sy_c_List_Olistrel1, type, listrel1: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 2.78/1.47 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.78/1.47 thf(sy_c_List_On__lists, type, n_lists: (!> [A:$tType]: ((nat > ((list @ A) > (list @ (list @ A))))))).
% 2.78/1.47 thf(sy_c_List_Onths, type, nths: (!> [A:$tType]: (((list @ A) > ((set @ nat) > (list @ A)))))).
% 2.78/1.47 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.78/1.47 thf(sy_c_List_Osubseqs, type, subseqs: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.78/1.47 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.78/1.47 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oexec1, type, pHoare1053570893_exec1: (set @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)))).
% 2.78/1.47 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oexecs, type, pHoare1053570959_execs: (state > ((list @ com) > (state > $o)))).
% 2.78/1.47 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oinf, type, pHoare1838713294le_inf: ((list @ com) > (state > $o))).
% 2.78/1.47 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Otermis, type, pHoare1335526537termis: ((list @ com) > (state > $o))).
% 2.78/1.47 thf(sy_c_PLang_Ocom_OCond, type, cond: ((state > $o) > (com > (com > com)))).
% 2.78/1.47 thf(sy_c_PLang_Ocom_ODo, type, do: ((state > (set @ state)) > com)).
% 2.78/1.47 thf(sy_c_PLang_Ocom_OSemi, type, semi: (com > (com > com))).
% 2.78/1.47 thf(sy_c_PLang_Ocom_OWhile, type, while: ((state > $o) > (com > com))).
% 2.78/1.47 thf(sy_c_PLang_Oexec, type, exec: (state > (com > (state > $o)))).
% 2.78/1.47 thf(sy_c_PTermi_Otermi, type, termi: (com > (state > $o))).
% 2.78/1.47 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.78/1.47 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.78/1.47 thf(sy_c_Relation_Oirrefl, type, irrefl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.78/1.47 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.78/1.47 thf(sy_c_Transitive__Closure_Ortrancl, type, transitive_rtrancl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ A) @ A)))))).
% 2.78/1.47 thf(sy_c_Transitive__Closure_Otrancl, type, transitive_trancl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ A) @ A)))))).
% 2.78/1.47 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.78/1.47 thf(sy_v_c, type, c: com).
% 2.78/1.47 thf(sy_v_f, type, f: (nat > ((product_prod @ (list @ com)) @ state))).
% 2.78/1.47 thf(sy_v_n, type, n: nat).
% 2.78/1.47 thf(sy_v_s, type, s: state).
% 2.78/1.47 thf(fact_0_exec1E_I1_J, axiom, (! [S:state,Cs:(list @ com),S2:state]: ((~ ((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (nil @ com)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ pHoare1053570893_exec1)))))).
% 2.78/1.47 thf(fact_1_renumber, axiom, (! [A:$tType,A2:A,F:(nat > A),R:(set @ ((product_prod @ A) @ A))]: (((! [I:nat]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ (F @ I))) @ ((transitive_rtrancl @ A) @ R)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (F @ I)) @ (F @ (suc @ I)))) @ R)))) => (? [F2:(nat > A)]: ((((F2 @ (zero_zero @ nat)) = A2) & (! [I2:nat]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (F2 @ I2)) @ (F2 @ (suc @ I2)))) @ R)))))))))).
% 2.78/1.47 thf(fact_2_renumber__aux, axiom, (! [A:$tType,A2:A,F:(nat > A),R:(set @ ((product_prod @ A) @ A)),B2:A]: (((! [I:nat]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ (F @ I))) @ ((transitive_rtrancl @ A) @ R)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (F @ I)) @ (F @ (suc @ I)))) @ R)))) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R)) => ((B2 = (F @ (zero_zero @ nat))) => (? [F2:(nat > A)]: ((((F2 @ (zero_zero @ nat)) = A2) & (! [I2:nat]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (F2 @ I2)) @ (F2 @ (suc @ I2)))) @ R)))))))))))).
% 2.78/1.47 thf(fact_3_execs__pres__termi, axiom, (! [C:com,S:state,C2:com,Cs:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C) @ (nil @ com))) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C2) @ Cs)) @ S2))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1)) => (((termi @ C) @ S) => ((termi @ C2) @ S2)))))).
% 2.78/1.47 thf(fact_4_rtrancl__trancl__absorb, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((transitive_trancl @ A) @ ((transitive_rtrancl @ A) @ R2)) = ((transitive_rtrancl @ A) @ R2))))).
% 2.78/1.47 thf(fact_5_trancl__rtrancl__absorb, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((transitive_rtrancl @ A) @ ((transitive_trancl @ A) @ R2)) = ((transitive_rtrancl @ A) @ R2))))).
% 2.78/1.47 thf(fact_6_trancl__induct2, axiom, (! [A:$tType,B:$tType,Ax:A,Ay:B,Bx:A,By:B,R:(set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))),P:(A > (B > $o))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Ax) @ Ay)) @ ((((product_Pair @ A) @ B) @ Bx) @ By))) @ ((transitive_trancl @ ((product_prod @ A) @ B)) @ R)) => ((! [A3:A,B3:B]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Ax) @ Ay)) @ ((((product_Pair @ A) @ B) @ A3) @ B3))) @ R) => ((P @ A3) @ B3)))) => ((! [A3:A,B3:B,Aa:A,Ba:B]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Ax) @ Ay)) @ ((((product_Pair @ A) @ B) @ A3) @ B3))) @ ((transitive_trancl @ ((product_prod @ A) @ B)) @ R)) => ((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) @ ((((product_Pair @ A) @ B) @ Aa) @ Ba))) @ R) => (((P @ A3) @ B3) => ((P @ Aa) @ Ba)))))) => ((P @ Bx) @ By))))))).
% 2.78/1.47 thf(fact_7_inf__def, axiom, (pHoare1838713294le_inf = (^ [Cs2:(list @ com),S3:state]: ((? [F3:(nat > ((product_prod @ (list @ com)) @ state))]: ((((F3 @ (zero_zero @ nat)) = ((((product_Pair @ (list @ com)) @ state) @ Cs2) @ S3)) & (! [I3:nat]: ((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ (F3 @ I3)) @ (F3 @ (suc @ I3)))) @ pHoare1053570893_exec1)))))))))).
% 2.78/1.47 thf(fact_8_rtrancl__induct2, axiom, (! [A:$tType,B:$tType,Ax:A,Ay:B,Bx:A,By:B,R:(set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))),P:(A > (B > $o))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Ax) @ Ay)) @ ((((product_Pair @ A) @ B) @ Bx) @ By))) @ ((transitive_rtrancl @ ((product_prod @ A) @ B)) @ R)) => (((P @ Ax) @ Ay) => ((! [A3:A,B3:B,Aa:A,Ba:B]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Ax) @ Ay)) @ ((((product_Pair @ A) @ B) @ A3) @ B3))) @ ((transitive_rtrancl @ ((product_prod @ A) @ B)) @ R)) => ((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) @ ((((product_Pair @ A) @ B) @ Aa) @ Ba))) @ R) => (((P @ A3) @ B3) => ((P @ Aa) @ Ba)))))) => ((P @ Bx) @ By))))))).
% 2.78/1.47 thf(fact_9_converse__rtranclE2, axiom, (! [B:$tType,A:$tType,Xa:A,Xb:B,Za:A,Zb:B,R:(set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Xa) @ Xb)) @ ((((product_Pair @ A) @ B) @ Za) @ Zb))) @ ((transitive_rtrancl @ ((product_prod @ A) @ B)) @ R)) => ((((((product_Pair @ A) @ B) @ Xa) @ Xb) != ((((product_Pair @ A) @ B) @ Za) @ Zb)) => (~ ((! [A3:A,B3:B]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Xa) @ Xb)) @ ((((product_Pair @ A) @ B) @ A3) @ B3))) @ R) => (~ ((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) @ ((((product_Pair @ A) @ B) @ Za) @ Zb))) @ ((transitive_rtrancl @ ((product_prod @ A) @ B)) @ R)))))))))))))).
% 2.78/1.47 thf(fact_10_converse__rtrancl__induct2, axiom, (! [A:$tType,B:$tType,Ax:A,Ay:B,Bx:A,By:B,R:(set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))),P:(A > (B > $o))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Ax) @ Ay)) @ ((((product_Pair @ A) @ B) @ Bx) @ By))) @ ((transitive_rtrancl @ ((product_prod @ A) @ B)) @ R)) => (((P @ Bx) @ By) => ((! [A3:A,B3:B,Aa:A,Ba:B]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) @ ((((product_Pair @ A) @ B) @ Aa) @ Ba))) @ R) => ((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Aa) @ Ba)) @ ((((product_Pair @ A) @ B) @ Bx) @ By))) @ ((transitive_rtrancl @ ((product_prod @ A) @ B)) @ R)) => (((P @ Aa) @ Ba) => ((P @ A3) @ B3)))))) => ((P @ Ax) @ Ay))))))).
% 2.78/1.47 thf(fact_11_tranclD, axiom, (! [A:$tType,X:A,Y:A,R2:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_trancl @ A) @ R2)) => (? [Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z)) @ R2) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z) @ Y)) @ ((transitive_rtrancl @ A) @ R2))))))))).
% 2.78/1.47 thf(fact_12_rtranclD, axiom, (! [A:$tType,A2:A,B2:A,R2:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R2)) => ((A2 = B2) | ((A2 != B2) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R2)))))))).
% 2.78/1.47 thf(fact_13_tranclD2, axiom, (! [A:$tType,X:A,Y:A,R2:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_trancl @ A) @ R2)) => (? [Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z)) @ ((transitive_rtrancl @ A) @ R2)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z) @ Y)) @ R2)))))))).
% 2.78/1.47 thf(fact_14_trancl__into__rtrancl, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R)))))).
% 2.78/1.47 thf(fact_15_rtrancl__eq__or__trancl, axiom, (! [A:$tType,X:A,Y:A,R2:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_rtrancl @ A) @ R2)) = ((X = Y) | ((X != Y) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_trancl @ A) @ R2)))))))).
% 2.78/1.47 thf(fact_16_r__into__rtrancl, axiom, (! [A:$tType,P2:((product_prod @ A) @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ P2) @ R) => (((member @ ((product_prod @ A) @ A)) @ P2) @ ((transitive_rtrancl @ A) @ R)))))).
% 2.78/1.47 thf(fact_17_rtrancl__idemp, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: ((((transitive_rtrancl @ A) @ ((transitive_rtrancl @ A) @ R)) = ((transitive_rtrancl @ A) @ R))))).
% 2.78/1.47 thf(fact_18_r__into__trancl_H, axiom, (! [A:$tType,P2:((product_prod @ A) @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ P2) @ R) => (((member @ ((product_prod @ A) @ A)) @ P2) @ ((transitive_trancl @ A) @ R)))))).
% 2.78/1.47 thf(fact_19_converse__rtrancl__into__rtrancl, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ ((transitive_rtrancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_rtrancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_20_rtrancl_Ortrancl__into__rtrancl, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_rtrancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_21_converse__rtrancl__induct, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),P:(A > $o)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R)) => ((P @ B2) => ((! [Y2:A,Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z) @ B2)) @ ((transitive_rtrancl @ A) @ R)) => ((P @ Z) => (P @ Y2)))))) => (P @ A2))))))).
% 2.78/1.47 thf(fact_22_rtrancl_Ortrancl__refl, axiom, (! [A:$tType,A2:A,R:(set @ ((product_prod @ A) @ A))]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ ((transitive_rtrancl @ A) @ R))))).
% 2.78/1.47 thf(fact_23_converse__rtranclE, axiom, (! [A:$tType,X:A,Z2:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ ((transitive_rtrancl @ A) @ R)) => ((X != Z2) => (~ ((! [Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y2)) @ R) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z2)) @ ((transitive_rtrancl @ A) @ R)))))))))))))).
% 2.78/1.47 thf(fact_24_rtrancl_Oinducts, axiom, (! [A:$tType,X1:A,X2:A,R:(set @ ((product_prod @ A) @ A)),P:(A > (A > $o))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X1) @ X2)) @ ((transitive_rtrancl @ A) @ R)) => ((! [A3:A]: (((P @ A3) @ A3))) => ((! [A3:A,B3:A,C3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ B3)) @ ((transitive_rtrancl @ A) @ R)) => (((P @ A3) @ B3) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B3) @ C3)) @ R) => ((P @ A3) @ C3)))))) => ((P @ X1) @ X2))))))).
% 2.78/1.47 thf(fact_25_rtrancl__induct, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),P:(A > $o)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R)) => ((P @ A2) => ((! [Y2:A,Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ Y2)) @ ((transitive_rtrancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z)) @ R) => ((P @ Y2) => (P @ Z)))))) => (P @ B2))))))).
% 2.78/1.47 thf(fact_26_rtrancl__trans, axiom, (! [A:$tType,X:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Z2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_rtrancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z2)) @ ((transitive_rtrancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ ((transitive_rtrancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_27_rtrancl_Osimps, axiom, (! [A:$tType,A1:A,A22:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A1) @ A22)) @ ((transitive_rtrancl @ A) @ R)) = ((? [A4:A]: (((A1 = A4) & (A22 = A4)))) | (? [A4:A,B4:A,C4:A]: (((A1 = A4) & ((A22 = C4) & ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ B4)) @ ((transitive_rtrancl @ A) @ R)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B4) @ C4)) @ R))))))))))).
% 2.78/1.47 thf(fact_28_rtrancl_Ocases, axiom, (! [A:$tType,A1:A,A22:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A1) @ A22)) @ ((transitive_rtrancl @ A) @ R)) => ((A22 != A1) => (~ ((! [B3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A1) @ B3)) @ ((transitive_rtrancl @ A) @ R)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B3) @ A22)) @ R))))))))))))).
% 2.78/1.47 thf(fact_29_rtranclE, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R)) => ((A2 != B2) => (~ ((! [Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ Y2)) @ ((transitive_rtrancl @ A) @ R)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ B2)) @ R))))))))))))).
% 2.78/1.47 thf(fact_30_trancl_Otrancl__into__trancl, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_trancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_31_converse__trancl__induct, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),P:(A > $o)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R)) => ((! [Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ B2)) @ R) => (P @ Y2)))) => ((! [Y2:A,Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z) @ B2)) @ ((transitive_trancl @ A) @ R)) => ((P @ Z) => (P @ Y2)))))) => (P @ A2))))))).
% 2.78/1.47 thf(fact_32_trancl_Or__into__trancl, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R)))))).
% 2.78/1.47 thf(fact_33_trancl__trans__induct, axiom, (! [A:$tType,X:A,Y:A,R:(set @ ((product_prod @ A) @ A)),P:(A > (A > $o))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_trancl @ A) @ R)) => ((! [X3:A,Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y2)) @ R) => ((P @ X3) @ Y2)))) => ((! [X3:A,Y2:A,Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y2)) @ ((transitive_trancl @ A) @ R)) => (((P @ X3) @ Y2) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z)) @ ((transitive_trancl @ A) @ R)) => (((P @ Y2) @ Z) => ((P @ X3) @ Z))))))) => ((P @ X) @ Y))))))).
% 2.78/1.47 thf(fact_34_trancl__into__trancl2, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ ((transitive_trancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_trancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_35_irrefl__trancl__rD, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X:A,Y:A]: (((! [X3:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ X3)) @ ((transitive_trancl @ A) @ R)))))) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) => (X != Y)))))).
% 2.78/1.47 thf(fact_36_converse__tranclE, axiom, (! [A:$tType,X:A,Z2:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ ((transitive_trancl @ A) @ R)) => ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ R))) => (~ ((! [Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y2)) @ R) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z2)) @ ((transitive_trancl @ A) @ R)))))))))))))).
% 2.78/1.47 thf(fact_37_r__r__into__trancl, axiom, (! [A:$tType,A2:A,B2:A,R2:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R2) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ R2) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_trancl @ A) @ R2))))))).
% 2.78/1.47 thf(fact_38_trancl_Oinducts, axiom, (! [A:$tType,X1:A,X2:A,R:(set @ ((product_prod @ A) @ A)),P:(A > (A > $o))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X1) @ X2)) @ ((transitive_trancl @ A) @ R)) => ((! [A3:A,B3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ B3)) @ R) => ((P @ A3) @ B3)))) => ((! [A3:A,B3:A,C3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ B3)) @ ((transitive_trancl @ A) @ R)) => (((P @ A3) @ B3) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B3) @ C3)) @ R) => ((P @ A3) @ C3)))))) => ((P @ X1) @ X2))))))).
% 2.78/1.47 thf(fact_39_trancl__induct, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),P:(A > $o)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R)) => ((! [Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ Y2)) @ R) => (P @ Y2)))) => ((! [Y2:A,Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ Y2)) @ ((transitive_trancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z)) @ R) => ((P @ Y2) => (P @ Z)))))) => (P @ B2))))))).
% 2.78/1.47 thf(fact_40_trancl__trans, axiom, (! [A:$tType,X:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Z2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_trancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z2)) @ ((transitive_trancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ ((transitive_trancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_41_trancl_Osimps, axiom, (! [A:$tType,A1:A,A22:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A1) @ A22)) @ ((transitive_trancl @ A) @ R)) = ((? [A4:A,B4:A]: (((A1 = A4) & ((A22 = B4) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ B4)) @ R))))) | (? [A4:A,B4:A,C4:A]: (((A1 = A4) & ((A22 = C4) & ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ B4)) @ ((transitive_trancl @ A) @ R)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B4) @ C4)) @ R))))))))))).
% 2.78/1.47 thf(fact_42_trancl_Ocases, axiom, (! [A:$tType,A1:A,A22:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A1) @ A22)) @ ((transitive_trancl @ A) @ R)) => ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A1) @ A22)) @ R))) => (~ ((! [B3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A1) @ B3)) @ ((transitive_trancl @ A) @ R)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B3) @ A22)) @ R))))))))))))).
% 2.78/1.47 thf(fact_43_tranclE, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R)) => ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R))) => (~ ((! [C3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C3)) @ ((transitive_trancl @ A) @ R)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ C3) @ B2)) @ R))))))))))))).
% 2.78/1.47 thf(fact_44_termi__impl__not__inf, axiom, (! [C:com,S:state]: ((((termi @ C) @ S) => (~ (((pHoare1838713294le_inf @ (((cons @ com) @ C) @ (nil @ com))) @ S))))))).
% 2.78/1.47 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.78/1.47 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A5)))) = A5)))).
% 2.78/1.47 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.78/1.47 thf(fact_48_trancl__rtrancl__trancl, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_trancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ ((transitive_rtrancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_trancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_49_rtrancl__trancl__trancl, axiom, (! [A:$tType,X:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Z2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_rtrancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z2)) @ ((transitive_trancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ ((transitive_trancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_50_rtrancl__into__trancl2, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ ((transitive_rtrancl @ A) @ R)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_trancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_51_rtrancl__into__trancl1, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),C:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((transitive_rtrancl @ A) @ R)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B2) @ C)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ C)) @ ((transitive_trancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_52_exec1s__impl__execs, axiom, (! [Cs3:(list @ com),S:state,T2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (nil @ com)) @ T2))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1)) => (((pHoare1053570959_execs @ S) @ Cs3) @ T2))))).
% 2.78/1.47 thf(fact_53_execs__pres__termis, axiom, (! [Cs3:(list @ com),S:state,Cs:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1)) => (((pHoare1335526537termis @ Cs3) @ S) => ((pHoare1335526537termis @ Cs) @ S2)))))).
% 2.78/1.47 thf(fact_54_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.78/1.47 thf(fact_55_nat_Oinject, axiom, (! [X2:nat,Y22:nat]: ((((suc @ X2) = (suc @ Y22)) = (X2 = Y22))))).
% 2.78/1.47 thf(fact_56_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y222:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y222)) = ((X21 = Y21) & (X22 = Y222)))))).
% 2.78/1.47 thf(fact_57_exec1s__impl__exec, axiom, (! [C:com,S:state,T2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C) @ (nil @ com))) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (nil @ com)) @ T2))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1)) => (((exec @ S) @ C) @ T2))))).
% 2.78/1.47 thf(fact_58_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B5:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B5)) = ((A2 = A6) & (B2 = B5)))))).
% 2.78/1.47 thf(fact_59_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X1 = Y1) & (X2 = Y22)))))).
% 2.78/1.47 thf(fact_60_execs_Ointros_I2_J, axiom, (! [S:state,C:com,T2:state,Cs3:(list @ com),U:state]: (((((exec @ S) @ C) @ T2) => ((((pHoare1053570959_execs @ T2) @ Cs3) @ U) => (((pHoare1053570959_execs @ S) @ (((cons @ com) @ C) @ Cs3)) @ U)))))).
% 2.78/1.47 thf(fact_61_execs_Ocases, axiom, (! [A1:state,A22:(list @ com),A32:state]: (((((pHoare1053570959_execs @ A1) @ A22) @ A32) => (((A22 = (nil @ com)) => (A32 != A1)) => (~ ((! [C3:com,T3:state,Cs4:(list @ com)]: (((A22 = (((cons @ com) @ C3) @ Cs4)) => ((((exec @ A1) @ C3) @ T3) => (~ ((((pHoare1053570959_execs @ T3) @ Cs4) @ A32)))))))))))))).
% 2.78/1.47 thf(fact_62_execs_Osimps, axiom, (pHoare1053570959_execs = (^ [A12:state,A23:(list @ com),A33:state]: (((? [S3:state]: (((A12 = S3) & ((A23 = (nil @ com)) & (A33 = S3))))) | (? [S3:state,C4:com,T4:state,Cs2:(list @ com),U2:state]: (((A12 = S3) & ((A23 = (((cons @ com) @ C4) @ Cs2)) & ((A33 = U2) & ((((exec @ S3) @ C4) @ T4) & (((pHoare1053570959_execs @ T4) @ Cs2) @ U2)))))))))))).
% 2.78/1.47 thf(fact_63_execs_Oinducts, axiom, (! [X1:state,X2:(list @ com),X32:state,P:(state > ((list @ com) > (state > $o)))]: (((((pHoare1053570959_execs @ X1) @ X2) @ X32) => ((! [S4:state]: ((((P @ S4) @ (nil @ com)) @ S4))) => ((! [S4:state,C3:com,T3:state,Cs4:(list @ com),U3:state]: (((((exec @ S4) @ C3) @ T3) => ((((pHoare1053570959_execs @ T3) @ Cs4) @ U3) => ((((P @ T3) @ Cs4) @ U3) => (((P @ S4) @ (((cons @ com) @ C3) @ Cs4)) @ U3)))))) => (((P @ X1) @ X2) @ X32))))))).
% 2.78/1.47 thf(fact_64_termis_Osimps_I2_J, axiom, (! [C:com,Cs3:(list @ com),S:state]: ((((pHoare1335526537termis @ (((cons @ com) @ C) @ Cs3)) @ S) = (((termi @ C) @ S) & (! [T4:state]: (((((exec @ S) @ C) @ T4) => ((pHoare1335526537termis @ Cs3) @ T4))))))))).
% 2.78/1.47 thf(fact_65_execs_Ointros_I1_J, axiom, (! [S:state]: ((((pHoare1053570959_execs @ S) @ (nil @ com)) @ S)))).
% 2.78/1.47 thf(fact_66_termis_Osimps_I1_J, axiom, (! [S:state]: (((pHoare1335526537termis @ (nil @ com)) @ S)))).
% 2.78/1.47 thf(fact_67_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.78/1.47 thf(fact_68_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X3:A,Y2:B]: ((P2 = ((((product_Pair @ A) @ B) @ X3) @ Y2))))))).
% 2.78/1.47 thf(fact_69_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A3:A,B3:B]: ((P @ ((((product_Pair @ A) @ B) @ A3) @ B3)))) => (P @ P2))))).
% 2.78/1.47 thf(fact_70_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B5:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B5)) => (~ (((A2 = A6) => (B2 != B5)))))))).
% 2.78/1.47 thf(fact_71_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A3:A,B3:B]: ((Y != ((((product_Pair @ A) @ B) @ A3) @ B3))))))))).
% 2.78/1.47 thf(fact_72_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A3:A,B3:B]: ((P @ ((((product_Pair @ A) @ B) @ A3) @ B3)))) => (P @ Prod))))).
% 2.78/1.47 thf(fact_73_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.78/1.47 thf(fact_74_Suc__inject, axiom, (! [X:nat,Y:nat]: ((((suc @ X) = (suc @ Y)) => (X = Y))))).
% 2.78/1.47 thf(fact_75_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.78/1.47 thf(fact_76_inf__cases, axiom, (! [C:com,Cs3:(list @ com),S:state]: ((((pHoare1838713294le_inf @ (((cons @ com) @ C) @ Cs3)) @ S) => (((pHoare1838713294le_inf @ (((cons @ com) @ C) @ (nil @ com))) @ S) | (? [T3:state]: (((((exec @ S) @ C) @ T3) & ((pHoare1838713294le_inf @ Cs3) @ T3))))))))).
% 2.78/1.47 thf(fact_77_nat_Odistinct_I1_J, axiom, (! [X2:nat]: (((zero_zero @ nat) != (suc @ X2))))).
% 2.78/1.47 thf(fact_78_old_Onat_Odistinct_I2_J, axiom, (! [Nat3:nat]: (((suc @ Nat3) != (zero_zero @ nat))))).
% 2.78/1.47 thf(fact_79_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.78/1.47 thf(fact_80_nat_OdiscI, axiom, (! [Nat:nat,X2:nat]: (((Nat = (suc @ X2)) => (Nat != (zero_zero @ nat)))))).
% 2.78/1.47 thf(fact_81_nat__induct, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((P @ N2) => (P @ (suc @ N2))))) => (P @ N)))))).
% 2.78/1.47 thf(fact_82_diff__induct, axiom, (! [P:(nat > (nat > $o)),M:nat,N:nat]: (((! [X3:nat]: (((P @ X3) @ (zero_zero @ nat)))) => ((! [Y2:nat]: (((P @ (zero_zero @ nat)) @ (suc @ Y2)))) => ((! [X3:nat,Y2:nat]: ((((P @ X3) @ Y2) => ((P @ (suc @ X3)) @ (suc @ Y2))))) => ((P @ M) @ N))))))).
% 2.78/1.47 thf(fact_83_zero__induct, axiom, (! [P:(nat > $o),K:nat]: (((P @ K) => ((! [N2:nat]: (((P @ (suc @ N2)) => (P @ N2)))) => (P @ (zero_zero @ nat))))))).
% 2.78/1.47 thf(fact_84_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 2.78/1.47 thf(fact_85_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.78/1.47 thf(fact_86_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.78/1.47 thf(fact_87_old_Onat_Oexhaust, axiom, (! [Y:nat]: (((Y != (zero_zero @ nat)) => (~ ((! [Nat4:nat]: ((Y != (suc @ Nat4)))))))))).
% 2.78/1.47 thf(fact_88_old_Onat_Oinducts, axiom, (! [P:(nat > $o),Nat:nat]: (((P @ (zero_zero @ nat)) => ((! [Nat4:nat]: (((P @ Nat4) => (P @ (suc @ Nat4))))) => (P @ Nat)))))).
% 2.78/1.47 thf(fact_89_not0__implies__Suc, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (? [M2:nat]: ((N = (suc @ M2)))))))).
% 2.78/1.47 thf(fact_90_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.78/1.47 thf(fact_91_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.78/1.47 thf(fact_92_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.78/1.47 thf(fact_93_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X12:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X12) @ X23))))) => (P @ List)))))).
% 2.78/1.47 thf(fact_94_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys)))))))).
% 2.78/1.47 thf(fact_95_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys2:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X3) @ Xs2)) @ (nil @ B)))) => ((! [Y2:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y2) @ Ys3)))) => ((! [X3:A,Xs2:(list @ A),Y2:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys3))))) => ((P @ Xs) @ Ys2)))))))).
% 2.78/1.47 thf(fact_96_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X3:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((P @ Ys3) @ Xs2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ Ys3)))) => ((P @ A0) @ A1)))))).
% 2.78/1.47 thf(fact_97_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Y2:A,Zs:(list @ A)]: (((P @ Zs) => ((P @ (((cons @ A) @ Y2) @ Zs)) => (P @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Zs))))))) => (P @ Xs))))))).
% 2.78/1.47 thf(fact_98_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X:(list @ A)]: (((! [X3:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X3) @ Xs2)))) => (X = (nil @ A))))))))).
% 2.78/1.47 thf(fact_99_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X3:A,Xs2:(list @ A)]: (((! [X213:A,X223:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X223)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X3) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.78/1.47 thf(fact_100_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X3:A,Xs2:(list @ A),Y2:A,Ys3:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y2) @ Ys3)) => (((P @ (((cons @ A) @ X3) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys3)))))) => ((P @ A0) @ A1))))))).
% 2.78/1.47 thf(fact_101_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X3:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ Xss))))))))))).
% 2.78/1.47 thf(fact_102_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X3:A]: ((X != (((cons @ A) @ X3) @ (nil @ A))))) => (~ ((! [X3:A,Y2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Xs2)))))))))))).
% 2.78/1.47 thf(fact_103_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P3:(A > (A > $o))]: (((P @ P3) @ (nil @ A)))) => ((! [P3:(A > (A > $o)),X3:A,Ys3:(list @ A)]: ((((P @ P3) @ Ys3) => ((P @ P3) @ (((cons @ A) @ X3) @ Ys3))))) => ((P @ A0) @ A1)))))).
% 2.78/1.47 thf(fact_104_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Y2:A,Xs2:(list @ A)]: ((((X3 = Y2) => (P @ (((cons @ A) @ X3) @ Xs2))) => (((X3 != Y2) => (P @ (((cons @ A) @ Y2) @ Xs2))) => (P @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P @ A0))))))).
% 2.78/1.47 thf(fact_105_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X3:A]: (((P @ F2) @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [F2:(A > B),X3:A,Y2:A,Zs:(list @ A)]: ((((P @ F2) @ (((cons @ A) @ Y2) @ Zs)) => ((P @ F2) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Zs)))))) => ((! [A3:(A > B)]: (((P @ A3) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.78/1.47 thf(fact_106_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P3:(A > (A > $o))]: (((P @ P3) @ (nil @ A)))) => ((! [P3:(A > (A > $o)),X3:A]: (((P @ P3) @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [P3:(A > (A > $o)),X3:A,Y2:A,Xs2:(list @ A)]: ((((P @ P3) @ (((cons @ A) @ Y2) @ Xs2)) => ((P @ P3) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.78/1.47 thf(fact_107_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X3) @ Xs2)))))) => (P @ Xs))))))).
% 2.78/1.47 thf(fact_108_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X_1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B),A3:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A3)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A3) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.78/1.47 thf(fact_109_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X3:A,Ys3:(list @ A)]: ((X != (((cons @ A) @ X3) @ Ys3))))))))))))).
% 2.78/1.47 thf(fact_110_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A,Ys3:(list @ A)]: (((P @ Ys3) => (P @ (((cons @ A) @ X3) @ Ys3))))) => (P @ A0))))))))).
% 2.78/1.47 thf(fact_111_splice_Ocases, axiom, (! [A:$tType,X:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys3:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys3)))) => (~ ((! [X3:A,Xs2:(list @ A),Ys3:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ Ys3)))))))))).
% 2.78/1.47 thf(fact_112_shuffles_Ocases, axiom, (! [A:$tType,X:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys3:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys3)))) => ((! [Xs2:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ (nil @ A))))) => (~ ((! [X3:A,Xs2:(list @ A),Y2:A,Ys3:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys3)))))))))))).
% 2.78/1.47 thf(fact_113_sorted__wrt_Ocases, axiom, (! [A:$tType,X:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P3:(A > (A > $o))]: ((X != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P3) @ (nil @ A))))) => (~ ((! [P3:(A > (A > $o)),X3:A,Ys3:(list @ A)]: ((X != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P3) @ (((cons @ A) @ X3) @ Ys3))))))))))).
% 2.78/1.47 thf(fact_114_successively_Ocases, axiom, (! [A:$tType,X:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P3:(A > (A > $o))]: ((X != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P3) @ (nil @ A))))) => ((! [P3:(A > (A > $o)),X3:A]: ((X != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P3) @ (((cons @ A) @ X3) @ (nil @ A)))))) => (~ ((! [P3:(A > (A > $o)),X3:A,Y2:A,Xs2:(list @ A)]: ((X != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P3) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Xs2))))))))))))).
% 2.78/1.47 thf(fact_115_arg__min__list_Ocases, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [X:((product_prod @ (A > B)) @ (list @ A))]: (((! [F2:(A > B),X3:A]: ((X != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X3) @ (nil @ A)))))) => ((! [F2:(A > B),X3:A,Y2:A,Zs:(list @ A)]: ((X != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Zs)))))) => (~ ((! [A3:(A > B)]: ((X != ((((product_Pair @ (A > B)) @ (list @ A)) @ A3) @ (nil @ A))))))))))))))).
% 2.78/1.47 thf(fact_116_map__tailrec__rev_Ocases, axiom, (! [A:$tType,B:$tType,X:((product_prod @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B)))]: (((! [F2:(A > B),Bs:(list @ B)]: ((X != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Bs))))) => (~ ((! [F2:(A > B),A3:A,As:(list @ A),Bs:(list @ B)]: ((X != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ A3) @ As)) @ Bs))))))))))).
% 2.78/1.47 thf(fact_117_exec__impl__execs, axiom, (! [S:state,C:com,S2:state,Cs3:(list @ com)]: (((((exec @ S) @ C) @ S2) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ S2))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1)))))).
% 2.78/1.47 thf(fact_118_prod__cases3, axiom, (! [A:$tType,B:$tType,C5:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C5))]: ((~ ((! [A3:A,B3:B,C3:C5]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C5)) @ A3) @ ((((product_Pair @ B) @ C5) @ B3) @ C3)))))))))).
% 2.78/1.47 thf(fact_119_prod__cases4, axiom, (! [A:$tType,B:$tType,C5:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D)))]: ((~ ((! [A3:A,B3:B,C3:C5,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ D)) @ B3) @ ((((product_Pair @ C5) @ D) @ C3) @ D2))))))))))).
% 2.78/1.47 thf(fact_120_prod__cases5, axiom, (! [A:$tType,B:$tType,C5:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ E))))]: ((~ ((! [A3:A,B3:B,C3:C5,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ E)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ E))) @ B3) @ ((((product_Pair @ C5) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.78/1.47 thf(fact_121_prod__cases6, axiom, (! [A:$tType,B:$tType,C5:$tType,D:$tType,E:$tType,F4:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: ((~ ((! [A3:A,B3:B,C3:C5,D2:D,E2:E,F2:F4]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B3) @ ((((product_Pair @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F2))))))))))))).
% 2.78/1.47 thf(fact_122_prod__cases7, axiom, (! [A:$tType,B:$tType,C5:$tType,D:$tType,E:$tType,F4:$tType,G:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G))))))]: ((~ ((! [A3:A,B3:B,C3:C5,D2:D,E2:E,F2:F4,G2:G]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G))))) @ B3) @ ((((product_Pair @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G)) @ E2) @ ((((product_Pair @ F4) @ G) @ F2) @ G2)))))))))))))).
% 2.78/1.47 thf(fact_123_prod__induct3, axiom, (! [C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C5)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C5))]: (((! [A3:A,B3:B,C3:C5]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C5)) @ A3) @ ((((product_Pair @ B) @ C5) @ B3) @ C3))))) => (P @ X))))).
% 2.78/1.47 thf(fact_124_prod__induct4, axiom, (! [D:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D)))]: (((! [A3:A,B3:B,C3:C5,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ D)) @ B3) @ ((((product_Pair @ C5) @ D) @ C3) @ D2)))))) => (P @ X))))).
% 2.78/1.47 thf(fact_125_prod__induct5, axiom, (! [E:$tType,D:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ E))))]: (((! [A3:A,B3:B,C3:C5,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ E)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ E))) @ B3) @ ((((product_Pair @ C5) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X))))).
% 2.78/1.47 thf(fact_126_prod__induct6, axiom, (! [F4:$tType,E:$tType,D:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: (((! [A3:A,B3:B,C3:C5,D2:D,E2:E,F2:F4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B3) @ ((((product_Pair @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F2)))))))) => (P @ X))))).
% 2.78/1.47 thf(fact_127_prod__induct7, axiom, (! [G:$tType,F4:$tType,E:$tType,D:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G))))))]: (((! [A3:A,B3:B,C3:C5,D2:D,E2:E,F2:F4,G2:G]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G))))) @ B3) @ ((((product_Pair @ C5) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G)) @ E2) @ ((((product_Pair @ F4) @ G) @ F2) @ G2))))))))) => (P @ X))))).
% 2.78/1.47 thf(fact_128_exec1__pres__termis, axiom, (! [Cs3:(list @ com),S:state,Cs:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ pHoare1053570893_exec1) => (((pHoare1335526537termis @ Cs3) @ S) => ((pHoare1335526537termis @ Cs) @ S2)))))).
% 2.78/1.47 thf(fact_129_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.78/1.47 thf(fact_130_dependent__nat__choice, axiom, (! [A:$tType,P:(nat > (A > $o)),Q:(nat > (A > (A > $o)))]: (((? [X_12:A]: (((P @ (zero_zero @ nat)) @ X_12))) => ((! [X3:A,N2:nat]: ((((P @ N2) @ X3) => (? [Y4:A]: ((((P @ (suc @ N2)) @ Y4) & (((Q @ N2) @ X3) @ Y4))))))) => (? [F2:(nat > A)]: ((! [N3:nat]: ((((P @ N3) @ (F2 @ N3)) & (((Q @ N3) @ (F2 @ N3)) @ (F2 @ (suc @ N3))))))))))))).
% 2.78/1.47 thf(fact_131_exec1E_I3_J, axiom, (! [C1:com,C22:com,Cs3:(list @ com),S:state,Cs:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ ((semi @ C1) @ C22)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ pHoare1053570893_exec1) => (~ (((Cs = (((cons @ com) @ C1) @ (((cons @ com) @ C22) @ Cs3))) => (S2 != S)))))))).
% 2.78/1.47 thf(fact_132_exec1_OSemi, axiom, (! [C1:com,C22:com,Cs3:(list @ com),S:state]: ((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ ((semi @ C1) @ C22)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C1) @ (((cons @ com) @ C22) @ Cs3))) @ S))) @ pHoare1053570893_exec1)))).
% 2.78/1.47 thf(fact_133_n__lists__Nil, axiom, (! [A:$tType,N:nat]: ((((N = (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) & ((N != (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (nil @ (list @ A)))))))).
% 2.78/1.47 thf(fact_134_exec1E_I2_J, axiom, (! [F:(state > (set @ state)),Cs3:(list @ com),S:state,Cs:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ (do @ F)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ pHoare1053570893_exec1) => (~ (((Cs = Cs3) => (~ ((((member @ state) @ S2) @ (F @ S))))))))))).
% 2.78/1.47 thf(fact_135_exec1_ODo, axiom, (! [T2:state,F:(state > (set @ state)),S:state,Cs3:(list @ com)]: (((((member @ state) @ T2) @ (F @ S)) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ (do @ F)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ T2))) @ pHoare1053570893_exec1))))).
% 2.78/1.47 thf(fact_136_n__lists_Osimps_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: (((((n_lists @ A) @ (zero_zero @ nat)) @ Xs) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.78/1.47 thf(fact_137_termi_OSemi, axiom, (! [C1:com,S0:state,C22:com]: ((((termi @ C1) @ S0) => ((! [S1:state]: (((((exec @ S0) @ C1) @ S1) => ((termi @ C22) @ S1)))) => ((termi @ ((semi @ C1) @ C22)) @ S0)))))).
% 2.78/1.47 thf(fact_138_com_Oinject_I2_J, axiom, (! [X21:com,X22:com,Y21:com,Y222:com]: (((((semi @ X21) @ X22) = ((semi @ Y21) @ Y222)) = ((X21 = Y21) & (X22 = Y222)))))).
% 2.78/1.47 thf(fact_139_com_Oinject_I1_J, axiom, (! [X1:(state > (set @ state)),Y1:(state > (set @ state))]: ((((do @ X1) = (do @ Y1)) = (X1 = Y1))))).
% 2.78/1.47 thf(fact_140_com_Odistinct_I1_J, axiom, (! [X1:(state > (set @ state)),X21:com,X22:com]: (((do @ X1) != ((semi @ X21) @ X22))))).
% 2.78/1.47 thf(fact_141_exec_ODo, axiom, (! [T2:state,F:(state > (set @ state)),S:state]: (((((member @ state) @ T2) @ (F @ S)) => (((exec @ S) @ (do @ F)) @ T2))))).
% 2.78/1.47 thf(fact_142_exec_OSemi, axiom, (! [S0:state,C1:com,S12:state,C22:com,S22:state]: (((((exec @ S0) @ C1) @ S12) => ((((exec @ S12) @ C22) @ S22) => (((exec @ S0) @ ((semi @ C1) @ C22)) @ S22)))))).
% 2.78/1.47 thf(fact_143_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.78/1.47 thf(fact_144_subseqs_Osimps_I1_J, axiom, (! [A:$tType]: ((((subseqs @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.78/1.47 thf(fact_145_exec1E_I4_J, axiom, (! [B2:(state > $o),C1:com,C22:com,Cs3:(list @ com),S:state,Cs:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ (((cond @ B2) @ C1) @ C22)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ pHoare1053570893_exec1) => (((Cs = (((cons @ com) @ C1) @ Cs3)) => ((S2 = S) => (~ ((B2 @ S))))) => (~ (((Cs = (((cons @ com) @ C22) @ Cs3)) => ((S2 = S) => (B2 @ S)))))))))).
% 2.78/1.47 thf(fact_146_com_Oinject_I3_J, axiom, (! [X31:(state > $o),X322:com,X33:com,Y31:(state > $o),Y32:com,Y33:com]: ((((((cond @ X31) @ X322) @ X33) = (((cond @ Y31) @ Y32) @ Y33)) = ((X31 = Y31) & ((X322 = Y32) & (X33 = Y33))))))).
% 2.78/1.47 thf(fact_147_exec_OIfTrue, axiom, (! [B2:(state > $o),S:state,C1:com,T2:state,C22:com]: (((B2 @ S) => ((((exec @ S) @ C1) @ T2) => (((exec @ S) @ (((cond @ B2) @ C1) @ C22)) @ T2)))))).
% 2.78/1.47 thf(fact_148_exec_OIfFalse, axiom, (! [B2:(state > $o),S:state,C22:com,T2:state,C1:com]: (((~ ((B2 @ S))) => ((((exec @ S) @ C22) @ T2) => (((exec @ S) @ (((cond @ B2) @ C1) @ C22)) @ T2)))))).
% 2.78/1.47 thf(fact_149_termi_OIfTrue, axiom, (! [B2:(state > $o),S:state,C1:com,C22:com]: (((B2 @ S) => (((termi @ C1) @ S) => ((termi @ (((cond @ B2) @ C1) @ C22)) @ S)))))).
% 2.78/1.47 thf(fact_150_termi_OIfFalse, axiom, (! [B2:(state > $o),S:state,C22:com,C1:com]: (((~ ((B2 @ S))) => (((termi @ C22) @ S) => ((termi @ (((cond @ B2) @ C1) @ C22)) @ S)))))).
% 2.78/1.47 thf(fact_151_com_Odistinct_I3_J, axiom, (! [X1:(state > (set @ state)),X31:(state > $o),X322:com,X33:com]: (((do @ X1) != (((cond @ X31) @ X322) @ X33))))).
% 2.78/1.47 thf(fact_152_com_Odistinct_I11_J, axiom, (! [X21:com,X22:com,X31:(state > $o),X322:com,X33:com]: ((((semi @ X21) @ X22) != (((cond @ X31) @ X322) @ X33))))).
% 2.78/1.47 thf(fact_153_exec1_OIfFalse, axiom, (! [B2:(state > $o),S:state,C1:com,C22:com,Cs3:(list @ com)]: (((~ ((B2 @ S))) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ (((cond @ B2) @ C1) @ C22)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C22) @ Cs3)) @ S))) @ pHoare1053570893_exec1))))).
% 2.78/1.47 thf(fact_154_exec1_OIfTrue, axiom, (! [B2:(state > $o),S:state,C1:com,C22:com,Cs3:(list @ com)]: (((B2 @ S) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ (((cond @ B2) @ C1) @ C22)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C1) @ Cs3)) @ S))) @ pHoare1053570893_exec1))))).
% 2.78/1.47 thf(fact_155_gen__length__code_I2_J, axiom, (! [B:$tType,N:nat,X:B,Xs:(list @ B)]: (((((gen_length @ B) @ N) @ (((cons @ B) @ X) @ Xs)) = (((gen_length @ B) @ (suc @ N)) @ Xs))))).
% 2.78/1.47 thf(fact_156_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.78/1.47 thf(fact_157_exec1_OWhileFalse, axiom, (! [B2:(state > $o),S:state,C:com,Cs3:(list @ com)]: (((~ ((B2 @ S))) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ ((while @ B2) @ C)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ S))) @ pHoare1053570893_exec1))))).
% 2.78/1.47 thf(fact_158_com_Oinject_I4_J, axiom, (! [X41:(state > $o),X42:com,Y41:(state > $o),Y42:com]: (((((while @ X41) @ X42) = ((while @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 2.78/1.47 thf(fact_159_com_Odistinct_I19_J, axiom, (! [X31:(state > $o),X322:com,X33:com,X41:(state > $o),X42:com]: (((((cond @ X31) @ X322) @ X33) != ((while @ X41) @ X42))))).
% 2.78/1.47 thf(fact_160_while__termiE, axiom, (! [B2:(state > $o),C:com,S:state]: ((((termi @ ((while @ B2) @ C)) @ S) => ((B2 @ S) => ((termi @ C) @ S)))))).
% 2.78/1.47 thf(fact_161_exec_OWhileFalse, axiom, (! [B2:(state > $o),S:state,C:com]: (((~ ((B2 @ S))) => (((exec @ S) @ ((while @ B2) @ C)) @ S))))).
% 2.78/1.47 thf(fact_162_exec_OWhileTrue, axiom, (! [B2:(state > $o),S:state,C:com,T2:state,U:state]: (((B2 @ S) => ((((exec @ S) @ C) @ T2) => ((((exec @ T2) @ ((while @ B2) @ C)) @ U) => (((exec @ S) @ ((while @ B2) @ C)) @ U))))))).
% 2.78/1.47 thf(fact_163_termi_OWhileFalse, axiom, (! [B2:(state > $o),S:state,C:com]: (((~ ((B2 @ S))) => ((termi @ ((while @ B2) @ C)) @ S))))).
% 2.78/1.47 thf(fact_164_com_Odistinct_I5_J, axiom, (! [X1:(state > (set @ state)),X41:(state > $o),X42:com]: (((do @ X1) != ((while @ X41) @ X42))))).
% 2.78/1.47 thf(fact_165_com_Odistinct_I13_J, axiom, (! [X21:com,X22:com,X41:(state > $o),X42:com]: ((((semi @ X21) @ X22) != ((while @ X41) @ X42))))).
% 2.78/1.47 thf(fact_166_termi_OWhileTrue, axiom, (! [B2:(state > $o),S:state,C:com]: (((B2 @ S) => (((termi @ C) @ S) => ((! [T3:state]: (((((exec @ S) @ C) @ T3) => ((termi @ ((while @ B2) @ C)) @ T3)))) => ((termi @ ((while @ B2) @ C)) @ S))))))).
% 2.78/1.47 thf(fact_167_while__termiE2, axiom, (! [B2:(state > $o),C:com,S:state,T2:state]: ((((termi @ ((while @ B2) @ C)) @ S) => ((B2 @ S) => ((((exec @ S) @ C) @ T2) => ((termi @ ((while @ B2) @ C)) @ T2))))))).
% 2.78/1.47 thf(fact_168_gen__length__code_I1_J, axiom, (! [A:$tType,N:nat]: (((((gen_length @ A) @ N) @ (nil @ A)) = N)))).
% 2.78/1.47 thf(fact_169_termi__while, axiom, (! [B2:(state > $o),C:com,F:(nat > state),K:nat]: ((((termi @ ((while @ B2) @ C)) @ (F @ K)) => ((! [I:nat]: ((((exec @ (F @ I)) @ C) @ (F @ (suc @ I))))) => (? [I:nat]: ((~ ((B2 @ (F @ I))))))))))).
% 2.78/1.47 thf(fact_170_termi__while__lemma, axiom, (! [W:com,Fk:state,F:(nat > state),K:nat,B2:(state > $o),C:com]: ((((termi @ W) @ Fk) => (((Fk = (F @ K)) & ((W = ((while @ B2) @ C)) & (! [I:nat]: ((((exec @ (F @ I)) @ C) @ (F @ (suc @ I))))))) => (? [I:nat]: ((~ ((B2 @ (F @ I))))))))))).
% 2.78/1.47 thf(fact_171_exec1E_I5_J, axiom, (! [B2:(state > $o),C:com,Cs3:(list @ com),S:state,Cs:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ ((while @ B2) @ C)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ pHoare1053570893_exec1) => (((Cs = Cs3) => ((S2 = S) => (B2 @ S))) => (~ (((Cs = (((cons @ com) @ C) @ (((cons @ com) @ ((while @ B2) @ C)) @ Cs3))) => ((S2 = S) => (~ ((B2 @ S)))))))))))).
% 2.78/1.47 thf(fact_172_exec1_OWhileTrue, axiom, (! [B2:(state > $o),S:state,C:com,Cs3:(list @ com)]: (((B2 @ S) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ ((while @ B2) @ C)) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C) @ (((cons @ com) @ ((while @ B2) @ C)) @ Cs3))) @ S))) @ pHoare1053570893_exec1))))).
% 2.78/1.47 thf(fact_173_nths__singleton, axiom, (! [A:$tType,A5:(set @ nat),X:A]: ((((((member @ nat) @ (zero_zero @ nat)) @ A5) => ((((nths @ A) @ (((cons @ A) @ X) @ (nil @ A))) @ A5) = (((cons @ A) @ X) @ (nil @ A)))) & ((~ ((((member @ nat) @ (zero_zero @ nat)) @ A5))) => ((((nths @ A) @ (((cons @ A) @ X) @ (nil @ A))) @ A5) = (nil @ A))))))).
% 2.78/1.47 thf(fact_174_app__execs, axiom, (! [Cs3:(list @ com),S:state,Cs:(list @ com),S2:state,Cs22:(list @ com)]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1)) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((append @ com) @ Cs3) @ Cs22)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((append @ com) @ Cs) @ Cs22)) @ S2))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1)))))).
% 2.78/1.47 thf(fact_175_listrel_Ocases, axiom, (! [B:$tType,A:$tType,A1:(list @ A),A22:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ A1) @ A22)) @ (((listrel @ A) @ B) @ R)) => (((A1 = (nil @ A)) => (A22 != (nil @ B))) => (~ ((! [X3:A,Y2:B,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys3:(list @ B)]: (((A22 = (((cons @ B) @ Y2) @ Ys3)) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y2)) @ R) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys3)) @ (((listrel @ A) @ B) @ R)))))))))))))))))).
% 2.78/1.47 thf(fact_176_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Xs) @ Zs2)) = (Ys2 = Zs2))))).
% 2.78/1.47 thf(fact_177_append__same__eq, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Ys2) @ Xs) = (((append @ A) @ Zs2) @ Xs)) = (Ys2 = Zs2))))).
% 2.78/1.47 thf(fact_178_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys2)) @ Zs2) = (((append @ A) @ Xs) @ (((append @ A) @ Ys2) @ Zs2)))))).
% 2.78/1.47 thf(fact_179_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B2)) @ C) = (((append @ A) @ A2) @ (((append @ A) @ B2) @ C)))))).
% 2.78/1.47 thf(fact_180_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.78/1.47 thf(fact_181_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Xs) = (Ys2 = (nil @ A)))))).
% 2.78/1.47 thf(fact_182_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys2)) = (Ys2 = (nil @ A)))))).
% 2.78/1.47 thf(fact_183_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Ys2) = (Xs = (nil @ A)))))).
% 2.78/1.47 thf(fact_184_self__append__conv2, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (((append @ A) @ Xs) @ Ys2)) = (Xs = (nil @ A)))))).
% 2.78/1.47 thf(fact_185_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys2)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.78/1.47 thf(fact_186_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.78/1.47 thf(fact_187_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 2.78/1.47 thf(fact_188_nths__nil, axiom, (! [A:$tType,A5:(set @ nat)]: (((((nths @ A) @ (nil @ A)) @ A5) = (nil @ A))))).
% 2.78/1.47 thf(fact_189_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys2:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys2) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys2) & (X = Y)))))).
% 2.78/1.47 thf(fact_190_listrel__rtrancl__refl, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Xs)) @ (((listrel @ A) @ A) @ ((transitive_rtrancl @ A) @ R)))))).
% 2.78/1.47 thf(fact_191_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs2) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs2) @ Us)) & ((((append @ A) @ Us) @ Ys2) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs2) & (Ys2 = (((append @ A) @ Us) @ Ts)))))))))).
% 2.78/1.47 thf(fact_192_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs2:(list @ A),Ys2:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs2) => ((Ys2 = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs2) @ Us2))))))).
% 2.78/1.47 thf(fact_193_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = Ys2) => (Xs = (((append @ A) @ (nil @ A)) @ Ys2)))))).
% 2.78/1.47 thf(fact_194_append__Nil, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.78/1.47 thf(fact_195_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 2.78/1.47 thf(fact_196_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys2:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys2) => ((Xs = (((append @ A) @ Xs1) @ Zs2)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys2) @ Zs2))))))).
% 2.78/1.47 thf(fact_197_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys2:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys2) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys2)))))).
% 2.78/1.47 thf(fact_198_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.78/1.47 thf(fact_199_append__eq__Cons__conv, axiom, (! [A:$tType,Ys2:(list @ A),Zs2:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys2) @ Zs2) = (((cons @ A) @ X) @ Xs)) = (((Ys2 = (nil @ A)) & (Zs2 = (((cons @ A) @ X) @ Xs))) | (? [Ys4:(list @ A)]: (((Ys2 = (((cons @ A) @ X) @ Ys4)) & ((((append @ A) @ Ys4) @ Zs2) = Xs))))))))).
% 2.78/1.47 thf(fact_200_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys2) @ Zs2)) = (((Ys2 = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs2)) | (? [Ys4:(list @ A)]: ((((((cons @ A) @ X) @ Ys4) = Ys2) & (Xs = (((append @ A) @ Ys4) @ Zs2)))))))))).
% 2.78/1.47 thf(fact_201_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y2:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y2) @ (nil @ A)))))))))))).
% 2.78/1.47 thf(fact_202_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.78/1.47 thf(fact_203_listrel_ONil, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B))]: ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ (nil @ B))) @ (((listrel @ A) @ B) @ R))))).
% 2.78/1.47 thf(fact_204_listrel__Nil1, axiom, (! [A:$tType,B:$tType,Xs:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Xs)) @ (((listrel @ A) @ B) @ R)) => (Xs = (nil @ B)))))).
% 2.78/1.47 thf(fact_205_listrel__Nil2, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ (nil @ B))) @ (((listrel @ A) @ B) @ R)) => (Xs = (nil @ A)))))).
% 2.78/1.47 thf(fact_206_listrel__rtrancl__trans, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A)),Zs2:(list @ A)]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ (((listrel @ A) @ A) @ ((transitive_rtrancl @ A) @ R))) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs2)) @ (((listrel @ A) @ A) @ ((transitive_rtrancl @ A) @ R))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Zs2)) @ (((listrel @ A) @ A) @ ((transitive_rtrancl @ A) @ R)))))))).
% 2.78/1.47 thf(fact_207_app__exec, axiom, (! [Cs3:(list @ com),S:state,Cs:(list @ com),S2:state,Cs22:(list @ com)]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs3) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ S2))) @ pHoare1053570893_exec1) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((append @ com) @ Cs3) @ Cs22)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((append @ com) @ Cs) @ Cs22)) @ S2))) @ pHoare1053570893_exec1))))).
% 2.78/1.47 thf(fact_208_listrel__Cons2, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Y:B,Ys2:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ (((cons @ B) @ Y) @ Ys2))) @ (((listrel @ A) @ B) @ R)) => (~ ((! [X3:A,Xs2:(list @ A)]: (((Xs = (((cons @ A) @ X3) @ Xs2)) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) @ R) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys2)) @ (((listrel @ A) @ B) @ R)))))))))))))).
% 2.78/1.47 thf(fact_209_listrel__Cons1, axiom, (! [B:$tType,A:$tType,Y:A,Ys2:(list @ A),Xs:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ Y) @ Ys2)) @ Xs)) @ (((listrel @ A) @ B) @ R)) => (~ ((! [Y2:B,Ys3:(list @ B)]: (((Xs = (((cons @ B) @ Y2) @ Ys3)) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Y) @ Y2)) @ R) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Ys2) @ Ys3)) @ (((listrel @ A) @ B) @ R)))))))))))))).
% 2.78/1.47 thf(fact_210_listrel_OCons, axiom, (! [B:$tType,A:$tType,X:A,Y:B,R:(set @ ((product_prod @ A) @ B)),Xs:(list @ A),Ys2:(list @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ R) => ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ Ys2)) @ (((listrel @ A) @ B) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ B) @ Y) @ Ys2))) @ (((listrel @ A) @ B) @ R))))))).
% 2.78/1.47 thf(fact_211_exec1__only1__aux, axiom, (! [Ccs:(list @ com),S:state,Cs:(list @ com),T2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Ccs) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ T2))) @ pHoare1053570893_exec1) => (! [C6:com,Cs5:(list @ com)]: (((Ccs = (((cons @ com) @ C6) @ Cs5)) => (? [Cs1:(list @ com)]: ((Cs = (((append @ com) @ Cs1) @ Cs5))))))))))).
% 2.78/1.47 thf(fact_212_exec1__only1, axiom, (! [C:com,Cs3:(list @ com),S:state,Cs:(list @ com),T2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ C) @ Cs3)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs) @ T2))) @ pHoare1053570893_exec1) => (? [Cs1:(list @ com)]: ((Cs = (((append @ com) @ Cs1) @ Cs3)))))))).
% 2.78/1.47 thf(fact_213_exec1__drop__suffix__aux, axiom, (! [Cs12:(list @ com),S:state,Cs1_2:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs12) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs1_2) @ S2))) @ pHoare1053570893_exec1) => (! [Cs13:(list @ com),Cs23:(list @ com),Cs14:(list @ com)]: ((((Cs12 = (((append @ com) @ Cs13) @ Cs23)) & ((Cs1_2 = (((append @ com) @ Cs14) @ Cs23)) & (Cs13 != (nil @ com)))) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs13) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs14) @ S2))) @ pHoare1053570893_exec1)))))))).
% 2.78/1.47 thf(fact_214_exec1__drop__suffix, axiom, (! [Cs15:(list @ com),Cs22:(list @ com),S:state,Cs16:(list @ com),S2:state]: (((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((append @ com) @ Cs15) @ Cs22)) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ (((append @ com) @ Cs16) @ Cs22)) @ S2))) @ pHoare1053570893_exec1) => ((Cs15 != (nil @ com)) => (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs15) @ S)) @ ((((product_Pair @ (list @ com)) @ state) @ Cs16) @ S2))) @ pHoare1053570893_exec1)))))).
% 2.78/1.47 thf(fact_215_listrel_Oinducts, axiom, (! [A:$tType,B:$tType,X1:(list @ A),X2:(list @ B),R:(set @ ((product_prod @ A) @ B)),P:((list @ A) > ((list @ B) > $o))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ X1) @ X2)) @ (((listrel @ A) @ B) @ R)) => (((P @ (nil @ A)) @ (nil @ B)) => ((! [X3:A,Y2:B,Xs2:(list @ A),Ys3:(list @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y2)) @ R) => ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys3)) @ (((listrel @ A) @ B) @ R)) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys3))))))) => ((P @ X1) @ X2))))))).
% 2.78/1.47 thf(fact_216_listrel_Osimps, axiom, (! [B:$tType,A:$tType,A1:(list @ A),A22:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ A1) @ A22)) @ (((listrel @ A) @ B) @ R)) = (((A1 = (nil @ A)) & (A22 = (nil @ B))) | (? [X4:A,Y3:B,Xs3:(list @ A),Ys:(list @ B)]: (((A1 = (((cons @ A) @ X4) @ Xs3)) & ((A22 = (((cons @ B) @ Y3) @ Ys)) & ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y3)) @ R) & (((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs3) @ Ys)) @ (((listrel @ A) @ B) @ R)))))))))))).
% 2.78/1.47 thf(fact_217_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X:B,Xs:(list @ B),F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X) @ Xs)) @ F) = (((append @ A) @ (F @ X)) @ ((((bind @ B) @ A) @ Xs) @ F)))))).
% 2.78/1.47 thf(fact_218_snoc__listrel1__snoc__iff, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys2:(list @ A),Y:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) @ (((append @ A) @ Ys2) @ (((cons @ A) @ Y) @ (nil @ A))))) @ ((listrel1 @ A) @ R)) = (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((listrel1 @ A) @ R)) & (X = Y)) | ((Xs = Ys2) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R))))))).
% 2.78/1.47 thf(fact_219_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F:(B > (list @ A)),X:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F) @ (((cons @ B) @ X) @ Xs)) = (((append @ A) @ (F @ X)) @ ((((maps @ B) @ A) @ F) @ Xs)))))).
% 2.78/1.47 thf(fact_220_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F) = (nil @ A))))).
% 2.78/1.47 thf(fact_221_Cons__listrel1__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))) @ ((listrel1 @ A) @ R)) = (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) & (Xs = Ys2)) | ((X = Y) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((listrel1 @ A) @ R)))))))).
% 2.78/1.47 thf(fact_222_rtrancl__listrel1__ConsI1, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A)),X:A]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((transitive_rtrancl @ (list @ A)) @ ((listrel1 @ A) @ R))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ X) @ Ys2))) @ ((transitive_rtrancl @ (list @ A)) @ ((listrel1 @ A) @ R))))))).
% 2.78/1.47 thf(fact_223_listrel1I2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A)),X:A]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((listrel1 @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ X) @ Ys2))) @ ((listrel1 @ A) @ R)))))).
% 2.78/1.47 thf(fact_224_not__listrel1__Nil, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ (nil @ A))) @ ((listrel1 @ A) @ R))))))).
% 2.78/1.47 thf(fact_225_not__Nil__listrel1, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Xs)) @ ((listrel1 @ A) @ R))))))).
% 2.78/1.47 thf(fact_226_append__listrel1I, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A)),Us2:(list @ A),Vs:(list @ A)]: (((((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((listrel1 @ A) @ R)) & (Us2 = Vs)) | ((Xs = Ys2) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Us2) @ Vs)) @ ((listrel1 @ A) @ R)))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Ys2) @ Vs))) @ ((listrel1 @ A) @ R)))))).
% 2.78/1.47 thf(fact_227_listrel__rtrancl__eq__rtrancl__listrel1, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: (((((listrel @ A) @ A) @ ((transitive_rtrancl @ A) @ R)) = ((transitive_rtrancl @ (list @ A)) @ ((listrel1 @ A) @ R)))))).
% 2.78/1.47 thf(fact_228_rtrancl__listrel1__if__listrel, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ (((listrel @ A) @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((transitive_rtrancl @ (list @ A)) @ ((listrel1 @ A) @ R))))))).
% 2.78/1.47 thf(fact_229_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((maps @ B) @ A) @ F) @ (nil @ B)) = (nil @ A))))).
% 2.78/1.47 thf(fact_230_listrel1I1, axiom, (! [A:$tType,X:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Xs))) @ ((listrel1 @ A) @ R)))))).
% 2.78/1.47 thf(fact_231_Cons__listrel1E1, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ Ys2)) @ ((listrel1 @ A) @ R)) => ((! [Y2:A]: (((Ys2 = (((cons @ A) @ Y2) @ Xs)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y2)) @ R)))))) => (~ ((! [Zs:(list @ A)]: (((Ys2 = (((cons @ A) @ X) @ Zs)) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Zs)) @ ((listrel1 @ A) @ R)))))))))))))).
% 2.78/1.47 thf(fact_232_Cons__listrel1E2, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ (((cons @ A) @ Y) @ Ys2))) @ ((listrel1 @ A) @ R)) => ((! [X3:A]: (((Xs = (((cons @ A) @ X3) @ Ys2)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y)) @ R)))))) => (~ ((! [Zs:(list @ A)]: (((Xs = (((cons @ A) @ Y) @ Zs)) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Zs) @ Ys2)) @ ((listrel1 @ A) @ R)))))))))))))).
% 2.78/1.47 thf(fact_233_listrel__reflcl__if__listrel1, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((listrel1 @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ (((listrel @ A) @ A) @ ((transitive_rtrancl @ A) @ R))))))).
% 2.78/1.47 thf(fact_234_listrel1I, axiom, (! [A:$tType,X:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A),Us2:(list @ A),Vs:(list @ A),Ys2:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) => ((Xs = (((append @ A) @ Us2) @ (((cons @ A) @ X) @ Vs))) => ((Ys2 = (((append @ A) @ Us2) @ (((cons @ A) @ Y) @ Vs))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((listrel1 @ A) @ R)))))))).
% 2.78/1.47 thf(fact_235_listrel1E, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((listrel1 @ A) @ R)) => (~ ((! [X3:A,Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y2)) @ R) => (! [Us3:(list @ A),Vs2:(list @ A)]: (((Xs = (((append @ A) @ Us3) @ (((cons @ A) @ X3) @ Vs2))) => (Ys2 != (((append @ A) @ Us3) @ (((cons @ A) @ Y2) @ Vs2))))))))))))))).
% 2.78/1.47 thf(fact_236_rtrancl__listrel1__ConsI2, axiom, (! [A:$tType,X:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A),Ys2:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((transitive_rtrancl @ A) @ R)) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys2)) @ ((transitive_rtrancl @ (list @ A)) @ ((listrel1 @ A) @ R))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))) @ ((transitive_rtrancl @ (list @ A)) @ ((listrel1 @ A) @ R)))))))).
% 2.78/1.47 thf(fact_237_concat__eq__append__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys2:(list @ A),Zs2:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys2) @ Zs2)) = (((Xss2 = (nil @ (list @ A))) => ((Ys2 = (nil @ A)) & (Zs2 = (nil @ A)))) & ((Xss2 != (nil @ (list @ A))) => (? [Xss1:(list @ (list @ A)),Xs3:(list @ A),Xs4:(list @ A),Xss22:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss1) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs3) @ Xs4)) @ Xss22))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss1)) @ Xs3)) & (Zs2 = (((append @ A) @ Xs4) @ ((concat @ A) @ Xss22))))))))))))).
% 2.78/1.47 thf(fact_238_lexord__append__left__rightI, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),U:(list @ A),X:(list @ A),Y:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ U) @ (((cons @ A) @ A2) @ X))) @ (((append @ A) @ U) @ (((cons @ A) @ B2) @ Y)))) @ ((lexord @ A) @ R)))))).
% 2.78/1.47 thf(fact_239_concat__append, axiom, (! [A:$tType,Xs:(list @ (list @ A)),Ys2:(list @ (list @ A))]: ((((concat @ A) @ (((append @ (list @ A)) @ Xs) @ Ys2)) = (((append @ A) @ ((concat @ A) @ Xs)) @ ((concat @ A) @ Ys2)))))).
% 2.78/1.47 thf(fact_240_lexord__cons__cons, axiom, (! [A:$tType,A2:A,X:(list @ A),B2:A,Y:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ A2) @ X)) @ (((cons @ A) @ B2) @ Y))) @ ((lexord @ A) @ R)) = ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) | ((A2 = B2) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X) @ Y)) @ ((lexord @ A) @ R)))))))).
% 2.78/1.47 thf(fact_241_lexord__Nil__left, axiom, (! [A:$tType,Y:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Y)) @ ((lexord @ A) @ R)) = (? [A4:A,X4:(list @ A)]: ((Y = (((cons @ A) @ A4) @ X4)))))))).
% 2.78/1.47 thf(fact_242_lexord__linear, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X:(list @ A),Y:(list @ A)]: (((! [A3:A,B3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ B3)) @ R) | ((A3 = B3) | (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B3) @ A3)) @ R))))) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X) @ Y)) @ ((lexord @ A) @ R)) | ((X = Y) | (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Y) @ X)) @ ((lexord @ A) @ R)))))))).
% 2.78/1.47 thf(fact_243_lexord__irreflexive, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A)]: (((! [X3:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ X3)) @ R))))) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Xs)) @ ((lexord @ A) @ R)))))))).
% 2.78/1.47 thf(fact_244_concat_Osimps_I1_J, axiom, (! [A:$tType]: ((((concat @ A) @ (nil @ (list @ A))) = (nil @ A))))).
% 2.78/1.47 thf(fact_245_lexord__Nil__right, axiom, (! [A:$tType,X:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X) @ (nil @ A))) @ ((lexord @ A) @ R))))))).
% 2.78/1.47 thf(fact_246_concat_Osimps_I2_J, axiom, (! [A:$tType,X:(list @ A),Xs:(list @ (list @ A))]: ((((concat @ A) @ (((cons @ (list @ A)) @ X) @ Xs)) = (((append @ A) @ X) @ ((concat @ A) @ Xs)))))).
% 2.78/1.47 thf(fact_247_lexord__append__leftI, axiom, (! [A:$tType,U:(list @ A),V:(list @ A),R:(set @ ((product_prod @ A) @ A)),X:(list @ A)]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ U) @ V)) @ ((lexord @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ X) @ U)) @ (((append @ A) @ X) @ V))) @ ((lexord @ A) @ R)))))).
% 2.78/1.47 thf(fact_248_lexord__append__leftD, axiom, (! [A:$tType,X:(list @ A),U:(list @ A),V:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ X) @ U)) @ (((append @ A) @ X) @ V))) @ ((lexord @ A) @ R)) => ((! [A3:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ A3)) @ R))))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ U) @ V)) @ ((lexord @ A) @ R))))))).
% 2.78/1.47 thf(fact_249_lexord__append__rightI, axiom, (! [A:$tType,Y:(list @ A),X:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((? [B6:A,Z3:(list @ A)]: ((Y = (((cons @ A) @ B6) @ Z3)))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X) @ (((append @ A) @ X) @ Y))) @ ((lexord @ A) @ R)))))).
% 2.78/1.47 thf(fact_250_concat__eq__appendD, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys2:(list @ A),Zs2:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys2) @ Zs2)) => ((Xss2 != (nil @ (list @ A))) => (? [Xss12:(list @ (list @ A)),Xs2:(list @ A),Xs5:(list @ A),Xss23:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss12) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs2) @ Xs5)) @ Xss23))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss12)) @ Xs2)) & (Zs2 = (((append @ A) @ Xs5) @ ((concat @ A) @ Xss23)))))))))))).
% 2.78/1.47 thf(fact_251_lexord__same__pref__if__irrefl, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: ((((irrefl @ A) @ R) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Ys2)) @ (((append @ A) @ Xs) @ Zs2))) @ ((lexord @ A) @ R)) = (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs2)) @ ((lexord @ A) @ R))))))).
% 2.78/1.47 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.78/1.47 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.78/1.47 thf(tcon_Nat_Onat___Orderings_Oord_1, axiom, (ord @ nat)).
% 2.78/1.47 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.78/1.47 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.78/1.47 thf(tcon_HOL_Obool___Orderings_Olinorder_3, axiom, (linorder @ $o)).
% 2.78/1.47 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, (ord @ $o)).
% 2.78/1.47 thf(conj_0, hypothesis, ((termi @ c) @ s)).
% 2.78/1.47 thf(conj_1, hypothesis, ((f @ (zero_zero @ nat)) = ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ c) @ (nil @ com))) @ s))).
% 2.78/1.47 thf(conj_2, hypothesis, (! [I2:nat]: ((((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ (f @ I2)) @ (f @ (suc @ I2)))) @ ((transitive_trancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1))))).
% 2.78/1.47 thf(conj_3, hypothesis, (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ c) @ (nil @ com))) @ s)) @ (f @ n))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1))).
% 2.78/1.47 thf(conj_4, conjecture, (((member @ ((product_prod @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state))) @ ((((product_Pair @ ((product_prod @ (list @ com)) @ state)) @ ((product_prod @ (list @ com)) @ state)) @ ((((product_Pair @ (list @ com)) @ state) @ (((cons @ com) @ c) @ (nil @ com))) @ s)) @ (f @ (suc @ n)))) @ ((transitive_rtrancl @ ((product_prod @ (list @ com)) @ state)) @ pHoare1053570893_exec1))).
% 2.78/1.47 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2DTF24138.p
% 2.78/1.47 ------------------------
% 2.99/1.51 ---- Cleaned THF ---
% 2.99/1.52 thf(ty_t_Product__Type_Oprod,type,
% 2.99/1.52 product_prod: $tType > $tType > $tType ).
% 2.99/1.52
% 2.99/1.52 thf(ty_t_PLang_Ostate,type,
% 2.99/1.52 state: $tType ).
% 2.99/1.52
% 2.99/1.52 thf(ty_t_PLang_Ocom,type,
% 2.99/1.52 com: $tType ).
% 2.99/1.52
% 2.99/1.52 thf(ty_t_List_Olist,type,
% 2.99/1.52 list: $tType > $tType ).
% 2.99/1.52
% 2.99/1.52 thf(ty_t_Set_Oset,type,
% 2.99/1.52 set: $tType > $tType ).
% 2.99/1.52
% 2.99/1.52 thf(ty_t_Nat_Onat,type,
% 2.99/1.52 nat: $tType ).
% 2.99/1.52
% 2.99/1.52 thf(sy_cl_HOL_Otype,type,
% 2.99/1.52 type:
% 2.99/1.52 !>[A: $tType] : $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_cl_Groups_Ozero,type,
% 2.99/1.52 zero:
% 2.99/1.52 !>[A: $tType] : $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_cl_Orderings_Oord,type,
% 2.99/1.52 ord:
% 2.99/1.52 !>[A: $tType] : $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_cl_Orderings_Olinorder,type,
% 2.99/1.52 linorder:
% 2.99/1.52 !>[A: $tType] : $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.99/1.52 zero_zero:
% 2.99/1.52 !>[A: $tType] : A ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Oappend,type,
% 2.99/1.52 append:
% 2.99/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Obind,type,
% 2.99/1.52 bind:
% 2.99/1.52 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Oconcat,type,
% 2.99/1.52 concat:
% 2.99/1.52 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Ogen__length,type,
% 2.99/1.52 gen_length:
% 2.99/1.52 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Oinsert,type,
% 2.99/1.52 insert:
% 2.99/1.52 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Olexord,type,
% 2.99/1.52 lexord:
% 2.99/1.52 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Olist_OCons,type,
% 2.99/1.52 cons:
% 2.99/1.52 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Olist_ONil,type,
% 2.99/1.52 nil:
% 2.99/1.52 !>[A: $tType] : ( list @ A ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Olistrel,type,
% 2.99/1.52 listrel:
% 2.99/1.52 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Olistrel1,type,
% 2.99/1.52 listrel1:
% 2.99/1.52 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Omaps,type,
% 2.99/1.52 maps:
% 2.99/1.52 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_On__lists,type,
% 2.99/1.52 n_lists:
% 2.99/1.52 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Onths,type,
% 2.99/1.52 nths:
% 2.99/1.52 !>[A: $tType] : ( ( list @ A ) > ( set @ nat ) > ( list @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Oproduct__lists,type,
% 2.99/1.52 product_lists:
% 2.99/1.52 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_List_Osubseqs,type,
% 2.99/1.52 subseqs:
% 2.99/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Nat_OSuc,type,
% 2.99/1.52 suc: nat > nat ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oexec1,type,
% 2.99/1.52 pHoare1053570893_exec1: set @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oexecs,type,
% 2.99/1.52 pHoare1053570959_execs: state > ( list @ com ) > state > $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Oinf,type,
% 2.99/1.52 pHoare1838713294le_inf: ( list @ com ) > state > $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PHoareTotal__Mirabelle__nfzgdgthbw_Otermis,type,
% 2.99/1.52 pHoare1335526537termis: ( list @ com ) > state > $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PLang_Ocom_OCond,type,
% 2.99/1.52 cond: ( state > $o ) > com > com > com ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PLang_Ocom_ODo,type,
% 2.99/1.52 do: ( state > ( set @ state ) ) > com ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PLang_Ocom_OSemi,type,
% 2.99/1.52 semi: com > com > com ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PLang_Ocom_OWhile,type,
% 2.99/1.52 while: ( state > $o ) > com > com ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PLang_Oexec,type,
% 2.99/1.52 exec: state > com > state > $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_PTermi_Otermi,type,
% 2.99/1.52 termi: com > state > $o ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Product__Type_OPair,type,
% 2.99/1.52 product_Pair:
% 2.99/1.52 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.99/1.52 product_rec_prod:
% 2.99/1.52 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Relation_Oirrefl,type,
% 2.99/1.52 irrefl:
% 2.99/1.52 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Set_OCollect,type,
% 2.99/1.52 collect:
% 2.99/1.52 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Transitive__Closure_Ortrancl,type,
% 2.99/1.52 transitive_rtrancl:
% 2.99/1.52 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_Transitive__Closure_Otrancl,type,
% 2.99/1.52 transitive_trancl:
% 2.99/1.52 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_c_member,type,
% 2.99/1.52 member:
% 2.99/1.52 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_v_c,type,
% 2.99/1.52 c: com ).
% 2.99/1.52
% 2.99/1.52 thf(sy_v_f,type,
% 2.99/1.52 f: nat > ( product_prod @ ( list @ com ) @ state ) ).
% 2.99/1.52
% 2.99/1.52 thf(sy_v_n,type,
% 2.99/1.52 n: nat ).
% 2.99/1.52
% 2.99/1.52 thf(sy_v_s,type,
% 2.99/1.52 s: state ).
% 2.99/1.52
% 2.99/1.52 thf(fact_0_exec1E_I1_J,axiom,
% 2.99/1.52 ! [S: state,Cs: list @ com,S2: state] :
% 2.99/1.52 ~ ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_1_renumber,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,F: nat > A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ! [I: nat] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ ( F @ I ) ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 2.99/1.52 => ? [F2: nat > A] :
% 2.99/1.52 ( ( ( F2 @ ( zero_zero @ nat ) )
% 2.99/1.52 = A2 )
% 2.99/1.52 & ! [I2: nat] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_2_renumber__aux,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,F: nat > A,R: set @ ( product_prod @ A @ A ),B2: A] :
% 2.99/1.52 ( ! [I: nat] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ ( F @ I ) ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F @ I ) @ ( F @ ( suc @ I ) ) ) @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( B2
% 2.99/1.52 = ( F @ ( zero_zero @ nat ) ) )
% 2.99/1.52 => ? [F2: nat > A] :
% 2.99/1.52 ( ( ( F2 @ ( zero_zero @ nat ) )
% 2.99/1.52 = A2 )
% 2.99/1.52 & ! [I2: nat] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( F2 @ I2 ) @ ( F2 @ ( suc @ I2 ) ) ) @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_3_execs__pres__termi,axiom,
% 2.99/1.52 ! [C: com,S: state,C2: com,Cs: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( nil @ com ) ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C2 @ Cs ) @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 2.99/1.52 => ( ( termi @ C @ S )
% 2.99/1.52 => ( termi @ C2 @ S2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_4_rtrancl__trancl__absorb,axiom,
% 2.99/1.52 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( transitive_trancl @ A @ ( transitive_rtrancl @ A @ R2 ) )
% 2.99/1.52 = ( transitive_rtrancl @ A @ R2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_5_trancl__rtrancl__absorb,axiom,
% 2.99/1.52 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( transitive_rtrancl @ A @ ( transitive_trancl @ A @ R2 ) )
% 2.99/1.52 = ( transitive_rtrancl @ A @ R2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_6_trancl__induct2,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,Ax: A,Ay: B,Bx: A,By: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ),P: A > B > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_trancl @ ( product_prod @ A @ B ) @ R ) )
% 2.99/1.52 => ( ! [A3: A,B3: B] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ R )
% 2.99/1.52 => ( P @ A3 @ B3 ) )
% 2.99/1.52 => ( ! [A3: A,B3: B,Aa: A,Ba: B] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ ( transitive_trancl @ ( product_prod @ A @ B ) @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Aa @ Ba ) ) @ R )
% 2.99/1.52 => ( ( P @ A3 @ B3 )
% 2.99/1.52 => ( P @ Aa @ Ba ) ) ) )
% 2.99/1.52 => ( P @ Bx @ By ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_7_inf__def,axiom,
% 2.99/1.52 ( pHoare1838713294le_inf
% 2.99/1.52 = ( ^ [Cs2: list @ com,S3: state] :
% 2.99/1.52 ? [F3: nat > ( product_prod @ ( list @ com ) @ state )] :
% 2.99/1.52 ( ( ( F3 @ ( zero_zero @ nat ) )
% 2.99/1.52 = ( product_Pair @ ( list @ com ) @ state @ Cs2 @ S3 ) )
% 2.99/1.52 & ! [I3: nat] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( F3 @ I3 ) @ ( F3 @ ( suc @ I3 ) ) ) @ pHoare1053570893_exec1 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_8_rtrancl__induct2,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,Ax: A,Ay: B,Bx: A,By: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ),P: A > B > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 2.99/1.52 => ( ( P @ Ax @ Ay )
% 2.99/1.52 => ( ! [A3: A,B3: B,Aa: A,Ba: B] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Aa @ Ba ) ) @ R )
% 2.99/1.52 => ( ( P @ A3 @ B3 )
% 2.99/1.52 => ( P @ Aa @ Ba ) ) ) )
% 2.99/1.52 => ( P @ Bx @ By ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_9_converse__rtranclE2,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,Xa: A,Xb: B,Za: A,Zb: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Xa @ Xb ) @ ( product_Pair @ A @ B @ Za @ Zb ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 2.99/1.52 => ( ( ( product_Pair @ A @ B @ Xa @ Xb )
% 2.99/1.52 != ( product_Pair @ A @ B @ Za @ Zb ) )
% 2.99/1.52 => ~ ! [A3: A,B3: B] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Xa @ Xb ) @ ( product_Pair @ A @ B @ A3 @ B3 ) ) @ R )
% 2.99/1.52 => ~ ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Za @ Zb ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_10_converse__rtrancl__induct2,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,Ax: A,Ay: B,Bx: A,By: B,R: set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ),P: A > B > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Ax @ Ay ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 2.99/1.52 => ( ( P @ Bx @ By )
% 2.99/1.52 => ( ! [A3: A,B3: B,Aa: A,Ba: B] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ Aa @ Ba ) ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Aa @ Ba ) @ ( product_Pair @ A @ B @ Bx @ By ) ) @ ( transitive_rtrancl @ ( product_prod @ A @ B ) @ R ) )
% 2.99/1.52 => ( ( P @ Aa @ Ba )
% 2.99/1.52 => ( P @ A3 @ B3 ) ) ) )
% 2.99/1.52 => ( P @ Ax @ Ay ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_11_tranclD,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R2 ) )
% 2.99/1.52 => ? [Z: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R2 )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ Y ) @ ( transitive_rtrancl @ A @ R2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_12_rtranclD,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R2 ) )
% 2.99/1.52 => ( ( A2 = B2 )
% 2.99/1.52 | ( ( A2 != B2 )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R2 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_13_tranclD2,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R2 ) )
% 2.99/1.52 => ? [Z: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ ( transitive_rtrancl @ A @ R2 ) )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ Y ) @ R2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_14_trancl__into__rtrancl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_15_rtrancl__eq__or__trancl,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R2 ) )
% 2.99/1.52 = ( ( X = Y )
% 2.99/1.52 | ( ( X != Y )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R2 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_16_r__into__rtrancl,axiom,
% 2.99/1.52 ! [A: $tType,P2: product_prod @ A @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ P2 @ R )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ P2 @ ( transitive_rtrancl @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_17_rtrancl__idemp,axiom,
% 2.99/1.52 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( transitive_rtrancl @ A @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 = ( transitive_rtrancl @ A @ R ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_18_r__into__trancl_H,axiom,
% 2.99/1.52 ! [A: $tType,P2: product_prod @ A @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ P2 @ R )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ P2 @ ( transitive_trancl @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_19_converse__rtrancl__into__rtrancl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_20_rtrancl_Ortrancl__into__rtrancl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_21_converse__rtrancl__induct,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ B2 )
% 2.99/1.52 => ( ! [Y2: A,Z: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ Z )
% 2.99/1.52 => ( P @ Y2 ) ) ) )
% 2.99/1.52 => ( P @ A2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_22_rtrancl_Ortrancl__refl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,R: set @ ( product_prod @ A @ A )] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( transitive_rtrancl @ A @ R ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_23_converse__rtranclE,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Z2: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( X != Z2 )
% 2.99/1.52 => ~ ! [Y2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z2 ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_24_rtrancl_Oinducts,axiom,
% 2.99/1.52 ! [A: $tType,X1: A,X2: A,R: set @ ( product_prod @ A @ A ),P: A > A > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X1 @ X2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ! [A3: A] : ( P @ A3 @ A3 )
% 2.99/1.52 => ( ! [A3: A,B3: A,C3: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ A3 @ B3 )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ C3 ) @ R )
% 2.99/1.52 => ( P @ A3 @ C3 ) ) ) )
% 2.99/1.52 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_25_rtrancl__induct,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ A2 )
% 2.99/1.52 => ( ! [Y2: A,Z: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 2.99/1.52 => ( ( P @ Y2 )
% 2.99/1.52 => ( P @ Z ) ) ) )
% 2.99/1.52 => ( P @ B2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_26_rtrancl__trans,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Z2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_27_rtrancl_Osimps,axiom,
% 2.99/1.52 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 = ( ? [A4: A] :
% 2.99/1.52 ( ( A1 = A4 )
% 2.99/1.52 & ( A22 = A4 ) )
% 2.99/1.52 | ? [A4: A,B4: A,C4: A] :
% 2.99/1.52 ( ( A1 = A4 )
% 2.99/1.52 & ( A22 = C4 )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ C4 ) @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_28_rtrancl_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( A22 != A1 )
% 2.99/1.52 => ~ ! [B3: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ B3 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ A22 ) @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_29_rtranclE,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( A2 != B2 )
% 2.99/1.52 => ~ ! [Y2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ B2 ) @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_30_trancl_Otrancl__into__trancl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_31_converse__trancl__induct,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ! [Y2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ B2 ) @ R )
% 2.99/1.52 => ( P @ Y2 ) )
% 2.99/1.52 => ( ! [Y2: A,Z: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ Z )
% 2.99/1.52 => ( P @ Y2 ) ) ) )
% 2.99/1.52 => ( P @ A2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_32_trancl_Or__into__trancl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_33_trancl__trans__induct,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),P: A > A > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ! [X3: A,Y2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y2 ) @ R )
% 2.99/1.52 => ( P @ X3 @ Y2 ) )
% 2.99/1.52 => ( ! [X3: A,Y2: A,Z: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ X3 @ Y2 )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ Y2 @ Z )
% 2.99/1.52 => ( P @ X3 @ Z ) ) ) ) )
% 2.99/1.52 => ( P @ X @ Y ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_34_trancl__into__trancl2,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_35_irrefl__trancl__rD,axiom,
% 2.99/1.52 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A] :
% 2.99/1.52 ( ! [X3: A] :
% 2.99/1.52 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ X3 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.99/1.52 => ( X != Y ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_36_converse__tranclE,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Z2: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ R )
% 2.99/1.52 => ~ ! [Y2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z2 ) @ ( transitive_trancl @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_37_r__r__into__trancl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R2: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R2 )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R2 )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_38_trancl_Oinducts,axiom,
% 2.99/1.52 ! [A: $tType,X1: A,X2: A,R: set @ ( product_prod @ A @ A ),P: A > A > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X1 @ X2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ! [A3: A,B3: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ R )
% 2.99/1.52 => ( P @ A3 @ B3 ) )
% 2.99/1.52 => ( ! [A3: A,B3: A,C3: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( P @ A3 @ B3 )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ C3 ) @ R )
% 2.99/1.52 => ( P @ A3 @ C3 ) ) ) )
% 2.99/1.52 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_39_trancl__induct,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),P: A > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ! [Y2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ R )
% 2.99/1.52 => ( P @ Y2 ) )
% 2.99/1.52 => ( ! [Y2: A,Z: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ Y2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 2.99/1.52 => ( ( P @ Y2 )
% 2.99/1.52 => ( P @ Z ) ) ) )
% 2.99/1.52 => ( P @ B2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_40_trancl__trans,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Z2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_41_trancl_Osimps,axiom,
% 2.99/1.52 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 = ( ? [A4: A,B4: A] :
% 2.99/1.52 ( ( A1 = A4 )
% 2.99/1.52 & ( A22 = B4 )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ R ) )
% 2.99/1.52 | ? [A4: A,B4: A,C4: A] :
% 2.99/1.52 ( ( A1 = A4 )
% 2.99/1.52 & ( A22 = C4 )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ C4 ) @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_42_trancl_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,A1: A,A22: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ A22 ) @ R )
% 2.99/1.52 => ~ ! [B3: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A1 @ B3 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ A22 ) @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_43_tranclE,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 2.99/1.52 => ~ ! [C3: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C3 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ C3 @ B2 ) @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_44_termi__impl__not__inf,axiom,
% 2.99/1.52 ! [C: com,S: state] :
% 2.99/1.52 ( ( termi @ C @ S )
% 2.99/1.52 => ~ ( pHoare1838713294le_inf @ ( cons @ com @ C @ ( nil @ com ) ) @ S ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_45_mem__Collect__eq,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,P: A > $o] :
% 2.99/1.52 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.99/1.52 = ( P @ A2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_46_Collect__mem__eq,axiom,
% 2.99/1.52 ! [A: $tType,A5: set @ A] :
% 2.99/1.52 ( ( collect @ A
% 2.99/1.52 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 2.99/1.52 = A5 ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_47_Collect__cong,axiom,
% 2.99/1.52 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.99/1.52 ( ! [X3: A] :
% 2.99/1.52 ( ( P @ X3 )
% 2.99/1.52 = ( Q @ X3 ) )
% 2.99/1.52 => ( ( collect @ A @ P )
% 2.99/1.52 = ( collect @ A @ Q ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_48_trancl__rtrancl__trancl,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_49_rtrancl__trancl__trancl,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Z2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( transitive_trancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_50_rtrancl__into__trancl2,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_51_rtrancl__into__trancl1,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),C: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B2 @ C ) @ R )
% 2.99/1.52 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ C ) @ ( transitive_trancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_52_exec1s__impl__execs,axiom,
% 2.99/1.52 ! [Cs3: list @ com,S: state,T2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ T2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 2.99/1.52 => ( pHoare1053570959_execs @ S @ Cs3 @ T2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_53_execs__pres__termis,axiom,
% 2.99/1.52 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 2.99/1.52 => ( ( pHoare1335526537termis @ Cs3 @ S )
% 2.99/1.52 => ( pHoare1335526537termis @ Cs @ S2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_54_old_Onat_Oinject,axiom,
% 2.99/1.52 ! [Nat: nat,Nat2: nat] :
% 2.99/1.52 ( ( ( suc @ Nat )
% 2.99/1.52 = ( suc @ Nat2 ) )
% 2.99/1.52 = ( Nat = Nat2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_55_nat_Oinject,axiom,
% 2.99/1.52 ! [X2: nat,Y22: nat] :
% 2.99/1.52 ( ( ( suc @ X2 )
% 2.99/1.52 = ( suc @ Y22 ) )
% 2.99/1.52 = ( X2 = Y22 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_56_list_Oinject,axiom,
% 2.99/1.52 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y222: list @ A] :
% 2.99/1.52 ( ( ( cons @ A @ X21 @ X22 )
% 2.99/1.52 = ( cons @ A @ Y21 @ Y222 ) )
% 2.99/1.52 = ( ( X21 = Y21 )
% 2.99/1.52 & ( X22 = Y222 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_57_exec1s__impl__exec,axiom,
% 2.99/1.52 ! [C: com,S: state,T2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( nil @ com ) ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ T2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 2.99/1.52 => ( exec @ S @ C @ T2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_58_old_Oprod_Oinject,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 2.99/1.52 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.99/1.52 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 2.99/1.52 = ( ( A2 = A6 )
% 2.99/1.52 & ( B2 = B5 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_59_prod_Oinject,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y22: B] :
% 2.99/1.52 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 2.99/1.52 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 2.99/1.52 = ( ( X1 = Y1 )
% 2.99/1.52 & ( X2 = Y22 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_60_execs_Ointros_I2_J,axiom,
% 2.99/1.52 ! [S: state,C: com,T2: state,Cs3: list @ com,U: state] :
% 2.99/1.52 ( ( exec @ S @ C @ T2 )
% 2.99/1.52 => ( ( pHoare1053570959_execs @ T2 @ Cs3 @ U )
% 2.99/1.52 => ( pHoare1053570959_execs @ S @ ( cons @ com @ C @ Cs3 ) @ U ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_61_execs_Ocases,axiom,
% 2.99/1.52 ! [A1: state,A22: list @ com,A32: state] :
% 2.99/1.52 ( ( pHoare1053570959_execs @ A1 @ A22 @ A32 )
% 2.99/1.52 => ( ( ( A22
% 2.99/1.52 = ( nil @ com ) )
% 2.99/1.52 => ( A32 != A1 ) )
% 2.99/1.52 => ~ ! [C3: com,T3: state,Cs4: list @ com] :
% 2.99/1.52 ( ( A22
% 2.99/1.52 = ( cons @ com @ C3 @ Cs4 ) )
% 2.99/1.52 => ( ( exec @ A1 @ C3 @ T3 )
% 2.99/1.52 => ~ ( pHoare1053570959_execs @ T3 @ Cs4 @ A32 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_62_execs_Osimps,axiom,
% 2.99/1.52 ( pHoare1053570959_execs
% 2.99/1.52 = ( ^ [A12: state,A23: list @ com,A33: state] :
% 2.99/1.52 ( ? [S3: state] :
% 2.99/1.52 ( ( A12 = S3 )
% 2.99/1.52 & ( A23
% 2.99/1.52 = ( nil @ com ) )
% 2.99/1.52 & ( A33 = S3 ) )
% 2.99/1.52 | ? [S3: state,C4: com,T4: state,Cs2: list @ com,U2: state] :
% 2.99/1.52 ( ( A12 = S3 )
% 2.99/1.52 & ( A23
% 2.99/1.52 = ( cons @ com @ C4 @ Cs2 ) )
% 2.99/1.52 & ( A33 = U2 )
% 2.99/1.52 & ( exec @ S3 @ C4 @ T4 )
% 2.99/1.52 & ( pHoare1053570959_execs @ T4 @ Cs2 @ U2 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_63_execs_Oinducts,axiom,
% 2.99/1.52 ! [X1: state,X2: list @ com,X32: state,P: state > ( list @ com ) > state > $o] :
% 2.99/1.52 ( ( pHoare1053570959_execs @ X1 @ X2 @ X32 )
% 2.99/1.52 => ( ! [S4: state] : ( P @ S4 @ ( nil @ com ) @ S4 )
% 2.99/1.52 => ( ! [S4: state,C3: com,T3: state,Cs4: list @ com,U3: state] :
% 2.99/1.52 ( ( exec @ S4 @ C3 @ T3 )
% 2.99/1.52 => ( ( pHoare1053570959_execs @ T3 @ Cs4 @ U3 )
% 2.99/1.52 => ( ( P @ T3 @ Cs4 @ U3 )
% 2.99/1.52 => ( P @ S4 @ ( cons @ com @ C3 @ Cs4 ) @ U3 ) ) ) )
% 2.99/1.52 => ( P @ X1 @ X2 @ X32 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_64_termis_Osimps_I2_J,axiom,
% 2.99/1.52 ! [C: com,Cs3: list @ com,S: state] :
% 2.99/1.52 ( ( pHoare1335526537termis @ ( cons @ com @ C @ Cs3 ) @ S )
% 2.99/1.52 = ( ( termi @ C @ S )
% 2.99/1.52 & ! [T4: state] :
% 2.99/1.52 ( ( exec @ S @ C @ T4 )
% 2.99/1.52 => ( pHoare1335526537termis @ Cs3 @ T4 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_65_execs_Ointros_I1_J,axiom,
% 2.99/1.52 ! [S: state] : ( pHoare1053570959_execs @ S @ ( nil @ com ) @ S ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_66_termis_Osimps_I1_J,axiom,
% 2.99/1.52 ! [S: state] : ( pHoare1335526537termis @ ( nil @ com ) @ S ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_67_zero__reorient,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( zero @ A )
% 2.99/1.52 => ! [X: A] :
% 2.99/1.52 ( ( ( zero_zero @ A )
% 2.99/1.52 = X )
% 2.99/1.52 = ( X
% 2.99/1.52 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_68_surj__pair,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 2.99/1.52 ? [X3: A,Y2: B] :
% 2.99/1.52 ( P2
% 2.99/1.52 = ( product_Pair @ A @ B @ X3 @ Y2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_69_prod__cases,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 2.99/1.52 ( ! [A3: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.99/1.52 => ( P @ P2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_70_Pair__inject,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 2.99/1.52 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.99/1.52 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 2.99/1.52 => ~ ( ( A2 = A6 )
% 2.99/1.52 => ( B2 != B5 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_71_old_Oprod_Oexhaust,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.99/1.52 ~ ! [A3: A,B3: B] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( product_Pair @ A @ B @ A3 @ B3 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_72_old_Oprod_Oinducts,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.99/1.52 ( ! [A3: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.99/1.52 => ( P @ Prod ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_73_not__Cons__self2,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.99/1.52 ( ( cons @ A @ X @ Xs )
% 2.99/1.52 != Xs ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_74_Suc__inject,axiom,
% 2.99/1.52 ! [X: nat,Y: nat] :
% 2.99/1.52 ( ( ( suc @ X )
% 2.99/1.52 = ( suc @ Y ) )
% 2.99/1.52 => ( X = Y ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_75_n__not__Suc__n,axiom,
% 2.99/1.52 ! [N: nat] :
% 2.99/1.52 ( N
% 2.99/1.52 != ( suc @ N ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_76_inf__cases,axiom,
% 2.99/1.52 ! [C: com,Cs3: list @ com,S: state] :
% 2.99/1.52 ( ( pHoare1838713294le_inf @ ( cons @ com @ C @ Cs3 ) @ S )
% 2.99/1.52 => ( ( pHoare1838713294le_inf @ ( cons @ com @ C @ ( nil @ com ) ) @ S )
% 2.99/1.52 | ? [T3: state] :
% 2.99/1.52 ( ( exec @ S @ C @ T3 )
% 2.99/1.52 & ( pHoare1838713294le_inf @ Cs3 @ T3 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_77_nat_Odistinct_I1_J,axiom,
% 2.99/1.52 ! [X2: nat] :
% 2.99/1.52 ( ( zero_zero @ nat )
% 2.99/1.52 != ( suc @ X2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_78_old_Onat_Odistinct_I2_J,axiom,
% 2.99/1.52 ! [Nat3: nat] :
% 2.99/1.52 ( ( suc @ Nat3 )
% 2.99/1.52 != ( zero_zero @ nat ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_79_old_Onat_Odistinct_I1_J,axiom,
% 2.99/1.52 ! [Nat2: nat] :
% 2.99/1.52 ( ( zero_zero @ nat )
% 2.99/1.52 != ( suc @ Nat2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_80_nat_OdiscI,axiom,
% 2.99/1.52 ! [Nat: nat,X2: nat] :
% 2.99/1.52 ( ( Nat
% 2.99/1.52 = ( suc @ X2 ) )
% 2.99/1.52 => ( Nat
% 2.99/1.52 != ( zero_zero @ nat ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_81_nat__induct,axiom,
% 2.99/1.52 ! [P: nat > $o,N: nat] :
% 2.99/1.52 ( ( P @ ( zero_zero @ nat ) )
% 2.99/1.52 => ( ! [N2: nat] :
% 2.99/1.52 ( ( P @ N2 )
% 2.99/1.52 => ( P @ ( suc @ N2 ) ) )
% 2.99/1.52 => ( P @ N ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_82_diff__induct,axiom,
% 2.99/1.52 ! [P: nat > nat > $o,M: nat,N: nat] :
% 2.99/1.52 ( ! [X3: nat] : ( P @ X3 @ ( zero_zero @ nat ) )
% 2.99/1.52 => ( ! [Y2: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y2 ) )
% 2.99/1.52 => ( ! [X3: nat,Y2: nat] :
% 2.99/1.52 ( ( P @ X3 @ Y2 )
% 2.99/1.52 => ( P @ ( suc @ X3 ) @ ( suc @ Y2 ) ) )
% 2.99/1.52 => ( P @ M @ N ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_83_zero__induct,axiom,
% 2.99/1.52 ! [P: nat > $o,K: nat] :
% 2.99/1.52 ( ( P @ K )
% 2.99/1.52 => ( ! [N2: nat] :
% 2.99/1.52 ( ( P @ ( suc @ N2 ) )
% 2.99/1.52 => ( P @ N2 ) )
% 2.99/1.52 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_84_Suc__neq__Zero,axiom,
% 2.99/1.52 ! [M: nat] :
% 2.99/1.52 ( ( suc @ M )
% 2.99/1.52 != ( zero_zero @ nat ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_85_Zero__neq__Suc,axiom,
% 2.99/1.52 ! [M: nat] :
% 2.99/1.52 ( ( zero_zero @ nat )
% 2.99/1.52 != ( suc @ M ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_86_Zero__not__Suc,axiom,
% 2.99/1.52 ! [M: nat] :
% 2.99/1.52 ( ( zero_zero @ nat )
% 2.99/1.52 != ( suc @ M ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_87_old_Onat_Oexhaust,axiom,
% 2.99/1.52 ! [Y: nat] :
% 2.99/1.52 ( ( Y
% 2.99/1.52 != ( zero_zero @ nat ) )
% 2.99/1.52 => ~ ! [Nat4: nat] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( suc @ Nat4 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_88_old_Onat_Oinducts,axiom,
% 2.99/1.52 ! [P: nat > $o,Nat: nat] :
% 2.99/1.52 ( ( P @ ( zero_zero @ nat ) )
% 2.99/1.52 => ( ! [Nat4: nat] :
% 2.99/1.52 ( ( P @ Nat4 )
% 2.99/1.52 => ( P @ ( suc @ Nat4 ) ) )
% 2.99/1.52 => ( P @ Nat ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_89_not0__implies__Suc,axiom,
% 2.99/1.52 ! [N: nat] :
% 2.99/1.52 ( ( N
% 2.99/1.52 != ( zero_zero @ nat ) )
% 2.99/1.52 => ? [M2: nat] :
% 2.99/1.52 ( N
% 2.99/1.52 = ( suc @ M2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_90_list_Odistinct_I1_J,axiom,
% 2.99/1.52 ! [A: $tType,X21: A,X22: list @ A] :
% 2.99/1.52 ( ( nil @ A )
% 2.99/1.52 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_91_list_OdiscI,axiom,
% 2.99/1.52 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.99/1.52 ( ( List
% 2.99/1.52 = ( cons @ A @ X21 @ X22 ) )
% 2.99/1.52 => ( List
% 2.99/1.52 != ( nil @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_92_list_Oexhaust,axiom,
% 2.99/1.52 ! [A: $tType,Y: list @ A] :
% 2.99/1.52 ( ( Y
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ~ ! [X212: A,X222: list @ A] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_93_list_Oinducts,axiom,
% 2.99/1.52 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.99/1.52 ( ( P @ ( nil @ A ) )
% 2.99/1.52 => ( ! [X12: A,X23: list @ A] :
% 2.99/1.52 ( ( P @ X23 )
% 2.99/1.52 => ( P @ ( cons @ A @ X12 @ X23 ) ) )
% 2.99/1.52 => ( P @ List ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_94_neq__Nil__conv,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 = ( ? [Y3: A,Ys: list @ A] :
% 2.99/1.52 ( Xs
% 2.99/1.52 = ( cons @ A @ Y3 @ Ys ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_95_list__induct2_H,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 2.99/1.52 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.99/1.52 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 2.99/1.52 => ( ! [Y2: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys3 ) )
% 2.99/1.52 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys3: list @ B] :
% 2.99/1.52 ( ( P @ Xs2 @ Ys3 )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys3 ) ) )
% 2.99/1.52 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_96_splice_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.99/1.52 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.99/1.52 => ( ! [X3: A,Xs2: list @ A,Ys3: list @ A] :
% 2.99/1.52 ( ( P @ Ys3 @ Xs2 )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ Ys3 ) )
% 2.99/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_97_induct__list012,axiom,
% 2.99/1.52 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.99/1.52 ( ( P @ ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.99/1.52 => ( ! [X3: A,Y2: A,Zs: list @ A] :
% 2.99/1.52 ( ( P @ Zs )
% 2.99/1.52 => ( ( P @ ( cons @ A @ Y2 @ Zs ) )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Zs ) ) ) ) )
% 2.99/1.52 => ( P @ Xs ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_98_min__list_Ocases,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( ord @ A )
% 2.99/1.52 => ! [X: list @ A] :
% 2.99/1.52 ( ! [X3: A,Xs2: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( cons @ A @ X3 @ Xs2 ) )
% 2.99/1.52 => ( X
% 2.99/1.52 = ( nil @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_99_min__list_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( ord @ A )
% 2.99/1.52 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.99/1.52 ( ! [X3: A,Xs2: list @ A] :
% 2.99/1.52 ( ! [X213: A,X223: list @ A] :
% 2.99/1.52 ( ( Xs2
% 2.99/1.52 = ( cons @ A @ X213 @ X223 ) )
% 2.99/1.52 => ( P @ Xs2 ) )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 2.99/1.52 => ( ( P @ ( nil @ A ) )
% 2.99/1.52 => ( P @ A0 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_100_shuffles_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.99/1.52 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.99/1.52 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 2.99/1.52 ( ( P @ Xs2 @ ( cons @ A @ Y2 @ Ys3 ) )
% 2.99/1.52 => ( ( P @ ( cons @ A @ X3 @ Xs2 ) @ Ys3 )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) ) )
% 2.99/1.52 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_101_transpose_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,X: list @ ( list @ A )] :
% 2.99/1.52 ( ( X
% 2.99/1.52 != ( nil @ ( list @ A ) ) )
% 2.99/1.52 => ( ! [Xss: list @ ( list @ A )] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.99/1.52 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_102_remdups__adj_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,X: list @ A] :
% 2.99/1.52 ( ( X
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.99/1.52 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_103_sorted__wrt_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.99/1.52 ( ! [P3: A > A > $o] : ( P @ P3 @ ( nil @ A ) )
% 2.99/1.52 => ( ! [P3: A > A > $o,X3: A,Ys3: list @ A] :
% 2.99/1.52 ( ( P @ P3 @ Ys3 )
% 2.99/1.52 => ( P @ P3 @ ( cons @ A @ X3 @ Ys3 ) ) )
% 2.99/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_104_remdups__adj_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.99/1.52 ( ( P @ ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.99/1.52 => ( ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.99/1.52 ( ( ( X3 = Y2 )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 2.99/1.52 => ( ( ( X3 != Y2 )
% 2.99/1.52 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 2.99/1.52 => ( P @ A0 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_105_arg__min__list_Oinduct,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType] :
% 2.99/1.52 ( ( linorder @ B )
% 2.99/1.52 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 2.99/1.52 ( ! [F2: A > B,X3: A] : ( P @ F2 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.99/1.52 => ( ! [F2: A > B,X3: A,Y2: A,Zs: list @ A] :
% 2.99/1.52 ( ( P @ F2 @ ( cons @ A @ Y2 @ Zs ) )
% 2.99/1.52 => ( P @ F2 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 2.99/1.52 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 2.99/1.52 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_106_successively_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.99/1.52 ( ! [P3: A > A > $o] : ( P @ P3 @ ( nil @ A ) )
% 2.99/1.52 => ( ! [P3: A > A > $o,X3: A] : ( P @ P3 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.99/1.52 => ( ! [P3: A > A > $o,X3: A,Y2: A,Xs2: list @ A] :
% 2.99/1.52 ( ( P @ P3 @ ( cons @ A @ Y2 @ Xs2 ) )
% 2.99/1.52 => ( P @ P3 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 2.99/1.52 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_107_list__nonempty__induct,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.99/1.52 => ( ! [X3: A,Xs2: list @ A] :
% 2.99/1.52 ( ( Xs2
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ( ( P @ Xs2 )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 2.99/1.52 => ( P @ Xs ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_108_map__tailrec__rev_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.99/1.52 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 2.99/1.52 => ( ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 2.99/1.52 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A3 ) @ Bs ) )
% 2.99/1.52 => ( P @ F2 @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 2.99/1.52 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_109_strict__sorted_Ocases,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( linorder @ A )
% 2.99/1.52 => ! [X: list @ A] :
% 2.99/1.52 ( ( X
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ~ ! [X3: A,Ys3: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( cons @ A @ X3 @ Ys3 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_110_strict__sorted_Oinduct,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( linorder @ A )
% 2.99/1.52 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.99/1.52 ( ( P @ ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A,Ys3: list @ A] :
% 2.99/1.52 ( ( P @ Ys3 )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Ys3 ) ) )
% 2.99/1.52 => ( P @ A0 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_111_splice_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,X: product_prod @ ( list @ A ) @ ( list @ A )] :
% 2.99/1.52 ( ! [Ys3: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 2.99/1.52 => ~ ! [X3: A,Xs2: list @ A,Ys3: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_112_shuffles_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,X: product_prod @ ( list @ A ) @ ( list @ A )] :
% 2.99/1.52 ( ! [Ys3: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 2.99/1.52 => ( ! [Xs2: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 2.99/1.52 => ~ ! [X3: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_113_sorted__wrt_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,X: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 2.99/1.52 ( ! [P3: A > A > $o] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( nil @ A ) ) )
% 2.99/1.52 => ~ ! [P3: A > A > $o,X3: A,Ys3: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( cons @ A @ X3 @ Ys3 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_114_successively_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,X: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 2.99/1.52 ( ! [P3: A > A > $o] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( nil @ A ) ) )
% 2.99/1.52 => ( ! [P3: A > A > $o,X3: A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 2.99/1.52 => ~ ! [P3: A > A > $o,X3: A,Y2: A,Xs2: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P3 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_115_arg__min__list_Ocases,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType] :
% 2.99/1.52 ( ( linorder @ B )
% 2.99/1.52 => ! [X: product_prod @ ( A > B ) @ ( list @ A )] :
% 2.99/1.52 ( ! [F2: A > B,X3: A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 2.99/1.52 => ( ! [F2: A > B,X3: A,Y2: A,Zs: list @ A] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 2.99/1.52 => ~ ! [A3: A > B] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A3 @ ( nil @ A ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_116_map__tailrec__rev_Ocases,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,X: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 2.99/1.52 ( ! [F2: A > B,Bs: list @ B] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 2.99/1.52 => ~ ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 2.99/1.52 ( X
% 2.99/1.52 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A3 @ As ) @ Bs ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_117_exec__impl__execs,axiom,
% 2.99/1.52 ! [S: state,C: com,S2: state,Cs3: list @ com] :
% 2.99/1.52 ( ( exec @ S @ C @ S2 )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_118_prod__cases3,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,C5: $tType,Y: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 2.99/1.52 ~ ! [A3: A,B3: B,C3: C5] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A3 @ ( product_Pair @ B @ C5 @ B3 @ C3 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_119_prod__cases4,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,C5: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) )] :
% 2.99/1.52 ~ ! [A3: A,B3: B,C3: C5,D2: D] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ D ) @ B3 @ ( product_Pair @ C5 @ D @ C3 @ D2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_120_prod__cases5,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,C5: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) )] :
% 2.99/1.52 ~ ! [A3: A,B3: B,C3: C5,D2: D,E2: E] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_121_prod__cases6,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,C5: $tType,D: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 2.99/1.52 ~ ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_122_prod__cases7,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,C5: $tType,D: $tType,E: $tType,F4: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) )] :
% 2.99/1.52 ~ ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4,G2: G] :
% 2.99/1.52 ( Y
% 2.99/1.52 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G ) @ E2 @ ( product_Pair @ F4 @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_123_prod__induct3,axiom,
% 2.99/1.52 ! [C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C5 ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 2.99/1.52 ( ! [A3: A,B3: B,C3: C5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A3 @ ( product_Pair @ B @ C5 @ B3 @ C3 ) ) )
% 2.99/1.52 => ( P @ X ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_124_prod__induct4,axiom,
% 2.99/1.52 ! [D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) )] :
% 2.99/1.52 ( ! [A3: A,B3: B,C3: C5,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ D ) @ B3 @ ( product_Pair @ C5 @ D @ C3 @ D2 ) ) ) )
% 2.99/1.52 => ( P @ X ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_125_prod__induct5,axiom,
% 2.99/1.52 ! [E: $tType,D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) )] :
% 2.99/1.52 ( ! [A3: A,B3: B,C3: C5,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.99/1.52 => ( P @ X ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_126_prod__induct6,axiom,
% 2.99/1.52 ! [F4: $tType,E: $tType,D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 2.99/1.52 ( ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) )
% 2.99/1.52 => ( P @ X ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_127_prod__induct7,axiom,
% 2.99/1.52 ! [G: $tType,F4: $tType,E: $tType,D: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) )] :
% 2.99/1.52 ( ! [A3: A,B3: B,C3: C5,D2: D,E2: E,F2: F4,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) ) @ B3 @ ( product_Pair @ C5 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G ) @ E2 @ ( product_Pair @ F4 @ G @ F2 @ G2 ) ) ) ) ) ) )
% 2.99/1.52 => ( P @ X ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_128_exec1__pres__termis,axiom,
% 2.99/1.52 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ( ( pHoare1335526537termis @ Cs3 @ S )
% 2.99/1.52 => ( pHoare1335526537termis @ Cs @ S2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_129_old_Oprod_Orec,axiom,
% 2.99/1.52 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.99/1.52 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.99/1.52 = ( F1 @ A2 @ B2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_130_dependent__nat__choice,axiom,
% 2.99/1.52 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 2.99/1.52 ( ? [X_12: A] : ( P @ ( zero_zero @ nat ) @ X_12 )
% 2.99/1.52 => ( ! [X3: A,N2: nat] :
% 2.99/1.52 ( ( P @ N2 @ X3 )
% 2.99/1.52 => ? [Y4: A] :
% 2.99/1.52 ( ( P @ ( suc @ N2 ) @ Y4 )
% 2.99/1.52 & ( Q @ N2 @ X3 @ Y4 ) ) )
% 2.99/1.52 => ? [F2: nat > A] :
% 2.99/1.52 ! [N3: nat] :
% 2.99/1.52 ( ( P @ N3 @ ( F2 @ N3 ) )
% 2.99/1.52 & ( Q @ N3 @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_131_exec1E_I3_J,axiom,
% 2.99/1.52 ! [C1: com,C22: com,Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ~ ( ( Cs
% 2.99/1.52 = ( cons @ com @ C1 @ ( cons @ com @ C22 @ Cs3 ) ) )
% 2.99/1.52 => ( S2 != S ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_132_exec1_OSemi,axiom,
% 2.99/1.52 ! [C1: com,C22: com,Cs3: list @ com,S: state] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C1 @ ( cons @ com @ C22 @ Cs3 ) ) @ S ) ) @ pHoare1053570893_exec1 ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_133_n__lists__Nil,axiom,
% 2.99/1.52 ! [A: $tType,N: nat] :
% 2.99/1.52 ( ( ( N
% 2.99/1.52 = ( zero_zero @ nat ) )
% 2.99/1.52 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 2.99/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 2.99/1.52 & ( ( N
% 2.99/1.52 != ( zero_zero @ nat ) )
% 2.99/1.52 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 2.99/1.52 = ( nil @ ( list @ A ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_134_exec1E_I2_J,axiom,
% 2.99/1.52 ! [F: state > ( set @ state ),Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ F ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ~ ( ( Cs = Cs3 )
% 2.99/1.52 => ~ ( member @ state @ S2 @ ( F @ S ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_135_exec1_ODo,axiom,
% 2.99/1.52 ! [T2: state,F: state > ( set @ state ),S: state,Cs3: list @ com] :
% 2.99/1.52 ( ( member @ state @ T2 @ ( F @ S ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ F ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ T2 ) ) @ pHoare1053570893_exec1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_136_n__lists_Osimps_I1_J,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A] :
% 2.99/1.52 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 2.99/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_137_termi_OSemi,axiom,
% 2.99/1.52 ! [C1: com,S0: state,C22: com] :
% 2.99/1.52 ( ( termi @ C1 @ S0 )
% 2.99/1.52 => ( ! [S1: state] :
% 2.99/1.52 ( ( exec @ S0 @ C1 @ S1 )
% 2.99/1.52 => ( termi @ C22 @ S1 ) )
% 2.99/1.52 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_138_com_Oinject_I2_J,axiom,
% 2.99/1.52 ! [X21: com,X22: com,Y21: com,Y222: com] :
% 2.99/1.52 ( ( ( semi @ X21 @ X22 )
% 2.99/1.52 = ( semi @ Y21 @ Y222 ) )
% 2.99/1.52 = ( ( X21 = Y21 )
% 2.99/1.52 & ( X22 = Y222 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_139_com_Oinject_I1_J,axiom,
% 2.99/1.52 ! [X1: state > ( set @ state ),Y1: state > ( set @ state )] :
% 2.99/1.52 ( ( ( do @ X1 )
% 2.99/1.52 = ( do @ Y1 ) )
% 2.99/1.52 = ( X1 = Y1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_140_com_Odistinct_I1_J,axiom,
% 2.99/1.52 ! [X1: state > ( set @ state ),X21: com,X22: com] :
% 2.99/1.52 ( ( do @ X1 )
% 2.99/1.52 != ( semi @ X21 @ X22 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_141_exec_ODo,axiom,
% 2.99/1.52 ! [T2: state,F: state > ( set @ state ),S: state] :
% 2.99/1.52 ( ( member @ state @ T2 @ ( F @ S ) )
% 2.99/1.52 => ( exec @ S @ ( do @ F ) @ T2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_142_exec_OSemi,axiom,
% 2.99/1.52 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 2.99/1.52 ( ( exec @ S0 @ C1 @ S12 )
% 2.99/1.52 => ( ( exec @ S12 @ C22 @ S22 )
% 2.99/1.52 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_143_product__lists_Osimps_I1_J,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.99/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_144_subseqs_Osimps_I1_J,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( subseqs @ A @ ( nil @ A ) )
% 2.99/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_145_exec1E_I4_J,axiom,
% 2.99/1.52 ! [B2: state > $o,C1: com,C22: com,Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ B2 @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ( ( ( Cs
% 2.99/1.52 = ( cons @ com @ C1 @ Cs3 ) )
% 2.99/1.52 => ( ( S2 = S )
% 2.99/1.52 => ~ ( B2 @ S ) ) )
% 2.99/1.52 => ~ ( ( Cs
% 2.99/1.52 = ( cons @ com @ C22 @ Cs3 ) )
% 2.99/1.52 => ( ( S2 = S )
% 2.99/1.52 => ( B2 @ S ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_146_com_Oinject_I3_J,axiom,
% 2.99/1.52 ! [X31: state > $o,X322: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 2.99/1.52 ( ( ( cond @ X31 @ X322 @ X33 )
% 2.99/1.52 = ( cond @ Y31 @ Y32 @ Y33 ) )
% 2.99/1.52 = ( ( X31 = Y31 )
% 2.99/1.52 & ( X322 = Y32 )
% 2.99/1.52 & ( X33 = Y33 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_147_exec_OIfTrue,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C1: com,T2: state,C22: com] :
% 2.99/1.52 ( ( B2 @ S )
% 2.99/1.52 => ( ( exec @ S @ C1 @ T2 )
% 2.99/1.52 => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_148_exec_OIfFalse,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C22: com,T2: state,C1: com] :
% 2.99/1.52 ( ~ ( B2 @ S )
% 2.99/1.52 => ( ( exec @ S @ C22 @ T2 )
% 2.99/1.52 => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_149_termi_OIfTrue,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C1: com,C22: com] :
% 2.99/1.52 ( ( B2 @ S )
% 2.99/1.52 => ( ( termi @ C1 @ S )
% 2.99/1.52 => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_150_termi_OIfFalse,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C22: com,C1: com] :
% 2.99/1.52 ( ~ ( B2 @ S )
% 2.99/1.52 => ( ( termi @ C22 @ S )
% 2.99/1.52 => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_151_com_Odistinct_I3_J,axiom,
% 2.99/1.52 ! [X1: state > ( set @ state ),X31: state > $o,X322: com,X33: com] :
% 2.99/1.52 ( ( do @ X1 )
% 2.99/1.52 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_152_com_Odistinct_I11_J,axiom,
% 2.99/1.52 ! [X21: com,X22: com,X31: state > $o,X322: com,X33: com] :
% 2.99/1.52 ( ( semi @ X21 @ X22 )
% 2.99/1.52 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_153_exec1_OIfFalse,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C1: com,C22: com,Cs3: list @ com] :
% 2.99/1.52 ( ~ ( B2 @ S )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ B2 @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C22 @ Cs3 ) @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_154_exec1_OIfTrue,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C1: com,C22: com,Cs3: list @ com] :
% 2.99/1.52 ( ( B2 @ S )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ B2 @ C1 @ C22 ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C1 @ Cs3 ) @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_155_gen__length__code_I2_J,axiom,
% 2.99/1.52 ! [B: $tType,N: nat,X: B,Xs: list @ B] :
% 2.99/1.52 ( ( gen_length @ B @ N @ ( cons @ B @ X @ Xs ) )
% 2.99/1.52 = ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_156_insert__Nil,axiom,
% 2.99/1.52 ! [A: $tType,X: A] :
% 2.99/1.52 ( ( insert @ A @ X @ ( nil @ A ) )
% 2.99/1.52 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_157_exec1_OWhileFalse,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C: com,Cs3: list @ com] :
% 2.99/1.52 ( ~ ( B2 @ S )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_158_com_Oinject_I4_J,axiom,
% 2.99/1.52 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 2.99/1.52 ( ( ( while @ X41 @ X42 )
% 2.99/1.52 = ( while @ Y41 @ Y42 ) )
% 2.99/1.52 = ( ( X41 = Y41 )
% 2.99/1.52 & ( X42 = Y42 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_159_com_Odistinct_I19_J,axiom,
% 2.99/1.52 ! [X31: state > $o,X322: com,X33: com,X41: state > $o,X42: com] :
% 2.99/1.52 ( ( cond @ X31 @ X322 @ X33 )
% 2.99/1.52 != ( while @ X41 @ X42 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_160_while__termiE,axiom,
% 2.99/1.52 ! [B2: state > $o,C: com,S: state] :
% 2.99/1.52 ( ( termi @ ( while @ B2 @ C ) @ S )
% 2.99/1.52 => ( ( B2 @ S )
% 2.99/1.52 => ( termi @ C @ S ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_161_exec_OWhileFalse,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C: com] :
% 2.99/1.52 ( ~ ( B2 @ S )
% 2.99/1.52 => ( exec @ S @ ( while @ B2 @ C ) @ S ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_162_exec_OWhileTrue,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C: com,T2: state,U: state] :
% 2.99/1.52 ( ( B2 @ S )
% 2.99/1.52 => ( ( exec @ S @ C @ T2 )
% 2.99/1.52 => ( ( exec @ T2 @ ( while @ B2 @ C ) @ U )
% 2.99/1.52 => ( exec @ S @ ( while @ B2 @ C ) @ U ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_163_termi_OWhileFalse,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C: com] :
% 2.99/1.52 ( ~ ( B2 @ S )
% 2.99/1.52 => ( termi @ ( while @ B2 @ C ) @ S ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_164_com_Odistinct_I5_J,axiom,
% 2.99/1.52 ! [X1: state > ( set @ state ),X41: state > $o,X42: com] :
% 2.99/1.52 ( ( do @ X1 )
% 2.99/1.52 != ( while @ X41 @ X42 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_165_com_Odistinct_I13_J,axiom,
% 2.99/1.52 ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 2.99/1.52 ( ( semi @ X21 @ X22 )
% 2.99/1.52 != ( while @ X41 @ X42 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_166_termi_OWhileTrue,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C: com] :
% 2.99/1.52 ( ( B2 @ S )
% 2.99/1.52 => ( ( termi @ C @ S )
% 2.99/1.52 => ( ! [T3: state] :
% 2.99/1.52 ( ( exec @ S @ C @ T3 )
% 2.99/1.52 => ( termi @ ( while @ B2 @ C ) @ T3 ) )
% 2.99/1.52 => ( termi @ ( while @ B2 @ C ) @ S ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_167_while__termiE2,axiom,
% 2.99/1.52 ! [B2: state > $o,C: com,S: state,T2: state] :
% 2.99/1.52 ( ( termi @ ( while @ B2 @ C ) @ S )
% 2.99/1.52 => ( ( B2 @ S )
% 2.99/1.52 => ( ( exec @ S @ C @ T2 )
% 2.99/1.52 => ( termi @ ( while @ B2 @ C ) @ T2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_168_gen__length__code_I1_J,axiom,
% 2.99/1.52 ! [A: $tType,N: nat] :
% 2.99/1.52 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 2.99/1.52 = N ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_169_termi__while,axiom,
% 2.99/1.52 ! [B2: state > $o,C: com,F: nat > state,K: nat] :
% 2.99/1.52 ( ( termi @ ( while @ B2 @ C ) @ ( F @ K ) )
% 2.99/1.52 => ( ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) )
% 2.99/1.52 => ? [I: nat] :
% 2.99/1.52 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_170_termi__while__lemma,axiom,
% 2.99/1.52 ! [W: com,Fk: state,F: nat > state,K: nat,B2: state > $o,C: com] :
% 2.99/1.52 ( ( termi @ W @ Fk )
% 2.99/1.52 => ( ( ( Fk
% 2.99/1.52 = ( F @ K ) )
% 2.99/1.52 & ( W
% 2.99/1.52 = ( while @ B2 @ C ) )
% 2.99/1.52 & ! [I: nat] : ( exec @ ( F @ I ) @ C @ ( F @ ( suc @ I ) ) ) )
% 2.99/1.52 => ? [I: nat] :
% 2.99/1.52 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_171_exec1E_I5_J,axiom,
% 2.99/1.52 ! [B2: state > $o,C: com,Cs3: list @ com,S: state,Cs: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ( ( ( Cs = Cs3 )
% 2.99/1.52 => ( ( S2 = S )
% 2.99/1.52 => ( B2 @ S ) ) )
% 2.99/1.52 => ~ ( ( Cs
% 2.99/1.52 = ( cons @ com @ C @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) ) )
% 2.99/1.52 => ( ( S2 = S )
% 2.99/1.52 => ~ ( B2 @ S ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_172_exec1_OWhileTrue,axiom,
% 2.99/1.52 ! [B2: state > $o,S: state,C: com,Cs3: list @ com] :
% 2.99/1.52 ( ( B2 @ S )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( cons @ com @ ( while @ B2 @ C ) @ Cs3 ) ) @ S ) ) @ pHoare1053570893_exec1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_173_nths__singleton,axiom,
% 2.99/1.52 ! [A: $tType,A5: set @ nat,X: A] :
% 2.99/1.52 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A5 )
% 2.99/1.52 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A5 )
% 2.99/1.52 = ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.99/1.52 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A5 )
% 2.99/1.52 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A5 )
% 2.99/1.52 = ( nil @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_174_app__execs,axiom,
% 2.99/1.52 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state,Cs22: list @ com] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs3 @ Cs22 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs @ Cs22 ) @ S2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_175_listrel_Ocases,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ( ( ( A1
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 => ( A22
% 2.99/1.52 != ( nil @ B ) ) )
% 2.99/1.52 => ~ ! [X3: A,Y2: B,Xs2: list @ A] :
% 2.99/1.52 ( ( A1
% 2.99/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.99/1.52 => ! [Ys3: list @ B] :
% 2.99/1.52 ( ( A22
% 2.99/1.52 = ( cons @ B @ Y2 @ Ys3 ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R )
% 2.99/1.52 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys3 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_176_same__append__eq,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Xs @ Ys2 )
% 2.99/1.52 = ( append @ A @ Xs @ Zs2 ) )
% 2.99/1.52 = ( Ys2 = Zs2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_177_append__same__eq,axiom,
% 2.99/1.52 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Ys2 @ Xs )
% 2.99/1.52 = ( append @ A @ Zs2 @ Xs ) )
% 2.99/1.52 = ( Ys2 = Zs2 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_178_append__assoc,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs2 )
% 2.99/1.52 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_179_append_Oassoc,axiom,
% 2.99/1.52 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.99/1.52 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C )
% 2.99/1.52 = ( append @ A @ A2 @ ( append @ A @ B2 @ C ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_180_append__Nil2,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A] :
% 2.99/1.52 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.99/1.52 = Xs ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_181_append__self__conv,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Xs @ Ys2 )
% 2.99/1.52 = Xs )
% 2.99/1.52 = ( Ys2
% 2.99/1.52 = ( nil @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_182_self__append__conv,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 = ( append @ A @ Xs @ Ys2 ) )
% 2.99/1.52 = ( Ys2
% 2.99/1.52 = ( nil @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_183_append__self__conv2,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Xs @ Ys2 )
% 2.99/1.52 = Ys2 )
% 2.99/1.52 = ( Xs
% 2.99/1.52 = ( nil @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_184_self__append__conv2,axiom,
% 2.99/1.52 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.99/1.52 ( ( Ys2
% 2.99/1.52 = ( append @ A @ Xs @ Ys2 ) )
% 2.99/1.52 = ( Xs
% 2.99/1.52 = ( nil @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_185_Nil__is__append__conv,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( ( nil @ A )
% 2.99/1.52 = ( append @ A @ Xs @ Ys2 ) )
% 2.99/1.52 = ( ( Xs
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 & ( Ys2
% 2.99/1.52 = ( nil @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_186_append__is__Nil__conv,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Xs @ Ys2 )
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 = ( ( Xs
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 & ( Ys2
% 2.99/1.52 = ( nil @ A ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_187_append_Oright__neutral,axiom,
% 2.99/1.52 ! [A: $tType,A2: list @ A] :
% 2.99/1.52 ( ( append @ A @ A2 @ ( nil @ A ) )
% 2.99/1.52 = A2 ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_188_nths__nil,axiom,
% 2.99/1.52 ! [A: $tType,A5: set @ nat] :
% 2.99/1.52 ( ( nths @ A @ ( nil @ A ) @ A5 )
% 2.99/1.52 = ( nil @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_189_append1__eq__conv,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y: A] :
% 2.99/1.52 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.99/1.52 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.99/1.52 = ( ( Xs = Ys2 )
% 2.99/1.52 & ( X = Y ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_190_listrel__rtrancl__refl,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] : ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_191_append__eq__append__conv2,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A,Ts: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Xs @ Ys2 )
% 2.99/1.52 = ( append @ A @ Zs2 @ Ts ) )
% 2.99/1.52 = ( ? [Us: list @ A] :
% 2.99/1.52 ( ( ( Xs
% 2.99/1.52 = ( append @ A @ Zs2 @ Us ) )
% 2.99/1.52 & ( ( append @ A @ Us @ Ys2 )
% 2.99/1.52 = Ts ) )
% 2.99/1.52 | ( ( ( append @ A @ Xs @ Us )
% 2.99/1.52 = Zs2 )
% 2.99/1.52 & ( Ys2
% 2.99/1.52 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_192_append__eq__appendI,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys2: list @ A,Us2: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Xs @ Xs1 )
% 2.99/1.52 = Zs2 )
% 2.99/1.52 => ( ( Ys2
% 2.99/1.52 = ( append @ A @ Xs1 @ Us2 ) )
% 2.99/1.52 => ( ( append @ A @ Xs @ Ys2 )
% 2.99/1.52 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_193_eq__Nil__appendI,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( Xs = Ys2 )
% 2.99/1.52 => ( Xs
% 2.99/1.52 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_194_append__Nil,axiom,
% 2.99/1.52 ! [A: $tType,Ys2: list @ A] :
% 2.99/1.52 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 2.99/1.52 = Ys2 ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_195_append_Oleft__neutral,axiom,
% 2.99/1.52 ! [A: $tType,A2: list @ A] :
% 2.99/1.52 ( ( append @ A @ ( nil @ A ) @ A2 )
% 2.99/1.52 = A2 ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_196_Cons__eq__appendI,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( ( cons @ A @ X @ Xs1 )
% 2.99/1.52 = Ys2 )
% 2.99/1.52 => ( ( Xs
% 2.99/1.52 = ( append @ A @ Xs1 @ Zs2 ) )
% 2.99/1.52 => ( ( cons @ A @ X @ Xs )
% 2.99/1.52 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_197_append__Cons,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys2 )
% 2.99/1.52 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_198_rev__nonempty__induct,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.99/1.52 => ( ! [X3: A,Xs2: list @ A] :
% 2.99/1.52 ( ( Xs2
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ( ( P @ Xs2 )
% 2.99/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) )
% 2.99/1.52 => ( P @ Xs ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_199_append__eq__Cons__conv,axiom,
% 2.99/1.52 ! [A: $tType,Ys2: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 2.99/1.52 ( ( ( append @ A @ Ys2 @ Zs2 )
% 2.99/1.52 = ( cons @ A @ X @ Xs ) )
% 2.99/1.52 = ( ( ( Ys2
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 & ( Zs2
% 2.99/1.52 = ( cons @ A @ X @ Xs ) ) )
% 2.99/1.52 | ? [Ys4: list @ A] :
% 2.99/1.52 ( ( Ys2
% 2.99/1.52 = ( cons @ A @ X @ Ys4 ) )
% 2.99/1.52 & ( ( append @ A @ Ys4 @ Zs2 )
% 2.99/1.52 = Xs ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_200_Cons__eq__append__conv,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( ( cons @ A @ X @ Xs )
% 2.99/1.52 = ( append @ A @ Ys2 @ Zs2 ) )
% 2.99/1.52 = ( ( ( Ys2
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 & ( ( cons @ A @ X @ Xs )
% 2.99/1.52 = Zs2 ) )
% 2.99/1.52 | ? [Ys4: list @ A] :
% 2.99/1.52 ( ( ( cons @ A @ X @ Ys4 )
% 2.99/1.52 = Ys2 )
% 2.99/1.52 & ( Xs
% 2.99/1.52 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_201_rev__exhaust,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 != ( nil @ A ) )
% 2.99/1.52 => ~ ! [Ys3: list @ A,Y2: A] :
% 2.99/1.52 ( Xs
% 2.99/1.52 != ( append @ A @ Ys3 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_202_rev__induct,axiom,
% 2.99/1.52 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.99/1.52 ( ( P @ ( nil @ A ) )
% 2.99/1.52 => ( ! [X3: A,Xs2: list @ A] :
% 2.99/1.52 ( ( P @ Xs2 )
% 2.99/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) )
% 2.99/1.52 => ( P @ Xs ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_203_listrel_ONil,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] : ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_204_listrel__Nil1,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ( Xs
% 2.99/1.52 = ( nil @ B ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_205_listrel__Nil2,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ B )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ( Xs
% 2.99/1.52 = ( nil @ A ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_206_listrel__rtrancl__trans,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Zs2: list @ A] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_207_app__exec,axiom,
% 2.99/1.52 ! [Cs3: list @ com,S: state,Cs: list @ com,S2: state,Cs22: list @ com] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs3 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs3 @ Cs22 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs @ Cs22 ) @ S2 ) ) @ pHoare1053570893_exec1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_208_listrel__Cons2,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,Xs: list @ A,Y: B,Ys2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( cons @ B @ Y @ Ys2 ) ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ~ ! [X3: A,Xs2: list @ A] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ R )
% 2.99/1.52 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_209_listrel__Cons1,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,Y: A,Ys2: list @ A,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ Y @ Ys2 ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ~ ! [Y2: B,Ys3: list @ B] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 = ( cons @ B @ Y2 @ Ys3 ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y @ Y2 ) @ R )
% 2.99/1.52 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Ys2 @ Ys3 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_210_listrel_OCons,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,X: A,Y: B,R: set @ ( product_prod @ A @ B ),Xs: list @ A,Ys2: list @ B] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ X @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) @ ( listrel @ A @ B @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_211_exec1__only1__aux,axiom,
% 2.99/1.52 ! [Ccs: list @ com,S: state,Cs: list @ com,T2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Ccs @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ T2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ! [C6: com,Cs5: list @ com] :
% 2.99/1.52 ( ( Ccs
% 2.99/1.52 = ( cons @ com @ C6 @ Cs5 ) )
% 2.99/1.52 => ? [Cs1: list @ com] :
% 2.99/1.52 ( Cs
% 2.99/1.52 = ( append @ com @ Cs1 @ Cs5 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_212_exec1__only1,axiom,
% 2.99/1.52 ! [C: com,Cs3: list @ com,S: state,Cs: list @ com,T2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ Cs3 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs @ T2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ? [Cs1: list @ com] :
% 2.99/1.52 ( Cs
% 2.99/1.52 = ( append @ com @ Cs1 @ Cs3 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_213_exec1__drop__suffix__aux,axiom,
% 2.99/1.52 ! [Cs12: list @ com,S: state,Cs1_2: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs12 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs1_2 @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ! [Cs13: list @ com,Cs23: list @ com,Cs14: list @ com] :
% 2.99/1.52 ( ( ( Cs12
% 2.99/1.52 = ( append @ com @ Cs13 @ Cs23 ) )
% 2.99/1.52 & ( Cs1_2
% 2.99/1.52 = ( append @ com @ Cs14 @ Cs23 ) )
% 2.99/1.52 & ( Cs13
% 2.99/1.52 != ( nil @ com ) ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs13 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs14 @ S2 ) ) @ pHoare1053570893_exec1 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_214_exec1__drop__suffix,axiom,
% 2.99/1.52 ! [Cs15: list @ com,Cs22: list @ com,S: state,Cs16: list @ com,S2: state] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs15 @ Cs22 ) @ S ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ Cs16 @ Cs22 ) @ S2 ) ) @ pHoare1053570893_exec1 )
% 2.99/1.52 => ( ( Cs15
% 2.99/1.52 != ( nil @ com ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ Cs15 @ S ) @ ( product_Pair @ ( list @ com ) @ state @ Cs16 @ S2 ) ) @ pHoare1053570893_exec1 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_215_listrel_Oinducts,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,X1: list @ A,X2: list @ B,R: set @ ( product_prod @ A @ B ),P: ( list @ A ) > ( list @ B ) > $o] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ X1 @ X2 ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.99/1.52 => ( ! [X3: A,Y2: B,Xs2: list @ A,Ys3: list @ B] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys3 ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 => ( ( P @ Xs2 @ Ys3 )
% 2.99/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys3 ) ) ) ) )
% 2.99/1.52 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_216_listrel_Osimps,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 2.99/1.52 = ( ( ( A1
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 & ( A22
% 2.99/1.52 = ( nil @ B ) ) )
% 2.99/1.52 | ? [X4: A,Y3: B,Xs3: list @ A,Ys: list @ B] :
% 2.99/1.52 ( ( A1
% 2.99/1.52 = ( cons @ A @ X4 @ Xs3 ) )
% 2.99/1.52 & ( A22
% 2.99/1.52 = ( cons @ B @ Y3 @ Ys ) )
% 2.99/1.52 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ R )
% 2.99/1.52 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs3 @ Ys ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_217_bind__simps_I2_J,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 2.99/1.52 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 2.99/1.52 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_218_snoc__listrel1__snoc__iff,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 = ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 & ( X = Y ) )
% 2.99/1.52 | ( ( Xs = Ys2 )
% 2.99/1.52 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_219_maps__simps_I1_J,axiom,
% 2.99/1.52 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 2.99/1.52 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 2.99/1.52 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_220_bind__simps_I1_J,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.99/1.52 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 2.99/1.52 = ( nil @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_221_Cons__listrel1__Cons,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.99/1.52 & ( Xs = Ys2 ) )
% 2.99/1.52 | ( ( X = Y )
% 2.99/1.52 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_222_rtrancl__listrel1__ConsI1,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),X: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ X @ Ys2 ) ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_223_listrel1I2,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),X: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ X @ Ys2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_224_not__listrel1__Nil,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_225_not__Nil__listrel1,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Xs ) @ ( listrel1 @ A @ R ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_226_append__listrel1I,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Us2: list @ A,Vs: list @ A] :
% 2.99/1.52 ( ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 & ( Us2 = Vs ) )
% 2.99/1.52 | ( ( Xs = Ys2 )
% 2.99/1.52 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Vs ) @ ( listrel1 @ A @ R ) ) ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys2 @ Vs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_227_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 2.99/1.52 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 = ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_228_rtrancl__listrel1__if__listrel,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel @ A @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_229_maps__simps_I2_J,axiom,
% 2.99/1.52 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.99/1.52 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 2.99/1.52 = ( nil @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_230_listrel1I1,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Xs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_231_Cons__listrel1E1,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 => ( ! [Y2: A] :
% 2.99/1.52 ( ( Ys2
% 2.99/1.52 = ( cons @ A @ Y2 @ Xs ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R ) )
% 2.99/1.52 => ~ ! [Zs: list @ A] :
% 2.99/1.52 ( ( Ys2
% 2.99/1.52 = ( cons @ A @ X @ Zs ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_232_Cons__listrel1E2,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( cons @ A @ Y @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 => ( ! [X3: A] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 = ( cons @ A @ X3 @ Ys2 ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y ) @ R ) )
% 2.99/1.52 => ~ ! [Zs: list @ A] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 = ( cons @ A @ Y @ Zs ) )
% 2.99/1.52 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Zs @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_233_listrel__reflcl__if__listrel1,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel @ A @ A @ ( transitive_rtrancl @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_234_listrel1I,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Us2: list @ A,Vs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.99/1.52 => ( ( Xs
% 2.99/1.52 = ( append @ A @ Us2 @ ( cons @ A @ X @ Vs ) ) )
% 2.99/1.52 => ( ( Ys2
% 2.99/1.52 = ( append @ A @ Us2 @ ( cons @ A @ Y @ Vs ) ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_235_listrel1E,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 2.99/1.52 => ~ ! [X3: A,Y2: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y2 ) @ R )
% 2.99/1.52 => ! [Us3: list @ A,Vs2: list @ A] :
% 2.99/1.52 ( ( Xs
% 2.99/1.52 = ( append @ A @ Us3 @ ( cons @ A @ X3 @ Vs2 ) ) )
% 2.99/1.52 => ( Ys2
% 2.99/1.52 != ( append @ A @ Us3 @ ( cons @ A @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_236_rtrancl__listrel1__ConsI2,axiom,
% 2.99/1.52 ! [A: $tType,X: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys2: list @ A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( transitive_rtrancl @ A @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys2 ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) @ ( transitive_rtrancl @ ( list @ A ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_237_concat__eq__append__conv,axiom,
% 2.99/1.52 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( ( concat @ A @ Xss2 )
% 2.99/1.52 = ( append @ A @ Ys2 @ Zs2 ) )
% 2.99/1.52 = ( ( ( Xss2
% 2.99/1.52 = ( nil @ ( list @ A ) ) )
% 2.99/1.52 => ( ( Ys2
% 2.99/1.52 = ( nil @ A ) )
% 2.99/1.52 & ( Zs2
% 2.99/1.52 = ( nil @ A ) ) ) )
% 2.99/1.52 & ( ( Xss2
% 2.99/1.52 != ( nil @ ( list @ A ) ) )
% 2.99/1.52 => ? [Xss1: list @ ( list @ A ),Xs3: list @ A,Xs4: list @ A,Xss22: list @ ( list @ A )] :
% 2.99/1.52 ( ( Xss2
% 2.99/1.52 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 2.99/1.52 & ( Ys2
% 2.99/1.52 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs3 ) )
% 2.99/1.52 & ( Zs2
% 2.99/1.52 = ( append @ A @ Xs4 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_238_lexord__append__left__rightI,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),U: list @ A,X: list @ A,Y: list @ A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ U @ ( cons @ A @ A2 @ X ) ) @ ( append @ A @ U @ ( cons @ A @ B2 @ Y ) ) ) @ ( lexord @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_239_concat__append,axiom,
% 2.99/1.52 ! [A: $tType,Xs: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 2.99/1.52 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys2 ) )
% 2.99/1.52 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys2 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_240_lexord__cons__cons,axiom,
% 2.99/1.52 ! [A: $tType,A2: A,X: list @ A,B2: A,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ A2 @ X ) @ ( cons @ A @ B2 @ Y ) ) @ ( lexord @ A @ R ) )
% 2.99/1.52 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 2.99/1.52 | ( ( A2 = B2 )
% 2.99/1.52 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ Y ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_241_lexord__Nil__left,axiom,
% 2.99/1.52 ! [A: $tType,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Y ) @ ( lexord @ A @ R ) )
% 2.99/1.52 = ( ? [A4: A,X4: list @ A] :
% 2.99/1.52 ( Y
% 2.99/1.52 = ( cons @ A @ A4 @ X4 ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_242_lexord__linear,axiom,
% 2.99/1.52 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: list @ A,Y: list @ A] :
% 2.99/1.52 ( ! [A3: A,B3: A] :
% 2.99/1.52 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B3 ) @ R )
% 2.99/1.52 | ( A3 = B3 )
% 2.99/1.52 | ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B3 @ A3 ) @ R ) )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ Y ) @ ( lexord @ A @ R ) )
% 2.99/1.52 | ( X = Y )
% 2.99/1.52 | ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Y @ X ) @ ( lexord @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_243_lexord__irreflexive,axiom,
% 2.99/1.52 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 2.99/1.52 ( ! [X3: A] :
% 2.99/1.52 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ X3 ) @ R )
% 2.99/1.52 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( lexord @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_244_concat_Osimps_I1_J,axiom,
% 2.99/1.52 ! [A: $tType] :
% 2.99/1.52 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 2.99/1.52 = ( nil @ A ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_245_lexord__Nil__right,axiom,
% 2.99/1.52 ! [A: $tType,X: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ ( nil @ A ) ) @ ( lexord @ A @ R ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_246_concat_Osimps_I2_J,axiom,
% 2.99/1.52 ! [A: $tType,X: list @ A,Xs: list @ ( list @ A )] :
% 2.99/1.52 ( ( concat @ A @ ( cons @ ( list @ A ) @ X @ Xs ) )
% 2.99/1.52 = ( append @ A @ X @ ( concat @ A @ Xs ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_247_lexord__append__leftI,axiom,
% 2.99/1.52 ! [A: $tType,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A ),X: list @ A] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X @ U ) @ ( append @ A @ X @ V ) ) @ ( lexord @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_248_lexord__append__leftD,axiom,
% 2.99/1.52 ! [A: $tType,X: list @ A,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X @ U ) @ ( append @ A @ X @ V ) ) @ ( lexord @ A @ R ) )
% 2.99/1.52 => ( ! [A3: A] :
% 2.99/1.52 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ A3 ) @ R )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_249_lexord__append__rightI,axiom,
% 2.99/1.52 ! [A: $tType,Y: list @ A,X: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.52 ( ? [B6: A,Z3: list @ A] :
% 2.99/1.52 ( Y
% 2.99/1.52 = ( cons @ A @ B6 @ Z3 ) )
% 2.99/1.52 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X @ ( append @ A @ X @ Y ) ) @ ( lexord @ A @ R ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_250_concat__eq__appendD,axiom,
% 2.99/1.52 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( ( concat @ A @ Xss2 )
% 2.99/1.52 = ( append @ A @ Ys2 @ Zs2 ) )
% 2.99/1.52 => ( ( Xss2
% 2.99/1.52 != ( nil @ ( list @ A ) ) )
% 2.99/1.52 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs5: list @ A,Xss23: list @ ( list @ A )] :
% 2.99/1.52 ( ( Xss2
% 2.99/1.52 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 2.99/1.52 & ( Ys2
% 2.99/1.52 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 2.99/1.52 & ( Zs2
% 2.99/1.52 = ( append @ A @ Xs5 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(fact_251_lexord__same__pref__if__irrefl,axiom,
% 2.99/1.52 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.99/1.52 ( ( irrefl @ A @ R )
% 2.99/1.52 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys2 ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lexord @ A @ R ) )
% 2.99/1.52 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(tcon_fun___Orderings_Oord,axiom,
% 2.99/1.52 ! [A7: $tType,A8: $tType] :
% 2.99/1.52 ( ( ord @ A8 )
% 2.99/1.52 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.99/1.52 linorder @ nat ).
% 2.99/1.52
% 2.99/1.52 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 2.99/1.52 ord @ nat ).
% 2.99/1.52
% 2.99/1.52 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.99/1.52 zero @ nat ).
% 2.99/1.52
% 2.99/1.52 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 2.99/1.52 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 2.99/1.52 linorder @ $o ).
% 2.99/1.52
% 2.99/1.52 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 2.99/1.52 ord @ $o ).
% 2.99/1.52
% 2.99/1.52 thf(conj_0,hypothesis,
% 2.99/1.52 termi @ c @ s ).
% 2.99/1.52
% 2.99/1.52 thf(conj_1,hypothesis,
% 2.99/1.52 ( ( f @ ( zero_zero @ nat ) )
% 2.99/1.52 = ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(conj_2,hypothesis,
% 2.99/1.52 ! [I2: nat] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( f @ I2 ) @ ( f @ ( suc @ I2 ) ) ) @ ( transitive_trancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(conj_3,hypothesis,
% 2.99/1.52 member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) @ ( f @ n ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ).
% 2.99/1.52
% 2.99/1.52 thf(conj_4,conjecture,
% 2.99/1.52 member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ).
% 2.99/1.52 ------------------------
% 2.99/1.55 % (24333)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/2Mi)
% 2.99/1.55 % (24334)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_24138 for (2999ds/2Mi)
% 2.99/1.55 % (24333)Instruction limit reached!
% 2.99/1.55 % (24333)------------------------------
% 2.99/1.55 % (24333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.55 % (24333)Termination reason: Unknown
% 2.99/1.55 % (24333)Termination phase: shuffling
% 2.99/1.55
% 2.99/1.55 % (24333)Memory used [KB]: 1407
% 2.99/1.55 % (24333)Time elapsed: 0.002 s
% 2.99/1.55 % (24333)Instructions burned: 2 (million)
% 2.99/1.55 % (24333)------------------------------
% 2.99/1.55 % (24333)------------------------------
% 2.99/1.55 % (24334)Instruction limit reached!
% 2.99/1.55 % (24334)------------------------------
% 2.99/1.55 % (24334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.55 % (24334)Termination reason: Unknown
% 2.99/1.55 % (24334)Termination phase: shuffling
% 2.99/1.55
% 2.99/1.55 % (24334)Memory used [KB]: 1407
% 2.99/1.55 % (24334)Time elapsed: 0.003 s
% 2.99/1.55 % (24334)Instructions burned: 3 (million)
% 2.99/1.55 % (24334)------------------------------
% 2.99/1.55 % (24334)------------------------------
% 2.99/1.55 % (24336)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/18Mi)
% 2.99/1.55 % (24335)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_24138 for (2999ds/275Mi)
% 2.99/1.55 % (24331)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_24138 for (2999ds/4Mi)
% 2.99/1.55 % (24330)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/183Mi)
% 2.99/1.55 % (24331)Instruction limit reached!
% 2.99/1.55 % (24331)------------------------------
% 2.99/1.55 % (24331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.55 % (24331)Termination reason: Unknown
% 2.99/1.55 % (24331)Termination phase: shuffling
% 2.99/1.55
% 2.99/1.55 % (24331)Memory used [KB]: 1535
% 2.99/1.55 % (24331)Time elapsed: 0.003 s
% 2.99/1.55 % (24331)Instructions burned: 5 (million)
% 2.99/1.55 % (24331)------------------------------
% 2.99/1.55 % (24331)------------------------------
% 2.99/1.56 % (24336)Instruction limit reached!
% 2.99/1.56 % (24336)------------------------------
% 2.99/1.56 % (24336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.56 % (24336)Termination reason: Unknown
% 2.99/1.56 % (24336)Termination phase: shuffling
% 2.99/1.56
% 2.99/1.56 % (24336)Memory used [KB]: 1791
% 2.99/1.56 % (24336)Time elapsed: 0.009 s
% 2.99/1.56 % (24336)Instructions burned: 19 (million)
% 2.99/1.56 % (24336)------------------------------
% 2.99/1.56 % (24336)------------------------------
% 2.99/1.56 % (24338)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_24138 for (2999ds/37Mi)
% 2.99/1.56 % (24332)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_24138 for (2999ds/27Mi)
% 2.99/1.57 % (24339)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_24138 for (2999ds/15Mi)
% 2.99/1.57 % (24337)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/3Mi)
% 2.99/1.57 % (24340)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_24138 for (2999ds/3Mi)
% 2.99/1.57 % (24337)Instruction limit reached!
% 2.99/1.57 % (24337)------------------------------
% 2.99/1.57 % (24337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (24337)Termination reason: Unknown
% 2.99/1.57 % (24337)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (24337)Memory used [KB]: 1407
% 2.99/1.57 % (24337)Time elapsed: 0.004 s
% 2.99/1.57 % (24337)Instructions burned: 4 (million)
% 2.99/1.57 % (24337)------------------------------
% 2.99/1.57 % (24337)------------------------------
% 2.99/1.57 % (24340)Instruction limit reached!
% 2.99/1.57 % (24340)------------------------------
% 2.99/1.57 % (24340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (24340)Termination reason: Unknown
% 2.99/1.57 % (24340)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (24340)Memory used [KB]: 1407
% 2.99/1.57 % (24340)Time elapsed: 0.003 s
% 2.99/1.57 % (24340)Instructions burned: 5 (million)
% 2.99/1.57 % (24340)------------------------------
% 2.99/1.57 % (24340)------------------------------
% 2.99/1.57 % (24338)Instruction limit reached!
% 2.99/1.57 % (24338)------------------------------
% 2.99/1.57 % (24338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (24338)Termination reason: Unknown
% 2.99/1.57 % (24338)Termination phase: shuffling
% 2.99/1.57 % (24339)Instruction limit reached!
% 2.99/1.57 % (24339)------------------------------
% 2.99/1.57 % (24339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57
% 2.99/1.57 % (24338)Memory used [KB]: 2174
% 2.99/1.57 % (24338)Time elapsed: 0.013 s
% 2.99/1.57 % (24338)Instructions burned: 37 (million)
% 2.99/1.57 % (24338)------------------------------
% 2.99/1.57 % (24338)------------------------------
% 2.99/1.57 % (24339)Termination reason: Unknown
% 2.99/1.57 % (24339)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (24339)Memory used [KB]: 1663
% 2.99/1.57 % (24339)Time elapsed: 0.007 s
% 2.99/1.57 % (24339)Instructions burned: 17 (million)
% 2.99/1.57 % (24339)------------------------------
% 2.99/1.57 % (24339)------------------------------
% 2.99/1.58 % (24332)Instruction limit reached!
% 2.99/1.58 % (24332)------------------------------
% 2.99/1.58 % (24332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (24332)Termination reason: Unknown
% 2.99/1.58 % (24332)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (24332)Memory used [KB]: 1791
% 2.99/1.58 % (24332)Time elapsed: 0.016 s
% 2.99/1.58 % (24332)Instructions burned: 27 (million)
% 2.99/1.58 % (24332)------------------------------
% 2.99/1.58 % (24332)------------------------------
% 2.99/1.58 % (24341)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_24138 for (2999ds/1041Mi)
% 2.99/1.58 % (24342)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/7Mi)
% 2.99/1.58 % (24343)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/16Mi)
% 2.99/1.58 % (24344)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_24138 for (2999ds/3Mi)
% 2.99/1.58 % (24342)Instruction limit reached!
% 2.99/1.58 % (24342)------------------------------
% 2.99/1.58 % (24342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (24342)Termination reason: Unknown
% 2.99/1.58 % (24342)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (24342)Memory used [KB]: 1535
% 2.99/1.58 % (24342)Time elapsed: 0.004 s
% 2.99/1.58 % (24342)Instructions burned: 8 (million)
% 2.99/1.58 % (24342)------------------------------
% 2.99/1.58 % (24342)------------------------------
% 2.99/1.58 % (24344)Instruction limit reached!
% 2.99/1.58 % (24344)------------------------------
% 2.99/1.58 % (24344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (24344)Termination reason: Unknown
% 2.99/1.58 % (24344)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (24344)Memory used [KB]: 1407
% 2.99/1.58 % (24344)Time elapsed: 0.002 s
% 2.99/1.58 % (24344)Instructions burned: 3 (million)
% 2.99/1.58 % (24344)------------------------------
% 2.99/1.58 % (24344)------------------------------
% 2.99/1.59 % (24343)Instruction limit reached!
% 2.99/1.59 % (24343)------------------------------
% 2.99/1.59 % (24343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.59 % (24343)Termination reason: Unknown
% 2.99/1.59 % (24343)Termination phase: shuffling
% 2.99/1.59
% 2.99/1.59 % (24343)Memory used [KB]: 1663
% 2.99/1.59 % (24343)Time elapsed: 0.008 s
% 2.99/1.59 % (24343)Instructions burned: 18 (million)
% 2.99/1.59 % (24343)------------------------------
% 2.99/1.59 % (24343)------------------------------
% 2.99/1.59 % (24346)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/7Mi)
% 2.99/1.59 % (24347)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/3Mi)
% 2.99/1.59 % (24347)Instruction limit reached!
% 2.99/1.59 % (24347)------------------------------
% 2.99/1.59 % (24347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.59 % (24347)Termination reason: Unknown
% 2.99/1.59 % (24347)Termination phase: shuffling
% 2.99/1.59
% 2.99/1.59 % (24347)Memory used [KB]: 1535
% 2.99/1.59 % (24347)Time elapsed: 0.003 s
% 2.99/1.59 % (24347)Instructions burned: 4 (million)
% 2.99/1.59 % (24347)------------------------------
% 2.99/1.59 % (24347)------------------------------
% 2.99/1.59 % (24346)Instruction limit reached!
% 2.99/1.59 % (24346)------------------------------
% 2.99/1.59 % (24346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.59 % (24346)Termination reason: Unknown
% 2.99/1.59 % (24346)Termination phase: shuffling
% 2.99/1.59
% 2.99/1.59 % (24346)Memory used [KB]: 1407
% 2.99/1.59 % (24346)Time elapsed: 0.004 s
% 2.99/1.59 % (24346)Instructions burned: 7 (million)
% 2.99/1.59 % (24346)------------------------------
% 2.99/1.59 % (24346)------------------------------
% 2.99/1.59 % (24345)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_24138 for (2999ds/3Mi)
% 3.02/1.60 % (24345)Instruction limit reached!
% 3.02/1.60 % (24345)------------------------------
% 3.02/1.60 % (24345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (24345)Termination reason: Unknown
% 3.02/1.60 % (24345)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (24345)Memory used [KB]: 1407
% 3.02/1.60 % (24345)Time elapsed: 0.003 s
% 3.02/1.60 % (24345)Instructions burned: 5 (million)
% 3.02/1.60 % (24345)------------------------------
% 3.02/1.60 % (24345)------------------------------
% 3.02/1.60 % (24348)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/4Mi)
% 3.02/1.60 % (24348)Instruction limit reached!
% 3.02/1.60 % (24348)------------------------------
% 3.02/1.60 % (24348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (24348)Termination reason: Unknown
% 3.02/1.60 % (24348)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (24348)Memory used [KB]: 1407
% 3.02/1.60 % (24348)Time elapsed: 0.003 s
% 3.02/1.60 % (24348)Instructions burned: 4 (million)
% 3.02/1.60 % (24348)------------------------------
% 3.02/1.60 % (24348)------------------------------
% 3.02/1.60 % (24350)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/710Mi)
% 3.02/1.60 % (24349)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/18Mi)
% 3.02/1.61 % (24330)Instruction limit reached!
% 3.02/1.61 % (24330)------------------------------
% 3.02/1.61 % (24330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (24330)Termination reason: Unknown
% 3.02/1.61 % (24330)Termination phase: Saturation
% 3.02/1.61
% 3.02/1.61 % (24330)Memory used [KB]: 7419
% 3.02/1.61 % (24330)Time elapsed: 0.053 s
% 3.02/1.61 % (24330)Instructions burned: 183 (million)
% 3.02/1.61 % (24330)------------------------------
% 3.02/1.61 % (24330)------------------------------
% 3.02/1.61 % (24351)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/6Mi)
% 3.02/1.61 % (24352)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_24138 for (2999ds/902Mi)
% 3.02/1.61 % (24351)Instruction limit reached!
% 3.02/1.61 % (24351)------------------------------
% 3.02/1.61 % (24351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (24351)Termination reason: Unknown
% 3.02/1.61 % (24351)Termination phase: shuffling
% 3.02/1.61
% 3.02/1.61 % (24351)Memory used [KB]: 1407
% 3.02/1.61 % (24351)Time elapsed: 0.003 s
% 3.02/1.61 % (24351)Instructions burned: 6 (million)
% 3.02/1.61 % (24351)------------------------------
% 3.02/1.61 % (24351)------------------------------
% 3.02/1.61 % (24349)Instruction limit reached!
% 3.02/1.61 % (24349)------------------------------
% 3.02/1.61 % (24349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (24349)Termination reason: Unknown
% 3.02/1.61 % (24349)Termination phase: shuffling
% 3.02/1.61
% 3.02/1.61 % (24349)Memory used [KB]: 1791
% 3.02/1.61 % (24349)Time elapsed: 0.009 s
% 3.02/1.61 % (24349)Instructions burned: 20 (million)
% 3.02/1.61 % (24349)------------------------------
% 3.02/1.61 % (24349)------------------------------
% 3.02/1.62 % (24353)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_24138 for (2999ds/21Mi)
% 3.02/1.62 % (24354)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/5Mi)
% 3.02/1.62 % (24355)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_24138 for (2999ds/6Mi)
% 3.02/1.62 % (24353)Instruction limit reached!
% 3.02/1.62 % (24353)------------------------------
% 3.02/1.62 % (24353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (24353)Termination reason: Unknown
% 3.02/1.62 % (24353)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (24353)Memory used [KB]: 1791
% 3.02/1.62 % (24353)Time elapsed: 0.008 s
% 3.02/1.62 % (24353)Instructions burned: 21 (million)
% 3.02/1.62 % (24353)------------------------------
% 3.02/1.62 % (24353)------------------------------
% 3.02/1.62 % (24354)Instruction limit reached!
% 3.02/1.62 % (24354)------------------------------
% 3.02/1.62 % (24354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (24354)Termination reason: Unknown
% 3.02/1.62 % (24354)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (24354)Memory used [KB]: 1535
% 3.02/1.62 % (24354)Time elapsed: 0.004 s
% 3.02/1.62 % (24354)Instructions burned: 7 (million)
% 3.02/1.62 % (24354)------------------------------
% 3.02/1.62 % (24354)------------------------------
% 3.02/1.62 % (24355)Instruction limit reached!
% 3.02/1.62 % (24355)------------------------------
% 3.02/1.62 % (24355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (24355)Termination reason: Unknown
% 3.02/1.62 % (24355)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (24355)Memory used [KB]: 1535
% 3.02/1.62 % (24355)Time elapsed: 0.004 s
% 3.02/1.62 % (24355)Instructions burned: 7 (million)
% 3.02/1.62 % (24355)------------------------------
% 3.02/1.62 % (24355)------------------------------
% 3.02/1.63 % (24359)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24138 for (2999ds/377Mi)
% 3.02/1.63 % (24363)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_24138 for (2999ds/19Mi)
% 3.02/1.64 % (24363)Instruction limit reached!
% 3.02/1.64 % (24363)------------------------------
% 3.02/1.64 % (24363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (24363)Termination reason: Unknown
% 3.02/1.64 % (24363)Termination phase: shuffling
% 3.02/1.64
% 3.02/1.64 % (24363)Memory used [KB]: 1918
% 3.02/1.64 % (24363)Time elapsed: 0.008 s
% 3.02/1.64 % (24363)Instructions burned: 20 (million)
% 3.02/1.64 % (24363)------------------------------
% 3.02/1.64 % (24363)------------------------------
% 3.02/1.64 % (24362)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_24138 for (2999ds/779Mi)
% 3.02/1.64 % (24335)Instruction limit reached!
% 3.02/1.64 % (24335)------------------------------
% 3.02/1.64 % (24335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (24335)Termination reason: Unknown
% 3.02/1.64 % (24335)Termination phase: Saturation
% 3.02/1.64
% 3.02/1.64 % (24335)Memory used [KB]: 8187
% 3.02/1.64 % (24335)Time elapsed: 0.091 s
% 3.02/1.64 % (24335)Instructions burned: 278 (million)
% 3.02/1.64 % (24335)------------------------------
% 3.02/1.64 % (24335)------------------------------
% 3.02/1.65 % (24364)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_24138 for (2998ds/879Mi)
% 3.02/1.65 % (24365)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_24138 for (2998ds/17Mi)
% 3.02/1.66 % (24365)Instruction limit reached!
% 3.02/1.66 % (24365)------------------------------
% 3.02/1.66 % (24365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66 % (24365)Termination reason: Unknown
% 3.02/1.66 % (24365)Termination phase: shuffling
% 3.02/1.66
% 3.02/1.66 % (24365)Memory used [KB]: 1663
% 3.02/1.66 % (24365)Time elapsed: 0.007 s
% 3.02/1.66 % (24365)Instructions burned: 18 (million)
% 3.02/1.66 % (24365)------------------------------
% 3.02/1.66 % (24365)------------------------------
% 3.02/1.67 % (24366)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24138 for (2998ds/3Mi)
% 3.02/1.67 % (24366)Instruction limit reached!
% 3.02/1.67 % (24366)------------------------------
% 3.02/1.67 % (24366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67 % (24366)Termination reason: Unknown
% 3.02/1.67 % (24366)Termination phase: shuffling
% 3.02/1.67
% 3.02/1.67 % (24366)Memory used [KB]: 1407
% 3.02/1.67 % (24366)Time elapsed: 0.002 s
% 3.02/1.67 % (24366)Instructions burned: 3 (million)
% 3.02/1.67 % (24366)------------------------------
% 3.02/1.67 % (24366)------------------------------
% 3.02/1.68 % (24367)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_24138 for (2998ds/30Mi)
% 3.02/1.69 % (24367)Instruction limit reached!
% 3.02/1.69 % (24367)------------------------------
% 3.02/1.69 % (24367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.69 % (24367)Termination reason: Unknown
% 3.02/1.69 % (24367)Termination phase: shuffling
% 3.02/1.69
% 3.02/1.69 % (24367)Memory used [KB]: 1918
% 3.02/1.69 % (24367)Time elapsed: 0.011 s
% 3.02/1.69 % (24367)Instructions burned: 31 (million)
% 3.02/1.69 % (24367)------------------------------
% 3.02/1.69 % (24367)------------------------------
% 3.02/1.70 % (24370)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_24138 for (2998ds/127Mi)
% 3.02/1.75 % (24370)Instruction limit reached!
% 3.02/1.75 % (24370)------------------------------
% 3.02/1.75 % (24370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.75 % (24370)Termination reason: Unknown
% 3.02/1.75 % (24370)Termination phase: Property scanning
% 3.02/1.75
% 3.02/1.75 % (24370)Memory used [KB]: 2814
% 3.02/1.75 % (24370)Time elapsed: 0.052 s
% 3.02/1.75 % (24370)Instructions burned: 128 (million)
% 3.02/1.75 % (24370)------------------------------
% 3.02/1.75 % (24370)------------------------------
% 3.02/1.77 % (24359)Instruction limit reached!
% 3.02/1.77 % (24359)------------------------------
% 3.02/1.77 % (24359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.77 % (24359)Termination reason: Unknown
% 3.02/1.77 % (24359)Termination phase: Saturation
% 3.02/1.77
% 3.02/1.77 % (24359)Memory used [KB]: 8699
% 3.02/1.77 % (24359)Time elapsed: 0.136 s
% 3.02/1.77 % (24359)Instructions burned: 377 (million)
% 3.02/1.77 % (24359)------------------------------
% 3.02/1.77 % (24359)------------------------------
% 3.02/1.77 % (24389)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_24138 for (2997ds/100Mi)
% 3.02/1.78 % (24395)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_24138 for (2997ds/3Mi)
% 3.02/1.78 % (24395)Instruction limit reached!
% 3.02/1.78 % (24395)------------------------------
% 3.02/1.78 % (24395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.78 % (24395)Termination reason: Unknown
% 3.02/1.78 % (24395)Termination phase: shuffling
% 3.02/1.78
% 3.02/1.78 % (24395)Memory used [KB]: 1407
% 3.02/1.78 % (24395)Time elapsed: 0.003 s
% 3.02/1.78 % (24395)Instructions burned: 3 (million)
% 3.02/1.78 % (24395)------------------------------
% 3.02/1.78 % (24395)------------------------------
% 3.02/1.80 % (24389)Instruction limit reached!
% 3.02/1.80 % (24389)------------------------------
% 3.02/1.80 % (24389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.80 % (24389)Termination reason: Unknown
% 3.02/1.80 % (24389)Termination phase: Property scanning
% 3.02/1.80
% 3.02/1.80 % (24389)Memory used [KB]: 2686
% 3.02/1.80 % (24389)Time elapsed: 0.031 s
% 3.02/1.80 % (24389)Instructions burned: 100 (million)
% 3.02/1.80 % (24389)------------------------------
% 3.02/1.80 % (24389)------------------------------
% 3.02/1.80 % (24399)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_24138 for (2997ds/20Mi)
% 3.02/1.81 % (24399)Instruction limit reached!
% 3.02/1.81 % (24399)------------------------------
% 3.02/1.81 % (24399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.81 % (24399)Termination reason: Unknown
% 3.02/1.81 % (24399)Termination phase: shuffling
% 3.02/1.81
% 3.02/1.81 % (24399)Memory used [KB]: 1791
% 3.02/1.81 % (24399)Time elapsed: 0.009 s
% 3.02/1.81 % (24399)Instructions burned: 22 (million)
% 3.02/1.81 % (24399)------------------------------
% 3.02/1.81 % (24399)------------------------------
% 3.02/1.81 % (24402)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_24138 for (2997ds/86Mi)
% 3.02/1.82 % (24403)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_24138 for (2997ds/107Mi)
% 3.02/1.84 % (24402)Instruction limit reached!
% 3.02/1.84 % (24402)------------------------------
% 3.02/1.84 % (24402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.84 % (24402)Termination reason: Unknown
% 3.02/1.84 % (24402)Termination phase: Preprocessing 3
% 3.02/1.84
% 3.02/1.84 % (24402)Memory used [KB]: 2686
% 3.02/1.84 % (24402)Time elapsed: 0.029 s
% 3.02/1.84 % (24402)Instructions burned: 87 (million)
% 3.02/1.84 % (24402)------------------------------
% 3.02/1.84 % (24402)------------------------------
% 3.02/1.84 % (24404)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_24138 for (2996ds/39Mi)
% 3.02/1.86 % (24403)Instruction limit reached!
% 3.02/1.86 % (24403)------------------------------
% 3.02/1.86 % (24403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.86 % (24403)Termination reason: Unknown
% 3.02/1.86 % (24403)Termination phase: Property scanning
% 3.02/1.86
% 3.02/1.86 % (24403)Memory used [KB]: 2814
% 3.02/1.86 % (24403)Time elapsed: 0.041 s
% 3.02/1.86 % (24403)Instructions burned: 108 (million)
% 3.02/1.86 % (24403)------------------------------
% 3.02/1.86 % (24403)------------------------------
% 3.02/1.86 % (24404)Instruction limit reached!
% 3.02/1.86 % (24404)------------------------------
% 3.02/1.86 % (24404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.86 % (24404)Termination reason: Unknown
% 3.02/1.86 % (24404)Termination phase: shuffling
% 3.02/1.86
% 3.02/1.86 % (24404)Memory used [KB]: 2302
% 3.02/1.86 % (24404)Time elapsed: 0.012 s
% 3.02/1.86 % (24404)Instructions burned: 41 (million)
% 3.02/1.86 % (24404)------------------------------
% 3.02/1.86 % (24404)------------------------------
% 3.02/1.86 % (24350)Instruction limit reached!
% 3.02/1.86 % (24350)------------------------------
% 3.02/1.86 % (24350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.86 % (24350)Termination reason: Unknown
% 3.02/1.86 % (24350)Termination phase: Saturation
% 3.02/1.86
% 3.02/1.86 % (24350)Memory used [KB]: 8699
% 3.02/1.86 % (24350)Time elapsed: 0.259 s
% 3.02/1.86 % (24350)Instructions burned: 710 (million)
% 3.02/1.86 % (24350)------------------------------
% 3.02/1.86 % (24350)------------------------------
% 3.02/1.87 % (24405)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_24138 for (2996ds/448Mi)
% 3.02/1.87 % (24406)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_24138 for (2996ds/46Mi)
% 3.02/1.87 % (24407)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_24138 for (2996ds/98Mi)
% 3.02/1.88 % (24406)Instruction limit reached!
% 3.02/1.88 % (24406)------------------------------
% 3.02/1.88 % (24406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.88 % (24406)Termination reason: Unknown
% 3.02/1.88 % (24406)Termination phase: Property scanning
% 3.02/1.88
% 3.02/1.88 % (24406)Memory used [KB]: 2046
% 3.02/1.88 % (24406)Time elapsed: 0.016 s
% 3.02/1.88 % (24406)Instructions burned: 46 (million)
% 3.02/1.88 % (24406)------------------------------
% 3.02/1.88 % (24406)------------------------------
% 3.02/1.89 % (24408)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_24138 for (2996ds/507Mi)
% 3.02/1.90 % (24407)Instruction limit reached!
% 3.02/1.90 % (24407)------------------------------
% 3.02/1.90 % (24407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.90 % (24407)Termination reason: Unknown
% 3.02/1.90 % (24407)Termination phase: Property scanning
% 3.02/1.90
% 3.02/1.90 % (24407)Memory used [KB]: 2686
% 3.02/1.90 % (24407)Time elapsed: 0.028 s
% 3.02/1.90 % (24407)Instructions burned: 100 (million)
% 3.02/1.90 % (24407)------------------------------
% 3.02/1.90 % (24407)------------------------------
% 3.02/1.91 % (24413)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_24138 for (2996ds/149Mi)
% 3.02/1.92 % (24352)Instruction limit reached!
% 3.02/1.92 % (24352)------------------------------
% 3.02/1.92 % (24352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.92 % (24352)Termination reason: Unknown
% 3.02/1.92 % (24352)Termination phase: Saturation
% 3.02/1.92
% 3.02/1.92 % (24352)Memory used [KB]: 9083
% 3.02/1.92 % (24352)Time elapsed: 0.308 s
% 3.02/1.92 % (24352)Instructions burned: 904 (million)
% 3.02/1.92 % (24352)------------------------------
% 3.02/1.92 % (24352)------------------------------
% 3.02/1.92 % (24362)Instruction limit reached!
% 3.02/1.92 % (24362)------------------------------
% 3.02/1.92 % (24362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.92 % (24362)Termination reason: Unknown
% 3.02/1.92 % (24362)Termination phase: Saturation
% 3.02/1.92
% 3.02/1.92 % (24362)Memory used [KB]: 9978
% 3.02/1.92 % (24362)Time elapsed: 0.280 s
% 3.02/1.92 % (24362)Instructions burned: 780 (million)
% 3.02/1.92 % (24362)------------------------------
% 3.02/1.92 % (24362)------------------------------
% 3.02/1.93 % (24421)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_24138 for (2996ds/39Mi)
% 3.02/1.93 % (24341)Instruction limit reached!
% 3.02/1.93 % (24341)------------------------------
% 3.02/1.93 % (24341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.93 % (24341)Termination reason: Unknown
% 3.02/1.93 % (24341)Termination phase: Saturation
% 3.02/1.93
% 3.02/1.93 % (24341)Memory used [KB]: 10362
% 3.02/1.93 % (24341)Time elapsed: 0.351 s
% 3.02/1.93 % (24341)Instructions burned: 1042 (million)
% 3.02/1.93 % (24341)------------------------------
% 3.02/1.93 % (24341)------------------------------
% 3.02/1.93 % (24423)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_24138 for (2996ds/6Mi)
% 3.02/1.93 % (24423)Instruction limit reached!
% 3.02/1.93 % (24423)------------------------------
% 3.02/1.93 % (24423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.93 % (24423)Termination reason: Unknown
% 3.02/1.93 % (24423)Termination phase: shuffling
% 3.02/1.93
% 3.02/1.93 % (24423)Memory used [KB]: 1535
% 3.02/1.93 % (24423)Time elapsed: 0.003 s
% 3.02/1.93 % (24423)Instructions burned: 6 (million)
% 3.02/1.93 % (24423)------------------------------
% 3.02/1.93 % (24423)------------------------------
% 3.02/1.94 % (24428)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_24138 for (2995ds/1087Mi)
% 3.02/1.94 % (24430)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/47Mi)
% 3.02/1.94 % (24421)Instruction limit reached!
% 3.02/1.94 % (24421)------------------------------
% 3.02/1.94 % (24421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.94 % (24421)Termination reason: Unknown
% 3.02/1.94 % (24421)Termination phase: shuffling
% 3.02/1.94
% 3.02/1.94 % (24421)Memory used [KB]: 2046
% 3.02/1.94 % (24421)Time elapsed: 0.015 s
% 3.02/1.94 % (24421)Instructions burned: 41 (million)
% 3.02/1.94 % (24421)------------------------------
% 3.02/1.94 % (24421)------------------------------
% 3.02/1.95 % (24435)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_24138 for (2995ds/44Mi)
% 3.02/1.95 % (24413)Instruction limit reached!
% 3.02/1.95 % (24413)------------------------------
% 3.02/1.95 % (24413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.95 % (24413)Termination reason: Unknown
% 3.02/1.95 % (24413)Termination phase: Property scanning
% 3.02/1.95
% 3.02/1.95 % (24413)Memory used [KB]: 2814
% 3.02/1.95 % (24413)Time elapsed: 0.044 s
% 3.02/1.95 % (24413)Instructions burned: 149 (million)
% 3.02/1.95 % (24413)------------------------------
% 3.02/1.95 % (24413)------------------------------
% 3.02/1.95 % (24364)Instruction limit reached!
% 3.02/1.95 % (24364)------------------------------
% 3.02/1.95 % (24364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.95 % (24364)Termination reason: Unknown
% 3.02/1.95 % (24364)Termination phase: Saturation
% 3.02/1.95
% 3.02/1.95 % (24364)Memory used [KB]: 8699
% 3.02/1.95 % (24364)Time elapsed: 0.306 s
% 3.02/1.95 % (24364)Instructions burned: 882 (million)
% 3.02/1.95 % (24364)------------------------------
% 3.02/1.95 % (24364)------------------------------
% 3.02/1.96 % (24430)Instruction limit reached!
% 3.02/1.96 % (24430)------------------------------
% 3.02/1.96 % (24430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.96 % (24430)Termination reason: Unknown
% 3.02/1.96 % (24430)Termination phase: Property scanning
% 3.02/1.96
% 3.02/1.96 % (24430)Memory used [KB]: 2046
% 3.02/1.96 % (24430)Time elapsed: 0.017 s
% 3.02/1.96 % (24430)Instructions burned: 49 (million)
% 3.02/1.96 % (24430)------------------------------
% 3.02/1.96 % (24430)------------------------------
% 3.02/1.96 % (24440)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_24138 for (2995ds/432Mi)
% 3.02/1.96 % (24435)Instruction limit reached!
% 3.02/1.96 % (24435)------------------------------
% 3.02/1.96 % (24435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.96 % (24435)Termination reason: Unknown
% 3.02/1.96 % (24435)Termination phase: shuffling
% 3.02/1.96
% 3.02/1.96 % (24435)Memory used [KB]: 2302
% 3.02/1.96 % (24435)Time elapsed: 0.014 s
% 3.02/1.96 % (24435)Instructions burned: 46 (million)
% 3.02/1.96 % (24435)------------------------------
% 3.02/1.96 % (24435)------------------------------
% 3.02/1.96 % (24442)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/62Mi)
% 3.02/1.96 % (24443)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_24138 for (2995ds/31Mi)
% 3.02/1.97 % (24447)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/96Mi)
% 3.02/1.98 % (24443)Instruction limit reached!
% 3.02/1.98 % (24443)------------------------------
% 3.02/1.98 % (24443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.98 % (24443)Termination reason: Unknown
% 3.02/1.98 % (24443)Termination phase: shuffling
% 3.02/1.98
% 3.02/1.98 % (24443)Memory used [KB]: 1918
% 3.02/1.98 % (24443)Time elapsed: 0.012 s
% 3.02/1.98 % (24443)Instructions burned: 34 (million)
% 3.02/1.98 % (24443)------------------------------
% 3.02/1.98 % (24443)------------------------------
% 3.02/1.98 % (24442)Instruction limit reached!
% 3.02/1.98 % (24442)------------------------------
% 3.02/1.98 % (24442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.98 % (24442)Termination reason: Unknown
% 3.02/1.98 % (24442)Termination phase: Property scanning
% 3.02/1.98
% 3.02/1.98 % (24442)Memory used [KB]: 2686
% 3.02/1.98 % (24442)Time elapsed: 0.019 s
% 3.02/1.98 % (24442)Instructions burned: 64 (million)
% 3.02/1.98 % (24442)------------------------------
% 3.02/1.98 % (24442)------------------------------
% 3.02/1.99 % (24456)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_24138 for (2995ds/453Mi)
% 3.02/1.99 % (24459)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_24138 for (2995ds/71Mi)
% 3.02/1.99 % (24405)Instruction limit reached!
% 3.02/1.99 % (24405)------------------------------
% 3.02/1.99 % (24405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.99 % (24405)Termination reason: Unknown
% 3.02/1.99 % (24405)Termination phase: Saturation
% 3.02/1.99
% 3.02/1.99 % (24405)Memory used [KB]: 9210
% 3.02/1.99 % (24405)Time elapsed: 0.129 s
% 3.02/1.99 % (24405)Instructions burned: 451 (million)
% 3.02/1.99 % (24405)------------------------------
% 3.02/1.99 % (24405)------------------------------
% 3.02/2.00 % (24447)Instruction limit reached!
% 3.02/2.00 % (24447)------------------------------
% 3.02/2.00 % (24447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/2.00 % (24447)Termination reason: Unknown
% 3.02/2.00 % (24447)Termination phase: Property scanning
% 3.02/2.00
% 3.02/2.00 % (24447)Memory used [KB]: 2814
% 3.02/2.00 % (24447)Time elapsed: 0.031 s
% 3.02/2.00 % (24447)Instructions burned: 96 (million)
% 3.02/2.00 % (24447)------------------------------
% 3.02/2.00 % (24447)------------------------------
% 3.02/2.00 % (24462)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/83Mi)
% 3.02/2.01 % (24467)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/11Mi)
% 6.27/2.01 % (24459)Instruction limit reached!
% 6.27/2.01 % (24459)------------------------------
% 6.27/2.01 % (24459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.01 % (24459)Termination reason: Unknown
% 6.27/2.01 % (24459)Termination phase: Preprocessing 1
% 6.27/2.01
% 6.27/2.01 % (24459)Memory used [KB]: 2174
% 6.27/2.01 % (24459)Time elapsed: 0.023 s
% 6.27/2.01 % (24459)Instructions burned: 71 (million)
% 6.27/2.01 % (24459)------------------------------
% 6.27/2.01 % (24459)------------------------------
% 6.27/2.01 % (24467)Instruction limit reached!
% 6.27/2.01 % (24467)------------------------------
% 6.27/2.01 % (24467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.01 % (24467)Termination reason: Unknown
% 6.27/2.01 % (24467)Termination phase: shuffling
% 6.27/2.01
% 6.27/2.01 % (24467)Memory used [KB]: 1663
% 6.27/2.01 % (24467)Time elapsed: 0.004 s
% 6.27/2.01 % (24467)Instructions burned: 11 (million)
% 6.27/2.01 % (24467)------------------------------
% 6.27/2.01 % (24467)------------------------------
% 6.27/2.02 % (24472)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_24138 for (2995ds/41Mi)
% 6.27/2.02 % (24474)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/6Mi)
% 6.27/2.03 % (24474)Instruction limit reached!
% 6.27/2.03 % (24474)------------------------------
% 6.27/2.03 % (24474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.03 % (24474)Termination reason: Unknown
% 6.27/2.03 % (24474)Termination phase: shuffling
% 6.27/2.03
% 6.27/2.03 % (24474)Memory used [KB]: 1407
% 6.27/2.03 % (24474)Time elapsed: 0.003 s
% 6.27/2.03 % (24474)Instructions burned: 6 (million)
% 6.27/2.03 % (24474)------------------------------
% 6.27/2.03 % (24474)------------------------------
% 6.27/2.03 % (24462)Instruction limit reached!
% 6.27/2.03 % (24462)------------------------------
% 6.27/2.03 % (24462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.03 % (24462)Termination reason: Unknown
% 6.27/2.03 % (24462)Termination phase: Preprocessing 3
% 6.27/2.03
% 6.27/2.03 % (24462)Memory used [KB]: 2430
% 6.27/2.03 % (24462)Time elapsed: 0.027 s
% 6.27/2.03 % (24462)Instructions burned: 85 (million)
% 6.27/2.03 % (24462)------------------------------
% 6.27/2.03 % (24462)------------------------------
% 6.27/2.03 % (24472)Instruction limit reached!
% 6.27/2.03 % (24472)------------------------------
% 6.27/2.03 % (24472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.03 % (24472)Termination reason: Unknown
% 6.27/2.03 % (24472)Termination phase: shuffling
% 6.27/2.03
% 6.27/2.03 % (24472)Memory used [KB]: 2302
% 6.27/2.03 % (24472)Time elapsed: 0.013 s
% 6.27/2.03 % (24472)Instructions burned: 43 (million)
% 6.27/2.03 % (24472)------------------------------
% 6.27/2.03 % (24472)------------------------------
% 6.27/2.03 % (24479)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/150Mi)
% 6.27/2.04 % (24481)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_24138 for (2995ds/343Mi)
% 6.27/2.04 % (24408)Instruction limit reached!
% 6.27/2.04 % (24408)------------------------------
% 6.27/2.04 % (24408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.04 % (24408)Termination reason: Unknown
% 6.27/2.04 % (24408)Termination phase: Saturation
% 6.27/2.04
% 6.27/2.04 % (24408)Memory used [KB]: 9210
% 6.27/2.04 % (24408)Time elapsed: 0.153 s
% 6.27/2.04 % (24408)Instructions burned: 507 (million)
% 6.27/2.04 % (24408)------------------------------
% 6.27/2.04 % (24408)------------------------------
% 6.27/2.04 % (24484)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_24138 for (2994ds/109Mi)
% 6.27/2.05 % (24486)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_24138 for (2994ds/253Mi)
% 6.27/2.08 % (24484)Instruction limit reached!
% 6.27/2.08 % (24484)------------------------------
% 6.27/2.08 % (24484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.08 % (24484)Termination reason: Unknown
% 6.27/2.08 % (24484)Termination phase: Property scanning
% 6.27/2.08
% 6.27/2.08 % (24484)Memory used [KB]: 2686
% 6.27/2.08 % (24484)Time elapsed: 0.036 s
% 6.27/2.08 % (24484)Instructions burned: 112 (million)
% 6.27/2.08 % (24484)------------------------------
% 6.27/2.08 % (24484)------------------------------
% 6.27/2.08 % (24479)Instruction limit reached!
% 6.27/2.08 % (24479)------------------------------
% 6.27/2.08 % (24479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.08 % (24479)Termination reason: Unknown
% 6.27/2.08 % (24479)Termination phase: Property scanning
% 6.27/2.08
% 6.27/2.08 % (24479)Memory used [KB]: 2942
% 6.27/2.08 % (24479)Time elapsed: 0.046 s
% 6.27/2.08 % (24479)Instructions burned: 150 (million)
% 6.27/2.08 % (24479)------------------------------
% 6.27/2.08 % (24479)------------------------------
% 6.27/2.09 % (24504)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_24138 for (2994ds/140Mi)
% 6.27/2.09 % (24440)Instruction limit reached!
% 6.27/2.09 % (24440)------------------------------
% 6.27/2.09 % (24440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.09 % (24440)Termination reason: Unknown
% 6.27/2.09 % (24440)Termination phase: Saturation
% 6.27/2.09
% 6.27/2.09 % (24440)Memory used [KB]: 4221
% 6.27/2.09 % (24440)Time elapsed: 0.130 s
% 6.27/2.09 % (24440)Instructions burned: 433 (million)
% 6.27/2.09 % (24440)------------------------------
% 6.27/2.09 % (24440)------------------------------
% 6.27/2.09 % (24506)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_24138 for (2994ds/614Mi)
% 6.27/2.10 % (24510)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_24138 for (2994ds/202Mi)
% 6.27/2.11 % (24456)Instruction limit reached!
% 6.27/2.11 % (24456)------------------------------
% 6.27/2.11 % (24456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.11 % (24456)Termination reason: Unknown
% 6.27/2.11 % (24456)Termination phase: Saturation
% 6.27/2.11
% 6.27/2.11 % (24456)Memory used [KB]: 8571
% 6.27/2.11 % (24456)Time elapsed: 0.126 s
% 6.27/2.11 % (24456)Instructions burned: 453 (million)
% 6.27/2.11 % (24456)------------------------------
% 6.27/2.11 % (24456)------------------------------
% 6.78/2.12 % (24518)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_24138 for (2994ds/339Mi)
% 6.78/2.13 % (24486)Instruction limit reached!
% 6.78/2.13 % (24486)------------------------------
% 6.78/2.13 % (24486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.13 % (24486)Termination reason: Unknown
% 6.78/2.13 % (24486)Termination phase: Saturation
% 6.78/2.13
% 6.78/2.13 % (24486)Memory used [KB]: 4221
% 6.78/2.13 % (24486)Time elapsed: 0.076 s
% 6.78/2.13 % (24486)Instructions burned: 253 (million)
% 6.78/2.13 % (24486)------------------------------
% 6.78/2.13 % (24486)------------------------------
% 6.78/2.13 % (24504)Instruction limit reached!
% 6.78/2.13 % (24504)------------------------------
% 6.78/2.13 % (24504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.13 % (24504)Termination reason: Unknown
% 6.78/2.13 % (24504)Termination phase: Saturation
% 6.78/2.13
% 6.78/2.13 % (24504)Memory used [KB]: 7291
% 6.78/2.13 % (24504)Time elapsed: 0.042 s
% 6.78/2.13 % (24504)Instructions burned: 140 (million)
% 6.78/2.13 % (24504)------------------------------
% 6.78/2.13 % (24504)------------------------------
% 6.78/2.14 % (24530)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_24138 for (2994ds/283Mi)
% 6.78/2.14 % (24535)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_24138 for (2994ds/134Mi)
% 6.78/2.14 % (24481)Instruction limit reached!
% 6.78/2.14 % (24481)------------------------------
% 6.78/2.14 % (24481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.14 % (24481)Termination reason: Unknown
% 6.78/2.14 % (24481)Termination phase: Saturation
% 6.78/2.14
% 6.78/2.14 % (24481)Memory used [KB]: 8187
% 6.78/2.14 % (24481)Time elapsed: 0.105 s
% 6.78/2.14 % (24481)Instructions burned: 343 (million)
% 6.78/2.14 % (24481)------------------------------
% 6.78/2.14 % (24481)------------------------------
% 6.78/2.15 % (24543)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_24138 for (2993ds/298Mi)
% 6.78/2.16 % (24510)Instruction limit reached!
% 6.78/2.16 % (24510)------------------------------
% 6.78/2.16 % (24510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.16 % (24510)Termination reason: Unknown
% 6.78/2.16 % (24510)Termination phase: Saturation
% 6.78/2.16
% 6.78/2.16 % (24510)Memory used [KB]: 3709
% 6.78/2.16 % (24510)Time elapsed: 0.060 s
% 6.78/2.16 % (24510)Instructions burned: 204 (million)
% 6.78/2.16 % (24510)------------------------------
% 6.78/2.16 % (24510)------------------------------
% 6.78/2.17 % (24546)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_24138 for (2993ds/192Mi)
% 6.78/2.18 % (24535)Instruction limit reached!
% 6.78/2.18 % (24535)------------------------------
% 6.78/2.18 % (24535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.18 % (24535)Termination reason: Unknown
% 6.78/2.18 % (24535)Termination phase: Property scanning
% 6.78/2.18
% 6.78/2.18 % (24535)Memory used [KB]: 2814
% 6.78/2.18 % (24535)Time elapsed: 0.041 s
% 6.78/2.18 % (24535)Instructions burned: 137 (million)
% 6.78/2.18 % (24535)------------------------------
% 6.78/2.18 % (24535)------------------------------
% 6.78/2.19 % (24562)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_24138 for (2993ds/258Mi)
% 7.23/2.22 % (24518)Instruction limit reached!
% 7.23/2.22 % (24518)------------------------------
% 7.23/2.22 % (24518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.22 % (24518)Termination reason: Unknown
% 7.23/2.22 % (24518)Termination phase: Saturation
% 7.23/2.22
% 7.23/2.22 % (24518)Memory used [KB]: 7803
% 7.23/2.22 % (24518)Time elapsed: 0.097 s
% 7.23/2.22 % (24518)Instructions burned: 339 (million)
% 7.23/2.22 % (24518)------------------------------
% 7.23/2.22 % (24518)------------------------------
% 7.23/2.22 % (24530)Instruction limit reached!
% 7.23/2.22 % (24530)------------------------------
% 7.23/2.22 % (24530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.22 % (24530)Termination reason: Unknown
% 7.23/2.22 % (24530)Termination phase: Saturation
% 7.23/2.22
% 7.23/2.22 % (24530)Memory used [KB]: 7675
% 7.23/2.22 % (24530)Time elapsed: 0.103 s
% 7.23/2.22 % (24530)Instructions burned: 285 (million)
% 7.23/2.22 % (24530)------------------------------
% 7.23/2.22 % (24530)------------------------------
% 7.23/2.22 % (24546)Instruction limit reached!
% 7.23/2.22 % (24546)------------------------------
% 7.23/2.22 % (24546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.22 % (24546)Termination reason: Unknown
% 7.23/2.22 % (24546)Termination phase: Saturation
% 7.23/2.22
% 7.23/2.22 % (24546)Memory used [KB]: 3326
% 7.23/2.22 % (24546)Time elapsed: 0.057 s
% 7.23/2.22 % (24546)Instructions burned: 193 (million)
% 7.23/2.22 % (24546)------------------------------
% 7.23/2.22 % (24546)------------------------------
% 7.23/2.23 % (24578)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_24138 for (2993ds/90Mi)
% 7.23/2.23 % (24579)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_24138 for (2993ds/231Mi)
% 7.23/2.23 % (24581)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_24138 for (2992ds/458Mi)
% 7.23/2.23 % (24543)Instruction limit reached!
% 7.23/2.23 % (24543)------------------------------
% 7.23/2.23 % (24543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.23 % (24543)Termination reason: Unknown
% 7.23/2.23 % (24543)Termination phase: Saturation
% 7.23/2.23
% 7.23/2.23 % (24543)Memory used [KB]: 7803
% 7.23/2.23 % (24543)Time elapsed: 0.083 s
% 7.23/2.23 % (24543)Instructions burned: 301 (million)
% 7.23/2.23 % (24543)------------------------------
% 7.23/2.23 % (24543)------------------------------
% 7.23/2.24 % (24586)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_24138 for (2992ds/31Mi)
% 7.23/2.25 % (24578)Instruction limit reached!
% 7.23/2.25 % (24578)------------------------------
% 7.23/2.25 % (24578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.25 % (24578)Termination reason: Unknown
% 7.23/2.25 % (24578)Termination phase: Preprocessing 3
% 7.23/2.25
% 7.23/2.25 % (24578)Memory used [KB]: 2686
% 7.23/2.25 % (24578)Time elapsed: 0.029 s
% 7.23/2.25 % (24578)Instructions burned: 90 (million)
% 7.23/2.25 % (24578)------------------------------
% 7.23/2.25 % (24578)------------------------------
% 7.23/2.26 % (24586)Instruction limit reached!
% 7.23/2.26 % (24586)------------------------------
% 7.23/2.26 % (24586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.26 % (24586)Termination reason: Unknown
% 7.23/2.26 % (24586)Termination phase: shuffling
% 7.23/2.26
% 7.23/2.26 % (24586)Memory used [KB]: 1918
% 7.23/2.26 % (24586)Time elapsed: 0.013 s
% 7.23/2.26 % (24586)Instructions burned: 32 (million)
% 7.23/2.26 % (24586)------------------------------
% 7.23/2.26 % (24586)------------------------------
% 7.23/2.26 % (24593)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_24138 for (2992ds/297Mi)
% 7.23/2.26 % (24562)Instruction limit reached!
% 7.23/2.26 % (24562)------------------------------
% 7.23/2.26 % (24562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.26 % (24562)Termination reason: Unknown
% 7.23/2.26 % (24562)Termination phase: Saturation
% 7.23/2.26
% 7.23/2.26 % (24562)Memory used [KB]: 8315
% 7.23/2.26 % (24562)Time elapsed: 0.077 s
% 7.23/2.26 % (24562)Instructions burned: 261 (million)
% 7.23/2.26 % (24562)------------------------------
% 7.23/2.26 % (24562)------------------------------
% 7.23/2.26 % (24594)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_24138 for (2992ds/987Mi)
% 7.23/2.27 % (24506)Instruction limit reached!
% 7.23/2.27 % (24506)------------------------------
% 7.23/2.27 % (24506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.27 % (24506)Termination reason: Unknown
% 7.23/2.27 % (24506)Termination phase: Saturation
% 7.23/2.27
% 7.23/2.27 % (24506)Memory used [KB]: 8955
% 7.23/2.27 % (24506)Time elapsed: 0.181 s
% 7.23/2.27 % (24506)Instructions burned: 615 (million)
% 7.23/2.27 % (24506)------------------------------
% 7.23/2.27 % (24506)------------------------------
% 7.23/2.27 % (24598)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_24138 for (2992ds/182Mi)
% 7.23/2.28 % (24428)Instruction limit reached!
% 7.23/2.28 % (24428)------------------------------
% 7.23/2.28 % (24428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.28 % (24428)Termination reason: Unknown
% 7.23/2.28 % (24428)Termination phase: Saturation
% 7.23/2.28
% 7.23/2.28 % (24428)Memory used [KB]: 8827
% 7.23/2.28 % (24428)Time elapsed: 0.341 s
% 7.23/2.28 % (24428)Instructions burned: 1088 (million)
% 7.23/2.28 % (24428)------------------------------
% 7.23/2.28 % (24428)------------------------------
% 7.23/2.28 % (24599)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_24138 for (2992ds/182Mi)
% 7.23/2.29 % (24603)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_24138 for (2992ds/154Mi)
% 7.23/2.29 % (24579)Instruction limit reached!
% 7.23/2.29 % (24579)------------------------------
% 7.23/2.29 % (24579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.29 % (24579)Termination reason: Unknown
% 7.23/2.29 % (24579)Termination phase: Saturation
% 7.23/2.29
% 7.23/2.29 % (24579)Memory used [KB]: 7419
% 7.23/2.29 % (24579)Time elapsed: 0.063 s
% 7.23/2.29 % (24579)Instructions burned: 232 (million)
% 7.23/2.29 % (24579)------------------------------
% 7.23/2.29 % (24579)------------------------------
% 8.08/2.30 % (24608)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_24138 for (2992ds/79Mi)
% 8.08/2.32 % (24608)Instruction limit reached!
% 8.08/2.32 % (24608)------------------------------
% 8.08/2.32 % (24608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.32 % (24608)Termination reason: Unknown
% 8.08/2.32 % (24608)Termination phase: Preprocessing 3
% 8.08/2.32
% 8.08/2.32 % (24608)Memory used [KB]: 2558
% 8.08/2.32 % (24608)Time elapsed: 0.026 s
% 8.08/2.32 % (24608)Instructions burned: 79 (million)
% 8.08/2.32 % (24608)------------------------------
% 8.08/2.32 % (24608)------------------------------
% 8.08/2.33 % (24598)Instruction limit reached!
% 8.08/2.33 % (24598)------------------------------
% 8.08/2.33 % (24598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.33 % (24598)Termination reason: Unknown
% 8.08/2.33 % (24598)Termination phase: Saturation
% 8.08/2.33
% 8.08/2.33 % (24598)Memory used [KB]: 7291
% 8.08/2.33 % (24598)Time elapsed: 0.054 s
% 8.08/2.33 % (24598)Instructions burned: 184 (million)
% 8.08/2.33 % (24598)------------------------------
% 8.08/2.33 % (24598)------------------------------
% 8.08/2.33 % (24603)Instruction limit reached!
% 8.08/2.33 % (24603)------------------------------
% 8.08/2.33 % (24603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.33 % (24603)Termination reason: Unknown
% 8.08/2.33 % (24603)Termination phase: Property scanning
% 8.08/2.33
% 8.08/2.33 % (24603)Memory used [KB]: 2814
% 8.08/2.33 % (24603)Time elapsed: 0.043 s
% 8.08/2.33 % (24603)Instructions burned: 154 (million)
% 8.08/2.33 % (24603)------------------------------
% 8.08/2.33 % (24603)------------------------------
% 8.08/2.33 % (24619)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_24138 for (2991ds/216Mi)
% 8.08/2.33 % (24599)Instruction limit reached!
% 8.08/2.33 % (24599)------------------------------
% 8.08/2.33 % (24599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.33 % (24599)Termination reason: Unknown
% 8.08/2.33 % (24599)Termination phase: Saturation
% 8.08/2.33
% 8.08/2.33 % (24599)Memory used [KB]: 7419
% 8.08/2.33 % (24599)Time elapsed: 0.054 s
% 8.08/2.33 % (24599)Instructions burned: 184 (million)
% 8.08/2.33 % (24599)------------------------------
% 8.08/2.33 % (24599)------------------------------
% 8.08/2.34 % (24622)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_24138 for (2991ds/114Mi)
% 8.08/2.34 % (24624)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_24138 for (2991ds/922Mi)
% 8.08/2.34 % (24625)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_24138 for (2991ds/182Mi)
% 8.08/2.35 % (24593)Instruction limit reached!
% 8.08/2.35 % (24593)------------------------------
% 8.08/2.35 % (24593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.35 % (24593)Termination reason: Unknown
% 8.08/2.35 % (24593)Termination phase: Saturation
% 8.08/2.35
% 8.08/2.35 % (24593)Memory used [KB]: 7803
% 8.08/2.35 % (24593)Time elapsed: 0.084 s
% 8.08/2.35 % (24593)Instructions burned: 298 (million)
% 8.08/2.35 % (24593)------------------------------
% 8.08/2.35 % (24593)------------------------------
% 8.08/2.36 % (24629)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_24138 for (2991ds/164Mi)
% 8.08/2.37 % (24581)Instruction limit reached!
% 8.08/2.37 % (24581)------------------------------
% 8.08/2.37 % (24581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.37 % (24581)Termination reason: Unknown
% 8.08/2.37 % (24581)Termination phase: Saturation
% 8.08/2.37
% 8.08/2.37 % (24581)Memory used [KB]: 8571
% 8.08/2.37 % (24581)Time elapsed: 0.138 s
% 8.08/2.37 % (24581)Instructions burned: 458 (million)
% 8.08/2.37 % (24581)------------------------------
% 8.08/2.37 % (24581)------------------------------
% 8.08/2.37 % (24622)Instruction limit reached!
% 8.08/2.37 % (24622)------------------------------
% 8.08/2.37 % (24622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.37 % (24622)Termination reason: Unknown
% 8.08/2.37 % (24622)Termination phase: Property scanning
% 8.08/2.37
% 8.08/2.37 % (24622)Memory used [KB]: 2814
% 8.08/2.37 % (24622)Time elapsed: 0.035 s
% 8.08/2.37 % (24622)Instructions burned: 115 (million)
% 8.08/2.37 % (24622)------------------------------
% 8.08/2.37 % (24622)------------------------------
% 8.08/2.38 % (24639)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_24138 for (2991ds/50Mi)
% 8.08/2.38 % (24640)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_24138 for (2991ds/368Mi)
% 8.08/2.39 % (24625)Instruction limit reached!
% 8.08/2.39 % (24625)------------------------------
% 8.08/2.39 % (24625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.39 % (24625)Termination reason: Unknown
% 8.08/2.39 % (24625)Termination phase: Property scanning
% 8.08/2.39
% 8.08/2.39 % (24625)Memory used [KB]: 2814
% 8.08/2.39 % (24625)Time elapsed: 0.050 s
% 8.08/2.39 % (24625)Instructions burned: 183 (million)
% 8.08/2.39 % (24625)------------------------------
% 8.08/2.39 % (24625)------------------------------
% 8.08/2.39 % (24619)Instruction limit reached!
% 8.08/2.39 % (24619)------------------------------
% 8.08/2.39 % (24619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.39 % (24619)Termination reason: Unknown
% 8.08/2.39 % (24619)Termination phase: Saturation
% 8.08/2.39
% 8.08/2.39 % (24619)Memory used [KB]: 7419
% 8.08/2.39 % (24619)Time elapsed: 0.060 s
% 8.08/2.39 % (24619)Instructions burned: 218 (million)
% 8.08/2.39 % (24619)------------------------------
% 8.08/2.39 % (24619)------------------------------
% 8.08/2.39 % (24639)Instruction limit reached!
% 8.08/2.39 % (24639)------------------------------
% 8.08/2.39 % (24639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.39 % (24639)Termination reason: Unknown
% 8.08/2.39 % (24639)Termination phase: shuffling
% 8.08/2.39
% 8.08/2.39 % (24639)Memory used [KB]: 2430
% 8.08/2.39 % (24639)Time elapsed: 0.016 s
% 8.08/2.39 % (24639)Instructions burned: 53 (million)
% 8.08/2.39 % (24639)------------------------------
% 8.08/2.39 % (24639)------------------------------
% 8.73/2.40 % (24646)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_24138 for (2991ds/1021Mi)
% 8.73/2.40 % (24647)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_24138 for (2991ds/267Mi)
% 8.73/2.40 % (24629)Instruction limit reached!
% 8.73/2.40 % (24629)------------------------------
% 8.73/2.40 % (24629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.40 % (24629)Termination reason: Unknown
% 8.73/2.40 % (24629)Termination phase: Saturation
% 8.73/2.40
% 8.73/2.40 % (24629)Memory used [KB]: 2814
% 8.73/2.40 % (24629)Time elapsed: 0.046 s
% 8.73/2.40 % (24629)Instructions burned: 164 (million)
% 8.73/2.40 % (24629)------------------------------
% 8.73/2.40 % (24629)------------------------------
% 8.73/2.40 % (24648)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_24138 for (2991ds/204Mi)
% 8.73/2.41 % (24649)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_24138 for (2991ds/26Mi)
% 8.73/2.42 % (24649)Instruction limit reached!
% 8.73/2.42 % (24649)------------------------------
% 8.73/2.42 % (24649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.42 % (24649)Termination reason: Unknown
% 8.73/2.42 % (24649)Termination phase: shuffling
% 8.73/2.42
% 8.73/2.42 % (24649)Memory used [KB]: 2046
% 8.73/2.42 % (24649)Time elapsed: 0.009 s
% 8.73/2.42 % (24649)Instructions burned: 29 (million)
% 8.73/2.42 % (24649)------------------------------
% 8.73/2.42 % (24649)------------------------------
% 8.73/2.43 % (24659)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_24138 for (2991ds/53Mi)
% 8.73/2.44 % (24659)Instruction limit reached!
% 8.73/2.44 % (24659)------------------------------
% 8.73/2.44 % (24659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.44 % (24659)Termination reason: Unknown
% 8.73/2.44 % (24659)Termination phase: shuffling
% 8.73/2.44
% 8.73/2.44 % (24659)Memory used [KB]: 2430
% 8.73/2.44 % (24659)Time elapsed: 0.016 s
% 8.73/2.44 % (24659)Instructions burned: 53 (million)
% 8.73/2.44 % (24659)------------------------------
% 8.73/2.44 % (24659)------------------------------
% 8.73/2.45 % (24674)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_24138 for (2990ds/4436Mi)
% 8.73/2.46 % (24648)Instruction limit reached!
% 8.73/2.46 % (24648)------------------------------
% 8.73/2.46 % (24648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.46 % (24648)Termination reason: Unknown
% 8.73/2.46 % (24648)Termination phase: Saturation
% 8.73/2.46
% 8.73/2.46 % (24648)Memory used [KB]: 7419
% 8.73/2.46 % (24648)Time elapsed: 0.060 s
% 8.73/2.46 % (24648)Instructions burned: 207 (million)
% 8.73/2.46 % (24648)------------------------------
% 8.73/2.46 % (24648)------------------------------
% 8.73/2.47 % (24686)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_24138 for (2990ds/1539Mi)
% 8.73/2.48 % (24647)Instruction limit reached!
% 8.73/2.48 % (24647)------------------------------
% 8.73/2.48 % (24647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.48 % (24647)Termination reason: Unknown
% 8.73/2.48 % (24647)Termination phase: Saturation
% 8.73/2.48
% 8.73/2.48 % (24647)Memory used [KB]: 7675
% 8.73/2.48 % (24647)Time elapsed: 0.076 s
% 8.73/2.48 % (24647)Instructions burned: 269 (million)
% 8.73/2.48 % (24647)------------------------------
% 8.73/2.48 % (24647)------------------------------
% 8.73/2.48 % (24689)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_24138 for (2990ds/408Mi)
% 8.73/2.49 % (24640)Instruction limit reached!
% 8.73/2.49 % (24640)------------------------------
% 8.73/2.49 % (24640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.49 % (24640)Termination reason: Unknown
% 8.73/2.49 % (24640)Termination phase: Saturation
% 8.73/2.49
% 8.73/2.49 % (24640)Memory used [KB]: 8315
% 8.73/2.49 % (24640)Time elapsed: 0.114 s
% 8.73/2.49 % (24640)Instructions burned: 370 (million)
% 8.73/2.49 % (24640)------------------------------
% 8.73/2.49 % (24640)------------------------------
% 9.10/2.50 % (24694)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_24138 for (2990ds/5205Mi)
% 9.10/2.57 % (24594)Instruction limit reached!
% 9.10/2.57 % (24594)------------------------------
% 9.10/2.57 % (24594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.57 % (24594)Termination reason: Unknown
% 9.10/2.57 % (24594)Termination phase: Saturation
% 9.10/2.57
% 9.10/2.57 % (24594)Memory used [KB]: 9850
% 9.10/2.57 % (24594)Time elapsed: 0.302 s
% 9.10/2.57 % (24594)Instructions burned: 987 (million)
% 9.10/2.57 % (24594)------------------------------
% 9.10/2.57 % (24594)------------------------------
% 9.10/2.58 % (24695)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_24138 for (2989ds/1913Mi)
% 9.41/2.60 % (24689)Instruction limit reached!
% 9.41/2.60 % (24689)------------------------------
% 9.41/2.60 % (24689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.60 % (24689)Termination reason: Unknown
% 9.41/2.60 % (24689)Termination phase: Saturation
% 9.41/2.60
% 9.41/2.60 % (24689)Memory used [KB]: 9338
% 9.41/2.60 % (24689)Time elapsed: 0.119 s
% 9.41/2.60 % (24689)Instructions burned: 409 (million)
% 9.41/2.60 % (24689)------------------------------
% 9.41/2.60 % (24689)------------------------------
% 9.41/2.61 % (24696)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_24138 for (2989ds/4350Mi)
% 9.41/2.62 % (24624)Instruction limit reached!
% 9.41/2.62 % (24624)------------------------------
% 9.41/2.62 % (24624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.62 % (24624)Termination reason: Unknown
% 9.41/2.62 % (24624)Termination phase: Saturation
% 9.41/2.62
% 9.41/2.62 % (24624)Memory used [KB]: 8059
% 9.41/2.62 % (24624)Time elapsed: 0.284 s
% 9.41/2.62 % (24624)Instructions burned: 923 (million)
% 9.41/2.62 % (24624)------------------------------
% 9.41/2.62 % (24624)------------------------------
% 9.41/2.63 % (24697)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_24138 for (2989ds/68Mi)
% 9.41/2.65 % (24697)Instruction limit reached!
% 9.41/2.65 % (24697)------------------------------
% 9.41/2.65 % (24697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.65 % (24697)Termination reason: Unknown
% 9.41/2.65 % (24697)Termination phase: SInE selection
% 9.41/2.65
% 9.41/2.65 % (24697)Memory used [KB]: 2046
% 9.41/2.65 % (24697)Time elapsed: 0.022 s
% 9.41/2.65 % (24697)Instructions burned: 70 (million)
% 9.41/2.65 % (24697)------------------------------
% 9.41/2.65 % (24697)------------------------------
% 9.41/2.66 % (24698)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_24138 for (2988ds/358Mi)
% 9.86/2.72 % (24646)Instruction limit reached!
% 9.86/2.72 % (24646)------------------------------
% 9.86/2.72 % (24646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.72 % (24646)Termination reason: Unknown
% 9.86/2.72 % (24646)Termination phase: Saturation
% 9.86/2.72
% 9.86/2.72 % (24646)Memory used [KB]: 8955
% 9.86/2.72 % (24646)Time elapsed: 0.317 s
% 9.86/2.72 % (24646)Instructions burned: 1023 (million)
% 9.86/2.72 % (24646)------------------------------
% 9.86/2.72 % (24646)------------------------------
% 9.86/2.73 % (24699)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_24138 for (2988ds/31Mi)
% 9.86/2.74 % (24699)Instruction limit reached!
% 9.86/2.74 % (24699)------------------------------
% 9.86/2.74 % (24699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.74 % (24699)Termination reason: Unknown
% 9.86/2.74 % (24699)Termination phase: shuffling
% 9.86/2.74
% 9.86/2.74 % (24699)Memory used [KB]: 1918
% 9.86/2.74 % (24699)Time elapsed: 0.011 s
% 9.86/2.74 % (24699)Instructions burned: 31 (million)
% 9.86/2.74 % (24699)------------------------------
% 9.86/2.74 % (24699)------------------------------
% 9.86/2.75 % (24700)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_24138 for (2988ds/279Mi)
% 9.86/2.77 % (24698)Instruction limit reached!
% 9.86/2.77 % (24698)------------------------------
% 9.86/2.77 % (24698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.77 % (24698)Termination reason: Unknown
% 9.86/2.77 % (24698)Termination phase: Saturation
% 9.86/2.77
% 9.86/2.77 % (24698)Memory used [KB]: 7675
% 9.86/2.77 % (24698)Time elapsed: 0.112 s
% 9.86/2.77 % (24698)Instructions burned: 358 (million)
% 9.86/2.77 % (24698)------------------------------
% 9.86/2.77 % (24698)------------------------------
% 9.86/2.78 % (24701)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_24138 for (2987ds/258Mi)
% 10.34/2.80 % (24700)Refutation not found, incomplete strategy
% 10.34/2.80 % (24700)------------------------------
% 10.34/2.80 % (24700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.34/2.80 % (24700)Termination reason: Refutation not found, incomplete strategy
% 10.34/2.80
% 10.34/2.80
% 10.34/2.80 % (24700)Memory used [KB]: 7675
% 10.34/2.80 % (24700)Time elapsed: 0.059 s
% 10.34/2.80 % (24700)Instructions burned: 207 (million)
% 10.34/2.80 % (24700)------------------------------
% 10.34/2.80 % (24700)------------------------------
% 10.34/2.81 % (24702)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_24138 for (2987ds/26Mi)
% 10.34/2.82 % (24702)Instruction limit reached!
% 10.34/2.82 % (24702)------------------------------
% 10.34/2.82 % (24702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.34/2.82 % (24702)Termination reason: Unknown
% 10.34/2.82 % (24702)Termination phase: shuffling
% 10.34/2.82
% 10.34/2.82 % (24702)Memory used [KB]: 2046
% 10.34/2.82 % (24702)Time elapsed: 0.008 s
% 10.34/2.82 % (24702)Instructions burned: 26 (million)
% 10.34/2.82 % (24702)------------------------------
% 10.34/2.82 % (24702)------------------------------
% 10.34/2.83 % (24703)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_24138 for (2987ds/995Mi)
% 10.34/2.86 % (24701)Instruction limit reached!
% 10.34/2.86 % (24701)------------------------------
% 10.34/2.86 % (24701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.34/2.86 % (24701)Termination reason: Unknown
% 10.34/2.86 % (24701)Termination phase: Saturation
% 10.34/2.86
% 10.34/2.86 % (24701)Memory used [KB]: 8059
% 10.34/2.86 % (24701)Time elapsed: 0.077 s
% 10.34/2.86 % (24701)Instructions burned: 259 (million)
% 10.34/2.86 % (24701)------------------------------
% 10.34/2.86 % (24701)------------------------------
% 10.34/2.87 % (24704)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_24138 for (2986ds/373Mi)
% 10.51/2.95 % (24686)Instruction limit reached!
% 10.51/2.95 % (24686)------------------------------
% 10.51/2.95 % (24686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.95 % (24686)Termination reason: Unknown
% 10.51/2.95 % (24686)Termination phase: Saturation
% 10.51/2.95
% 10.51/2.95 % (24686)Memory used [KB]: 11257
% 10.51/2.95 % (24686)Time elapsed: 0.474 s
% 10.51/2.95 % (24686)Instructions burned: 1540 (million)
% 10.51/2.95 % (24686)------------------------------
% 10.51/2.95 % (24686)------------------------------
% 10.51/2.96 % (24705)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_24138 for (2985ds/253Mi)
% 10.51/2.97 % (24704)Instruction limit reached!
% 10.51/2.97 % (24704)------------------------------
% 10.51/2.97 % (24704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.97 % (24704)Termination reason: Unknown
% 10.51/2.97 % (24704)Termination phase: Saturation
% 10.51/2.97
% 10.51/2.97 % (24704)Memory used [KB]: 8443
% 10.51/2.97 % (24704)Time elapsed: 0.130 s
% 10.51/2.97 % (24704)Instructions burned: 375 (million)
% 10.51/2.97 % (24704)------------------------------
% 10.51/2.97 % (24704)------------------------------
% 10.51/2.98 % (24706)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_24138 for (2985ds/832Mi)
% 13.35/3.02 % (24705)Instruction limit reached!
% 13.35/3.02 % (24705)------------------------------
% 13.35/3.02 % (24705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.02 % (24705)Termination reason: Unknown
% 13.35/3.02 % (24705)Termination phase: Saturation
% 13.35/3.02
% 13.35/3.02 % (24705)Memory used [KB]: 7547
% 13.35/3.02 % (24705)Time elapsed: 0.070 s
% 13.35/3.02 % (24705)Instructions burned: 255 (million)
% 13.35/3.02 % (24705)------------------------------
% 13.35/3.02 % (24705)------------------------------
% 13.35/3.03 % (24707)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_24138 for (2985ds/668Mi)
% 13.35/3.12 % (24703)Instruction limit reached!
% 13.35/3.12 % (24703)------------------------------
% 13.35/3.12 % (24703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.12 % (24703)Termination reason: Unknown
% 13.35/3.12 % (24703)Termination phase: Saturation
% 13.35/3.12
% 13.35/3.12 % (24703)Memory used [KB]: 9850
% 13.35/3.12 % (24703)Time elapsed: 0.289 s
% 13.35/3.12 % (24703)Instructions burned: 997 (million)
% 13.35/3.12 % (24703)------------------------------
% 13.35/3.12 % (24703)------------------------------
% 13.97/3.13 % (24708)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_24138 for (2984ds/40Mi)
% 13.97/3.14 % (24695)Instruction limit reached!
% 13.97/3.14 % (24695)------------------------------
% 13.97/3.14 % (24695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.97/3.14 % (24695)Termination reason: Unknown
% 13.97/3.14 % (24695)Termination phase: Saturation
% 13.97/3.14
% 13.97/3.14 % (24695)Memory used [KB]: 3837
% 13.97/3.14 % (24695)Time elapsed: 0.565 s
% 13.97/3.14 % (24695)Instructions burned: 1913 (million)
% 13.97/3.14 % (24695)------------------------------
% 13.97/3.14 % (24695)------------------------------
% 13.97/3.14 % (24708)Instruction limit reached!
% 13.97/3.14 % (24708)------------------------------
% 13.97/3.14 % (24708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.97/3.14 % (24708)Termination reason: Unknown
% 13.97/3.14 % (24708)Termination phase: shuffling
% 13.97/3.14
% 13.97/3.14 % (24708)Memory used [KB]: 2302
% 13.97/3.14 % (24708)Time elapsed: 0.013 s
% 13.97/3.14 % (24708)Instructions burned: 41 (million)
% 13.97/3.14 % (24708)------------------------------
% 13.97/3.14 % (24708)------------------------------
% 13.97/3.15 % (24709)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_24138 for (2983ds/294Mi)
% 13.97/3.15 % (24710)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_24138 for (2983ds/187Mi)
% 14.32/3.20 % (24710)Instruction limit reached!
% 14.32/3.20 % (24710)------------------------------
% 14.32/3.20 % (24710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.32/3.20 % (24710)Termination reason: Unknown
% 14.32/3.20 % (24710)Termination phase: Saturation
% 14.32/3.20
% 14.32/3.20 % (24710)Memory used [KB]: 7419
% 14.32/3.20 % (24710)Time elapsed: 0.054 s
% 14.32/3.20 % (24710)Instructions burned: 187 (million)
% 14.32/3.20 % (24710)------------------------------
% 14.32/3.20 % (24710)------------------------------
% 14.32/3.21 % (24709)Refutation not found, incomplete strategy
% 14.32/3.21 % (24709)------------------------------
% 14.32/3.21 % (24709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.32/3.21 % (24709)Termination reason: Refutation not found, incomplete strategy
% 14.32/3.21
% 14.32/3.21
% 14.32/3.21 % (24709)Memory used [KB]: 7547
% 14.32/3.21 % (24709)Time elapsed: 0.062 s
% 14.32/3.21 % (24709)Instructions burned: 226 (million)
% 14.32/3.21 % (24709)------------------------------
% 14.32/3.21 % (24709)------------------------------
% 14.32/3.21 % (24711)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_24138 for (2983ds/371Mi)
% 14.32/3.22 % (24712)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_24138 for (2983ds/1827Mi)
% 14.32/3.23 % (24707)Instruction limit reached!
% 14.32/3.23 % (24707)------------------------------
% 14.32/3.23 % (24707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.32/3.23 % (24707)Termination reason: Unknown
% 14.32/3.23 % (24707)Termination phase: Saturation
% 14.32/3.23
% 14.32/3.23 % (24707)Memory used [KB]: 14200
% 14.32/3.23 % (24707)Time elapsed: 0.194 s
% 14.32/3.23 % (24707)Instructions burned: 668 (million)
% 14.32/3.23 % (24707)------------------------------
% 14.32/3.23 % (24707)------------------------------
% 14.32/3.24 % (24713)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_24138 for (2983ds/70Mi)
% 14.32/3.24 % (24706)Instruction limit reached!
% 14.32/3.24 % (24706)------------------------------
% 14.32/3.24 % (24706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.32/3.24 % (24706)Termination reason: Unknown
% 14.32/3.24 % (24706)Termination phase: Saturation
% 14.32/3.24
% 14.32/3.24 % (24706)Memory used [KB]: 9210
% 14.32/3.24 % (24706)Time elapsed: 0.255 s
% 14.32/3.24 % (24706)Instructions burned: 833 (million)
% 14.32/3.24 % (24706)------------------------------
% 14.32/3.24 % (24706)------------------------------
% 14.32/3.25 % (24714)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_24138 for (2982ds/316Mi)
% 14.32/3.26 % (24713)Instruction limit reached!
% 14.32/3.26 % (24713)------------------------------
% 14.32/3.26 % (24713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.32/3.26 % (24713)Termination reason: Unknown
% 14.32/3.26 % (24713)Termination phase: Property scanning
% 14.32/3.26
% 14.32/3.26 % (24713)Memory used [KB]: 2686
% 14.32/3.26 % (24713)Time elapsed: 0.021 s
% 14.32/3.26 % (24713)Instructions burned: 71 (million)
% 14.32/3.26 % (24713)------------------------------
% 14.32/3.26 % (24713)------------------------------
% 14.32/3.27 % (24715)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_24138 for (2982ds/932Mi)
% 15.03/3.33 % (24711)Instruction limit reached!
% 15.03/3.33 % (24711)------------------------------
% 15.03/3.33 % (24711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.03/3.33 % (24711)Termination reason: Unknown
% 15.03/3.33 % (24711)Termination phase: Saturation
% 15.03/3.33
% 15.03/3.33 % (24711)Memory used [KB]: 8571
% 15.03/3.33 % (24711)Time elapsed: 0.114 s
% 15.03/3.33 % (24711)Instructions burned: 373 (million)
% 15.03/3.33 % (24711)------------------------------
% 15.03/3.33 % (24711)------------------------------
% 15.03/3.33 % (24714)Refutation not found, incomplete strategy
% 15.03/3.33 % (24714)------------------------------
% 15.03/3.33 % (24714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.03/3.33 % (24714)Termination reason: Refutation not found, incomplete strategy
% 15.03/3.33
% 15.03/3.33
% 15.03/3.33 % (24714)Memory used [KB]: 7931
% 15.03/3.33 % (24714)Time elapsed: 0.101 s
% 15.03/3.33 % (24714)Instructions burned: 292 (million)
% 15.03/3.33 % (24714)------------------------------
% 15.03/3.33 % (24714)------------------------------
% 15.03/3.34 % (24716)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_24138 for (2982ds/4714Mi)
% 15.03/3.34 % (24717)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_24138 for (2982ds/8250Mi)
% 15.54/3.43 % (24716)Refutation not found, incomplete strategy
% 15.54/3.43 % (24716)------------------------------
% 15.54/3.43 % (24716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.43 % (24716)Termination reason: Refutation not found, incomplete strategy
% 15.54/3.43
% 15.54/3.43
% 15.54/3.43 % (24716)Memory used [KB]: 8059
% 15.54/3.43 % (24716)Time elapsed: 0.093 s
% 15.54/3.43 % (24716)Instructions burned: 329 (million)
% 15.54/3.43 % (24716)------------------------------
% 15.54/3.43 % (24716)------------------------------
% 15.54/3.44 % (24718)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_24138 for (2981ds/770Mi)
% 15.94/3.54 % (24715)Instruction limit reached!
% 15.94/3.54 % (24715)------------------------------
% 15.94/3.54 % (24715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.94/3.54 % (24715)Termination reason: Unknown
% 15.94/3.54 % (24715)Termination phase: Saturation
% 15.94/3.54
% 15.94/3.54 % (24715)Memory used [KB]: 11769
% 15.94/3.54 % (24715)Time elapsed: 0.294 s
% 15.94/3.54 % (24715)Instructions burned: 934 (million)
% 15.94/3.54 % (24715)------------------------------
% 15.94/3.54 % (24715)------------------------------
% 15.94/3.55 % (24719)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_24138 for (2979ds/794Mi)
% 16.52/3.67 % (24718)Instruction limit reached!
% 16.52/3.67 % (24718)------------------------------
% 16.52/3.67 % (24718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/3.67 % (24718)Termination reason: Unknown
% 16.52/3.67 % (24718)Termination phase: Saturation
% 16.52/3.67
% 16.52/3.67 % (24718)Memory used [KB]: 9978
% 16.52/3.67 % (24718)Time elapsed: 0.253 s
% 16.52/3.67 % (24718)Instructions burned: 772 (million)
% 16.52/3.67 % (24718)------------------------------
% 16.52/3.67 % (24718)------------------------------
% 16.52/3.68 % (24720)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_24138 for (2978ds/464Mi)
% 17.07/3.72 % (24712)Instruction limit reached!
% 17.07/3.72 % (24712)------------------------------
% 17.07/3.72 % (24712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.72 % (24712)Termination reason: Unknown
% 17.07/3.72 % (24712)Termination phase: Saturation
% 17.07/3.72
% 17.07/3.72 % (24712)Memory used [KB]: 9850
% 17.07/3.72 % (24712)Time elapsed: 0.504 s
% 17.07/3.72 % (24712)Instructions burned: 1830 (million)
% 17.07/3.72 % (24712)------------------------------
% 17.07/3.72 % (24712)------------------------------
% 17.07/3.73 % (24721)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_24138 for (2977ds/1376Mi)
% 17.07/3.79 % (24719)Instruction limit reached!
% 17.07/3.79 % (24719)------------------------------
% 17.07/3.79 % (24719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.79 % (24719)Termination reason: Unknown
% 17.07/3.79 % (24719)Termination phase: Saturation
% 17.07/3.79
% 17.07/3.79 % (24719)Memory used [KB]: 6524
% 17.07/3.79 % (24719)Time elapsed: 0.239 s
% 17.07/3.79 % (24719)Instructions burned: 794 (million)
% 17.07/3.79 % (24719)------------------------------
% 17.07/3.79 % (24719)------------------------------
% 17.07/3.80 % (24734)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_24138 for (2977ds/906Mi)
% 18.13/3.80 % (24674)Instruction limit reached!
% 18.13/3.80 % (24674)------------------------------
% 18.13/3.80 % (24674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.13/3.80 % (24674)Termination reason: Unknown
% 18.13/3.80 % (24674)Termination phase: Saturation
% 18.13/3.80
% 18.13/3.80 % (24674)Memory used [KB]: 13176
% 18.13/3.80 % (24674)Time elapsed: 1.354 s
% 18.13/3.80 % (24674)Instructions burned: 4436 (million)
% 18.13/3.80 % (24674)------------------------------
% 18.13/3.80 % (24674)------------------------------
% 18.13/3.82 % (24739)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_24138 for (2977ds/434Mi)
% 18.13/3.82 % (24720)Instruction limit reached!
% 18.13/3.82 % (24720)------------------------------
% 18.13/3.82 % (24720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.13/3.82 % (24720)Termination reason: Unknown
% 18.13/3.82 % (24720)Termination phase: Saturation
% 18.13/3.82
% 18.13/3.82 % (24720)Memory used [KB]: 8059
% 18.13/3.82 % (24720)Time elapsed: 0.142 s
% 18.13/3.82 % (24720)Instructions burned: 465 (million)
% 18.13/3.82 % (24720)------------------------------
% 18.13/3.82 % (24720)------------------------------
% 18.13/3.83 % (24740)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_24138 for (2977ds/865Mi)
% 18.13/3.88 % (24696)Instruction limit reached!
% 18.13/3.88 % (24696)------------------------------
% 18.13/3.88 % (24696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.13/3.88 % (24696)Termination reason: Unknown
% 18.13/3.88 % (24696)Termination phase: Saturation
% 18.13/3.88
% 18.13/3.88 % (24696)Memory used [KB]: 13176
% 18.13/3.88 % (24696)Time elapsed: 1.273 s
% 18.13/3.88 % (24696)Instructions burned: 4351 (million)
% 18.13/3.88 % (24696)------------------------------
% 18.13/3.88 % (24696)------------------------------
% 18.13/3.89 % (24741)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_24138 for (2976ds/593Mi)
% 18.51/3.94 % (24739)Instruction limit reached!
% 18.51/3.94 % (24739)------------------------------
% 18.51/3.94 % (24739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.51/3.94 % (24739)Termination reason: Unknown
% 18.51/3.94 % (24739)Termination phase: Saturation
% 18.51/3.94
% 18.51/3.94 % (24739)Memory used [KB]: 8699
% 18.51/3.94 % (24739)Time elapsed: 0.129 s
% 18.51/3.94 % (24739)Instructions burned: 436 (million)
% 18.51/3.94 % (24739)------------------------------
% 18.51/3.94 % (24739)------------------------------
% 18.51/3.95 % (24742)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_24138 for (2975ds/443Mi)
% 20.39/4.05 % (24694)Instruction limit reached!
% 20.39/4.05 % (24694)------------------------------
% 20.39/4.05 % (24694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.39/4.05 % (24694)Termination reason: Unknown
% 20.39/4.05 % (24694)Termination phase: Saturation
% 20.39/4.05
% 20.39/4.05 % (24694)Memory used [KB]: 15223
% 20.39/4.05 % (24694)Time elapsed: 1.551 s
% 20.39/4.05 % (24694)Instructions burned: 5206 (million)
% 20.39/4.05 % (24694)------------------------------
% 20.39/4.05 % (24694)------------------------------
% 20.39/4.06 % (24741)Instruction limit reached!
% 20.39/4.06 % (24741)------------------------------
% 20.39/4.06 % (24741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.39/4.06 % (24741)Termination reason: Unknown
% 20.39/4.06 % (24741)Termination phase: Saturation
% 20.39/4.06
% 20.39/4.06 % (24741)Memory used [KB]: 11001
% 20.39/4.06 % (24741)Time elapsed: 0.164 s
% 20.39/4.06 % (24741)Instructions burned: 594 (million)
% 20.39/4.06 % (24741)------------------------------
% 20.39/4.06 % (24741)------------------------------
% 20.39/4.06 % (24743)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_24138 for (2974ds/594Mi)
% 20.39/4.07 % (24744)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_24138 for (2974ds/327Mi)
% 20.39/4.08 % (24740)Instruction limit reached!
% 20.39/4.08 % (24740)------------------------------
% 20.39/4.08 % (24740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.39/4.08 % (24740)Termination reason: Unknown
% 20.39/4.08 % (24740)Termination phase: Saturation
% 20.39/4.08
% 20.39/4.08 % (24740)Memory used [KB]: 9594
% 20.39/4.08 % (24740)Time elapsed: 0.249 s
% 20.39/4.08 % (24740)Instructions burned: 865 (million)
% 20.39/4.08 % (24740)------------------------------
% 20.39/4.08 % (24740)------------------------------
% 20.39/4.08 % (24742)Instruction limit reached!
% 20.39/4.08 % (24742)------------------------------
% 20.39/4.08 % (24742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.39/4.08 % (24742)Termination reason: Unknown
% 20.39/4.08 % (24742)Termination phase: Saturation
% 20.39/4.08
% 20.39/4.08 % (24742)Memory used [KB]: 8187
% 20.39/4.08 % (24742)Time elapsed: 0.132 s
% 20.39/4.08 % (24742)Instructions burned: 444 (million)
% 20.39/4.08 % (24742)------------------------------
% 20.39/4.08 % (24742)------------------------------
% 20.39/4.09 % (24745)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_24138 for (2974ds/5411Mi)
% 20.39/4.09 % (24746)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_24138 for (2974ds/1762Mi)
% 20.39/4.11 % (24734)Instruction limit reached!
% 20.39/4.11 % (24734)------------------------------
% 20.39/4.11 % (24734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.39/4.11 % (24734)Termination reason: Unknown
% 20.39/4.11 % (24734)Termination phase: Saturation
% 20.39/4.11
% 20.39/4.11 % (24734)Memory used [KB]: 12920
% 20.39/4.11 % (24734)Time elapsed: 0.315 s
% 20.39/4.11 % (24734)Instructions burned: 906 (million)
% 20.39/4.11 % (24734)------------------------------
% 20.39/4.11 % (24734)------------------------------
% 20.39/4.12 % (24747)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_24138 for (2974ds/96Mi)
% 20.90/4.15 % (24747)Instruction limit reached!
% 20.90/4.15 % (24747)------------------------------
% 20.90/4.15 % (24747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.90/4.15 % (24747)Termination reason: Unknown
% 20.90/4.15 % (24747)Termination phase: Property scanning
% 20.90/4.15
% 20.90/4.15 % (24747)Memory used [KB]: 2686
% 20.90/4.15 % (24747)Time elapsed: 0.027 s
% 20.90/4.15 % (24747)Instructions burned: 97 (million)
% 20.90/4.15 % (24747)------------------------------
% 20.90/4.15 % (24747)------------------------------
% 20.90/4.15 % (24721)Instruction limit reached!
% 20.90/4.15 % (24721)------------------------------
% 20.90/4.15 % (24721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.90/4.15 % (24721)Termination reason: Unknown
% 20.90/4.15 % (24721)Termination phase: Saturation
% 20.90/4.15
% 20.90/4.15 % (24721)Memory used [KB]: 13304
% 20.90/4.15 % (24721)Time elapsed: 0.417 s
% 20.90/4.15 % (24721)Instructions burned: 1378 (million)
% 20.90/4.15 % (24721)------------------------------
% 20.90/4.15 % (24721)------------------------------
% 20.90/4.16 % (24748)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_24138 for (2973ds/503Mi)
% 20.90/4.16 % (24749)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_24138 for (2973ds/90Mi)
% 20.90/4.17 % (24744)Instruction limit reached!
% 20.90/4.17 % (24744)------------------------------
% 20.90/4.17 % (24744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.90/4.17 % (24744)Termination reason: Unknown
% 20.90/4.17 % (24744)Termination phase: Saturation
% 20.90/4.17
% 20.90/4.17 % (24744)Memory used [KB]: 8315
% 20.90/4.17 % (24744)Time elapsed: 0.100 s
% 20.90/4.17 % (24744)Instructions burned: 329 (million)
% 20.90/4.17 % (24744)------------------------------
% 20.90/4.17 % (24744)------------------------------
% 20.90/4.18 % (24750)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_24138 for (2973ds/593Mi)
% 20.90/4.19 % (24749)Instruction limit reached!
% 20.90/4.19 % (24749)------------------------------
% 20.90/4.19 % (24749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.90/4.19 % (24749)Termination reason: Unknown
% 20.90/4.19 % (24749)Termination phase: Preprocessing 3
% 20.90/4.19
% 20.90/4.19 % (24749)Memory used [KB]: 2686
% 20.90/4.19 % (24749)Time elapsed: 0.029 s
% 20.90/4.19 % (24749)Instructions burned: 90 (million)
% 20.90/4.19 % (24749)------------------------------
% 20.90/4.19 % (24749)------------------------------
% 21.19/4.20 % (24751)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_24138 for (2973ds/1512Mi)
% 21.19/4.25 % (24743)Instruction limit reached!
% 21.19/4.25 % (24743)------------------------------
% 21.19/4.25 % (24743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.19/4.25 % (24743)Termination reason: Unknown
% 21.19/4.25 % (24743)Termination phase: Saturation
% 21.19/4.25
% 21.19/4.25 % (24743)Memory used [KB]: 7931
% 21.19/4.25 % (24743)Time elapsed: 0.187 s
% 21.19/4.25 % (24743)Instructions burned: 595 (million)
% 21.19/4.25 % (24743)------------------------------
% 21.19/4.25 % (24743)------------------------------
% 21.19/4.26 % (24752)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_24138 for (2972ds/569Mi)
% 21.49/4.31 % (24748)Instruction limit reached!
% 21.49/4.31 % (24748)------------------------------
% 21.49/4.31 % (24748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.31 % (24748)Termination reason: Unknown
% 21.49/4.31 % (24748)Termination phase: Saturation
% 21.49/4.31
% 21.49/4.31 % (24748)Memory used [KB]: 9338
% 21.49/4.31 % (24748)Time elapsed: 0.152 s
% 21.49/4.31 % (24748)Instructions burned: 505 (million)
% 21.49/4.31 % (24748)------------------------------
% 21.49/4.31 % (24748)------------------------------
% 21.49/4.32 % (24753)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_24138 for (2972ds/501Mi)
% 21.49/4.35 % (24750)Instruction limit reached!
% 21.49/4.35 % (24750)------------------------------
% 21.49/4.35 % (24750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.35 % (24750)Termination reason: Unknown
% 21.49/4.35 % (24750)Termination phase: Saturation
% 21.49/4.35
% 21.49/4.35 % (24750)Memory used [KB]: 9083
% 21.49/4.35 % (24750)Time elapsed: 0.179 s
% 21.49/4.35 % (24750)Instructions burned: 593 (million)
% 21.49/4.35 % (24750)------------------------------
% 21.49/4.35 % (24750)------------------------------
% 21.49/4.36 % (24754)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_24138 for (2971ds/562Mi)
% 21.93/4.42 % (24752)Instruction limit reached!
% 21.93/4.42 % (24752)------------------------------
% 21.93/4.42 % (24752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.42 % (24752)Termination reason: Unknown
% 21.93/4.42 % (24752)Termination phase: Saturation
% 21.93/4.42
% 21.93/4.42 % (24752)Memory used [KB]: 8955
% 21.93/4.42 % (24752)Time elapsed: 0.160 s
% 21.93/4.42 % (24752)Instructions burned: 571 (million)
% 21.93/4.42 % (24752)------------------------------
% 21.93/4.42 % (24752)------------------------------
% 21.93/4.43 % (24755)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_24138 for (2971ds/406Mi)
% 21.93/4.46 % (24753)Instruction limit reached!
% 21.93/4.46 % (24753)------------------------------
% 21.93/4.46 % (24753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.46 % (24753)Termination reason: Unknown
% 21.93/4.46 % (24753)Termination phase: Saturation
% 21.93/4.46
% 21.93/4.46 % (24753)Memory used [KB]: 9594
% 21.93/4.46 % (24753)Time elapsed: 0.148 s
% 21.93/4.46 % (24753)Instructions burned: 501 (million)
% 21.93/4.46 % (24753)------------------------------
% 21.93/4.46 % (24753)------------------------------
% 21.93/4.47 % (24756)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_24138 for (2970ds/582Mi)
% 22.37/4.52 % (24754)Instruction limit reached!
% 22.37/4.52 % (24754)------------------------------
% 22.37/4.52 % (24754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.37/4.52 % (24754)Termination reason: Unknown
% 22.37/4.52 % (24754)Termination phase: Saturation
% 22.37/4.52
% 22.37/4.52 % (24754)Memory used [KB]: 9083
% 22.37/4.52 % (24754)Time elapsed: 0.161 s
% 22.37/4.52 % (24754)Instructions burned: 562 (million)
% 22.37/4.52 % (24754)------------------------------
% 22.37/4.52 % (24754)------------------------------
% 22.37/4.53 % (24757)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_24138 for (2970ds/456Mi)
% 22.37/4.55 % (24755)Instruction limit reached!
% 22.37/4.55 % (24755)------------------------------
% 22.37/4.55 % (24755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.37/4.55 % (24755)Termination reason: Unknown
% 22.37/4.55 % (24755)Termination phase: Saturation
% 22.37/4.55
% 22.37/4.55 % (24755)Memory used [KB]: 8571
% 22.37/4.55 % (24755)Time elapsed: 0.122 s
% 22.37/4.55 % (24755)Instructions burned: 406 (million)
% 22.37/4.55 % (24755)------------------------------
% 22.37/4.55 % (24755)------------------------------
% 22.37/4.56 % (24758)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_24138 for (2969ds/393Mi)
% 22.37/4.57 % (24746)Instruction limit reached!
% 22.37/4.57 % (24746)------------------------------
% 22.37/4.57 % (24746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.37/4.57 % (24746)Termination reason: Unknown
% 22.37/4.57 % (24746)Termination phase: Saturation
% 22.37/4.57
% 22.37/4.57 % (24746)Memory used [KB]: 10490
% 22.37/4.57 % (24746)Time elapsed: 0.480 s
% 22.37/4.57 % (24746)Instructions burned: 1763 (million)
% 22.37/4.57 % (24746)------------------------------
% 22.37/4.57 % (24746)------------------------------
% 22.37/4.58 % (24759)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_24138 for (2969ds/1335Mi)
% 23.26/4.65 % (24756)Instruction limit reached!
% 23.26/4.65 % (24756)------------------------------
% 23.26/4.65 % (24756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.26/4.65 % (24756)Termination reason: Unknown
% 23.26/4.65 % (24756)Termination phase: Saturation
% 23.26/4.65
% 23.26/4.65 % (24756)Memory used [KB]: 8059
% 23.26/4.65 % (24756)Time elapsed: 0.179 s
% 23.26/4.65 % (24756)Instructions burned: 582 (million)
% 23.26/4.65 % (24756)------------------------------
% 23.26/4.65 % (24756)------------------------------
% 23.26/4.66 % (24751)Instruction limit reached!
% 23.26/4.66 % (24751)------------------------------
% 23.26/4.66 % (24751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.26/4.66 % (24751)Termination reason: Unknown
% 23.26/4.66 % (24751)Termination phase: Saturation
% 23.26/4.66
% 23.26/4.66 % (24751)Memory used [KB]: 9466
% 23.26/4.66 % (24751)Time elapsed: 0.462 s
% 23.26/4.66 % (24751)Instructions burned: 1512 (million)
% 23.26/4.66 % (24751)------------------------------
% 23.26/4.66 % (24751)------------------------------
% 23.26/4.66 % (24760)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_24138 for (2968ds/3373Mi)
% 23.26/4.67 % (24761)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_24138 for (2968ds/474Mi)
% 23.26/4.67 % (24758)Instruction limit reached!
% 23.26/4.67 % (24758)------------------------------
% 23.26/4.67 % (24758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.26/4.67 % (24758)Termination reason: Unknown
% 23.26/4.67 % (24758)Termination phase: Saturation
% 23.26/4.67
% 23.26/4.67 % (24758)Memory used [KB]: 7931
% 23.26/4.67 % (24758)Time elapsed: 0.111 s
% 23.26/4.67 % (24758)Instructions burned: 395 (million)
% 23.26/4.67 % (24758)------------------------------
% 23.26/4.67 % (24758)------------------------------
% 23.26/4.67 % (24757)Instruction limit reached!
% 23.26/4.67 % (24757)------------------------------
% 23.26/4.67 % (24757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.26/4.67 % (24757)Termination reason: Unknown
% 23.26/4.67 % (24757)Termination phase: Saturation
% 23.26/4.67
% 23.26/4.67 % (24757)Memory used [KB]: 9210
% 23.26/4.67 % (24757)Time elapsed: 0.138 s
% 23.26/4.67 % (24757)Instructions burned: 458 (million)
% 23.26/4.67 % (24757)------------------------------
% 23.26/4.67 % (24757)------------------------------
% 23.26/4.68 % (24762)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_24138 for (2968ds/157Mi)
% 23.26/4.68 % (24763)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_24138 for (2968ds/590Mi)
% 24.28/4.72 % (24762)Instruction limit reached!
% 24.28/4.72 % (24762)------------------------------
% 24.28/4.72 % (24762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.28/4.72 % (24762)Termination reason: Unknown
% 24.28/4.72 % (24762)Termination phase: Property scanning
% 24.28/4.72
% 24.28/4.72 % (24762)Memory used [KB]: 2814
% 24.28/4.72 % (24762)Time elapsed: 0.045 s
% 24.28/4.72 % (24762)Instructions burned: 158 (million)
% 24.28/4.72 % (24762)------------------------------
% 24.28/4.72 % (24762)------------------------------
% 24.28/4.73 % (24764)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_24138 for (2968ds/104Mi)
% 24.28/4.76 % (24764)Instruction limit reached!
% 24.28/4.76 % (24764)------------------------------
% 24.28/4.76 % (24764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.28/4.76 % (24764)Termination reason: Unknown
% 24.28/4.76 % (24764)Termination phase: Property scanning
% 24.28/4.76
% 24.28/4.76 % (24764)Memory used [KB]: 2814
% 24.28/4.76 % (24764)Time elapsed: 0.034 s
% 24.28/4.76 % (24764)Instructions burned: 106 (million)
% 24.28/4.76 % (24764)------------------------------
% 24.28/4.76 % (24764)------------------------------
% 24.28/4.77 % (24765)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_24138 for (2967ds/414Mi)
% 24.28/4.78 % (24717)Instruction limit reached!
% 24.28/4.78 % (24717)------------------------------
% 24.28/4.78 % (24717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.28/4.78 % (24717)Termination reason: Unknown
% 24.28/4.78 % (24717)Termination phase: Saturation
% 24.28/4.78
% 24.28/4.78 % (24717)Memory used [KB]: 8955
% 24.28/4.78 % (24717)Time elapsed: 1.462 s
% 24.28/4.78 % (24717)Instructions burned: 8256 (million)
% 24.28/4.78 % (24717)------------------------------
% 24.28/4.78 % (24717)------------------------------
% 24.28/4.79 % (24766)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_24138 for (2967ds/715Mi)
% 24.46/4.81 % (24761)Instruction limit reached!
% 24.46/4.81 % (24761)------------------------------
% 24.46/4.81 % (24761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.46/4.81 % (24761)Termination reason: Unknown
% 24.46/4.81 % (24761)Termination phase: Saturation
% 24.46/4.81
% 24.46/4.81 % (24761)Memory used [KB]: 8699
% 24.46/4.81 % (24761)Time elapsed: 0.140 s
% 24.46/4.81 % (24761)Instructions burned: 475 (million)
% 24.46/4.81 % (24761)------------------------------
% 24.46/4.81 % (24761)------------------------------
% 24.46/4.82 % (24767)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_24138 for (2967ds/961Mi)
% 24.46/4.85 % (24763)Instruction limit reached!
% 24.46/4.85 % (24763)------------------------------
% 24.46/4.85 % (24763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.46/4.85 % (24763)Termination reason: Unknown
% 24.46/4.85 % (24763)Termination phase: Saturation
% 24.46/4.85
% 24.46/4.85 % (24763)Memory used [KB]: 8187
% 24.46/4.85 % (24763)Time elapsed: 0.170 s
% 24.46/4.85 % (24763)Instructions burned: 591 (million)
% 24.46/4.85 % (24763)------------------------------
% 24.46/4.85 % (24763)------------------------------
% 24.46/4.86 % (24768)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_24138 for (2966ds/1213Mi)
% 24.46/4.88 % (24765)Instruction limit reached!
% 24.46/4.88 % (24765)------------------------------
% 24.46/4.88 % (24765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.46/4.88 % (24765)Termination reason: Unknown
% 24.46/4.88 % (24765)Termination phase: Saturation
% 24.46/4.88
% 24.46/4.88 % (24765)Memory used [KB]: 8571
% 24.46/4.88 % (24765)Time elapsed: 0.112 s
% 24.46/4.88 % (24765)Instructions burned: 414 (million)
% 24.46/4.88 % (24765)------------------------------
% 24.46/4.88 % (24765)------------------------------
% 24.46/4.89 % (24769)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_24138 for (2966ds/1979Mi)
% 24.93/4.97 % (24759)Instruction limit reached!
% 24.93/4.97 % (24759)------------------------------
% 24.93/4.97 % (24759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.93/4.97 % (24759)Termination reason: Unknown
% 24.93/4.97 % (24759)Termination phase: Saturation
% 24.93/4.97
% 24.93/4.97 % (24759)Memory used [KB]: 10106
% 24.93/4.97 % (24759)Time elapsed: 0.391 s
% 24.93/4.97 % (24759)Instructions burned: 1335 (million)
% 24.93/4.97 % (24759)------------------------------
% 24.93/4.97 % (24759)------------------------------
% 24.93/4.98 % (24770)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_24138 for (2965ds/481Mi)
% 24.93/5.00 % (24766)Instruction limit reached!
% 24.93/5.00 % (24766)------------------------------
% 24.93/5.00 % (24766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.93/5.00 % (24766)Termination reason: Unknown
% 24.93/5.00 % (24766)Termination phase: Saturation
% 24.93/5.00
% 24.93/5.00 % (24766)Memory used [KB]: 4221
% 24.93/5.00 % (24766)Time elapsed: 0.240 s
% 24.93/5.00 % (24766)Instructions burned: 715 (million)
% 24.93/5.00 % (24766)------------------------------
% 24.93/5.00 % (24766)------------------------------
% 24.93/5.01 % (24771)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_24138 for (2965ds/783Mi)
% 27.41/5.11 % (24767)Instruction limit reached!
% 27.41/5.11 % (24767)------------------------------
% 27.41/5.11 % (24767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.41/5.11 % (24767)Termination reason: Unknown
% 27.41/5.11 % (24767)Termination phase: Saturation
% 27.41/5.11
% 27.41/5.11 % (24767)Memory used [KB]: 8059
% 27.41/5.11 % (24767)Time elapsed: 0.318 s
% 27.41/5.11 % (24767)Instructions burned: 963 (million)
% 27.41/5.11 % (24767)------------------------------
% 27.41/5.11 % (24767)------------------------------
% 27.41/5.12 % (24772)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_24138 for (2964ds/432Mi)
% 27.41/5.12 % (24770)Instruction limit reached!
% 27.41/5.12 % (24770)------------------------------
% 27.41/5.12 % (24770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.41/5.12 % (24770)Termination reason: Unknown
% 27.41/5.12 % (24770)Termination phase: Saturation
% 27.41/5.12
% 27.41/5.12 % (24770)Memory used [KB]: 8187
% 27.41/5.12 % (24770)Time elapsed: 0.167 s
% 27.41/5.12 % (24770)Instructions burned: 483 (million)
% 27.41/5.12 % (24770)------------------------------
% 27.41/5.12 % (24770)------------------------------
% 27.86/5.14 % (24773)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_24138 for (2964ds/1670Mi)
% 28.30/5.23 % (24768)Instruction limit reached!
% 28.30/5.23 % (24768)------------------------------
% 28.30/5.23 % (24768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.23 % (24768)Termination reason: Unknown
% 28.30/5.23 % (24768)Termination phase: Saturation
% 28.30/5.23
% 28.30/5.23 % (24768)Memory used [KB]: 9850
% 28.30/5.23 % (24768)Time elapsed: 0.396 s
% 28.30/5.23 % (24768)Instructions burned: 1213 (million)
% 28.30/5.23 % (24768)------------------------------
% 28.30/5.23 % (24768)------------------------------
% 28.30/5.24 % (24774)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_24138 for (2962ds/90Mi)
% 28.30/5.25 % (24771)Instruction limit reached!
% 28.30/5.25 % (24771)------------------------------
% 28.30/5.25 % (24771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.25 % (24771)Termination reason: Unknown
% 28.30/5.25 % (24771)Termination phase: Saturation
% 28.30/5.25
% 28.30/5.25 % (24771)Memory used [KB]: 9338
% 28.30/5.25 % (24771)Time elapsed: 0.235 s
% 28.30/5.25 % (24771)Instructions burned: 786 (million)
% 28.30/5.25 % (24771)------------------------------
% 28.30/5.25 % (24771)------------------------------
% 28.30/5.25 % (24772)Instruction limit reached!
% 28.30/5.25 % (24772)------------------------------
% 28.30/5.25 % (24772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.25 % (24772)Termination reason: Unknown
% 28.30/5.25 % (24772)Termination phase: Saturation
% 28.30/5.25
% 28.30/5.25 % (24772)Memory used [KB]: 8187
% 28.30/5.25 % (24772)Time elapsed: 0.133 s
% 28.30/5.25 % (24772)Instructions burned: 434 (million)
% 28.30/5.25 % (24772)------------------------------
% 28.30/5.25 % (24772)------------------------------
% 28.30/5.26 % (24775)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_24138 for (2962ds/346Mi)
% 28.30/5.26 % (24776)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_24138 for (2962ds/401Mi)
% 28.30/5.27 % (24774)Instruction limit reached!
% 28.30/5.27 % (24774)------------------------------
% 28.30/5.27 % (24774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.27 % (24774)Termination reason: Unknown
% 28.30/5.27 % (24774)Termination phase: Preprocessing 3
% 28.30/5.27
% 28.30/5.27 % (24774)Memory used [KB]: 2686
% 28.30/5.27 % (24774)Time elapsed: 0.029 s
% 28.30/5.27 % (24774)Instructions burned: 92 (million)
% 28.30/5.27 % (24774)------------------------------
% 28.30/5.27 % (24774)------------------------------
% 28.30/5.28 % (24777)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_24138 for (2962ds/6454Mi)
% 29.06/5.36 % (24775)Instruction limit reached!
% 29.06/5.36 % (24775)------------------------------
% 29.06/5.36 % (24775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/5.36 % (24775)Termination reason: Unknown
% 29.06/5.36 % (24775)Termination phase: Saturation
% 29.06/5.36
% 29.06/5.36 % (24775)Memory used [KB]: 7931
% 29.06/5.36 % (24775)Time elapsed: 0.102 s
% 29.06/5.36 % (24775)Instructions burned: 347 (million)
% 29.06/5.36 % (24775)------------------------------
% 29.06/5.36 % (24775)------------------------------
% 29.06/5.37 % (24778)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_24138 for (2961ds/283Mi)
% 29.06/5.37 % (24776)Instruction limit reached!
% 29.06/5.37 % (24776)------------------------------
% 29.06/5.37 % (24776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/5.37 % (24776)Termination reason: Unknown
% 29.06/5.37 % (24776)Termination phase: Saturation
% 29.06/5.37
% 29.06/5.37 % (24776)Memory used [KB]: 8955
% 29.06/5.37 % (24776)Time elapsed: 0.112 s
% 29.06/5.37 % (24776)Instructions burned: 401 (million)
% 29.06/5.37 % (24776)------------------------------
% 29.06/5.37 % (24776)------------------------------
% 29.06/5.38 % (24779)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_24138 for (2961ds/865Mi)
% 29.60/5.45 % (24778)Instruction limit reached!
% 29.60/5.45 % (24778)------------------------------
% 29.60/5.45 % (24778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.60/5.45 % (24778)Termination reason: Unknown
% 29.60/5.45 % (24778)Termination phase: Saturation
% 29.60/5.45
% 29.60/5.45 % (24778)Memory used [KB]: 8059
% 29.60/5.45 % (24778)Time elapsed: 0.085 s
% 29.60/5.45 % (24778)Instructions burned: 285 (million)
% 29.60/5.45 % (24778)------------------------------
% 29.60/5.45 % (24778)------------------------------
% 29.60/5.46 % (24769)Instruction limit reached!
% 29.60/5.46 % (24769)------------------------------
% 29.60/5.46 % (24769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.60/5.46 % (24769)Termination reason: Unknown
% 29.60/5.46 % (24769)Termination phase: Saturation
% 29.60/5.46
% 29.60/5.46 % (24769)Memory used [KB]: 9466
% 29.60/5.46 % (24769)Time elapsed: 0.586 s
% 29.60/5.46 % (24769)Instructions burned: 1980 (million)
% 29.60/5.46 % (24769)------------------------------
% 29.60/5.46 % (24769)------------------------------
% 29.60/5.46 % (24780)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_24138 for (2960ds/4528Mi)
% 29.60/5.47 % (24781)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_24138 for (2960ds/1001Mi)
% 30.16/5.65 % (24779)Instruction limit reached!
% 30.16/5.65 % (24779)------------------------------
% 30.16/5.65 % (24779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.16/5.65 % (24779)Termination reason: Unknown
% 30.16/5.65 % (24779)Termination phase: Saturation
% 30.16/5.65
% 30.16/5.65 % (24779)Memory used [KB]: 10234
% 30.16/5.65 % (24779)Time elapsed: 0.272 s
% 30.16/5.65 % (24779)Instructions burned: 865 (million)
% 30.16/5.65 % (24779)------------------------------
% 30.16/5.65 % (24779)------------------------------
% 30.16/5.66 % (24760)Instruction limit reached!
% 30.16/5.66 % (24760)------------------------------
% 30.16/5.66 % (24760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.16/5.66 % (24760)Termination reason: Unknown
% 30.16/5.66 % (24760)Termination phase: Saturation
% 30.16/5.66
% 30.16/5.66 % (24760)Memory used [KB]: 11641
% 30.16/5.66 % (24760)Time elapsed: 0.999 s
% 30.16/5.66 % (24760)Instructions burned: 3374 (million)
% 30.16/5.66 % (24760)------------------------------
% 30.16/5.66 % (24760)------------------------------
% 30.16/5.66 % (24782)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_24138 for (2958ds/102Mi)
% 30.16/5.67 % (24783)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_24138 for (2958ds/952Mi)
% 30.16/5.69 % (24782)Instruction limit reached!
% 30.16/5.69 % (24782)------------------------------
% 30.16/5.69 % (24782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.16/5.69 % (24782)Termination reason: Unknown
% 30.16/5.69 % (24782)Termination phase: Preprocessing 1
% 30.16/5.69
% 30.16/5.69 % (24782)Memory used [KB]: 2686
% 30.16/5.69 % (24782)Time elapsed: 0.029 s
% 30.16/5.69 % (24782)Instructions burned: 104 (million)
% 30.16/5.69 % (24782)------------------------------
% 30.16/5.69 % (24782)------------------------------
% 30.65/5.70 % (24773)Instruction limit reached!
% 30.65/5.70 % (24773)------------------------------
% 30.65/5.70 % (24773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.70 % (24773)Termination reason: Unknown
% 30.65/5.70 % (24773)Termination phase: Saturation
% 30.65/5.70
% 30.65/5.70 % (24773)Memory used [KB]: 12537
% 30.65/5.70 % (24773)Time elapsed: 0.559 s
% 30.65/5.70 % (24773)Instructions burned: 1671 (million)
% 30.65/5.70 % (24773)------------------------------
% 30.65/5.70 % (24773)------------------------------
% 30.65/5.70 % (24784)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_24138 for (2958ds/578Mi)
% 30.65/5.71 % (24785)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_24138 for (2958ds/643Mi)
% 30.65/5.71 % (24781)Instruction limit reached!
% 30.65/5.71 % (24781)------------------------------
% 30.65/5.71 % (24781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.71 % (24781)Termination reason: Unknown
% 30.65/5.71 % (24781)Termination phase: Saturation
% 30.65/5.71
% 30.65/5.71 % (24781)Memory used [KB]: 8315
% 30.65/5.71 % (24781)Time elapsed: 0.248 s
% 30.65/5.71 % (24781)Instructions burned: 1005 (million)
% 30.65/5.71 % (24781)------------------------------
% 30.65/5.71 % (24781)------------------------------
% 30.65/5.72 % (24745)Refutation not found, non-redundant clauses discarded% (24745)------------------------------
% 30.65/5.72 % (24745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.72 % (24745)Termination reason: Refutation not found, non-redundant clauses discarded
% 30.65/5.72
% 30.65/5.72 % (24745)Memory used [KB]: 11513
% 30.65/5.72 % (24745)Time elapsed: 1.633 s
% 30.65/5.72 % (24745)Instructions burned: 5407 (million)
% 30.65/5.72 % (24745)------------------------------
% 30.65/5.72 % (24745)------------------------------
% 30.65/5.72 % (24786)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_24138 for (2958ds/865Mi)
% 30.65/5.73 % (24787)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_24138 for (2958ds/1174Mi)
% 31.52/5.87 % (24784)Instruction limit reached!
% 31.52/5.87 % (24784)------------------------------
% 31.52/5.87 % (24784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.52/5.87 % (24784)Termination reason: Unknown
% 31.52/5.87 % (24784)Termination phase: Saturation
% 31.52/5.87
% 31.52/5.87 % (24784)Memory used [KB]: 9338
% 31.52/5.87 % (24784)Time elapsed: 0.166 s
% 31.52/5.87 % (24784)Instructions burned: 580 (million)
% 31.52/5.87 % (24784)------------------------------
% 31.52/5.87 % (24784)------------------------------
% 31.52/5.88 % (24818)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_24138 for (2956ds/644Mi)
% 31.52/5.89 % (24785)Instruction limit reached!
% 31.52/5.89 % (24785)------------------------------
% 31.52/5.89 % (24785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.52/5.89 % (24785)Termination reason: Unknown
% 31.52/5.89 % (24785)Termination phase: Saturation
% 31.52/5.89
% 31.52/5.89 % (24785)Memory used [KB]: 9978
% 31.52/5.89 % (24785)Time elapsed: 0.183 s
% 31.52/5.89 % (24785)Instructions burned: 645 (million)
% 31.52/5.89 % (24785)------------------------------
% 31.52/5.89 % (24785)------------------------------
% 31.89/5.90 % (24819)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_24138 for (2956ds/1201Mi)
% 31.89/5.96 % (24783)Instruction limit reached!
% 31.89/5.96 % (24783)------------------------------
% 31.89/5.96 % (24783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.89/5.96 % (24783)Termination reason: Unknown
% 31.89/5.96 % (24783)Termination phase: Saturation
% 31.89/5.96
% 31.89/5.96 % (24783)Memory used [KB]: 9850
% 31.89/5.96 % (24783)Time elapsed: 0.294 s
% 31.89/5.96 % (24783)Instructions burned: 954 (million)
% 31.89/5.96 % (24783)------------------------------
% 31.89/5.96 % (24783)------------------------------
% 31.89/5.97 % (24821)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_24138 for (2955ds/1046Mi)
% 31.89/5.99 % (24786)Instruction limit reached!
% 31.89/5.99 % (24786)------------------------------
% 31.89/5.99 % (24786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.89/5.99 % (24786)Termination reason: Unknown
% 31.89/5.99 % (24786)Termination phase: Saturation
% 31.89/5.99
% 31.89/5.99 % (24786)Memory used [KB]: 9850
% 31.89/5.99 % (24786)Time elapsed: 0.265 s
% 31.89/5.99 % (24786)Instructions burned: 865 (million)
% 31.89/5.99 % (24786)------------------------------
% 31.89/5.99 % (24786)------------------------------
% 31.89/6.00 % (24822)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_24138 for (2955ds/222Mi)
% 34.32/6.05 % (24822)Instruction limit reached!
% 34.32/6.05 % (24822)------------------------------
% 34.32/6.05 % (24822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.32/6.05 % (24822)Termination reason: Unknown
% 34.32/6.05 % (24822)Termination phase: Saturation
% 34.32/6.05
% 34.32/6.05 % (24822)Memory used [KB]: 7419
% 34.32/6.05 % (24822)Time elapsed: 0.059 s
% 34.32/6.05 % (24822)Instructions burned: 222 (million)
% 34.32/6.05 % (24822)------------------------------
% 34.32/6.05 % (24822)------------------------------
% 34.32/6.06 % (24823)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_24138 for (2954ds/68Mi)
% 34.32/6.07 % (24818)Instruction limit reached!
% 34.32/6.07 % (24818)------------------------------
% 34.32/6.07 % (24818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.32/6.07 % (24818)Termination reason: Unknown
% 34.32/6.07 % (24818)Termination phase: Saturation
% 34.32/6.07
% 34.32/6.07 % (24818)Memory used [KB]: 11257
% 34.32/6.07 % (24818)Time elapsed: 0.198 s
% 34.32/6.07 % (24818)Instructions burned: 645 (million)
% 34.32/6.07 % (24818)------------------------------
% 34.32/6.07 % (24818)------------------------------
% 34.32/6.08 % (24824)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_24138 for (2954ds/454Mi)
% 34.32/6.09 % (24823)Instruction limit reached!
% 34.32/6.09 % (24823)------------------------------
% 34.32/6.09 % (24823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.32/6.09 % (24823)Termination reason: Unknown
% 34.32/6.09 % (24823)Termination phase: SInE selection
% 34.32/6.09
% 34.32/6.09 % (24823)Memory used [KB]: 2046
% 34.32/6.09 % (24823)Time elapsed: 0.023 s
% 34.32/6.09 % (24823)Instructions burned: 71 (million)
% 34.32/6.09 % (24823)------------------------------
% 34.32/6.09 % (24823)------------------------------
% 34.32/6.09 % (24787)Instruction limit reached!
% 34.32/6.09 % (24787)------------------------------
% 34.32/6.09 % (24787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.32/6.09 % (24787)Termination reason: Unknown
% 34.32/6.09 % (24787)Termination phase: Saturation
% 34.32/6.09
% 34.32/6.09 % (24787)Memory used [KB]: 11129
% 34.32/6.09 % (24787)Time elapsed: 0.363 s
% 34.32/6.09 % (24787)Instructions burned: 1175 (million)
% 34.32/6.09 % (24787)------------------------------
% 34.32/6.09 % (24787)------------------------------
% 34.32/6.10 % (24825)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_24138 for (2954ds/360Mi)
% 34.32/6.10 % (24826)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_24138 for (2954ds/157Mi)
% 34.99/6.14 % (24826)Instruction limit reached!
% 34.99/6.14 % (24826)------------------------------
% 34.99/6.14 % (24826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.99/6.14 % (24826)Termination reason: Unknown
% 34.99/6.14 % (24826)Termination phase: Property scanning
% 34.99/6.14
% 34.99/6.14 % (24826)Memory used [KB]: 2814
% 34.99/6.14 % (24826)Time elapsed: 0.044 s
% 34.99/6.14 % (24826)Instructions burned: 160 (million)
% 34.99/6.14 % (24826)------------------------------
% 34.99/6.14 % (24826)------------------------------
% 34.99/6.15 % (24827)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_24138 for (2953ds/5061Mi)
% 34.99/6.20 % (24825)Instruction limit reached!
% 34.99/6.20 % (24825)------------------------------
% 34.99/6.20 % (24825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.99/6.20 % (24825)Termination reason: Unknown
% 34.99/6.20 % (24825)Termination phase: Saturation
% 34.99/6.20
% 34.99/6.20 % (24825)Memory used [KB]: 8699
% 34.99/6.20 % (24825)Time elapsed: 0.101 s
% 34.99/6.20 % (24825)Instructions burned: 363 (million)
% 34.99/6.20 % (24825)------------------------------
% 34.99/6.20 % (24825)------------------------------
% 35.37/6.21 % (24828)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_24138 for (2953ds/2401Mi)
% 35.37/6.21 % (24824)Instruction limit reached!
% 35.37/6.21 % (24824)------------------------------
% 35.37/6.21 % (24824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.37/6.21 % (24824)Termination reason: Unknown
% 35.37/6.21 % (24824)Termination phase: Saturation
% 35.37/6.21
% 35.37/6.21 % (24824)Memory used [KB]: 13432
% 35.37/6.21 % (24824)Time elapsed: 0.129 s
% 35.37/6.21 % (24824)Instructions burned: 455 (million)
% 35.37/6.21 % (24824)------------------------------
% 35.37/6.21 % (24824)------------------------------
% 35.37/6.22 % (24829)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_24138 for (2953ds/5798Mi)
% 35.37/6.28 % (24821)Instruction limit reached!
% 35.37/6.28 % (24821)------------------------------
% 35.37/6.28 % (24821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.37/6.28 % (24821)Termination reason: Unknown
% 35.37/6.28 % (24821)Termination phase: Saturation
% 35.37/6.28
% 35.37/6.28 % (24821)Memory used [KB]: 9594
% 35.37/6.28 % (24821)Time elapsed: 0.305 s
% 35.37/6.28 % (24821)Instructions burned: 1048 (million)
% 35.37/6.28 % (24821)------------------------------
% 35.37/6.28 % (24821)------------------------------
% 35.37/6.29 % (24830)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_24138 for (2952ds/346Mi)
% 36.01/6.30 % (24819)Instruction limit reached!
% 36.01/6.30 % (24819)------------------------------
% 36.01/6.30 % (24819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.01/6.30 % (24819)Termination reason: Unknown
% 36.01/6.30 % (24819)Termination phase: Saturation
% 36.01/6.30
% 36.01/6.30 % (24819)Memory used [KB]: 10234
% 36.01/6.30 % (24819)Time elapsed: 0.400 s
% 36.01/6.30 % (24819)Instructions burned: 1202 (million)
% 36.01/6.30 % (24819)------------------------------
% 36.01/6.30 % (24819)------------------------------
% 36.01/6.31 % (24831)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_24138 for (2952ds/1321Mi)
% 36.01/6.39 % (24830)Instruction limit reached!
% 36.01/6.39 % (24830)------------------------------
% 36.01/6.39 % (24830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.01/6.39 % (24830)Termination reason: Unknown
% 36.01/6.39 % (24830)Termination phase: Saturation
% 36.01/6.39
% 36.01/6.39 % (24830)Memory used [KB]: 7931
% 36.01/6.39 % (24830)Time elapsed: 0.103 s
% 36.01/6.39 % (24830)Instructions burned: 347 (million)
% 36.01/6.39 % (24830)------------------------------
% 36.01/6.39 % (24830)------------------------------
% 36.34/6.40 % (24832)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_24138 for (2951ds/1312Mi)
% 36.95/6.71 % (24831)Instruction limit reached!
% 36.95/6.71 % (24831)------------------------------
% 36.95/6.71 % (24831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.95/6.71 % (24831)Termination reason: Unknown
% 36.95/6.71 % (24831)Termination phase: Saturation
% 36.95/6.71
% 36.95/6.71 % (24831)Memory used [KB]: 8443
% 36.95/6.71 % (24831)Time elapsed: 0.400 s
% 36.95/6.71 % (24831)Instructions burned: 1324 (million)
% 36.95/6.71 % (24831)------------------------------
% 36.95/6.71 % (24831)------------------------------
% 36.95/6.72 % (24833)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_24138 for (2948ds/672Mi)
% 36.95/6.80 % (24832)Instruction limit reached!
% 36.95/6.80 % (24832)------------------------------
% 36.95/6.80 % (24832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.95/6.80 % (24832)Termination reason: Unknown
% 36.95/6.80 % (24832)Termination phase: Saturation
% 36.95/6.80
% 36.95/6.80 % (24832)Memory used [KB]: 10234
% 36.95/6.80 % (24832)Time elapsed: 0.400 s
% 36.95/6.80 % (24832)Instructions burned: 1312 (million)
% 36.95/6.80 % (24832)------------------------------
% 36.95/6.80 % (24832)------------------------------
% 37.55/6.81 % (24834)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_24138 for (2947ds/1897Mi)
% 37.55/6.83 % (24780)Instruction limit reached!
% 37.55/6.83 % (24780)------------------------------
% 37.55/6.83 % (24780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/6.83 % (24780)Termination reason: Unknown
% 37.55/6.83 % (24780)Termination phase: Saturation
% 37.55/6.83
% 37.55/6.83 % (24780)Memory used [KB]: 12537
% 37.55/6.83 % (24780)Time elapsed: 1.367 s
% 37.55/6.83 % (24780)Instructions burned: 4529 (million)
% 37.55/6.83 % (24780)------------------------------
% 37.55/6.83 % (24780)------------------------------
% 37.55/6.84 % (24835)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_24138 for (2947ds/1202Mi)
% 38.10/6.93 % (24833)Instruction limit reached!
% 38.10/6.93 % (24833)------------------------------
% 38.10/6.93 % (24833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.10/6.93 % (24833)Termination reason: Unknown
% 38.10/6.93 % (24833)Termination phase: Saturation
% 38.10/6.93
% 38.10/6.93 % (24833)Memory used [KB]: 8955
% 38.10/6.93 % (24833)Time elapsed: 0.215 s
% 38.10/6.93 % (24833)Instructions burned: 673 (million)
% 38.10/6.93 % (24833)------------------------------
% 38.10/6.93 % (24833)------------------------------
% 38.10/6.94 % (24836)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_24138 for (2946ds/1493Mi)
% 38.10/6.97 % (24828)Instruction limit reached!
% 38.10/6.97 % (24828)------------------------------
% 38.10/6.97 % (24828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.10/6.97 % (24828)Termination reason: Unknown
% 38.10/6.97 % (24828)Termination phase: Saturation
% 38.10/6.97
% 38.10/6.97 % (24828)Memory used [KB]: 8315
% 38.10/6.97 % (24828)Time elapsed: 0.762 s
% 38.10/6.97 % (24828)Instructions burned: 2401 (million)
% 38.10/6.97 % (24828)------------------------------
% 38.10/6.97 % (24828)------------------------------
% 38.10/6.98 % (24837)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_24138 for (2945ds/7679Mi)
% 38.10/7.00 % (24836)Refutation not found, incomplete strategy
% 38.10/7.00 % (24836)------------------------------
% 38.10/7.00 % (24836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.10/7.00 % (24836)Termination reason: Refutation not found, incomplete strategy
% 38.10/7.00
% 38.10/7.00
% 38.10/7.00 % (24836)Memory used [KB]: 7675
% 38.10/7.00 % (24836)Time elapsed: 0.060 s
% 38.10/7.00 % (24836)Instructions burned: 213 (million)
% 38.10/7.00 % (24836)------------------------------
% 38.10/7.00 % (24836)------------------------------
% 38.10/7.01 % (24838)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_24138 for (2945ds/340Mi)
% 41.42/7.11 % (24838)Instruction limit reached!
% 41.42/7.11 % (24838)------------------------------
% 41.42/7.11 % (24838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.42/7.11 % (24838)Termination reason: Unknown
% 41.42/7.11 % (24838)Termination phase: Saturation
% 41.42/7.11
% 41.42/7.11 % (24838)Memory used [KB]: 9210
% 41.42/7.11 % (24838)Time elapsed: 0.099 s
% 41.42/7.11 % (24838)Instructions burned: 340 (million)
% 41.42/7.11 % (24838)------------------------------
% 41.42/7.11 % (24838)------------------------------
% 41.42/7.12 % (24839)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_24138 for (2944ds/3672Mi)
% 42.14/7.19 % (24777)Instruction limit reached!
% 42.14/7.19 % (24777)------------------------------
% 42.14/7.19 % (24777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.14/7.19 % (24777)Termination reason: Unknown
% 42.14/7.19 % (24777)Termination phase: Saturation
% 42.14/7.19
% 42.14/7.19 % (24777)Memory used [KB]: 16886
% 42.14/7.19 % (24777)Time elapsed: 1.911 s
% 42.14/7.19 % (24777)Instructions burned: 6456 (million)
% 42.14/7.19 % (24777)------------------------------
% 42.14/7.19 % (24777)------------------------------
% 42.57/7.20 % (24840)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_24138 for (2943ds/1535Mi)
% 42.57/7.21 % (24835)Instruction limit reached!
% 42.57/7.21 % (24835)------------------------------
% 42.57/7.21 % (24835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.57/7.21 % (24835)Termination reason: Unknown
% 42.57/7.21 % (24835)Termination phase: Saturation
% 42.57/7.21
% 42.57/7.21 % (24835)Memory used [KB]: 6652
% 42.57/7.21 % (24835)Time elapsed: 0.372 s
% 42.57/7.21 % (24835)Instructions burned: 1204 (million)
% 42.57/7.21 % (24835)------------------------------
% 42.57/7.21 % (24835)------------------------------
% 42.57/7.22 % (24841)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_24138 for (2943ds/4637Mi)
% 42.99/7.38 % (24834)Instruction limit reached!
% 42.99/7.38 % (24834)------------------------------
% 42.99/7.38 % (24834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.99/7.38 % (24834)Termination reason: Unknown
% 42.99/7.38 % (24834)Termination phase: Saturation
% 42.99/7.38
% 42.99/7.38 % (24834)Memory used [KB]: 10490
% 42.99/7.38 % (24834)Time elapsed: 0.572 s
% 42.99/7.38 % (24834)Instructions burned: 1897 (million)
% 42.99/7.38 % (24834)------------------------------
% 42.99/7.38 % (24834)------------------------------
% 42.99/7.39 % (24842)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_24138 for (2941ds/3174Mi)
% 44.00/7.66 % (24840)Instruction limit reached!
% 44.00/7.66 % (24840)------------------------------
% 44.00/7.66 % (24840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.00/7.66 % (24840)Termination reason: Unknown
% 44.00/7.66 % (24840)Termination phase: Saturation
% 44.00/7.66
% 44.00/7.66 % (24840)Memory used [KB]: 12792
% 44.00/7.66 % (24840)Time elapsed: 0.463 s
% 44.00/7.66 % (24840)Instructions burned: 1535 (million)
% 44.00/7.66 % (24840)------------------------------
% 44.00/7.66 % (24840)------------------------------
% 44.00/7.67 % (24843)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_24138 for (2938ds/307Mi)
% 44.77/7.70 % (24827)Instruction limit reached!
% 44.77/7.70 % (24827)------------------------------
% 44.77/7.70 % (24827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.77/7.70 % (24827)Termination reason: Unknown
% 44.77/7.70 % (24827)Termination phase: Saturation
% 44.77/7.70
% 44.77/7.70 % (24827)Memory used [KB]: 14200
% 44.77/7.70 % (24827)Time elapsed: 1.547 s
% 44.77/7.70 % (24827)Instructions burned: 5062 (million)
% 44.77/7.70 % (24827)------------------------------
% 44.77/7.70 % (24827)------------------------------
% 44.77/7.71 % (24844)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_24138 for (2938ds/3619Mi)
% 44.77/7.75 % (24843)Instruction limit reached!
% 44.77/7.75 % (24843)------------------------------
% 44.77/7.75 % (24843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.77/7.75 % (24843)Termination reason: Unknown
% 44.77/7.75 % (24843)Termination phase: Saturation
% 44.77/7.75
% 44.77/7.75 % (24843)Memory used [KB]: 7675
% 44.77/7.75 % (24843)Time elapsed: 0.084 s
% 44.77/7.75 % (24843)Instructions burned: 310 (million)
% 44.77/7.75 % (24843)------------------------------
% 44.77/7.75 % (24843)------------------------------
% 44.77/7.76 % (24845)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_24138 for (2937ds/2325Mi)
% 48.45/8.03 % (24829)Instruction limit reached!
% 48.45/8.03 % (24829)------------------------------
% 48.45/8.03 % (24829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.45/8.03 % (24829)Termination reason: Unknown
% 48.45/8.03 % (24829)Termination phase: Saturation
% 48.45/8.03
% 48.45/8.03 % (24829)Memory used [KB]: 9978
% 48.45/8.03 % (24829)Time elapsed: 1.807 s
% 48.45/8.03 % (24829)Instructions burned: 5798 (million)
% 48.45/8.03 % (24829)------------------------------
% 48.45/8.03 % (24829)------------------------------
% 48.45/8.04 % (24846)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_24138 for (2935ds/2341Mi)
% 49.52/8.26 % (24839)Instruction limit reached!
% 49.52/8.26 % (24839)------------------------------
% 49.52/8.26 % (24839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.52/8.26 % (24839)Termination reason: Unknown
% 49.52/8.26 % (24839)Termination phase: Saturation
% 49.52/8.26
% 49.52/8.26 % (24839)Memory used [KB]: 11129
% 49.52/8.26 % (24839)Time elapsed: 1.167 s
% 49.52/8.26 % (24839)Instructions burned: 3672 (million)
% 49.52/8.26 % (24839)------------------------------
% 49.52/8.26 % (24839)------------------------------
% 49.52/8.27 % (24847)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_24138 for (2932ds/7257Mi)
% 50.09/8.37 % (24842)Instruction limit reached!
% 50.09/8.37 % (24842)------------------------------
% 50.09/8.37 % (24842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.09/8.37 % (24842)Termination reason: Unknown
% 50.09/8.37 % (24842)Termination phase: Saturation
% 50.09/8.37
% 50.09/8.37 % (24842)Memory used [KB]: 13688
% 50.09/8.37 % (24842)Time elapsed: 0.979 s
% 50.09/8.37 % (24842)Instructions burned: 3176 (million)
% 50.09/8.37 % (24842)------------------------------
% 50.09/8.37 % (24842)------------------------------
% 50.09/8.38 % (24848)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_24138 for (2931ds/3710Mi)
% 50.58/8.49 % (24845)Instruction limit reached!
% 50.58/8.49 % (24845)------------------------------
% 50.58/8.49 % (24845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.58/8.49 % (24845)Termination reason: Unknown
% 50.58/8.49 % (24845)Termination phase: Saturation
% 50.58/8.49
% 50.58/8.49 % (24845)Memory used [KB]: 11769
% 50.58/8.49 % (24845)Time elapsed: 0.728 s
% 50.58/8.49 % (24845)Instructions burned: 2325 (million)
% 50.58/8.49 % (24845)------------------------------
% 50.58/8.49 % (24845)------------------------------
% 50.98/8.50 % (24849)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_24138 for (2930ds/326Mi)
% 51.27/8.60 % (24849)Instruction limit reached!
% 51.27/8.60 % (24849)------------------------------
% 51.27/8.60 % (24849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.27/8.60 % (24849)Termination reason: Unknown
% 51.27/8.60 % (24849)Termination phase: Saturation
% 51.27/8.60
% 51.27/8.60 % (24849)Memory used [KB]: 8059
% 51.27/8.60 % (24849)Time elapsed: 0.101 s
% 51.27/8.60 % (24849)Instructions burned: 327 (million)
% 51.27/8.60 % (24849)------------------------------
% 51.27/8.60 % (24849)------------------------------
% 51.27/8.61 % (24850)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_24138 for (2929ds/1100Mi)
% 51.27/8.61 % (24841)Instruction limit reached!
% 51.27/8.61 % (24841)------------------------------
% 51.27/8.61 % (24841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.27/8.61 % (24841)Termination reason: Unknown
% 51.27/8.61 % (24841)Termination phase: Saturation
% 51.27/8.61
% 51.27/8.61 % (24841)Memory used [KB]: 17398
% 51.27/8.61 % (24841)Time elapsed: 1.396 s
% 51.27/8.61 % (24841)Instructions burned: 4639 (million)
% 51.27/8.61 % (24841)------------------------------
% 51.27/8.61 % (24841)------------------------------
% 51.27/8.62 % (24851)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_24138 for (2929ds/406Mi)
% 51.61/8.75 % (24851)Instruction limit reached!
% 51.61/8.75 % (24851)------------------------------
% 51.61/8.75 % (24851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.61/8.75 % (24851)Termination reason: Unknown
% 51.61/8.75 % (24851)Termination phase: Saturation
% 51.61/8.75
% 51.61/8.75 % (24851)Memory used [KB]: 8571
% 51.61/8.75 % (24851)Time elapsed: 0.122 s
% 51.61/8.75 % (24851)Instructions burned: 406 (million)
% 51.61/8.75 % (24851)------------------------------
% 51.61/8.75 % (24851)------------------------------
% 51.61/8.75 % (24844)Instruction limit reached!
% 51.61/8.75 % (24844)------------------------------
% 51.61/8.75 % (24844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.61/8.75 % (24844)Termination reason: Unknown
% 51.61/8.75 % (24844)Termination phase: Saturation
% 51.61/8.75
% 51.61/8.75 % (24844)Memory used [KB]: 11385
% 51.61/8.75 % (24844)Time elapsed: 1.042 s
% 51.61/8.75 % (24844)Instructions burned: 3620 (million)
% 51.61/8.75 % (24844)------------------------------
% 51.61/8.75 % (24844)------------------------------
% 51.61/8.76 % (24852)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_24138 for (2927ds/1871Mi)
% 51.61/8.76 % (24853)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_24138 for (2927ds/1194Mi)
% 51.61/8.77 % (24846)Instruction limit reached!
% 51.61/8.77 % (24846)------------------------------
% 51.61/8.77 % (24846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.61/8.77 % (24846)Termination reason: Unknown
% 51.61/8.77 % (24846)Termination phase: Saturation
% 51.61/8.77
% 51.61/8.77 % (24846)Memory used [KB]: 9338
% 51.61/8.77 % (24846)Time elapsed: 0.760 s
% 51.61/8.77 % (24846)Instructions burned: 2342 (million)
% 51.61/8.77 % (24846)------------------------------
% 51.61/8.77 % (24846)------------------------------
% 51.61/8.78 % (24854)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_24138 for (2927ds/474Mi)
% 52.76/8.92 % (24854)Instruction limit reached!
% 52.76/8.92 % (24854)------------------------------
% 52.76/8.92 % (24854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.76/8.92 % (24854)Termination reason: Unknown
% 52.76/8.92 % (24854)Termination phase: Saturation
% 52.76/8.92
% 52.76/8.92 % (24854)Memory used [KB]: 8699
% 52.76/8.92 % (24854)Time elapsed: 0.141 s
% 52.76/8.92 % (24854)Instructions burned: 474 (million)
% 52.76/8.92 % (24854)------------------------------
% 52.76/8.92 % (24854)------------------------------
% 52.76/8.93 % (24855)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_24138 for (2925ds/3115Mi)
% 52.76/8.95 % (24850)Instruction limit reached!
% 52.76/8.95 % (24850)------------------------------
% 52.76/8.95 % (24850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.76/8.95 % (24850)Termination reason: Unknown
% 52.76/8.95 % (24850)Termination phase: Saturation
% 52.76/8.95
% 52.76/8.95 % (24850)Memory used [KB]: 12025
% 52.76/8.95 % (24850)Time elapsed: 0.344 s
% 52.76/8.95 % (24850)Instructions burned: 1100 (million)
% 52.76/8.95 % (24850)------------------------------
% 52.76/8.95 % (24850)------------------------------
% 52.76/8.96 % (24856)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_24138 for (2925ds/831Mi)
% 56.19/9.13 % (24853)Instruction limit reached!
% 56.19/9.13 % (24853)------------------------------
% 56.19/9.13 % (24853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.19/9.13 % (24853)Termination reason: Unknown
% 56.19/9.13 % (24853)Termination phase: Saturation
% 56.19/9.13
% 56.19/9.13 % (24853)Memory used [KB]: 9083
% 56.19/9.13 % (24853)Time elapsed: 0.372 s
% 56.19/9.13 % (24853)Instructions burned: 1195 (million)
% 56.19/9.13 % (24853)------------------------------
% 56.19/9.13 % (24853)------------------------------
% 56.19/9.14 % (24857)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_24138 for (2923ds/1188Mi)
% 56.64/9.21 % (24837)Instruction limit reached!
% 56.64/9.21 % (24837)------------------------------
% 56.64/9.21 % (24837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.64/9.21 % (24837)Termination reason: Unknown
% 56.64/9.21 % (24837)Termination phase: Saturation
% 56.64/9.21
% 56.64/9.21 % (24837)Memory used [KB]: 13816
% 56.64/9.21 % (24837)Time elapsed: 2.232 s
% 56.64/9.21 % (24837)Instructions burned: 7682 (million)
% 56.64/9.21 % (24837)------------------------------
% 56.64/9.21 % (24837)------------------------------
% 56.64/9.21 % (24856)Instruction limit reached!
% 56.64/9.21 % (24856)------------------------------
% 56.64/9.21 % (24856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.64/9.21 % (24856)Termination reason: Unknown
% 56.64/9.21 % (24856)Termination phase: Saturation
% 56.64/9.21
% 56.64/9.21 % (24856)Memory used [KB]: 11385
% 56.64/9.21 % (24856)Time elapsed: 0.250 s
% 56.64/9.21 % (24856)Instructions burned: 833 (million)
% 56.64/9.21 % (24856)------------------------------
% 56.64/9.21 % (24856)------------------------------
% 56.64/9.22 % (24858)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_24138 for (2923ds/2868Mi)
% 56.64/9.22 % (24859)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_24138 for (2923ds/1516Mi)
% 57.08/9.31 % (24858)Refutation not found, incomplete strategy
% 57.08/9.31 % (24858)------------------------------
% 57.08/9.31 % (24858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.08/9.31 % (24858)Termination reason: Refutation not found, incomplete strategy
% 57.08/9.31
% 57.08/9.31
% 57.08/9.31 % (24858)Memory used [KB]: 8059
% 57.08/9.31 % (24858)Time elapsed: 0.092 s
% 57.08/9.31 % (24858)Instructions burned: 339 (million)
% 57.08/9.31 % (24858)------------------------------
% 57.08/9.31 % (24858)------------------------------
% 57.08/9.32 % (24860)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_24138 for (2922ds/2321Mi)
% 57.08/9.33 % (24852)Instruction limit reached!
% 57.08/9.33 % (24852)------------------------------
% 57.08/9.33 % (24852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.08/9.33 % (24852)Termination reason: Unknown
% 57.08/9.33 % (24852)Termination phase: Saturation
% 57.08/9.33
% 57.08/9.33 % (24852)Memory used [KB]: 10106
% 57.08/9.33 % (24852)Time elapsed: 0.578 s
% 57.08/9.33 % (24852)Instructions burned: 1871 (million)
% 57.08/9.33 % (24852)------------------------------
% 57.08/9.33 % (24852)------------------------------
% 57.08/9.34 % (24861)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_24138 for (2921ds/2812Mi)
% 57.53/9.41 % (24860)Refutation not found, incomplete strategy
% 57.53/9.41 % (24860)------------------------------
% 57.53/9.41 % (24860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.53/9.41 % (24860)Termination reason: Refutation not found, incomplete strategy
% 57.53/9.41
% 57.53/9.41
% 57.53/9.41 % (24860)Memory used [KB]: 8059
% 57.53/9.41 % (24860)Time elapsed: 0.094 s
% 57.53/9.41 % (24860)Instructions burned: 344 (million)
% 57.53/9.41 % (24860)------------------------------
% 57.53/9.41 % (24860)------------------------------
% 57.53/9.42 % (24862)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_24138 for (2921ds/4604Mi)
% 57.53/9.47 % (24848)Instruction limit reached!
% 57.53/9.47 % (24848)------------------------------
% 57.53/9.47 % (24848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.53/9.47 % (24848)Termination reason: Unknown
% 57.53/9.47 % (24848)Termination phase: Saturation
% 57.53/9.47
% 57.53/9.47 % (24848)Memory used [KB]: 20724
% 57.53/9.47 % (24848)Time elapsed: 1.093 s
% 57.53/9.47 % (24848)Instructions burned: 3710 (million)
% 57.53/9.47 % (24848)------------------------------
% 57.53/9.47 % (24848)------------------------------
% 57.53/9.48 % (24863)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_24138 for (2920ds/2678Mi)
% 57.53/9.49 % (24857)Instruction limit reached!
% 57.53/9.49 % (24857)------------------------------
% 57.53/9.49 % (24857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.53/9.49 % (24857)Termination reason: Unknown
% 57.53/9.49 % (24857)Termination phase: Saturation
% 57.53/9.49
% 57.53/9.49 % (24857)Memory used [KB]: 11641
% 57.53/9.49 % (24857)Time elapsed: 0.351 s
% 57.53/9.49 % (24857)Instructions burned: 1190 (million)
% 57.53/9.49 % (24857)------------------------------
% 57.53/9.49 % (24857)------------------------------
% 58.28/9.50 % (24864)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_24138 for (2920ds/643Mi)
% 58.49/9.69 % (24864)Instruction limit reached!
% 58.49/9.69 % (24864)------------------------------
% 58.49/9.69 % (24864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.49/9.69 % (24864)Termination reason: Unknown
% 58.49/9.69 % (24864)Termination phase: Saturation
% 58.49/9.69
% 58.49/9.69 % (24864)Memory used [KB]: 9978
% 58.49/9.69 % (24864)Time elapsed: 0.190 s
% 58.49/9.69 % (24864)Instructions burned: 645 (million)
% 58.49/9.69 % (24864)------------------------------
% 58.49/9.69 % (24864)------------------------------
% 58.49/9.69 % (24859)Instruction limit reached!
% 58.49/9.69 % (24859)------------------------------
% 58.49/9.69 % (24859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.49/9.69 % (24859)Termination reason: Unknown
% 58.49/9.69 % (24859)Termination phase: Saturation
% 58.49/9.69
% 58.49/9.69 % (24859)Memory used [KB]: 8187
% 58.49/9.69 % (24859)Time elapsed: 0.471 s
% 58.49/9.69 % (24859)Instructions burned: 1518 (million)
% 58.49/9.69 % (24859)------------------------------
% 58.49/9.69 % (24859)------------------------------
% 59.37/9.70 % (24865)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_24138 for (2918ds/458Mi)
% 59.37/9.70 % (24866)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_24138 for (2918ds/2546Mi)
% 59.57/9.83 % (24865)Instruction limit reached!
% 59.57/9.83 % (24865)------------------------------
% 59.57/9.83 % (24865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.57/9.83 % (24865)Termination reason: Unknown
% 59.57/9.83 % (24865)Termination phase: Saturation
% 59.57/9.83
% 59.57/9.83 % (24865)Memory used [KB]: 8699
% 59.57/9.83 % (24865)Time elapsed: 0.130 s
% 59.57/9.83 % (24865)Instructions burned: 460 (million)
% 59.57/9.83 % (24865)------------------------------
% 59.57/9.83 % (24865)------------------------------
% 59.57/9.84 % (24867)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_24138 for (2916ds/1432Mi)
% 59.57/9.87 % (24855)Instruction limit reached!
% 59.57/9.87 % (24855)------------------------------
% 59.57/9.87 % (24855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.57/9.87 % (24855)Termination reason: Unknown
% 59.57/9.87 % (24855)Termination phase: Saturation
% 59.57/9.87
% 59.57/9.87 % (24855)Memory used [KB]: 12920
% 59.57/9.87 % (24855)Time elapsed: 0.934 s
% 59.57/9.87 % (24855)Instructions burned: 3115 (million)
% 59.57/9.87 % (24855)------------------------------
% 59.57/9.87 % (24855)------------------------------
% 59.57/9.88 % (24868)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_24138 for (2916ds/386Mi)
% 59.90/9.99 % (24868)Instruction limit reached!
% 59.90/9.99 % (24868)------------------------------
% 59.90/9.99 % (24868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.90/9.99 % (24868)Termination reason: Unknown
% 59.90/9.99 % (24868)Termination phase: Saturation
% 59.90/9.99
% 59.90/9.99 % (24868)Memory used [KB]: 8827
% 59.90/9.99 % (24868)Time elapsed: 0.110 s
% 59.90/9.99 % (24868)Instructions burned: 386 (million)
% 59.90/9.99 % (24868)------------------------------
% 59.90/9.99 % (24868)------------------------------
% 59.90/10.00 % (24869)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_24138 for (2915ds/360Mi)
% 62.48/10.09 % (24869)Instruction limit reached!
% 62.48/10.09 % (24869)------------------------------
% 62.48/10.09 % (24869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.48/10.09 % (24869)Termination reason: Unknown
% 62.48/10.09 % (24869)Termination phase: Saturation
% 62.48/10.09
% 62.48/10.09 % (24869)Memory used [KB]: 8699
% 62.48/10.09 % (24869)Time elapsed: 0.099 s
% 62.48/10.09 % (24869)Instructions burned: 362 (million)
% 62.48/10.09 % (24869)------------------------------
% 62.48/10.09 % (24869)------------------------------
% 62.48/10.10 % (24870)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_24138 for (2914ds/5446Mi)
% 63.65/10.23 % (24861)Instruction limit reached!
% 63.65/10.23 % (24861)------------------------------
% 63.65/10.23 % (24861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.65/10.23 % (24861)Termination reason: Unknown
% 63.65/10.23 % (24861)Termination phase: Saturation
% 63.65/10.23
% 63.65/10.23 % (24861)Memory used [KB]: 9722
% 63.65/10.23 % (24861)Time elapsed: 0.889 s
% 63.65/10.23 % (24861)Instructions burned: 2813 (million)
% 63.65/10.23 % (24861)------------------------------
% 63.65/10.23 % (24861)------------------------------
% 63.65/10.24 % (24867)Instruction limit reached!
% 63.65/10.24 % (24867)------------------------------
% 63.65/10.24 % (24867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.65/10.24 % (24867)Termination reason: Unknown
% 63.65/10.24 % (24867)Termination phase: Saturation
% 63.65/10.24
% 63.65/10.24 % (24867)Memory used [KB]: 13304
% 63.65/10.24 % (24867)Time elapsed: 0.397 s
% 63.65/10.24 % (24867)Instructions burned: 1434 (million)
% 63.65/10.24 % (24867)------------------------------
% 63.65/10.24 % (24867)------------------------------
% 63.65/10.24 % (24871)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_24138 for (2912ds/2573Mi)
% 63.65/10.25 % (24872)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_24138 for (2912ds/2655Mi)
% 63.65/10.29 % (24863)Instruction limit reached!
% 63.65/10.29 % (24863)------------------------------
% 63.65/10.29 % (24863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.65/10.29 % (24863)Termination reason: Unknown
% 63.65/10.29 % (24863)Termination phase: Saturation
% 63.65/10.29
% 63.65/10.29 % (24863)Memory used [KB]: 13816
% 63.65/10.29 % (24863)Time elapsed: 0.812 s
% 63.65/10.29 % (24863)Instructions burned: 2679 (million)
% 63.65/10.29 % (24863)------------------------------
% 63.65/10.29 % (24863)------------------------------
% 64.14/10.30 % (24873)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_24138 for (2912ds/2781Mi)
% 64.44/10.42 % (24847)Instruction limit reached!
% 64.44/10.42 % (24847)------------------------------
% 64.44/10.42 % (24847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.44/10.42 % (24847)Termination reason: Unknown
% 64.44/10.42 % (24847)Termination phase: Saturation
% 64.44/10.42
% 64.44/10.42 % (24847)Memory used [KB]: 19829
% 64.44/10.42 % (24847)Time elapsed: 2.167 s
% 64.44/10.42 % (24847)Instructions burned: 7259 (million)
% 64.44/10.42 % (24847)------------------------------
% 64.44/10.42 % (24847)------------------------------
% 64.44/10.43 % (24874)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_24138 for (2911ds/307Mi)
% 64.67/10.50 % (24866)Instruction limit reached!
% 64.67/10.50 % (24866)------------------------------
% 64.67/10.50 % (24866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.67/10.50 % (24866)Termination reason: Unknown
% 64.67/10.50 % (24866)Termination phase: Saturation
% 64.67/10.50
% 64.67/10.50 % (24866)Memory used [KB]: 10618
% 64.67/10.50 % (24866)Time elapsed: 0.799 s
% 64.67/10.50 % (24866)Instructions burned: 2547 (million)
% 64.67/10.50 % (24866)------------------------------
% 64.67/10.50 % (24866)------------------------------
% 64.67/10.51 % (24875)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_24138 for (2910ds/1548Mi)
% 64.67/10.51 % (24874)Instruction limit reached!
% 64.67/10.51 % (24874)------------------------------
% 64.67/10.51 % (24874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.67/10.51 % (24874)Termination reason: Unknown
% 64.67/10.51 % (24874)Termination phase: Saturation
% 64.67/10.51
% 64.67/10.51 % (24874)Memory used [KB]: 7803
% 64.67/10.51 % (24874)Time elapsed: 0.084 s
% 64.67/10.51 % (24874)Instructions burned: 307 (million)
% 64.67/10.51 % (24874)------------------------------
% 64.67/10.51 % (24874)------------------------------
% 64.67/10.52 % (24876)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_24138 for (2910ds/5214Mi)
% 64.97/10.76 % (24862)Instruction limit reached!
% 64.97/10.76 % (24862)------------------------------
% 64.97/10.76 % (24862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.97/10.76 % (24862)Termination reason: Unknown
% 64.97/10.76 % (24862)Termination phase: Saturation
% 64.97/10.76
% 64.97/10.76 % (24862)Memory used [KB]: 13688
% 64.97/10.76 % (24862)Time elapsed: 1.337 s
% 64.97/10.76 % (24862)Instructions burned: 4606 (million)
% 64.97/10.76 % (24862)------------------------------
% 64.97/10.76 % (24862)------------------------------
% 64.97/10.77 % (24877)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_24138 for (2907ds/3201Mi)
% 65.05/10.98 % (24875)Instruction limit reached!
% 65.05/10.98 % (24875)------------------------------
% 65.05/10.98 % (24875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.05/10.98 % (24875)Termination reason: Unknown
% 65.05/10.98 % (24875)Termination phase: Saturation
% 65.05/10.98
% 65.05/10.98 % (24875)Memory used [KB]: 8955
% 65.05/10.98 % (24875)Time elapsed: 0.472 s
% 65.05/10.98 % (24875)Instructions burned: 1550 (million)
% 65.05/10.98 % (24875)------------------------------
% 65.05/10.98 % (24875)------------------------------
% 65.05/10.99 % (24878)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_24138 for (2905ds/454Mi)
% 65.05/11.01 % (24871)Instruction limit reached!
% 65.05/11.01 % (24871)------------------------------
% 65.05/11.01 % (24871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.05/11.01 % (24871)Termination reason: Unknown
% 65.05/11.01 % (24871)Termination phase: Saturation
% 65.05/11.01
% 65.05/11.01 % (24871)Memory used [KB]: 16247
% 65.05/11.01 % (24871)Time elapsed: 0.773 s
% 65.05/11.01 % (24871)Instructions burned: 2573 (million)
% 65.05/11.01 % (24871)------------------------------
% 65.05/11.01 % (24871)------------------------------
% 65.05/11.02 % (24872)Instruction limit reached!
% 65.05/11.02 % (24872)------------------------------
% 65.05/11.02 % (24872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.05/11.02 % (24872)Termination reason: Unknown
% 65.05/11.02 % (24872)Termination phase: Saturation
% 65.05/11.02
% 65.05/11.02 % (24872)Memory used [KB]: 20212
% 65.05/11.02 % (24872)Time elapsed: 0.778 s
% 65.05/11.02 % (24872)Instructions burned: 2657 (million)
% 65.05/11.02 % (24872)------------------------------
% 65.05/11.02 % (24872)------------------------------
% 65.05/11.02 % (24879)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_24138 for (2905ds/3049Mi)
% 68.74/11.03 % (24880)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_24138 for (2905ds/7311Mi)
% 68.74/11.12 % (24878)Instruction limit reached!
% 68.74/11.12 % (24878)------------------------------
% 68.74/11.12 % (24878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.74/11.12 % (24878)Termination reason: Unknown
% 68.74/11.12 % (24878)Termination phase: Saturation
% 68.74/11.12
% 68.74/11.12 % (24878)Memory used [KB]: 13432
% 68.74/11.12 % (24878)Time elapsed: 0.129 s
% 68.74/11.12 % (24878)Instructions burned: 454 (million)
% 68.74/11.12 % (24878)------------------------------
% 68.74/11.12 % (24878)------------------------------
% 70.03/11.13 % (24881)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_24138 for (2904ds/6804Mi)
% 70.03/11.16 % (24873)Instruction limit reached!
% 70.03/11.16 % (24873)------------------------------
% 70.03/11.16 % (24873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.03/11.16 % (24873)Termination reason: Unknown
% 70.03/11.16 % (24873)Termination phase: Saturation
% 70.03/11.16
% 70.03/11.16 % (24873)Memory used [KB]: 6268
% 70.03/11.16 % (24873)Time elapsed: 0.858 s
% 70.03/11.16 % (24873)Instructions burned: 2783 (million)
% 70.03/11.16 % (24873)------------------------------
% 70.03/11.16 % (24873)------------------------------
% 70.03/11.17 % (24882)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_24138 for (2903ds/1683Mi)
% 71.51/11.63 % (24882)Instruction limit reached!
% 71.51/11.63 % (24882)------------------------------
% 71.51/11.63 % (24882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.51/11.63 % (24882)Termination reason: Unknown
% 71.51/11.63 % (24882)Termination phase: Saturation
% 71.51/11.63
% 71.51/11.63 % (24882)Memory used [KB]: 9338
% 71.51/11.63 % (24882)Time elapsed: 0.462 s
% 71.51/11.63 % (24882)Instructions burned: 1686 (million)
% 71.51/11.63 % (24882)------------------------------
% 71.51/11.63 % (24882)------------------------------
% 71.51/11.64 % (24883)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_24138 for (2898ds/4688Mi)
% 72.29/11.73 % (24877)Instruction limit reached!
% 72.29/11.73 % (24877)------------------------------
% 72.29/11.73 % (24877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.29/11.73 % (24877)Termination reason: Unknown
% 72.29/11.73 % (24877)Termination phase: Saturation
% 72.29/11.73
% 72.29/11.73 % (24877)Memory used [KB]: 12409
% 72.29/11.73 % (24877)Time elapsed: 0.963 s
% 72.29/11.73 % (24877)Instructions burned: 3204 (million)
% 72.29/11.73 % (24877)------------------------------
% 72.29/11.73 % (24877)------------------------------
% 72.29/11.74 % (24884)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_24138 for (2897ds/2207Mi)
% 72.54/11.84 % (24870)Instruction limit reached!
% 72.54/11.84 % (24870)------------------------------
% 72.54/11.84 % (24870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.54/11.84 % (24870)Termination reason: Unknown
% 72.54/11.84 % (24870)Termination phase: Saturation
% 72.54/11.84
% 72.54/11.84 % (24870)Memory used [KB]: 15479
% 72.54/11.84 % (24870)Time elapsed: 1.743 s
% 72.54/11.84 % (24870)Instructions burned: 5446 (million)
% 72.54/11.84 % (24870)------------------------------
% 72.54/11.84 % (24870)------------------------------
% 72.54/11.86 % (24885)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_24138 for (2896ds/8216Mi)
% 72.70/11.98 % (24879)Instruction limit reached!
% 72.70/11.98 % (24879)------------------------------
% 72.70/11.98 % (24879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.70/11.98 % (24879)Termination reason: Unknown
% 72.70/11.98 % (24879)Termination phase: Saturation
% 72.70/11.98
% 72.70/11.98 % (24879)Memory used [KB]: 10106
% 72.70/11.98 % (24879)Time elapsed: 0.982 s
% 72.70/11.98 % (24879)Instructions burned: 3051 (million)
% 72.70/11.98 % (24879)------------------------------
% 72.70/11.98 % (24879)------------------------------
% 72.70/11.99 % (24886)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_24138 for (2895ds/430Mi)
% 76.56/12.11 % (24886)Instruction limit reached!
% 76.56/12.11 % (24886)------------------------------
% 76.56/12.11 % (24886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.56/12.11 % (24886)Termination reason: Unknown
% 76.56/12.11 % (24886)Termination phase: Saturation
% 76.56/12.11
% 76.56/12.11 % (24886)Memory used [KB]: 8699
% 76.56/12.11 % (24886)Time elapsed: 0.124 s
% 76.56/12.11 % (24886)Instructions burned: 431 (million)
% 76.56/12.11 % (24886)------------------------------
% 76.56/12.11 % (24886)------------------------------
% 76.56/12.12 % (24887)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_24138 for (2894ds/2012Mi)
% 76.56/12.12 % (24876)Instruction limit reached!
% 76.56/12.12 % (24876)------------------------------
% 76.56/12.12 % (24876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.56/12.12 % (24876)Termination reason: Unknown
% 76.56/12.12 % (24876)Termination phase: Saturation
% 76.56/12.12
% 76.56/12.12 % (24876)Memory used [KB]: 18293
% 76.56/12.12 % (24876)Time elapsed: 1.604 s
% 76.56/12.12 % (24876)Instructions burned: 5216 (million)
% 76.56/12.12 % (24876)------------------------------
% 76.56/12.12 % (24876)------------------------------
% 77.26/12.13 % (24888)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_24138 for (2894ds/631Mi)
% 78.13/12.33 % (24888)Instruction limit reached!
% 78.13/12.33 % (24888)------------------------------
% 78.13/12.33 % (24888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.13/12.33 % (24888)Termination reason: Unknown
% 78.13/12.33 % (24888)Termination phase: Saturation
% 78.13/12.33
% 78.13/12.33 % (24888)Memory used [KB]: 11129
% 78.13/12.33 % (24888)Time elapsed: 0.197 s
% 78.13/12.33 % (24888)Instructions burned: 633 (million)
% 78.13/12.33 % (24888)------------------------------
% 78.13/12.33 % (24888)------------------------------
% 78.13/12.34 % (24889)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_24138 for (2892ds/8785Mi)
% 78.84/12.45 % (24884)Instruction limit reached!
% 78.84/12.45 % (24884)------------------------------
% 78.84/12.45 % (24884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.84/12.45 % (24884)Termination reason: Unknown
% 78.84/12.45 % (24884)Termination phase: Saturation
% 78.84/12.45
% 78.84/12.45 % (24884)Memory used [KB]: 9338
% 78.84/12.45 % (24884)Time elapsed: 0.705 s
% 78.84/12.45 % (24884)Instructions burned: 2208 (million)
% 78.84/12.45 % (24884)------------------------------
% 78.84/12.45 % (24884)------------------------------
% 78.84/12.46 % (24890)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_24138 for (2890ds/739Mi)
% 79.70/12.68 % (24890)Instruction limit reached!
% 79.70/12.68 % (24890)------------------------------
% 79.70/12.68 % (24890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.70/12.68 % (24890)Termination reason: Unknown
% 79.70/12.68 % (24890)Termination phase: Saturation
% 79.70/12.68
% 79.70/12.68 % (24890)Memory used [KB]: 9466
% 79.70/12.68 % (24890)Time elapsed: 0.226 s
% 79.70/12.68 % (24890)Instructions burned: 739 (million)
% 79.70/12.68 % (24890)------------------------------
% 79.70/12.68 % (24890)------------------------------
% 79.70/12.69 % (24891)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_24138 for (2888ds/5473Mi)
% 80.34/12.73 % (24887)Instruction limit reached!
% 80.34/12.73 % (24887)------------------------------
% 80.34/12.73 % (24887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.34/12.73 % (24887)Termination reason: Unknown
% 80.34/12.73 % (24887)Termination phase: Saturation
% 80.34/12.73
% 80.34/12.73 % (24887)Memory used [KB]: 18549
% 80.34/12.73 % (24887)Time elapsed: 0.611 s
% 80.34/12.73 % (24887)Instructions burned: 2013 (million)
% 80.34/12.73 % (24887)------------------------------
% 80.34/12.73 % (24887)------------------------------
% 80.34/12.74 % (24892)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_24138 for (2888ds/43570Mi)
% 83.54/13.04 % (24883)Instruction limit reached!
% 83.54/13.04 % (24883)------------------------------
% 83.54/13.04 % (24883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.54/13.04 % (24883)Termination reason: Unknown
% 83.54/13.04 % (24883)Termination phase: Saturation
% 83.54/13.04
% 83.54/13.04 % (24883)Memory used [KB]: 11001
% 83.54/13.04 % (24883)Time elapsed: 1.405 s
% 83.54/13.04 % (24883)Instructions burned: 4690 (million)
% 83.54/13.04 % (24883)------------------------------
% 83.54/13.04 % (24883)------------------------------
% 83.54/13.05 % (24893)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_24138 for (2884ds/8382Mi)
% 84.66/13.21 % (24881)Instruction limit reached!
% 84.66/13.21 % (24881)------------------------------
% 84.66/13.21 % (24881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.66/13.21 % (24881)Termination reason: Unknown
% 84.66/13.21 % (24881)Termination phase: Saturation
% 84.66/13.21
% 84.66/13.21 % (24881)Memory used [KB]: 11385
% 84.66/13.21 % (24881)Time elapsed: 2.085 s
% 84.66/13.21 % (24881)Instructions burned: 6806 (million)
% 84.66/13.21 % (24881)------------------------------
% 84.66/13.21 % (24881)------------------------------
% 84.66/13.22 % (24894)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_24138 for (2883ds/407Mi)
% 84.66/13.24 % (24880)Refutation not found, non-redundant clauses discarded% (24880)------------------------------
% 84.66/13.24 % (24880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.66/13.24 % (24880)Termination reason: Refutation not found, non-redundant clauses discarded
% 84.66/13.24
% 84.66/13.24 % (24880)Memory used [KB]: 16119
% 84.66/13.24 % (24880)Time elapsed: 2.232 s
% 84.66/13.24 % (24880)Instructions burned: 7167 (million)
% 84.66/13.24 % (24880)------------------------------
% 84.66/13.24 % (24880)------------------------------
% 84.66/13.25 % (24895)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_24138 for (2882ds/2971Mi)
% 85.12/13.34 % (24895)Refutation not found, incomplete strategy
% 85.12/13.34 % (24895)------------------------------
% 85.12/13.34 % (24895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.12/13.34 % (24895)Termination reason: Refutation not found, incomplete strategy
% 85.12/13.34
% 85.12/13.34
% 85.12/13.34 % (24895)Memory used [KB]: 8059
% 85.12/13.34 % (24895)Time elapsed: 0.092 s
% 85.12/13.34 % (24895)Instructions burned: 338 (million)
% 85.12/13.34 % (24895)------------------------------
% 85.12/13.34 % (24895)------------------------------
% 85.12/13.34 % (24894)Instruction limit reached!
% 85.12/13.34 % (24894)------------------------------
% 85.12/13.34 % (24894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.12/13.34 % (24894)Termination reason: Unknown
% 85.12/13.34 % (24894)Termination phase: Saturation
% 85.12/13.34
% 85.12/13.34 % (24894)Memory used [KB]: 8443
% 85.12/13.34 % (24894)Time elapsed: 0.123 s
% 85.12/13.34 % (24894)Instructions burned: 408 (million)
% 85.12/13.34 % (24894)------------------------------
% 85.12/13.34 % (24894)------------------------------
% 85.12/13.35 % (24896)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_24138 for (2881ds/9822Mi)
% 85.12/13.35 % (24897)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_24138 for (2881ds/8425Mi)
% 92.50/14.37 % (24885)Instruction limit reached!
% 92.50/14.37 % (24885)------------------------------
% 92.50/14.37 % (24885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.50/14.37 % (24885)Termination reason: Unknown
% 92.50/14.37 % (24885)Termination phase: Saturation
% 92.50/14.37
% 92.50/14.37 % (24885)Memory used [KB]: 14583
% 92.50/14.37 % (24885)Time elapsed: 2.515 s
% 92.50/14.37 % (24885)Instructions burned: 8216 (million)
% 92.50/14.37 % (24885)------------------------------
% 92.50/14.37 % (24885)------------------------------
% 92.50/14.37 % (24891)Instruction limit reached!
% 92.50/14.37 % (24891)------------------------------
% 92.50/14.37 % (24891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.50/14.37 % (24891)Termination reason: Unknown
% 92.50/14.37 % (24891)Termination phase: Saturation
% 92.50/14.37
% 92.50/14.37 % (24891)Memory used [KB]: 9210
% 92.50/14.37 % (24891)Time elapsed: 1.682 s
% 92.50/14.37 % (24891)Instructions burned: 5474 (million)
% 92.50/14.37 % (24891)------------------------------
% 92.50/14.37 % (24891)------------------------------
% 92.50/14.38 % (24934)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_24138 for (2871ds/3107Mi)
% 92.50/14.38 % (24935)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_24138 for (2871ds/7967Mi)
% 93.17/14.47 % (24935)Refutation not found, incomplete strategy
% 93.17/14.47 % (24935)------------------------------
% 93.17/14.47 % (24935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.17/14.47 % (24935)Termination reason: Refutation not found, incomplete strategy
% 93.17/14.47
% 93.17/14.47
% 93.17/14.47 % (24935)Memory used [KB]: 8059
% 93.17/14.47 % (24935)Time elapsed: 0.089 s
% 93.17/14.47 % (24935)Instructions burned: 324 (million)
% 93.17/14.47 % (24935)------------------------------
% 93.17/14.47 % (24935)------------------------------
% 93.17/14.48 % (24982)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_24138 for (2870ds/3629Mi)
% 97.59/15.04 % (24889)Instruction limit reached!
% 97.59/15.04 % (24889)------------------------------
% 97.59/15.04 % (24889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.59/15.04 % (24889)Termination reason: Unknown
% 97.59/15.04 % (24889)Termination phase: Saturation
% 97.59/15.04
% 97.59/15.04 % (24889)Memory used [KB]: 15223
% 97.59/15.04 % (24889)Time elapsed: 2.697 s
% 97.59/15.04 % (24889)Instructions burned: 8785 (million)
% 97.59/15.04 % (24889)------------------------------
% 97.59/15.04 % (24889)------------------------------
% 97.59/15.05 % (25130)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_24138 for (2864ds/939Mi)
% 99.27/15.34 % (25130)Instruction limit reached!
% 99.27/15.34 % (25130)------------------------------
% 99.27/15.34 % (25130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.27/15.34 % (25130)Termination reason: Unknown
% 99.27/15.34 % (25130)Termination phase: Saturation
% 99.27/15.34
% 99.27/15.34 % (25130)Memory used [KB]: 9466
% 99.27/15.34 % (25130)Time elapsed: 0.291 s
% 99.27/15.34 % (25130)Instructions burned: 941 (million)
% 99.27/15.34 % (25130)------------------------------
% 99.27/15.34 % (25130)------------------------------
% 99.27/15.34 % (24934)Instruction limit reached!
% 99.27/15.34 % (24934)------------------------------
% 99.27/15.34 % (24934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.27/15.34 % (24934)Termination reason: Unknown
% 99.27/15.34 % (24934)Termination phase: Saturation
% 99.27/15.34
% 99.27/15.34 % (24934)Memory used [KB]: 13944
% 99.27/15.34 % (24934)Time elapsed: 0.959 s
% 99.27/15.34 % (24934)Instructions burned: 3109 (million)
% 99.27/15.34 % (24934)------------------------------
% 99.27/15.34 % (24934)------------------------------
% 99.27/15.35 % (25270)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_24138 for (2861ds/1188Mi)
% 99.27/15.35 % (25271)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_24138 for (2861ds/3205Mi)
% 100.64/15.56 % (24982)Instruction limit reached!
% 100.64/15.56 % (24982)------------------------------
% 100.64/15.56 % (24982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.64/15.56 % (24982)Termination reason: Unknown
% 100.64/15.56 % (24982)Termination phase: Saturation
% 100.64/15.56
% 100.64/15.56 % (24982)Memory used [KB]: 12920
% 100.64/15.56 % (24982)Time elapsed: 1.077 s
% 100.64/15.56 % (24982)Instructions burned: 3629 (million)
% 100.64/15.56 % (24982)------------------------------
% 100.64/15.56 % (24982)------------------------------
% 100.64/15.57 % (25272)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_24138 for (2859ds/865Mi)
% 101.10/15.62 % (24893)Instruction limit reached!
% 101.10/15.62 % (24893)------------------------------
% 101.10/15.62 % (24893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.10/15.62 % (24893)Termination reason: Unknown
% 101.10/15.62 % (24893)Termination phase: Saturation
% 101.10/15.62
% 101.10/15.62 % (24893)Memory used [KB]: 15735
% 101.10/15.62 % (24893)Time elapsed: 2.565 s
% 101.10/15.62 % (24893)Instructions burned: 8384 (million)
% 101.10/15.62 % (24893)------------------------------
% 101.10/15.62 % (24893)------------------------------
% 101.10/15.63 % (25273)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_24138 for (2859ds/7469Mi)
% 101.10/15.69 % (25270)Instruction limit reached!
% 101.10/15.69 % (25270)------------------------------
% 101.10/15.69 % (25270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.10/15.69 % (25270)Termination reason: Unknown
% 101.10/15.69 % (25270)Termination phase: Saturation
% 101.10/15.69
% 101.10/15.69 % (25270)Memory used [KB]: 12025
% 101.10/15.69 % (25270)Time elapsed: 0.347 s
% 101.10/15.69 % (25270)Instructions burned: 1188 (million)
% 101.10/15.69 % (25270)------------------------------
% 101.10/15.69 % (25270)------------------------------
% 101.10/15.69 % (24892)First to succeed.
% 98.84/15.70 % (24892)Refutation found. Thanks to Tanya!
% 98.84/15.70 % SZS status Theorem for DTF2THF_24138
% 98.84/15.70 % SZS output start Proof for DTF2THF_24138
% 98.84/15.70 thf(type_def_5, type, list: ($tType) > $tType).
% 98.84/15.70 thf(type_def_7, type, nat: $tType).
% 98.84/15.70 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 98.84/15.70 thf(type_def_9, type, set: ($tType) > $tType).
% 98.84/15.70 thf(type_def_10, type, com: $tType).
% 98.84/15.70 thf(type_def_11, type, state: $tType).
% 98.84/15.70 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 98.84/15.70 thf(func_def_1, type, state: $tType).
% 98.84/15.70 thf(func_def_2, type, com: $tType).
% 98.84/15.70 thf(func_def_3, type, list: ($tType) > $tType).
% 98.84/15.70 thf(func_def_4, type, set: ($tType) > $tType).
% 98.84/15.70 thf(func_def_5, type, nat: $tType).
% 98.84/15.70 thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 98.84/15.70 thf(func_def_7, type, zero: !>[X0: $tType]:($o)).
% 98.84/15.70 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 98.84/15.70 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 98.84/15.70 thf(func_def_10, type, zero_zero: !>[X0: $tType]:(X0)).
% 98.84/15.70 thf(func_def_11, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_12, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 98.84/15.70 thf(func_def_13, type, concat: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_14, type, gen_length: !>[X0: $tType]:(nat > list @ X0 > nat)).
% 98.84/15.70 thf(func_def_15, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_16, type, lexord: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 98.84/15.70 thf(func_def_17, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_18, type, nil: !>[X0: $tType]:(list @ X0)).
% 98.84/15.70 thf(func_def_19, type, listrel: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X1 > set @ product_prod @ list @ X0 @ list @ X1)).
% 98.84/15.70 thf(func_def_20, type, listrel1: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 98.84/15.70 thf(func_def_21, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 98.84/15.70 thf(func_def_22, type, n_lists: !>[X0: $tType]:(nat > list @ X0 > list @ list @ X0)).
% 98.84/15.70 thf(func_def_23, type, nths: !>[X0: $tType]:(list @ X0 > set @ nat > list @ X0)).
% 98.84/15.70 thf(func_def_24, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 98.84/15.70 thf(func_def_25, type, subseqs: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 98.84/15.70 thf(func_def_26, type, suc: nat > nat).
% 98.84/15.70 thf(func_def_27, type, pHoare1053570893_exec1: set @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state).
% 98.84/15.70 thf(func_def_28, type, pHoare1053570959_execs: state > list @ com > state > $o).
% 98.84/15.70 thf(func_def_29, type, pHoare1838713294le_inf: list @ com > state > $o).
% 98.84/15.70 thf(func_def_30, type, pHoare1335526537termis: list @ com > state > $o).
% 98.84/15.70 thf(func_def_31, type, cond: (state > $o) > com > com > com).
% 98.84/15.70 thf(func_def_32, type, do: (state > set @ state) > com).
% 98.84/15.70 thf(func_def_33, type, semi: com > com > com).
% 98.84/15.70 thf(func_def_34, type, while: (state > $o) > com > com).
% 98.84/15.70 thf(func_def_35, type, exec: state > com > state > $o).
% 98.84/15.70 thf(func_def_36, type, termi: com > state > $o).
% 98.84/15.70 thf(func_def_37, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 98.84/15.70 thf(func_def_38, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 98.84/15.70 thf(func_def_39, type, irrefl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 98.84/15.70 thf(func_def_40, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 98.84/15.70 thf(func_def_41, type, transitive_rtrancl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0)).
% 98.84/15.70 thf(func_def_42, type, transitive_trancl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0)).
% 98.84/15.70 thf(func_def_43, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 98.84/15.70 thf(func_def_44, type, c: com).
% 98.84/15.70 thf(func_def_45, type, f: nat > product_prod @ list @ com @ state).
% 98.84/15.70 thf(func_def_46, type, n: nat).
% 98.84/15.70 thf(func_def_47, type, s: state).
% 98.84/15.70 thf(func_def_65, type, sP0: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X0 > $o) > $o)).
% 98.84/15.70 thf(func_def_66, type, sP1: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_67, type, sP2: state > state > (state > $o) > com > list @ com > list @ com > $o).
% 98.84/15.70 thf(func_def_68, type, sP3: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_69, type, sK4: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_70, type, sK5: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_71, type, sK6: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_72, type, sK7: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_73, type, sK8: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_74, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_75, type, sK10: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_76, type, sK11: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_77, type, sK12: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_78, type, sK13: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_79, type, sK14: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_80, type, sK15: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_81, type, sK16: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_82, type, sK17: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_83, type, sK18: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_84, type, sK19: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_85, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0)).
% 98.84/15.70 thf(func_def_86, type, sK21: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_87, type, sK22: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0)).
% 98.84/15.70 thf(func_def_88, type, sK23: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_89, type, sK24: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_90, type, sK25: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_91, type, sK26: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_92, type, sK27: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_93, type, sK28: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_94, type, sK29: (nat > $o) > nat).
% 98.84/15.70 thf(func_def_95, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 98.84/15.70 thf(func_def_96, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 98.84/15.70 thf(func_def_97, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 98.84/15.70 thf(func_def_98, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 98.84/15.70 thf(func_def_99, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 98.84/15.70 thf(func_def_100, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 98.84/15.70 thf(func_def_101, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_102, type, sK37: nat > nat).
% 98.84/15.70 thf(func_def_103, type, sK38: com > (nat > state) > nat).
% 98.84/15.70 thf(func_def_104, type, sK39: (state > $o) > (nat > state) > nat).
% 98.84/15.70 thf(func_def_105, type, sK40: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_106, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 98.84/15.70 thf(func_def_107, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 98.84/15.70 thf(func_def_108, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 98.84/15.70 thf(func_def_109, type, sK44: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_110, type, sK45: !>[X0: $tType]:(list @ X0 > X0)).
% 98.84/15.70 thf(func_def_111, type, sK46: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > (nat > X0) > X0 > nat)).
% 98.84/15.70 thf(func_def_112, type, sK47: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > nat > X0)).
% 98.84/15.70 thf(func_def_113, type, sK48: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_114, type, sK49: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_115, type, sK50: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_116, type, sK51: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_117, type, sK52: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_118, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 98.84/15.70 thf(func_def_119, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 98.84/15.70 thf(func_def_120, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 98.84/15.70 thf(func_def_121, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_122, type, sK57: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_123, type, sK58: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_124, type, sK59: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_125, type, sK60: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_126, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 98.84/15.70 thf(func_def_127, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 98.84/15.70 thf(func_def_128, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 98.84/15.70 thf(func_def_129, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 98.84/15.70 thf(func_def_130, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_131, type, sK66: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_132, type, sK67: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_133, type, sK68: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_134, type, sK69: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_135, type, sK70: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_136, type, sK71: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_137, type, sK72: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_138, type, sK73: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_139, type, sK74: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_140, type, sK75: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_141, type, sK76: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_142, type, sK77: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_143, type, sK78: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_144, type, sK79: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_145, type, sK80: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_146, type, sK81: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_147, type, sK82: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_148, type, sK83: (nat > $o) > nat).
% 98.84/15.70 thf(func_def_149, type, sK84: list @ com > list @ com > list @ com).
% 98.84/15.70 thf(func_def_150, type, sK85: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_151, type, sK86: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_152, type, sK87: !>[X0: $tType]:(X0 > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_153, type, sK88: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_154, type, sK89: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_155, type, sK90: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_156, type, sK91: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_157, type, sK92: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_158, type, sK93: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_159, type, sK94: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_160, type, sK95: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_161, type, sK96: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_162, type, sK97: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_163, type, sK98: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_164, type, sK99: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat)).
% 98.84/15.70 thf(func_def_165, type, sK100: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0)).
% 98.84/15.70 thf(func_def_166, type, sK101: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_167, type, sK102: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_168, type, sK103: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_169, type, sK104: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_170, type, sK105: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_171, type, sK106: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_172, type, sK107: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_173, type, sK108: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 98.84/15.70 thf(func_def_174, type, sK109: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 98.84/15.70 thf(func_def_175, type, sK110: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 98.84/15.70 thf(func_def_176, type, sK111: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 98.84/15.70 thf(func_def_177, type, sK112: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 98.84/15.70 thf(func_def_178, type, sK113: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 98.84/15.70 thf(func_def_179, type, sK114: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_180, type, sK115: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 98.84/15.70 thf(func_def_181, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 98.84/15.70 thf(func_def_182, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 98.84/15.70 thf(func_def_183, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 98.84/15.70 thf(func_def_184, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 98.84/15.70 thf(func_def_185, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 98.84/15.70 thf(func_def_186, type, sK121: !>[X0: $tType]:(list @ X0 > X0)).
% 98.84/15.70 thf(func_def_187, type, sK122: !>[X0: $tType]:(list @ X0 > X0)).
% 98.84/15.70 thf(func_def_188, type, sK123: !>[X0: $tType]:(list @ X0 > X0)).
% 98.84/15.70 thf(func_def_189, type, sK124: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_190, type, sK125: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 98.84/15.70 thf(func_def_191, type, sK126: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_192, type, sK127: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 98.84/15.70 thf(func_def_193, type, sK128: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 98.84/15.70 thf(func_def_194, type, sK129: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 98.84/15.70 thf(func_def_195, type, sK130: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_196, type, sK131: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 98.84/15.70 thf(func_def_197, type, sK132: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 98.84/15.70 thf(func_def_198, type, sK133: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_199, type, sK134: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_200, type, sK135: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_201, type, sK136: !>[X0: $tType]:((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0)).
% 98.84/15.70 thf(func_def_202, type, sK137: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 98.84/15.70 thf(func_def_203, type, sK138: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 98.84/15.70 thf(func_def_204, type, sK139: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0)).
% 98.84/15.70 thf(func_def_205, type, sK140: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_206, type, sK141: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0)).
% 98.84/15.70 thf(func_def_207, type, sK142: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_208, type, sK143: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0)).
% 98.84/15.70 thf(func_def_209, type, sK144: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_210, type, sK145: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 98.84/15.70 thf(func_def_211, type, sK146: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 98.84/15.70 thf(func_def_212, type, sK147: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 98.84/15.70 thf(func_def_213, type, sK148: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 98.84/15.70 thf(func_def_214, type, sK149: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 98.84/15.70 thf(func_def_215, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 98.84/15.70 thf(func_def_216, type, sK151: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 98.84/15.70 thf(func_def_217, type, sK152: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_218, type, sK153: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_219, type, sK154: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_220, type, sK155: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 98.84/15.70 thf(func_def_221, type, sK156: !>[X0: $tType]:(list @ X0 > X0)).
% 98.84/15.70 thf(func_def_222, type, sK157: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_223, type, sK158: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_224, type, sK159: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_225, type, sK160: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_226, type, sK161: (nat > state) > com > nat).
% 98.84/15.70 thf(func_def_227, type, sK162: (nat > state) > (state > $o) > nat).
% 98.84/15.70 thf(func_def_228, type, sK163: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 98.84/15.70 thf(func_def_229, type, sK164: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 98.84/15.70 thf(func_def_230, type, sK165: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 98.84/15.70 thf(func_def_231, type, sK166: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 98.84/15.70 thf(func_def_232, type, sK167: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 98.84/15.70 thf(func_def_233, type, sK168: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 98.84/15.70 thf(func_def_234, type, sK169: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 98.84/15.70 thf(func_def_235, type, sK170: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 98.84/15.70 thf(func_def_236, type, sK171: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_237, type, sK172: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 98.84/15.70 thf(func_def_238, type, sK173: com > state > (state > $o) > state).
% 98.84/15.70 thf(func_def_239, type, sK174: !>[X0: $tType, X1: $tType]:(set @ product_prod @ product_prod @ X1 @ X0 @ product_prod @ X1 @ X0 > X0 > X1 > X0 > X1 > X1)).
% 98.84/15.70 thf(func_def_240, type, sK175: !>[X0: $tType, X1: $tType]:(set @ product_prod @ product_prod @ X1 @ X0 @ product_prod @ X1 @ X0 > X0 > X1 > X0 > X1 > X0)).
% 98.84/15.70 thf(func_def_241, type, sK176: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_242, type, sK177: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_243, type, sK178: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_244, type, sK179: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_245, type, sK180: (nat > $o) > nat).
% 98.84/15.70 thf(func_def_246, type, sK181: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 98.84/15.70 thf(func_def_247, type, sK182: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_248, type, sK183: !>[X0: $tType]:(list @ X0 > X0)).
% 98.84/15.70 thf(func_def_249, type, sK184: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 98.84/15.70 thf(func_def_250, type, sK185: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_251, type, sK186: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_252, type, sK187: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_253, type, sK188: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_254, type, sK189: !>[X0: $tType]:((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_255, type, sK190: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_256, type, sK191: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_257, type, sK192: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_258, type, sK193: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_259, type, sK194: (nat > nat > $o) > nat).
% 98.84/15.70 thf(func_def_260, type, sK195: (nat > nat > $o) > nat).
% 98.84/15.70 thf(func_def_261, type, sK196: (nat > nat > $o) > nat).
% 98.84/15.70 thf(func_def_262, type, sK197: (nat > nat > $o) > nat).
% 98.84/15.70 thf(func_def_263, type, sK198: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0 > list @ X0)).
% 98.84/15.70 thf(func_def_264, type, sK199: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0)).
% 98.84/15.70 thf(func_def_265, type, sK200: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_266, type, sK201: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0)).
% 98.84/15.70 thf(func_def_267, type, sK202: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_268, type, sK203: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 98.84/15.70 thf(func_def_269, type, sK204: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_270, type, sK205: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 98.84/15.70 thf(func_def_271, type, sK206: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 98.84/15.70 thf(func_def_272, type, sK207: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_273, type, sK208: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_274, type, sK209: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_275, type, sK210: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_276, type, sK211: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_277, type, sK212: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_278, type, sK213: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 98.84/15.70 thf(func_def_279, type, sK214: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 98.84/15.70 thf(func_def_280, type, sK215: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 98.84/15.70 thf(func_def_281, type, sK216: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 98.84/15.70 thf(func_def_282, type, sK217: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 98.84/15.70 thf(func_def_283, type, sK218: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_284, type, sK219: list @ com > list @ com > list @ com).
% 98.84/15.70 thf(func_def_285, type, sK220: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 98.84/15.70 thf(func_def_286, type, sK221: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 98.84/15.70 thf(func_def_287, type, sK222: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 98.84/15.70 thf(func_def_288, type, sK223: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 98.84/15.70 thf(func_def_289, type, sK224: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_290, type, sK225: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0)).
% 98.84/15.70 thf(func_def_291, type, sK226: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0)).
% 98.84/15.70 thf(func_def_292, type, sK227: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 98.84/15.70 thf(func_def_293, type, sK228: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 98.84/15.70 thf(func_def_294, type, sK229: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 98.84/15.70 thf(func_def_295, type, sK230: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > nat > X0)).
% 98.84/15.70 thf(func_def_296, type, sK231: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > (nat > X0) > X0 > nat)).
% 98.84/15.70 thf(func_def_297, type, sK232: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_298, type, sK233: !>[X0: $tType]:(X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_299, type, sK234: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_300, type, sK235: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_301, type, sK236: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 98.84/15.70 thf(func_def_302, type, sK237: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 98.84/15.70 thf(func_def_303, type, sK238: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 98.84/15.70 thf(func_def_304, type, sK239: nat > nat).
% 98.84/15.70 thf(func_def_306, type, ph241: !>[X0: $tType]:(X0)).
% 98.84/15.70 thf(f8010,plain,(
% 98.84/15.70 $false),
% 98.84/15.70 inference(avatar_sat_refutation,[status(thm)],[f1640,f8006])).
% 98.84/15.70 thf(f8006,plain,(
% 98.84/15.70 spl240_2),
% 98.84/15.70 inference(avatar_contradiction_clause,[status(thm)],[f8005])).
% 98.84/15.70 thf(f8005,plain,(
% 98.84/15.70 $false | spl240_2),
% 98.84/15.70 inference(subsumption_resolution,[status(thm)],[f7998,f1511])).
% 98.84/15.70 thf(f1511,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ (f @ n)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) = $true)),
% 98.84/15.70 inference(forward_demodulation,[status(thm)],[f1388,f1259])).
% 98.84/15.70 thf(f1259,plain,(
% 98.84/15.70 ((f @ zero_zero @ nat) = (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s))),
% 98.84/15.70 inference(cnf_transformation,[status(thm)],[f261])).
% 98.84/15.70 thf(f261,axiom,(
% 98.84/15.70 ((f @ zero_zero @ nat) = (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s))),
% 98.84/15.70 file('/export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2THF_24138.p',conj_1)).
% 98.84/15.70 thf(f1388,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ n)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) = $true)),
% 98.84/15.70 inference(cnf_transformation,[status(thm)],[f462])).
% 98.84/15.70 thf(f462,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ n)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) = $true)),
% 98.84/15.70 inference(fool_elimination,[status(thm)],[f461])).
% 98.84/15.70 thf(f461,plain,(
% 98.84/15.70 (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ n)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 98.84/15.70 inference(rectify,[status(thm)],[f263])).
% 98.84/15.70 thf(f263,axiom,(
% 98.84/15.70 (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ n)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 98.84/15.70 file('/export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2THF_24138.p',conj_3)).
% 98.84/15.70 thf(f7998,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ (f @ n)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true) | spl240_2),
% 98.84/15.70 inference(trivial_inequality_removal,[status(thm)],[f7973])).
% 98.84/15.70 thf(f7973,plain,(
% 98.84/15.70 ($true != $true) | ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ (f @ n)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true) | spl240_2),
% 98.84/15.70 inference(superposition,[status(thm)],[f1924,f1380])).
% 98.84/15.70 thf(f1380,plain,(
% 98.84/15.70 ( ! [X0 : nat] : (((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ X0) @ (f @ (suc @ X0))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) = $true)) )),
% 98.84/15.70 inference(cnf_transformation,[status(thm)],[f422])).
% 98.84/15.70 thf(f422,plain,(
% 98.84/15.70 ! [X0 : nat] : ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ X0) @ (f @ (suc @ X0))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) = $true)),
% 98.84/15.70 inference(fool_elimination,[status(thm)],[f421])).
% 98.84/15.70 thf(f421,plain,(
% 98.84/15.70 ! [X0 : nat] : (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ X0) @ (f @ (suc @ X0))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 98.84/15.70 inference(rectify,[status(thm)],[f262])).
% 98.84/15.70 thf(f262,axiom,(
% 98.84/15.70 ! [X11 : nat] : (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ X11) @ (f @ (suc @ X11))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 98.84/15.70 file('/export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2THF_24138.p',conj_2)).
% 98.84/15.70 thf(f1924,plain,(
% 98.84/15.70 ( ! [X0 : product_prod @ list @ com @ state] : (((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ X0 @ (f @ (suc @ n))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true) | ($true != (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ X0) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)))) ) | spl240_2),
% 98.84/15.70 inference(trivial_inequality_removal,[status(thm)],[f1898])).
% 98.84/15.70 thf(f1898,plain,(
% 98.84/15.70 ( ! [X0 : product_prod @ list @ com @ state] : (((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ X0 @ (f @ (suc @ n))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true) | ($true != $true) | ($true != (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ X0) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)))) ) | spl240_2),
% 98.84/15.70 inference(superposition,[status(thm)],[f1636,f1147])).
% 98.84/15.70 thf(f1147,plain,(
% 98.84/15.70 ( ! [X0 : $tType,X2 : X0,X3 : set @ product_prod @ X0 @ X0,X1 : X0,X4 : X0] : (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X4) @ (transitive_trancl @ X0 @ X3)) = $true) | ($true != (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X2 @ X4) @ (transitive_trancl @ X0 @ X3))) | ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) != $true)) )),
% 98.84/15.70 inference(cnf_transformation,[status(thm)],[f864])).
% 98.84/15.70 thf(f864,plain,(
% 98.84/15.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ product_prod @ X0 @ X0,X4 : X0] : (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X4) @ (transitive_trancl @ X0 @ X3)) = $true) | ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) != $true) | ($true != (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X2 @ X4) @ (transitive_trancl @ X0 @ X3))))),
% 98.84/15.70 inference(flattening,[status(thm)],[f863])).
% 98.84/15.70 thf(f863,plain,(
% 98.84/15.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ product_prod @ X0 @ X0,X4 : X0] : ((((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X4) @ (transitive_trancl @ X0 @ X3)) = $true) | ($true != (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X2 @ X4) @ (transitive_trancl @ X0 @ X3)))) | ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) != $true))),
% 98.84/15.70 inference(ennf_transformation,[status(thm)],[f274])).
% 98.84/15.70 thf(f274,plain,(
% 98.84/15.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ product_prod @ X0 @ X0,X4 : X0] : (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) = $true) => (($true = (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X2 @ X4) @ (transitive_trancl @ X0 @ X3))) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X4) @ (transitive_trancl @ X0 @ X3)) = $true)))),
% 98.84/15.70 inference(fool_elimination,[status(thm)],[f273])).
% 98.84/15.70 thf(f273,plain,(
% 98.84/15.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ product_prod @ X0 @ X0,X4 : X0] : ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X2 @ X4) @ (transitive_trancl @ X0 @ X3)) => (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X4) @ (transitive_trancl @ X0 @ X3))))),
% 98.84/15.70 inference(rectify,[status(thm)],[f50])).
% 98.84/15.70 thf(f50,axiom,(
% 98.84/15.70 ! [X0 : $tType,X33 : X0,X34 : X0,X8 : set @ product_prod @ X0 @ X0,X38 : X0] : ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X33 @ X34) @ (transitive_rtrancl @ X0 @ X8)) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X34 @ X38) @ (transitive_trancl @ X0 @ X8)) => (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X33 @ X38) @ (transitive_trancl @ X0 @ X8))))),
% 98.84/15.70 file('/export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2THF_24138.p',fact_49_rtrancl__trancl__trancl)).
% 98.84/15.70 thf(f1636,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ (f @ (suc @ n))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true) | spl240_2),
% 98.84/15.70 inference(avatar_component_clause,[status(thm)],[f1634])).
% 98.84/15.70 thf(f1634,definition,(
% 98.84/15.70 spl240_2 <=> ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ (f @ (suc @ n))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) = $true)),
% 98.84/15.70 introduced(definition,[new_symbols(naming,[spl240_2])],[avatar_definition])).
% 98.84/15.70 thf(f1640,plain,(
% 98.84/15.70 ~spl240_2),
% 98.84/15.70 inference(avatar_split_clause,[status(thm)],[f1639,f1634])).
% 98.84/15.70 thf(f1639,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (f @ zero_zero @ nat) @ (f @ (suc @ n))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true)),
% 98.84/15.70 inference(forward_demodulation,[status(thm)],[f1618,f1259])).
% 98.84/15.70 thf(f1618,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true)),
% 98.84/15.70 inference(trivial_inequality_removal,[status(thm)],[f1615])).
% 98.84/15.70 thf(f1615,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_trancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true) | ($true != $true)),
% 98.84/15.70 inference(superposition,[status(thm)],[f1276,f1154])).
% 98.84/15.70 thf(f1154,plain,(
% 98.84/15.70 ( ! [X0 : $tType,X2 : X0,X3 : set @ product_prod @ X0 @ X0,X1 : X0] : (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) = $true) | ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_trancl @ X0 @ X3)) != $true)) )),
% 98.84/15.70 inference(cnf_transformation,[status(thm)],[f808])).
% 98.84/15.70 thf(f808,plain,(
% 98.84/15.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ product_prod @ X0 @ X0] : (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_trancl @ X0 @ X3)) != $true) | ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) = $true))),
% 98.84/15.70 inference(ennf_transformation,[status(thm)],[f312])).
% 98.84/15.70 thf(f312,plain,(
% 98.84/15.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ product_prod @ X0 @ X0] : (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_trancl @ X0 @ X3)) = $true) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)) = $true))),
% 98.84/15.70 inference(fool_elimination,[status(thm)],[f311])).
% 98.84/15.70 thf(f311,plain,(
% 98.84/15.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ product_prod @ X0 @ X0] : ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_trancl @ X0 @ X3)) => (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ (transitive_rtrancl @ X0 @ X3)))),
% 98.84/15.70 inference(rectify,[status(thm)],[f15])).
% 98.84/15.70 thf(f15,axiom,(
% 98.84/15.70 ! [X0 : $tType,X6 : X0,X12 : X0,X8 : set @ product_prod @ X0 @ X0] : ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X6 @ X12) @ (transitive_trancl @ X0 @ X8)) => (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X6 @ X12) @ (transitive_rtrancl @ X0 @ X8)))),
% 98.84/15.70 file('/export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2THF_24138.p',fact_14_trancl__into__rtrancl)).
% 98.84/15.70 thf(f1276,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true)),
% 98.84/15.70 inference(cnf_transformation,[status(thm)],[f653])).
% 98.84/15.70 thf(f653,plain,(
% 98.84/15.70 ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) != $true)),
% 98.84/15.70 inference(flattening,[status(thm)],[f572])).
% 98.84/15.70 thf(f572,plain,(
% 98.84/15.70 ~((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) = $true)),
% 98.84/15.70 inference(fool_elimination,[status(thm)],[f571])).
% 98.84/15.70 thf(f571,plain,(
% 98.84/15.70 ~(member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 98.84/15.70 inference(rectify,[status(thm)],[f265])).
% 98.84/15.70 thf(f265,negated_conjecture,(
% 98.84/15.70 ~(member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 98.84/15.70 inference(negated_conjecture,[status(cth)],[f264])).
% 98.84/15.70 thf(f264,conjecture,(
% 98.84/15.70 (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (f @ (suc @ n))) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 98.84/15.70 file('/export/starexec/sandbox/tmp/tmp.sIAd6FWccy/DTF2THF_24138.p',conj_4)).
% 98.84/15.70 % SZS output end Proof for DTF2THF_24138
% 98.84/15.70 % (24892)------------------------------
% 98.84/15.70 % (24892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.84/15.70 % (24892)Termination reason: Refutation
% 98.84/15.70
% 98.84/15.70 % (24892)Memory used [KB]: 14200
% 98.84/15.70 % (24892)Time elapsed: 2.955 s
% 98.84/15.70 % (24892)Instructions burned: 9336 (million)
% 98.84/15.70 % (24892)------------------------------
% 98.84/15.70 % (24892)------------------------------
% 98.84/15.70 % (24329)Success in time 14.176 s
%------------------------------------------------------------------------------