%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP057^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 08:55:12 AM UTC 2026
% Result : Theorem 3.37s 1.94s
% Output : Refutation 3.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP057^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:24:57 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.22/0.43 ---- Original DTF file ---
% 0.22/0.44 thf(spec,logic,$$dhol).
% 0.22/0.44 %------------------------------------------------------------------------------
% 0.22/0.44 % File : ITP057^2 : TPTP v9.2.1. Released v7.5.0.
% 0.22/0.44 % Domain : Interactive Theorem Proving
% 0.22/0.44 % Problem : Sledgehammer FLPTheorem problem prob_165__3291512_1
% 0.22/0.44 % Version : Especial.
% 0.22/0.44 % English :
% 0.22/0.44
% 0.22/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.22/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.22/0.44 % Source : [Des21]
% 0.22/0.44 % Names : FLPTheorem/prob_165__3291512_1 [Des21]
% 0.22/0.44
% 0.22/0.44 % Status : Theorem
% 0.22/0.44 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.22/0.44 % Syntax : Number of formulae : 348 ( 122 unt; 63 typ; 0 def)
% 0.22/0.44 % Number of atoms : 958 ( 225 equ; 0 cnn)
% 0.22/0.44 % Maximal formula atoms : 13 ( 3 avg)
% 0.22/0.44 % Number of connectives : 6606 ( 108 ~; 20 |; 106 &;5968 @)
% 0.22/0.44 % ( 0 <=>; 404 =>; 0 <=; 0 <~>)
% 0.22/0.44 % Maximal formula depth : 30 ( 10 avg)
% 0.22/0.44 % Number of types : 6 ( 5 usr)
% 0.22/0.44 % Number of type conns : 580 ( 580 >; 0 *; 0 +; 0 <<)
% 0.22/0.44 % Number of symbols : 61 ( 58 usr; 12 con; 0-9 aty)
% 0.22/0.44 % Number of variables : 1245 ( 98 ^;1007 !; 56 ?;1245 :)
% 0.22/0.44 % ( 84 !>; 0 ?*; 0 @-; 0 @+)
% 0.22/0.44 % SPC : TH1_THM_EQU_NAR
% 0.22/0.44
% 0.22/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 16:15:46.166
% 0.22/0.44 %------------------------------------------------------------------------------
% 0.22/0.44 % Could-be-implicit typings (10)
% 0.22/0.44 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.22/0.44 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_t_AsynchronousSystem_OmessageValue,type,
% 0.22/0.44 messageValue: $tType > $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.22/0.44 message: $tType > $tType > $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_t_Product__Type_Ounit,type,
% 0.22/0.44 product_unit: $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_t_List_Olist,type,
% 0.22/0.44 list: $tType > $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_t_Set_Oset,type,
% 0.22/0.44 set: $tType > $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_t_Nat_Onat,type,
% 0.22/0.44 nat: $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_tf_v,type,
% 0.22/0.44 v: $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_tf_s,type,
% 0.22/0.44 s: $tType ).
% 0.22/0.44
% 0.22/0.44 thf(ty_tf_p,type,
% 0.22/0.44 p: $tType ).
% 0.22/0.44
% 0.22/0.44 % Explicit typings (53)
% 0.22/0.44 thf(sy_cl_HOL_Otype,type,
% 0.22/0.44 type:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_cl_Orderings_Obot,type,
% 0.22/0.44 bot:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_cl_Orderings_Oord,type,
% 0.22/0.44 ord:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_cl_Orderings_Oorder,type,
% 0.22/0.44 order:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_cl_Orderings_Olinorder,type,
% 0.22/0.44 linorder:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_cl_Orderings_Opreorder,type,
% 0.22/0.44 preorder:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.22/0.44 order_bot:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.22/0.44 dense_linorder:
% 0.22/0.44 !>[A: $tType] : $o ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OinitReachable,type,
% 0.22/0.44 initReachable:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oinitial,type,
% 0.22/0.44 initial:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OqReachable,type,
% 0.22/0.44 qReachable:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( set @ P ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oreachable,type,
% 0.22/0.44 reachable:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OstepReachable,type,
% 0.22/0.44 stepReachable:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Osteps,type,
% 0.22/0.44 steps:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs,type,
% 0.22/0.44 msgs:
% 0.22/0.44 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > ( message @ P @ V ) > nat ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_Oconfiguration_Ostates,type,
% 0.22/0.44 states:
% 0.22/0.44 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > P > S ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 0.22/0.44 enabled:
% 0.22/0.44 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_OisReceiverOf,type,
% 0.22/0.44 isReceiverOf:
% 0.22/0.44 !>[P: $tType,V: $tType] : ( P > ( message @ P @ V ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_AsynchronousSystem_Omessage_OOutMsg,type,
% 0.22/0.44 outMsg:
% 0.22/0.44 !>[P: $tType,V: $tType] : ( $o > ( message @ P @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Execution_Oexecution,type,
% 0.22/0.44 execution:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 0.22/0.44 firstOccurrence:
% 0.22/0.44 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Execution_Oexecution_OminimalEnabled,type,
% 0.22/0.44 minimalEnabled:
% 0.22/0.44 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPSystem_OflpSystem,type,
% 0.22/0.44 flpSystem:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPSystem_OflpSystem_Oagreement,type,
% 0.22/0.44 agreement:
% 0.22/0.44 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPSystem_OflpSystem_OagreementInit,type,
% 0.22/0.44 agreementInit:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPSystem_OflpSystem_OpSilDecVal,type,
% 0.22/0.44 pSilDecVal:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o > P > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPSystem_OflpSystem_OterminationPseudo,type,
% 0.22/0.44 terminationPseudo:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > nat > ( configuration_ext @ P @ V @ S @ product_unit ) > ( set @ P ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPSystem_OflpSystem_OvUniform,type,
% 0.22/0.44 vUniform:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPSystem_OflpSystem_Ovalidity,type,
% 0.22/0.44 validity:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus,type,
% 0.22/0.44 fLPThe1922692578sensus:
% 0.22/0.44 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.22/0.44 one_one:
% 0.22/0.44 !>[A: $tType] : A ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.22/0.44 zero_zero:
% 0.22/0.44 !>[A: $tType] : A ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_ListUtilities_OprefixList,type,
% 0.22/0.44 prefixList:
% 0.22/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_List_Olast,type,
% 0.22/0.44 last:
% 0.22/0.44 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.22/0.44 bot_bot:
% 0.22/0.44 !>[A: $tType] : A ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.22/0.44 ord_less:
% 0.22/0.44 !>[A: $tType] : ( A > A > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.22/0.44 ord_less_eq:
% 0.22/0.44 !>[A: $tType] : ( A > A > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Set_OCollect,type,
% 0.22/0.44 collect:
% 0.22/0.44 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_Set_Oinsert,type,
% 0.22/0.44 insert:
% 0.22/0.44 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_c_member,type,
% 0.22/0.44 member:
% 0.22/0.44 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_cMsg____,type,
% 0.22/0.44 cMsg: configuration_ext @ p @ v @ s @ product_unit ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_c_H____,type,
% 0.22/0.44 c: configuration_ext @ p @ v @ s @ product_unit ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_exec,type,
% 0.22/0.44 exec: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_execMsga____,type,
% 0.22/0.44 execMsga: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_exec_H____,type,
% 0.22/0.44 exec2: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_msg,type,
% 0.22/0.44 msg: message @ p @ v ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_p,type,
% 0.22/0.44 p2: p ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_sends,type,
% 0.22/0.44 sends: p > s > ( messageValue @ v ) > ( message @ p @ v ) > nat ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_start,type,
% 0.22/0.44 start: p > s ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_trace,type,
% 0.22/0.44 trace: list @ ( message @ p @ v ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_traceMsga____,type,
% 0.22/0.44 traceMsga: list @ ( message @ p @ v ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_trace_H____,type,
% 0.22/0.44 trace2: list @ ( message @ p @ v ) ).
% 0.22/0.44
% 0.22/0.44 thf(sy_v_trans,type,
% 0.22/0.44 trans: p > s > ( messageValue @ v ) > s ).
% 0.22/0.44
% 0.22/0.44 % Relevant facts (256)
% 0.22/0.44 thf(fact_0_PisReceiverOf,axiom,
% 0.22/0.44 isReceiverOf @ p @ v @ p2 @ msg ).
% 0.22/0.44
% 0.22/0.44 % PisReceiverOf
% 0.22/0.44 thf(fact_1_InitReachLastExec_H,axiom,
% 0.22/0.44 initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ).
% 0.22/0.44
% 0.22/0.44 % InitReachLastExec'
% 0.22/0.44 thf(fact_2_NewExec_I3_J,axiom,
% 0.22/0.44 ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 )
% 0.22/0.44 = c ) ).
% 0.22/0.44
% 0.22/0.44 % NewExec(3)
% 0.22/0.44 thf(fact_3_CMsg,axiom,
% 0.22/0.44 steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg ).
% 0.22/0.44
% 0.22/0.44 % CMsg
% 0.22/0.44 thf(fact_4_flpPseudoConsensus__axioms,axiom,
% 0.22/0.44 fLPThe1922692578sensus @ p @ s @ v @ trans @ sends @ start ).
% 0.22/0.44
% 0.22/0.44 % flpPseudoConsensus_axioms
% 0.22/0.44 thf(fact_5_ExecMsg_I3_J,axiom,
% 0.22/0.44 ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga )
% 0.22/0.44 = cMsg ) ).
% 0.22/0.44
% 0.22/0.44 % ExecMsg(3)
% 0.22/0.44 thf(fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062,axiom,
% 0.22/0.44 ( ( p2 = p2 )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ p2 @ msg )
% 0.22/0.44 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
% 0.22/0.44 => ( ord_less_eq @ ( set @ $o )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ cMsg ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % \<open>\<lbrakk>p = p; last exec' \<turnstile> msg \<mapsto> cMsg; isReceiverOf p msg; initReachable (last exec')\<rbrakk> \<Longrightarrow> val[p,last exec'] \<subseteq> val[p,cMsg]\<close>
% 0.22/0.44 thf(fact_7_DiamondOne,axiom,
% 0.22/0.44 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg1: configuration_ext @ p @ v @ s @ product_unit,P2: p,Q: p,M2: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg @ M @ Cfg1 )
% 0.22/0.44 => ( ( P2 != Q )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ P2 @ M )
% 0.22/0.44 => ( ~ ( isReceiverOf @ p @ v @ P2 @ M2 )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ Q @ M2 )
% 0.22/0.44 => ( ~ ( isReceiverOf @ p @ v @ Q @ M )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg @ M2 @ Cfg2 )
% 0.22/0.44 => ? [Cfg3: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M2 @ Cfg3 )
% 0.22/0.44 & ( steps @ p @ s @ v @ trans @ sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % DiamondOne
% 0.22/0.44 thf(fact_8_True,axiom,
% 0.22/0.44 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg ).
% 0.22/0.44
% 0.22/0.44 % True
% 0.22/0.44 thf(fact_9__092_060open_062_092_060exists_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_092_060close_062,axiom,
% 0.22/0.44 ? [X_1: configuration_ext @ p @ v @ s @ product_unit] : ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ X_1 ) ).
% 0.22/0.44
% 0.22/0.44 % \<open>\<exists>cMsg. last exec' \<turnstile> msg \<mapsto> cMsg\<close>
% 0.22/0.44 thf(fact_10__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.22/0.44 ~ ! [CMsg: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ~ ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ CMsg ) ).
% 0.22/0.44
% 0.22/0.44 % \<open>\<And>thesis. (\<And>cMsg. last exec' \<turnstile> msg \<mapsto> cMsg \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.22/0.44 thf(fact_11_Agreement,axiom,
% 0.22/0.44 ! [I: configuration_ext @ p @ v @ s @ product_unit,C: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ I @ C ) ).
% 0.22/0.44
% 0.22/0.44 % Agreement
% 0.22/0.44 thf(fact_12_ActiveProcessSilentDecisionValuesIncrease,axiom,
% 0.22/0.44 ! [P2: p,Q: p,C: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,C2: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( P2 = Q )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ C @ Msg @ C2 )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ P2 @ Msg )
% 0.22/0.44 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 => ( ord_less_eq @ ( set @ $o )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C ) )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C2 ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ActiveProcessSilentDecisionValuesIncrease
% 0.22/0.44 thf(fact_13_InactiveProcessSilentDecisionValuesDecrease,axiom,
% 0.22/0.44 ! [P2: p,Q: p,C: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,C2: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( P2 != Q )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ C @ Msg @ C2 )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ P2 @ Msg )
% 0.22/0.44 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 => ( ord_less_eq @ ( set @ $o )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C2 ) )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % InactiveProcessSilentDecisionValuesDecrease
% 0.22/0.44 thf(fact_14_nonUniformC_H,axiom,
% 0.22/0.44 ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % nonUniformC'
% 0.22/0.44 thf(fact_15_InitReachLastExecMsg,axiom,
% 0.22/0.44 initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ) ).
% 0.22/0.44
% 0.22/0.44 % InitReachLastExecMsg
% 0.22/0.44 thf(fact_16_NewExec_I1_J,axiom,
% 0.22/0.44 execution @ p @ s @ v @ trans @ sends @ start @ exec2 @ trace2 ).
% 0.22/0.44
% 0.22/0.44 % NewExec(1)
% 0.22/0.44 thf(fact_17_InitialIsInitReachable,axiom,
% 0.22/0.44 ! [C: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( initial @ p @ s @ v @ start @ C )
% 0.22/0.44 => ( initReachable @ p @ s @ v @ trans @ sends @ start @ C ) ) ).
% 0.22/0.44
% 0.22/0.44 % InitialIsInitReachable
% 0.22/0.44 thf(fact_18_flpSystem__axioms,axiom,
% 0.22/0.44 flpSystem @ p @ s @ v @ sends ).
% 0.22/0.44
% 0.22/0.44 % flpSystem_axioms
% 0.22/0.44 thf(fact_19_subsetI,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ! [X: A] :
% 0.22/0.44 ( ( member @ A @ X @ A2 )
% 0.22/0.44 => ( member @ A @ X @ B ) )
% 0.22/0.44 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 0.22/0.44
% 0.22/0.44 % subsetI
% 0.22/0.44 thf(fact_20_subset__antisym,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.22/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 0.22/0.44 => ( A2 = B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_antisym
% 0.22/0.44 thf(fact_21_QReachableTrans,axiom,
% 0.22/0.44 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg32: configuration_ext @ p @ v @ s @ product_unit,Cfg1: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg2 @ Q2 @ Cfg32 )
% 0.22/0.44 => ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % QReachableTrans
% 0.22/0.44 thf(fact_22_InitQ,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p] : ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 0.22/0.44
% 0.22/0.44 % InitQ
% 0.22/0.44 thf(fact_23_order__refl,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( preorder @ A )
% 0.22/0.44 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % order_refl
% 0.22/0.44 thf(fact_24_OnlyOccurenceDisables,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,M2: message @ p @ v] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ( enabled @ p @ v @ s @ Cfg1 @ M2 )
% 0.22/0.44 => ( ~ ( enabled @ p @ v @ s @ Cfg2 @ M2 )
% 0.22/0.44 => ( M = M2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % OnlyOccurenceDisables
% 0.22/0.44 thf(fact_25_qReachable_Osimps,axiom,
% 0.22/0.44 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: set @ p,A3: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ A3 )
% 0.22/0.44 = ( ( A3 = A1 )
% 0.22/0.44 | ? [Cfg22: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ Cfg22 )
% 0.22/0.44 & ? [Msg2: message @ p @ v] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg22 @ Msg2 @ A3 )
% 0.22/0.44 & ? [X3: p] :
% 0.22/0.44 ( ( member @ p @ X3 @ A22 )
% 0.22/0.44 & ( isReceiverOf @ p @ v @ X3 @ Msg2 ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % qReachable.simps
% 0.22/0.44 thf(fact_26_qReachable_Oinducts,axiom,
% 0.22/0.44 ! [X1: configuration_ext @ p @ v @ s @ product_unit,X22: set @ p,X32: configuration_ext @ p @ v @ s @ product_unit,P3: ( configuration_ext @ p @ v @ s @ product_unit ) > ( set @ p ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ X1 @ X22 @ X32 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Q3: set @ p] : ( P3 @ Cfg12 @ Q3 @ Cfg12 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Q3: set @ p,Cfg23: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg12 @ Q3 @ Cfg23 )
% 0.22/0.44 => ( ( P3 @ Cfg12 @ Q3 @ Cfg23 )
% 0.22/0.44 => ! [Msg3: message @ p @ v,Cfg33: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.22/0.44 => ( ? [X: p] :
% 0.22/0.44 ( ( member @ p @ X @ Q3 )
% 0.22/0.44 & ( isReceiverOf @ p @ v @ X @ Msg3 ) )
% 0.22/0.44 => ( P3 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 0.22/0.44 => ( P3 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % qReachable.inducts
% 0.22/0.44 thf(fact_27_qReachable_Ocases,axiom,
% 0.22/0.44 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: set @ p,A3: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ A3 )
% 0.22/0.44 => ( ( A3 != A1 )
% 0.22/0.44 => ~ ! [Cfg23: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ Cfg23 )
% 0.22/0.44 => ! [Msg3: message @ p @ v] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ A3 )
% 0.22/0.44 => ~ ? [X: p] :
% 0.22/0.44 ( ( member @ p @ X @ A22 )
% 0.22/0.44 & ( isReceiverOf @ p @ v @ X @ Msg3 ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % qReachable.cases
% 0.22/0.44 thf(fact_28_StepQ,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,Cfg32: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 0.22/0.44 => ( ? [X4: p] :
% 0.22/0.44 ( ( member @ p @ X4 @ Q2 )
% 0.22/0.44 & ( isReceiverOf @ p @ v @ X4 @ Msg ) )
% 0.22/0.44 => ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % StepQ
% 0.22/0.44 thf(fact_29_ExecMsg_I1_J,axiom,
% 0.22/0.44 prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ execMsga ).
% 0.22/0.44
% 0.22/0.44 % ExecMsg(1)
% 0.22/0.44 thf(fact_30_isExecution,axiom,
% 0.22/0.44 execution @ p @ s @ v @ trans @ sends @ start @ execMsga @ traceMsga ).
% 0.22/0.44
% 0.22/0.44 % isExecution
% 0.22/0.44 thf(fact_31_MsgEnabled,axiom,
% 0.22/0.44 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg ).
% 0.22/0.44
% 0.22/0.44 % MsgEnabled
% 0.22/0.44 thf(fact_32_NonUniformLexec,axiom,
% 0.22/0.44 ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NonUniformLexec
% 0.22/0.44 thf(fact_33_flpPseudoConsensus_Oaxioms_I1_J,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S] :
% 0.22/0.44 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.22/0.44 => ( flpSystem @ P @ S @ V @ Sends ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpPseudoConsensus.axioms(1)
% 0.22/0.44 thf(fact_34_flpPseudoConsensus_OAgreement,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,I: configuration_ext @ P @ V @ S @ product_unit,C: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.22/0.44 => ( agreementInit @ P @ S @ V @ Trans @ Sends @ Start @ I @ C ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpPseudoConsensus.Agreement
% 0.22/0.44 thf(fact_35_less__eq__set__def,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.22/0.44 = ( ^ [A4: set @ A,B2: set @ A] :
% 0.22/0.44 ( ord_less_eq @ ( A > $o )
% 0.22/0.44 @ ^ [X3: A] : ( member @ A @ X3 @ A4 )
% 0.22/0.44 @ ^ [X3: A] : ( member @ A @ X3 @ B2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % less_eq_set_def
% 0.22/0.44 thf(fact_36_dual__order_Oantisym,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [B3: A,A5: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ B3 @ A5 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( A5 = B3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.antisym
% 0.22/0.44 thf(fact_37_dual__order_Oeq__iff,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ( ( ^ [Y: A,Z2: A] : ( Y = Z2 ) )
% 0.22/0.44 = ( ^ [A6: A,B4: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ B4 @ A6 )
% 0.22/0.44 & ( ord_less_eq @ A @ A6 @ B4 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.eq_iff
% 0.22/0.44 thf(fact_38_dual__order_Otrans,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [B3: A,A5: A,C: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ B3 @ A5 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.22/0.44 => ( ord_less_eq @ A @ C @ A5 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.trans
% 0.22/0.44 thf(fact_39_linorder__wlog,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( linorder @ A )
% 0.22/0.44 => ! [P3: A > A > $o,A5: A,B3: A] :
% 0.22/0.44 ( ! [A7: A,B5: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A7 @ B5 )
% 0.22/0.44 => ( P3 @ A7 @ B5 ) )
% 0.22/0.44 => ( ! [A7: A,B5: A] :
% 0.22/0.44 ( ( P3 @ B5 @ A7 )
% 0.22/0.44 => ( P3 @ A7 @ B5 ) )
% 0.22/0.44 => ( P3 @ A5 @ B3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % linorder_wlog
% 0.22/0.44 thf(fact_40_dual__order_Orefl,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [A5: A] : ( ord_less_eq @ A @ A5 @ A5 ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.refl
% 0.22/0.44 thf(fact_41_order__trans,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( preorder @ A )
% 0.22/0.44 => ! [X2: A,Y2: A,Z3: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.22/0.44 => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order_trans
% 0.22/0.44 thf(fact_42_order__class_Oorder_Oantisym,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [A5: A,B3: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ B3 @ A5 )
% 0.22/0.44 => ( A5 = B3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order_class.order.antisym
% 0.22/0.44 thf(fact_43_ord__le__eq__trans,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( ord @ A )
% 0.22/0.44 => ! [A5: A,B3: A,C: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( ( B3 = C )
% 0.22/0.44 => ( ord_less_eq @ A @ A5 @ C ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ord_le_eq_trans
% 0.22/0.44 thf(fact_44_ord__eq__le__trans,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( ord @ A )
% 0.22/0.44 => ! [A5: A,B3: A,C: A] :
% 0.22/0.44 ( ( A5 = B3 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.22/0.44 => ( ord_less_eq @ A @ A5 @ C ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ord_eq_le_trans
% 0.22/0.44 thf(fact_45_mem__Collect__eq,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,P3: A > $o] :
% 0.22/0.44 ( ( member @ A @ A5 @ ( collect @ A @ P3 ) )
% 0.22/0.44 = ( P3 @ A5 ) ) ).
% 0.22/0.44
% 0.22/0.44 % mem_Collect_eq
% 0.22/0.44 thf(fact_46_Collect__mem__eq,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A] :
% 0.22/0.44 ( ( collect @ A
% 0.22/0.44 @ ^ [X3: A] : ( member @ A @ X3 @ A2 ) )
% 0.22/0.44 = A2 ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_mem_eq
% 0.22/0.44 thf(fact_47_Collect__cong,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.22/0.44 ( ! [X: A] :
% 0.22/0.44 ( ( P3 @ X )
% 0.22/0.44 = ( Q2 @ X ) )
% 0.22/0.44 => ( ( collect @ A @ P3 )
% 0.22/0.44 = ( collect @ A @ Q2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_cong
% 0.22/0.44 thf(fact_48_ext,axiom,
% 0.22/0.44 ! [B6: $tType,A: $tType,F: A > B6,G: A > B6] :
% 0.22/0.44 ( ! [X: A] :
% 0.22/0.44 ( ( F @ X )
% 0.22/0.44 = ( G @ X ) )
% 0.22/0.44 => ( F = G ) ) ).
% 0.22/0.44
% 0.22/0.44 % ext
% 0.22/0.44 thf(fact_49_order__class_Oorder_Oeq__iff,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ( ( ^ [Y: A,Z2: A] : ( Y = Z2 ) )
% 0.22/0.44 = ( ^ [A6: A,B4: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A6 @ B4 )
% 0.22/0.44 & ( ord_less_eq @ A @ B4 @ A6 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order_class.order.eq_iff
% 0.22/0.44 thf(fact_50_antisym__conv,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [Y2: A,X2: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 = ( X2 = Y2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % antisym_conv
% 0.22/0.44 thf(fact_51_le__cases3,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( linorder @ A )
% 0.22/0.44 => ! [X2: A,Y2: A,Z3: A] :
% 0.22/0.44 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 0.22/0.44 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.22/0.44 => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 0.22/0.44 => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 0.22/0.44 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 0.22/0.44 => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 0.22/0.44 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.22/0.44 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.22/0.44 => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 0.22/0.44 => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.22/0.44 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_cases3
% 0.22/0.44 thf(fact_52_order_Otrans,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [A5: A,B3: A,C: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.22/0.44 => ( ord_less_eq @ A @ A5 @ C ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order.trans
% 0.22/0.44 thf(fact_53_le__cases,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( linorder @ A )
% 0.22/0.44 => ! [X2: A,Y2: A] :
% 0.22/0.44 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_cases
% 0.22/0.44 thf(fact_54_eq__refl,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( preorder @ A )
% 0.22/0.44 => ! [X2: A,Y2: A] :
% 0.22/0.44 ( ( X2 = Y2 )
% 0.22/0.44 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % eq_refl
% 0.22/0.44 thf(fact_55_linear,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( linorder @ A )
% 0.22/0.44 => ! [X2: A,Y2: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % linear
% 0.22/0.44 thf(fact_56_antisym,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [X2: A,Y2: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.22/0.44 => ( X2 = Y2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % antisym
% 0.22/0.44 thf(fact_57_eq__iff,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ( ( ^ [Y: A,Z2: A] : ( Y = Z2 ) )
% 0.22/0.44 = ( ^ [X3: A,Y3: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.22/0.44 & ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % eq_iff
% 0.22/0.44 thf(fact_58_ord__le__eq__subst,axiom,
% 0.22/0.44 ! [A: $tType,B6: $tType] :
% 0.22/0.44 ( ( ( ord @ B6 )
% 0.22/0.44 & ( ord @ A ) )
% 0.22/0.44 => ! [A5: A,B3: A,F: A > B6,C: B6] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( ( ( F @ B3 )
% 0.22/0.44 = C )
% 0.22/0.44 => ( ! [X: A,Y4: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.22/0.44 => ( ord_less_eq @ B6 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.22/0.44 => ( ord_less_eq @ B6 @ ( F @ A5 ) @ C ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ord_le_eq_subst
% 0.22/0.44 thf(fact_59_ord__eq__le__subst,axiom,
% 0.22/0.44 ! [A: $tType,B6: $tType] :
% 0.22/0.44 ( ( ( ord @ B6 )
% 0.22/0.44 & ( ord @ A ) )
% 0.22/0.44 => ! [A5: A,F: B6 > A,B3: B6,C: B6] :
% 0.22/0.44 ( ( A5
% 0.22/0.44 = ( F @ B3 ) )
% 0.22/0.44 => ( ( ord_less_eq @ B6 @ B3 @ C )
% 0.22/0.44 => ( ! [X: B6,Y4: B6] :
% 0.22/0.44 ( ( ord_less_eq @ B6 @ X @ Y4 )
% 0.22/0.44 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.22/0.44 => ( ord_less_eq @ A @ A5 @ ( F @ C ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ord_eq_le_subst
% 0.22/0.44 thf(fact_60_order__subst2,axiom,
% 0.22/0.44 ! [A: $tType,C3: $tType] :
% 0.22/0.44 ( ( ( order @ C3 )
% 0.22/0.44 & ( order @ A ) )
% 0.22/0.44 => ! [A5: A,B3: A,F: A > C3,C: C3] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( ( ord_less_eq @ C3 @ ( F @ B3 ) @ C )
% 0.22/0.44 => ( ! [X: A,Y4: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.22/0.44 => ( ord_less_eq @ C3 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.22/0.44 => ( ord_less_eq @ C3 @ ( F @ A5 ) @ C ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order_subst2
% 0.22/0.44 thf(fact_61_order__subst1,axiom,
% 0.22/0.44 ! [A: $tType,B6: $tType] :
% 0.22/0.44 ( ( ( order @ B6 )
% 0.22/0.44 & ( order @ A ) )
% 0.22/0.44 => ! [A5: A,F: B6 > A,B3: B6,C: B6] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ ( F @ B3 ) )
% 0.22/0.44 => ( ( ord_less_eq @ B6 @ B3 @ C )
% 0.22/0.44 => ( ! [X: B6,Y4: B6] :
% 0.22/0.44 ( ( ord_less_eq @ B6 @ X @ Y4 )
% 0.22/0.44 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.22/0.44 => ( ord_less_eq @ A @ A5 @ ( F @ C ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order_subst1
% 0.22/0.44 thf(fact_62_le__fun__def,axiom,
% 0.22/0.44 ! [B6: $tType,A: $tType] :
% 0.22/0.44 ( ( ord @ B6 )
% 0.22/0.44 => ( ( ord_less_eq @ ( A > B6 ) )
% 0.22/0.44 = ( ^ [F2: A > B6,G2: A > B6] :
% 0.22/0.44 ! [X3: A] : ( ord_less_eq @ B6 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_fun_def
% 0.22/0.44 thf(fact_63_le__funI,axiom,
% 0.22/0.44 ! [B6: $tType,A: $tType] :
% 0.22/0.44 ( ( ord @ B6 )
% 0.22/0.44 => ! [F: A > B6,G: A > B6] :
% 0.22/0.44 ( ! [X: A] : ( ord_less_eq @ B6 @ ( F @ X ) @ ( G @ X ) )
% 0.22/0.44 => ( ord_less_eq @ ( A > B6 ) @ F @ G ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_funI
% 0.22/0.44 thf(fact_64_le__funE,axiom,
% 0.22/0.44 ! [B6: $tType,A: $tType] :
% 0.22/0.44 ( ( ord @ B6 )
% 0.22/0.44 => ! [F: A > B6,G: A > B6,X2: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( A > B6 ) @ F @ G )
% 0.22/0.44 => ( ord_less_eq @ B6 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_funE
% 0.22/0.44 thf(fact_65_le__funD,axiom,
% 0.22/0.44 ! [B6: $tType,A: $tType] :
% 0.22/0.44 ( ( ord @ B6 )
% 0.22/0.44 => ! [F: A > B6,G: A > B6,X2: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( A > B6 ) @ F @ G )
% 0.22/0.44 => ( ord_less_eq @ B6 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_funD
% 0.22/0.44 thf(fact_66_Collect__mono__iff,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) )
% 0.22/0.44 = ( ! [X3: A] :
% 0.22/0.44 ( ( P3 @ X3 )
% 0.22/0.44 => ( Q2 @ X3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_mono_iff
% 0.22/0.44 thf(fact_67_set__eq__subset,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( ^ [Y: set @ A,Z2: set @ A] : ( Y = Z2 ) )
% 0.22/0.44 = ( ^ [A4: set @ A,B2: set @ A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.22/0.44 & ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % set_eq_subset
% 0.22/0.44 thf(fact_68_subset__trans,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.22/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.22/0.44 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_trans
% 0.22/0.44 thf(fact_69_Collect__mono,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.22/0.44 ( ! [X: A] :
% 0.22/0.44 ( ( P3 @ X )
% 0.22/0.44 => ( Q2 @ X ) )
% 0.22/0.44 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_mono
% 0.22/0.44 thf(fact_70_subset__refl,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.22/0.44
% 0.22/0.44 % subset_refl
% 0.22/0.44 thf(fact_71_subset__iff,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.22/0.44 = ( ^ [A4: set @ A,B2: set @ A] :
% 0.22/0.44 ! [T: A] :
% 0.22/0.44 ( ( member @ A @ T @ A4 )
% 0.22/0.44 => ( member @ A @ T @ B2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_iff
% 0.22/0.44 thf(fact_72_equalityD2,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ( A2 = B )
% 0.22/0.44 => ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % equalityD2
% 0.22/0.44 thf(fact_73_equalityD1,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ( A2 = B )
% 0.22/0.44 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 0.22/0.44
% 0.22/0.44 % equalityD1
% 0.22/0.44 thf(fact_74_subset__eq,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.22/0.44 = ( ^ [A4: set @ A,B2: set @ A] :
% 0.22/0.44 ! [X3: A] :
% 0.22/0.44 ( ( member @ A @ X3 @ A4 )
% 0.22/0.44 => ( member @ A @ X3 @ B2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_eq
% 0.22/0.44 thf(fact_75_equalityE,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ( A2 = B )
% 0.22/0.44 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.22/0.44 => ~ ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % equalityE
% 0.22/0.44 thf(fact_76_subsetD,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A,C: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.22/0.44 => ( ( member @ A @ C @ A2 )
% 0.22/0.44 => ( member @ A @ C @ B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subsetD
% 0.22/0.44 thf(fact_77_in__mono,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A,X2: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.22/0.44 => ( ( member @ A @ X2 @ A2 )
% 0.22/0.44 => ( member @ A @ X2 @ B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % in_mono
% 0.22/0.44 thf(fact_78_Collect__subset,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,P3: A > $o] :
% 0.22/0.44 ( ord_less_eq @ ( set @ A )
% 0.22/0.44 @ ( collect @ A
% 0.22/0.44 @ ^ [X3: A] :
% 0.22/0.44 ( ( member @ A @ X3 @ A2 )
% 0.22/0.44 & ( P3 @ X3 ) ) )
% 0.22/0.44 @ A2 ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_subset
% 0.22/0.44 thf(fact_79_flpSystem_OInactiveProcessSilentDecisionValuesDecrease,axiom,
% 0.22/0.44 ! [P: $tType,V: $tType,S: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,P2: P,Q: P,Trans: P > S > ( messageValue @ V ) > S,C: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,C2: configuration_ext @ P @ V @ S @ product_unit,Start: P > S] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ( P2 != Q )
% 0.22/0.44 => ( ( steps @ P @ S @ V @ Trans @ Sends @ C @ Msg @ C2 )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 0.22/0.44 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 0.22/0.44 => ( ord_less_eq @ ( set @ $o )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C2 ) )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.InactiveProcessSilentDecisionValuesDecrease
% 0.22/0.44 thf(fact_80_flpSystem_OActiveProcessSilentDecisionValuesIncrease,axiom,
% 0.22/0.44 ! [P: $tType,V: $tType,S: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,P2: P,Q: P,Trans: P > S > ( messageValue @ V ) > S,C: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,C2: configuration_ext @ P @ V @ S @ product_unit,Start: P > S] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ( P2 = Q )
% 0.22/0.44 => ( ( steps @ P @ S @ V @ Trans @ Sends @ C @ Msg @ C2 )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 0.22/0.44 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 0.22/0.44 => ( ord_less_eq @ ( set @ $o )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C ) )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C2 ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.ActiveProcessSilentDecisionValuesIncrease
% 0.22/0.44 thf(fact_81_NotStepReachable,axiom,
% 0.22/0.44 ~ ( stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ c ) ).
% 0.22/0.44
% 0.22/0.44 % NotStepReachable
% 0.22/0.44 thf(fact_82_cMsgLastReachable,axiom,
% 0.22/0.44 reachable @ p @ s @ v @ trans @ sends @ cMsg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ) ).
% 0.22/0.44
% 0.22/0.44 % cMsgLastReachable
% 0.22/0.44 thf(fact_83_NoReceivingNoChange,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ~ ( isReceiverOf @ p @ v @ P2 @ M )
% 0.22/0.44 => ( ( states @ p @ v @ s @ product_unit @ Cfg1 @ P2 )
% 0.22/0.44 = ( states @ p @ v @ s @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NoReceivingNoChange
% 0.22/0.44 thf(fact_84_initReachable__def,axiom,
% 0.22/0.44 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ Cfg )
% 0.22/0.44 = ( ? [Cfg0: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( initial @ p @ s @ v @ start @ Cfg0 )
% 0.22/0.44 & ( reachable @ p @ s @ v @ trans @ sends @ Cfg0 @ Cfg ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % initReachable_def
% 0.22/0.44 thf(fact_85_ReachableStepFirst,axiom,
% 0.22/0.44 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,Cfg4: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg @ Cfg4 )
% 0.22/0.44 => ( ( Cfg = Cfg4 )
% 0.22/0.44 | ? [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Msg3: message @ p @ v,P4: p] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg @ Msg3 @ Cfg12 )
% 0.22/0.44 & ( enabled @ p @ v @ s @ Cfg @ Msg3 )
% 0.22/0.44 & ( isReceiverOf @ p @ v @ P4 @ Msg3 )
% 0.22/0.44 & ( reachable @ p @ s @ v @ trans @ sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ReachableStepFirst
% 0.22/0.44 thf(fact_86_NotInQFrozenQReachability,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( ~ ( member @ p @ P2 @ Q2 )
% 0.22/0.44 => ( ( states @ p @ v @ s @ product_unit @ Cfg1 @ P2 )
% 0.22/0.44 = ( states @ p @ v @ s @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NotInQFrozenQReachability
% 0.22/0.44 thf(fact_87_C_H_I2_J,axiom,
% 0.22/0.44 ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ c ) )
% 0.22/0.44 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % C'(2)
% 0.22/0.44 thf(fact_88_NoActivityNoMessageLoss,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p,M2: message @ p @ v] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( ~ ( member @ p @ P2 @ Q2 )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ P2 @ M2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NoActivityNoMessageLoss
% 0.22/0.44 thf(fact_89_ReachableTrans,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Cfg2: configuration_ext @ p @ v @ s @ product_unit,Cfg32: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 )
% 0.22/0.44 => ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg2 @ Cfg32 )
% 0.22/0.44 => ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ReachableTrans
% 0.22/0.44 thf(fact_90_init,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit] : ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg1 ) ).
% 0.22/0.44
% 0.22/0.44 % init
% 0.22/0.44 thf(fact_91_bot__apply,axiom,
% 0.22/0.44 ! [C3: $tType,D: $tType] :
% 0.22/0.44 ( ( bot @ C3 )
% 0.22/0.44 => ( ( bot_bot @ ( D > C3 ) )
% 0.22/0.44 = ( ^ [X3: D] : ( bot_bot @ C3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % bot_apply
% 0.22/0.44 thf(fact_92_empty__iff,axiom,
% 0.22/0.44 ! [A: $tType,C: A] :
% 0.22/0.44 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % empty_iff
% 0.22/0.44 thf(fact_93_all__not__in__conv,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A] :
% 0.22/0.44 ( ( ! [X3: A] :
% 0.22/0.44 ~ ( member @ A @ X3 @ A2 ) )
% 0.22/0.44 = ( A2
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % all_not_in_conv
% 0.22/0.44 thf(fact_94_Collect__empty__eq,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o] :
% 0.22/0.44 ( ( ( collect @ A @ P3 )
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.22/0.44 = ( ! [X3: A] :
% 0.22/0.44 ~ ( P3 @ X3 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_empty_eq
% 0.22/0.44 thf(fact_95_empty__Collect__eq,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o] :
% 0.22/0.44 ( ( ( bot_bot @ ( set @ A ) )
% 0.22/0.44 = ( collect @ A @ P3 ) )
% 0.22/0.44 = ( ! [X3: A] :
% 0.22/0.44 ~ ( P3 @ X3 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % empty_Collect_eq
% 0.22/0.44 thf(fact_96_insertCI,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,B: set @ A,B3: A] :
% 0.22/0.44 ( ( ~ ( member @ A @ A5 @ B )
% 0.22/0.44 => ( A5 = B3 ) )
% 0.22/0.44 => ( member @ A @ A5 @ ( insert @ A @ B3 @ B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insertCI
% 0.22/0.44 thf(fact_97_insert__iff,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,B3: A,A2: set @ A] :
% 0.22/0.44 ( ( member @ A @ A5 @ ( insert @ A @ B3 @ A2 ) )
% 0.22/0.44 = ( ( A5 = B3 )
% 0.22/0.44 | ( member @ A @ A5 @ A2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_iff
% 0.22/0.44 thf(fact_98_insert__absorb2,axiom,
% 0.22/0.44 ! [A: $tType,X2: A,A2: set @ A] :
% 0.22/0.44 ( ( insert @ A @ X2 @ ( insert @ A @ X2 @ A2 ) )
% 0.22/0.44 = ( insert @ A @ X2 @ A2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_absorb2
% 0.22/0.44 thf(fact_99_C_H_I1_J,axiom,
% 0.22/0.44 reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ c ).
% 0.22/0.44
% 0.22/0.44 % C'(1)
% 0.22/0.44 thf(fact_100_predicate1I,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.22/0.44 ( ! [X: A] :
% 0.22/0.44 ( ( P3 @ X )
% 0.22/0.44 => ( Q2 @ X ) )
% 0.22/0.44 => ( ord_less_eq @ ( A > $o ) @ P3 @ Q2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % predicate1I
% 0.22/0.44 thf(fact_101_reachable_Ocases,axiom,
% 0.22/0.44 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ A1 @ A22 )
% 0.22/0.44 => ( ( A22 != A1 )
% 0.22/0.44 => ~ ! [Cfg23: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ A1 @ Cfg23 )
% 0.22/0.44 => ! [Msg3: message @ p @ v] :
% 0.22/0.44 ~ ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ A22 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % reachable.cases
% 0.22/0.44 thf(fact_102_reachable_Oinducts,axiom,
% 0.22/0.44 ! [X1: configuration_ext @ p @ v @ s @ product_unit,X22: configuration_ext @ p @ v @ s @ product_unit,P3: ( configuration_ext @ p @ v @ s @ product_unit ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ X1 @ X22 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit] : ( P3 @ Cfg12 @ Cfg12 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Cfg23: configuration_ext @ p @ v @ s @ product_unit,Msg3: message @ p @ v,Cfg33: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg12 @ Cfg23 )
% 0.22/0.44 => ( ( P3 @ Cfg12 @ Cfg23 )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.22/0.44 => ( P3 @ Cfg12 @ Cfg33 ) ) ) )
% 0.22/0.44 => ( P3 @ X1 @ X22 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % reachable.inducts
% 0.22/0.44 thf(fact_103_reachable_Osimps,axiom,
% 0.22/0.44 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ A1 @ A22 )
% 0.22/0.44 = ( ? [Cfg13: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( A1 = Cfg13 )
% 0.22/0.44 & ( A22 = Cfg13 ) )
% 0.22/0.44 | ? [Cfg13: configuration_ext @ p @ v @ s @ product_unit,Cfg22: configuration_ext @ p @ v @ s @ product_unit,Msg2: message @ p @ v,Cfg34: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( A1 = Cfg13 )
% 0.22/0.44 & ( A22 = Cfg34 )
% 0.22/0.44 & ( reachable @ p @ s @ v @ trans @ sends @ Cfg13 @ Cfg22 )
% 0.22/0.44 & ( steps @ p @ s @ v @ trans @ sends @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % reachable.simps
% 0.22/0.44 thf(fact_104_reachable_Ostep,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Cfg2: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,Cfg32: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 0.22/0.44 => ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % reachable.step
% 0.22/0.44 thf(fact_105_QReachImplReach,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % QReachImplReach
% 0.22/0.44 thf(fact_106_isPrefixListExec,axiom,
% 0.22/0.44 prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ execMsga ).
% 0.22/0.44
% 0.22/0.44 % isPrefixListExec
% 0.22/0.44 thf(fact_107_OtherMessagesOnlyGrowing,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,M2: message @ p @ v] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ( M != M2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ M2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % OtherMessagesOnlyGrowing
% 0.22/0.44 thf(fact_108_stepReachable__def,axiom,
% 0.22/0.44 ! [C1: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,C22: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( stepReachable @ p @ s @ v @ trans @ sends @ C1 @ Msg @ C22 )
% 0.22/0.44 = ( ? [C5: configuration_ext @ p @ v @ s @ product_unit,C6: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ C1 @ C5 )
% 0.22/0.44 & ( steps @ p @ s @ v @ trans @ sends @ C5 @ Msg @ C6 )
% 0.22/0.44 & ( reachable @ p @ s @ v @ trans @ sends @ C6 @ C22 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % stepReachable_def
% 0.22/0.44 thf(fact_109_StepReachable,axiom,
% 0.22/0.44 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,Cfg4: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg @ Cfg4 )
% 0.22/0.44 => ( ( enabled @ p @ v @ s @ Cfg @ Msg )
% 0.22/0.44 => ( ~ ( enabled @ p @ v @ s @ Cfg4 @ Msg )
% 0.22/0.44 => ( stepReachable @ p @ s @ v @ trans @ sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % StepReachable
% 0.22/0.44 thf(fact_110_NoMessageLossStep,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p,M2: message @ p @ v] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ P2 @ M )
% 0.22/0.44 => ( ~ ( isReceiverOf @ p @ v @ P2 @ M2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NoMessageLossStep
% 0.22/0.44 thf(fact_111_subset__empty,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.22/0.44 = ( A2
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_empty
% 0.22/0.44 thf(fact_112_empty__subsetI,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 0.22/0.44
% 0.22/0.44 % empty_subsetI
% 0.22/0.44 thf(fact_113_singletonI,axiom,
% 0.22/0.44 ! [A: $tType,A5: A] : ( member @ A @ A5 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % singletonI
% 0.22/0.44 thf(fact_114_insert__subset,axiom,
% 0.22/0.44 ! [A: $tType,X2: A,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X2 @ A2 ) @ B )
% 0.22/0.44 = ( ( member @ A @ X2 @ B )
% 0.22/0.44 & ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_subset
% 0.22/0.44 thf(fact_115_ExecMsg_I2_J,axiom,
% 0.22/0.44 prefixList @ ( message @ p @ v ) @ trace2 @ traceMsga ).
% 0.22/0.44
% 0.22/0.44 % ExecMsg(2)
% 0.22/0.44 thf(fact_116_lastExecExec_HReachable,axiom,
% 0.22/0.44 reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ).
% 0.22/0.44
% 0.22/0.44 % lastExecExec'Reachable
% 0.22/0.44 thf(fact_117_singleton__conv,axiom,
% 0.22/0.44 ! [A: $tType,A5: A] :
% 0.22/0.44 ( ( collect @ A
% 0.22/0.44 @ ^ [X3: A] : ( X3 = A5 ) )
% 0.22/0.44 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % singleton_conv
% 0.22/0.44 thf(fact_118_singleton__conv2,axiom,
% 0.22/0.44 ! [A: $tType,A5: A] :
% 0.22/0.44 ( ( collect @ A
% 0.22/0.44 @ ( ^ [Y: A,Z2: A] : ( Y = Z2 )
% 0.22/0.44 @ A5 ) )
% 0.22/0.44 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % singleton_conv2
% 0.22/0.44 thf(fact_119_ExecIsExecution,axiom,
% 0.22/0.44 execution @ p @ s @ v @ trans @ sends @ start @ exec @ trace ).
% 0.22/0.44
% 0.22/0.44 % ExecIsExecution
% 0.22/0.44 thf(fact_120_vUniform__def,axiom,
% 0.22/0.44 ! [V3: $o,C: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( vUniform @ p @ s @ v @ trans @ sends @ start @ V3 @ C )
% 0.22/0.44 = ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 & ! [P5: p] :
% 0.22/0.44 ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P5 @ C ) )
% 0.22/0.44 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % vUniform_def
% 0.22/0.44 thf(fact_121_singleton__insert__inj__eq_H,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,A2: set @ A,B3: A] :
% 0.22/0.44 ( ( ( insert @ A @ A5 @ A2 )
% 0.22/0.44 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.22/0.44 = ( ( A5 = B3 )
% 0.22/0.44 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % singleton_insert_inj_eq'
% 0.22/0.44 thf(fact_122_singleton__insert__inj__eq,axiom,
% 0.22/0.44 ! [A: $tType,B3: A,A5: A,A2: set @ A] :
% 0.22/0.44 ( ( ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) )
% 0.22/0.44 = ( insert @ A @ A5 @ A2 ) )
% 0.22/0.44 = ( ( A5 = B3 )
% 0.22/0.44 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % singleton_insert_inj_eq
% 0.22/0.44 thf(fact_123_ExecMsg_I4_J,axiom,
% 0.22/0.44 ( ( last @ ( message @ p @ v ) @ traceMsga )
% 0.22/0.44 = msg ) ).
% 0.22/0.44
% 0.22/0.44 % ExecMsg(4)
% 0.22/0.44 thf(fact_124_isStepReachable,axiom,
% 0.22/0.44 stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ) ).
% 0.22/0.44
% 0.22/0.44 % isStepReachable
% 0.22/0.44 thf(fact_125_SilentDecisionValueNotInverting,axiom,
% 0.22/0.44 ! [Q: p,C: configuration_ext @ p @ v @ s @ product_unit,V3: $o,Msg: message @ p @ v,C2: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 0.22/0.44 ( ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C ) )
% 0.22/0.44 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) )
% 0.22/0.44 => ( ( steps @ p @ s @ v @ trans @ sends @ C @ Msg @ C2 )
% 0.22/0.44 => ( ( isReceiverOf @ p @ v @ P2 @ Msg )
% 0.22/0.44 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 => ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C2 ) )
% 0.22/0.44 != ( insert @ $o @ ~ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % SilentDecisionValueNotInverting
% 0.22/0.44 thf(fact_126__092_060open_062_092_060And_062p_O_A_092_060exists_062c_H_O_Areachable_A_Ilast_Aexec_J_Ac_H_A_092_060and_062_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060close_062,axiom,
% 0.22/0.44 ! [P2: p] :
% 0.22/0.44 ? [C7: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ C7 )
% 0.22/0.44 & ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P2 @ C7 ) )
% 0.22/0.44 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % \<open>\<And>p. \<exists>c'. reachable (last exec) c' \<and> val[p,c'] = {True, False}\<close>
% 0.22/0.44 thf(fact_127__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_H_O_A_092_060lbrakk_062reachable_A_Ilast_Aexec_J_Ac_H_059_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.22/0.44 ~ ! [C7: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ C7 )
% 0.22/0.44 => ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ C7 ) )
% 0.22/0.44 != ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % \<open>\<And>thesis. (\<And>c'. \<lbrakk>reachable (last exec) c'; val[p,c'] = {True, False}\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.22/0.44 thf(fact_128_Agree,axiom,
% 0.22/0.44 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ Cfg )
% 0.22/0.44 => ( agreement @ p @ v @ s @ Cfg ) ) ).
% 0.22/0.44
% 0.22/0.44 % Agree
% 0.22/0.44 thf(fact_129_emptyE,axiom,
% 0.22/0.44 ! [A: $tType,A5: A] :
% 0.22/0.44 ~ ( member @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % emptyE
% 0.22/0.44 thf(fact_130_insertE,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,B3: A,A2: set @ A] :
% 0.22/0.44 ( ( member @ A @ A5 @ ( insert @ A @ B3 @ A2 ) )
% 0.22/0.44 => ( ( A5 != B3 )
% 0.22/0.44 => ( member @ A @ A5 @ A2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insertE
% 0.22/0.44 thf(fact_131_equals0D,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,A5: A] :
% 0.22/0.44 ( ( A2
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.22/0.44 => ~ ( member @ A @ A5 @ A2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % equals0D
% 0.22/0.44 thf(fact_132_equals0I,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A] :
% 0.22/0.44 ( ! [Y4: A] :
% 0.22/0.44 ~ ( member @ A @ Y4 @ A2 )
% 0.22/0.44 => ( A2
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % equals0I
% 0.22/0.44 thf(fact_133_insertI1,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,B: set @ A] : ( member @ A @ A5 @ ( insert @ A @ A5 @ B ) ) ).
% 0.22/0.44
% 0.22/0.44 % insertI1
% 0.22/0.44 thf(fact_134_insertI2,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,B: set @ A,B3: A] :
% 0.22/0.44 ( ( member @ A @ A5 @ B )
% 0.22/0.44 => ( member @ A @ A5 @ ( insert @ A @ B3 @ B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insertI2
% 0.22/0.44 thf(fact_135_ex__in__conv,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A] :
% 0.22/0.44 ( ( ? [X3: A] : ( member @ A @ X3 @ A2 ) )
% 0.22/0.44 = ( A2
% 0.22/0.44 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ex_in_conv
% 0.22/0.44 thf(fact_136_Set_Oset__insert,axiom,
% 0.22/0.44 ! [A: $tType,X2: A,A2: set @ A] :
% 0.22/0.44 ( ( member @ A @ X2 @ A2 )
% 0.22/0.44 => ~ ! [B7: set @ A] :
% 0.22/0.44 ( ( A2
% 0.22/0.44 = ( insert @ A @ X2 @ B7 ) )
% 0.22/0.44 => ( member @ A @ X2 @ B7 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % Set.set_insert
% 0.22/0.44 thf(fact_137_singletonD,axiom,
% 0.22/0.44 ! [A: $tType,B3: A,A5: A] :
% 0.22/0.44 ( ( member @ A @ B3 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.22/0.44 => ( B3 = A5 ) ) ).
% 0.22/0.44
% 0.22/0.44 % singletonD
% 0.22/0.44 thf(fact_138_insert__ident,axiom,
% 0.22/0.44 ! [A: $tType,X2: A,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ~ ( member @ A @ X2 @ A2 )
% 0.22/0.44 => ( ~ ( member @ A @ X2 @ B )
% 0.22/0.44 => ( ( ( insert @ A @ X2 @ A2 )
% 0.22/0.44 = ( insert @ A @ X2 @ B ) )
% 0.22/0.44 = ( A2 = B ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_ident
% 0.22/0.44 thf(fact_139_insert__absorb,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,A2: set @ A] :
% 0.22/0.44 ( ( member @ A @ A5 @ A2 )
% 0.22/0.44 => ( ( insert @ A @ A5 @ A2 )
% 0.22/0.44 = A2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_absorb
% 0.22/0.44 thf(fact_140_insert__eq__iff,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,A2: set @ A,B3: A,B: set @ A] :
% 0.22/0.44 ( ~ ( member @ A @ A5 @ A2 )
% 0.22/0.44 => ( ~ ( member @ A @ B3 @ B )
% 0.22/0.44 => ( ( ( insert @ A @ A5 @ A2 )
% 0.22/0.44 = ( insert @ A @ B3 @ B ) )
% 0.22/0.44 = ( ( ( A5 = B3 )
% 0.22/0.44 => ( A2 = B ) )
% 0.22/0.44 & ( ( A5 != B3 )
% 0.22/0.44 => ? [C8: set @ A] :
% 0.22/0.44 ( ( A2
% 0.22/0.44 = ( insert @ A @ B3 @ C8 ) )
% 0.22/0.44 & ~ ( member @ A @ B3 @ C8 )
% 0.22/0.44 & ( B
% 0.22/0.44 = ( insert @ A @ A5 @ C8 ) )
% 0.22/0.44 & ~ ( member @ A @ A5 @ C8 ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_eq_iff
% 0.22/0.44 thf(fact_141_singleton__iff,axiom,
% 0.22/0.44 ! [A: $tType,B3: A,A5: A] :
% 0.22/0.44 ( ( member @ A @ B3 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.22/0.44 = ( B3 = A5 ) ) ).
% 0.22/0.44
% 0.22/0.44 % singleton_iff
% 0.22/0.44 thf(fact_142_insert__commute,axiom,
% 0.22/0.44 ! [A: $tType,X2: A,Y2: A,A2: set @ A] :
% 0.22/0.44 ( ( insert @ A @ X2 @ ( insert @ A @ Y2 @ A2 ) )
% 0.22/0.44 = ( insert @ A @ Y2 @ ( insert @ A @ X2 @ A2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_commute
% 0.22/0.44 thf(fact_143_Collect__conv__if,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,A5: A] :
% 0.22/0.44 ( ( ( P3 @ A5 )
% 0.22/0.44 => ( ( collect @ A
% 0.22/0.44 @ ^ [X3: A] :
% 0.22/0.44 ( ( X3 = A5 )
% 0.22/0.44 & ( P3 @ X3 ) ) )
% 0.22/0.44 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.22/0.44 & ( ~ ( P3 @ A5 )
% 0.22/0.44 => ( ( collect @ A
% 0.22/0.44 @ ^ [X3: A] :
% 0.22/0.44 ( ( X3 = A5 )
% 0.22/0.44 & ( P3 @ X3 ) ) )
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_conv_if
% 0.22/0.44 thf(fact_144_Collect__conv__if2,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,A5: A] :
% 0.22/0.44 ( ( ( P3 @ A5 )
% 0.22/0.44 => ( ( collect @ A
% 0.22/0.44 @ ^ [X3: A] :
% 0.22/0.44 ( ( A5 = X3 )
% 0.22/0.44 & ( P3 @ X3 ) ) )
% 0.22/0.44 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.22/0.44 & ( ~ ( P3 @ A5 )
% 0.22/0.44 => ( ( collect @ A
% 0.22/0.44 @ ^ [X3: A] :
% 0.22/0.44 ( ( A5 = X3 )
% 0.22/0.44 & ( P3 @ X3 ) ) )
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % Collect_conv_if2
% 0.22/0.44 thf(fact_145_doubleton__eq__iff,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,B3: A,C: A,D2: A] :
% 0.22/0.44 ( ( ( insert @ A @ A5 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.22/0.44 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.22/0.44 = ( ( ( A5 = C )
% 0.22/0.44 & ( B3 = D2 ) )
% 0.22/0.44 | ( ( A5 = D2 )
% 0.22/0.44 & ( B3 = C ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % doubleton_eq_iff
% 0.22/0.44 thf(fact_146_insert__not__empty,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,A2: set @ A] :
% 0.22/0.44 ( ( insert @ A @ A5 @ A2 )
% 0.22/0.44 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_not_empty
% 0.22/0.44 thf(fact_147_singleton__inject,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,B3: A] :
% 0.22/0.44 ( ( ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 0.22/0.44 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.22/0.44 => ( A5 = B3 ) ) ).
% 0.22/0.44
% 0.22/0.44 % singleton_inject
% 0.22/0.44 thf(fact_148_bot__fun__def,axiom,
% 0.22/0.44 ! [B6: $tType,A: $tType] :
% 0.22/0.44 ( ( bot @ B6 )
% 0.22/0.44 => ( ( bot_bot @ ( A > B6 ) )
% 0.22/0.44 = ( ^ [X3: A] : ( bot_bot @ B6 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % bot_fun_def
% 0.22/0.44 thf(fact_149_predicate1D,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,Q2: A > $o,X2: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q2 )
% 0.22/0.44 => ( ( P3 @ X2 )
% 0.22/0.44 => ( Q2 @ X2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % predicate1D
% 0.22/0.44 thf(fact_150_subset__singletonD,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,X2: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.22/0.44 => ( ( A2
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.22/0.44 | ( A2
% 0.22/0.44 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_singletonD
% 0.22/0.44 thf(fact_151_mk__disjoint__insert,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,A2: set @ A] :
% 0.22/0.44 ( ( member @ A @ A5 @ A2 )
% 0.22/0.44 => ? [B7: set @ A] :
% 0.22/0.44 ( ( A2
% 0.22/0.44 = ( insert @ A @ A5 @ B7 ) )
% 0.22/0.44 & ~ ( member @ A @ A5 @ B7 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % mk_disjoint_insert
% 0.22/0.44 thf(fact_152_subset__singleton__iff,axiom,
% 0.22/0.44 ! [A: $tType,X5: set @ A,A5: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ X5 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.22/0.44 = ( ( X5
% 0.22/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.22/0.44 | ( X5
% 0.22/0.44 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_singleton_iff
% 0.22/0.44 thf(fact_153_rev__predicate1D,axiom,
% 0.22/0.44 ! [A: $tType,P3: A > $o,X2: A,Q2: A > $o] :
% 0.22/0.44 ( ( P3 @ X2 )
% 0.22/0.44 => ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q2 )
% 0.22/0.44 => ( Q2 @ X2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % rev_predicate1D
% 0.22/0.44 thf(fact_154_insert__Collect,axiom,
% 0.22/0.44 ! [A: $tType,A5: A,P3: A > $o] :
% 0.22/0.44 ( ( insert @ A @ A5 @ ( collect @ A @ P3 ) )
% 0.22/0.44 = ( collect @ A
% 0.22/0.44 @ ^ [U: A] :
% 0.22/0.44 ( ( U != A5 )
% 0.22/0.44 => ( P3 @ U ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_Collect
% 0.22/0.44 thf(fact_155_insert__compr,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( insert @ A )
% 0.22/0.44 = ( ^ [A6: A,B2: set @ A] :
% 0.22/0.44 ( collect @ A
% 0.22/0.44 @ ^ [X3: A] :
% 0.22/0.44 ( ( X3 = A6 )
% 0.22/0.44 | ( member @ A @ X3 @ B2 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_compr
% 0.22/0.44 thf(fact_156_empty__def,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( bot_bot @ ( set @ A ) )
% 0.22/0.44 = ( collect @ A
% 0.22/0.44 @ ^ [X3: A] : $false ) ) ).
% 0.22/0.44
% 0.22/0.44 % empty_def
% 0.22/0.44 thf(fact_157_bot_Oextremum,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order_bot @ A )
% 0.22/0.44 => ! [A5: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A5 ) ) ).
% 0.22/0.44
% 0.22/0.44 % bot.extremum
% 0.22/0.44 thf(fact_158_bot_Oextremum__unique,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order_bot @ A )
% 0.22/0.44 => ! [A5: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ ( bot_bot @ A ) )
% 0.22/0.44 = ( A5
% 0.22/0.44 = ( bot_bot @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % bot.extremum_unique
% 0.22/0.44 thf(fact_159_bot_Oextremum__uniqueI,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order_bot @ A )
% 0.22/0.44 => ! [A5: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ ( bot_bot @ A ) )
% 0.22/0.44 => ( A5
% 0.22/0.44 = ( bot_bot @ A ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % bot.extremum_uniqueI
% 0.22/0.44 thf(fact_160_insert__mono,axiom,
% 0.22/0.44 ! [A: $tType,C4: set @ A,D3: set @ A,A5: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 0.22/0.44 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A5 @ C4 ) @ ( insert @ A @ A5 @ D3 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % insert_mono
% 0.22/0.44 thf(fact_161_subset__insert,axiom,
% 0.22/0.44 ! [A: $tType,X2: A,A2: set @ A,B: set @ A] :
% 0.22/0.44 ( ~ ( member @ A @ X2 @ A2 )
% 0.22/0.44 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X2 @ B ) )
% 0.22/0.44 = ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_insert
% 0.22/0.44 thf(fact_162_subset__insertI,axiom,
% 0.22/0.44 ! [A: $tType,B: set @ A,A5: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A5 @ B ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_insertI
% 0.22/0.44 thf(fact_163_subset__insertI2,axiom,
% 0.22/0.44 ! [A: $tType,A2: set @ A,B: set @ A,B3: A] :
% 0.22/0.44 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.22/0.44 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ B ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % subset_insertI2
% 0.22/0.44 thf(fact_164_flpSystem_OvUniform__def,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,V3: $o,C: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ V3 @ C )
% 0.22/0.44 = ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 0.22/0.44 & ! [P5: P] :
% 0.22/0.44 ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ P5 @ C ) )
% 0.22/0.44 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.vUniform_def
% 0.22/0.44 thf(fact_165_flpSystem_OSilentDecisionValueNotInverting,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,Q: P,C: configuration_ext @ P @ V @ S @ product_unit,V3: $o,Msg: message @ P @ V,C2: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C ) )
% 0.22/0.44 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) )
% 0.22/0.44 => ( ( steps @ P @ S @ V @ Trans @ Sends @ C @ Msg @ C2 )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 0.22/0.44 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 0.22/0.44 => ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C2 ) )
% 0.22/0.44 != ( insert @ $o @ ~ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.SilentDecisionValueNotInverting
% 0.22/0.44 thf(fact_166_flpSystem_OpSilDecVal_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( pSilDecVal @ P @ S @ V )
% 0.22/0.44 = ( pSilDecVal @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.pSilDecVal.cong
% 0.22/0.44 thf(fact_167_flpSystem_OvUniform_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( vUniform @ P @ S @ V )
% 0.22/0.44 = ( vUniform @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.vUniform.cong
% 0.22/0.44 thf(fact_168_flpSystem_OagreementInit_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( agreementInit @ P @ S @ V )
% 0.22/0.44 = ( agreementInit @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.agreementInit.cong
% 0.22/0.44 thf(fact_169_expandExecutionReachable,axiom,
% 0.22/0.44 ! [CfgLast: configuration_ext @ p @ v @ s @ product_unit,Cfg: configuration_ext @ p @ v @ s @ product_unit,Exec: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace: list @ ( message @ p @ v )] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ CfgLast @ Cfg )
% 0.22/0.44 => ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec @ Trace )
% 0.22/0.44 => ( ( CfgLast
% 0.22/0.44 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec ) )
% 0.22/0.44 => ? [Exec2: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace2: list @ ( message @ p @ v )] :
% 0.22/0.44 ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 0.22/0.44 & ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec @ Exec2 )
% 0.22/0.44 & ( prefixList @ ( message @ p @ v ) @ Trace @ Trace2 ) )
% 0.22/0.44 | ( ( Exec = Exec2 )
% 0.22/0.44 & ( Trace = Trace2 ) ) )
% 0.22/0.44 & ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec2 )
% 0.22/0.44 = Cfg ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % expandExecutionReachable
% 0.22/0.44 thf(fact_170_NewExec_I2_J,axiom,
% 0.22/0.44 ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ exec2 )
% 0.22/0.44 & ( prefixList @ ( message @ p @ v ) @ trace @ trace2 ) )
% 0.22/0.44 | ( ( exec = exec2 )
% 0.22/0.44 & ( trace = trace2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NewExec(2)
% 0.22/0.44 thf(fact_171_NoOutMessageLoss,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Cfg2: configuration_ext @ p @ v @ s @ product_unit,V3: $o] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ ( outMsg @ p @ v @ V3 ) ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ ( outMsg @ p @ v @ V3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NoOutMessageLoss
% 0.22/0.44 thf(fact_172_asynchronousSystem_OReachableStepFirst,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg: configuration_ext @ P @ V @ S @ product_unit,Cfg4: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg @ Cfg4 )
% 0.22/0.44 => ( ( Cfg = Cfg4 )
% 0.22/0.44 | ? [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Msg3: message @ P @ V,P4: P] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg @ Msg3 @ Cfg12 )
% 0.22/0.44 & ( enabled @ P @ V @ S @ Cfg @ Msg3 )
% 0.22/0.44 & ( isReceiverOf @ P @ V @ P4 @ Msg3 )
% 0.22/0.44 & ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.ReachableStepFirst
% 0.22/0.44 thf(fact_173_asynchronousSystem_ONoActivityNoMessageLoss,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P,M2: message @ P @ V] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( ~ ( member @ P @ P2 @ Q2 )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ P2 @ M2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.NoActivityNoMessageLoss
% 0.22/0.44 thf(fact_174_asynchronousSystem_ONoMessageLossStep,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P,M2: message @ P @ V] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ P2 @ M )
% 0.22/0.44 => ( ~ ( isReceiverOf @ P @ V @ P2 @ M2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.NoMessageLossStep
% 0.22/0.44 thf(fact_175_message_Oinject_I2_J,axiom,
% 0.22/0.44 ! [V: $tType,P: $tType,X22: $o,Y22: $o] :
% 0.22/0.44 ( ( ( outMsg @ P @ V @ X22 )
% 0.22/0.44 = ( outMsg @ P @ V @ Y22 ) )
% 0.22/0.44 = ( X22 = Y22 ) ) ).
% 0.22/0.44
% 0.22/0.44 % message.inject(2)
% 0.22/0.44 thf(fact_176_StepOutMsg,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,V3: $o,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ~ ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ ( outMsg @ p @ v @ V3 ) @ Cfg2 ) ).
% 0.22/0.44
% 0.22/0.44 % StepOutMsg
% 0.22/0.44 thf(fact_177_isPrefixListTrace,axiom,
% 0.22/0.44 prefixList @ ( message @ p @ v ) @ trace @ traceMsga ).
% 0.22/0.44
% 0.22/0.44 % isPrefixListTrace
% 0.22/0.44 thf(fact_178_expandExecutionStep,axiom,
% 0.22/0.44 ! [Exec3: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Msg: message @ p @ v,CMsg2: configuration_ext @ p @ v @ s @ product_unit,Trace3: list @ ( message @ p @ v )] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec3 ) @ Msg @ CMsg2 )
% 0.22/0.44 => ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec3 @ Trace3 )
% 0.22/0.44 => ? [Exec4: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace4: list @ ( message @ p @ v )] :
% 0.22/0.44 ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec4 @ Trace4 )
% 0.22/0.44 & ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec3 @ Exec4 )
% 0.22/0.44 & ( prefixList @ ( message @ p @ v ) @ Trace3 @ Trace4 )
% 0.22/0.44 & ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec4 )
% 0.22/0.44 = CMsg2 )
% 0.22/0.44 & ( ( last @ ( message @ p @ v ) @ Trace4 )
% 0.22/0.44 = Msg ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % expandExecutionStep
% 0.22/0.44 thf(fact_179__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062exec_H_Atrace_H_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_Aexec_H_Atrace_H_059_AprefixList_Aexec_Aexec_H_A_092_060and_062_AprefixList_Atrace_Atrace_H_A_092_060or_062_Aexec_A_061_Aexec_H_A_092_060and_062_Atrace_A_061_Atrace_H_059_Alast_Aexec_H_A_061_Ac_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.22/0.44 ~ ! [Exec2: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace2: list @ ( message @ p @ v )] :
% 0.22/0.44 ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 0.22/0.44 => ( ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ Exec2 )
% 0.22/0.44 & ( prefixList @ ( message @ p @ v ) @ trace @ Trace2 ) )
% 0.22/0.44 | ( ( exec = Exec2 )
% 0.22/0.44 & ( trace = Trace2 ) ) )
% 0.22/0.44 => ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec2 )
% 0.22/0.44 != c ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % \<open>\<And>thesis. (\<And>exec' trace'. \<lbrakk>execution trans sends start exec' trace'; prefixList exec exec' \<and> prefixList trace trace' \<or> exec = exec' \<and> trace = trace'; last exec' = c'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.22/0.44 thf(fact_180__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.22/0.44 ~ ! [ExecMsg: list @ ( configuration_ext @ p @ v @ s @ product_unit ),TraceMsg: list @ ( message @ p @ v )] :
% 0.22/0.44 ( ( execution @ p @ s @ v @ trans @ sends @ start @ ExecMsg @ TraceMsg )
% 0.22/0.44 => ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ ExecMsg )
% 0.22/0.44 => ( ( prefixList @ ( message @ p @ v ) @ trace2 @ TraceMsg )
% 0.22/0.44 => ( ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ExecMsg )
% 0.22/0.44 = cMsg )
% 0.22/0.44 => ( ( last @ ( message @ p @ v ) @ TraceMsg )
% 0.22/0.44 != msg ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % \<open>\<And>thesis. (\<And>execMsg traceMsg. \<lbrakk>execution trans sends start execMsg traceMsg; prefixList exec' execMsg; prefixList trace' traceMsg; last execMsg = cMsg; last traceMsg = msg\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.22/0.44 thf(fact_181_bot__set__def,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( bot_bot @ ( set @ A ) )
% 0.22/0.44 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % bot_set_def
% 0.22/0.44 thf(fact_182_asynchronousSystem_OStepOutMsg,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,V3: $o,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ~ ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ ( outMsg @ P @ V @ V3 ) @ Cfg2 ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.StepOutMsg
% 0.22/0.44 thf(fact_183_isReceiverOf_Osimps_I3_J,axiom,
% 0.22/0.44 ! [P: $tType,V: $tType,P1: P,V3: $o] :
% 0.22/0.44 ~ ( isReceiverOf @ P @ V @ P1 @ ( outMsg @ P @ V @ V3 ) ) ).
% 0.22/0.44
% 0.22/0.44 % isReceiverOf.simps(3)
% 0.22/0.44 thf(fact_184_asynchronousSystem_ONoOutMessageLoss,axiom,
% 0.22/0.44 ! [S: $tType,P: $tType,V: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Cfg2: configuration_ext @ P @ V @ S @ product_unit,V3: $o] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ ( outMsg @ P @ V @ V3 ) ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ ( outMsg @ P @ V @ V3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.NoOutMessageLoss
% 0.22/0.44 thf(fact_185_asynchronousSystem_Osteps_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( steps @ P @ S @ V )
% 0.22/0.44 = ( steps @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.steps.cong
% 0.22/0.44 thf(fact_186_asynchronousSystem_OReachableTrans,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Cfg32: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 0.22/0.44 => ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Cfg32 )
% 0.22/0.44 => ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.ReachableTrans
% 0.22/0.44 thf(fact_187_asynchronousSystem_Oreachable_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( reachable @ P @ S @ V )
% 0.22/0.44 = ( reachable @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.reachable.cong
% 0.22/0.44 thf(fact_188_asynchronousSystem_Oinit,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit] : ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg1 ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.init
% 0.22/0.44 thf(fact_189_UniqueReceiverOf,axiom,
% 0.22/0.44 ! [V: $tType,P: $tType,Q: P,Msg: message @ P @ V,P2: P] :
% 0.22/0.44 ( ( isReceiverOf @ P @ V @ Q @ Msg )
% 0.22/0.44 => ( ( P2 != Q )
% 0.22/0.44 => ~ ( isReceiverOf @ P @ V @ P2 @ Msg ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % UniqueReceiverOf
% 0.22/0.44 thf(fact_190_asynchronousSystem_OQReachableTrans,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg32: configuration_ext @ P @ V @ S @ product_unit,Cfg1: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Q2 @ Cfg32 )
% 0.22/0.44 => ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.QReachableTrans
% 0.22/0.44 thf(fact_191_asynchronousSystem_OqReachable_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V )
% 0.22/0.44 = ( qReachable @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.qReachable.cong
% 0.22/0.44 thf(fact_192_asynchronousSystem_OInitQ,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P] : ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.InitQ
% 0.22/0.44 thf(fact_193_asynchronousSystem_OinitReachable_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( initReachable @ P @ S @ V )
% 0.22/0.44 = ( initReachable @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.initReachable.cong
% 0.22/0.44 thf(fact_194_asynchronousSystem_Oinitial_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( initial @ P @ S @ V )
% 0.22/0.44 = ( initial @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.initial.cong
% 0.22/0.44 thf(fact_195_asynchronousSystem_OstepReachable_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( stepReachable @ P @ S @ V )
% 0.22/0.44 = ( stepReachable @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.stepReachable.cong
% 0.22/0.44 thf(fact_196_asynchronousSystem_Ostep,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,Cfg32: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 0.22/0.44 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 0.22/0.44 => ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.step
% 0.22/0.44 thf(fact_197_asynchronousSystem_Oreachable_Ocases,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A1: configuration_ext @ P @ V @ S @ product_unit,A22: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ A1 @ A22 )
% 0.22/0.44 => ( ( A22 != A1 )
% 0.22/0.44 => ~ ! [Cfg23: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ A1 @ Cfg23 )
% 0.22/0.44 => ! [Msg3: message @ P @ V] :
% 0.22/0.44 ~ ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ A22 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.reachable.cases
% 0.22/0.44 thf(fact_198_asynchronousSystem_Oreachable_Osimps,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( reachable @ P @ S @ V )
% 0.22/0.44 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A12: configuration_ext @ P @ V @ S @ product_unit,A23: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ? [Cfg13: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( A12 = Cfg13 )
% 0.22/0.44 & ( A23 = Cfg13 ) )
% 0.22/0.44 | ? [Cfg13: configuration_ext @ P @ V @ S @ product_unit,Cfg22: configuration_ext @ P @ V @ S @ product_unit,Msg2: message @ P @ V,Cfg34: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( A12 = Cfg13 )
% 0.22/0.44 & ( A23 = Cfg34 )
% 0.22/0.44 & ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ Cfg13 @ Cfg22 )
% 0.22/0.44 & ( steps @ P @ S @ V @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.reachable.simps
% 0.22/0.44 thf(fact_199_asynchronousSystem_Oreachable_Oinducts,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,X1: configuration_ext @ P @ V @ S @ product_unit,X22: configuration_ext @ P @ V @ S @ product_unit,P3: ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ X1 @ X22 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit] : ( P3 @ Cfg12 @ Cfg12 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Cfg23: configuration_ext @ P @ V @ S @ product_unit,Msg3: message @ P @ V,Cfg33: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg12 @ Cfg23 )
% 0.22/0.44 => ( ( P3 @ Cfg12 @ Cfg23 )
% 0.22/0.44 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.22/0.44 => ( P3 @ Cfg12 @ Cfg33 ) ) ) )
% 0.22/0.44 => ( P3 @ X1 @ X22 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.reachable.inducts
% 0.22/0.44 thf(fact_200_asynchronousSystem_ODiamondOne,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg1: configuration_ext @ P @ V @ S @ product_unit,P2: P,Q: P,M2: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg @ M @ Cfg1 )
% 0.22/0.44 => ( ( P2 != Q )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ P2 @ M )
% 0.22/0.44 => ( ~ ( isReceiverOf @ P @ V @ P2 @ M2 )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ Q @ M2 )
% 0.22/0.44 => ( ~ ( isReceiverOf @ P @ V @ Q @ M )
% 0.22/0.44 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg @ M2 @ Cfg2 )
% 0.22/0.44 => ? [Cfg3: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M2 @ Cfg3 )
% 0.22/0.44 & ( steps @ P @ S @ V @ Trans @ Sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.DiamondOne
% 0.22/0.44 thf(fact_201_asynchronousSystem_OQReachImplReach,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.QReachImplReach
% 0.22/0.44 thf(fact_202_asynchronousSystem_OOnlyOccurenceDisables,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,M2: message @ P @ V] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ( enabled @ P @ V @ S @ Cfg1 @ M2 )
% 0.22/0.44 => ( ~ ( enabled @ P @ V @ S @ Cfg2 @ M2 )
% 0.22/0.44 => ( M = M2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.OnlyOccurenceDisables
% 0.22/0.44 thf(fact_203_asynchronousSystem_ONotInQFrozenQReachability,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( ~ ( member @ P @ P2 @ Q2 )
% 0.22/0.44 => ( ( states @ P @ V @ S @ product_unit @ Cfg1 @ P2 )
% 0.22/0.44 = ( states @ P @ V @ S @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.NotInQFrozenQReachability
% 0.22/0.44 thf(fact_204_asynchronousSystem_OInitialIsInitReachable,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Start: P > S,C: configuration_ext @ P @ V @ S @ product_unit,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat] :
% 0.22/0.44 ( ( initial @ P @ S @ V @ Start @ C )
% 0.22/0.44 => ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.InitialIsInitReachable
% 0.22/0.44 thf(fact_205_asynchronousSystem_OOtherMessagesOnlyGrowing,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,M2: message @ P @ V] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ( M != M2 )
% 0.22/0.44 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ M2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.OtherMessagesOnlyGrowing
% 0.22/0.44 thf(fact_206_asynchronousSystem_OStepQ,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,Cfg32: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.22/0.44 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 0.22/0.44 => ( ? [X4: P] :
% 0.22/0.44 ( ( member @ P @ X4 @ Q2 )
% 0.22/0.44 & ( isReceiverOf @ P @ V @ X4 @ Msg ) )
% 0.22/0.44 => ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.StepQ
% 0.22/0.44 thf(fact_207_asynchronousSystem_OqReachable_Ocases,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A1: configuration_ext @ P @ V @ S @ product_unit,A22: set @ P,A3: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ A1 @ A22 @ A3 )
% 0.22/0.44 => ( ( A3 != A1 )
% 0.22/0.44 => ~ ! [Cfg23: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ A1 @ A22 @ Cfg23 )
% 0.22/0.44 => ! [Msg3: message @ P @ V] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ A3 )
% 0.22/0.44 => ~ ? [X: P] :
% 0.22/0.44 ( ( member @ P @ X @ A22 )
% 0.22/0.44 & ( isReceiverOf @ P @ V @ X @ Msg3 ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.qReachable.cases
% 0.22/0.44 thf(fact_208_asynchronousSystem_OqReachable_Osimps,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V )
% 0.22/0.44 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A12: configuration_ext @ P @ V @ S @ product_unit,A23: set @ P,A32: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( A32 = A12 )
% 0.22/0.44 | ? [Cfg22: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans2 @ Sends2 @ A12 @ A23 @ Cfg22 )
% 0.22/0.44 & ? [Msg2: message @ P @ V] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ A32 )
% 0.22/0.44 & ? [X3: P] :
% 0.22/0.44 ( ( member @ P @ X3 @ A23 )
% 0.22/0.44 & ( isReceiverOf @ P @ V @ X3 @ Msg2 ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.qReachable.simps
% 0.22/0.44 thf(fact_209_asynchronousSystem_OqReachable_Oinducts,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,X1: configuration_ext @ P @ V @ S @ product_unit,X22: set @ P,X32: configuration_ext @ P @ V @ S @ product_unit,P3: ( configuration_ext @ P @ V @ S @ product_unit ) > ( set @ P ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ X1 @ X22 @ X32 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Q3: set @ P] : ( P3 @ Cfg12 @ Q3 @ Cfg12 )
% 0.22/0.44 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Q3: set @ P,Cfg23: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg12 @ Q3 @ Cfg23 )
% 0.22/0.44 => ( ( P3 @ Cfg12 @ Q3 @ Cfg23 )
% 0.22/0.44 => ! [Msg3: message @ P @ V,Cfg33: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.22/0.44 => ( ? [X: P] :
% 0.22/0.44 ( ( member @ P @ X @ Q3 )
% 0.22/0.44 & ( isReceiverOf @ P @ V @ X @ Msg3 ) )
% 0.22/0.44 => ( P3 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 0.22/0.44 => ( P3 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.qReachable.inducts
% 0.22/0.44 thf(fact_210_asynchronousSystem_ONoReceivingNoChange,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ~ ( isReceiverOf @ P @ V @ P2 @ M )
% 0.22/0.44 => ( ( states @ P @ V @ S @ product_unit @ Cfg1 @ P2 )
% 0.22/0.44 = ( states @ P @ V @ S @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.NoReceivingNoChange
% 0.22/0.44 thf(fact_211_asynchronousSystem_OinitReachable__def,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( initReachable @ P @ S @ V )
% 0.22/0.44 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start2: P > S,Cfg5: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ? [Cfg0: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( initial @ P @ S @ V @ Start2 @ Cfg0 )
% 0.22/0.44 & ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ Cfg0 @ Cfg5 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.initReachable_def
% 0.22/0.44 thf(fact_212_asynchronousSystem_OstepReachable__def,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( stepReachable @ P @ S @ V )
% 0.22/0.44 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,C12: configuration_ext @ P @ V @ S @ product_unit,Msg2: message @ P @ V,C23: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ? [C5: configuration_ext @ P @ V @ S @ product_unit,C6: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ C12 @ C5 )
% 0.22/0.44 & ( steps @ P @ S @ V @ Trans2 @ Sends2 @ C5 @ Msg2 @ C6 )
% 0.22/0.44 & ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ C6 @ C23 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.stepReachable_def
% 0.22/0.44 thf(fact_213_asynchronousSystem_OStepReachable,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg: configuration_ext @ P @ V @ S @ product_unit,Cfg4: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg @ Cfg4 )
% 0.22/0.44 => ( ( enabled @ P @ V @ S @ Cfg @ Msg )
% 0.22/0.44 => ( ~ ( enabled @ P @ V @ S @ Cfg4 @ Msg )
% 0.22/0.44 => ( stepReachable @ P @ S @ V @ Trans @ Sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.StepReachable
% 0.22/0.44 thf(fact_214_asynchronousSystem_OexpandExecutionStep,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Exec3: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Msg: message @ P @ V,CMsg2: configuration_ext @ P @ V @ S @ product_unit,Start: P > S,Trace3: list @ ( message @ P @ V )] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec3 ) @ Msg @ CMsg2 )
% 0.22/0.44 => ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec3 @ Trace3 )
% 0.22/0.44 => ? [Exec4: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace4: list @ ( message @ P @ V )] :
% 0.22/0.44 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec4 @ Trace4 )
% 0.22/0.44 & ( prefixList @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec3 @ Exec4 )
% 0.22/0.44 & ( prefixList @ ( message @ P @ V ) @ Trace3 @ Trace4 )
% 0.22/0.44 & ( ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec4 )
% 0.22/0.44 = CMsg2 )
% 0.22/0.44 & ( ( last @ ( message @ P @ V ) @ Trace4 )
% 0.22/0.44 = Msg ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.expandExecutionStep
% 0.22/0.44 thf(fact_215_asynchronousSystem_OexpandExecutionReachable,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,CfgLast: configuration_ext @ P @ V @ S @ product_unit,Cfg: configuration_ext @ P @ V @ S @ product_unit,Start: P > S,Exec: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace: list @ ( message @ P @ V )] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ CfgLast @ Cfg )
% 0.22/0.44 => ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec @ Trace )
% 0.22/0.44 => ( ( CfgLast
% 0.22/0.44 = ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec ) )
% 0.22/0.44 => ? [Exec2: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace2: list @ ( message @ P @ V )] :
% 0.22/0.44 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec2 @ Trace2 )
% 0.22/0.44 & ( ( ( prefixList @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec @ Exec2 )
% 0.22/0.44 & ( prefixList @ ( message @ P @ V ) @ Trace @ Trace2 ) )
% 0.22/0.44 | ( ( Exec = Exec2 )
% 0.22/0.44 & ( Trace = Trace2 ) ) )
% 0.22/0.44 & ( ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec2 )
% 0.22/0.44 = Cfg ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.expandExecutionReachable
% 0.22/0.44 thf(fact_216_NonUniformCanReachSilentBivalence,axiom,
% 0.22/0.44 ! [C: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 0.22/0.44 ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ C )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ C ) )
% 0.22/0.44 => ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ! [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ Cfg6 )
% 0.22/0.44 => ( agreement @ p @ v @ s @ Cfg6 ) )
% 0.22/0.44 => ? [C7: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ C7 )
% 0.22/0.44 & ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P2 @ C7 ) )
% 0.22/0.44 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NonUniformCanReachSilentBivalence
% 0.22/0.44 thf(fact_217_PseudoTermination,axiom,
% 0.22/0.44 ! [Cc2: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc2 @ Q2 ) ).
% 0.22/0.44
% 0.22/0.44 % PseudoTermination
% 0.22/0.44 thf(fact_218_DecisionValuesExist,axiom,
% 0.22/0.44 ! [C: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 0.22/0.44 ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 => ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P2 @ C ) )
% 0.22/0.44 != ( bot_bot @ ( set @ $o ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % DecisionValuesExist
% 0.22/0.44 thf(fact_219_InitialNonUniformCfg,axiom,
% 0.22/0.44 ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ! [I2: configuration_ext @ p @ v @ s @ product_unit,X_1: configuration_ext @ p @ v @ s @ product_unit] : ( validity @ p @ s @ v @ trans @ sends @ start @ I2 @ X_1 )
% 0.22/0.44 => ( ! [I2: configuration_ext @ p @ v @ s @ product_unit,X_1: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ I2 @ X_1 )
% 0.22/0.44 => ? [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( initial @ p @ s @ v @ start @ Cfg6 )
% 0.22/0.44 & ( initReachable @ p @ s @ v @ trans @ sends @ start @ Cfg6 )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ Cfg6 )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ Cfg6 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % InitialNonUniformCfg
% 0.22/0.44 thf(fact_220_flpPseudoConsensus_OPseudoTermination,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,Cc2: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P] :
% 0.22/0.44 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.22/0.44 => ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc2 @ Q2 ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpPseudoConsensus.PseudoTermination
% 0.22/0.44 thf(fact_221_flpSystem_OterminationPseudo_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( terminationPseudo @ P @ S @ V )
% 0.22/0.44 = ( terminationPseudo @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.terminationPseudo.cong
% 0.22/0.44 thf(fact_222_flpSystem_ODecisionValuesExist,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,C: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ! [Cc: configuration_ext @ P @ V @ S @ product_unit,X_1: set @ P] : ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 0.22/0.44 => ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ P2 @ C ) )
% 0.22/0.44 != ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.DecisionValuesExist
% 0.22/0.44 thf(fact_223_flpSystem_ONonUniformCanReachSilentBivalence,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,C: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 0.22/0.44 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $false @ C )
% 0.22/0.44 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $true @ C ) )
% 0.22/0.44 => ( ! [Cc: configuration_ext @ P @ V @ S @ product_unit,X_1: set @ P] : ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ! [Cfg6: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ C @ Cfg6 )
% 0.22/0.44 => ( agreement @ P @ V @ S @ Cfg6 ) )
% 0.22/0.44 => ? [C7: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( reachable @ P @ S @ V @ Trans @ Sends @ C @ C7 )
% 0.22/0.44 & ( ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ P2 @ C7 ) )
% 0.22/0.44 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.NonUniformCanReachSilentBivalence
% 0.22/0.44 thf(fact_224_flpSystem_OInitialNonUniformCfg,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ! [Cc: configuration_ext @ P @ V @ S @ product_unit,X_1: set @ P] : ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ! [I2: configuration_ext @ P @ V @ S @ product_unit,X_1: configuration_ext @ P @ V @ S @ product_unit] : ( validity @ P @ S @ V @ Trans @ Sends @ Start @ I2 @ X_1 )
% 0.22/0.44 => ( ! [I2: configuration_ext @ P @ V @ S @ product_unit,X_1: configuration_ext @ P @ V @ S @ product_unit] : ( agreementInit @ P @ S @ V @ Trans @ Sends @ Start @ I2 @ X_1 )
% 0.22/0.44 => ? [Cfg6: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( initial @ P @ S @ V @ Start @ Cfg6 )
% 0.22/0.44 & ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ Cfg6 )
% 0.22/0.44 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $false @ Cfg6 )
% 0.22/0.44 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $true @ Cfg6 ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.InitialNonUniformCfg
% 0.22/0.44 thf(fact_225_execution_OExistImpliesMinEnabled,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,Exec: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace: list @ ( message @ P @ V ),P2: P,Msg: message @ P @ V] :
% 0.22/0.44 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec @ Trace )
% 0.22/0.44 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 0.22/0.44 => ( ( enabled @ P @ V @ S @ ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec ) @ Msg )
% 0.22/0.44 => ? [X_1: message @ P @ V] : ( minimalEnabled @ P @ V @ S @ Exec @ Trace @ X_1 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % execution.ExistImpliesMinEnabled
% 0.22/0.44 thf(fact_226_execution_OminimalEnabled_Ocong,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType] :
% 0.22/0.44 ( ( minimalEnabled @ P @ V @ S )
% 0.22/0.44 = ( minimalEnabled @ P @ V @ S ) ) ).
% 0.22/0.44
% 0.22/0.44 % execution.minimalEnabled.cong
% 0.22/0.44 thf(fact_227_flpSystem_Ovalidity_Ocong,axiom,
% 0.22/0.44 ! [V: $tType,S: $tType,P: $tType] :
% 0.22/0.44 ( ( validity @ P @ S @ V )
% 0.22/0.44 = ( validity @ P @ S @ V ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.validity.cong
% 0.22/0.44 thf(fact_228_execution_OFirstOccurrenceExists,axiom,
% 0.22/0.44 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,Exec: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace: list @ ( message @ P @ V ),Msg: message @ P @ V] :
% 0.22/0.44 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec @ Trace )
% 0.22/0.44 => ( ( enabled @ P @ V @ S @ ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec ) @ Msg )
% 0.22/0.44 => ( ? [P6: P] : ( isReceiverOf @ P @ V @ P6 @ Msg )
% 0.22/0.44 => ? [X_1: nat] : ( firstOccurrence @ P @ V @ S @ Exec @ Trace @ Msg @ X_1 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % execution.FirstOccurrenceExists
% 0.22/0.44 thf(fact_229_NonUniformImpliesNotDecided,axiom,
% 0.22/0.44 ! [C: configuration_ext @ p @ v @ s @ product_unit,V3: $o] :
% 0.22/0.44 ( ! [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ Cfg6 )
% 0.22/0.44 => ( agreement @ p @ v @ s @ Cfg6 ) )
% 0.22/0.44 => ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ C )
% 0.22/0.44 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ C ) )
% 0.22/0.44 => ~ ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 & ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V3 ) ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % NonUniformImpliesNotDecided
% 0.22/0.44 thf(fact_230_agreement__def,axiom,
% 0.22/0.44 ( ( agreement @ p @ v @ s )
% 0.22/0.44 = ( ^ [C9: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ! [V1: $o] :
% 0.22/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C9 @ ( outMsg @ p @ v @ V1 ) ) )
% 0.22/0.44 => ! [V22: $o] :
% 0.22/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C9 @ ( outMsg @ p @ v @ V22 ) ) )
% 0.22/0.44 = ( V22 = V1 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % agreement_def
% 0.22/0.44 thf(fact_231_ExistsMsg,axiom,
% 0.22/0.44 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % ExistsMsg
% 0.22/0.44 thf(fact_232_agreementInit__def,axiom,
% 0.22/0.44 ! [I: configuration_ext @ p @ v @ s @ product_unit,C: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( agreementInit @ p @ s @ v @ trans @ sends @ start @ I @ C )
% 0.22/0.44 = ( ( ( initial @ p @ s @ v @ start @ I )
% 0.22/0.44 & ( reachable @ p @ s @ v @ trans @ sends @ I @ C ) )
% 0.22/0.44 => ! [V1: $o] :
% 0.22/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V1 ) ) )
% 0.22/0.44 => ! [V22: $o] :
% 0.22/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V22 ) ) )
% 0.22/0.44 = ( V22 = V1 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % agreementInit_def
% 0.22/0.44 thf(fact_233_DecidedImpliesUniform,axiom,
% 0.22/0.44 ! [C: configuration_ext @ p @ v @ s @ product_unit,V3: $o] :
% 0.22/0.44 ( ! [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 0.22/0.44 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ Cfg6 )
% 0.22/0.44 => ( agreement @ p @ v @ s @ Cfg6 ) )
% 0.22/0.44 => ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 0.22/0.44 => ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 0.22/0.44 & ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V3 ) ) ) )
% 0.22/0.44 => ( vUniform @ p @ s @ v @ trans @ sends @ start @ V3 @ C ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % DecidedImpliesUniform
% 0.22/0.44 thf(fact_234_flpSystem_Oagreement__def,axiom,
% 0.22/0.44 ! [V: $tType,P: $tType,S: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,C: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( flpSystem @ P @ S @ V @ Sends )
% 0.22/0.44 => ( ( agreement @ P @ V @ S @ C )
% 0.22/0.44 = ( ! [V1: $o] :
% 0.22/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ C @ ( outMsg @ P @ V @ V1 ) ) )
% 0.22/0.44 => ! [V22: $o] :
% 0.22/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ C @ ( outMsg @ P @ V @ V22 ) ) )
% 0.22/0.44 = ( V22 = V1 ) ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % flpSystem.agreement_def
% 0.22/0.44 thf(fact_235_enabled__def,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType] :
% 0.22/0.44 ( ( enabled @ P @ V @ S )
% 0.22/0.44 = ( ^ [Cfg5: configuration_ext @ P @ V @ S @ product_unit,Msg2: message @ P @ V] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg5 @ Msg2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % enabled_def
% 0.22/0.44 thf(fact_236_asynchronousSystem_OExistsMsg,axiom,
% 0.22/0.44 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 0.22/0.44 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.22/0.44 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % asynchronousSystem.ExistsMsg
% 0.22/0.44 thf(fact_237_order_Onot__eq__order__implies__strict,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [A5: A,B3: A] :
% 0.22/0.44 ( ( A5 != B3 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( ord_less @ A @ A5 @ B3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order.not_eq_order_implies_strict
% 0.22/0.44 thf(fact_238_dual__order_Ostrict__implies__order,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [B3: A,A5: A] :
% 0.22/0.44 ( ( ord_less @ A @ B3 @ A5 )
% 0.22/0.44 => ( ord_less_eq @ A @ B3 @ A5 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.strict_implies_order
% 0.22/0.44 thf(fact_239_dual__order_Ostrict__iff__order,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ( ( ord_less @ A )
% 0.22/0.44 = ( ^ [B4: A,A6: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ B4 @ A6 )
% 0.22/0.44 & ( A6 != B4 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.strict_iff_order
% 0.22/0.44 thf(fact_240_dual__order_Oorder__iff__strict,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ( ( ord_less_eq @ A )
% 0.22/0.44 = ( ^ [B4: A,A6: A] :
% 0.22/0.44 ( ( ord_less @ A @ B4 @ A6 )
% 0.22/0.44 | ( A6 = B4 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.order_iff_strict
% 0.22/0.44 thf(fact_241_order_Ostrict__implies__order,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [A5: A,B3: A] :
% 0.22/0.44 ( ( ord_less @ A @ A5 @ B3 )
% 0.22/0.44 => ( ord_less_eq @ A @ A5 @ B3 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order.strict_implies_order
% 0.22/0.44 thf(fact_242_dense__le__bounded,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( dense_linorder @ A )
% 0.22/0.44 => ! [X2: A,Y2: A,Z3: A] :
% 0.22/0.44 ( ( ord_less @ A @ X2 @ Y2 )
% 0.22/0.44 => ( ! [W: A] :
% 0.22/0.44 ( ( ord_less @ A @ X2 @ W )
% 0.22/0.44 => ( ( ord_less @ A @ W @ Y2 )
% 0.22/0.44 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.22/0.44 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dense_le_bounded
% 0.22/0.44 thf(fact_243_dense__ge__bounded,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( dense_linorder @ A )
% 0.22/0.44 => ! [Z3: A,X2: A,Y2: A] :
% 0.22/0.44 ( ( ord_less @ A @ Z3 @ X2 )
% 0.22/0.44 => ( ! [W: A] :
% 0.22/0.44 ( ( ord_less @ A @ Z3 @ W )
% 0.22/0.44 => ( ( ord_less @ A @ W @ X2 )
% 0.22/0.44 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 0.22/0.44 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dense_ge_bounded
% 0.22/0.44 thf(fact_244_dual__order_Ostrict__trans2,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [B3: A,A5: A,C: A] :
% 0.22/0.44 ( ( ord_less @ A @ B3 @ A5 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.22/0.44 => ( ord_less @ A @ C @ A5 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.strict_trans2
% 0.22/0.44 thf(fact_245_dual__order_Ostrict__trans1,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [B3: A,A5: A,C: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ B3 @ A5 )
% 0.22/0.44 => ( ( ord_less @ A @ C @ B3 )
% 0.22/0.44 => ( ord_less @ A @ C @ A5 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dual_order.strict_trans1
% 0.22/0.44 thf(fact_246_order_Ostrict__iff__order,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ( ( ord_less @ A )
% 0.22/0.44 = ( ^ [A6: A,B4: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A6 @ B4 )
% 0.22/0.44 & ( A6 != B4 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order.strict_iff_order
% 0.22/0.44 thf(fact_247_order_Oorder__iff__strict,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ( ( ord_less_eq @ A )
% 0.22/0.44 = ( ^ [A6: A,B4: A] :
% 0.22/0.44 ( ( ord_less @ A @ A6 @ B4 )
% 0.22/0.44 | ( A6 = B4 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order.order_iff_strict
% 0.22/0.44 thf(fact_248_order_Ostrict__trans2,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [A5: A,B3: A,C: A] :
% 0.22/0.44 ( ( ord_less @ A @ A5 @ B3 )
% 0.22/0.44 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.22/0.44 => ( ord_less @ A @ A5 @ C ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order.strict_trans2
% 0.22/0.44 thf(fact_249_order_Ostrict__trans1,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [A5: A,B3: A,C: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.22/0.44 => ( ( ord_less @ A @ B3 @ C )
% 0.22/0.44 => ( ord_less @ A @ A5 @ C ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % order.strict_trans1
% 0.22/0.44 thf(fact_250_not__le__imp__less,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( linorder @ A )
% 0.22/0.44 => ! [Y2: A,X2: A] :
% 0.22/0.44 ( ~ ( ord_less_eq @ A @ Y2 @ X2 )
% 0.22/0.44 => ( ord_less @ A @ X2 @ Y2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % not_le_imp_less
% 0.22/0.44 thf(fact_251_less__le__not__le,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( preorder @ A )
% 0.22/0.44 => ( ( ord_less @ A )
% 0.22/0.44 = ( ^ [X3: A,Y3: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.22/0.44 & ~ ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % less_le_not_le
% 0.22/0.44 thf(fact_252_le__imp__less__or__eq,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( order @ A )
% 0.22/0.44 => ! [X2: A,Y2: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 => ( ( ord_less @ A @ X2 @ Y2 )
% 0.22/0.44 | ( X2 = Y2 ) ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_imp_less_or_eq
% 0.22/0.44 thf(fact_253_le__less__linear,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( linorder @ A )
% 0.22/0.44 => ! [X2: A,Y2: A] :
% 0.22/0.44 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.22/0.44 | ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % le_less_linear
% 0.22/0.44 thf(fact_254_dense__le,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( dense_linorder @ A )
% 0.22/0.44 => ! [Y2: A,Z3: A] :
% 0.22/0.44 ( ! [X: A] :
% 0.22/0.44 ( ( ord_less @ A @ X @ Y2 )
% 0.22/0.44 => ( ord_less_eq @ A @ X @ Z3 ) )
% 0.22/0.44 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dense_le
% 0.22/0.44 thf(fact_255_dense__ge,axiom,
% 0.22/0.44 ! [A: $tType] :
% 0.22/0.44 ( ( dense_linorder @ A )
% 0.22/0.44 => ! [Z3: A,Y2: A] :
% 0.22/0.44 ( ! [X: A] :
% 0.22/0.44 ( ( ord_less @ A @ Z3 @ X )
% 0.22/0.44 => ( ord_less_eq @ A @ Y2 @ X ) )
% 0.22/0.44 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 % dense_ge
% 0.22/0.44
% 0.22/0.44 % Type constructors (28)
% 0.22/0.44 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.22/0.44 ! [A8: $tType,A9: $tType] :
% 0.22/0.44 ( ( order_bot @ A9 )
% 0.22/0.44 => ( order_bot @ ( A8 > A9 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.22/0.44 ! [A8: $tType,A9: $tType] :
% 0.22/0.44 ( ( preorder @ A9 )
% 0.22/0.44 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.22/0.44 ! [A8: $tType,A9: $tType] :
% 0.22/0.44 ( ( order @ A9 )
% 0.22/0.44 => ( order @ ( A8 > A9 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_fun___Orderings_Oord,axiom,
% 0.22/0.44 ! [A8: $tType,A9: $tType] :
% 0.22/0.44 ( ( ord @ A9 )
% 0.22/0.44 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_fun___Orderings_Obot,axiom,
% 0.22/0.44 ! [A8: $tType,A9: $tType] :
% 0.22/0.44 ( ( bot @ A9 )
% 0.22/0.44 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1,axiom,
% 0.22/0.44 order_bot @ nat ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 0.22/0.44 preorder @ nat ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.22/0.44 linorder @ nat ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Nat_Onat___Orderings_Oorder_3,axiom,
% 0.22/0.44 order @ nat ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Nat_Onat___Orderings_Oord_4,axiom,
% 0.22/0.44 ord @ nat ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 0.22/0.44 bot @ nat ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 0.22/0.44 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 0.22/0.44 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 0.22/0.44 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 0.22/0.44 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 0.22/0.44 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11,axiom,
% 0.22/0.44 order_bot @ $o ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 0.22/0.44 preorder @ $o ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_HOL_Obool___Orderings_Olinorder_13,axiom,
% 0.22/0.44 linorder @ $o ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 0.22/0.44 order @ $o ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 0.22/0.44 ord @ $o ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 0.22/0.44 bot @ $o ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_17,axiom,
% 0.22/0.44 order_bot @ product_unit ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_18,axiom,
% 0.22/0.44 preorder @ product_unit ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_19,axiom,
% 0.22/0.44 linorder @ product_unit ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Product__Type_Ounit___Orderings_Oorder_20,axiom,
% 0.22/0.44 order @ product_unit ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Product__Type_Ounit___Orderings_Oord_21,axiom,
% 0.22/0.44 ord @ product_unit ).
% 0.22/0.44
% 0.22/0.44 thf(tcon_Product__Type_Ounit___Orderings_Obot_22,axiom,
% 0.22/0.44 bot @ product_unit ).
% 0.22/0.44
% 0.22/0.44 % Conjectures (1)
% 0.22/0.44 thf(conj_0,conjecture,
% 0.22/0.44 ( ord_less_eq @ ( set @ $o )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
% 0.22/0.44 @ ( collect @ $o
% 0.22/0.44 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ cMsg ) ) ) ).
% 0.22/0.44
% 0.22/0.44 %------------------------------------------------------------------------------
% 0.22/0.44 ------------------------
% 3.29/1.72 ---- Embedded in THF ---
% 3.29/1.72 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.29/1.72 %%% Generated on Tue Feb 24 08:24:58 EST 2026
% 3.29/1.72 %%% using '$$dhol' embedding, version 1.3.0.
% 3.29/1.72 %%% Logic specification used:
% 3.29/1.72 %%% thf(spec, logic, $$dhol).
% 3.29/1.72
% 3.29/1.72 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2DTF14509.p
% 3.29/1.72 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext, type, configuration_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 3.29/1.72 thf(ty_t_AsynchronousSystem_OmessageValue, type, messageValue: ($tType > $tType)).
% 3.29/1.72 thf(ty_t_AsynchronousSystem_Omessage, type, message: ($tType > ($tType > $tType))).
% 3.29/1.72 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 3.29/1.72 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 3.29/1.72 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.29/1.72 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.29/1.72 thf(ty_tf_v, type, v: $tType).
% 3.29/1.72 thf(ty_tf_s, type, s: $tType).
% 3.29/1.72 thf(ty_tf_p, type, p: $tType).
% 3.29/1.72 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OinitReachable, type, initReachable: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o))))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oinitial, type, initial: (!> [P:$tType,S:$tType,V:$tType]: (((P > S) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OqReachable, type, qReachable: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > ((set @ P) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oreachable, type, reachable: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o))))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OstepReachable, type, stepReachable: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((message @ P) @ V) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Osteps, type, steps: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((message @ P) @ V) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs, type, msgs: (!> [P:$tType,V:$tType,S:$tType,Z:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ Z) > (((message @ P) @ V) > nat))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_Oconfiguration_Ostates, type, states: (!> [P:$tType,V:$tType,S:$tType,Z:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ Z) > (P > S))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_Oenabled, type, enabled: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((message @ P) @ V) > $o))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_OisReceiverOf, type, isReceiverOf: (!> [P:$tType,V:$tType]: ((P > (((message @ P) @ V) > $o))))).
% 3.29/1.72 thf(sy_c_AsynchronousSystem_Omessage_OOutMsg, type, outMsg: (!> [P:$tType,V:$tType]: (($o > ((message @ P) @ V))))).
% 3.29/1.72 thf(sy_c_Execution_Oexecution, type, execution: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > ((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > $o)))))))).
% 3.29/1.72 thf(sy_c_Execution_Oexecution_OfirstOccurrence, type, firstOccurrence: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > (nat > $o))))))).
% 3.29/1.72 thf(sy_c_Execution_Oexecution_OminimalEnabled, type, minimalEnabled: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > $o)))))).
% 3.29/1.72 thf(sy_c_FLPSystem_OflpSystem, type, flpSystem: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > $o)))).
% 3.29/1.72 thf(sy_c_FLPSystem_OflpSystem_Oagreement, type, agreement: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))).
% 3.29/1.72 thf(sy_c_FLPSystem_OflpSystem_OagreementInit, type, agreementInit: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))))))).
% 3.29/1.72 thf(sy_c_FLPSystem_OflpSystem_OpSilDecVal, type, pSilDecVal: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > ($o > (P > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o))))))))).
% 3.29/1.72 thf(sy_c_FLPSystem_OflpSystem_OterminationPseudo, type, terminationPseudo: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > (nat > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > ((set @ P) > $o))))))))).
% 3.29/1.72 thf(sy_c_FLPSystem_OflpSystem_OvUniform, type, vUniform: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > ($o > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))))))).
% 3.29/1.72 thf(sy_c_FLPSystem_OflpSystem_Ovalidity, type, validity: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))))))).
% 3.29/1.72 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus, type, fLPThe1922692578sensus: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > $o)))))).
% 3.29/1.72 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 3.29/1.72 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 3.29/1.72 thf(sy_c_ListUtilities_OprefixList, type, prefixList: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 3.29/1.72 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 3.29/1.72 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 3.29/1.72 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 3.29/1.72 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.29/1.72 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.29/1.72 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.29/1.72 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.29/1.72 thf(sy_v_cMsg____, type, cMsg: ((((configuration_ext @ p) @ v) @ s) @ product_unit)).
% 3.29/1.72 thf(sy_v_c_H____, type, c: ((((configuration_ext @ p) @ v) @ s) @ product_unit)).
% 3.29/1.72 thf(sy_v_exec, type, exec: (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))).
% 3.29/1.72 thf(sy_v_execMsga____, type, execMsga: (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))).
% 3.29/1.72 thf(sy_v_exec_H____, type, exec2: (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))).
% 3.29/1.72 thf(sy_v_msg, type, msg: ((message @ p) @ v)).
% 3.29/1.72 thf(sy_v_p, type, p2: p).
% 3.29/1.72 thf(sy_v_sends, type, sends: (p > (s > ((messageValue @ v) > (((message @ p) @ v) > nat))))).
% 3.29/1.72 thf(sy_v_start, type, start: (p > s)).
% 3.29/1.72 thf(sy_v_trace, type, trace: (list @ ((message @ p) @ v))).
% 3.29/1.72 thf(sy_v_traceMsga____, type, traceMsga: (list @ ((message @ p) @ v))).
% 3.29/1.72 thf(sy_v_trace_H____, type, trace2: (list @ ((message @ p) @ v))).
% 3.29/1.72 thf(sy_v_trans, type, trans: (p > (s > ((messageValue @ v) > s)))).
% 3.29/1.72 thf(fact_0_PisReceiverOf, axiom, ((((isReceiverOf @ p) @ v) @ p2) @ msg)).
% 3.29/1.72 thf(fact_1_InitReachLastExec_H, axiom, (((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2))).
% 3.29/1.72 thf(fact_2_NewExec_I3_J, axiom, (((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2) = c)).
% 3.29/1.72 thf(fact_3_CMsg, axiom, ((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)) @ msg) @ cMsg)).
% 3.29/1.72 thf(fact_4_flpPseudoConsensus__axioms, axiom, ((((((fLPThe1922692578sensus @ p) @ s) @ v) @ trans) @ sends) @ start)).
% 3.29/1.72 thf(fact_5_ExecMsg_I3_J, axiom, (((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ execMsga) = cMsg)).
% 3.29/1.72 thf(fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062, axiom, ((p2 = p2) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)) @ msg) @ cMsg) => (((((isReceiverOf @ p) @ v) @ p2) @ msg) => ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)) => (((ord_less_eq @ (set @ $o)) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ p2) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)))))) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ p2) @ cMsg)))))))))).
% 3.29/1.72 thf(fact_7_DiamondOne, axiom, (! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),M:((message @ p) @ v),Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p,Q:p,M2:((message @ p) @ v),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg) @ M) @ Cfg1) => ((P2 != Q) => (((((isReceiverOf @ p) @ v) @ P2) @ M) => ((~ (((((isReceiverOf @ p) @ v) @ P2) @ M2))) => (((((isReceiverOf @ p) @ v) @ Q) @ M2) => ((~ (((((isReceiverOf @ p) @ v) @ Q) @ M))) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg) @ M2) @ Cfg2) => (? [Cfg3:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ M2) @ Cfg3) & ((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg2) @ M) @ Cfg3)))))))))))))).
% 3.29/1.72 thf(fact_8_True, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)) @ msg)).
% 3.29/1.72 thf(fact_9__092_060open_062_092_060exists_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_092_060close_062, axiom, (? [X_1:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)) @ msg) @ X_1)))).
% 3.29/1.72 thf(fact_10__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [CMsg:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((~ (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)) @ msg) @ CMsg)))))))).
% 3.29/1.72 thf(fact_11_Agreement, axiom, (! [I:((((configuration_ext @ p) @ v) @ s) @ product_unit),C:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((agreementInit @ p) @ s) @ v) @ trans) @ sends) @ start) @ I) @ C)))).
% 3.29/1.72 thf(fact_12_ActiveProcessSilentDecisionValuesIncrease, axiom, (! [P2:p,Q:p,C:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg:((message @ p) @ v),C2:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((P2 = Q) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ C) @ Msg) @ C2) => (((((isReceiverOf @ p) @ v) @ P2) @ Msg) => ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) => (((ord_less_eq @ (set @ $o)) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ Q) @ C))))) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ Q) @ C2)))))))))))).
% 3.29/1.72 thf(fact_13_InactiveProcessSilentDecisionValuesDecrease, axiom, (! [P2:p,Q:p,C:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg:((message @ p) @ v),C2:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((P2 != Q) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ C) @ Msg) @ C2) => (((((isReceiverOf @ p) @ v) @ P2) @ Msg) => ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) => (((ord_less_eq @ (set @ $o)) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ Q) @ C2))))) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ Q) @ C)))))))))))).
% 3.29/1.72 thf(fact_14_nonUniformC_H, axiom, ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)) & ((~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $false) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)))) & (~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $true) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2))))))).
% 3.29/1.72 thf(fact_15_InitReachLastExecMsg, axiom, (((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ execMsga))).
% 3.29/1.72 thf(fact_16_NewExec_I1_J, axiom, ((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ exec2) @ trace2)).
% 3.29/1.72 thf(fact_17_InitialIsInitReachable, axiom, (! [C:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((initial @ p) @ s) @ v) @ start) @ C) => (((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C))))).
% 3.29/1.72 thf(fact_18_flpSystem__axioms, axiom, ((((flpSystem @ p) @ s) @ v) @ sends)).
% 3.29/1.72 thf(fact_19_subsetI, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((! [X:A]: (((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B))))).
% 3.29/1.72 thf(fact_20_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ A2) => (A2 = B)))))).
% 3.29/1.72 thf(fact_21_QReachableTrans, axiom, (! [Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q2:(set @ p),Cfg32:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg2) @ Q2) @ Cfg32) => (((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg2) => ((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg32)))))).
% 3.29/1.72 thf(fact_22_InitQ, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q2:(set @ p)]: (((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg1)))).
% 3.29/1.72 thf(fact_23_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 3.29/1.72 thf(fact_24_OnlyOccurenceDisables, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),M:((message @ p) @ v),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),M2:((message @ p) @ v)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ M) @ Cfg2) => ((((((enabled @ p) @ v) @ s) @ Cfg1) @ M2) => ((~ ((((((enabled @ p) @ v) @ s) @ Cfg2) @ M2))) => (M = M2))))))).
% 3.29/1.72 thf(fact_25_qReachable_Osimps, axiom, (! [A1:((((configuration_ext @ p) @ v) @ s) @ product_unit),A22:(set @ p),A3:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ A1) @ A22) @ A3) = ((A3 = A1) | (? [Cfg22:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ A1) @ A22) @ Cfg22) & (? [Msg2:((message @ p) @ v)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg22) @ Msg2) @ A3) & (? [X3:p]: (((((member @ p) @ X3) @ A22) & ((((isReceiverOf @ p) @ v) @ X3) @ Msg2))))))))))))))).
% 3.29/1.72 thf(fact_26_qReachable_Oinducts, axiom, (! [X1:((((configuration_ext @ p) @ v) @ s) @ product_unit),X22:(set @ p),X32:((((configuration_ext @ p) @ v) @ s) @ product_unit),P3:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > ((set @ p) > (((((configuration_ext @ p) @ v) @ s) @ product_unit) > $o)))]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ X1) @ X22) @ X32) => ((! [Cfg12:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q3:(set @ p)]: ((((P3 @ Cfg12) @ Q3) @ Cfg12))) => ((! [Cfg12:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q3:(set @ p),Cfg23:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg12) @ Q3) @ Cfg23) => ((((P3 @ Cfg12) @ Q3) @ Cfg23) => (! [Msg3:((message @ p) @ v),Cfg33:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg23) @ Msg3) @ Cfg33) => ((? [X:p]: (((((member @ p) @ X) @ Q3) & ((((isReceiverOf @ p) @ v) @ X) @ Msg3)))) => (((P3 @ Cfg12) @ Q3) @ Cfg33))))))))) => (((P3 @ X1) @ X22) @ X32))))))).
% 3.29/1.72 thf(fact_27_qReachable_Ocases, axiom, (! [A1:((((configuration_ext @ p) @ v) @ s) @ product_unit),A22:(set @ p),A3:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ A1) @ A22) @ A3) => ((A3 != A1) => (~ ((! [Cfg23:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ A1) @ A22) @ Cfg23) => (! [Msg3:((message @ p) @ v)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg23) @ Msg3) @ A3) => (~ ((? [X:p]: (((((member @ p) @ X) @ A22) & ((((isReceiverOf @ p) @ v) @ X) @ Msg3))))))))))))))))))).
% 3.29/1.72 thf(fact_28_StepQ, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q2:(set @ p),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg:((message @ p) @ v),Cfg32:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg2) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg2) @ Msg) @ Cfg32) => ((? [X4:p]: (((((member @ p) @ X4) @ Q2) & ((((isReceiverOf @ p) @ v) @ X4) @ Msg)))) => ((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg32))))))).
% 3.29/1.72 thf(fact_29_ExecMsg_I1_J, axiom, (((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2) @ execMsga)).
% 3.29/1.72 thf(fact_30_isExecution, axiom, ((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ execMsga) @ traceMsga)).
% 3.29/1.72 thf(fact_31_MsgEnabled, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ msg)).
% 3.29/1.72 thf(fact_32_NonUniformLexec, axiom, ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) & ((~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $false) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)))) & (~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $true) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec))))))).
% 3.29/1.72 thf(fact_33_flpPseudoConsensus_Oaxioms_I1_J, axiom, (! [V:$tType,S:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S)]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((((flpSystem @ P) @ S) @ V) @ Sends))))).
% 3.29/1.72 thf(fact_34_flpPseudoConsensus_OAgreement, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),I:((((configuration_ext @ P) @ V) @ S) @ product_unit),C:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((((((((agreementInit @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ I) @ C))))).
% 3.29/1.72 thf(fact_35_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B2:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X3:A]: ((((member @ A) @ X3) @ A4)))) @ (^ [X3:A]: ((((member @ A) @ X3) @ B2)))))))))).
% 3.29/1.72 thf(fact_36_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A5:A]: (((((ord_less_eq @ A) @ B3) @ A5) => ((((ord_less_eq @ A) @ A5) @ B3) => (A5 = B3))))))))).
% 3.29/1.72 thf(fact_37_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z2:A]: ((Y = Z2))) = (^ [A6:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A6) & (((ord_less_eq @ A) @ A6) @ B4))))))))).
% 3.29/1.72 thf(fact_38_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A5:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A5) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less_eq @ A) @ C) @ A5))))))))).
% 3.29/1.72 thf(fact_39_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P3:(A > (A > $o)),A5:A,B3:A]: (((! [A7:A,B5:A]: (((((ord_less_eq @ A) @ A7) @ B5) => ((P3 @ A7) @ B5)))) => ((! [A7:A,B5:A]: ((((P3 @ B5) @ A7) => ((P3 @ A7) @ B5)))) => ((P3 @ A5) @ B3))))))))).
% 3.29/1.72 thf(fact_40_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A5:A]: ((((ord_less_eq @ A) @ A5) @ A5))))))).
% 3.29/1.72 thf(fact_41_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z3) => (((ord_less_eq @ A) @ X2) @ Z3))))))))).
% 3.29/1.72 thf(fact_42_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A5:A,B3:A]: (((((ord_less_eq @ A) @ A5) @ B3) => ((((ord_less_eq @ A) @ B3) @ A5) => (A5 = B3))))))))).
% 3.29/1.72 thf(fact_43_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A5:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A5) @ B3) => ((B3 = C) => (((ord_less_eq @ A) @ A5) @ C))))))))).
% 3.29/1.72 thf(fact_44_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A5:A,B3:A,C:A]: (((A5 = B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A5) @ C))))))))).
% 3.29/1.72 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A5:A,P3:(A > $o)]: (((((member @ A) @ A5) @ ((collect @ A) @ P3)) = (P3 @ A5))))).
% 3.29/1.72 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A2)))) = A2)))).
% 3.29/1.72 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((! [X:A]: (((P3 @ X) = (Q2 @ X)))) => (((collect @ A) @ P3) = ((collect @ A) @ Q2)))))).
% 3.29/1.72 thf(fact_48_ext, axiom, (! [B6:$tType,A:$tType,F:(A > B6),G:(A > B6)]: (((! [X:A]: (((F @ X) = (G @ X)))) => (F = G))))).
% 3.29/1.72 thf(fact_49_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z2:A]: ((Y = Z2))) = (^ [A6:A,B4:A]: (((((ord_less_eq @ A) @ A6) @ B4) & (((ord_less_eq @ A) @ B4) @ A6))))))))).
% 3.29/1.72 thf(fact_50_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X2:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y2) = (X2 = Y2))))))))).
% 3.29/1.72 thf(fact_51_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A,Z3:A]: ((((((ord_less_eq @ A) @ X2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z3)))) => (((((ord_less_eq @ A) @ Y2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z3)))) => (((((ord_less_eq @ A) @ X2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y2)))) => (((((ord_less_eq @ A) @ Z3) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X2)))) => (((((ord_less_eq @ A) @ Y2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y2))))))))))))))))).
% 3.29/1.72 thf(fact_52_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A5:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A5) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A5) @ C))))))))).
% 3.29/1.72 thf(fact_53_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.29/1.72 thf(fact_54_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((X2 = Y2) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 3.29/1.72 thf(fact_55_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.29/1.72 thf(fact_56_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X2) => (X2 = Y2))))))))).
% 3.29/1.72 thf(fact_57_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z2:A]: ((Y = Z2))) = (^ [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X3))))))))).
% 3.29/1.72 thf(fact_58_ord__le__eq__subst, axiom, (! [A:$tType,B6:$tType]: ((((ord @ B6) & (ord @ A)) => (! [A5:A,B3:A,F:(A > B6),C:B6]: (((((ord_less_eq @ A) @ A5) @ B3) => (((F @ B3) = C) => ((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ B6) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ B6) @ (F @ A5)) @ C)))))))))).
% 3.29/1.72 thf(fact_59_ord__eq__le__subst, axiom, (! [A:$tType,B6:$tType]: ((((ord @ B6) & (ord @ A)) => (! [A5:A,F:(B6 > A),B3:B6,C:B6]: (((A5 = (F @ B3)) => ((((ord_less_eq @ B6) @ B3) @ C) => ((! [X:B6,Y4:B6]: (((((ord_less_eq @ B6) @ X) @ Y4) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A5) @ (F @ C))))))))))).
% 3.29/1.72 thf(fact_60_order__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A5:A,B3:A,F:(A > C3),C:C3]: (((((ord_less_eq @ A) @ A5) @ B3) => ((((ord_less_eq @ C3) @ (F @ B3)) @ C) => ((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ C3) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ C3) @ (F @ A5)) @ C)))))))))).
% 3.29/1.72 thf(fact_61_order__subst1, axiom, (! [A:$tType,B6:$tType]: ((((order @ B6) & (order @ A)) => (! [A5:A,F:(B6 > A),B3:B6,C:B6]: (((((ord_less_eq @ A) @ A5) @ (F @ B3)) => ((((ord_less_eq @ B6) @ B3) @ C) => ((! [X:B6,Y4:B6]: (((((ord_less_eq @ B6) @ X) @ Y4) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A5) @ (F @ C))))))))))).
% 3.29/1.72 thf(fact_62_le__fun__def, axiom, (! [B6:$tType,A:$tType]: (((ord @ B6) => ((ord_less_eq @ (A > B6)) = (^ [F2:(A > B6),G2:(A > B6)]: ((! [X3:A]: ((((ord_less_eq @ B6) @ (F2 @ X3)) @ (G2 @ X3))))))))))).
% 3.29/1.72 thf(fact_63_le__funI, axiom, (! [B6:$tType,A:$tType]: (((ord @ B6) => (! [F:(A > B6),G:(A > B6)]: (((! [X:A]: ((((ord_less_eq @ B6) @ (F @ X)) @ (G @ X)))) => (((ord_less_eq @ (A > B6)) @ F) @ G)))))))).
% 3.29/1.72 thf(fact_64_le__funE, axiom, (! [B6:$tType,A:$tType]: (((ord @ B6) => (! [F:(A > B6),G:(A > B6),X2:A]: (((((ord_less_eq @ (A > B6)) @ F) @ G) => (((ord_less_eq @ B6) @ (F @ X2)) @ (G @ X2))))))))).
% 3.29/1.72 thf(fact_65_le__funD, axiom, (! [B6:$tType,A:$tType]: (((ord @ B6) => (! [F:(A > B6),G:(A > B6),X2:A]: (((((ord_less_eq @ (A > B6)) @ F) @ G) => (((ord_less_eq @ B6) @ (F @ X2)) @ (G @ X2))))))))).
% 3.29/1.72 thf(fact_66_Collect__mono__iff, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q2)) = (! [X3:A]: (((P3 @ X3) => (Q2 @ X3)))))))).
% 3.29/1.72 thf(fact_67_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y:(set @ A),Z2:(set @ A)]: ((Y = Z2))) = (^ [A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) & (((ord_less_eq @ (set @ A)) @ B2) @ A4)))))))).
% 3.29/1.72 thf(fact_68_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ A2) @ C4)))))).
% 3.29/1.72 thf(fact_69_Collect__mono, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((! [X:A]: (((P3 @ X) => (Q2 @ X)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q2)))))).
% 3.29/1.72 thf(fact_70_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 3.29/1.72 thf(fact_71_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B2:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A4) => (((member @ A) @ T) @ B2)))))))))).
% 3.29/1.72 thf(fact_72_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((A2 = B) => (((ord_less_eq @ (set @ A)) @ B) @ A2))))).
% 3.29/1.72 thf(fact_73_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((A2 = B) => (((ord_less_eq @ (set @ A)) @ A2) @ B))))).
% 3.29/1.72 thf(fact_74_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B2:(set @ A)]: ((! [X3:A]: (((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B2)))))))))).
% 3.29/1.72 thf(fact_75_equalityE, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((A2 = B) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B) => (~ ((((ord_less_eq @ (set @ A)) @ B) @ A2)))))))))).
% 3.29/1.72 thf(fact_76_subsetD, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B)))))).
% 3.29/1.72 thf(fact_77_in__mono, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((member @ A) @ X2) @ A2) => (((member @ A) @ X2) @ B)))))).
% 3.29/1.72 thf(fact_78_Collect__subset, axiom, (! [A:$tType,A2:(set @ A),P3:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ A2) & (P3 @ X3)))))) @ A2)))).
% 3.29/1.72 thf(fact_79_flpSystem_OInactiveProcessSilentDecisionValuesDecrease, axiom, (! [P:$tType,V:$tType,S:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),P2:P,Q:P,Trans:(P > (S > ((messageValue @ V) > S))),C:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg:((message @ P) @ V),C2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Start:(P > S)]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => ((P2 != Q) => (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ C) @ Msg) @ C2) => (((((isReceiverOf @ P) @ V) @ P2) @ Msg) => ((((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ C) => (((ord_less_eq @ (set @ $o)) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ Q) @ C2))))) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ Q) @ C))))))))))))).
% 3.29/1.72 thf(fact_80_flpSystem_OActiveProcessSilentDecisionValuesIncrease, axiom, (! [P:$tType,V:$tType,S:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),P2:P,Q:P,Trans:(P > (S > ((messageValue @ V) > S))),C:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg:((message @ P) @ V),C2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Start:(P > S)]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => ((P2 = Q) => (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ C) @ Msg) @ C2) => (((((isReceiverOf @ P) @ V) @ P2) @ Msg) => ((((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ C) => (((ord_less_eq @ (set @ $o)) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ Q) @ C))))) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ Q) @ C2))))))))))))).
% 3.29/1.72 thf(fact_81_NotStepReachable, axiom, (~ (((((((((stepReachable @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ msg) @ c)))).
% 3.29/1.72 thf(fact_82_cMsgLastReachable, axiom, (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ cMsg) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ execMsga))).
% 3.29/1.72 thf(fact_83_NoReceivingNoChange, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),M:((message @ p) @ v),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ M) @ Cfg2) => ((~ (((((isReceiverOf @ p) @ v) @ P2) @ M))) => (((((((states @ p) @ v) @ s) @ product_unit) @ Cfg1) @ P2) = ((((((states @ p) @ v) @ s) @ product_unit) @ Cfg2) @ P2))))))).
% 3.29/1.72 thf(fact_84_initReachable__def, axiom, (! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ Cfg) = (? [Cfg0:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((initial @ p) @ s) @ v) @ start) @ Cfg0) & (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg0) @ Cfg)))))))).
% 3.29/1.72 thf(fact_85_ReachableStepFirst, axiom, (! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg4:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg) @ Cfg4) => ((Cfg = Cfg4) | (? [Cfg12:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg3:((message @ p) @ v),P4:p]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg) @ Msg3) @ Cfg12) & ((((((enabled @ p) @ v) @ s) @ Cfg) @ Msg3) & (((((isReceiverOf @ p) @ v) @ P4) @ Msg3) & (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg12) @ Cfg4))))))))))).
% 3.29/1.72 thf(fact_86_NotInQFrozenQReachability, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q2:(set @ p),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg2) => ((~ ((((member @ p) @ P2) @ Q2))) => (((((((states @ p) @ v) @ s) @ product_unit) @ Cfg1) @ P2) = ((((((states @ p) @ v) @ s) @ product_unit) @ Cfg2) @ P2))))))).
% 3.29/1.72 thf(fact_87_C_H_I2_J, axiom, (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ p2) @ c)))) = (((insert @ $o) @ $true) @ (((insert @ $o) @ $false) @ (bot_bot @ (set @ $o)))))).
% 3.29/1.72 thf(fact_88_NoActivityNoMessageLoss, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q2:(set @ p),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p,M2:((message @ p) @ v)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg2) => ((~ ((((member @ p) @ P2) @ Q2))) => (((((isReceiverOf @ p) @ v) @ P2) @ M2) => (((ord_less_eq @ nat) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg1) @ M2)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg2) @ M2)))))))).
% 3.29/1.72 thf(fact_89_ReachableTrans, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg32:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Cfg2) => ((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg2) @ Cfg32) => (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Cfg32)))))).
% 3.29/1.72 thf(fact_90_init, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Cfg1)))).
% 3.29/1.72 thf(fact_91_bot__apply, axiom, (! [C3:$tType,D:$tType]: (((bot @ C3) => ((bot_bot @ (D > C3)) = (^ [X3:D]: ((bot_bot @ C3)))))))).
% 3.29/1.72 thf(fact_92_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 3.29/1.72 thf(fact_93_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((~ ((((member @ A) @ X3) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 3.29/1.72 thf(fact_94_Collect__empty__eq, axiom, (! [A:$tType,P3:(A > $o)]: (((((collect @ A) @ P3) = (bot_bot @ (set @ A))) = (! [X3:A]: ((~ ((P3 @ X3))))))))).
% 3.29/1.72 thf(fact_95_empty__Collect__eq, axiom, (! [A:$tType,P3:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P3)) = (! [X3:A]: ((~ ((P3 @ X3))))))))).
% 3.29/1.72 thf(fact_96_insertCI, axiom, (! [A:$tType,A5:A,B:(set @ A),B3:A]: ((((~ ((((member @ A) @ A5) @ B))) => (A5 = B3)) => (((member @ A) @ A5) @ (((insert @ A) @ B3) @ B)))))).
% 3.29/1.72 thf(fact_97_insert__iff, axiom, (! [A:$tType,A5:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A5) @ (((insert @ A) @ B3) @ A2)) = ((A5 = B3) | (((member @ A) @ A5) @ A2)))))).
% 3.29/1.72 thf(fact_98_insert__absorb2, axiom, (! [A:$tType,X2:A,A2:(set @ A)]: (((((insert @ A) @ X2) @ (((insert @ A) @ X2) @ A2)) = (((insert @ A) @ X2) @ A2))))).
% 3.29/1.72 thf(fact_99_C_H_I1_J, axiom, (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ c)).
% 3.29/1.72 thf(fact_100_predicate1I, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((! [X:A]: (((P3 @ X) => (Q2 @ X)))) => (((ord_less_eq @ (A > $o)) @ P3) @ Q2))))).
% 3.29/1.72 thf(fact_101_reachable_Ocases, axiom, (! [A1:((((configuration_ext @ p) @ v) @ s) @ product_unit),A22:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ A1) @ A22) => ((A22 != A1) => (~ ((! [Cfg23:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ A1) @ Cfg23) => (! [Msg3:((message @ p) @ v)]: ((~ (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg23) @ Msg3) @ A22))))))))))))))).
% 3.29/1.72 thf(fact_102_reachable_Oinducts, axiom, (! [X1:((((configuration_ext @ p) @ v) @ s) @ product_unit),X22:((((configuration_ext @ p) @ v) @ s) @ product_unit),P3:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((((configuration_ext @ p) @ v) @ s) @ product_unit) > $o))]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ X1) @ X22) => ((! [Cfg12:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((P3 @ Cfg12) @ Cfg12))) => ((! [Cfg12:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg23:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg3:((message @ p) @ v),Cfg33:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg12) @ Cfg23) => (((P3 @ Cfg12) @ Cfg23) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg23) @ Msg3) @ Cfg33) => ((P3 @ Cfg12) @ Cfg33)))))) => ((P3 @ X1) @ X22))))))).
% 3.29/1.72 thf(fact_103_reachable_Osimps, axiom, (! [A1:((((configuration_ext @ p) @ v) @ s) @ product_unit),A22:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ A1) @ A22) = ((? [Cfg13:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((A1 = Cfg13) & (A22 = Cfg13)))) | (? [Cfg13:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg22:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg2:((message @ p) @ v),Cfg34:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((A1 = Cfg13) & ((A22 = Cfg34) & ((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg13) @ Cfg22) & ((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg22) @ Msg2) @ Cfg34))))))))))).
% 3.29/1.72 thf(fact_104_reachable_Ostep, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg:((message @ p) @ v),Cfg32:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Cfg2) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg2) @ Msg) @ Cfg32) => (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Cfg32)))))).
% 3.29/1.72 thf(fact_105_QReachImplReach, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q2:(set @ p),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((qReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Q2) @ Cfg2) => (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Cfg2))))).
% 3.29/1.72 thf(fact_106_isPrefixListExec, axiom, (((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec) @ execMsga)).
% 3.29/1.72 thf(fact_107_OtherMessagesOnlyGrowing, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),M:((message @ p) @ v),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),M2:((message @ p) @ v)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ M) @ Cfg2) => ((M != M2) => (((ord_less_eq @ nat) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg1) @ M2)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg2) @ M2))))))).
% 3.29/1.72 thf(fact_108_stepReachable__def, axiom, (! [C1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg:((message @ p) @ v),C22:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((stepReachable @ p) @ s) @ v) @ trans) @ sends) @ C1) @ Msg) @ C22) = (? [C5:((((configuration_ext @ p) @ v) @ s) @ product_unit),C6:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ C1) @ C5) & (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ C5) @ Msg) @ C6) & (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ C6) @ C22))))))))).
% 3.29/1.72 thf(fact_109_StepReachable, axiom, (! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg4:((((configuration_ext @ p) @ v) @ s) @ product_unit),Msg:((message @ p) @ v)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg) @ Cfg4) => ((((((enabled @ p) @ v) @ s) @ Cfg) @ Msg) => ((~ ((((((enabled @ p) @ v) @ s) @ Cfg4) @ Msg))) => ((((((((stepReachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg) @ Msg) @ Cfg4))))))).
% 3.29/1.72 thf(fact_110_NoMessageLossStep, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),M:((message @ p) @ v),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p,M2:((message @ p) @ v)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ M) @ Cfg2) => (((((isReceiverOf @ p) @ v) @ P2) @ M) => ((~ (((((isReceiverOf @ p) @ v) @ P2) @ M2))) => (((ord_less_eq @ nat) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg1) @ M2)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg2) @ M2)))))))).
% 3.29/1.72 thf(fact_111_subset__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (A2 = (bot_bot @ (set @ A))))))).
% 3.29/1.72 thf(fact_112_empty__subsetI, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2)))).
% 3.29/1.72 thf(fact_113_singletonI, axiom, (! [A:$tType,A5:A]: ((((member @ A) @ A5) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A))))))).
% 3.29/1.72 thf(fact_114_insert__subset, axiom, (! [A:$tType,X2:A,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X2) @ A2)) @ B) = ((((member @ A) @ X2) @ B) & (((ord_less_eq @ (set @ A)) @ A2) @ B)))))).
% 3.29/1.72 thf(fact_115_ExecMsg_I2_J, axiom, (((prefixList @ ((message @ p) @ v)) @ trace2) @ traceMsga)).
% 3.29/1.72 thf(fact_116_lastExecExec_HReachable, axiom, (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2))).
% 3.29/1.72 thf(fact_117_singleton__conv, axiom, (! [A:$tType,A5:A]: ((((collect @ A) @ (^ [X3:A]: ((X3 = A5)))) = (((insert @ A) @ A5) @ (bot_bot @ (set @ A))))))).
% 3.29/1.72 thf(fact_118_singleton__conv2, axiom, (! [A:$tType,A5:A]: ((((collect @ A) @ ((^ [Y:A,Z2:A]: ((Y = Z2))) @ A5)) = (((insert @ A) @ A5) @ (bot_bot @ (set @ A))))))).
% 3.29/1.72 thf(fact_119_ExecIsExecution, axiom, ((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ exec) @ trace)).
% 3.29/1.72 thf(fact_120_vUniform__def, axiom, (! [V3:$o,C:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ V3) @ C) = ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) & (! [P5:p]: ((((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ P5) @ C)))) = (((insert @ $o) @ V3) @ (bot_bot @ (set @ $o))))))))))).
% 3.29/1.72 thf(fact_121_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A5:A,A2:(set @ A),B3:A]: ((((((insert @ A) @ A5) @ A2) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = ((A5 = B3) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A))))))))).
% 3.29/1.72 thf(fact_122_singleton__insert__inj__eq, axiom, (! [A:$tType,B3:A,A5:A,A2:(set @ A)]: ((((((insert @ A) @ B3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A5) @ A2)) = ((A5 = B3) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A))))))))).
% 3.29/1.72 thf(fact_123_ExecMsg_I4_J, axiom, (((last @ ((message @ p) @ v)) @ traceMsga) = msg)).
% 3.29/1.72 thf(fact_124_isStepReachable, axiom, ((((((((stepReachable @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ msg) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ execMsga))).
% 3.29/1.72 thf(fact_125_SilentDecisionValueNotInverting, axiom, (! [Q:p,C:((((configuration_ext @ p) @ v) @ s) @ product_unit),V3:$o,Msg:((message @ p) @ v),C2:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p]: (((((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ Q) @ C)))) = (((insert @ $o) @ V3) @ (bot_bot @ (set @ $o)))) => (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ C) @ Msg) @ C2) => (((((isReceiverOf @ p) @ v) @ P2) @ Msg) => ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) => (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ Q) @ C2)))) != (((insert @ $o) @ (~ (V3))) @ (bot_bot @ (set @ $o))))))))))).
% 3.29/1.72 thf(fact_126__092_060open_062_092_060And_062p_O_A_092_060exists_062c_H_O_Areachable_A_Ilast_Aexec_J_Ac_H_A_092_060and_062_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060close_062, axiom, (! [P2:p]: ((? [C7:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ C7) & (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ P2) @ C7)))) = (((insert @ $o) @ $true) @ (((insert @ $o) @ $false) @ (bot_bot @ (set @ $o))))))))))).
% 3.29/1.72 thf(fact_127__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_H_O_A_092_060lbrakk_062reachable_A_Ilast_Aexec_J_Ac_H_059_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [C7:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ C7) => (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ p2) @ C7)))) != (((insert @ $o) @ $true) @ (((insert @ $o) @ $false) @ (bot_bot @ (set @ $o))))))))))).
% 3.29/1.72 thf(fact_128_Agree, axiom, (! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec)) @ Cfg) => ((((agreement @ p) @ v) @ s) @ Cfg))))).
% 3.29/1.72 thf(fact_129_emptyE, axiom, (! [A:$tType,A5:A]: ((~ ((((member @ A) @ A5) @ (bot_bot @ (set @ A)))))))).
% 3.29/1.72 thf(fact_130_insertE, axiom, (! [A:$tType,A5:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A5) @ (((insert @ A) @ B3) @ A2)) => ((A5 != B3) => (((member @ A) @ A5) @ A2)))))).
% 3.29/1.72 thf(fact_131_equals0D, axiom, (! [A:$tType,A2:(set @ A),A5:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A5) @ A2))))))).
% 3.29/1.72 thf(fact_132_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 3.29/1.72 thf(fact_133_insertI1, axiom, (! [A:$tType,A5:A,B:(set @ A)]: ((((member @ A) @ A5) @ (((insert @ A) @ A5) @ B))))).
% 3.29/1.72 thf(fact_134_insertI2, axiom, (! [A:$tType,A5:A,B:(set @ A),B3:A]: (((((member @ A) @ A5) @ B) => (((member @ A) @ A5) @ (((insert @ A) @ B3) @ B)))))).
% 3.29/1.72 thf(fact_135_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X3:A]: ((((member @ A) @ X3) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 3.29/1.72 thf(fact_136_Set_Oset__insert, axiom, (! [A:$tType,X2:A,A2:(set @ A)]: (((((member @ A) @ X2) @ A2) => (~ ((! [B7:(set @ A)]: (((A2 = (((insert @ A) @ X2) @ B7)) => (((member @ A) @ X2) @ B7)))))))))).
% 3.29/1.72 thf(fact_137_singletonD, axiom, (! [A:$tType,B3:A,A5:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))) => (B3 = A5))))).
% 3.29/1.72 thf(fact_138_insert__ident, axiom, (! [A:$tType,X2:A,A2:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X2) @ A2))) => ((~ ((((member @ A) @ X2) @ B))) => (((((insert @ A) @ X2) @ A2) = (((insert @ A) @ X2) @ B)) = (A2 = B))))))).
% 3.29/1.72 thf(fact_139_insert__absorb, axiom, (! [A:$tType,A5:A,A2:(set @ A)]: (((((member @ A) @ A5) @ A2) => ((((insert @ A) @ A5) @ A2) = A2))))).
% 3.29/1.72 thf(fact_140_insert__eq__iff, axiom, (! [A:$tType,A5:A,A2:(set @ A),B3:A,B:(set @ A)]: (((~ ((((member @ A) @ A5) @ A2))) => ((~ ((((member @ A) @ B3) @ B))) => (((((insert @ A) @ A5) @ A2) = (((insert @ A) @ B3) @ B)) = (((A5 = B3) => (A2 = B)) & ((A5 != B3) => (? [C8:(set @ A)]: (((A2 = (((insert @ A) @ B3) @ C8)) & ((~ ((((member @ A) @ B3) @ C8))) & ((B = (((insert @ A) @ A5) @ C8)) & (~ ((((member @ A) @ A5) @ C8)))))))))))))))).
% 3.29/1.72 thf(fact_141_singleton__iff, axiom, (! [A:$tType,B3:A,A5:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))) = (B3 = A5))))).
% 3.29/1.72 thf(fact_142_insert__commute, axiom, (! [A:$tType,X2:A,Y2:A,A2:(set @ A)]: (((((insert @ A) @ X2) @ (((insert @ A) @ Y2) @ A2)) = (((insert @ A) @ Y2) @ (((insert @ A) @ X2) @ A2)))))).
% 3.29/1.72 thf(fact_143_Collect__conv__if, axiom, (! [A:$tType,P3:(A > $o),A5:A]: ((((P3 @ A5) => (((collect @ A) @ (^ [X3:A]: (((X3 = A5) & (P3 @ X3))))) = (((insert @ A) @ A5) @ (bot_bot @ (set @ A))))) & ((~ ((P3 @ A5))) => (((collect @ A) @ (^ [X3:A]: (((X3 = A5) & (P3 @ X3))))) = (bot_bot @ (set @ A)))))))).
% 3.29/1.72 thf(fact_144_Collect__conv__if2, axiom, (! [A:$tType,P3:(A > $o),A5:A]: ((((P3 @ A5) => (((collect @ A) @ (^ [X3:A]: (((A5 = X3) & (P3 @ X3))))) = (((insert @ A) @ A5) @ (bot_bot @ (set @ A))))) & ((~ ((P3 @ A5))) => (((collect @ A) @ (^ [X3:A]: (((A5 = X3) & (P3 @ X3))))) = (bot_bot @ (set @ A)))))))).
% 3.29/1.72 thf(fact_145_doubleton__eq__iff, axiom, (! [A:$tType,A5:A,B3:A,C:A,D2:A]: ((((((insert @ A) @ A5) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A5 = C) & (B3 = D2)) | ((A5 = D2) & (B3 = C))))))).
% 3.29/1.72 thf(fact_146_insert__not__empty, axiom, (! [A:$tType,A5:A,A2:(set @ A)]: (((((insert @ A) @ A5) @ A2) != (bot_bot @ (set @ A)))))).
% 3.29/1.72 thf(fact_147_singleton__inject, axiom, (! [A:$tType,A5:A,B3:A]: ((((((insert @ A) @ A5) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A5 = B3))))).
% 3.29/1.72 thf(fact_148_bot__fun__def, axiom, (! [B6:$tType,A:$tType]: (((bot @ B6) => ((bot_bot @ (A > B6)) = (^ [X3:A]: ((bot_bot @ B6)))))))).
% 3.29/1.72 thf(fact_149_predicate1D, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o),X2:A]: (((((ord_less_eq @ (A > $o)) @ P3) @ Q2) => ((P3 @ X2) => (Q2 @ X2)))))).
% 3.29/1.72 thf(fact_150_subset__singletonD, axiom, (! [A:$tType,A2:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))) => ((A2 = (bot_bot @ (set @ A))) | (A2 = (((insert @ A) @ X2) @ (bot_bot @ (set @ A))))))))).
% 3.29/1.72 thf(fact_151_mk__disjoint__insert, axiom, (! [A:$tType,A5:A,A2:(set @ A)]: (((((member @ A) @ A5) @ A2) => (? [B7:(set @ A)]: (((A2 = (((insert @ A) @ A5) @ B7)) & (~ ((((member @ A) @ A5) @ B7)))))))))).
% 3.29/1.72 thf(fact_152_subset__singleton__iff, axiom, (! [A:$tType,X5:(set @ A),A5:A]: (((((ord_less_eq @ (set @ A)) @ X5) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))) = ((X5 = (bot_bot @ (set @ A))) | (X5 = (((insert @ A) @ A5) @ (bot_bot @ (set @ A))))))))).
% 3.29/1.72 thf(fact_153_rev__predicate1D, axiom, (! [A:$tType,P3:(A > $o),X2:A,Q2:(A > $o)]: (((P3 @ X2) => ((((ord_less_eq @ (A > $o)) @ P3) @ Q2) => (Q2 @ X2)))))).
% 3.29/1.72 thf(fact_154_insert__Collect, axiom, (! [A:$tType,A5:A,P3:(A > $o)]: (((((insert @ A) @ A5) @ ((collect @ A) @ P3)) = ((collect @ A) @ (^ [U:A]: (((U != A5) => (P3 @ U))))))))).
% 3.29/1.72 thf(fact_155_insert__compr, axiom, (! [A:$tType]: (((insert @ A) = (^ [A6:A,B2:(set @ A)]: (((collect @ A) @ (^ [X3:A]: (((X3 = A6) | (((member @ A) @ X3) @ B2))))))))))).
% 3.29/1.72 thf(fact_156_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X3:A]: ($false))))))).
% 3.29/1.72 thf(fact_157_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A5:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A5))))))).
% 3.29/1.72 thf(fact_158_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A5:A]: (((((ord_less_eq @ A) @ A5) @ (bot_bot @ A)) = (A5 = (bot_bot @ A))))))))).
% 3.29/1.72 thf(fact_159_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A5:A]: (((((ord_less_eq @ A) @ A5) @ (bot_bot @ A)) => (A5 = (bot_bot @ A))))))))).
% 3.29/1.72 thf(fact_160_insert__mono, axiom, (! [A:$tType,C4:(set @ A),D3:(set @ A),A5:A]: (((((ord_less_eq @ (set @ A)) @ C4) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A5) @ C4)) @ (((insert @ A) @ A5) @ D3)))))).
% 3.29/1.72 thf(fact_161_subset__insert, axiom, (! [A:$tType,X2:A,A2:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X2) @ A2))) => ((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X2) @ B)) = (((ord_less_eq @ (set @ A)) @ A2) @ B)))))).
% 3.29/1.72 thf(fact_162_subset__insertI, axiom, (! [A:$tType,B:(set @ A),A5:A]: ((((ord_less_eq @ (set @ A)) @ B) @ (((insert @ A) @ A5) @ B))))).
% 3.29/1.72 thf(fact_163_subset__insertI2, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),B3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B3) @ B)))))).
% 3.29/1.72 thf(fact_164_flpSystem_OvUniform__def, axiom, (! [V:$tType,S:$tType,P:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Trans:(P > (S > ((messageValue @ V) > S))),Start:(P > S),V3:$o,C:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => (((((((((vUniform @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V3) @ C) = ((((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ C) & (! [P5:P]: ((((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ P5) @ C)))) = (((insert @ $o) @ V3) @ (bot_bot @ (set @ $o)))))))))))).
% 3.29/1.72 thf(fact_165_flpSystem_OSilentDecisionValueNotInverting, axiom, (! [S:$tType,V:$tType,P:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Trans:(P > (S > ((messageValue @ V) > S))),Start:(P > S),Q:P,C:((((configuration_ext @ P) @ V) @ S) @ product_unit),V3:$o,Msg:((message @ P) @ V),C2:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => ((((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ Q) @ C)))) = (((insert @ $o) @ V3) @ (bot_bot @ (set @ $o)))) => (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ C) @ Msg) @ C2) => (((((isReceiverOf @ P) @ V) @ P2) @ Msg) => ((((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ C) => (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ Q) @ C2)))) != (((insert @ $o) @ (~ (V3))) @ (bot_bot @ (set @ $o)))))))))))).
% 3.29/1.72 thf(fact_166_flpSystem_OpSilDecVal_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((pSilDecVal @ P) @ S) @ V) = (((pSilDecVal @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_167_flpSystem_OvUniform_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((vUniform @ P) @ S) @ V) = (((vUniform @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_168_flpSystem_OagreementInit_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((agreementInit @ P) @ S) @ V) = (((agreementInit @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_169_expandExecutionReachable, axiom, (! [CfgLast:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),Exec:(list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)),Trace:(list @ ((message @ p) @ v))]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ CfgLast) @ Cfg) => (((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ Exec) @ Trace) => ((CfgLast = ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Exec)) => (? [Exec2:(list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)),Trace2:(list @ ((message @ p) @ v))]: ((((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ Exec2) @ Trace2) & ((((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Exec) @ Exec2) & (((prefixList @ ((message @ p) @ v)) @ Trace) @ Trace2)) | ((Exec = Exec2) & (Trace = Trace2))) & (((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Exec2) = Cfg))))))))))).
% 3.29/1.72 thf(fact_170_NewExec_I2_J, axiom, (((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec) @ exec2) & (((prefixList @ ((message @ p) @ v)) @ trace) @ trace2)) | ((exec = exec2) & (trace = trace2)))).
% 3.29/1.72 thf(fact_171_NoOutMessageLoss, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),V3:$o]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ Cfg2) => (((ord_less_eq @ nat) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg1) @ (((outMsg @ p) @ v) @ V3))) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg2) @ (((outMsg @ p) @ v) @ V3))))))).
% 3.29/1.72 thf(fact_172_asynchronousSystem_OReachableStepFirst, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg4:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg) @ Cfg4) => ((Cfg = Cfg4) | (? [Cfg12:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg3:((message @ P) @ V),P4:P]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg) @ Msg3) @ Cfg12) & ((((((enabled @ P) @ V) @ S) @ Cfg) @ Msg3) & (((((isReceiverOf @ P) @ V) @ P4) @ Msg3) & (((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg12) @ Cfg4))))))))))).
% 3.29/1.72 thf(fact_173_asynchronousSystem_ONoActivityNoMessageLoss, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q2:(set @ P),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P,M2:((message @ P) @ V)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg2) => ((~ ((((member @ P) @ P2) @ Q2))) => (((((isReceiverOf @ P) @ V) @ P2) @ M2) => (((ord_less_eq @ nat) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg1) @ M2)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg2) @ M2)))))))).
% 3.29/1.72 thf(fact_174_asynchronousSystem_ONoMessageLossStep, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),M:((message @ P) @ V),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P,M2:((message @ P) @ V)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ M) @ Cfg2) => (((((isReceiverOf @ P) @ V) @ P2) @ M) => ((~ (((((isReceiverOf @ P) @ V) @ P2) @ M2))) => (((ord_less_eq @ nat) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg1) @ M2)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg2) @ M2)))))))).
% 3.29/1.72 thf(fact_175_message_Oinject_I2_J, axiom, (! [V:$tType,P:$tType,X22:$o,Y22:$o]: ((((((outMsg @ P) @ V) @ X22) = (((outMsg @ P) @ V) @ Y22)) = (X22 = Y22))))).
% 3.29/1.72 thf(fact_176_StepOutMsg, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),V3:$o,Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((~ (((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ (((outMsg @ p) @ v) @ V3)) @ Cfg2)))))).
% 3.29/1.72 thf(fact_177_isPrefixListTrace, axiom, (((prefixList @ ((message @ p) @ v)) @ trace) @ traceMsga)).
% 3.29/1.72 thf(fact_178_expandExecutionStep, axiom, (! [Exec3:(list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)),Msg:((message @ p) @ v),CMsg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),Trace3:(list @ ((message @ p) @ v))]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Exec3)) @ Msg) @ CMsg2) => (((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ Exec3) @ Trace3) => (? [Exec4:(list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)),Trace4:(list @ ((message @ p) @ v))]: ((((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ Exec4) @ Trace4) & ((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Exec3) @ Exec4) & ((((prefixList @ ((message @ p) @ v)) @ Trace3) @ Trace4) & ((((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Exec4) = CMsg2) & (((last @ ((message @ p) @ v)) @ Trace4) = Msg)))))))))))).
% 3.29/1.72 thf(fact_179__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062exec_H_Atrace_H_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_Aexec_H_Atrace_H_059_AprefixList_Aexec_Aexec_H_A_092_060and_062_AprefixList_Atrace_Atrace_H_A_092_060or_062_Aexec_A_061_Aexec_H_A_092_060and_062_Atrace_A_061_Atrace_H_059_Alast_Aexec_H_A_061_Ac_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Exec2:(list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)),Trace2:(list @ ((message @ p) @ v))]: ((((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ Exec2) @ Trace2) => ((((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec) @ Exec2) & (((prefixList @ ((message @ p) @ v)) @ trace) @ Trace2)) | ((exec = Exec2) & (trace = Trace2))) => (((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Exec2) != c)))))))).
% 3.29/1.72 thf(fact_180__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [ExecMsg:(list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)),TraceMsg:(list @ ((message @ p) @ v))]: ((((((((((execution @ p) @ s) @ v) @ trans) @ sends) @ start) @ ExecMsg) @ TraceMsg) => ((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2) @ ExecMsg) => ((((prefixList @ ((message @ p) @ v)) @ trace2) @ TraceMsg) => ((((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ ExecMsg) = cMsg) => (((last @ ((message @ p) @ v)) @ TraceMsg) != msg)))))))))).
% 3.29/1.72 thf(fact_181_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 3.29/1.72 thf(fact_182_asynchronousSystem_OStepOutMsg, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),V3:$o,Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((~ (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ (((outMsg @ P) @ V) @ V3)) @ Cfg2)))))).
% 3.29/1.72 thf(fact_183_isReceiverOf_Osimps_I3_J, axiom, (! [P:$tType,V:$tType,P1:P,V3:$o]: ((~ (((((isReceiverOf @ P) @ V) @ P1) @ (((outMsg @ P) @ V) @ V3))))))).
% 3.29/1.72 thf(fact_184_asynchronousSystem_ONoOutMessageLoss, axiom, (! [S:$tType,P:$tType,V:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),V3:$o]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Cfg2) => (((ord_less_eq @ nat) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg1) @ (((outMsg @ P) @ V) @ V3))) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg2) @ (((outMsg @ P) @ V) @ V3))))))).
% 3.29/1.72 thf(fact_185_asynchronousSystem_Osteps_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((steps @ P) @ S) @ V) = (((steps @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_186_asynchronousSystem_OReachableTrans, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg32:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Cfg2) => ((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg2) @ Cfg32) => (((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Cfg32)))))).
% 3.29/1.72 thf(fact_187_asynchronousSystem_Oreachable_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((reachable @ P) @ S) @ V) = (((reachable @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_188_asynchronousSystem_Oinit, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Cfg1)))).
% 3.29/1.72 thf(fact_189_UniqueReceiverOf, axiom, (! [V:$tType,P:$tType,Q:P,Msg:((message @ P) @ V),P2:P]: ((((((isReceiverOf @ P) @ V) @ Q) @ Msg) => ((P2 != Q) => (~ (((((isReceiverOf @ P) @ V) @ P2) @ Msg)))))))).
% 3.29/1.72 thf(fact_190_asynchronousSystem_OQReachableTrans, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q2:(set @ P),Cfg32:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg2) @ Q2) @ Cfg32) => (((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg2) => ((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg32)))))).
% 3.29/1.72 thf(fact_191_asynchronousSystem_OqReachable_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((qReachable @ P) @ S) @ V) = (((qReachable @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_192_asynchronousSystem_OInitQ, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q2:(set @ P)]: (((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg1)))).
% 3.29/1.72 thf(fact_193_asynchronousSystem_OinitReachable_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((initReachable @ P) @ S) @ V) = (((initReachable @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_194_asynchronousSystem_Oinitial_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((initial @ P) @ S) @ V) = (((initial @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_195_asynchronousSystem_OstepReachable_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((stepReachable @ P) @ S) @ V) = (((stepReachable @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_196_asynchronousSystem_Ostep, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg:((message @ P) @ V),Cfg32:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Cfg2) => (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg2) @ Msg) @ Cfg32) => (((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Cfg32)))))).
% 3.29/1.72 thf(fact_197_asynchronousSystem_Oreachable_Ocases, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),A1:((((configuration_ext @ P) @ V) @ S) @ product_unit),A22:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ A1) @ A22) => ((A22 != A1) => (~ ((! [Cfg23:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ A1) @ Cfg23) => (! [Msg3:((message @ P) @ V)]: ((~ (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg23) @ Msg3) @ A22))))))))))))))).
% 3.29/1.72 thf(fact_198_asynchronousSystem_Oreachable_Osimps, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((reachable @ P) @ S) @ V) = (^ [Trans2:(P > (S > ((messageValue @ V) > S))),Sends2:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),A12:((((configuration_ext @ P) @ V) @ S) @ product_unit),A23:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((? [Cfg13:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((A12 = Cfg13) & (A23 = Cfg13)))) | (? [Cfg13:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg22:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg2:((message @ P) @ V),Cfg34:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((A12 = Cfg13) & ((A23 = Cfg34) & ((((((((reachable @ P) @ S) @ V) @ Trans2) @ Sends2) @ Cfg13) @ Cfg22) & ((((((((steps @ P) @ S) @ V) @ Trans2) @ Sends2) @ Cfg22) @ Msg2) @ Cfg34))))))))))))).
% 3.29/1.72 thf(fact_199_asynchronousSystem_Oreachable_Oinducts, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),X1:((((configuration_ext @ P) @ V) @ S) @ product_unit),X22:((((configuration_ext @ P) @ V) @ S) @ product_unit),P3:(((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o))]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ X1) @ X22) => ((! [Cfg12:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((P3 @ Cfg12) @ Cfg12))) => ((! [Cfg12:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg23:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg3:((message @ P) @ V),Cfg33:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg12) @ Cfg23) => (((P3 @ Cfg12) @ Cfg23) => (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg23) @ Msg3) @ Cfg33) => ((P3 @ Cfg12) @ Cfg33)))))) => ((P3 @ X1) @ X22))))))).
% 3.29/1.72 thf(fact_200_asynchronousSystem_ODiamondOne, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),M:((message @ P) @ V),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P,Q:P,M2:((message @ P) @ V),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg) @ M) @ Cfg1) => ((P2 != Q) => (((((isReceiverOf @ P) @ V) @ P2) @ M) => ((~ (((((isReceiverOf @ P) @ V) @ P2) @ M2))) => (((((isReceiverOf @ P) @ V) @ Q) @ M2) => ((~ (((((isReceiverOf @ P) @ V) @ Q) @ M))) => (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg) @ M2) @ Cfg2) => (? [Cfg3:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ M2) @ Cfg3) & ((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg2) @ M) @ Cfg3)))))))))))))).
% 3.29/1.72 thf(fact_201_asynchronousSystem_OQReachImplReach, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q2:(set @ P),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg2) => (((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Cfg2))))).
% 3.29/1.72 thf(fact_202_asynchronousSystem_OOnlyOccurenceDisables, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),M:((message @ P) @ V),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),M2:((message @ P) @ V)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ M) @ Cfg2) => ((((((enabled @ P) @ V) @ S) @ Cfg1) @ M2) => ((~ ((((((enabled @ P) @ V) @ S) @ Cfg2) @ M2))) => (M = M2))))))).
% 3.29/1.72 thf(fact_203_asynchronousSystem_ONotInQFrozenQReachability, axiom, (! [V:$tType,S:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q2:(set @ P),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg2) => ((~ ((((member @ P) @ P2) @ Q2))) => (((((((states @ P) @ V) @ S) @ product_unit) @ Cfg1) @ P2) = ((((((states @ P) @ V) @ S) @ product_unit) @ Cfg2) @ P2))))))).
% 3.29/1.72 thf(fact_204_asynchronousSystem_OInitialIsInitReachable, axiom, (! [S:$tType,V:$tType,P:$tType,Start:(P > S),C:((((configuration_ext @ P) @ V) @ S) @ product_unit),Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat))))]: (((((((initial @ P) @ S) @ V) @ Start) @ C) => (((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ C))))).
% 3.29/1.72 thf(fact_205_asynchronousSystem_OOtherMessagesOnlyGrowing, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),M:((message @ P) @ V),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),M2:((message @ P) @ V)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ M) @ Cfg2) => ((M != M2) => (((ord_less_eq @ nat) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg1) @ M2)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg2) @ M2))))))).
% 3.29/1.72 thf(fact_206_asynchronousSystem_OStepQ, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q2:(set @ P),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg:((message @ P) @ V),Cfg32:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg2) => (((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg2) @ Msg) @ Cfg32) => ((? [X4:P]: (((((member @ P) @ X4) @ Q2) & ((((isReceiverOf @ P) @ V) @ X4) @ Msg)))) => ((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ Q2) @ Cfg32))))))).
% 3.29/1.72 thf(fact_207_asynchronousSystem_OqReachable_Ocases, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),A1:((((configuration_ext @ P) @ V) @ S) @ product_unit),A22:(set @ P),A3:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ A1) @ A22) @ A3) => ((A3 != A1) => (~ ((! [Cfg23:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ A1) @ A22) @ Cfg23) => (! [Msg3:((message @ P) @ V)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg23) @ Msg3) @ A3) => (~ ((? [X:P]: (((((member @ P) @ X) @ A22) & ((((isReceiverOf @ P) @ V) @ X) @ Msg3))))))))))))))))))).
% 3.29/1.72 thf(fact_208_asynchronousSystem_OqReachable_Osimps, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((qReachable @ P) @ S) @ V) = (^ [Trans2:(P > (S > ((messageValue @ V) > S))),Sends2:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),A12:((((configuration_ext @ P) @ V) @ S) @ product_unit),A23:(set @ P),A32:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((A32 = A12) | (? [Cfg22:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans2) @ Sends2) @ A12) @ A23) @ Cfg22) & (? [Msg2:((message @ P) @ V)]: ((((((((((steps @ P) @ S) @ V) @ Trans2) @ Sends2) @ Cfg22) @ Msg2) @ A32) & (? [X3:P]: (((((member @ P) @ X3) @ A23) & ((((isReceiverOf @ P) @ V) @ X3) @ Msg2))))))))))))))))).
% 3.29/1.72 thf(fact_209_asynchronousSystem_OqReachable_Oinducts, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),X1:((((configuration_ext @ P) @ V) @ S) @ product_unit),X22:(set @ P),X32:((((configuration_ext @ P) @ V) @ S) @ product_unit),P3:(((((configuration_ext @ P) @ V) @ S) @ product_unit) > ((set @ P) > (((((configuration_ext @ P) @ V) @ S) @ product_unit) > $o)))]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ X1) @ X22) @ X32) => ((! [Cfg12:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q3:(set @ P)]: ((((P3 @ Cfg12) @ Q3) @ Cfg12))) => ((! [Cfg12:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q3:(set @ P),Cfg23:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((qReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg12) @ Q3) @ Cfg23) => ((((P3 @ Cfg12) @ Q3) @ Cfg23) => (! [Msg3:((message @ P) @ V),Cfg33:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg23) @ Msg3) @ Cfg33) => ((? [X:P]: (((((member @ P) @ X) @ Q3) & ((((isReceiverOf @ P) @ V) @ X) @ Msg3)))) => (((P3 @ Cfg12) @ Q3) @ Cfg33))))))))) => (((P3 @ X1) @ X22) @ X32))))))).
% 3.29/1.72 thf(fact_210_asynchronousSystem_ONoReceivingNoChange, axiom, (! [V:$tType,S:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),M:((message @ P) @ V),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ M) @ Cfg2) => ((~ (((((isReceiverOf @ P) @ V) @ P2) @ M))) => (((((((states @ P) @ V) @ S) @ product_unit) @ Cfg1) @ P2) = ((((((states @ P) @ V) @ S) @ product_unit) @ Cfg2) @ P2))))))).
% 3.29/1.72 thf(fact_211_asynchronousSystem_OinitReachable__def, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((initReachable @ P) @ S) @ V) = (^ [Trans2:(P > (S > ((messageValue @ V) > S))),Sends2:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start2:(P > S),Cfg5:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((? [Cfg0:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((initial @ P) @ S) @ V) @ Start2) @ Cfg0) & (((((((reachable @ P) @ S) @ V) @ Trans2) @ Sends2) @ Cfg0) @ Cfg5)))))))))).
% 3.29/1.72 thf(fact_212_asynchronousSystem_OstepReachable__def, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((stepReachable @ P) @ S) @ V) = (^ [Trans2:(P > (S > ((messageValue @ V) > S))),Sends2:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),C12:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg2:((message @ P) @ V),C23:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((? [C5:((((configuration_ext @ P) @ V) @ S) @ product_unit),C6:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans2) @ Sends2) @ C12) @ C5) & (((((((((steps @ P) @ S) @ V) @ Trans2) @ Sends2) @ C5) @ Msg2) @ C6) & (((((((reachable @ P) @ S) @ V) @ Trans2) @ Sends2) @ C6) @ C23))))))))))).
% 3.29/1.72 thf(fact_213_asynchronousSystem_OStepReachable, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg4:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg:((message @ P) @ V)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg) @ Cfg4) => ((((((enabled @ P) @ V) @ S) @ Cfg) @ Msg) => ((~ ((((((enabled @ P) @ V) @ S) @ Cfg4) @ Msg))) => ((((((((stepReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg) @ Msg) @ Cfg4))))))).
% 3.29/1.72 thf(fact_214_asynchronousSystem_OexpandExecutionStep, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Exec3:(list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)),Msg:((message @ P) @ V),CMsg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Start:(P > S),Trace3:(list @ ((message @ P) @ V))]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ ((last @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec3)) @ Msg) @ CMsg2) => (((((((((execution @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ Exec3) @ Trace3) => (? [Exec4:(list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)),Trace4:(list @ ((message @ P) @ V))]: ((((((((((execution @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ Exec4) @ Trace4) & ((((prefixList @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec3) @ Exec4) & ((((prefixList @ ((message @ P) @ V)) @ Trace3) @ Trace4) & ((((last @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec4) = CMsg2) & (((last @ ((message @ P) @ V)) @ Trace4) = Msg)))))))))))).
% 3.29/1.72 thf(fact_215_asynchronousSystem_OexpandExecutionReachable, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),CfgLast:((((configuration_ext @ P) @ V) @ S) @ product_unit),Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),Start:(P > S),Exec:(list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)),Trace:(list @ ((message @ P) @ V))]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ CfgLast) @ Cfg) => (((((((((execution @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ Exec) @ Trace) => ((CfgLast = ((last @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec)) => (? [Exec2:(list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)),Trace2:(list @ ((message @ P) @ V))]: ((((((((((execution @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ Exec2) @ Trace2) & ((((((prefixList @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec) @ Exec2) & (((prefixList @ ((message @ P) @ V)) @ Trace) @ Trace2)) | ((Exec = Exec2) & (Trace = Trace2))) & (((last @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec2) = Cfg))))))))))).
% 3.29/1.72 thf(fact_216_NonUniformCanReachSilentBivalence, axiom, (! [C:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p]: ((((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) & ((~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $false) @ C))) & (~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $true) @ C))))) => ((! [Cc:((((configuration_ext @ p) @ v) @ s) @ product_unit),X_1:(set @ p)]: ((((((((((terminationPseudo @ p) @ s) @ v) @ trans) @ sends) @ start) @ (one_one @ nat)) @ Cc) @ X_1))) => ((! [Cfg6:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ C) @ Cfg6) => ((((agreement @ p) @ v) @ s) @ Cfg6)))) => (? [C7:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ C) @ C7) & (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ P2) @ C7)))) = (((insert @ $o) @ $true) @ (((insert @ $o) @ $false) @ (bot_bot @ (set @ $o)))))))))))))).
% 3.29/1.72 thf(fact_217_PseudoTermination, axiom, (! [Cc2:((((configuration_ext @ p) @ v) @ s) @ product_unit),Q2:(set @ p)]: ((((((((((terminationPseudo @ p) @ s) @ v) @ trans) @ sends) @ start) @ (one_one @ nat)) @ Cc2) @ Q2)))).
% 3.29/1.72 thf(fact_218_DecisionValuesExist, axiom, (! [C:((((configuration_ext @ p) @ v) @ s) @ product_unit),P2:p]: (((! [Cc:((((configuration_ext @ p) @ v) @ s) @ product_unit),X_1:(set @ p)]: ((((((((((terminationPseudo @ p) @ s) @ v) @ trans) @ sends) @ start) @ (one_one @ nat)) @ Cc) @ X_1))) => ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) => (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ P2) @ C)))) != (bot_bot @ (set @ $o)))))))).
% 3.29/1.72 thf(fact_219_InitialNonUniformCfg, axiom, ((! [Cc:((((configuration_ext @ p) @ v) @ s) @ product_unit),X_1:(set @ p)]: ((((((((((terminationPseudo @ p) @ s) @ v) @ trans) @ sends) @ start) @ (one_one @ nat)) @ Cc) @ X_1))) => ((! [I2:((((configuration_ext @ p) @ v) @ s) @ product_unit),X_1:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((validity @ p) @ s) @ v) @ trans) @ sends) @ start) @ I2) @ X_1))) => ((! [I2:((((configuration_ext @ p) @ v) @ s) @ product_unit),X_1:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((agreementInit @ p) @ s) @ v) @ trans) @ sends) @ start) @ I2) @ X_1))) => (? [Cfg6:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((initial @ p) @ s) @ v) @ start) @ Cfg6) & ((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ Cfg6) & ((~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $false) @ Cfg6))) & (~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $true) @ Cfg6)))))))))))).
% 3.29/1.72 thf(fact_220_flpPseudoConsensus_OPseudoTermination, axiom, (! [V:$tType,S:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),Cc2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Q2:(set @ P)]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => (((((((((terminationPseudo @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ (one_one @ nat)) @ Cc2) @ Q2))))).
% 3.29/1.72 thf(fact_221_flpSystem_OterminationPseudo_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((terminationPseudo @ P) @ S) @ V) = (((terminationPseudo @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_222_flpSystem_ODecisionValuesExist, axiom, (! [S:$tType,V:$tType,P:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Trans:(P > (S > ((messageValue @ V) > S))),Start:(P > S),C:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => ((! [Cc:((((configuration_ext @ P) @ V) @ S) @ product_unit),X_1:(set @ P)]: ((((((((((terminationPseudo @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ (one_one @ nat)) @ Cc) @ X_1))) => ((((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ C) => (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ P2) @ C)))) != (bot_bot @ (set @ $o))))))))).
% 3.29/1.72 thf(fact_223_flpSystem_ONonUniformCanReachSilentBivalence, axiom, (! [S:$tType,V:$tType,P:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Trans:(P > (S > ((messageValue @ V) > S))),Start:(P > S),C:((((configuration_ext @ P) @ V) @ S) @ product_unit),P2:P]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => (((((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ C) & ((~ (((((((((vUniform @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ $false) @ C))) & (~ (((((((((vUniform @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ $true) @ C))))) => ((! [Cc:((((configuration_ext @ P) @ V) @ S) @ product_unit),X_1:(set @ P)]: ((((((((((terminationPseudo @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ (one_one @ nat)) @ Cc) @ X_1))) => ((! [Cfg6:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ C) @ Cfg6) => ((((agreement @ P) @ V) @ S) @ Cfg6)))) => (? [C7:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((reachable @ P) @ S) @ V) @ Trans) @ Sends) @ C) @ C7) & (((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ V2) @ P2) @ C7)))) = (((insert @ $o) @ $true) @ (((insert @ $o) @ $false) @ (bot_bot @ (set @ $o))))))))))))))).
% 3.29/1.72 thf(fact_224_flpSystem_OInitialNonUniformCfg, axiom, (! [S:$tType,V:$tType,P:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Trans:(P > (S > ((messageValue @ V) > S))),Start:(P > S)]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => ((! [Cc:((((configuration_ext @ P) @ V) @ S) @ product_unit),X_1:(set @ P)]: ((((((((((terminationPseudo @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ (one_one @ nat)) @ Cc) @ X_1))) => ((! [I2:((((configuration_ext @ P) @ V) @ S) @ product_unit),X_1:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((validity @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ I2) @ X_1))) => ((! [I2:((((configuration_ext @ P) @ V) @ S) @ product_unit),X_1:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((((agreementInit @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ I2) @ X_1))) => (? [Cfg6:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: (((((((initial @ P) @ S) @ V) @ Start) @ Cfg6) & ((((((((initReachable @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ Cfg6) & ((~ (((((((((vUniform @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ $false) @ Cfg6))) & (~ (((((((((vUniform @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ $true) @ Cfg6))))))))))))))).
% 3.29/1.72 thf(fact_225_execution_OExistImpliesMinEnabled, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),Exec:(list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)),Trace:(list @ ((message @ P) @ V)),P2:P,Msg:((message @ P) @ V)]: ((((((((((execution @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ Exec) @ Trace) => (((((isReceiverOf @ P) @ V) @ P2) @ Msg) => ((((((enabled @ P) @ V) @ S) @ ((last @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec)) @ Msg) => (? [X_1:((message @ P) @ V)]: (((((((minimalEnabled @ P) @ V) @ S) @ Exec) @ Trace) @ X_1))))))))).
% 3.29/1.72 thf(fact_226_execution_OminimalEnabled_Ocong, axiom, (! [S:$tType,V:$tType,P:$tType]: (((((minimalEnabled @ P) @ V) @ S) = (((minimalEnabled @ P) @ V) @ S))))).
% 3.29/1.72 thf(fact_227_flpSystem_Ovalidity_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((validity @ P) @ S) @ V) = (((validity @ P) @ S) @ V))))).
% 3.29/1.72 thf(fact_228_execution_OFirstOccurrenceExists, axiom, (! [P:$tType,V:$tType,S:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),Exec:(list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)),Trace:(list @ ((message @ P) @ V)),Msg:((message @ P) @ V)]: ((((((((((execution @ P) @ S) @ V) @ Trans) @ Sends) @ Start) @ Exec) @ Trace) => ((((((enabled @ P) @ V) @ S) @ ((last @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Exec)) @ Msg) => ((? [P6:P]: (((((isReceiverOf @ P) @ V) @ P6) @ Msg))) => (? [X_1:nat]: ((((((((firstOccurrence @ P) @ V) @ S) @ Exec) @ Trace) @ Msg) @ X_1))))))))).
% 3.29/1.72 thf(fact_229_NonUniformImpliesNotDecided, axiom, (! [C:((((configuration_ext @ p) @ v) @ s) @ product_unit),V3:$o]: (((! [Cfg6:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ C) @ Cfg6) => ((((agreement @ p) @ v) @ s) @ Cfg6)))) => ((! [Cc:((((configuration_ext @ p) @ v) @ s) @ product_unit),X_1:(set @ p)]: ((((((((((terminationPseudo @ p) @ s) @ v) @ trans) @ sends) @ start) @ (one_one @ nat)) @ Cc) @ X_1))) => (((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) & ((~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $false) @ C))) & (~ (((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ $true) @ C))))) => (~ (((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) & (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ C) @ (((outMsg @ p) @ v) @ V3)))))))))))).
% 3.29/1.72 thf(fact_230_agreement__def, axiom, ((((agreement @ p) @ v) @ s) = (^ [C9:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((! [V1:$o]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ C9) @ (((outMsg @ p) @ v) @ V1))) => (! [V22:$o]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ C9) @ (((outMsg @ p) @ v) @ V22))) = (V22 = V1))))))))))).
% 3.29/1.72 thf(fact_231_ExistsMsg, axiom, (! [Cfg1:((((configuration_ext @ p) @ v) @ s) @ product_unit),M:((message @ p) @ v),Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((steps @ p) @ s) @ v) @ trans) @ sends) @ Cfg1) @ M) @ Cfg2) => (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ Cfg1) @ M)))))).
% 3.29/1.72 thf(fact_232_agreementInit__def, axiom, (! [I:((((configuration_ext @ p) @ v) @ s) @ product_unit),C:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: ((((((((((agreementInit @ p) @ s) @ v) @ trans) @ sends) @ start) @ I) @ C) = (((((((initial @ p) @ s) @ v) @ start) @ I) & (((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ I) @ C)) => (! [V1:$o]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ C) @ (((outMsg @ p) @ v) @ V1))) => (! [V22:$o]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ C) @ (((outMsg @ p) @ v) @ V22))) = (V22 = V1)))))))))))).
% 3.29/1.72 thf(fact_233_DecidedImpliesUniform, axiom, (! [C:((((configuration_ext @ p) @ v) @ s) @ product_unit),V3:$o]: (((! [Cfg6:((((configuration_ext @ p) @ v) @ s) @ product_unit)]: (((((((((reachable @ p) @ s) @ v) @ trans) @ sends) @ C) @ Cfg6) => ((((agreement @ p) @ v) @ s) @ Cfg6)))) => ((! [Cc:((((configuration_ext @ p) @ v) @ s) @ product_unit),X_1:(set @ p)]: ((((((((((terminationPseudo @ p) @ s) @ v) @ trans) @ sends) @ start) @ (one_one @ nat)) @ Cc) @ X_1))) => (((((((((initReachable @ p) @ s) @ v) @ trans) @ sends) @ start) @ C) & (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ C) @ (((outMsg @ p) @ v) @ V3)))) => ((((((((vUniform @ p) @ s) @ v) @ trans) @ sends) @ start) @ V3) @ C))))))).
% 3.29/1.72 thf(fact_234_flpSystem_Oagreement__def, axiom, (! [V:$tType,P:$tType,S:$tType,Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),C:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((flpSystem @ P) @ S) @ V) @ Sends) => (((((agreement @ P) @ V) @ S) @ C) = (! [V1:$o]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ C) @ (((outMsg @ P) @ V) @ V1))) => (! [V22:$o]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ C) @ (((outMsg @ P) @ V) @ V22))) = (V22 = V1)))))))))))).
% 3.29/1.72 thf(fact_235_enabled__def, axiom, (! [S:$tType,V:$tType,P:$tType]: (((((enabled @ P) @ V) @ S) = (^ [Cfg5:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg2:((message @ P) @ V)]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg5) @ Msg2)))))))).
% 3.29/1.72 thf(fact_236_asynchronousSystem_OExistsMsg, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Cfg1:((((configuration_ext @ P) @ V) @ S) @ product_unit),M:((message @ P) @ V),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit)]: ((((((((((steps @ P) @ S) @ V) @ Trans) @ Sends) @ Cfg1) @ M) @ Cfg2) => (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg1) @ M)))))).
% 3.29/1.72 thf(fact_237_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A5:A,B3:A]: (((A5 != B3) => ((((ord_less_eq @ A) @ A5) @ B3) => (((ord_less @ A) @ A5) @ B3))))))))).
% 3.29/1.72 thf(fact_238_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A5:A]: (((((ord_less @ A) @ B3) @ A5) => (((ord_less_eq @ A) @ B3) @ A5)))))))).
% 3.29/1.72 thf(fact_239_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B4:A,A6:A]: (((((ord_less_eq @ A) @ B4) @ A6) & (A6 != B4))))))))).
% 3.29/1.72 thf(fact_240_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B4:A,A6:A]: (((((ord_less @ A) @ B4) @ A6) | (A6 = B4))))))))).
% 3.29/1.72 thf(fact_241_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A5:A,B3:A]: (((((ord_less @ A) @ A5) @ B3) => (((ord_less_eq @ A) @ A5) @ B3)))))))).
% 3.29/1.72 thf(fact_242_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y2) => ((! [W:A]: (((((ord_less @ A) @ X2) @ W) => ((((ord_less @ A) @ W) @ Y2) => (((ord_less_eq @ A) @ W) @ Z3))))) => (((ord_less_eq @ A) @ Y2) @ Z3))))))))).
% 3.29/1.72 thf(fact_243_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,X2:A,Y2:A]: (((((ord_less @ A) @ Z3) @ X2) => ((! [W:A]: (((((ord_less @ A) @ Z3) @ W) => ((((ord_less @ A) @ W) @ X2) => (((ord_less_eq @ A) @ Y2) @ W))))) => (((ord_less_eq @ A) @ Y2) @ Z3))))))))).
% 3.29/1.72 thf(fact_244_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A5:A,C:A]: (((((ord_less @ A) @ B3) @ A5) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A5))))))))).
% 3.29/1.72 thf(fact_245_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A5:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A5) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A5))))))))).
% 3.29/1.72 thf(fact_246_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A6:A,B4:A]: (((((ord_less_eq @ A) @ A6) @ B4) & (A6 != B4))))))))).
% 3.29/1.72 thf(fact_247_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A6:A,B4:A]: (((((ord_less @ A) @ A6) @ B4) | (A6 = B4))))))))).
% 3.29/1.72 thf(fact_248_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A5:A,B3:A,C:A]: (((((ord_less @ A) @ A5) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less @ A) @ A5) @ C))))))))).
% 3.29/1.72 thf(fact_249_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A5:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A5) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A5) @ C))))))))).
% 3.29/1.72 thf(fact_250_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X2:A]: (((~ ((((ord_less_eq @ A) @ Y2) @ X2))) => (((ord_less @ A) @ X2) @ Y2)))))))).
% 3.29/1.72 thf(fact_251_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) & (~ ((((ord_less_eq @ A) @ Y3) @ X3))))))))))).
% 3.29/1.72 thf(fact_252_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less @ A) @ X2) @ Y2) | (X2 = Y2))))))))).
% 3.29/1.72 thf(fact_253_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less @ A) @ Y2) @ X2)))))))).
% 3.29/1.72 thf(fact_254_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y2:A,Z3:A]: (((! [X:A]: (((((ord_less @ A) @ X) @ Y2) => (((ord_less_eq @ A) @ X) @ Z3)))) => (((ord_less_eq @ A) @ Y2) @ Z3)))))))).
% 3.29/1.72 thf(fact_255_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,Y2:A]: (((! [X:A]: (((((ord_less @ A) @ Z3) @ X) => (((ord_less_eq @ A) @ Y2) @ X)))) => (((ord_less_eq @ A) @ Y2) @ Z3)))))))).
% 3.29/1.72 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A8:$tType,A9:$tType]: (((order_bot @ A9) => (order_bot @ (A8 > A9)))))).
% 3.29/1.72 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 3.29/1.72 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 3.29/1.72 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 3.29/1.72 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 3.29/1.72 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1, axiom, (order_bot @ nat)).
% 3.29/1.72 thf(tcon_Nat_Onat___Orderings_Opreorder_2, axiom, (preorder @ nat)).
% 3.29/1.72 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 3.29/1.72 thf(tcon_Nat_Onat___Orderings_Oorder_3, axiom, (order @ nat)).
% 3.29/1.72 thf(tcon_Nat_Onat___Orderings_Oord_4, axiom, (ord @ nat)).
% 3.29/1.72 thf(tcon_Nat_Onat___Orderings_Obot_5, axiom, (bot @ nat)).
% 3.29/1.72 thf(tcon_Set_Oset___Orderings_Oorder__bot_6, axiom, (! [A8:$tType]: ((order_bot @ (set @ A8))))).
% 3.29/1.72 thf(tcon_Set_Oset___Orderings_Opreorder_7, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 3.29/1.72 thf(tcon_Set_Oset___Orderings_Oorder_8, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 3.29/1.72 thf(tcon_Set_Oset___Orderings_Oord_9, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 3.29/1.72 thf(tcon_Set_Oset___Orderings_Obot_10, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 3.29/1.72 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11, axiom, (order_bot @ $o)).
% 3.29/1.72 thf(tcon_HOL_Obool___Orderings_Opreorder_12, axiom, (preorder @ $o)).
% 3.29/1.72 thf(tcon_HOL_Obool___Orderings_Olinorder_13, axiom, (linorder @ $o)).
% 3.29/1.72 thf(tcon_HOL_Obool___Orderings_Oorder_14, axiom, (order @ $o)).
% 3.29/1.72 thf(tcon_HOL_Obool___Orderings_Oord_15, axiom, (ord @ $o)).
% 3.29/1.72 thf(tcon_HOL_Obool___Orderings_Obot_16, axiom, (bot @ $o)).
% 3.29/1.72 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_17, axiom, (order_bot @ product_unit)).
% 3.29/1.72 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_18, axiom, (preorder @ product_unit)).
% 3.29/1.72 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_19, axiom, (linorder @ product_unit)).
% 3.29/1.72 thf(tcon_Product__Type_Ounit___Orderings_Oorder_20, axiom, (order @ product_unit)).
% 3.29/1.72 thf(tcon_Product__Type_Ounit___Orderings_Oord_21, axiom, (ord @ product_unit)).
% 3.29/1.72 thf(tcon_Product__Type_Ounit___Orderings_Obot_22, axiom, (bot @ product_unit)).
% 3.29/1.72 thf(conj_0, conjecture, (((ord_less_eq @ (set @ $o)) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ p2) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ exec2)))))) @ ((collect @ $o) @ (^ [V2:$o]: ((((((((((pSilDecVal @ p) @ s) @ v) @ trans) @ sends) @ start) @ V2) @ p2) @ cMsg)))))).
% 3.29/1.72 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2DTF14509.p
% 3.29/1.72 ------------------------
% 3.29/1.79 ---- Cleaned THF ---
% 3.29/1.79 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 3.29/1.79 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_t_AsynchronousSystem_OmessageValue,type,
% 3.29/1.79 messageValue: $tType > $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_t_AsynchronousSystem_Omessage,type,
% 3.29/1.79 message: $tType > $tType > $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_t_Product__Type_Ounit,type,
% 3.29/1.79 product_unit: $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_t_List_Olist,type,
% 3.29/1.79 list: $tType > $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_t_Set_Oset,type,
% 3.29/1.79 set: $tType > $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_t_Nat_Onat,type,
% 3.29/1.79 nat: $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_tf_v,type,
% 3.29/1.79 v: $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_tf_s,type,
% 3.29/1.79 s: $tType ).
% 3.29/1.79
% 3.29/1.79 thf(ty_tf_p,type,
% 3.29/1.79 p: $tType ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_HOL_Otype,type,
% 3.29/1.79 type:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_Orderings_Obot,type,
% 3.29/1.79 bot:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_Orderings_Oord,type,
% 3.29/1.79 ord:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_Orderings_Oorder,type,
% 3.29/1.79 order:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_Orderings_Olinorder,type,
% 3.29/1.79 linorder:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_Orderings_Opreorder,type,
% 3.29/1.79 preorder:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_Orderings_Oorder__bot,type,
% 3.29/1.79 order_bot:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_cl_Orderings_Odense__linorder,type,
% 3.29/1.79 dense_linorder:
% 3.29/1.79 !>[A: $tType] : $o ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OinitReachable,type,
% 3.29/1.79 initReachable:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oinitial,type,
% 3.29/1.79 initial:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OqReachable,type,
% 3.29/1.79 qReachable:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( set @ P ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oreachable,type,
% 3.29/1.79 reachable:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OstepReachable,type,
% 3.29/1.79 stepReachable:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Osteps,type,
% 3.29/1.79 steps:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs,type,
% 3.29/1.79 msgs:
% 3.29/1.79 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > ( message @ P @ V ) > nat ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_Oconfiguration_Ostates,type,
% 3.29/1.79 states:
% 3.29/1.79 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > P > S ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 3.29/1.79 enabled:
% 3.29/1.79 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_OisReceiverOf,type,
% 3.29/1.79 isReceiverOf:
% 3.29/1.79 !>[P: $tType,V: $tType] : ( P > ( message @ P @ V ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_AsynchronousSystem_Omessage_OOutMsg,type,
% 3.29/1.79 outMsg:
% 3.29/1.79 !>[P: $tType,V: $tType] : ( $o > ( message @ P @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Execution_Oexecution,type,
% 3.29/1.79 execution:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 3.29/1.79 firstOccurrence:
% 3.29/1.79 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Execution_Oexecution_OminimalEnabled,type,
% 3.29/1.79 minimalEnabled:
% 3.29/1.79 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPSystem_OflpSystem,type,
% 3.29/1.79 flpSystem:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPSystem_OflpSystem_Oagreement,type,
% 3.29/1.79 agreement:
% 3.29/1.79 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPSystem_OflpSystem_OagreementInit,type,
% 3.29/1.79 agreementInit:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPSystem_OflpSystem_OpSilDecVal,type,
% 3.29/1.79 pSilDecVal:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o > P > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPSystem_OflpSystem_OterminationPseudo,type,
% 3.29/1.79 terminationPseudo:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > nat > ( configuration_ext @ P @ V @ S @ product_unit ) > ( set @ P ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPSystem_OflpSystem_OvUniform,type,
% 3.29/1.79 vUniform:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPSystem_OflpSystem_Ovalidity,type,
% 3.29/1.79 validity:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus,type,
% 3.29/1.79 fLPThe1922692578sensus:
% 3.29/1.79 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Groups_Oone__class_Oone,type,
% 3.29/1.79 one_one:
% 3.29/1.79 !>[A: $tType] : A ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 3.29/1.79 zero_zero:
% 3.29/1.79 !>[A: $tType] : A ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_ListUtilities_OprefixList,type,
% 3.29/1.79 prefixList:
% 3.29/1.79 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_List_Olast,type,
% 3.29/1.79 last:
% 3.29/1.79 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.29/1.79 bot_bot:
% 3.29/1.79 !>[A: $tType] : A ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Orderings_Oord__class_Oless,type,
% 3.29/1.79 ord_less:
% 3.29/1.79 !>[A: $tType] : ( A > A > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.29/1.79 ord_less_eq:
% 3.29/1.79 !>[A: $tType] : ( A > A > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Set_OCollect,type,
% 3.29/1.79 collect:
% 3.29/1.79 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_Set_Oinsert,type,
% 3.29/1.79 insert:
% 3.29/1.79 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_c_member,type,
% 3.29/1.79 member:
% 3.29/1.79 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_cMsg____,type,
% 3.29/1.79 cMsg: configuration_ext @ p @ v @ s @ product_unit ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_c_H____,type,
% 3.29/1.79 c: configuration_ext @ p @ v @ s @ product_unit ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_exec,type,
% 3.29/1.79 exec: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_execMsga____,type,
% 3.29/1.79 execMsga: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_exec_H____,type,
% 3.29/1.79 exec2: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_msg,type,
% 3.29/1.79 msg: message @ p @ v ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_p,type,
% 3.29/1.79 p2: p ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_sends,type,
% 3.29/1.79 sends: p > s > ( messageValue @ v ) > ( message @ p @ v ) > nat ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_start,type,
% 3.29/1.79 start: p > s ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_trace,type,
% 3.29/1.79 trace: list @ ( message @ p @ v ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_traceMsga____,type,
% 3.29/1.79 traceMsga: list @ ( message @ p @ v ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_trace_H____,type,
% 3.29/1.79 trace2: list @ ( message @ p @ v ) ).
% 3.29/1.79
% 3.29/1.79 thf(sy_v_trans,type,
% 3.29/1.79 trans: p > s > ( messageValue @ v ) > s ).
% 3.29/1.79
% 3.29/1.79 thf(fact_0_PisReceiverOf,axiom,
% 3.29/1.79 isReceiverOf @ p @ v @ p2 @ msg ).
% 3.29/1.79
% 3.29/1.79 thf(fact_1_InitReachLastExec_H,axiom,
% 3.29/1.79 initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_2_NewExec_I3_J,axiom,
% 3.29/1.79 ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 )
% 3.29/1.79 = c ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_3_CMsg,axiom,
% 3.29/1.79 steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg ).
% 3.29/1.79
% 3.29/1.79 thf(fact_4_flpPseudoConsensus__axioms,axiom,
% 3.29/1.79 fLPThe1922692578sensus @ p @ s @ v @ trans @ sends @ start ).
% 3.29/1.79
% 3.29/1.79 thf(fact_5_ExecMsg_I3_J,axiom,
% 3.29/1.79 ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga )
% 3.29/1.79 = cMsg ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062,axiom,
% 3.29/1.79 ( ( p2 = p2 )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ p2 @ msg )
% 3.29/1.79 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
% 3.29/1.79 => ( ord_less_eq @ ( set @ $o )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ cMsg ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_7_DiamondOne,axiom,
% 3.29/1.79 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg1: configuration_ext @ p @ v @ s @ product_unit,P2: p,Q: p,M2: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg @ M @ Cfg1 )
% 3.29/1.79 => ( ( P2 != Q )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ P2 @ M )
% 3.29/1.79 => ( ~ ( isReceiverOf @ p @ v @ P2 @ M2 )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ Q @ M2 )
% 3.29/1.79 => ( ~ ( isReceiverOf @ p @ v @ Q @ M )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg @ M2 @ Cfg2 )
% 3.29/1.79 => ? [Cfg3: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M2 @ Cfg3 )
% 3.29/1.79 & ( steps @ p @ s @ v @ trans @ sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_8_True,axiom,
% 3.29/1.79 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg ).
% 3.29/1.79
% 3.29/1.79 thf(fact_9__092_060open_062_092_060exists_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_092_060close_062,axiom,
% 3.29/1.79 ? [X_1: configuration_ext @ p @ v @ s @ product_unit] : ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ X_1 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_10__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.29/1.79 ~ ! [CMsg: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ~ ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ CMsg ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_11_Agreement,axiom,
% 3.29/1.79 ! [I: configuration_ext @ p @ v @ s @ product_unit,C: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ I @ C ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_12_ActiveProcessSilentDecisionValuesIncrease,axiom,
% 3.29/1.79 ! [P2: p,Q: p,C: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,C2: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( P2 = Q )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ C @ Msg @ C2 )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ P2 @ Msg )
% 3.29/1.79 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 => ( ord_less_eq @ ( set @ $o )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C ) )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C2 ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_13_InactiveProcessSilentDecisionValuesDecrease,axiom,
% 3.29/1.79 ! [P2: p,Q: p,C: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,C2: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( P2 != Q )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ C @ Msg @ C2 )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ P2 @ Msg )
% 3.29/1.79 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 => ( ord_less_eq @ ( set @ $o )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C2 ) )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_14_nonUniformC_H,axiom,
% 3.29/1.79 ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_15_InitReachLastExecMsg,axiom,
% 3.29/1.79 initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_16_NewExec_I1_J,axiom,
% 3.29/1.79 execution @ p @ s @ v @ trans @ sends @ start @ exec2 @ trace2 ).
% 3.29/1.79
% 3.29/1.79 thf(fact_17_InitialIsInitReachable,axiom,
% 3.29/1.79 ! [C: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( initial @ p @ s @ v @ start @ C )
% 3.29/1.79 => ( initReachable @ p @ s @ v @ trans @ sends @ start @ C ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_18_flpSystem__axioms,axiom,
% 3.29/1.79 flpSystem @ p @ s @ v @ sends ).
% 3.29/1.79
% 3.29/1.79 thf(fact_19_subsetI,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ! [X: A] :
% 3.29/1.79 ( ( member @ A @ X @ A2 )
% 3.29/1.79 => ( member @ A @ X @ B ) )
% 3.29/1.79 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_20_subset__antisym,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.29/1.79 => ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 3.29/1.79 => ( A2 = B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_21_QReachableTrans,axiom,
% 3.29/1.79 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg32: configuration_ext @ p @ v @ s @ product_unit,Cfg1: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg2 @ Q2 @ Cfg32 )
% 3.29/1.79 => ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_22_InitQ,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p] : ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_23_order__refl,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( preorder @ A )
% 3.29/1.79 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_24_OnlyOccurenceDisables,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,M2: message @ p @ v] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ( enabled @ p @ v @ s @ Cfg1 @ M2 )
% 3.29/1.79 => ( ~ ( enabled @ p @ v @ s @ Cfg2 @ M2 )
% 3.29/1.79 => ( M = M2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_25_qReachable_Osimps,axiom,
% 3.29/1.79 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: set @ p,A3: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ A3 )
% 3.29/1.79 = ( ( A3 = A1 )
% 3.29/1.79 | ? [Cfg22: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ Cfg22 )
% 3.29/1.79 & ? [Msg2: message @ p @ v] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg22 @ Msg2 @ A3 )
% 3.29/1.79 & ? [X3: p] :
% 3.29/1.79 ( ( member @ p @ X3 @ A22 )
% 3.29/1.79 & ( isReceiverOf @ p @ v @ X3 @ Msg2 ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_26_qReachable_Oinducts,axiom,
% 3.29/1.79 ! [X1: configuration_ext @ p @ v @ s @ product_unit,X22: set @ p,X32: configuration_ext @ p @ v @ s @ product_unit,P3: ( configuration_ext @ p @ v @ s @ product_unit ) > ( set @ p ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ X1 @ X22 @ X32 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Q3: set @ p] : ( P3 @ Cfg12 @ Q3 @ Cfg12 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Q3: set @ p,Cfg23: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg12 @ Q3 @ Cfg23 )
% 3.29/1.79 => ( ( P3 @ Cfg12 @ Q3 @ Cfg23 )
% 3.29/1.79 => ! [Msg3: message @ p @ v,Cfg33: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 3.29/1.79 => ( ? [X: p] :
% 3.29/1.79 ( ( member @ p @ X @ Q3 )
% 3.29/1.79 & ( isReceiverOf @ p @ v @ X @ Msg3 ) )
% 3.29/1.79 => ( P3 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 3.29/1.79 => ( P3 @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_27_qReachable_Ocases,axiom,
% 3.29/1.79 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: set @ p,A3: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ A3 )
% 3.29/1.79 => ( ( A3 != A1 )
% 3.29/1.79 => ~ ! [Cfg23: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ A1 @ A22 @ Cfg23 )
% 3.29/1.79 => ! [Msg3: message @ p @ v] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ A3 )
% 3.29/1.79 => ~ ? [X: p] :
% 3.29/1.79 ( ( member @ p @ X @ A22 )
% 3.29/1.79 & ( isReceiverOf @ p @ v @ X @ Msg3 ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_28_StepQ,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,Cfg32: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 3.29/1.79 => ( ? [X4: p] :
% 3.29/1.79 ( ( member @ p @ X4 @ Q2 )
% 3.29/1.79 & ( isReceiverOf @ p @ v @ X4 @ Msg ) )
% 3.29/1.79 => ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_29_ExecMsg_I1_J,axiom,
% 3.29/1.79 prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ execMsga ).
% 3.29/1.79
% 3.29/1.79 thf(fact_30_isExecution,axiom,
% 3.29/1.79 execution @ p @ s @ v @ trans @ sends @ start @ execMsga @ traceMsga ).
% 3.29/1.79
% 3.29/1.79 thf(fact_31_MsgEnabled,axiom,
% 3.29/1.79 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg ).
% 3.29/1.79
% 3.29/1.79 thf(fact_32_NonUniformLexec,axiom,
% 3.29/1.79 ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_33_flpPseudoConsensus_Oaxioms_I1_J,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S] :
% 3.29/1.79 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 3.29/1.79 => ( flpSystem @ P @ S @ V @ Sends ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_34_flpPseudoConsensus_OAgreement,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,I: configuration_ext @ P @ V @ S @ product_unit,C: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 3.29/1.79 => ( agreementInit @ P @ S @ V @ Trans @ Sends @ Start @ I @ C ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_35_less__eq__set__def,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) )
% 3.29/1.79 = ( ^ [A4: set @ A,B2: set @ A] :
% 3.29/1.79 ( ord_less_eq @ ( A > $o )
% 3.29/1.79 @ ^ [X3: A] : ( member @ A @ X3 @ A4 )
% 3.29/1.79 @ ^ [X3: A] : ( member @ A @ X3 @ B2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_36_dual__order_Oantisym,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [B3: A,A5: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ B3 @ A5 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.79 => ( A5 = B3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_37_dual__order_Oeq__iff,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ( ( ^ [Y: A,Z2: A] : ( Y = Z2 ) )
% 3.29/1.79 = ( ^ [A6: A,B4: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ B4 @ A6 )
% 3.29/1.79 & ( ord_less_eq @ A @ A6 @ B4 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_38_dual__order_Otrans,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [B3: A,A5: A,C: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ B3 @ A5 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ C @ B3 )
% 3.29/1.79 => ( ord_less_eq @ A @ C @ A5 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_39_linorder__wlog,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( linorder @ A )
% 3.29/1.79 => ! [P3: A > A > $o,A5: A,B3: A] :
% 3.29/1.79 ( ! [A7: A,B5: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A7 @ B5 )
% 3.29/1.79 => ( P3 @ A7 @ B5 ) )
% 3.29/1.79 => ( ! [A7: A,B5: A] :
% 3.29/1.79 ( ( P3 @ B5 @ A7 )
% 3.29/1.79 => ( P3 @ A7 @ B5 ) )
% 3.29/1.79 => ( P3 @ A5 @ B3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_40_dual__order_Orefl,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [A5: A] : ( ord_less_eq @ A @ A5 @ A5 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_41_order__trans,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( preorder @ A )
% 3.29/1.79 => ! [X2: A,Y2: A,Z3: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 3.29/1.79 => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_42_order__class_Oorder_Oantisym,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [A5: A,B3: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ B3 @ A5 )
% 3.29/1.79 => ( A5 = B3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_43_ord__le__eq__trans,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( ord @ A )
% 3.29/1.79 => ! [A5: A,B3: A,C: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.79 => ( ( B3 = C )
% 3.29/1.79 => ( ord_less_eq @ A @ A5 @ C ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_44_ord__eq__le__trans,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( ord @ A )
% 3.29/1.79 => ! [A5: A,B3: A,C: A] :
% 3.29/1.79 ( ( A5 = B3 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ B3 @ C )
% 3.29/1.79 => ( ord_less_eq @ A @ A5 @ C ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_45_mem__Collect__eq,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,P3: A > $o] :
% 3.29/1.79 ( ( member @ A @ A5 @ ( collect @ A @ P3 ) )
% 3.29/1.79 = ( P3 @ A5 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_46_Collect__mem__eq,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A] :
% 3.29/1.79 ( ( collect @ A
% 3.29/1.79 @ ^ [X3: A] : ( member @ A @ X3 @ A2 ) )
% 3.29/1.79 = A2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_47_Collect__cong,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 3.29/1.79 ( ! [X: A] :
% 3.29/1.79 ( ( P3 @ X )
% 3.29/1.79 = ( Q2 @ X ) )
% 3.29/1.79 => ( ( collect @ A @ P3 )
% 3.29/1.79 = ( collect @ A @ Q2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_48_ext,axiom,
% 3.29/1.79 ! [B6: $tType,A: $tType,F: A > B6,G: A > B6] :
% 3.29/1.79 ( ! [X: A] :
% 3.29/1.79 ( ( F @ X )
% 3.29/1.79 = ( G @ X ) )
% 3.29/1.79 => ( F = G ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_49_order__class_Oorder_Oeq__iff,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ( ( ^ [Y: A,Z2: A] : ( Y = Z2 ) )
% 3.29/1.79 = ( ^ [A6: A,B4: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A6 @ B4 )
% 3.29/1.79 & ( ord_less_eq @ A @ B4 @ A6 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_50_antisym__conv,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [Y2: A,X2: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.79 = ( X2 = Y2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_51_le__cases3,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( linorder @ A )
% 3.29/1.79 => ! [X2: A,Y2: A,Z3: A] :
% 3.29/1.79 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.79 => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 3.29/1.79 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.29/1.79 => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 3.29/1.79 => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 3.29/1.79 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 3.29/1.79 => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 3.29/1.79 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 3.29/1.79 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 3.29/1.79 => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 3.29/1.79 => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 3.29/1.79 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_52_order_Otrans,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [A5: A,B3: A,C: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ B3 @ C )
% 3.29/1.79 => ( ord_less_eq @ A @ A5 @ C ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_53_le__cases,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( linorder @ A )
% 3.29/1.79 => ! [X2: A,Y2: A] :
% 3.29/1.79 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.79 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_54_eq__refl,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( preorder @ A )
% 3.29/1.79 => ! [X2: A,Y2: A] :
% 3.29/1.79 ( ( X2 = Y2 )
% 3.29/1.79 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_55_linear,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( linorder @ A )
% 3.29/1.79 => ! [X2: A,Y2: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.79 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_56_antisym,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [X2: A,Y2: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.29/1.79 => ( X2 = Y2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_57_eq__iff,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ( ( ^ [Y: A,Z2: A] : ( Y = Z2 ) )
% 3.29/1.79 = ( ^ [X3: A,Y3: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 3.29/1.79 & ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_58_ord__le__eq__subst,axiom,
% 3.29/1.79 ! [A: $tType,B6: $tType] :
% 3.29/1.79 ( ( ( ord @ B6 )
% 3.29/1.79 & ( ord @ A ) )
% 3.29/1.79 => ! [A5: A,B3: A,F: A > B6,C: B6] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.79 => ( ( ( F @ B3 )
% 3.29/1.79 = C )
% 3.29/1.79 => ( ! [X: A,Y4: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ X @ Y4 )
% 3.29/1.79 => ( ord_less_eq @ B6 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.29/1.79 => ( ord_less_eq @ B6 @ ( F @ A5 ) @ C ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_59_ord__eq__le__subst,axiom,
% 3.29/1.79 ! [A: $tType,B6: $tType] :
% 3.29/1.79 ( ( ( ord @ B6 )
% 3.29/1.79 & ( ord @ A ) )
% 3.29/1.79 => ! [A5: A,F: B6 > A,B3: B6,C: B6] :
% 3.29/1.79 ( ( A5
% 3.29/1.79 = ( F @ B3 ) )
% 3.29/1.79 => ( ( ord_less_eq @ B6 @ B3 @ C )
% 3.29/1.79 => ( ! [X: B6,Y4: B6] :
% 3.29/1.79 ( ( ord_less_eq @ B6 @ X @ Y4 )
% 3.29/1.79 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.29/1.79 => ( ord_less_eq @ A @ A5 @ ( F @ C ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_60_order__subst2,axiom,
% 3.29/1.79 ! [A: $tType,C3: $tType] :
% 3.29/1.79 ( ( ( order @ C3 )
% 3.29/1.79 & ( order @ A ) )
% 3.29/1.79 => ! [A5: A,B3: A,F: A > C3,C: C3] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.79 => ( ( ord_less_eq @ C3 @ ( F @ B3 ) @ C )
% 3.29/1.79 => ( ! [X: A,Y4: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ X @ Y4 )
% 3.29/1.79 => ( ord_less_eq @ C3 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.29/1.79 => ( ord_less_eq @ C3 @ ( F @ A5 ) @ C ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_61_order__subst1,axiom,
% 3.29/1.79 ! [A: $tType,B6: $tType] :
% 3.29/1.79 ( ( ( order @ B6 )
% 3.29/1.79 & ( order @ A ) )
% 3.29/1.79 => ! [A5: A,F: B6 > A,B3: B6,C: B6] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ ( F @ B3 ) )
% 3.29/1.79 => ( ( ord_less_eq @ B6 @ B3 @ C )
% 3.29/1.79 => ( ! [X: B6,Y4: B6] :
% 3.29/1.79 ( ( ord_less_eq @ B6 @ X @ Y4 )
% 3.29/1.79 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.29/1.79 => ( ord_less_eq @ A @ A5 @ ( F @ C ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_62_le__fun__def,axiom,
% 3.29/1.79 ! [B6: $tType,A: $tType] :
% 3.29/1.79 ( ( ord @ B6 )
% 3.29/1.79 => ( ( ord_less_eq @ ( A > B6 ) )
% 3.29/1.79 = ( ^ [F2: A > B6,G2: A > B6] :
% 3.29/1.79 ! [X3: A] : ( ord_less_eq @ B6 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_63_le__funI,axiom,
% 3.29/1.79 ! [B6: $tType,A: $tType] :
% 3.29/1.79 ( ( ord @ B6 )
% 3.29/1.79 => ! [F: A > B6,G: A > B6] :
% 3.29/1.79 ( ! [X: A] : ( ord_less_eq @ B6 @ ( F @ X ) @ ( G @ X ) )
% 3.29/1.79 => ( ord_less_eq @ ( A > B6 ) @ F @ G ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_64_le__funE,axiom,
% 3.29/1.79 ! [B6: $tType,A: $tType] :
% 3.29/1.79 ( ( ord @ B6 )
% 3.29/1.79 => ! [F: A > B6,G: A > B6,X2: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( A > B6 ) @ F @ G )
% 3.29/1.79 => ( ord_less_eq @ B6 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_65_le__funD,axiom,
% 3.29/1.79 ! [B6: $tType,A: $tType] :
% 3.29/1.79 ( ( ord @ B6 )
% 3.29/1.79 => ! [F: A > B6,G: A > B6,X2: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( A > B6 ) @ F @ G )
% 3.29/1.79 => ( ord_less_eq @ B6 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_66_Collect__mono__iff,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) )
% 3.29/1.79 = ( ! [X3: A] :
% 3.29/1.79 ( ( P3 @ X3 )
% 3.29/1.79 => ( Q2 @ X3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_67_set__eq__subset,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( ^ [Y: set @ A,Z2: set @ A] : ( Y = Z2 ) )
% 3.29/1.79 = ( ^ [A4: set @ A,B2: set @ A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 3.29/1.79 & ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_68_subset__trans,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.29/1.79 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 3.29/1.79 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_69_Collect__mono,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 3.29/1.79 ( ! [X: A] :
% 3.29/1.79 ( ( P3 @ X )
% 3.29/1.79 => ( Q2 @ X ) )
% 3.29/1.79 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_70_subset__refl,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_71_subset__iff,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) )
% 3.29/1.79 = ( ^ [A4: set @ A,B2: set @ A] :
% 3.29/1.79 ! [T: A] :
% 3.29/1.79 ( ( member @ A @ T @ A4 )
% 3.29/1.79 => ( member @ A @ T @ B2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_72_equalityD2,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ( A2 = B )
% 3.29/1.79 => ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_73_equalityD1,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ( A2 = B )
% 3.29/1.79 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_74_subset__eq,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) )
% 3.29/1.79 = ( ^ [A4: set @ A,B2: set @ A] :
% 3.29/1.79 ! [X3: A] :
% 3.29/1.79 ( ( member @ A @ X3 @ A4 )
% 3.29/1.79 => ( member @ A @ X3 @ B2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_75_equalityE,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ( A2 = B )
% 3.29/1.79 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.29/1.79 => ~ ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_76_subsetD,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A,C: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.29/1.79 => ( ( member @ A @ C @ A2 )
% 3.29/1.79 => ( member @ A @ C @ B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_77_in__mono,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A,X2: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.29/1.79 => ( ( member @ A @ X2 @ A2 )
% 3.29/1.79 => ( member @ A @ X2 @ B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_78_Collect__subset,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,P3: A > $o] :
% 3.29/1.79 ( ord_less_eq @ ( set @ A )
% 3.29/1.79 @ ( collect @ A
% 3.29/1.79 @ ^ [X3: A] :
% 3.29/1.79 ( ( member @ A @ X3 @ A2 )
% 3.29/1.79 & ( P3 @ X3 ) ) )
% 3.29/1.79 @ A2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_79_flpSystem_OInactiveProcessSilentDecisionValuesDecrease,axiom,
% 3.29/1.79 ! [P: $tType,V: $tType,S: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,P2: P,Q: P,Trans: P > S > ( messageValue @ V ) > S,C: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,C2: configuration_ext @ P @ V @ S @ product_unit,Start: P > S] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ( P2 != Q )
% 3.29/1.79 => ( ( steps @ P @ S @ V @ Trans @ Sends @ C @ Msg @ C2 )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 3.29/1.79 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 3.29/1.79 => ( ord_less_eq @ ( set @ $o )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C2 ) )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_80_flpSystem_OActiveProcessSilentDecisionValuesIncrease,axiom,
% 3.29/1.79 ! [P: $tType,V: $tType,S: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,P2: P,Q: P,Trans: P > S > ( messageValue @ V ) > S,C: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,C2: configuration_ext @ P @ V @ S @ product_unit,Start: P > S] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ( P2 = Q )
% 3.29/1.79 => ( ( steps @ P @ S @ V @ Trans @ Sends @ C @ Msg @ C2 )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 3.29/1.79 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 3.29/1.79 => ( ord_less_eq @ ( set @ $o )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C ) )
% 3.29/1.79 @ ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C2 ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_81_NotStepReachable,axiom,
% 3.29/1.79 ~ ( stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ c ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_82_cMsgLastReachable,axiom,
% 3.29/1.79 reachable @ p @ s @ v @ trans @ sends @ cMsg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_83_NoReceivingNoChange,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ~ ( isReceiverOf @ p @ v @ P2 @ M )
% 3.29/1.79 => ( ( states @ p @ v @ s @ product_unit @ Cfg1 @ P2 )
% 3.29/1.79 = ( states @ p @ v @ s @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_84_initReachable__def,axiom,
% 3.29/1.79 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ Cfg )
% 3.29/1.79 = ( ? [Cfg0: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( initial @ p @ s @ v @ start @ Cfg0 )
% 3.29/1.79 & ( reachable @ p @ s @ v @ trans @ sends @ Cfg0 @ Cfg ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_85_ReachableStepFirst,axiom,
% 3.29/1.79 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,Cfg4: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg @ Cfg4 )
% 3.29/1.79 => ( ( Cfg = Cfg4 )
% 3.29/1.79 | ? [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Msg3: message @ p @ v,P4: p] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg @ Msg3 @ Cfg12 )
% 3.29/1.79 & ( enabled @ p @ v @ s @ Cfg @ Msg3 )
% 3.29/1.79 & ( isReceiverOf @ p @ v @ P4 @ Msg3 )
% 3.29/1.79 & ( reachable @ p @ s @ v @ trans @ sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_86_NotInQFrozenQReachability,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( ~ ( member @ p @ P2 @ Q2 )
% 3.29/1.79 => ( ( states @ p @ v @ s @ product_unit @ Cfg1 @ P2 )
% 3.29/1.79 = ( states @ p @ v @ s @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_87_C_H_I2_J,axiom,
% 3.29/1.79 ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ c ) )
% 3.29/1.79 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_88_NoActivityNoMessageLoss,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p,M2: message @ p @ v] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( ~ ( member @ p @ P2 @ Q2 )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ P2 @ M2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_89_ReachableTrans,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Cfg2: configuration_ext @ p @ v @ s @ product_unit,Cfg32: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 )
% 3.29/1.79 => ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg2 @ Cfg32 )
% 3.29/1.79 => ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_90_init,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit] : ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg1 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_91_bot__apply,axiom,
% 3.29/1.79 ! [C3: $tType,D: $tType] :
% 3.29/1.79 ( ( bot @ C3 )
% 3.29/1.79 => ( ( bot_bot @ ( D > C3 ) )
% 3.29/1.79 = ( ^ [X3: D] : ( bot_bot @ C3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_92_empty__iff,axiom,
% 3.29/1.79 ! [A: $tType,C: A] :
% 3.29/1.79 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_93_all__not__in__conv,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A] :
% 3.29/1.79 ( ( ! [X3: A] :
% 3.29/1.79 ~ ( member @ A @ X3 @ A2 ) )
% 3.29/1.79 = ( A2
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_94_Collect__empty__eq,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o] :
% 3.29/1.79 ( ( ( collect @ A @ P3 )
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.29/1.79 = ( ! [X3: A] :
% 3.29/1.79 ~ ( P3 @ X3 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_95_empty__Collect__eq,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o] :
% 3.29/1.79 ( ( ( bot_bot @ ( set @ A ) )
% 3.29/1.79 = ( collect @ A @ P3 ) )
% 3.29/1.79 = ( ! [X3: A] :
% 3.29/1.79 ~ ( P3 @ X3 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_96_insertCI,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,B: set @ A,B3: A] :
% 3.29/1.79 ( ( ~ ( member @ A @ A5 @ B )
% 3.29/1.79 => ( A5 = B3 ) )
% 3.29/1.79 => ( member @ A @ A5 @ ( insert @ A @ B3 @ B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_97_insert__iff,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,B3: A,A2: set @ A] :
% 3.29/1.79 ( ( member @ A @ A5 @ ( insert @ A @ B3 @ A2 ) )
% 3.29/1.79 = ( ( A5 = B3 )
% 3.29/1.79 | ( member @ A @ A5 @ A2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_98_insert__absorb2,axiom,
% 3.29/1.79 ! [A: $tType,X2: A,A2: set @ A] :
% 3.29/1.79 ( ( insert @ A @ X2 @ ( insert @ A @ X2 @ A2 ) )
% 3.29/1.79 = ( insert @ A @ X2 @ A2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_99_C_H_I1_J,axiom,
% 3.29/1.79 reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ c ).
% 3.29/1.79
% 3.29/1.79 thf(fact_100_predicate1I,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 3.29/1.79 ( ! [X: A] :
% 3.29/1.79 ( ( P3 @ X )
% 3.29/1.79 => ( Q2 @ X ) )
% 3.29/1.79 => ( ord_less_eq @ ( A > $o ) @ P3 @ Q2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_101_reachable_Ocases,axiom,
% 3.29/1.79 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ A1 @ A22 )
% 3.29/1.79 => ( ( A22 != A1 )
% 3.29/1.79 => ~ ! [Cfg23: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ A1 @ Cfg23 )
% 3.29/1.79 => ! [Msg3: message @ p @ v] :
% 3.29/1.79 ~ ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ A22 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_102_reachable_Oinducts,axiom,
% 3.29/1.79 ! [X1: configuration_ext @ p @ v @ s @ product_unit,X22: configuration_ext @ p @ v @ s @ product_unit,P3: ( configuration_ext @ p @ v @ s @ product_unit ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ X1 @ X22 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit] : ( P3 @ Cfg12 @ Cfg12 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ p @ v @ s @ product_unit,Cfg23: configuration_ext @ p @ v @ s @ product_unit,Msg3: message @ p @ v,Cfg33: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg12 @ Cfg23 )
% 3.29/1.79 => ( ( P3 @ Cfg12 @ Cfg23 )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 3.29/1.79 => ( P3 @ Cfg12 @ Cfg33 ) ) ) )
% 3.29/1.79 => ( P3 @ X1 @ X22 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_103_reachable_Osimps,axiom,
% 3.29/1.79 ! [A1: configuration_ext @ p @ v @ s @ product_unit,A22: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ A1 @ A22 )
% 3.29/1.79 = ( ? [Cfg13: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( A1 = Cfg13 )
% 3.29/1.79 & ( A22 = Cfg13 ) )
% 3.29/1.79 | ? [Cfg13: configuration_ext @ p @ v @ s @ product_unit,Cfg22: configuration_ext @ p @ v @ s @ product_unit,Msg2: message @ p @ v,Cfg34: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( A1 = Cfg13 )
% 3.29/1.79 & ( A22 = Cfg34 )
% 3.29/1.79 & ( reachable @ p @ s @ v @ trans @ sends @ Cfg13 @ Cfg22 )
% 3.29/1.79 & ( steps @ p @ s @ v @ trans @ sends @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_104_reachable_Ostep,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Cfg2: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,Cfg32: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 3.29/1.79 => ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_105_QReachImplReach,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( qReachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_106_isPrefixListExec,axiom,
% 3.29/1.79 prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ execMsga ).
% 3.29/1.79
% 3.29/1.79 thf(fact_107_OtherMessagesOnlyGrowing,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,M2: message @ p @ v] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ( M != M2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ M2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_108_stepReachable__def,axiom,
% 3.29/1.79 ! [C1: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v,C22: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( stepReachable @ p @ s @ v @ trans @ sends @ C1 @ Msg @ C22 )
% 3.29/1.79 = ( ? [C5: configuration_ext @ p @ v @ s @ product_unit,C6: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ C1 @ C5 )
% 3.29/1.79 & ( steps @ p @ s @ v @ trans @ sends @ C5 @ Msg @ C6 )
% 3.29/1.79 & ( reachable @ p @ s @ v @ trans @ sends @ C6 @ C22 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_109_StepReachable,axiom,
% 3.29/1.79 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,Cfg4: configuration_ext @ p @ v @ s @ product_unit,Msg: message @ p @ v] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg @ Cfg4 )
% 3.29/1.79 => ( ( enabled @ p @ v @ s @ Cfg @ Msg )
% 3.29/1.79 => ( ~ ( enabled @ p @ v @ s @ Cfg4 @ Msg )
% 3.29/1.79 => ( stepReachable @ p @ s @ v @ trans @ sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_110_NoMessageLossStep,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit,P2: p,M2: message @ p @ v] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ P2 @ M )
% 3.29/1.79 => ( ~ ( isReceiverOf @ p @ v @ P2 @ M2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_111_subset__empty,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.29/1.79 = ( A2
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_112_empty__subsetI,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_113_singletonI,axiom,
% 3.29/1.79 ! [A: $tType,A5: A] : ( member @ A @ A5 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_114_insert__subset,axiom,
% 3.29/1.79 ! [A: $tType,X2: A,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X2 @ A2 ) @ B )
% 3.29/1.79 = ( ( member @ A @ X2 @ B )
% 3.29/1.79 & ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_115_ExecMsg_I2_J,axiom,
% 3.29/1.79 prefixList @ ( message @ p @ v ) @ trace2 @ traceMsga ).
% 3.29/1.79
% 3.29/1.79 thf(fact_116_lastExecExec_HReachable,axiom,
% 3.29/1.79 reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_117_singleton__conv,axiom,
% 3.29/1.79 ! [A: $tType,A5: A] :
% 3.29/1.79 ( ( collect @ A
% 3.29/1.79 @ ^ [X3: A] : ( X3 = A5 ) )
% 3.29/1.79 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_118_singleton__conv2,axiom,
% 3.29/1.79 ! [A: $tType,A5: A] :
% 3.29/1.79 ( ( collect @ A
% 3.29/1.79 @ ( ^ [Y: A,Z2: A] : ( Y = Z2 )
% 3.29/1.79 @ A5 ) )
% 3.29/1.79 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_119_ExecIsExecution,axiom,
% 3.29/1.79 execution @ p @ s @ v @ trans @ sends @ start @ exec @ trace ).
% 3.29/1.79
% 3.29/1.79 thf(fact_120_vUniform__def,axiom,
% 3.29/1.79 ! [V3: $o,C: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( vUniform @ p @ s @ v @ trans @ sends @ start @ V3 @ C )
% 3.29/1.79 = ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 & ! [P5: p] :
% 3.29/1.79 ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P5 @ C ) )
% 3.29/1.79 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_121_singleton__insert__inj__eq_H,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,A2: set @ A,B3: A] :
% 3.29/1.79 ( ( ( insert @ A @ A5 @ A2 )
% 3.29/1.79 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.29/1.79 = ( ( A5 = B3 )
% 3.29/1.79 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_122_singleton__insert__inj__eq,axiom,
% 3.29/1.79 ! [A: $tType,B3: A,A5: A,A2: set @ A] :
% 3.29/1.79 ( ( ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) )
% 3.29/1.79 = ( insert @ A @ A5 @ A2 ) )
% 3.29/1.79 = ( ( A5 = B3 )
% 3.29/1.79 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_123_ExecMsg_I4_J,axiom,
% 3.29/1.79 ( ( last @ ( message @ p @ v ) @ traceMsga )
% 3.29/1.79 = msg ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_124_isStepReachable,axiom,
% 3.29/1.79 stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_125_SilentDecisionValueNotInverting,axiom,
% 3.29/1.79 ! [Q: p,C: configuration_ext @ p @ v @ s @ product_unit,V3: $o,Msg: message @ p @ v,C2: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 3.29/1.79 ( ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C ) )
% 3.29/1.79 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) )
% 3.29/1.79 => ( ( steps @ p @ s @ v @ trans @ sends @ C @ Msg @ C2 )
% 3.29/1.79 => ( ( isReceiverOf @ p @ v @ P2 @ Msg )
% 3.29/1.79 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 => ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ Q @ C2 ) )
% 3.29/1.79 != ( insert @ $o @ ~ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_126__092_060open_062_092_060And_062p_O_A_092_060exists_062c_H_O_Areachable_A_Ilast_Aexec_J_Ac_H_A_092_060and_062_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060close_062,axiom,
% 3.29/1.79 ! [P2: p] :
% 3.29/1.79 ? [C7: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ C7 )
% 3.29/1.79 & ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P2 @ C7 ) )
% 3.29/1.79 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_127__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_H_O_A_092_060lbrakk_062reachable_A_Ilast_Aexec_J_Ac_H_059_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.29/1.79 ~ ! [C7: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ C7 )
% 3.29/1.79 => ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ C7 ) )
% 3.29/1.79 != ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_128_Agree,axiom,
% 3.29/1.79 ! [Cfg: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ Cfg )
% 3.29/1.79 => ( agreement @ p @ v @ s @ Cfg ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_129_emptyE,axiom,
% 3.29/1.79 ! [A: $tType,A5: A] :
% 3.29/1.79 ~ ( member @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_130_insertE,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,B3: A,A2: set @ A] :
% 3.29/1.79 ( ( member @ A @ A5 @ ( insert @ A @ B3 @ A2 ) )
% 3.29/1.79 => ( ( A5 != B3 )
% 3.29/1.79 => ( member @ A @ A5 @ A2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_131_equals0D,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,A5: A] :
% 3.29/1.79 ( ( A2
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.29/1.79 => ~ ( member @ A @ A5 @ A2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_132_equals0I,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A] :
% 3.29/1.79 ( ! [Y4: A] :
% 3.29/1.79 ~ ( member @ A @ Y4 @ A2 )
% 3.29/1.79 => ( A2
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_133_insertI1,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,B: set @ A] : ( member @ A @ A5 @ ( insert @ A @ A5 @ B ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_134_insertI2,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,B: set @ A,B3: A] :
% 3.29/1.79 ( ( member @ A @ A5 @ B )
% 3.29/1.79 => ( member @ A @ A5 @ ( insert @ A @ B3 @ B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_135_ex__in__conv,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A] :
% 3.29/1.79 ( ( ? [X3: A] : ( member @ A @ X3 @ A2 ) )
% 3.29/1.79 = ( A2
% 3.29/1.79 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_136_Set_Oset__insert,axiom,
% 3.29/1.79 ! [A: $tType,X2: A,A2: set @ A] :
% 3.29/1.79 ( ( member @ A @ X2 @ A2 )
% 3.29/1.79 => ~ ! [B7: set @ A] :
% 3.29/1.79 ( ( A2
% 3.29/1.79 = ( insert @ A @ X2 @ B7 ) )
% 3.29/1.79 => ( member @ A @ X2 @ B7 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_137_singletonD,axiom,
% 3.29/1.79 ! [A: $tType,B3: A,A5: A] :
% 3.29/1.79 ( ( member @ A @ B3 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.29/1.79 => ( B3 = A5 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_138_insert__ident,axiom,
% 3.29/1.79 ! [A: $tType,X2: A,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ~ ( member @ A @ X2 @ A2 )
% 3.29/1.79 => ( ~ ( member @ A @ X2 @ B )
% 3.29/1.79 => ( ( ( insert @ A @ X2 @ A2 )
% 3.29/1.79 = ( insert @ A @ X2 @ B ) )
% 3.29/1.79 = ( A2 = B ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_139_insert__absorb,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,A2: set @ A] :
% 3.29/1.79 ( ( member @ A @ A5 @ A2 )
% 3.29/1.79 => ( ( insert @ A @ A5 @ A2 )
% 3.29/1.79 = A2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_140_insert__eq__iff,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,A2: set @ A,B3: A,B: set @ A] :
% 3.29/1.79 ( ~ ( member @ A @ A5 @ A2 )
% 3.29/1.79 => ( ~ ( member @ A @ B3 @ B )
% 3.29/1.79 => ( ( ( insert @ A @ A5 @ A2 )
% 3.29/1.79 = ( insert @ A @ B3 @ B ) )
% 3.29/1.79 = ( ( ( A5 = B3 )
% 3.29/1.79 => ( A2 = B ) )
% 3.29/1.79 & ( ( A5 != B3 )
% 3.29/1.79 => ? [C8: set @ A] :
% 3.29/1.79 ( ( A2
% 3.29/1.79 = ( insert @ A @ B3 @ C8 ) )
% 3.29/1.79 & ~ ( member @ A @ B3 @ C8 )
% 3.29/1.79 & ( B
% 3.29/1.79 = ( insert @ A @ A5 @ C8 ) )
% 3.29/1.79 & ~ ( member @ A @ A5 @ C8 ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_141_singleton__iff,axiom,
% 3.29/1.79 ! [A: $tType,B3: A,A5: A] :
% 3.29/1.79 ( ( member @ A @ B3 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.29/1.79 = ( B3 = A5 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_142_insert__commute,axiom,
% 3.29/1.79 ! [A: $tType,X2: A,Y2: A,A2: set @ A] :
% 3.29/1.79 ( ( insert @ A @ X2 @ ( insert @ A @ Y2 @ A2 ) )
% 3.29/1.79 = ( insert @ A @ Y2 @ ( insert @ A @ X2 @ A2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_143_Collect__conv__if,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,A5: A] :
% 3.29/1.79 ( ( ( P3 @ A5 )
% 3.29/1.79 => ( ( collect @ A
% 3.29/1.79 @ ^ [X3: A] :
% 3.29/1.79 ( ( X3 = A5 )
% 3.29/1.79 & ( P3 @ X3 ) ) )
% 3.29/1.79 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.29/1.79 & ( ~ ( P3 @ A5 )
% 3.29/1.79 => ( ( collect @ A
% 3.29/1.79 @ ^ [X3: A] :
% 3.29/1.79 ( ( X3 = A5 )
% 3.29/1.79 & ( P3 @ X3 ) ) )
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_144_Collect__conv__if2,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,A5: A] :
% 3.29/1.79 ( ( ( P3 @ A5 )
% 3.29/1.79 => ( ( collect @ A
% 3.29/1.79 @ ^ [X3: A] :
% 3.29/1.79 ( ( A5 = X3 )
% 3.29/1.79 & ( P3 @ X3 ) ) )
% 3.29/1.79 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.29/1.79 & ( ~ ( P3 @ A5 )
% 3.29/1.79 => ( ( collect @ A
% 3.29/1.79 @ ^ [X3: A] :
% 3.29/1.79 ( ( A5 = X3 )
% 3.29/1.79 & ( P3 @ X3 ) ) )
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_145_doubleton__eq__iff,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,B3: A,C: A,D2: A] :
% 3.29/1.79 ( ( ( insert @ A @ A5 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.29/1.79 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.29/1.79 = ( ( ( A5 = C )
% 3.29/1.79 & ( B3 = D2 ) )
% 3.29/1.79 | ( ( A5 = D2 )
% 3.29/1.79 & ( B3 = C ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_146_insert__not__empty,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,A2: set @ A] :
% 3.29/1.79 ( ( insert @ A @ A5 @ A2 )
% 3.29/1.79 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_147_singleton__inject,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,B3: A] :
% 3.29/1.79 ( ( ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 3.29/1.79 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.29/1.79 => ( A5 = B3 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_148_bot__fun__def,axiom,
% 3.29/1.79 ! [B6: $tType,A: $tType] :
% 3.29/1.79 ( ( bot @ B6 )
% 3.29/1.79 => ( ( bot_bot @ ( A > B6 ) )
% 3.29/1.79 = ( ^ [X3: A] : ( bot_bot @ B6 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_149_predicate1D,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,Q2: A > $o,X2: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q2 )
% 3.29/1.79 => ( ( P3 @ X2 )
% 3.29/1.79 => ( Q2 @ X2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_150_subset__singletonD,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,X2: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.29/1.79 => ( ( A2
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.29/1.79 | ( A2
% 3.29/1.79 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_151_mk__disjoint__insert,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,A2: set @ A] :
% 3.29/1.79 ( ( member @ A @ A5 @ A2 )
% 3.29/1.79 => ? [B7: set @ A] :
% 3.29/1.79 ( ( A2
% 3.29/1.79 = ( insert @ A @ A5 @ B7 ) )
% 3.29/1.79 & ~ ( member @ A @ A5 @ B7 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_152_subset__singleton__iff,axiom,
% 3.29/1.79 ! [A: $tType,X5: set @ A,A5: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ X5 @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.29/1.79 = ( ( X5
% 3.29/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.29/1.79 | ( X5
% 3.29/1.79 = ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_153_rev__predicate1D,axiom,
% 3.29/1.79 ! [A: $tType,P3: A > $o,X2: A,Q2: A > $o] :
% 3.29/1.79 ( ( P3 @ X2 )
% 3.29/1.79 => ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q2 )
% 3.29/1.79 => ( Q2 @ X2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_154_insert__Collect,axiom,
% 3.29/1.79 ! [A: $tType,A5: A,P3: A > $o] :
% 3.29/1.79 ( ( insert @ A @ A5 @ ( collect @ A @ P3 ) )
% 3.29/1.79 = ( collect @ A
% 3.29/1.79 @ ^ [U: A] :
% 3.29/1.79 ( ( U != A5 )
% 3.29/1.79 => ( P3 @ U ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_155_insert__compr,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( insert @ A )
% 3.29/1.79 = ( ^ [A6: A,B2: set @ A] :
% 3.29/1.79 ( collect @ A
% 3.29/1.79 @ ^ [X3: A] :
% 3.29/1.79 ( ( X3 = A6 )
% 3.29/1.79 | ( member @ A @ X3 @ B2 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_156_empty__def,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( bot_bot @ ( set @ A ) )
% 3.29/1.79 = ( collect @ A
% 3.29/1.79 @ ^ [X3: A] : $false ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_157_bot_Oextremum,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order_bot @ A )
% 3.29/1.79 => ! [A5: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A5 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_158_bot_Oextremum__unique,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order_bot @ A )
% 3.29/1.79 => ! [A5: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ ( bot_bot @ A ) )
% 3.29/1.79 = ( A5
% 3.29/1.79 = ( bot_bot @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_159_bot_Oextremum__uniqueI,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order_bot @ A )
% 3.29/1.79 => ! [A5: A] :
% 3.29/1.79 ( ( ord_less_eq @ A @ A5 @ ( bot_bot @ A ) )
% 3.29/1.79 => ( A5
% 3.29/1.79 = ( bot_bot @ A ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_160_insert__mono,axiom,
% 3.29/1.79 ! [A: $tType,C4: set @ A,D3: set @ A,A5: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 3.29/1.79 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A5 @ C4 ) @ ( insert @ A @ A5 @ D3 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_161_subset__insert,axiom,
% 3.29/1.79 ! [A: $tType,X2: A,A2: set @ A,B: set @ A] :
% 3.29/1.79 ( ~ ( member @ A @ X2 @ A2 )
% 3.29/1.79 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X2 @ B ) )
% 3.29/1.79 = ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_162_subset__insertI,axiom,
% 3.29/1.79 ! [A: $tType,B: set @ A,A5: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A5 @ B ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_163_subset__insertI2,axiom,
% 3.29/1.79 ! [A: $tType,A2: set @ A,B: set @ A,B3: A] :
% 3.29/1.79 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.29/1.79 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ B ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_164_flpSystem_OvUniform__def,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,V3: $o,C: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ V3 @ C )
% 3.29/1.79 = ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 3.29/1.79 & ! [P5: P] :
% 3.29/1.79 ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ P5 @ C ) )
% 3.29/1.79 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_165_flpSystem_OSilentDecisionValueNotInverting,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,Q: P,C: configuration_ext @ P @ V @ S @ product_unit,V3: $o,Msg: message @ P @ V,C2: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C ) )
% 3.29/1.79 = ( insert @ $o @ V3 @ ( bot_bot @ ( set @ $o ) ) ) )
% 3.29/1.79 => ( ( steps @ P @ S @ V @ Trans @ Sends @ C @ Msg @ C2 )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 3.29/1.79 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 3.29/1.79 => ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ Q @ C2 ) )
% 3.29/1.79 != ( insert @ $o @ ~ V3 @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_166_flpSystem_OpSilDecVal_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( pSilDecVal @ P @ S @ V )
% 3.29/1.79 = ( pSilDecVal @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_167_flpSystem_OvUniform_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( vUniform @ P @ S @ V )
% 3.29/1.79 = ( vUniform @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_168_flpSystem_OagreementInit_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( agreementInit @ P @ S @ V )
% 3.29/1.79 = ( agreementInit @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_169_expandExecutionReachable,axiom,
% 3.29/1.79 ! [CfgLast: configuration_ext @ p @ v @ s @ product_unit,Cfg: configuration_ext @ p @ v @ s @ product_unit,Exec: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace: list @ ( message @ p @ v )] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ CfgLast @ Cfg )
% 3.29/1.79 => ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec @ Trace )
% 3.29/1.79 => ( ( CfgLast
% 3.29/1.79 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec ) )
% 3.29/1.79 => ? [Exec2: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace2: list @ ( message @ p @ v )] :
% 3.29/1.79 ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 3.29/1.79 & ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec @ Exec2 )
% 3.29/1.79 & ( prefixList @ ( message @ p @ v ) @ Trace @ Trace2 ) )
% 3.29/1.79 | ( ( Exec = Exec2 )
% 3.29/1.79 & ( Trace = Trace2 ) ) )
% 3.29/1.79 & ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec2 )
% 3.29/1.79 = Cfg ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_170_NewExec_I2_J,axiom,
% 3.29/1.79 ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ exec2 )
% 3.29/1.79 & ( prefixList @ ( message @ p @ v ) @ trace @ trace2 ) )
% 3.29/1.79 | ( ( exec = exec2 )
% 3.29/1.79 & ( trace = trace2 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_171_NoOutMessageLoss,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,Cfg2: configuration_ext @ p @ v @ s @ product_unit,V3: $o] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ Cfg1 @ Cfg2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ ( outMsg @ p @ v @ V3 ) ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg2 @ ( outMsg @ p @ v @ V3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_172_asynchronousSystem_OReachableStepFirst,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg: configuration_ext @ P @ V @ S @ product_unit,Cfg4: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg @ Cfg4 )
% 3.29/1.79 => ( ( Cfg = Cfg4 )
% 3.29/1.79 | ? [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Msg3: message @ P @ V,P4: P] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg @ Msg3 @ Cfg12 )
% 3.29/1.79 & ( enabled @ P @ V @ S @ Cfg @ Msg3 )
% 3.29/1.79 & ( isReceiverOf @ P @ V @ P4 @ Msg3 )
% 3.29/1.79 & ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_173_asynchronousSystem_ONoActivityNoMessageLoss,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P,M2: message @ P @ V] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( ~ ( member @ P @ P2 @ Q2 )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ P2 @ M2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_174_asynchronousSystem_ONoMessageLossStep,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P,M2: message @ P @ V] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ P2 @ M )
% 3.29/1.79 => ( ~ ( isReceiverOf @ P @ V @ P2 @ M2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_175_message_Oinject_I2_J,axiom,
% 3.29/1.79 ! [V: $tType,P: $tType,X22: $o,Y22: $o] :
% 3.29/1.79 ( ( ( outMsg @ P @ V @ X22 )
% 3.29/1.79 = ( outMsg @ P @ V @ Y22 ) )
% 3.29/1.79 = ( X22 = Y22 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_176_StepOutMsg,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,V3: $o,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ~ ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ ( outMsg @ p @ v @ V3 ) @ Cfg2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_177_isPrefixListTrace,axiom,
% 3.29/1.79 prefixList @ ( message @ p @ v ) @ trace @ traceMsga ).
% 3.29/1.79
% 3.29/1.79 thf(fact_178_expandExecutionStep,axiom,
% 3.29/1.79 ! [Exec3: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Msg: message @ p @ v,CMsg2: configuration_ext @ p @ v @ s @ product_unit,Trace3: list @ ( message @ p @ v )] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec3 ) @ Msg @ CMsg2 )
% 3.29/1.79 => ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec3 @ Trace3 )
% 3.29/1.79 => ? [Exec4: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace4: list @ ( message @ p @ v )] :
% 3.29/1.79 ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec4 @ Trace4 )
% 3.29/1.79 & ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec3 @ Exec4 )
% 3.29/1.79 & ( prefixList @ ( message @ p @ v ) @ Trace3 @ Trace4 )
% 3.29/1.79 & ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec4 )
% 3.29/1.79 = CMsg2 )
% 3.29/1.79 & ( ( last @ ( message @ p @ v ) @ Trace4 )
% 3.29/1.79 = Msg ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_179__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062exec_H_Atrace_H_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_Aexec_H_Atrace_H_059_AprefixList_Aexec_Aexec_H_A_092_060and_062_AprefixList_Atrace_Atrace_H_A_092_060or_062_Aexec_A_061_Aexec_H_A_092_060and_062_Atrace_A_061_Atrace_H_059_Alast_Aexec_H_A_061_Ac_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.29/1.79 ~ ! [Exec2: list @ ( configuration_ext @ p @ v @ s @ product_unit ),Trace2: list @ ( message @ p @ v )] :
% 3.29/1.79 ( ( execution @ p @ s @ v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 3.29/1.79 => ( ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ Exec2 )
% 3.29/1.79 & ( prefixList @ ( message @ p @ v ) @ trace @ Trace2 ) )
% 3.29/1.79 | ( ( exec = Exec2 )
% 3.29/1.79 & ( trace = Trace2 ) ) )
% 3.29/1.79 => ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Exec2 )
% 3.29/1.79 != c ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_180__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.29/1.79 ~ ! [ExecMsg: list @ ( configuration_ext @ p @ v @ s @ product_unit ),TraceMsg: list @ ( message @ p @ v )] :
% 3.29/1.79 ( ( execution @ p @ s @ v @ trans @ sends @ start @ ExecMsg @ TraceMsg )
% 3.29/1.79 => ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ ExecMsg )
% 3.29/1.79 => ( ( prefixList @ ( message @ p @ v ) @ trace2 @ TraceMsg )
% 3.29/1.79 => ( ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ExecMsg )
% 3.29/1.79 = cMsg )
% 3.29/1.79 => ( ( last @ ( message @ p @ v ) @ TraceMsg )
% 3.29/1.79 != msg ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_181_bot__set__def,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( bot_bot @ ( set @ A ) )
% 3.29/1.79 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_182_asynchronousSystem_OStepOutMsg,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,V3: $o,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ~ ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ ( outMsg @ P @ V @ V3 ) @ Cfg2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_183_isReceiverOf_Osimps_I3_J,axiom,
% 3.29/1.79 ! [P: $tType,V: $tType,P1: P,V3: $o] :
% 3.29/1.79 ~ ( isReceiverOf @ P @ V @ P1 @ ( outMsg @ P @ V @ V3 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_184_asynchronousSystem_ONoOutMessageLoss,axiom,
% 3.29/1.79 ! [S: $tType,P: $tType,V: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Cfg2: configuration_ext @ P @ V @ S @ product_unit,V3: $o] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ ( outMsg @ P @ V @ V3 ) ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ ( outMsg @ P @ V @ V3 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_185_asynchronousSystem_Osteps_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( steps @ P @ S @ V )
% 3.29/1.79 = ( steps @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_186_asynchronousSystem_OReachableTrans,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Cfg32: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 3.29/1.79 => ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Cfg32 )
% 3.29/1.79 => ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_187_asynchronousSystem_Oreachable_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( reachable @ P @ S @ V )
% 3.29/1.79 = ( reachable @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_188_asynchronousSystem_Oinit,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit] : ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg1 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_189_UniqueReceiverOf,axiom,
% 3.29/1.79 ! [V: $tType,P: $tType,Q: P,Msg: message @ P @ V,P2: P] :
% 3.29/1.79 ( ( isReceiverOf @ P @ V @ Q @ Msg )
% 3.29/1.79 => ( ( P2 != Q )
% 3.29/1.79 => ~ ( isReceiverOf @ P @ V @ P2 @ Msg ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_190_asynchronousSystem_OQReachableTrans,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg32: configuration_ext @ P @ V @ S @ product_unit,Cfg1: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Q2 @ Cfg32 )
% 3.29/1.79 => ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_191_asynchronousSystem_OqReachable_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V )
% 3.29/1.79 = ( qReachable @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_192_asynchronousSystem_OInitQ,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P] : ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_193_asynchronousSystem_OinitReachable_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( initReachable @ P @ S @ V )
% 3.29/1.79 = ( initReachable @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_194_asynchronousSystem_Oinitial_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( initial @ P @ S @ V )
% 3.29/1.79 = ( initial @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_195_asynchronousSystem_OstepReachable_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( stepReachable @ P @ S @ V )
% 3.29/1.79 = ( stepReachable @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_196_asynchronousSystem_Ostep,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,Cfg32: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 3.29/1.79 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 3.29/1.79 => ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_197_asynchronousSystem_Oreachable_Ocases,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A1: configuration_ext @ P @ V @ S @ product_unit,A22: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ A1 @ A22 )
% 3.29/1.79 => ( ( A22 != A1 )
% 3.29/1.79 => ~ ! [Cfg23: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ A1 @ Cfg23 )
% 3.29/1.79 => ! [Msg3: message @ P @ V] :
% 3.29/1.79 ~ ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ A22 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_198_asynchronousSystem_Oreachable_Osimps,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( reachable @ P @ S @ V )
% 3.29/1.79 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A12: configuration_ext @ P @ V @ S @ product_unit,A23: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ? [Cfg13: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( A12 = Cfg13 )
% 3.29/1.79 & ( A23 = Cfg13 ) )
% 3.29/1.79 | ? [Cfg13: configuration_ext @ P @ V @ S @ product_unit,Cfg22: configuration_ext @ P @ V @ S @ product_unit,Msg2: message @ P @ V,Cfg34: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( A12 = Cfg13 )
% 3.29/1.79 & ( A23 = Cfg34 )
% 3.29/1.79 & ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ Cfg13 @ Cfg22 )
% 3.29/1.79 & ( steps @ P @ S @ V @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_199_asynchronousSystem_Oreachable_Oinducts,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,X1: configuration_ext @ P @ V @ S @ product_unit,X22: configuration_ext @ P @ V @ S @ product_unit,P3: ( configuration_ext @ P @ V @ S @ product_unit ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ X1 @ X22 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit] : ( P3 @ Cfg12 @ Cfg12 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Cfg23: configuration_ext @ P @ V @ S @ product_unit,Msg3: message @ P @ V,Cfg33: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg12 @ Cfg23 )
% 3.29/1.79 => ( ( P3 @ Cfg12 @ Cfg23 )
% 3.29/1.79 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 3.29/1.79 => ( P3 @ Cfg12 @ Cfg33 ) ) ) )
% 3.29/1.79 => ( P3 @ X1 @ X22 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_200_asynchronousSystem_ODiamondOne,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg1: configuration_ext @ P @ V @ S @ product_unit,P2: P,Q: P,M2: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg @ M @ Cfg1 )
% 3.29/1.79 => ( ( P2 != Q )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ P2 @ M )
% 3.29/1.79 => ( ~ ( isReceiverOf @ P @ V @ P2 @ M2 )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ Q @ M2 )
% 3.29/1.79 => ( ~ ( isReceiverOf @ P @ V @ Q @ M )
% 3.29/1.79 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg @ M2 @ Cfg2 )
% 3.29/1.79 => ? [Cfg3: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M2 @ Cfg3 )
% 3.29/1.79 & ( steps @ P @ S @ V @ Trans @ Sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_201_asynchronousSystem_OQReachImplReach,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Cfg2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_202_asynchronousSystem_OOnlyOccurenceDisables,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,M2: message @ P @ V] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ( enabled @ P @ V @ S @ Cfg1 @ M2 )
% 3.29/1.79 => ( ~ ( enabled @ P @ V @ S @ Cfg2 @ M2 )
% 3.29/1.79 => ( M = M2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_203_asynchronousSystem_ONotInQFrozenQReachability,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( ~ ( member @ P @ P2 @ Q2 )
% 3.29/1.79 => ( ( states @ P @ V @ S @ product_unit @ Cfg1 @ P2 )
% 3.29/1.79 = ( states @ P @ V @ S @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_204_asynchronousSystem_OInitialIsInitReachable,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Start: P > S,C: configuration_ext @ P @ V @ S @ product_unit,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat] :
% 3.29/1.79 ( ( initial @ P @ S @ V @ Start @ C )
% 3.29/1.79 => ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_205_asynchronousSystem_OOtherMessagesOnlyGrowing,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,M2: message @ P @ V] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ( M != M2 )
% 3.29/1.79 => ( ord_less_eq @ nat @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M2 ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ M2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_206_asynchronousSystem_OStepQ,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P,Cfg2: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V,Cfg32: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 3.29/1.79 => ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 3.29/1.79 => ( ? [X4: P] :
% 3.29/1.79 ( ( member @ P @ X4 @ Q2 )
% 3.29/1.79 & ( isReceiverOf @ P @ V @ X4 @ Msg ) )
% 3.29/1.79 => ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_207_asynchronousSystem_OqReachable_Ocases,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A1: configuration_ext @ P @ V @ S @ product_unit,A22: set @ P,A3: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ A1 @ A22 @ A3 )
% 3.29/1.79 => ( ( A3 != A1 )
% 3.29/1.79 => ~ ! [Cfg23: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ A1 @ A22 @ Cfg23 )
% 3.29/1.79 => ! [Msg3: message @ P @ V] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ A3 )
% 3.29/1.79 => ~ ? [X: P] :
% 3.29/1.79 ( ( member @ P @ X @ A22 )
% 3.29/1.79 & ( isReceiverOf @ P @ V @ X @ Msg3 ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_208_asynchronousSystem_OqReachable_Osimps,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V )
% 3.29/1.79 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,A12: configuration_ext @ P @ V @ S @ product_unit,A23: set @ P,A32: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( A32 = A12 )
% 3.29/1.79 | ? [Cfg22: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans2 @ Sends2 @ A12 @ A23 @ Cfg22 )
% 3.29/1.79 & ? [Msg2: message @ P @ V] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ A32 )
% 3.29/1.79 & ? [X3: P] :
% 3.29/1.79 ( ( member @ P @ X3 @ A23 )
% 3.29/1.79 & ( isReceiverOf @ P @ V @ X3 @ Msg2 ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_209_asynchronousSystem_OqReachable_Oinducts,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,X1: configuration_ext @ P @ V @ S @ product_unit,X22: set @ P,X32: configuration_ext @ P @ V @ S @ product_unit,P3: ( configuration_ext @ P @ V @ S @ product_unit ) > ( set @ P ) > ( configuration_ext @ P @ V @ S @ product_unit ) > $o] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ X1 @ X22 @ X32 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Q3: set @ P] : ( P3 @ Cfg12 @ Q3 @ Cfg12 )
% 3.29/1.79 => ( ! [Cfg12: configuration_ext @ P @ V @ S @ product_unit,Q3: set @ P,Cfg23: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( qReachable @ P @ S @ V @ Trans @ Sends @ Cfg12 @ Q3 @ Cfg23 )
% 3.29/1.79 => ( ( P3 @ Cfg12 @ Q3 @ Cfg23 )
% 3.29/1.79 => ! [Msg3: message @ P @ V,Cfg33: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 3.29/1.79 => ( ? [X: P] :
% 3.29/1.79 ( ( member @ P @ X @ Q3 )
% 3.29/1.79 & ( isReceiverOf @ P @ V @ X @ Msg3 ) )
% 3.29/1.79 => ( P3 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 3.29/1.79 => ( P3 @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_210_asynchronousSystem_ONoReceivingNoChange,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ~ ( isReceiverOf @ P @ V @ P2 @ M )
% 3.29/1.79 => ( ( states @ P @ V @ S @ product_unit @ Cfg1 @ P2 )
% 3.29/1.79 = ( states @ P @ V @ S @ product_unit @ Cfg2 @ P2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_211_asynchronousSystem_OinitReachable__def,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( initReachable @ P @ S @ V )
% 3.29/1.79 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start2: P > S,Cfg5: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ? [Cfg0: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( initial @ P @ S @ V @ Start2 @ Cfg0 )
% 3.29/1.79 & ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ Cfg0 @ Cfg5 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_212_asynchronousSystem_OstepReachable__def,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( stepReachable @ P @ S @ V )
% 3.29/1.79 = ( ^ [Trans2: P > S > ( messageValue @ V ) > S,Sends2: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,C12: configuration_ext @ P @ V @ S @ product_unit,Msg2: message @ P @ V,C23: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ? [C5: configuration_ext @ P @ V @ S @ product_unit,C6: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ C12 @ C5 )
% 3.29/1.79 & ( steps @ P @ S @ V @ Trans2 @ Sends2 @ C5 @ Msg2 @ C6 )
% 3.29/1.79 & ( reachable @ P @ S @ V @ Trans2 @ Sends2 @ C6 @ C23 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_213_asynchronousSystem_OStepReachable,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg: configuration_ext @ P @ V @ S @ product_unit,Cfg4: configuration_ext @ P @ V @ S @ product_unit,Msg: message @ P @ V] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ Cfg @ Cfg4 )
% 3.29/1.79 => ( ( enabled @ P @ V @ S @ Cfg @ Msg )
% 3.29/1.79 => ( ~ ( enabled @ P @ V @ S @ Cfg4 @ Msg )
% 3.29/1.79 => ( stepReachable @ P @ S @ V @ Trans @ Sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_214_asynchronousSystem_OexpandExecutionStep,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Exec3: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Msg: message @ P @ V,CMsg2: configuration_ext @ P @ V @ S @ product_unit,Start: P > S,Trace3: list @ ( message @ P @ V )] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec3 ) @ Msg @ CMsg2 )
% 3.29/1.79 => ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec3 @ Trace3 )
% 3.29/1.79 => ? [Exec4: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace4: list @ ( message @ P @ V )] :
% 3.29/1.79 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec4 @ Trace4 )
% 3.29/1.79 & ( prefixList @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec3 @ Exec4 )
% 3.29/1.79 & ( prefixList @ ( message @ P @ V ) @ Trace3 @ Trace4 )
% 3.29/1.79 & ( ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec4 )
% 3.29/1.79 = CMsg2 )
% 3.29/1.79 & ( ( last @ ( message @ P @ V ) @ Trace4 )
% 3.29/1.79 = Msg ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_215_asynchronousSystem_OexpandExecutionReachable,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,CfgLast: configuration_ext @ P @ V @ S @ product_unit,Cfg: configuration_ext @ P @ V @ S @ product_unit,Start: P > S,Exec: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace: list @ ( message @ P @ V )] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ CfgLast @ Cfg )
% 3.29/1.79 => ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec @ Trace )
% 3.29/1.79 => ( ( CfgLast
% 3.29/1.79 = ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec ) )
% 3.29/1.79 => ? [Exec2: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace2: list @ ( message @ P @ V )] :
% 3.29/1.79 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec2 @ Trace2 )
% 3.29/1.79 & ( ( ( prefixList @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec @ Exec2 )
% 3.29/1.79 & ( prefixList @ ( message @ P @ V ) @ Trace @ Trace2 ) )
% 3.29/1.79 | ( ( Exec = Exec2 )
% 3.29/1.79 & ( Trace = Trace2 ) ) )
% 3.29/1.79 & ( ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec2 )
% 3.29/1.79 = Cfg ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_216_NonUniformCanReachSilentBivalence,axiom,
% 3.29/1.79 ! [C: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 3.29/1.79 ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ C )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ C ) )
% 3.29/1.79 => ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ! [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ Cfg6 )
% 3.29/1.79 => ( agreement @ p @ v @ s @ Cfg6 ) )
% 3.29/1.79 => ? [C7: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ C7 )
% 3.29/1.79 & ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P2 @ C7 ) )
% 3.29/1.79 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_217_PseudoTermination,axiom,
% 3.29/1.79 ! [Cc2: configuration_ext @ p @ v @ s @ product_unit,Q2: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc2 @ Q2 ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_218_DecisionValuesExist,axiom,
% 3.29/1.79 ! [C: configuration_ext @ p @ v @ s @ product_unit,P2: p] :
% 3.29/1.79 ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 => ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ P2 @ C ) )
% 3.29/1.79 != ( bot_bot @ ( set @ $o ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_219_InitialNonUniformCfg,axiom,
% 3.29/1.79 ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ! [I2: configuration_ext @ p @ v @ s @ product_unit,X_1: configuration_ext @ p @ v @ s @ product_unit] : ( validity @ p @ s @ v @ trans @ sends @ start @ I2 @ X_1 )
% 3.29/1.79 => ( ! [I2: configuration_ext @ p @ v @ s @ product_unit,X_1: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ I2 @ X_1 )
% 3.29/1.79 => ? [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( initial @ p @ s @ v @ start @ Cfg6 )
% 3.29/1.79 & ( initReachable @ p @ s @ v @ trans @ sends @ start @ Cfg6 )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ Cfg6 )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ Cfg6 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_220_flpPseudoConsensus_OPseudoTermination,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,Cc2: configuration_ext @ P @ V @ S @ product_unit,Q2: set @ P] :
% 3.29/1.79 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 3.29/1.79 => ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc2 @ Q2 ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_221_flpSystem_OterminationPseudo_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( terminationPseudo @ P @ S @ V )
% 3.29/1.79 = ( terminationPseudo @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_222_flpSystem_ODecisionValuesExist,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,C: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ! [Cc: configuration_ext @ P @ V @ S @ product_unit,X_1: set @ P] : ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 3.29/1.79 => ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ P2 @ C ) )
% 3.29/1.79 != ( bot_bot @ ( set @ $o ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_223_flpSystem_ONonUniformCanReachSilentBivalence,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S,C: configuration_ext @ P @ V @ S @ product_unit,P2: P] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ( ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ C )
% 3.29/1.79 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $false @ C )
% 3.29/1.79 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $true @ C ) )
% 3.29/1.79 => ( ! [Cc: configuration_ext @ P @ V @ S @ product_unit,X_1: set @ P] : ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ! [Cfg6: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ C @ Cfg6 )
% 3.29/1.79 => ( agreement @ P @ V @ S @ Cfg6 ) )
% 3.29/1.79 => ? [C7: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( reachable @ P @ S @ V @ Trans @ Sends @ C @ C7 )
% 3.29/1.79 & ( ( collect @ $o
% 3.29/1.79 @ ^ [V2: $o] : ( pSilDecVal @ P @ S @ V @ Trans @ Sends @ Start @ V2 @ P2 @ C7 ) )
% 3.29/1.79 = ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_224_flpSystem_OInitialNonUniformCfg,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Trans: P > S > ( messageValue @ V ) > S,Start: P > S] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ! [Cc: configuration_ext @ P @ V @ S @ product_unit,X_1: set @ P] : ( terminationPseudo @ P @ S @ V @ Trans @ Sends @ Start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ! [I2: configuration_ext @ P @ V @ S @ product_unit,X_1: configuration_ext @ P @ V @ S @ product_unit] : ( validity @ P @ S @ V @ Trans @ Sends @ Start @ I2 @ X_1 )
% 3.29/1.79 => ( ! [I2: configuration_ext @ P @ V @ S @ product_unit,X_1: configuration_ext @ P @ V @ S @ product_unit] : ( agreementInit @ P @ S @ V @ Trans @ Sends @ Start @ I2 @ X_1 )
% 3.29/1.79 => ? [Cfg6: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( initial @ P @ S @ V @ Start @ Cfg6 )
% 3.29/1.79 & ( initReachable @ P @ S @ V @ Trans @ Sends @ Start @ Cfg6 )
% 3.29/1.79 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $false @ Cfg6 )
% 3.29/1.79 & ~ ( vUniform @ P @ S @ V @ Trans @ Sends @ Start @ $true @ Cfg6 ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_225_execution_OExistImpliesMinEnabled,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,Exec: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace: list @ ( message @ P @ V ),P2: P,Msg: message @ P @ V] :
% 3.29/1.79 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec @ Trace )
% 3.29/1.79 => ( ( isReceiverOf @ P @ V @ P2 @ Msg )
% 3.29/1.79 => ( ( enabled @ P @ V @ S @ ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec ) @ Msg )
% 3.29/1.79 => ? [X_1: message @ P @ V] : ( minimalEnabled @ P @ V @ S @ Exec @ Trace @ X_1 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_226_execution_OminimalEnabled_Ocong,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType] :
% 3.29/1.79 ( ( minimalEnabled @ P @ V @ S )
% 3.29/1.79 = ( minimalEnabled @ P @ V @ S ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_227_flpSystem_Ovalidity_Ocong,axiom,
% 3.29/1.79 ! [V: $tType,S: $tType,P: $tType] :
% 3.29/1.79 ( ( validity @ P @ S @ V )
% 3.29/1.79 = ( validity @ P @ S @ V ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_228_execution_OFirstOccurrenceExists,axiom,
% 3.29/1.79 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,Exec: list @ ( configuration_ext @ P @ V @ S @ product_unit ),Trace: list @ ( message @ P @ V ),Msg: message @ P @ V] :
% 3.29/1.79 ( ( execution @ P @ S @ V @ Trans @ Sends @ Start @ Exec @ Trace )
% 3.29/1.79 => ( ( enabled @ P @ V @ S @ ( last @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Exec ) @ Msg )
% 3.29/1.79 => ( ? [P6: P] : ( isReceiverOf @ P @ V @ P6 @ Msg )
% 3.29/1.79 => ? [X_1: nat] : ( firstOccurrence @ P @ V @ S @ Exec @ Trace @ Msg @ X_1 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_229_NonUniformImpliesNotDecided,axiom,
% 3.29/1.79 ! [C: configuration_ext @ p @ v @ s @ product_unit,V3: $o] :
% 3.29/1.79 ( ! [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ Cfg6 )
% 3.29/1.79 => ( agreement @ p @ v @ s @ Cfg6 ) )
% 3.29/1.79 => ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ C )
% 3.29/1.79 & ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ C ) )
% 3.29/1.79 => ~ ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 & ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V3 ) ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_230_agreement__def,axiom,
% 3.29/1.79 ( ( agreement @ p @ v @ s )
% 3.29/1.79 = ( ^ [C9: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ! [V1: $o] :
% 3.29/1.79 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C9 @ ( outMsg @ p @ v @ V1 ) ) )
% 3.29/1.79 => ! [V22: $o] :
% 3.29/1.79 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C9 @ ( outMsg @ p @ v @ V22 ) ) )
% 3.29/1.79 = ( V22 = V1 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_231_ExistsMsg,axiom,
% 3.29/1.79 ! [Cfg1: configuration_ext @ p @ v @ s @ product_unit,M: message @ p @ v,Cfg2: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( steps @ p @ s @ v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ Cfg1 @ M ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_232_agreementInit__def,axiom,
% 3.29/1.79 ! [I: configuration_ext @ p @ v @ s @ product_unit,C: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( agreementInit @ p @ s @ v @ trans @ sends @ start @ I @ C )
% 3.29/1.79 = ( ( ( initial @ p @ s @ v @ start @ I )
% 3.29/1.79 & ( reachable @ p @ s @ v @ trans @ sends @ I @ C ) )
% 3.29/1.79 => ! [V1: $o] :
% 3.29/1.79 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V1 ) ) )
% 3.29/1.79 => ! [V22: $o] :
% 3.29/1.79 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V22 ) ) )
% 3.29/1.79 = ( V22 = V1 ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_233_DecidedImpliesUniform,axiom,
% 3.29/1.79 ! [C: configuration_ext @ p @ v @ s @ product_unit,V3: $o] :
% 3.29/1.79 ( ! [Cfg6: configuration_ext @ p @ v @ s @ product_unit] :
% 3.29/1.79 ( ( reachable @ p @ s @ v @ trans @ sends @ C @ Cfg6 )
% 3.29/1.79 => ( agreement @ p @ v @ s @ Cfg6 ) )
% 3.29/1.79 => ( ! [Cc: configuration_ext @ p @ v @ s @ product_unit,X_1: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ Cc @ X_1 )
% 3.29/1.79 => ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
% 3.29/1.79 & ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ C @ ( outMsg @ p @ v @ V3 ) ) ) )
% 3.29/1.79 => ( vUniform @ p @ s @ v @ trans @ sends @ start @ V3 @ C ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_234_flpSystem_Oagreement__def,axiom,
% 3.29/1.79 ! [V: $tType,P: $tType,S: $tType,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,C: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( flpSystem @ P @ S @ V @ Sends )
% 3.29/1.79 => ( ( agreement @ P @ V @ S @ C )
% 3.29/1.79 = ( ! [V1: $o] :
% 3.29/1.79 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ C @ ( outMsg @ P @ V @ V1 ) ) )
% 3.29/1.79 => ! [V22: $o] :
% 3.29/1.79 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ C @ ( outMsg @ P @ V @ V22 ) ) )
% 3.29/1.79 = ( V22 = V1 ) ) ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_235_enabled__def,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType] :
% 3.29/1.79 ( ( enabled @ P @ V @ S )
% 3.29/1.79 = ( ^ [Cfg5: configuration_ext @ P @ V @ S @ product_unit,Msg2: message @ P @ V] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg5 @ Msg2 ) ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_236_asynchronousSystem_OExistsMsg,axiom,
% 3.29/1.79 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Cfg1: configuration_ext @ P @ V @ S @ product_unit,M: message @ P @ V,Cfg2: configuration_ext @ P @ V @ S @ product_unit] :
% 3.29/1.79 ( ( steps @ P @ S @ V @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 3.29/1.79 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg1 @ M ) ) ) ).
% 3.29/1.79
% 3.29/1.79 thf(fact_237_order_Onot__eq__order__implies__strict,axiom,
% 3.29/1.79 ! [A: $tType] :
% 3.29/1.79 ( ( order @ A )
% 3.29/1.79 => ! [A5: A,B3: A] :
% 3.29/1.79 ( ( A5 != B3 )
% 3.29/1.79 => ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.79 => ( ord_less @ A @ A5 @ B3 ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_238_dual__order_Ostrict__implies__order,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ! [B3: A,A5: A] :
% 3.29/1.80 ( ( ord_less @ A @ B3 @ A5 )
% 3.29/1.80 => ( ord_less_eq @ A @ B3 @ A5 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_239_dual__order_Ostrict__iff__order,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ( ( ord_less @ A )
% 3.29/1.80 = ( ^ [B4: A,A6: A] :
% 3.29/1.80 ( ( ord_less_eq @ A @ B4 @ A6 )
% 3.29/1.80 & ( A6 != B4 ) ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_240_dual__order_Oorder__iff__strict,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ( ( ord_less_eq @ A )
% 3.29/1.80 = ( ^ [B4: A,A6: A] :
% 3.29/1.80 ( ( ord_less @ A @ B4 @ A6 )
% 3.29/1.80 | ( A6 = B4 ) ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_241_order_Ostrict__implies__order,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ! [A5: A,B3: A] :
% 3.29/1.80 ( ( ord_less @ A @ A5 @ B3 )
% 3.29/1.80 => ( ord_less_eq @ A @ A5 @ B3 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_242_dense__le__bounded,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( dense_linorder @ A )
% 3.29/1.80 => ! [X2: A,Y2: A,Z3: A] :
% 3.29/1.80 ( ( ord_less @ A @ X2 @ Y2 )
% 3.29/1.80 => ( ! [W: A] :
% 3.29/1.80 ( ( ord_less @ A @ X2 @ W )
% 3.29/1.80 => ( ( ord_less @ A @ W @ Y2 )
% 3.29/1.80 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 3.29/1.80 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_243_dense__ge__bounded,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( dense_linorder @ A )
% 3.29/1.80 => ! [Z3: A,X2: A,Y2: A] :
% 3.29/1.80 ( ( ord_less @ A @ Z3 @ X2 )
% 3.29/1.80 => ( ! [W: A] :
% 3.29/1.80 ( ( ord_less @ A @ Z3 @ W )
% 3.29/1.80 => ( ( ord_less @ A @ W @ X2 )
% 3.29/1.80 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 3.29/1.80 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_244_dual__order_Ostrict__trans2,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ! [B3: A,A5: A,C: A] :
% 3.29/1.80 ( ( ord_less @ A @ B3 @ A5 )
% 3.29/1.80 => ( ( ord_less_eq @ A @ C @ B3 )
% 3.29/1.80 => ( ord_less @ A @ C @ A5 ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_245_dual__order_Ostrict__trans1,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ! [B3: A,A5: A,C: A] :
% 3.29/1.80 ( ( ord_less_eq @ A @ B3 @ A5 )
% 3.29/1.80 => ( ( ord_less @ A @ C @ B3 )
% 3.29/1.80 => ( ord_less @ A @ C @ A5 ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_246_order_Ostrict__iff__order,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ( ( ord_less @ A )
% 3.29/1.80 = ( ^ [A6: A,B4: A] :
% 3.29/1.80 ( ( ord_less_eq @ A @ A6 @ B4 )
% 3.29/1.80 & ( A6 != B4 ) ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_247_order_Oorder__iff__strict,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ( ( ord_less_eq @ A )
% 3.29/1.80 = ( ^ [A6: A,B4: A] :
% 3.29/1.80 ( ( ord_less @ A @ A6 @ B4 )
% 3.29/1.80 | ( A6 = B4 ) ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_248_order_Ostrict__trans2,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ! [A5: A,B3: A,C: A] :
% 3.29/1.80 ( ( ord_less @ A @ A5 @ B3 )
% 3.29/1.80 => ( ( ord_less_eq @ A @ B3 @ C )
% 3.29/1.80 => ( ord_less @ A @ A5 @ C ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_249_order_Ostrict__trans1,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ! [A5: A,B3: A,C: A] :
% 3.29/1.80 ( ( ord_less_eq @ A @ A5 @ B3 )
% 3.29/1.80 => ( ( ord_less @ A @ B3 @ C )
% 3.29/1.80 => ( ord_less @ A @ A5 @ C ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_250_not__le__imp__less,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( linorder @ A )
% 3.29/1.80 => ! [Y2: A,X2: A] :
% 3.29/1.80 ( ~ ( ord_less_eq @ A @ Y2 @ X2 )
% 3.29/1.80 => ( ord_less @ A @ X2 @ Y2 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_251_less__le__not__le,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( preorder @ A )
% 3.29/1.80 => ( ( ord_less @ A )
% 3.29/1.80 = ( ^ [X3: A,Y3: A] :
% 3.29/1.80 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 3.29/1.80 & ~ ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_252_le__imp__less__or__eq,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( order @ A )
% 3.29/1.80 => ! [X2: A,Y2: A] :
% 3.29/1.80 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.80 => ( ( ord_less @ A @ X2 @ Y2 )
% 3.29/1.80 | ( X2 = Y2 ) ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_253_le__less__linear,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( linorder @ A )
% 3.29/1.80 => ! [X2: A,Y2: A] :
% 3.29/1.80 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.29/1.80 | ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_254_dense__le,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( dense_linorder @ A )
% 3.29/1.80 => ! [Y2: A,Z3: A] :
% 3.29/1.80 ( ! [X: A] :
% 3.29/1.80 ( ( ord_less @ A @ X @ Y2 )
% 3.29/1.80 => ( ord_less_eq @ A @ X @ Z3 ) )
% 3.29/1.80 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(fact_255_dense__ge,axiom,
% 3.29/1.80 ! [A: $tType] :
% 3.29/1.80 ( ( dense_linorder @ A )
% 3.29/1.80 => ! [Z3: A,Y2: A] :
% 3.29/1.80 ( ! [X: A] :
% 3.29/1.80 ( ( ord_less @ A @ Z3 @ X )
% 3.29/1.80 => ( ord_less_eq @ A @ Y2 @ X ) )
% 3.29/1.80 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 3.29/1.80 ! [A8: $tType,A9: $tType] :
% 3.29/1.80 ( ( order_bot @ A9 )
% 3.29/1.80 => ( order_bot @ ( A8 > A9 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.29/1.80 ! [A8: $tType,A9: $tType] :
% 3.29/1.80 ( ( preorder @ A9 )
% 3.29/1.80 => ( preorder @ ( A8 > A9 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.29/1.80 ! [A8: $tType,A9: $tType] :
% 3.29/1.80 ( ( order @ A9 )
% 3.29/1.80 => ( order @ ( A8 > A9 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_fun___Orderings_Oord,axiom,
% 3.29/1.80 ! [A8: $tType,A9: $tType] :
% 3.29/1.80 ( ( ord @ A9 )
% 3.29/1.80 => ( ord @ ( A8 > A9 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_fun___Orderings_Obot,axiom,
% 3.29/1.80 ! [A8: $tType,A9: $tType] :
% 3.29/1.80 ( ( bot @ A9 )
% 3.29/1.80 => ( bot @ ( A8 > A9 ) ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1,axiom,
% 3.29/1.80 order_bot @ nat ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 3.29/1.80 preorder @ nat ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.29/1.80 linorder @ nat ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Nat_Onat___Orderings_Oorder_3,axiom,
% 3.29/1.80 order @ nat ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Nat_Onat___Orderings_Oord_4,axiom,
% 3.29/1.80 ord @ nat ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 3.29/1.80 bot @ nat ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 3.29/1.80 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 3.29/1.80 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 3.29/1.80 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 3.29/1.80 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 3.29/1.80 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11,axiom,
% 3.29/1.80 order_bot @ $o ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 3.29/1.80 preorder @ $o ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_HOL_Obool___Orderings_Olinorder_13,axiom,
% 3.29/1.80 linorder @ $o ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 3.29/1.80 order @ $o ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 3.29/1.80 ord @ $o ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 3.29/1.80 bot @ $o ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_17,axiom,
% 3.29/1.80 order_bot @ product_unit ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_18,axiom,
% 3.29/1.80 preorder @ product_unit ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_19,axiom,
% 3.29/1.80 linorder @ product_unit ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Product__Type_Ounit___Orderings_Oorder_20,axiom,
% 3.29/1.80 order @ product_unit ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Product__Type_Ounit___Orderings_Oord_21,axiom,
% 3.29/1.80 ord @ product_unit ).
% 3.29/1.80
% 3.29/1.80 thf(tcon_Product__Type_Ounit___Orderings_Obot_22,axiom,
% 3.29/1.80 bot @ product_unit ).
% 3.29/1.80
% 3.29/1.80 thf(conj_0,conjecture,
% 3.29/1.80 ( ord_less_eq @ ( set @ $o )
% 3.29/1.80 @ ( collect @ $o
% 3.29/1.80 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
% 3.29/1.80 @ ( collect @ $o
% 3.29/1.80 @ ^ [V2: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ V2 @ p2 @ cMsg ) ) ) ).
% 3.29/1.80 ------------------------
% 3.37/1.82 % (14608)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/183Mi)
% 3.37/1.82 % (14610)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_14509 for (2999ds/27Mi)
% 3.37/1.83 % (14611)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/2Mi)
% 3.37/1.83 % (14613)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_14509 for (2999ds/275Mi)
% 3.37/1.83 % (14612)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_14509 for (2999ds/2Mi)
% 3.37/1.83 % (14610)Instruction limit reached!
% 3.37/1.83 % (14610)------------------------------
% 3.37/1.83 % (14610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.83 % (14610)Termination reason: Unknown
% 3.37/1.83 % (14610)Termination phase: shuffling
% 3.37/1.83
% 3.37/1.83 % (14610)Memory used [KB]: 1791
% 3.37/1.83 % (14610)Time elapsed: 0.010 s
% 3.37/1.83 % (14610)Instructions burned: 27 (million)
% 3.37/1.83 % (14610)------------------------------
% 3.37/1.83 % (14610)------------------------------
% 3.37/1.83 % (14614)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/18Mi)
% 3.37/1.83 % (14611)Instruction limit reached!
% 3.37/1.83 % (14611)------------------------------
% 3.37/1.83 % (14611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.83 % (14611)Termination reason: Unknown
% 3.37/1.83 % (14612)Instruction limit reached!
% 3.37/1.83 % (14612)------------------------------
% 3.37/1.83 % (14612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.83 % (14611)Termination phase: shuffling
% 3.37/1.83
% 3.37/1.83 % (14611)Memory used [KB]: 1407
% 3.37/1.83 % (14611)Time elapsed: 0.003 s
% 3.37/1.83 % (14611)Instructions burned: 3 (million)
% 3.37/1.83 % (14611)------------------------------
% 3.37/1.83 % (14611)------------------------------
% 3.37/1.83 % (14612)Termination reason: Unknown
% 3.37/1.83 % (14612)Termination phase: shuffling
% 3.37/1.83
% 3.37/1.83 % (14612)Memory used [KB]: 1407
% 3.37/1.83 % (14612)Time elapsed: 0.003 s
% 3.37/1.83 % (14612)Instructions burned: 3 (million)
% 3.37/1.83 % (14612)------------------------------
% 3.37/1.83 % (14612)------------------------------
% 3.37/1.83 % (14609)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_14509 for (2999ds/4Mi)
% 3.37/1.83 % (14609)Instruction limit reached!
% 3.37/1.83 % (14609)------------------------------
% 3.37/1.83 % (14609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.83 % (14609)Termination reason: Unknown
% 3.37/1.83 % (14609)Termination phase: shuffling
% 3.37/1.83
% 3.37/1.83 % (14609)Memory used [KB]: 1535
% 3.37/1.83 % (14609)Time elapsed: 0.003 s
% 3.37/1.83 % (14609)Instructions burned: 6 (million)
% 3.37/1.83 % (14609)------------------------------
% 3.37/1.83 % (14609)------------------------------
% 3.37/1.84 % (14615)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/3Mi)
% 3.37/1.84 % (14614)Instruction limit reached!
% 3.37/1.84 % (14614)------------------------------
% 3.37/1.84 % (14614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.84 % (14614)Termination reason: Unknown
% 3.37/1.84 % (14614)Termination phase: shuffling
% 3.37/1.84
% 3.37/1.84 % (14614)Memory used [KB]: 1663
% 3.37/1.84 % (14614)Time elapsed: 0.011 s
% 3.37/1.84 % (14614)Instructions burned: 18 (million)
% 3.37/1.84 % (14614)------------------------------
% 3.37/1.84 % (14614)------------------------------
% 3.37/1.84 % (14615)Instruction limit reached!
% 3.37/1.84 % (14615)------------------------------
% 3.37/1.84 % (14615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.84 % (14615)Termination reason: Unknown
% 3.37/1.84 % (14615)Termination phase: shuffling
% 3.37/1.84
% 3.37/1.84 % (14615)Memory used [KB]: 1407
% 3.37/1.84 % (14615)Time elapsed: 0.002 s
% 3.37/1.84 % (14615)Instructions burned: 3 (million)
% 3.37/1.84 % (14615)------------------------------
% 3.37/1.84 % (14615)------------------------------
% 3.37/1.84 % (14616)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_14509 for (2999ds/37Mi)
% 3.37/1.85 % (14617)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_14509 for (2999ds/15Mi)
% 3.37/1.85 % (14620)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/7Mi)
% 3.37/1.85 % (14618)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_14509 for (2999ds/3Mi)
% 3.37/1.85 % (14620)Instruction limit reached!
% 3.37/1.85 % (14620)------------------------------
% 3.37/1.85 % (14620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.85 % (14620)Termination reason: Unknown
% 3.37/1.85 % (14620)Termination phase: shuffling
% 3.37/1.85
% 3.37/1.85 % (14620)Memory used [KB]: 1535
% 3.37/1.85 % (14620)Time elapsed: 0.004 s
% 3.37/1.85 % (14620)Instructions burned: 10 (million)
% 3.37/1.85 % (14620)------------------------------
% 3.37/1.85 % (14620)------------------------------
% 3.37/1.85 % (14618)Instruction limit reached!
% 3.37/1.85 % (14618)------------------------------
% 3.37/1.85 % (14618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.85 % (14618)Termination reason: Unknown
% 3.37/1.85 % (14618)Termination phase: shuffling
% 3.37/1.85
% 3.37/1.85 % (14618)Memory used [KB]: 1407
% 3.37/1.85 % (14618)Time elapsed: 0.004 s
% 3.37/1.85 % (14618)Instructions burned: 4 (million)
% 3.37/1.85 % (14618)------------------------------
% 3.37/1.85 % (14618)------------------------------
% 3.37/1.85 % (14616)Instruction limit reached!
% 3.37/1.85 % (14616)------------------------------
% 3.37/1.85 % (14616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.85 % (14616)Termination reason: Unknown
% 3.37/1.85 % (14616)Termination phase: shuffling
% 3.37/1.85
% 3.37/1.85 % (14616)Memory used [KB]: 2174
% 3.37/1.85 % (14616)Time elapsed: 0.012 s
% 3.37/1.85 % (14616)Instructions burned: 40 (million)
% 3.37/1.85 % (14616)------------------------------
% 3.37/1.85 % (14616)------------------------------
% 3.37/1.85 % (14617)Instruction limit reached!
% 3.37/1.85 % (14617)------------------------------
% 3.37/1.85 % (14617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.85 % (14617)Termination reason: Unknown
% 3.37/1.85 % (14617)Termination phase: shuffling
% 3.37/1.85
% 3.37/1.85 % (14617)Memory used [KB]: 1535
% 3.37/1.85 % (14617)Time elapsed: 0.010 s
% 3.37/1.85 % (14617)Instructions burned: 15 (million)
% 3.37/1.85 % (14617)------------------------------
% 3.37/1.85 % (14617)------------------------------
% 3.37/1.86 % (14619)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_14509 for (2999ds/1041Mi)
% 3.37/1.86 % (14621)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/16Mi)
% 3.37/1.86 % (14623)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_14509 for (2999ds/3Mi)
% 3.37/1.86 % (14623)Instruction limit reached!
% 3.37/1.86 % (14623)------------------------------
% 3.37/1.86 % (14623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.86 % (14623)Termination reason: Unknown
% 3.37/1.86 % (14623)Termination phase: shuffling
% 3.37/1.86
% 3.37/1.86 % (14623)Memory used [KB]: 1407
% 3.37/1.86 % (14623)Time elapsed: 0.002 s
% 3.37/1.86 % (14623)Instructions burned: 3 (million)
% 3.37/1.86 % (14623)------------------------------
% 3.37/1.86 % (14623)------------------------------
% 3.37/1.87 % (14621)Instruction limit reached!
% 3.37/1.87 % (14621)------------------------------
% 3.37/1.87 % (14621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.87 % (14621)Termination reason: Unknown
% 3.37/1.87 % (14621)Termination phase: shuffling
% 3.37/1.87
% 3.37/1.87 % (14621)Memory used [KB]: 1663
% 3.37/1.87 % (14621)Time elapsed: 0.006 s
% 3.37/1.87 % (14621)Instructions burned: 16 (million)
% 3.37/1.87 % (14621)------------------------------
% 3.37/1.87 % (14621)------------------------------
% 3.37/1.87 % (14622)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_14509 for (2999ds/3Mi)
% 3.37/1.87 % (14624)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/7Mi)
% 3.37/1.87 % (14625)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/3Mi)
% 3.37/1.87 % (14622)Instruction limit reached!
% 3.37/1.87 % (14622)------------------------------
% 3.37/1.87 % (14622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.87 % (14622)Termination reason: Unknown
% 3.37/1.87 % (14622)Termination phase: shuffling
% 3.37/1.87
% 3.37/1.87 % (14622)Memory used [KB]: 1407
% 3.37/1.87 % (14622)Time elapsed: 0.004 s
% 3.37/1.87 % (14622)Instructions burned: 4 (million)
% 3.37/1.87 % (14622)------------------------------
% 3.37/1.87 % (14622)------------------------------
% 3.37/1.87 % (14625)Instruction limit reached!
% 3.37/1.87 % (14625)------------------------------
% 3.37/1.87 % (14625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.87 % (14625)Termination reason: Unknown
% 3.37/1.87 % (14625)Termination phase: shuffling
% 3.37/1.87
% 3.37/1.87 % (14625)Memory used [KB]: 1407
% 3.37/1.87 % (14625)Time elapsed: 0.002 s
% 3.37/1.87 % (14625)Instructions burned: 3 (million)
% 3.37/1.87 % (14625)------------------------------
% 3.37/1.87 % (14625)------------------------------
% 3.37/1.88 % (14626)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/4Mi)
% 3.37/1.88 % (14624)Instruction limit reached!
% 3.37/1.88 % (14624)------------------------------
% 3.37/1.88 % (14624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.88 % (14624)Termination reason: Unknown
% 3.37/1.88 % (14624)Termination phase: shuffling
% 3.37/1.88
% 3.37/1.88 % (14624)Memory used [KB]: 1535
% 3.37/1.88 % (14624)Time elapsed: 0.006 s
% 3.37/1.88 % (14624)Instructions burned: 8 (million)
% 3.37/1.88 % (14624)------------------------------
% 3.37/1.88 % (14624)------------------------------
% 3.37/1.88 % (14626)Instruction limit reached!
% 3.37/1.88 % (14626)------------------------------
% 3.37/1.88 % (14626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.88 % (14626)Termination reason: Unknown
% 3.37/1.88 % (14626)Termination phase: shuffling
% 3.37/1.88
% 3.37/1.88 % (14626)Memory used [KB]: 1535
% 3.37/1.88 % (14626)Time elapsed: 0.003 s
% 3.37/1.88 % (14626)Instructions burned: 6 (million)
% 3.37/1.88 % (14626)------------------------------
% 3.37/1.88 % (14626)------------------------------
% 3.37/1.88 % (14628)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/710Mi)
% 3.37/1.89 % (14630)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_14509 for (2999ds/902Mi)
% 3.37/1.89 % (14629)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/6Mi)
% 3.37/1.89 % (14627)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/18Mi)
% 3.37/1.90 % (14629)Instruction limit reached!
% 3.37/1.90 % (14629)------------------------------
% 3.37/1.90 % (14629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.90 % (14629)Termination reason: Unknown
% 3.37/1.90 % (14629)Termination phase: shuffling
% 3.37/1.90
% 3.37/1.90 % (14629)Memory used [KB]: 1535
% 3.37/1.90 % (14629)Time elapsed: 0.005 s
% 3.37/1.90 % (14629)Instructions burned: 6 (million)
% 3.37/1.90 % (14629)------------------------------
% 3.37/1.90 % (14629)------------------------------
% 3.37/1.90 % (14627)Instruction limit reached!
% 3.37/1.90 % (14627)------------------------------
% 3.37/1.90 % (14627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.90 % (14627)Termination reason: Unknown
% 3.37/1.90 % (14627)Termination phase: shuffling
% 3.37/1.90
% 3.37/1.90 % (14627)Memory used [KB]: 1663
% 3.37/1.90 % (14627)Time elapsed: 0.011 s
% 3.37/1.90 % (14627)Instructions burned: 18 (million)
% 3.37/1.90 % (14627)------------------------------
% 3.37/1.90 % (14627)------------------------------
% 3.37/1.90 % (14608)Instruction limit reached!
% 3.37/1.90 % (14608)------------------------------
% 3.37/1.90 % (14608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.90 % (14608)Termination reason: Unknown
% 3.37/1.91 % (14608)Termination phase: Saturation
% 3.37/1.91
% 3.37/1.91 % (14608)Memory used [KB]: 2686
% 3.37/1.91 % (14608)Time elapsed: 0.083 s
% 3.37/1.91 % (14608)Instructions burned: 184 (million)
% 3.37/1.91 % (14608)------------------------------
% 3.37/1.91 % (14608)------------------------------
% 3.37/1.91 % (14631)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_14509 for (2999ds/21Mi)
% 3.37/1.91 % (14631)Instruction limit reached!
% 3.37/1.91 % (14631)------------------------------
% 3.37/1.91 % (14631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.91 % (14631)Termination reason: Unknown
% 3.37/1.91 % (14631)Termination phase: shuffling
% 3.37/1.91
% 3.37/1.91 % (14631)Memory used [KB]: 1663
% 3.37/1.91 % (14631)Time elapsed: 0.008 s
% 3.37/1.91 % (14631)Instructions burned: 21 (million)
% 3.37/1.91 % (14631)------------------------------
% 3.37/1.91 % (14631)------------------------------
% 3.37/1.92 % (14633)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_14509 for (2999ds/6Mi)
% 3.37/1.92 % (14634)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14509 for (2998ds/377Mi)
% 3.37/1.92 % (14632)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14509 for (2999ds/5Mi)
% 3.37/1.93 % (14633)Instruction limit reached!
% 3.37/1.93 % (14633)------------------------------
% 3.37/1.93 % (14633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.93 % (14633)Termination reason: Unknown
% 3.37/1.93 % (14633)Termination phase: shuffling
% 3.37/1.93
% 3.37/1.93 % (14633)Memory used [KB]: 1535
% 3.37/1.93 % (14633)Time elapsed: 0.005 s
% 3.37/1.93 % (14633)Instructions burned: 6 (million)
% 3.37/1.93 % (14633)------------------------------
% 3.37/1.93 % (14633)------------------------------
% 3.37/1.93 % (14632)Instruction limit reached!
% 3.37/1.93 % (14632)------------------------------
% 3.37/1.93 % (14632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.93 % (14632)Termination reason: Unknown
% 3.37/1.93 % (14632)Termination phase: shuffling
% 3.37/1.93
% 3.37/1.93 % (14632)Memory used [KB]: 1535
% 3.37/1.93 % (14632)Time elapsed: 0.005 s
% 3.37/1.93 % (14632)Instructions burned: 6 (million)
% 3.37/1.93 % (14632)------------------------------
% 3.37/1.93 % (14632)------------------------------
% 3.37/1.93 % (14628)First to succeed.
% 3.37/1.94 % (14613)Instruction limit reached!
% 3.37/1.94 % (14613)------------------------------
% 3.37/1.94 % (14613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.94 % (14613)Termination reason: Unknown
% 3.37/1.94 % (14613)Termination phase: Saturation
% 3.37/1.94
% 3.37/1.94 % (14613)Memory used [KB]: 7419
% 3.37/1.94 % (14613)Time elapsed: 0.111 s
% 3.37/1.94 % (14613)Instructions burned: 276 (million)
% 3.37/1.94 % (14613)------------------------------
% 3.37/1.94 % (14613)------------------------------
% 3.37/1.94 % (14628)Refutation found. Thanks to Tanya!
% 3.37/1.94 % SZS status Theorem for DTF2THF_14509
% 3.37/1.94 % SZS output start Proof for DTF2THF_14509
% 3.37/1.94 thf(type_def_5, type, messageValue: ($tType) > $tType).
% 3.37/1.94 thf(type_def_7, type, message: ($tType * $tType) > $tType).
% 3.37/1.94 thf(type_def_8, type, nat: $tType).
% 3.37/1.94 thf(type_def_9, type, product_unit: $tType).
% 3.37/1.94 thf(type_def_10, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.37/1.94 thf(type_def_11, type, set: ($tType) > $tType).
% 3.37/1.94 thf(type_def_12, type, list: ($tType) > $tType).
% 3.37/1.94 thf(type_def_13, type, p: $tType).
% 3.37/1.94 thf(type_def_14, type, v: $tType).
% 3.37/1.94 thf(type_def_15, type, s: $tType).
% 3.37/1.94 thf(func_def_0, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.37/1.94 thf(func_def_1, type, messageValue: ($tType) > $tType).
% 3.37/1.94 thf(func_def_2, type, message: ($tType * $tType) > $tType).
% 3.37/1.94 thf(func_def_3, type, product_unit: $tType).
% 3.37/1.94 thf(func_def_4, type, list: ($tType) > $tType).
% 3.37/1.94 thf(func_def_5, type, set: ($tType) > $tType).
% 3.37/1.94 thf(func_def_6, type, nat: $tType).
% 3.37/1.94 thf(func_def_7, type, v: $tType).
% 3.37/1.94 thf(func_def_8, type, s: $tType).
% 3.37/1.94 thf(func_def_9, type, p: $tType).
% 3.37/1.94 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_11, type, bot: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_12, type, ord: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_16, type, order_bot: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_17, type, dense_linorder: !>[X0: $tType]:($o)).
% 3.37/1.94 thf(func_def_18, type, initReachable: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_19, type, initial: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_20, type, qReachable: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > set @ X0 > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_21, type, reachable: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_22, type, stepReachable: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > message @ X0 @ X2 > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_23, type, steps: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > message @ X0 @ X2 > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_24, type, msgs: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ X3 > message @ X0 @ X1 > nat)).
% 3.37/1.94 thf(func_def_25, type, states: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ X3 > X0 > X2)).
% 3.37/1.94 thf(func_def_26, type, enabled: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > message @ X0 @ X1 > $o)).
% 3.37/1.94 thf(func_def_27, type, isReceiverOf: !>[X0: $tType, X1: $tType]:(X0 > message @ X0 @ X1 > $o)).
% 3.37/1.94 thf(func_def_28, type, outMsg: !>[X0: $tType, X1: $tType]:($o > message @ X0 @ X1)).
% 3.37/1.94 thf(func_def_29, type, execution: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > list @ configuration_ext @ X0 @ X2 @ X1 @ product_unit > list @ message @ X0 @ X2 > $o)).
% 3.37/1.94 thf(func_def_30, type, firstOccurrence: !>[X0: $tType, X1: $tType, X2: $tType]:(list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > message @ X0 @ X1 > nat > $o)).
% 3.37/1.94 thf(func_def_31, type, minimalEnabled: !>[X0: $tType, X1: $tType, X2: $tType]:(list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > message @ X0 @ X1 > $o)).
% 3.37/1.94 thf(func_def_32, type, flpSystem: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > $o)).
% 3.37/1.94 thf(func_def_33, type, agreement: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_34, type, agreementInit: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_35, type, pSilDecVal: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > $o > X0 > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_36, type, terminationPseudo: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > nat > configuration_ext @ X0 @ X2 @ X1 @ product_unit > set @ X0 > $o)).
% 3.37/1.94 thf(func_def_37, type, vUniform: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > $o > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_38, type, validity: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > configuration_ext @ X0 @ X2 @ X1 @ product_unit > configuration_ext @ X0 @ X2 @ X1 @ product_unit > $o)).
% 3.37/1.94 thf(func_def_39, type, fLPThe1922692578sensus: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > $o)).
% 3.37/1.94 thf(func_def_40, type, one_one: !>[X0: $tType]:(X0)).
% 3.37/1.94 thf(func_def_41, type, zero_zero: !>[X0: $tType]:(X0)).
% 3.37/1.94 thf(func_def_42, type, prefixList: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 3.37/1.94 thf(func_def_43, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 3.37/1.94 thf(func_def_44, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.37/1.94 thf(func_def_45, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.37/1.94 thf(func_def_46, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.37/1.94 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.37/1.94 thf(func_def_48, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.37/1.94 thf(func_def_49, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.37/1.94 thf(func_def_50, type, cMsg: configuration_ext @ p @ v @ s @ product_unit).
% 3.37/1.94 thf(func_def_51, type, c: configuration_ext @ p @ v @ s @ product_unit).
% 3.37/1.94 thf(func_def_52, type, exec: list @ configuration_ext @ p @ v @ s @ product_unit).
% 3.37/1.94 thf(func_def_53, type, execMsga: list @ configuration_ext @ p @ v @ s @ product_unit).
% 3.37/1.94 thf(func_def_54, type, exec2: list @ configuration_ext @ p @ v @ s @ product_unit).
% 3.37/1.94 thf(func_def_55, type, msg: message @ p @ v).
% 3.37/1.94 thf(func_def_56, type, p2: p).
% 3.37/1.94 thf(func_def_57, type, sends: p > s > messageValue @ v > message @ p @ v > nat).
% 3.37/1.94 thf(func_def_58, type, start: p > s).
% 3.37/1.94 thf(func_def_59, type, trace: list @ message @ p @ v).
% 3.37/1.94 thf(func_def_60, type, traceMsga: list @ message @ p @ v).
% 3.37/1.94 thf(func_def_61, type, trace2: list @ message @ p @ v).
% 3.37/1.94 thf(func_def_62, type, trans: p > s > messageValue @ v > s).
% 3.37/1.94 thf(func_def_82, type, sK0: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.37/1.94 thf(func_def_83, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.37/1.94 thf(func_def_84, type, sK2: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.37/1.94 thf(func_def_85, type, sK3: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.37/1.94 thf(func_def_86, type, sK4: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.37/1.94 thf(func_def_87, type, sK5: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.37/1.94 thf(func_def_88, type, sK6: list @ configuration_ext @ p @ v @ s @ product_unit).
% 3.37/1.94 thf(func_def_89, type, sK7: list @ message @ p @ v).
% 3.37/1.94 thf(func_def_90, type, sK8: configuration_ext @ p @ v @ s @ product_unit).
% 3.37/1.94 thf(func_def_91, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.37/1.94 thf(f949,plain,(
% 3.37/1.94 $false),
% 3.37/1.94 inference(avatar_sat_refutation,[status(thm)],[f944,f945,f946,f947,f948])).
% 3.37/1.94 thf(f948,plain,(
% 3.37/1.94 spl10_4),
% 3.37/1.94 inference(avatar_split_clause,[status(thm)],[f886,f941])).
% 3.37/1.94 thf(f941,definition,(
% 3.37/1.94 spl10_4 <=> ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) = $true)),
% 3.37/1.94 introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition])).
% 3.37/1.94 thf(f886,plain,(
% 3.37/1.94 ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) = $true)),
% 3.37/1.94 inference(cnf_transformation,[status(thm)],[f419])).
% 3.37/1.94 thf(f419,plain,(
% 3.37/1.94 ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) = $true)),
% 3.37/1.94 inference(fool_elimination,[status(thm)],[f418])).
% 3.37/1.94 thf(f418,plain,(
% 3.37/1.94 (initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2))),
% 3.37/1.94 inference(rectify,[status(thm)],[f2])).
% 3.37/1.94 thf(f2,axiom,(
% 3.37/1.94 (initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2))),
% 3.37/1.94 file('/export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2THF_14509.p',fact_1_InitReachLastExec_H)).
% 3.37/1.94 thf(f947,plain,(
% 3.37/1.94 spl10_1),
% 3.37/1.94 inference(avatar_split_clause,[status(thm)],[f914,f929])).
% 3.37/1.94 thf(f929,definition,(
% 3.37/1.94 spl10_1 <=> ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ (last @ message @ p @ v @ sK7) @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga)) = $true)),
% 3.37/1.94 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 3.37/1.94 thf(f914,plain,(
% 3.37/1.94 ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ (last @ message @ p @ v @ sK7) @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga)) = $true)),
% 3.37/1.94 inference(definition_unfolding,[status(thm)],[f885,f901,f888])).
% 3.37/1.94 thf(f888,plain,(
% 3.37/1.94 (cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga))),
% 3.37/1.94 inference(cnf_transformation,[status(thm)],[f6])).
% 3.37/1.94 thf(f6,axiom,(
% 3.37/1.94 (cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga))),
% 3.37/1.94 file('/export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2THF_14509.p',fact_5_ExecMsg_I3_J)).
% 3.37/1.94 thf(f901,plain,(
% 3.37/1.94 (msg = (last @ message @ p @ v @ sK7))),
% 3.37/1.94 inference(cnf_transformation,[status(thm)],[f864])).
% 3.37/1.94 thf(f864,plain,(
% 3.37/1.94 ($true = (prefixList @ message @ p @ v @ trace2 @ sK7)) & (cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ sK6)) & ($true = (execution @ p @ s @ v @ trans @ sends @ start @ sK6 @ sK7)) & ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ sK6) = $true) & (msg = (last @ message @ p @ v @ sK7))),
% 3.37/1.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f825,f863])).
% 3.37/1.94 thf(f863,plain,(
% 3.37/1.94 ? [X0 : list @ configuration_ext @ p @ v @ s @ product_unit,X1 : list @ message @ p @ v] : (((prefixList @ message @ p @ v @ trace2 @ X1) = $true) & (cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ X0)) & ($true = (execution @ p @ s @ v @ trans @ sends @ start @ X0 @ X1)) & ($true = (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ X0)) & (msg = (last @ message @ p @ v @ X1))) => (($true = (prefixList @ message @ p @ v @ trace2 @ sK7)) & (cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ sK6)) & ($true = (execution @ p @ s @ v @ trans @ sends @ start @ sK6 @ sK7)) & ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ sK6) = $true) & (msg = (last @ message @ p @ v @ sK7)))),
% 3.37/1.94 introduced(definition,[],[choice_axiom])).
% 3.37/1.94 thf(f825,plain,(
% 3.37/1.94 ? [X0 : list @ configuration_ext @ p @ v @ s @ product_unit,X1 : list @ message @ p @ v] : (((prefixList @ message @ p @ v @ trace2 @ X1) = $true) & (cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ X0)) & ($true = (execution @ p @ s @ v @ trans @ sends @ start @ X0 @ X1)) & ($true = (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ X0)) & (msg = (last @ message @ p @ v @ X1)))),
% 3.37/1.94 inference(flattening,[status(thm)],[f824])).
% 3.37/1.94 thf(f824,plain,(
% 3.37/1.94 ? [X0 : list @ configuration_ext @ p @ v @ s @ product_unit,X1 : list @ message @ p @ v] : (((((msg = (last @ message @ p @ v @ X1)) & (cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ X0))) & ((prefixList @ message @ p @ v @ trace2 @ X1) = $true)) & ($true = (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ X0))) & ($true = (execution @ p @ s @ v @ trans @ sends @ start @ X0 @ X1)))),
% 3.37/1.94 inference(ennf_transformation,[status(thm)],[f669])).
% 3.37/1.94 thf(f669,plain,(
% 3.37/1.94 ~! [X0 : list @ configuration_ext @ p @ v @ s @ product_unit,X1 : list @ message @ p @ v] : (($true = (execution @ p @ s @ v @ trans @ sends @ start @ X0 @ X1)) => (($true = (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ X0)) => (((prefixList @ message @ p @ v @ trace2 @ X1) = $true) => ((cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ X0)) => (msg != (last @ message @ p @ v @ X1))))))),
% 3.37/1.94 inference(fool_elimination,[status(thm)],[f668])).
% 3.37/1.94 thf(f668,plain,(
% 3.37/1.94 ~! [X0 : list @ configuration_ext @ p @ v @ s @ product_unit,X1 : list @ message @ p @ v] : ((execution @ p @ s @ v @ trans @ sends @ start @ X0 @ X1) => ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ X0) => ((prefixList @ message @ p @ v @ trace2 @ X1) => ((cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ X0)) => (msg != (last @ message @ p @ v @ X1))))))),
% 3.37/1.94 inference(rectify,[status(thm)],[f181])).
% 3.37/1.94 thf(f181,axiom,(
% 3.37/1.94 ~! [X97 : list @ configuration_ext @ p @ v @ s @ product_unit,X98 : list @ message @ p @ v] : ((execution @ p @ s @ v @ trans @ sends @ start @ X97 @ X98) => ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ exec2 @ X97) => ((prefixList @ message @ p @ v @ trace2 @ X98) => ((cMsg = (last @ configuration_ext @ p @ v @ s @ product_unit @ X97)) => (msg != (last @ message @ p @ v @ X98))))))),
% 3.37/1.94 file('/export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2THF_14509.p',fact_180__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 3.37/1.94 thf(f885,plain,(
% 3.37/1.94 ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) = $true)),
% 3.37/1.94 inference(cnf_transformation,[status(thm)],[f485])).
% 3.37/1.94 thf(f485,plain,(
% 3.37/1.94 ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) = $true)),
% 3.37/1.94 inference(fool_elimination,[status(thm)],[f484])).
% 3.37/1.94 thf(f484,plain,(
% 3.37/1.94 (steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg)),
% 3.37/1.94 inference(rectify,[status(thm)],[f4])).
% 3.37/1.94 thf(f4,axiom,(
% 3.37/1.94 (steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg)),
% 3.37/1.94 file('/export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2THF_14509.p',fact_3_CMsg)).
% 3.37/1.94 thf(f946,plain,(
% 3.37/1.94 spl10_3),
% 3.37/1.94 inference(avatar_split_clause,[status(thm)],[f915,f937])).
% 3.37/1.94 thf(f937,definition,(
% 3.37/1.94 spl10_3 <=> ($true = (isReceiverOf @ p @ v @ p2 @ (last @ message @ p @ v @ sK7)))),
% 3.37/1.94 introduced(definition,[new_symbols(naming,[spl10_3])],[avatar_definition])).
% 3.37/1.94 thf(f915,plain,(
% 3.37/1.94 ($true = (isReceiverOf @ p @ v @ p2 @ (last @ message @ p @ v @ sK7)))),
% 3.37/1.94 inference(definition_unfolding,[status(thm)],[f898,f901])).
% 3.37/1.94 thf(f898,plain,(
% 3.37/1.94 ((isReceiverOf @ p @ v @ p2 @ msg) = $true)),
% 3.37/1.94 inference(cnf_transformation,[status(thm)],[f437])).
% 3.37/1.94 thf(f437,plain,(
% 3.37/1.94 ((isReceiverOf @ p @ v @ p2 @ msg) = $true)),
% 3.37/1.94 inference(fool_elimination,[status(thm)],[f436])).
% 3.37/1.94 thf(f436,plain,(
% 3.37/1.94 (isReceiverOf @ p @ v @ p2 @ msg)),
% 3.37/1.94 inference(rectify,[status(thm)],[f1])).
% 3.37/1.94 thf(f1,axiom,(
% 3.37/1.94 (isReceiverOf @ p @ v @ p2 @ msg)),
% 3.37/1.94 file('/export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2THF_14509.p',fact_0_PisReceiverOf)).
% 3.37/1.94 thf(f945,plain,(
% 3.37/1.94 ~spl10_2),
% 3.37/1.94 inference(avatar_split_clause,[status(thm)],[f913,f933])).
% 3.37/1.94 thf(f933,definition,(
% 3.37/1.94 spl10_2 <=> ($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga))))))),
% 3.37/1.94 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 3.37/1.94 thf(f913,plain,(
% 3.37/1.94 ($true != (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga))))))),
% 3.37/1.94 inference(definition_unfolding,[status(thm)],[f883,f888])).
% 3.37/1.94 thf(f883,plain,(
% 3.37/1.94 ($true != (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))))),
% 3.37/1.94 inference(cnf_transformation,[status(thm)],[f812])).
% 3.37/1.94 thf(f812,plain,(
% 3.37/1.94 ($true != (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))))),
% 3.37/1.94 inference(flattening,[status(thm)],[f315])).
% 3.37/1.94 thf(f315,plain,(
% 3.37/1.94 ~($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))))),
% 3.37/1.94 inference(fool_elimination,[status(thm)],[f314])).
% 3.37/1.94 thf(f314,plain,(
% 3.37/1.94 ~(ord_less_eq @ set @ $o @ (collect @ $o @ (^[X0 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[X1 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X1 @ p2 @ cMsg))))),
% 3.37/1.94 inference(rectify,[status(thm)],[f286])).
% 3.37/1.94 thf(f286,negated_conjecture,(
% 3.37/1.94 ~(ord_less_eq @ set @ $o @ (collect @ $o @ (^[X5 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X5 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[X5 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X5 @ p2 @ cMsg))))),
% 3.37/1.94 inference(negated_conjecture,[status(cth)],[f285])).
% 3.37/1.94 thf(f285,conjecture,(
% 3.37/1.94 (ord_less_eq @ set @ $o @ (collect @ $o @ (^[X5 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X5 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[X5 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X5 @ p2 @ cMsg))))),
% 3.37/1.94 file('/export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2THF_14509.p',conj_0)).
% 3.37/1.94 thf(f944,plain,(
% 3.37/1.94 ~spl10_1 | spl10_2 | ~spl10_3 | ~spl10_4),
% 3.37/1.94 inference(avatar_split_clause,[status(thm)],[f927,f941,f937,f933,f929])).
% 3.37/1.94 thf(f927,plain,(
% 3.37/1.94 ($true != (isReceiverOf @ p @ v @ p2 @ (last @ message @ p @ v @ sK7))) | ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ (last @ message @ p @ v @ sK7) @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga)) != $true) | ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) != $true) | ($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga))))))),
% 3.37/1.94 inference(trivial_inequality_removal,[status(thm)],[f917])).
% 3.37/1.94 thf(f917,plain,(
% 3.37/1.94 ($true != (isReceiverOf @ p @ v @ p2 @ (last @ message @ p @ v @ sK7))) | ($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga)))))) | ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ (last @ message @ p @ v @ sK7) @ (last @ configuration_ext @ p @ v @ s @ product_unit @ execMsga)) != $true) | ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) != $true) | (p2 != p2)),
% 3.37/1.94 inference(definition_unfolding,[status(thm)],[f907,f888,f901,f888,f901])).
% 3.37/1.94 thf(f907,plain,(
% 3.37/1.94 (p2 != p2) | ($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ cMsg))))) | ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) != $true) | ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) != $true) | ((isReceiverOf @ p @ v @ p2 @ msg) != $true)),
% 3.37/1.94 inference(cnf_transformation,[status(thm)],[f821])).
% 3.37/1.94 thf(f821,plain,(
% 3.37/1.94 (p2 != p2) | ($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ cMsg))))) | ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) != $true) | ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) != $true) | ((isReceiverOf @ p @ v @ p2 @ msg) != $true)),
% 3.37/1.94 inference(flattening,[status(thm)],[f820])).
% 3.37/1.94 thf(f820,plain,(
% 3.37/1.94 (((($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ cMsg))))) | ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) != $true)) | ((isReceiverOf @ p @ v @ p2 @ msg) != $true)) | ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) != $true)) | (p2 != p2)),
% 3.37/1.94 inference(ennf_transformation,[status(thm)],[f739])).
% 3.37/1.94 thf(f739,plain,(
% 3.37/1.94 (p2 = p2) => (((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) = $true) => (((isReceiverOf @ p @ v @ p2 @ msg) = $true) => (((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) = $true) => ($true = (ord_less_eq @ set @ $o @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[Y0 : $o]: (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ Y0 @ p2 @ cMsg))))))))),
% 3.37/1.94 inference(fool_elimination,[status(thm)],[f738])).
% 3.37/1.94 thf(f738,plain,(
% 3.37/1.94 (p2 = p2) => ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) => ((isReceiverOf @ p @ v @ p2 @ msg) => ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) => (ord_less_eq @ set @ $o @ (collect @ $o @ (^[X0 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X0 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[X1 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X1 @ p2 @ cMsg)))))))),
% 3.37/1.94 inference(rectify,[status(thm)],[f7])).
% 3.37/1.94 thf(f7,axiom,(
% 3.37/1.94 (p2 = p2) => ((steps @ p @ s @ v @ trans @ sends @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2) @ msg @ cMsg) => ((isReceiverOf @ p @ v @ p2 @ msg) => ((initReachable @ p @ s @ v @ trans @ sends @ start @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)) => (ord_less_eq @ set @ $o @ (collect @ $o @ (^[X5 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X5 @ p2 @ (last @ configuration_ext @ p @ v @ s @ product_unit @ exec2)))) @ (collect @ $o @ (^[X5 : $o] : (pSilDecVal @ p @ s @ v @ trans @ sends @ start @ X5 @ p2 @ cMsg)))))))),
% 3.37/1.94 file('/export/starexec/sandbox2/tmp/tmp.wSYbkGIeTa/DTF2THF_14509.p',fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062)).
% 3.37/1.94 % SZS output end Proof for DTF2THF_14509
% 3.37/1.94 % (14628)------------------------------
% 3.37/1.94 % (14628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.94 % (14628)Termination reason: Refutation
% 3.37/1.94
% 3.37/1.94 % (14628)Memory used [KB]: 6780
% 3.37/1.94 % (14628)Time elapsed: 0.053 s
% 3.37/1.94 % (14628)Instructions burned: 101 (million)
% 3.37/1.94 % (14628)------------------------------
% 3.37/1.94 % (14628)------------------------------
% 3.37/1.94 % (14607)Success in time 0.13 s
%------------------------------------------------------------------------------