%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP183^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.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 08:56:14 AM UTC 2026
% Result : Theorem 2.71s 1.64s
% Output : Refutation 2.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP183^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:29:06 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : ITP183^2 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.47 % Domain : Interactive Theorem Proving
% 0.27/0.47 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_329__3411594_1
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Des21]
% 0.27/0.47 % Names : Strong_Late_Sim_SC/prob_329__3411594_1 [Des21]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v7.5.0
% 0.27/0.47 % Syntax : Number of formulae : 324 ( 136 unt; 50 typ; 0 def)
% 0.27/0.47 % Number of atoms : 735 ( 233 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 17 ( 2 avg)
% 0.27/0.47 % Number of connectives : 4007 ( 134 ~; 5 |; 49 &;3430 @)
% 0.27/0.47 % ( 0 <=>; 389 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 28 ( 9 avg)
% 0.27/0.47 % Number of types : 6 ( 5 usr)
% 0.27/0.47 % Number of type conns : 147 ( 147 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 46 ( 45 usr; 9 con; 0-5 aty)
% 0.27/0.47 % Number of variables : 1242 ( 28 ^;1179 !; 13 ?;1242 :)
% 0.27/0.47 % ( 22 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.47 % SPC : TH1_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:12.846
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % Could-be-implicit typings (8)
% 0.27/0.47 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.27/0.47 late_residual: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_t_Late__Semantics_Osubject,type,
% 0.27/0.47 late_subject: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.27/0.47 late_freeRes: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_t_Product__Type_Oprod,type,
% 0.27/0.47 product_prod: $tType > $tType > $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_t_Nominal_Onoption,type,
% 0.27/0.47 noption: $tType > $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_t_Agent_Oname,type,
% 0.27/0.47 name: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_t_Agent_Opi,type,
% 0.27/0.47 pi: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_t_Set_Oset,type,
% 0.27/0.47 set: $tType > $tType ).
% 0.27/0.47
% 0.27/0.47 % Explicit typings (42)
% 0.27/0.47 thf(sy_cl_HOL_Otype,type,
% 0.27/0.47 type:
% 0.27/0.47 !>[A: $tType] : $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_cl_Agent_Ofs__name,type,
% 0.27/0.47 fs_name:
% 0.27/0.47 !>[A: $tType] : $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.27/0.47 ord:
% 0.27/0.47 !>[A: $tType] : $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.27/0.47 order:
% 0.27/0.47 !>[A: $tType] : $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.27/0.47 linorder:
% 0.27/0.47 !>[A: $tType] : $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.27/0.47 preorder:
% 0.27/0.47 !>[A: $tType] : $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_OInput,type,
% 0.27/0.47 input: name > name > pi > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.27/0.47 mismatch: name > name > pi > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_OOutput,type,
% 0.27/0.47 output: name > name > pi > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_OPar,type,
% 0.27/0.47 par: pi > pi > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.27/0.47 piNil: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_ORes,type,
% 0.27/0.47 res: name > pi > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_OSum,type,
% 0.27/0.47 sum: pi > pi > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Opi_OTau,type,
% 0.27/0.47 tau: pi > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Agent_Osubs,type,
% 0.27/0.47 subs: pi > name > name > pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.27/0.47 late_OutputR: name > name > late_freeRes ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.27/0.47 late_TauR: late_freeRes ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.27/0.47 late_freeRes_rec:
% 0.27/0.47 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.27/0.47 late_BoundR: late_subject > name > pi > late_residual ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.27/0.47 late_FreeR: late_freeRes > pi > late_residual ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.27/0.47 late_BoundOutputS: name > late_subject ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.27/0.47 late_InputS: name > late_subject ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.27/0.47 late_subject_rec:
% 0.27/0.47 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.27/0.47 late_transitions: pi > late_residual > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Oabs__fun,type,
% 0.27/0.47 abs_fun:
% 0.27/0.47 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Ofresh,type,
% 0.27/0.47 fresh:
% 0.27/0.47 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.27/0.47 ord_less_eq:
% 0.27/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair,type,
% 0.27/0.47 product_Pair:
% 0.27/0.47 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.27/0.47 product_rec_prod:
% 0.27/0.47 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Rel_Oeqvt,type,
% 0.27/0.47 eqvt:
% 0.27/0.47 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Relation_OId,type,
% 0.27/0.47 id:
% 0.27/0.47 !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect,type,
% 0.27/0.47 collect:
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.27/0.47 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.27/0.47 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member,type,
% 0.27/0.47 member:
% 0.27/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_P,type,
% 0.27/0.47 p: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_PQ____,type,
% 0.27/0.47 pq: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_Q,type,
% 0.27/0.47 q: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_Q_H____,type,
% 0.27/0.47 q2: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_Rel,type,
% 0.27/0.47 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v__092_060alpha_062____,type,
% 0.27/0.47 alpha: late_freeRes ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_x,type,
% 0.27/0.47 x: name ).
% 0.27/0.47
% 0.27/0.47 % Relevant facts (256)
% 0.27/0.47 thf(fact_0_cRes_Ohyps_I2_J,axiom,
% 0.27/0.47 fresh @ name @ late_freeRes @ x @ alpha ).
% 0.27/0.47
% 0.27/0.47 % cRes.hyps(2)
% 0.27/0.47 thf(fact_1_Eqvt,axiom,
% 0.27/0.47 eqvt @ pi @ rel ).
% 0.27/0.47
% 0.27/0.47 % Eqvt
% 0.27/0.47 thf(fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062,axiom,
% 0.27/0.47 late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) ).
% 0.27/0.47
% 0.27/0.47 % \<open>P \<oplus> Q \<longmapsto> \<alpha> \<prec> Q'\<close>
% 0.27/0.47 thf(fact_3_cRes_Ohyps_I1_J,axiom,
% 0.27/0.47 late_transitions @ q @ ( late_FreeR @ alpha @ q2 ) ).
% 0.27/0.47
% 0.27/0.47 % cRes.hyps(1)
% 0.27/0.47 thf(fact_4_cSum2_Ohyps,axiom,
% 0.27/0.47 late_transitions @ ( res @ x @ q ) @ ( late_FreeR @ alpha @ pq ) ).
% 0.27/0.47
% 0.27/0.47 % cSum2.hyps
% 0.27/0.47 thf(fact_5_Free_Ohyps,axiom,
% 0.27/0.47 late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pq ) ).
% 0.27/0.47
% 0.27/0.47 % Free.hyps
% 0.27/0.47 thf(fact_6_pi_Odistinct_I81_J,axiom,
% 0.27/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.27/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.27/0.47 != ( res @ Name @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(81)
% 0.27/0.47 thf(fact_7_sumCases,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.27/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.27/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumCases
% 0.27/0.47 thf(fact_8_sumCases_H,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.27/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.27/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumCases'
% 0.27/0.47 thf(fact_9_Sum1,axiom,
% 0.27/0.47 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ Rs )
% 0.27/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.27/0.47
% 0.27/0.47 % Sum1
% 0.27/0.47 thf(fact_10_Sum2,axiom,
% 0.27/0.47 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ Rs )
% 0.27/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.27/0.47
% 0.27/0.47 % Sum2
% 0.27/0.47 thf(fact_11_resCasesF,axiom,
% 0.27/0.47 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.27/0.47 => ( ! [P2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 0.27/0.47 => ( F @ ( res @ X2 @ P2 ) ) ) )
% 0.27/0.47 => ( F @ XP ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCasesF
% 0.27/0.47 thf(fact_12_resCasesF_H,axiom,
% 0.27/0.47 ! [X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 0.27/0.47 ( ( ( res @ X2 @ P )
% 0.27/0.47 = ( res @ Y @ P4 ) )
% 0.27/0.47 => ( ( ( late_FreeR @ Alpha @ P3 )
% 0.27/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 0.27/0.47 => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCasesF'
% 0.27/0.47 thf(fact_13_ResF,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_freeRes @ Y2 @ Alpha )
% 0.27/0.47 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y2 @ P3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ResF
% 0.27/0.47 thf(fact_14_pi_Oinject_I6_J,axiom,
% 0.27/0.47 ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.27/0.47 ( ( ( sum @ X22 @ X1 )
% 0.27/0.47 = ( sum @ Y22 @ Y1 ) )
% 0.27/0.47 = ( ( X22 = Y22 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.inject(6)
% 0.27/0.47 thf(fact_15_residual_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X22: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 0.27/0.47 ( ( ( late_FreeR @ X22 @ X1 )
% 0.27/0.47 = ( late_FreeR @ Y22 @ Y1 ) )
% 0.27/0.47 = ( ( X22 = Y22 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.inject(2)
% 0.27/0.47 thf(fact_16_resInputFreeTrans,axiom,
% 0.27/0.47 ! [X2: name,A2: name,Y2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resInputFreeTrans
% 0.27/0.47 thf(fact_17_resZeroTrans,axiom,
% 0.27/0.47 ! [X2: name,Rs: late_residual] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 0.27/0.47
% 0.27/0.47 % resZeroTrans
% 0.27/0.47 thf(fact_18_pi_Odistinct_I5_J,axiom,
% 0.27/0.47 ! [Name1: name,Name2: name,Pi: pi] :
% 0.27/0.47 ( piNil
% 0.27/0.47 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(5)
% 0.27/0.47 thf(fact_19_name__exists__fresh,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( fs_name @ A )
% 0.27/0.47 => ! [X2: A] :
% 0.27/0.47 ~ ! [C: name] :
% 0.27/0.47 ~ ( fresh @ name @ A @ C @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_exists_fresh
% 0.27/0.47 thf(fact_20_pi_Odistinct_I57_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.47 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( res @ Name @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(57)
% 0.27/0.47 thf(fact_21_zeroTrans,axiom,
% 0.27/0.47 ! [Rs: late_residual] :
% 0.27/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.27/0.47
% 0.27/0.47 % zeroTrans
% 0.27/0.47 thf(fact_22_nilCases_H,axiom,
% 0.27/0.47 ! [Rs: late_residual] :
% 0.27/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.27/0.47
% 0.27/0.47 % nilCases'
% 0.27/0.47 thf(fact_23_pi_Odistinct_I53_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(53)
% 0.27/0.47 thf(fact_24_pi_Odistinct_I15_J,axiom,
% 0.27/0.47 ! [Name: name,Pi: pi] :
% 0.27/0.47 ( piNil
% 0.27/0.47 != ( res @ Name @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(15)
% 0.27/0.47 thf(fact_25_pi_Odistinct_I11_J,axiom,
% 0.27/0.47 ! [Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( piNil
% 0.27/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(11)
% 0.27/0.47 thf(fact_26_resTrans_I2_J,axiom,
% 0.27/0.47 ! [X2: name,Y2: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y2 @ P ) ) @ Rs ) ).
% 0.27/0.47
% 0.27/0.47 % resTrans(2)
% 0.27/0.47 thf(fact_27_inputFreeTrans,axiom,
% 0.27/0.47 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputFreeTrans
% 0.27/0.47 thf(fact_28_Id,axiom,
% 0.27/0.47 ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 0.27/0.47
% 0.27/0.47 % Id
% 0.27/0.47 thf(fact_29_outputFreshTrans,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.27/0.47 | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % outputFreshTrans
% 0.27/0.47 thf(fact_30_freshFreeDerivative_I1_J,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.27/0.47 => ( fresh @ name @ late_freeRes @ Y2 @ Alpha ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshFreeDerivative(1)
% 0.27/0.47 thf(fact_31_nilSim_I2_J,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 0.27/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % nilSim(2)
% 0.27/0.47 thf(fact_32_resTrans_I1_J,axiom,
% 0.27/0.47 ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 0.27/0.47
% 0.27/0.47 % resTrans(1)
% 0.27/0.47 thf(fact_33_freeRes_Ofresh_I2_J,axiom,
% 0.27/0.47 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.fresh(2)
% 0.27/0.47 thf(fact_34_freshFreeDerivative_I2_J,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.27/0.47 => ( fresh @ name @ pi @ Y2 @ P3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshFreeDerivative(2)
% 0.27/0.47 thf(fact_35_residual_Ostrong__induct,axiom,
% 0.27/0.47 ! [N: $tType] :
% 0.27/0.47 ( ( fs_name @ N )
% 0.27/0.47 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: N] :
% 0.27/0.47 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ Name3 @ Subject )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_induct
% 0.27/0.47 thf(fact_36_residual_Ostrong__inducts,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( fs_name @ A )
% 0.27/0.47 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: A] :
% 0.27/0.47 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ Name3 @ Subject )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_inducts
% 0.27/0.47 thf(fact_37_Par2F,axiom,
% 0.27/0.47 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Par2F
% 0.27/0.47 thf(fact_38_pi_Ofresh_I8_J,axiom,
% 0.27/0.47 ! [A2: name,X22: pi,X1: pi] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.27/0.47 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.27/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(8)
% 0.27/0.47 thf(fact_39_pi_Ofresh_I7_J,axiom,
% 0.27/0.47 ! [A2: name,X22: pi,X1: pi] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 0.27/0.47 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.27/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(7)
% 0.27/0.47 thf(fact_40_pi_Ofresh_I2_J,axiom,
% 0.27/0.47 ! [A2: name,X3: name,X22: name,X1: pi] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ ( output @ X3 @ X22 @ X1 ) )
% 0.27/0.47 = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.27/0.47 & ( fresh @ name @ name @ A2 @ X22 )
% 0.27/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(2)
% 0.27/0.47 thf(fact_41_pi_Ofresh_I1_J,axiom,
% 0.27/0.47 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(1)
% 0.27/0.47 thf(fact_42_residual_Ofresh_I2_J,axiom,
% 0.27/0.47 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.27/0.47 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.27/0.47 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.27/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.fresh(2)
% 0.27/0.47 thf(fact_43_pi_Oinject_I7_J,axiom,
% 0.27/0.47 ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.27/0.47 ( ( ( par @ X22 @ X1 )
% 0.27/0.47 = ( par @ Y22 @ Y1 ) )
% 0.27/0.47 = ( ( X22 = Y22 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.inject(7)
% 0.27/0.47 thf(fact_44_pi_Oinject_I1_J,axiom,
% 0.27/0.47 ! [X3: name,X22: name,X1: pi,Y3: name,Y22: name,Y1: pi] :
% 0.27/0.47 ( ( ( output @ X3 @ X22 @ X1 )
% 0.27/0.47 = ( output @ Y3 @ Y22 @ Y1 ) )
% 0.27/0.47 = ( ( X3 = Y3 )
% 0.27/0.47 & ( X22 = Y22 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.inject(1)
% 0.27/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.27/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.27/0.47 = ( P @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A] :
% 0.27/0.47 ( ( collect @ A
% 0.27/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.27/0.47 = A3 ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_47_Collect__cong,axiom,
% 0.27/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.27/0.47 ( ! [X5: A] :
% 0.27/0.47 ( ( P @ X5 )
% 0.27/0.47 = ( Q @ X5 ) )
% 0.27/0.47 => ( ( collect @ A @ P )
% 0.27/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_cong
% 0.27/0.47 thf(fact_48_pi_Odistinct_I29_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(29)
% 0.27/0.47 thf(fact_49_freshBoundDerivative_I2_J,axiom,
% 0.27/0.47 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.27/0.47 => ( ( Y2 != X2 )
% 0.27/0.47 => ( fresh @ name @ pi @ Y2 @ P3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshBoundDerivative(2)
% 0.27/0.47 thf(fact_50_freshBoundDerivative_I1_J,axiom,
% 0.27/0.47 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.27/0.47 => ( fresh @ name @ late_subject @ Y2 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshBoundDerivative(1)
% 0.27/0.47 thf(fact_51_Late__Semantics_OPar1B,axiom,
% 0.27/0.47 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Par1B
% 0.27/0.47 thf(fact_52_Late__Semantics_OPar2B,axiom,
% 0.27/0.47 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Par2B
% 0.27/0.47 thf(fact_53_parCasesB,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( ! [P2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.27/0.47 => ( Prop @ ( par @ P2 @ Q ) ) )
% 0.27/0.47 => ( ! [Q3: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q3 ) )
% 0.27/0.47 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.27/0.47 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % parCasesB
% 0.27/0.47 thf(fact_54_parCasesB_H,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,B2: late_subject,Y2: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y2 @ P3 ) )
% 0.27/0.47 => ( ! [P4: pi,A4: late_subject,X5: name,P2: pi,Q4: pi] :
% 0.27/0.47 ( ( ( par @ P @ Q )
% 0.27/0.47 = ( par @ P4 @ Q4 ) )
% 0.27/0.47 => ( ( ( late_BoundR @ B2 @ Y2 @ P3 )
% 0.27/0.47 = ( late_BoundR @ A4 @ X5 @ ( par @ P2 @ Q4 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.27/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 0.27/0.47 => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.27/0.47 ( ( ( par @ P @ Q )
% 0.27/0.47 = ( par @ P4 @ Q4 ) )
% 0.27/0.47 => ( ( ( late_BoundR @ B2 @ Y2 @ P3 )
% 0.27/0.47 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.27/0.47 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.27/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % parCasesB'
% 0.27/0.47 thf(fact_55_freshResidual,axiom,
% 0.27/0.47 ! [P: pi,Rs: late_residual,X2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ Rs )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshResidual
% 0.27/0.47 thf(fact_56_transitions_OPar1B,axiom,
% 0.27/0.47 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Par1B
% 0.27/0.47 thf(fact_57_transitions_OPar2B,axiom,
% 0.27/0.47 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Par2B
% 0.27/0.47 thf(fact_58_sumIdempRight,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumIdempRight
% 0.27/0.47 thf(fact_59_sumAssocRight,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumAssocRight
% 0.27/0.47 thf(fact_60_sumIdempLeft,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumIdempLeft
% 0.27/0.47 thf(fact_61_sumAssocLeft,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R ) @ Rel @ ( sum @ P @ ( sum @ Q @ R ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumAssocLeft
% 0.27/0.47 thf(fact_62_sumSym,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumSym
% 0.27/0.47 thf(fact_63_outputBoundTrans,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,C2: late_subject,X2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X2 @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % outputBoundTrans
% 0.27/0.47 thf(fact_64_transitions_OResB,axiom,
% 0.27/0.47 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 0.27/0.47 => ( ( Y2 != X2 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.27/0.47 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P3 ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.ResB
% 0.27/0.47 thf(fact_65_nilSim_I3_J,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.27/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % nilSim(3)
% 0.27/0.47 thf(fact_66_sumZeroRight,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumZeroRight
% 0.27/0.47 thf(fact_67_sumZeroLeft,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumZeroLeft
% 0.27/0.47 thf(fact_68_Late__Semantics_OResB,axiom,
% 0.27/0.47 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 0.27/0.47 => ( ( Y2 != X2 )
% 0.27/0.47 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P3 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.ResB
% 0.27/0.47 thf(fact_69_inputIneqTrans,axiom,
% 0.27/0.47 ! [A2: name,X2: name,P: pi,B2: late_subject,Y2: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y2 @ P3 ) )
% 0.27/0.47 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputIneqTrans
% 0.27/0.47 thf(fact_70_pi_Odistinct_I85_J,axiom,
% 0.27/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.27/0.47 ( ( par @ Pi1 @ Pi2 )
% 0.27/0.47 != ( res @ Name @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(85)
% 0.27/0.47 thf(fact_71_freshRes,axiom,
% 0.27/0.47 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshRes
% 0.27/0.47 thf(fact_72_residual_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Subject2: late_subject,Name4: name,Pi3: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.27/0.47 ( ( late_BoundR @ Subject2 @ Name4 @ Pi3 )
% 0.27/0.47 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.distinct(1)
% 0.27/0.47 thf(fact_73_residual_Oinducts,axiom,
% 0.27/0.47 ! [P: late_residual > $o,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) )
% 0.27/0.47 => ( ! [FreeRes: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.27/0.47 => ( P @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.inducts
% 0.27/0.47 thf(fact_74_pi_Odistinct_I79_J,axiom,
% 0.27/0.47 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.27/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(79)
% 0.27/0.47 thf(fact_75_pi_Odistinct_I55_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(55)
% 0.27/0.47 thf(fact_76_sumResLeft,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),X2: name,P: pi,Q: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( ( eqvt @ pi @ Rel )
% 0.27/0.47 => ( strong743114133lation @ ( sum @ ( res @ X2 @ P ) @ ( res @ X2 @ Q ) ) @ Rel @ ( res @ X2 @ ( sum @ P @ Q ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sumResLeft
% 0.27/0.47 thf(fact_77_pi_Odistinct_I13_J,axiom,
% 0.27/0.47 ! [Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( piNil
% 0.27/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(13)
% 0.27/0.47 thf(fact_78_outputTauTrans,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % outputTauTrans
% 0.27/0.47 thf(fact_79_pi_Odistinct_I31_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.47 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( res @ Name @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(31)
% 0.27/0.47 thf(fact_80_pi_Odistinct_I27_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(27)
% 0.27/0.47 thf(fact_81_pi_Odistinct_I21_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.47 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(21)
% 0.27/0.47 thf(fact_82_pi_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Name1: name,Name2: name,Pi: pi] :
% 0.27/0.47 ( piNil
% 0.27/0.47 != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(1)
% 0.27/0.47 thf(fact_83_nilSimRight,axiom,
% 0.27/0.47 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.27/0.47
% 0.27/0.47 % nilSimRight
% 0.27/0.47 thf(fact_84_resOutputTauTrans,axiom,
% 0.27/0.47 ! [X2: name,A2: name,B2: name,P: pi,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resOutputTauTrans
% 0.27/0.47 thf(fact_85_Par1F,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Par1F
% 0.27/0.47 thf(fact_86_Strong__Late__Sim_Oreflexive,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % Strong_Late_Sim.reflexive
% 0.27/0.47 thf(fact_87_subset__antisym,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.27/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 0.27/0.47 => ( A3 = B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_antisym
% 0.27/0.47 thf(fact_88_subsetI,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.27/0.47 ( ! [X5: A] :
% 0.27/0.47 ( ( member @ A @ X5 @ A3 )
% 0.27/0.47 => ( member @ A @ X5 @ B3 ) )
% 0.27/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % subsetI
% 0.27/0.47 thf(fact_89_monotonic,axiom,
% 0.27/0.47 ! [P: pi,A3: set @ ( product_prod @ pi @ pi ),P3: pi,B3: set @ ( product_prod @ pi @ pi )] :
% 0.27/0.47 ( ( strong743114133lation @ P @ A3 @ P3 )
% 0.27/0.47 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 0.27/0.47 => ( strong743114133lation @ P @ B3 @ P3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % monotonic
% 0.27/0.47 thf(fact_90_order__refl,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( preorder @ A )
% 0.27/0.47 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_refl
% 0.27/0.47 thf(fact_91_resOutputInputTrans,axiom,
% 0.27/0.47 ! [X2: name,A2: name,B2: name,P: pi,C2: name,Y2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y2 @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resOutputInputTrans
% 0.27/0.47 thf(fact_92_resInputBoundOutputTrans,axiom,
% 0.27/0.47 ! [X2: name,A2: name,Y2: name,P: pi,B2: name,Z: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resInputBoundOutputTrans
% 0.27/0.47 thf(fact_93_freeRes_Orecs_I2_J,axiom,
% 0.27/0.47 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T] :
% 0.27/0.47 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.27/0.47 => ( ( P @ F2 )
% 0.27/0.47 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ late_TauR )
% 0.27/0.47 = F2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.recs(2)
% 0.27/0.47 thf(fact_94_resOutputOutputTrans,axiom,
% 0.27/0.47 ! [X2: name,A2: name,P: pi,B2: name,Y2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y2 ) @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resOutputOutputTrans
% 0.27/0.47 thf(fact_95_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.27/0.47 ! [X22: name,X1: name,Y22: name,Y1: name] :
% 0.27/0.47 ( ( ( late_OutputR @ X22 @ X1 )
% 0.27/0.47 = ( late_OutputR @ Y22 @ Y1 ) )
% 0.27/0.47 = ( ( X22 = Y22 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.freeRes.inject
% 0.27/0.47 thf(fact_96_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X1: name,Y1: name] :
% 0.27/0.47 ( ( ( late_BoundOutputS @ X1 )
% 0.27/0.47 = ( late_BoundOutputS @ Y1 ) )
% 0.27/0.47 = ( X1 = Y1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.subject.inject(2)
% 0.27/0.47 thf(fact_97_name__fresh,axiom,
% 0.27/0.47 ( ( fresh @ name @ name )
% 0.27/0.47 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh
% 0.27/0.47 thf(fact_98_subject_Ofresh_I1_J,axiom,
% 0.27/0.47 ! [A2: name,X1: name] :
% 0.27/0.47 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.27/0.47 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.fresh(1)
% 0.27/0.47 thf(fact_99_subject_Ofresh_I2_J,axiom,
% 0.27/0.47 ! [A2: name,X1: name] :
% 0.27/0.47 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.27/0.47 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.fresh(2)
% 0.27/0.47 thf(fact_100_freeRes_Ofresh_I1_J,axiom,
% 0.27/0.47 ! [A2: name,X22: name,X1: name] :
% 0.27/0.47 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.27/0.47 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.27/0.47 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.fresh(1)
% 0.27/0.47 thf(fact_101_subject_Ostrong__inducts,axiom,
% 0.27/0.47 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 0.27/0.47 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.27/0.47 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.27/0.47 => ( P @ Z @ Subject2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.strong_inducts
% 0.27/0.47 thf(fact_102_subject_Ostrong__induct_H,axiom,
% 0.27/0.47 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 0.27/0.47 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.27/0.47 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.27/0.47 => ( P @ Z @ Subject2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.strong_induct'
% 0.27/0.47 thf(fact_103_subject_Oinducts,axiom,
% 0.27/0.47 ! [P: late_subject > $o,Subject2: late_subject] :
% 0.27/0.47 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.27/0.47 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.27/0.47 => ( P @ Subject2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.inducts
% 0.27/0.47 thf(fact_104_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Name4: name,Name: name] :
% 0.27/0.47 ( ( late_InputS @ Name4 )
% 0.27/0.47 != ( late_BoundOutputS @ Name ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.subject.distinct(1)
% 0.27/0.47 thf(fact_105_freeRes_Orecs_I1_J,axiom,
% 0.27/0.47 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T,Name12: name,Name22: name] :
% 0.27/0.47 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.27/0.47 => ( ( P @ F2 )
% 0.27/0.47 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ ( late_OutputR @ Name12 @ Name22 ) )
% 0.27/0.47 = ( F1 @ Name12 @ Name22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.recs(1)
% 0.27/0.47 thf(fact_106_freeRes_Ostrong__inducts,axiom,
% 0.27/0.47 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.27/0.47 ( ! [Name13: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.27/0.47 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.27/0.47 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.strong_inducts
% 0.27/0.47 thf(fact_107_freeRes_Ostrong__induct_H,axiom,
% 0.27/0.47 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.27/0.47 ( ! [Name13: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.27/0.47 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.27/0.47 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.strong_induct'
% 0.27/0.47 thf(fact_108_freeRes_Oinducts,axiom,
% 0.27/0.47 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.27/0.47 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.27/0.47 => ( ( P @ late_TauR )
% 0.27/0.47 => ( P @ FreeRes3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.inducts
% 0.27/0.47 thf(fact_109_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name] :
% 0.27/0.47 ( ( late_OutputR @ Name12 @ Name22 )
% 0.27/0.47 != late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.freeRes.distinct(1)
% 0.27/0.47 thf(fact_110_Open,axiom,
% 0.27/0.47 ! [P: pi,A2: name,B2: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Open
% 0.27/0.47 thf(fact_111_le__funD,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType] :
% 0.27/0.47 ( ( ord @ B )
% 0.27/0.47 => ! [F3: A > B,G: A > B,X2: A] :
% 0.27/0.47 ( ( ord_less_eq @ ( A > B ) @ F3 @ G )
% 0.27/0.47 => ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_funD
% 0.27/0.47 thf(fact_112_le__funE,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType] :
% 0.27/0.47 ( ( ord @ B )
% 0.27/0.47 => ! [F3: A > B,G: A > B,X2: A] :
% 0.27/0.47 ( ( ord_less_eq @ ( A > B ) @ F3 @ G )
% 0.27/0.47 => ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_funE
% 0.27/0.47 thf(fact_113_le__funI,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType] :
% 0.27/0.47 ( ( ord @ B )
% 0.27/0.47 => ! [F3: A > B,G: A > B] :
% 0.27/0.47 ( ! [X5: A] : ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( G @ X5 ) )
% 0.27/0.47 => ( ord_less_eq @ ( A > B ) @ F3 @ G ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_funI
% 0.27/0.47 thf(fact_114_le__fun__def,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType] :
% 0.27/0.47 ( ( ord @ B )
% 0.27/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.27/0.47 = ( ^ [F4: A > B,G2: A > B] :
% 0.27/0.47 ! [X4: A] : ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_fun_def
% 0.27/0.47 thf(fact_115_order__subst1,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType] :
% 0.27/0.47 ( ( ( order @ B )
% 0.27/0.47 & ( order @ A ) )
% 0.27/0.47 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A2 @ ( F3 @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.27/0.47 => ( ! [X5: B,Y: B] :
% 0.27/0.47 ( ( ord_less_eq @ B @ X5 @ Y )
% 0.27/0.47 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.27/0.47 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst1
% 0.27/0.47 thf(fact_116_order__subst2,axiom,
% 0.27/0.47 ! [A: $tType,C3: $tType] :
% 0.27/0.47 ( ( ( order @ C3 )
% 0.27/0.47 & ( order @ A ) )
% 0.27/0.47 => ! [A2: A,B2: A,F3: A > C3,C2: C3] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq @ C3 @ ( F3 @ B2 ) @ C2 )
% 0.27/0.47 => ( ! [X5: A,Y: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ X5 @ Y )
% 0.27/0.47 => ( ord_less_eq @ C3 @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.27/0.47 => ( ord_less_eq @ C3 @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst2
% 0.27/0.47 thf(fact_117_ord__eq__le__subst,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType] :
% 0.27/0.47 ( ( ( ord @ B )
% 0.27/0.47 & ( ord @ A ) )
% 0.27/0.47 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F3 @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.27/0.47 => ( ! [X5: B,Y: B] :
% 0.27/0.47 ( ( ord_less_eq @ B @ X5 @ Y )
% 0.27/0.47 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.27/0.47 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_subst
% 0.27/0.47 thf(fact_118_ord__le__eq__subst,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType] :
% 0.27/0.47 ( ( ( ord @ B )
% 0.27/0.47 & ( ord @ A ) )
% 0.27/0.47 => ! [A2: A,B2: A,F3: A > B,C2: B] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F3 @ B2 )
% 0.27/0.47 = C2 )
% 0.27/0.47 => ( ! [X5: A,Y: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ X5 @ Y )
% 0.27/0.47 => ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.27/0.47 => ( ord_less_eq @ B @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_subst
% 0.27/0.47 thf(fact_119_eq__iff,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.27/0.47 = ( ^ [X4: A,Y5: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.27/0.47 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_iff
% 0.27/0.47 thf(fact_120_antisym,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ! [X2: A,Y2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.27/0.47 => ( X2 = Y2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym
% 0.27/0.47 thf(fact_121_linear,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( linorder @ A )
% 0.27/0.47 => ! [X2: A,Y2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.27/0.47 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % linear
% 0.27/0.47 thf(fact_122_eq__refl,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( preorder @ A )
% 0.27/0.47 => ! [X2: A,Y2: A] :
% 0.27/0.47 ( ( X2 = Y2 )
% 0.27/0.47 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_refl
% 0.27/0.47 thf(fact_123_le__cases,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( linorder @ A )
% 0.27/0.47 => ! [X2: A,Y2: A] :
% 0.27/0.47 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.27/0.47 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_cases
% 0.27/0.47 thf(fact_124_order_Otrans,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.27/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.trans
% 0.27/0.47 thf(fact_125_le__cases3,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( linorder @ A )
% 0.27/0.47 => ! [X2: A,Y2: A,Z: A] :
% 0.27/0.47 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.27/0.47 => ~ ( ord_less_eq @ A @ Y2 @ Z ) )
% 0.27/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.27/0.47 => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 0.27/0.47 => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 0.27/0.47 => ~ ( ord_less_eq @ A @ Z @ Y2 ) )
% 0.27/0.47 => ( ( ( ord_less_eq @ A @ Z @ Y2 )
% 0.27/0.47 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.27/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ Z )
% 0.27/0.47 => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 0.27/0.47 => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 0.27/0.47 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_cases3
% 0.27/0.47 thf(fact_126_antisym__conv,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ! [Y2: A,X2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.27/0.47 = ( X2 = Y2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv
% 0.27/0.47 thf(fact_127_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.27/0.47 = ( ^ [A5: A,B4: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.27/0.47 & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.eq_iff
% 0.27/0.47 thf(fact_128_ord__eq__le__trans,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( ord @ A )
% 0.27/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.27/0.47 ( ( A2 = B2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.27/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_trans
% 0.27/0.47 thf(fact_129_ord__le__eq__trans,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( ord @ A )
% 0.27/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.27/0.47 => ( ( B2 = C2 )
% 0.27/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_trans
% 0.27/0.47 thf(fact_130_order__class_Oorder_Oantisym,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ! [A2: A,B2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.27/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.antisym
% 0.27/0.47 thf(fact_131_order__trans,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( preorder @ A )
% 0.27/0.47 => ! [X2: A,Y2: A,Z: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ Y2 @ Z )
% 0.27/0.47 => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_trans
% 0.27/0.47 thf(fact_132_dual__order_Orefl,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.refl
% 0.27/0.47 thf(fact_133_linorder__wlog,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( linorder @ A )
% 0.27/0.47 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.27/0.47 ( ! [A4: A,B5: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ A4 @ B5 )
% 0.27/0.47 => ( P @ A4 @ B5 ) )
% 0.27/0.47 => ( ! [A4: A,B5: A] :
% 0.27/0.47 ( ( P @ B5 @ A4 )
% 0.27/0.47 => ( P @ A4 @ B5 ) )
% 0.27/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % linorder_wlog
% 0.27/0.47 thf(fact_134_dual__order_Otrans,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.27/0.47 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.trans
% 0.27/0.47 thf(fact_135_dual__order_Oeq__iff,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.27/0.47 = ( ^ [A5: A,B4: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.27/0.47 & ( ord_less_eq @ A @ A5 @ B4 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.eq_iff
% 0.27/0.47 thf(fact_136_dual__order_Oantisym,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( order @ A )
% 0.27/0.47 => ! [B2: A,A2: A] :
% 0.27/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.27/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.antisym
% 0.27/0.47 thf(fact_137_in__mono,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,X2: A] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.27/0.47 => ( ( member @ A @ X2 @ A3 )
% 0.27/0.47 => ( member @ A @ X2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_mono
% 0.27/0.47 thf(fact_138_subsetD,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,C2: A] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.27/0.47 => ( ( member @ A @ C2 @ A3 )
% 0.27/0.47 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subsetD
% 0.27/0.47 thf(fact_139_equalityE,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.27/0.47 ( ( A3 = B3 )
% 0.27/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.27/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityE
% 0.27/0.47 thf(fact_140_subset__eq,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.27/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.27/0.47 ! [X4: A] :
% 0.27/0.47 ( ( member @ A @ X4 @ A6 )
% 0.27/0.47 => ( member @ A @ X4 @ B6 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_eq
% 0.27/0.47 thf(fact_141_equalityD1,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.27/0.47 ( ( A3 = B3 )
% 0.27/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityD1
% 0.27/0.47 thf(fact_142_equalityD2,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.27/0.47 ( ( A3 = B3 )
% 0.27/0.47 => ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityD2
% 0.27/0.47 thf(fact_143_subset__iff,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.27/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.27/0.47 ! [T2: A] :
% 0.27/0.47 ( ( member @ A @ T2 @ A6 )
% 0.27/0.47 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_iff
% 0.27/0.47 thf(fact_144_subset__refl,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.27/0.47
% 0.27/0.47 % subset_refl
% 0.27/0.47 thf(fact_145_Collect__mono,axiom,
% 0.27/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.27/0.47 ( ! [X5: A] :
% 0.27/0.47 ( ( P @ X5 )
% 0.27/0.47 => ( Q @ X5 ) )
% 0.27/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mono
% 0.27/0.47 thf(fact_146_subset__trans,axiom,
% 0.27/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,C4: set @ A] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.27/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C4 )
% 0.27/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_trans
% 0.27/0.47 thf(fact_147_set__eq__subset,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 0.27/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.27/0.47 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % set_eq_subset
% 0.27/0.47 thf(fact_148_Collect__mono__iff,axiom,
% 0.27/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.27/0.47 = ( ! [X4: A] :
% 0.27/0.47 ( ( P @ X4 )
% 0.27/0.47 => ( Q @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mono_iff
% 0.27/0.47 thf(fact_149_resCasesB_H,axiom,
% 0.27/0.47 ! [X6: name,P: pi,A2: late_subject,Y6: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y6 @ P3 ) )
% 0.27/0.47 => ( ! [P4: pi,A4: name,B5: name] :
% 0.27/0.47 ( ( ( res @ X6 @ P )
% 0.27/0.47 = ( res @ B5 @ P4 ) )
% 0.27/0.47 => ! [P2: pi] :
% 0.27/0.47 ( ( ( late_BoundR @ A2 @ Y6 @ P3 )
% 0.27/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B5 @ P2 ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B5 ) @ P2 ) )
% 0.27/0.47 => ( A4 = B5 ) ) ) )
% 0.27/0.47 => ~ ! [P4: pi,A4: late_subject,X5: name,P2: pi,Y: name] :
% 0.27/0.47 ( ( ( res @ X6 @ P )
% 0.27/0.47 = ( res @ Y @ P4 ) )
% 0.27/0.47 => ( ( ( late_BoundR @ A2 @ Y6 @ P3 )
% 0.27/0.47 = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P2 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P2 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 0.27/0.47 => ( ( Y != X5 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.27/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCasesB'
% 0.27/0.47 thf(fact_150_Output,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % Output
% 0.27/0.47 thf(fact_151_outputIneqTrans,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,C2: name,D: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D ) @ P3 ) )
% 0.27/0.47 => ~ ( ( A2 != C2 )
% 0.27/0.47 | ( B2 != D ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % outputIneqTrans
% 0.27/0.47 thf(fact_152_outputCases_H,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 0.27/0.47 => ~ ! [A4: name,B5: name,P4: pi] :
% 0.27/0.47 ( ( ( A2 = A4 )
% 0.27/0.47 & ( B2 = B5 )
% 0.27/0.47 & ( P = P4 ) )
% 0.27/0.47 => ( Rs
% 0.27/0.47 != ( late_FreeR @ ( late_OutputR @ A4 @ B5 ) @ P4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % outputCases'
% 0.27/0.47 thf(fact_153_outputCases,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( ( Alpha
% 0.27/0.47 = ( late_OutputR @ A2 @ B2 ) )
% 0.27/0.47 => ( ( P = P3 )
% 0.27/0.47 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 0.27/0.47 => ( Prop @ Alpha @ P3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % outputCases
% 0.27/0.47 thf(fact_154_Late__Semantics_OInput,axiom,
% 0.27/0.47 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Input
% 0.27/0.47 thf(fact_155_transitions_OInput,axiom,
% 0.27/0.47 ! [X2: name,A2: name,P: pi] :
% 0.27/0.47 ( ( X2 != A2 )
% 0.27/0.47 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Input
% 0.27/0.47 thf(fact_156_inputBoundOutputTrans,axiom,
% 0.27/0.47 ! [A2: name,X2: name,P: pi,B2: name,Y2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y2 @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputBoundOutputTrans
% 0.27/0.47 thf(fact_157_resCases_H,axiom,
% 0.27/0.47 ! [X2: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 0.27/0.47 => ( ! [P4: pi,A4: name,B5: name] :
% 0.27/0.47 ( ( ( res @ X2 @ P )
% 0.27/0.47 = ( res @ B5 @ P4 ) )
% 0.27/0.47 => ! [P2: pi] :
% 0.27/0.47 ( ( Rs
% 0.27/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B5 @ P2 ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B5 ) @ P2 ) )
% 0.27/0.47 => ( A4 = B5 ) ) ) )
% 0.27/0.47 => ( ! [P4: pi,A4: late_subject,X5: name,P2: pi,Y: name] :
% 0.27/0.47 ( ( ( res @ X2 @ P )
% 0.27/0.47 = ( res @ Y @ P4 ) )
% 0.27/0.47 => ( ( Rs
% 0.27/0.47 = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P2 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P2 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 0.27/0.47 => ( ( Y != X5 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.27/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 0.27/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 0.27/0.47 ( ( ( res @ X2 @ P )
% 0.27/0.47 = ( res @ Y @ P4 ) )
% 0.27/0.47 => ( ( Rs
% 0.27/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 0.27/0.47 => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCases'
% 0.27/0.47 thf(fact_158_transitions_OClose2,axiom,
% 0.27/0.47 ! [P: pi,A2: name,Y2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.27/0.47 => ( ( X2 != A2 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 0.27/0.47 => ( ( Y2 != A2 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ Q2 )
% 0.27/0.47 => ( ( X2 != Y2 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Close2
% 0.27/0.47 thf(fact_159_transitions_OClose1,axiom,
% 0.27/0.47 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.27/0.47 => ( ( X2 != A2 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.27/0.47 => ( ( Y2 != A2 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P3 )
% 0.27/0.47 => ( ( X2 != Y2 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Close1
% 0.27/0.47 thf(fact_160_Late__Semantics_OClose2,axiom,
% 0.27/0.47 ! [P: pi,A2: name,Y2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Close2
% 0.27/0.47 thf(fact_161_Late__Semantics_OClose1,axiom,
% 0.27/0.47 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Close1
% 0.27/0.47 thf(fact_162_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X22: name,Y22: name] :
% 0.27/0.47 ( ( ( late_BoundOutputS @ X22 )
% 0.27/0.47 = ( late_BoundOutputS @ Y22 ) )
% 0.27/0.47 = ( X22 = Y22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.subject.inject(2)
% 0.27/0.47 thf(fact_163_subst__identity,axiom,
% 0.27/0.47 ! [P: pi,A2: name] :
% 0.27/0.47 ( ( subs @ P @ A2 @ A2 )
% 0.27/0.47 = P ) ).
% 0.27/0.47
% 0.27/0.47 % subst_identity
% 0.27/0.47 thf(fact_164_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.27/0.47 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.27/0.47 ( ( ( late_OutputR @ X11 @ X122 )
% 0.27/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.27/0.47 = ( ( X11 = Y11 )
% 0.27/0.47 & ( X122 = Y12 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.freeRes.inject
% 0.27/0.47 thf(fact_165_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.27/0.47 ! [X1: name,Y1: name] :
% 0.27/0.47 ( ( ( late_InputS @ X1 )
% 0.27/0.47 = ( late_InputS @ Y1 ) )
% 0.27/0.47 = ( X1 = Y1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.subject.inject(1)
% 0.27/0.47 thf(fact_166_simps_I9_J,axiom,
% 0.27/0.47 ! [X2: name,C2: name,D: name,P: pi] :
% 0.27/0.47 ( ( X2 != C2 )
% 0.27/0.47 => ( ( X2 != D )
% 0.27/0.47 => ( ( subs @ ( res @ X2 @ P ) @ C2 @ D )
% 0.27/0.47 = ( res @ X2 @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simps(9)
% 0.27/0.47 thf(fact_167_simps_I8_J,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.27/0.47 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 0.27/0.47 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simps(8)
% 0.27/0.47 thf(fact_168_substTrans,axiom,
% 0.27/0.47 ! [B2: name,P: pi,A2: name,C2: name] :
% 0.27/0.47 ( ( fresh @ name @ pi @ B2 @ P )
% 0.27/0.47 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 0.27/0.47 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % substTrans
% 0.27/0.47 thf(fact_169_simps_I7_J,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.27/0.47 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D )
% 0.27/0.47 = ( sum @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simps(7)
% 0.27/0.47 thf(fact_170_simps_I1_J,axiom,
% 0.27/0.47 ! [C2: name,D: name] :
% 0.27/0.47 ( ( subs @ piNil @ C2 @ D )
% 0.27/0.47 = piNil ) ).
% 0.27/0.47
% 0.27/0.47 % simps(1)
% 0.27/0.47 thf(fact_171_forget,axiom,
% 0.27/0.47 ! [A2: name,P: pi,B2: name] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ P )
% 0.27/0.47 => ( ( subs @ P @ A2 @ B2 )
% 0.27/0.47 = P ) ) ).
% 0.27/0.47
% 0.27/0.47 % forget
% 0.27/0.47 thf(fact_172_fresh__fact1,axiom,
% 0.27/0.47 ! [A2: name,P: pi,C2: name,B2: name] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ P )
% 0.27/0.47 => ( ( A2 != C2 )
% 0.27/0.47 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_fact1
% 0.27/0.47 thf(fact_173_fresh__fact2,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi] :
% 0.27/0.47 ( ( A2 != B2 )
% 0.27/0.47 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_fact2
% 0.27/0.47 thf(fact_174_substRes3,axiom,
% 0.27/0.47 ! [B2: name,P: pi,A2: name] :
% 0.27/0.47 ( ( fresh @ name @ pi @ B2 @ P )
% 0.27/0.47 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.27/0.47 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % substRes3
% 0.27/0.47 thf(fact_175_substRes2,axiom,
% 0.27/0.47 ! [B2: name,P: pi,A2: name] :
% 0.27/0.47 ( ( fresh @ name @ pi @ B2 @ P )
% 0.27/0.47 => ( ( res @ A2 @ P )
% 0.27/0.47 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % substRes2
% 0.27/0.47 thf(fact_176_freeRes_Oexhaust,axiom,
% 0.27/0.47 ! [Y2: late_freeRes] :
% 0.27/0.47 ( ! [X112: name,X123: name] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( late_OutputR @ X112 @ X123 ) )
% 0.27/0.47 => ( Y2 = late_TauR ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.exhaust
% 0.27/0.47 thf(fact_177_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X11: name,X122: name] :
% 0.27/0.47 ( ( late_OutputR @ X11 @ X122 )
% 0.27/0.47 != late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.freeRes.distinct(1)
% 0.27/0.47 thf(fact_178_subject_Oexhaust,axiom,
% 0.27/0.47 ! [Y2: late_subject] :
% 0.27/0.47 ( ! [X12: name] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( late_InputS @ X12 ) )
% 0.27/0.47 => ~ ! [X23: name] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.exhaust
% 0.27/0.47 thf(fact_179_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X1: name,X22: name] :
% 0.27/0.47 ( ( late_InputS @ X1 )
% 0.27/0.47 != ( late_BoundOutputS @ X22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.subject.distinct(1)
% 0.27/0.47 thf(fact_180_Late__Semantics_OComm1,axiom,
% 0.27/0.47 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Comm1
% 0.27/0.47 thf(fact_181_Late__Semantics_OComm2,axiom,
% 0.27/0.47 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Comm2
% 0.27/0.47 thf(fact_182_transitions_OComm1,axiom,
% 0.27/0.47 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( ( X2 != A2 )
% 0.27/0.47 => ( ( X2 != B2 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Comm1
% 0.27/0.47 thf(fact_183_transitions_OComm2,axiom,
% 0.27/0.47 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.27/0.47 => ( ( X2 != A2 )
% 0.27/0.47 => ( ( X2 != B2 )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Comm2
% 0.27/0.47 thf(fact_184_resSimCases,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( fs_name @ A )
% 0.27/0.47 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C4: A] :
% 0.27/0.47 ( ( eqvt @ pi @ Rel )
% 0.27/0.47 => ( ! [Q3: pi,A4: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q3 ) )
% 0.27/0.47 => ( ( A4 != X2 )
% 0.27/0.47 => ? [P5: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P5 ) )
% 0.27/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 0.27/0.47 => ( ! [Q3: pi,A4: late_subject,Y: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 0.27/0.47 => ( ( X2 != Y )
% 0.27/0.47 => ( ( fresh @ name @ A @ Y @ C4 )
% 0.27/0.47 => ? [P5: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 0.27/0.47 & ( strong2129052853vative @ P5 @ ( res @ X2 @ Q3 ) @ A4 @ Y @ Rel ) ) ) ) ) )
% 0.27/0.47 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.27/0.47 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 0.27/0.47 => ? [P5: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.27/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ ( res @ X2 @ Q3 ) ) @ Rel ) ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resSimCases
% 0.27/0.47 thf(fact_185_simE_I1_J,axiom,
% 0.27/0.47 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 0.27/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.27/0.47 => ? [P2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.27/0.47 & ( strong2129052853vative @ P2 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simE(1)
% 0.27/0.47 thf(fact_186_simCasesCont,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( fs_name @ A )
% 0.27/0.47 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.27/0.47 ( ( eqvt @ pi @ Rel )
% 0.27/0.47 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.27/0.47 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.27/0.47 => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 0.27/0.47 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.27/0.47 => ? [P5: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 0.27/0.47 & ( strong2129052853vative @ P5 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.27/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.27/0.47 => ? [P5: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.27/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simCasesCont
% 0.27/0.47 thf(fact_187_derivativeMonotonic,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,A2: late_subject,X2: name,A3: set @ ( product_prod @ pi @ pi ),B3: set @ ( product_prod @ pi @ pi )] :
% 0.27/0.47 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ A3 )
% 0.27/0.47 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 0.27/0.47 => ( strong2129052853vative @ P @ Q @ A2 @ X2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % derivativeMonotonic
% 0.27/0.47 thf(fact_188_simulation__def,axiom,
% 0.27/0.47 ( strong743114133lation
% 0.27/0.47 = ( ^ [P6: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.27/0.47 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.27/0.47 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.27/0.47 & ( fresh @ name @ pi @ X4 @ P6 ) )
% 0.27/0.47 => ? [P7: pi] :
% 0.27/0.47 ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X4 @ P7 ) )
% 0.27/0.47 & ( strong2129052853vative @ P7 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.27/0.47 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.27/0.47 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.27/0.47 => ? [P7: pi] :
% 0.27/0.47 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 0.27/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simulation_def
% 0.27/0.47 thf(fact_189_simCases,axiom,
% 0.27/0.47 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.27/0.47 ( ! [A4: late_subject,Y: name,Q3: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 0.27/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.27/0.47 => ? [P5: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 0.27/0.47 & ( strong2129052853vative @ P5 @ Q3 @ A4 @ Y @ Rel ) ) ) )
% 0.27/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.27/0.47 => ? [P5: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.27/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simCases
% 0.27/0.47 thf(fact_190_simE_I2_J,axiom,
% 0.27/0.47 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.27/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.47 => ? [P2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.27/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P2 @ Q2 ) @ Rel ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simE(2)
% 0.27/0.47 thf(fact_191_derivativeReflexive,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,A2: late_subject,X2: name] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( strong2129052853vative @ P @ P @ A2 @ X2 @ Rel ) ) ).
% 0.27/0.47
% 0.27/0.47 % derivativeReflexive
% 0.27/0.47 thf(fact_192_pair__in__Id__conv,axiom,
% 0.27/0.47 ! [A: $tType,A2: A,B2: A] :
% 0.27/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.27/0.47 = ( A2 = B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pair_in_Id_conv
% 0.27/0.47 thf(fact_193_IdI,axiom,
% 0.27/0.47 ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % IdI
% 0.27/0.47 thf(fact_194_subrelI,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.27/0.47 ( ! [X5: A,Y: B] :
% 0.27/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ R2 )
% 0.27/0.47 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ S ) )
% 0.27/0.47 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S ) ) ).
% 0.27/0.47
% 0.27/0.47 % subrelI
% 0.27/0.47 thf(fact_195_IdE,axiom,
% 0.27/0.47 ! [A: $tType,P8: product_prod @ A @ A] :
% 0.27/0.47 ( ( member @ ( product_prod @ A @ A ) @ P8 @ ( id @ A ) )
% 0.27/0.47 => ~ ! [X5: A] :
% 0.27/0.47 ( P8
% 0.27/0.47 != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % IdE
% 0.27/0.47 thf(fact_196_fresh__prod,axiom,
% 0.27/0.47 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y2: B] :
% 0.27/0.47 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y2 ) )
% 0.27/0.47 = ( ( fresh @ X @ A @ A2 @ X2 )
% 0.27/0.47 & ( fresh @ X @ B @ A2 @ Y2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_197_old_Oprod_Oinject,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.27/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.27/0.47 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.27/0.47 = ( ( A2 = A7 )
% 0.27/0.47 & ( B2 = B7 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.prod.inject
% 0.27/0.47 thf(fact_198_prod_Oinject,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 0.27/0.47 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.27/0.47 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.27/0.47 = ( ( X1 = Y1 )
% 0.27/0.47 & ( X22 = Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod.inject
% 0.27/0.47 thf(fact_199_surj__pair,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,P8: product_prod @ A @ B] :
% 0.27/0.47 ? [X5: A,Y: B] :
% 0.27/0.47 ( P8
% 0.27/0.47 = ( product_Pair @ A @ B @ X5 @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % surj_pair
% 0.27/0.47 thf(fact_200_prod__cases,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P8: product_prod @ A @ B] :
% 0.27/0.47 ( ! [A4: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B5 ) )
% 0.27/0.47 => ( P @ P8 ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_cases
% 0.27/0.47 thf(fact_201_Pair__inject,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.27/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.27/0.47 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.27/0.47 => ~ ( ( A2 = A7 )
% 0.27/0.47 => ( B2 != B7 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Pair_inject
% 0.27/0.47 thf(fact_202_prod__cases3,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,C3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.27/0.47 ~ ! [A4: A,B5: B,C: C3] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B5 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_cases3
% 0.27/0.47 thf(fact_203_prod__cases4,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 0.27/0.47 ~ ! [A4: A,B5: B,C: C3,D3: D2] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B5 @ ( product_Pair @ C3 @ D2 @ C @ D3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_cases4
% 0.27/0.47 thf(fact_204_prod__cases5,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 0.27/0.47 ~ ! [A4: A,B5: B,C: C3,D3: D2,E2: E] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_cases5
% 0.27/0.47 thf(fact_205_prod__cases6,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F5: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.27/0.47 ~ ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ F5 ) @ D3 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_cases6
% 0.27/0.47 thf(fact_206_prod__cases7,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F5: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 0.27/0.47 ~ ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5,G4: G3] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_cases7
% 0.27/0.47 thf(fact_207_prod__induct3,axiom,
% 0.27/0.47 ! [C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.27/0.47 ( ! [A4: A,B5: B,C: C3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B5 @ C ) ) )
% 0.27/0.47 => ( P @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_induct3
% 0.27/0.47 thf(fact_208_prod__induct4,axiom,
% 0.27/0.47 ! [D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 0.27/0.47 ( ! [A4: A,B5: B,C: C3,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B5 @ ( product_Pair @ C3 @ D2 @ C @ D3 ) ) ) )
% 0.27/0.47 => ( P @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_induct4
% 0.27/0.47 thf(fact_209_prod__induct5,axiom,
% 0.27/0.47 ! [E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 0.27/0.47 ( ! [A4: A,B5: B,C: C3,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 0.27/0.47 => ( P @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_induct5
% 0.27/0.47 thf(fact_210_prod__induct6,axiom,
% 0.27/0.47 ! [F5: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.27/0.47 ( ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ F5 ) @ D3 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 0.27/0.47 => ( P @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_induct6
% 0.27/0.47 thf(fact_211_prod__induct7,axiom,
% 0.27/0.47 ! [G3: $tType,F5: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 0.27/0.47 ( ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) )
% 0.27/0.47 => ( P @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % prod_induct7
% 0.27/0.47 thf(fact_212_old_Oprod_Oexhaust,axiom,
% 0.27/0.47 ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 0.27/0.47 ~ ! [A4: A,B5: B] :
% 0.27/0.47 ( Y2
% 0.27/0.47 != ( product_Pair @ A @ B @ A4 @ B5 ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.prod.exhaust
% 0.27/0.47 thf(fact_213_old_Oprod_Oinducts,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.27/0.47 ( ! [A4: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B5 ) )
% 0.27/0.47 => ( P @ Prod ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.prod.inducts
% 0.27/0.47 thf(fact_214_fresh__prodD_I2_J,axiom,
% 0.27/0.47 ! [B: $tType,A: $tType,C3: $tType,A2: A,X2: B,Y2: C3] :
% 0.27/0.47 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y2 ) )
% 0.27/0.47 => ( fresh @ A @ C3 @ A2 @ Y2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(2)
% 0.27/0.47 thf(fact_215_fresh__prodD_I1_J,axiom,
% 0.27/0.47 ! [C3: $tType,A: $tType,B: $tType,A2: A,X2: B,Y2: C3] :
% 0.27/0.47 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y2 ) )
% 0.27/0.47 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(1)
% 0.27/0.47 thf(fact_216_old_Oprod_Orec,axiom,
% 0.27/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.27/0.47 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.27/0.47 = ( F1 @ A2 @ B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.prod.rec
% 0.27/0.47 thf(fact_217_IdD,axiom,
% 0.27/0.47 ! [A: $tType,A2: A,B2: A] :
% 0.27/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.27/0.47 => ( A2 = B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % IdD
% 0.27/0.47 thf(fact_218_subject_Orecs_I2_J,axiom,
% 0.27/0.47 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name4: name] :
% 0.27/0.47 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.27/0.47 => ( ! [X12: name] : ( P @ ( F2 @ X12 ) )
% 0.27/0.47 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_BoundOutputS @ Name4 ) )
% 0.27/0.47 = ( F2 @ Name4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.recs(2)
% 0.27/0.47 thf(fact_219_subject_Orecs_I1_J,axiom,
% 0.27/0.47 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name4: name] :
% 0.27/0.47 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.27/0.47 => ( ! [X12: name] : ( P @ ( F2 @ X12 ) )
% 0.27/0.47 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_InputS @ Name4 ) )
% 0.27/0.47 = ( F1 @ Name4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.recs(1)
% 0.27/0.47 thf(fact_220_resTauOutputTrans,axiom,
% 0.27/0.47 ! [X2: name,P: pi,A2: name,B2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resTauOutputTrans
% 0.27/0.47 thf(fact_221_residual_Ofresh_I1_J,axiom,
% 0.27/0.47 ! [A2: name,X3: late_subject,X1: name,X22: pi] :
% 0.27/0.47 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X3 @ X1 @ X22 ) )
% 0.27/0.47 = ( ( fresh @ name @ late_subject @ A2 @ X3 )
% 0.27/0.47 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.fresh(1)
% 0.27/0.47 thf(fact_222_pi_Ofresh_I3_J,axiom,
% 0.27/0.47 ! [A2: name,X1: pi] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.27/0.47 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(3)
% 0.27/0.47 thf(fact_223_simps_I2_J,axiom,
% 0.27/0.47 ! [P: pi,C2: name,D: name] :
% 0.27/0.47 ( ( subs @ ( tau @ P ) @ C2 @ D )
% 0.27/0.47 = ( tau @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simps(2)
% 0.27/0.47 thf(fact_224_pi_Ofresh_I9_J,axiom,
% 0.27/0.47 ! [A2: name,X1: name,X22: pi] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.27/0.47 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(9)
% 0.27/0.47 thf(fact_225_pi_Ofresh_I4_J,axiom,
% 0.27/0.47 ! [A2: name,X3: name,X1: name,X22: pi] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ ( input @ X3 @ X1 @ X22 ) )
% 0.27/0.47 = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.27/0.47 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(4)
% 0.27/0.47 thf(fact_226_name__fresh__abs,axiom,
% 0.27/0.47 ! [A: $tType] :
% 0.27/0.47 ( ( fs_name @ A )
% 0.27/0.47 => ! [B2: name,A2: name,X2: A] :
% 0.27/0.47 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 0.27/0.47 = ( ( B2 = A2 )
% 0.27/0.47 | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_abs
% 0.27/0.47 thf(fact_227_abs__fresh_I1_J,axiom,
% 0.27/0.47 ! [X7: $tType] :
% 0.27/0.47 ( ( fs_name @ X7 )
% 0.27/0.47 => ! [B2: name,A2: name,X2: X7] :
% 0.27/0.47 ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B2 @ ( abs_fun @ name @ X7 @ A2 @ X2 ) )
% 0.27/0.47 = ( ( B2 = A2 )
% 0.27/0.47 | ( fresh @ name @ X7 @ B2 @ X2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abs_fresh(1)
% 0.27/0.47 thf(fact_228_pi_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X1: pi,Y1: pi] :
% 0.27/0.47 ( ( ( tau @ X1 )
% 0.27/0.47 = ( tau @ Y1 ) )
% 0.27/0.47 = ( X1 = Y1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.inject(2)
% 0.27/0.47 thf(fact_229_pi_Odistinct_I3_J,axiom,
% 0.27/0.47 ! [Pi: pi] :
% 0.27/0.47 ( piNil
% 0.27/0.47 != ( tau @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(3)
% 0.27/0.47 thf(fact_230_pi_Odistinct_I19_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.27/0.47 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( tau @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(19)
% 0.27/0.47 thf(fact_231_pi_Odistinct_I35_J,axiom,
% 0.27/0.47 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.47 ( ( tau @ Pi3 )
% 0.27/0.47 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(35)
% 0.27/0.47 thf(fact_232_pi_Odistinct_I41_J,axiom,
% 0.27/0.47 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( tau @ Pi3 )
% 0.27/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(41)
% 0.27/0.47 thf(fact_233_pi_Odistinct_I43_J,axiom,
% 0.27/0.47 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( tau @ Pi3 )
% 0.27/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(43)
% 0.27/0.47 thf(fact_234_pi_Odistinct_I45_J,axiom,
% 0.27/0.47 ! [Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.47 ( ( tau @ Pi3 )
% 0.27/0.47 != ( res @ Name @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(45)
% 0.27/0.47 thf(fact_235_pi_Oinject_I3_J,axiom,
% 0.27/0.47 ! [X3: name,X1: name,X22: pi,Y3: name,Y1: name,Y22: pi] :
% 0.27/0.47 ( ( ( input @ X3 @ X1 @ X22 )
% 0.27/0.47 = ( input @ Y3 @ Y1 @ Y22 ) )
% 0.27/0.47 = ( ( X3 = Y3 )
% 0.27/0.47 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.27/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.inject(3)
% 0.27/0.47 thf(fact_236_residual_Oinject_I1_J,axiom,
% 0.27/0.47 ! [X3: late_subject,X1: name,X22: pi,Y3: late_subject,Y1: name,Y22: pi] :
% 0.27/0.47 ( ( ( late_BoundR @ X3 @ X1 @ X22 )
% 0.27/0.47 = ( late_BoundR @ Y3 @ Y1 @ Y22 ) )
% 0.27/0.47 = ( ( X3 = Y3 )
% 0.27/0.47 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.27/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.inject(1)
% 0.27/0.47 thf(fact_237_pi_Oinject_I8_J,axiom,
% 0.27/0.47 ! [X1: name,X22: pi,Y1: name,Y22: pi] :
% 0.27/0.47 ( ( ( res @ X1 @ X22 )
% 0.27/0.47 = ( res @ Y1 @ Y22 ) )
% 0.27/0.47 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.27/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.inject(8)
% 0.27/0.47 thf(fact_238_tauBoundTrans,axiom,
% 0.27/0.47 ! [P: pi,A2: late_subject,X2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % tauBoundTrans
% 0.27/0.47 thf(fact_239_nilSim_I1_J,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.27/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % nilSim(1)
% 0.27/0.47 thf(fact_240_resTauBoundTrans,axiom,
% 0.27/0.47 ! [X2: name,P: pi,A2: late_subject,Y2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y2 @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resTauBoundTrans
% 0.27/0.47 thf(fact_241_tauOutputTrans,axiom,
% 0.27/0.47 ! [P: pi,A2: name,B2: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % tauOutputTrans
% 0.27/0.47 thf(fact_242_tauCases,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( ( Alpha = late_TauR )
% 0.27/0.47 => ( ( P = P3 )
% 0.27/0.47 => ( Prop @ late_TauR @ P ) ) )
% 0.27/0.47 => ( Prop @ Alpha @ P3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % tauCases
% 0.27/0.47 thf(fact_243_tauCases_H,axiom,
% 0.27/0.47 ! [P: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.27/0.47 => ~ ! [P4: pi] :
% 0.27/0.47 ( ( ( tau @ P )
% 0.27/0.47 = ( tau @ P4 ) )
% 0.27/0.47 => ( Rs
% 0.27/0.47 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % tauCases'
% 0.27/0.47 thf(fact_244_Tau,axiom,
% 0.27/0.47 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % Tau
% 0.27/0.47 thf(fact_245_inputCases_H,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 0.27/0.47 => ~ ! [X5: name,A4: name,P4: pi] :
% 0.27/0.47 ( ( ( A2 = A4 )
% 0.27/0.47 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 0.27/0.47 = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 0.27/0.47 => ( ( Rs
% 0.27/0.47 = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P4 ) )
% 0.27/0.47 => ( X5 = A4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputCases'
% 0.27/0.47 thf(fact_246_mismatchIdRight,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A2 @ B2 @ P ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mismatchIdRight
% 0.27/0.47 thf(fact_247_mismatchIdLeft,axiom,
% 0.27/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.27/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( strong743114133lation @ ( mismatch @ A2 @ B2 @ P ) @ Rel @ P ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mismatchIdLeft
% 0.27/0.47 thf(fact_248_pi_Ofresh_I6_J,axiom,
% 0.27/0.47 ! [A2: name,X3: name,X22: name,X1: pi] :
% 0.27/0.47 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X3 @ X22 @ X1 ) )
% 0.27/0.47 = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.27/0.47 & ( fresh @ name @ name @ A2 @ X22 )
% 0.27/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(6)
% 0.27/0.47 thf(fact_249_pi_Odistinct_I39_J,axiom,
% 0.27/0.47 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.47 ( ( tau @ Pi3 )
% 0.27/0.47 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(39)
% 0.27/0.47 thf(fact_250_mismatchCases,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.27/0.47 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.27/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( F @ A2 @ B2 ) ) )
% 0.27/0.47 => ( F @ A2 @ B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mismatchCases
% 0.27/0.47 thf(fact_251_mismatchTrans,axiom,
% 0.27/0.47 ! [A2: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.27/0.47
% 0.27/0.47 % mismatchTrans
% 0.27/0.47 thf(fact_252_mismatchCases_H,axiom,
% 0.27/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.27/0.47 => ~ ! [P4: pi,A4: name,B5: name] :
% 0.27/0.47 ( ( ( A2 = A4 )
% 0.27/0.47 & ( B2 = B5 )
% 0.27/0.47 & ( P = P4 ) )
% 0.27/0.47 => ( ( late_transitions @ P4 @ Rs )
% 0.27/0.47 => ( A4 = B5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mismatchCases'
% 0.27/0.47 thf(fact_253_Mismatch,axiom,
% 0.27/0.47 ! [P: pi,Rs: late_residual,A2: name,B2: name] :
% 0.27/0.47 ( ( late_transitions @ P @ Rs )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Mismatch
% 0.27/0.47 thf(fact_254_pi_Odistinct_I75_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.47 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( res @ Name @ Pi ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(75)
% 0.27/0.47 thf(fact_255_pi_Odistinct_I73_J,axiom,
% 0.27/0.47 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.27/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(73)
% 0.27/0.47
% 0.27/0.47 % Type constructors (17)
% 0.27/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.27/0.47 ! [A8: $tType,A9: $tType] :
% 0.27/0.47 ( ( preorder @ A9 )
% 0.27/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.27/0.47 ! [A8: $tType,A9: $tType] :
% 0.27/0.47 ( ( order @ A9 )
% 0.27/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.27/0.47 ! [A8: $tType,A9: $tType] :
% 0.27/0.47 ( ( ord @ A9 )
% 0.27/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 0.27/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.27/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 0.27/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.27/0.47 fs_name @ pi ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.27/0.47 preorder @ $o ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.27/0.47 linorder @ $o ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 0.27/0.47 order @ $o ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 0.27/0.47 ord @ $o ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_HOL_Obool___Agent_Ofs__name_7,axiom,
% 0.27/0.47 fs_name @ $o ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Agent_Oname___Agent_Ofs__name_8,axiom,
% 0.27/0.47 fs_name @ name ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9,axiom,
% 0.27/0.47 ! [A8: $tType,A9: $tType] :
% 0.27/0.47 ( ( ( fs_name @ A8 )
% 0.27/0.47 & ( fs_name @ A9 ) )
% 0.27/0.47 => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10,axiom,
% 0.27/0.47 fs_name @ late_freeRes ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 0.27/0.47 fs_name @ late_subject ).
% 0.27/0.47
% 0.27/0.47 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12,axiom,
% 0.27/0.47 fs_name @ late_residual ).
% 0.27/0.47
% 0.27/0.47 % Conjectures (1)
% 0.27/0.47 thf(conj_0,conjecture,
% 0.27/0.47 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 0.31/1.50 ---- Embedded in THF ---
% 0.31/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.50 %%% Generated on Tue Feb 24 08:29:07 EST 2026
% 0.31/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.50 %%% Logic specification used:
% 0.31/1.50 %%% thf(spec, logic, $$dhol).
% 0.31/1.50
% 0.31/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pF5X09mbQh/DTF2DTF1767.p
% 0.31/1.50 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 0.31/1.50 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 0.31/1.50 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 0.31/1.50 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.31/1.50 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_Agent_Oname, type, name: $tType).
% 0.31/1.50 thf(ty_t_Agent_Opi, type, pi: $tType).
% 0.31/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.31/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 0.31/1.50 thf(sy_c_Agent_Opi_OMismatch, type, mismatch: (name > (name > (pi > pi)))).
% 0.31/1.50 thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 0.31/1.50 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 0.31/1.50 thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 0.31/1.50 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 0.31/1.50 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 0.31/1.50 thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 0.31/1.50 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 0.31/1.50 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 0.31/1.50 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 0.31/1.50 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 0.31/1.50 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 0.31/1.50 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 0.31/1.50 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 0.31/1.50 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 0.31/1.50 thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 0.31/1.50 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 0.31/1.50 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 0.31/1.50 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 0.31/1.50 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 0.31/1.50 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 0.31/1.50 thf(sy_c_Relation_OId, type, id: (!> [A:$tType]: ((set @ ((product_prod @ A) @ A))))).
% 0.31/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.31/1.50 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 0.31/1.50 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 0.31/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.31/1.50 thf(sy_v_P, type, p: pi).
% 0.31/1.50 thf(sy_v_PQ____, type, pq: pi).
% 0.31/1.50 thf(sy_v_Q, type, q: pi).
% 0.31/1.50 thf(sy_v_Q_H____, type, q2: pi).
% 0.31/1.50 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 0.31/1.50 thf(sy_v__092_060alpha_062____, type, alpha: late_freeRes).
% 0.31/1.50 thf(sy_v_x, type, x: name).
% 0.31/1.50 thf(fact_0_cRes_Ohyps_I2_J, axiom, ((((fresh @ name) @ late_freeRes) @ x) @ alpha)).
% 0.31/1.50 thf(fact_1_Eqvt, axiom, ((eqvt @ pi) @ rel)).
% 0.31/1.50 thf(fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062, axiom, ((late_transitions @ ((sum @ p) @ q)) @ ((late_FreeR @ alpha) @ q2))).
% 0.31/1.50 thf(fact_3_cRes_Ohyps_I1_J, axiom, ((late_transitions @ q) @ ((late_FreeR @ alpha) @ q2))).
% 0.31/1.50 thf(fact_4_cSum2_Ohyps, axiom, ((late_transitions @ ((res @ x) @ q)) @ ((late_FreeR @ alpha) @ pq))).
% 0.31/1.50 thf(fact_5_Free_Ohyps, axiom, ((late_transitions @ ((sum @ ((res @ x) @ p)) @ ((res @ x) @ q))) @ ((late_FreeR @ alpha) @ pq))).
% 0.31/1.50 thf(fact_6_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((sum @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 0.31/1.50 thf(fact_7_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 0.31/1.50 thf(fact_8_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 0.31/1.50 thf(fact_9_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 0.31/1.50 thf(fact_10_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 0.31/1.50 thf(fact_11_resCasesF, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,XP:pi,F:(pi > $o)]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha) => (F @ ((res @ X2) @ P2)))))) => (F @ XP)))))).
% 0.31/1.50 thf(fact_12_resCasesF_H, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,P3:pi]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P3)) => (~ ((! [P4:pi,Alpha2:late_freeRes,P2:pi,Y:name]: (((((res @ X2) @ P) = ((res @ Y) @ P4)) => ((((late_FreeR @ Alpha) @ P3) = ((late_FreeR @ Alpha2) @ ((res @ Y) @ P2))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P2)) => (~ (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha2)))))))))))))).
% 0.31/1.50 thf(fact_13_ResF, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Y2:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ late_freeRes) @ Y2) @ Alpha) => ((late_transitions @ ((res @ Y2) @ P)) @ ((late_FreeR @ Alpha) @ ((res @ Y2) @ P3)))))))).
% 0.31/1.50 thf(fact_14_pi_Oinject_I6_J, axiom, (! [X22:pi,X1:pi,Y22:pi,Y1:pi]: (((((sum @ X22) @ X1) = ((sum @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 0.31/1.50 thf(fact_15_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y22:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 0.31/1.50 thf(fact_16_resInputFreeTrans, axiom, (! [X2:name,A2:name,Y2:name,P:pi,Alpha:late_freeRes,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y2) @ P))) @ ((late_FreeR @ Alpha) @ P3))))))).
% 0.31/1.50 thf(fact_17_resZeroTrans, axiom, (! [X2:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ piNil)) @ Rs)))))).
% 0.31/1.50 thf(fact_18_pi_Odistinct_I5_J, axiom, (! [Name1:name,Name2:name,Pi:pi]: ((piNil != (((input @ Name1) @ Name2) @ Pi))))).
% 0.31/1.50 thf(fact_19_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X2:A]: ((~ ((! [C:name]: ((~ (((((fresh @ name) @ A) @ C) @ X2))))))))))))).
% 0.31/1.50 thf(fact_20_pi_Odistinct_I57_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((input @ Name12) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 0.31/1.50 thf(fact_21_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 0.31/1.50 thf(fact_22_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 0.31/1.50 thf(fact_23_pi_Odistinct_I53_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name22) @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_24_pi_Odistinct_I15_J, axiom, (! [Name:name,Pi:pi]: ((piNil != ((res @ Name) @ Pi))))).
% 0.31/1.50 thf(fact_25_pi_Odistinct_I11_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((sum @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_26_resTrans_I2_J, axiom, (! [X2:name,Y2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ X2) @ Y2) @ P))) @ Rs)))))).
% 0.31/1.50 thf(fact_27_inputFreeTrans, axiom, (! [A2:name,X2:name,P:pi,Alpha:late_freeRes,P3:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P3))))))).
% 0.31/1.50 thf(fact_28_Id, axiom, (((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ rel)).
% 0.31/1.50 thf(fact_29_outputFreshTrans, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P3:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P3)) => (~ ((((((fresh @ name) @ late_freeRes) @ A2) @ Alpha) | ((((fresh @ name) @ late_freeRes) @ B2) @ Alpha)))))))).
% 0.31/1.50 thf(fact_30_freshFreeDerivative_I1_J, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Y2:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((((fresh @ name) @ late_freeRes) @ Y2) @ Alpha)))))).
% 0.31/1.50 thf(fact_31_nilSim_I2_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,X2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((input @ A2) @ X2) @ P))))))).
% 0.31/1.50 thf(fact_32_resTrans_I1_J, axiom, (! [X2:name,B2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ X2) @ B2) @ P))) @ Rs)))))).
% 0.31/1.50 thf(fact_33_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 0.31/1.50 thf(fact_34_freshFreeDerivative_I2_J, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Y2:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((((fresh @ name) @ pi) @ Y2) @ P3)))))).
% 0.31/1.50 thf(fact_35_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject:late_subject,Name3:name,Pi4:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name3) @ Pi4)))))) => ((! [FreeRes:late_freeRes,Pi4:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 0.31/1.50 thf(fact_36_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject:late_subject,Name3:name,Pi4:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name3) @ Pi4)))))) => ((! [FreeRes:late_freeRes,Pi4:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 0.31/1.50 thf(fact_37_Par2F, axiom, (! [Q:pi,Alpha:late_freeRes,Q2:pi,P:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P) @ Q2))))))).
% 0.31/1.50 thf(fact_38_pi_Ofresh_I8_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 0.31/1.50 thf(fact_39_pi_Ofresh_I7_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((sum @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 0.31/1.50 thf(fact_40_pi_Ofresh_I2_J, axiom, (! [A2:name,X3:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((output @ X3) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X3) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 0.31/1.50 thf(fact_41_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 0.31/1.50 thf(fact_42_residual_Ofresh_I2_J, axiom, (! [A2:name,X22:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X22) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 0.31/1.50 thf(fact_43_pi_Oinject_I7_J, axiom, (! [X22:pi,X1:pi,Y22:pi,Y1:pi]: (((((par @ X22) @ X1) = ((par @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 0.31/1.50 thf(fact_44_pi_Oinject_I1_J, axiom, (! [X3:name,X22:name,X1:pi,Y3:name,Y22:name,Y1:pi]: ((((((output @ X3) @ X22) @ X1) = (((output @ Y3) @ Y22) @ Y1)) = ((X3 = Y3) & ((X22 = Y22) & (X1 = Y1))))))).
% 0.31/1.50 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.31/1.50 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 0.31/1.50 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.31/1.50 thf(fact_48_pi_Odistinct_I29_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_49_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((Y2 != X2) => ((((fresh @ name) @ pi) @ Y2) @ P3))))))).
% 0.31/1.50 thf(fact_50_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((((fresh @ name) @ late_subject) @ Y2) @ A2)))))).
% 0.31/1.50 thf(fact_51_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P3) @ Q)))))))).
% 0.31/1.50 thf(fact_52_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))).
% 0.31/1.50 thf(fact_53_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ PQ)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((! [P2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (Prop @ ((par @ P2) @ Q))))) => ((! [Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q3)) => (Prop @ ((par @ P) @ Q3))))) => (Prop @ PQ))))))))).
% 0.31/1.50 thf(fact_54_parCasesB_H, axiom, (! [P:pi,Q:pi,B2:late_subject,Y2:name,P3:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B2) @ Y2) @ P3)) => ((! [P4:pi,A4:late_subject,X5:name,P2:pi,Q4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y2) @ P3) = (((late_BoundR @ A4) @ X5) @ ((par @ P2) @ Q4))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X5) @ P2)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))) => (~ ((! [Q4:pi,A4:late_subject,X5:name,Q3:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y2) @ P3) = (((late_BoundR @ A4) @ X5) @ ((par @ P4) @ Q3))) => (((late_transitions @ Q4) @ (((late_BoundR @ A4) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))))))))).
% 0.31/1.50 thf(fact_55_freshResidual, axiom, (! [P:pi,Rs:late_residual,X2:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X2) @ P) => ((((fresh @ name) @ late_residual) @ X2) @ Rs)))))).
% 0.31/1.50 thf(fact_56_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P3) @ Q)))))))))).
% 0.31/1.50 thf(fact_57_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))))).
% 0.31/1.50 thf(fact_58_sumIdempRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ P)) @ Rel) @ P))))).
% 0.31/1.50 thf(fact_59_sumAssocRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ ((sum @ Q) @ R))) @ Rel) @ ((sum @ ((sum @ P) @ Q)) @ R)))))).
% 0.31/1.50 thf(fact_60_sumIdempLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ ((sum @ P) @ P)))))).
% 0.31/1.50 thf(fact_61_sumAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ ((sum @ P) @ Q)) @ R)) @ Rel) @ ((sum @ P) @ ((sum @ Q) @ R))))))).
% 0.31/1.50 thf(fact_62_sumSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ Q)) @ Rel) @ ((sum @ Q) @ P)))))).
% 0.31/1.50 thf(fact_63_outputBoundTrans, axiom, (! [A2:name,B2:name,P:pi,C2:late_subject,X2:name,P3:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ (((late_BoundR @ C2) @ X2) @ P3))))))).
% 0.31/1.50 thf(fact_64_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ late_subject) @ Y2) @ A2) => ((Y2 != X2) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((res @ Y2) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y2) @ P3))))))))))).
% 0.31/1.50 thf(fact_65_nilSim_I3_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((output @ A2) @ B2) @ P))))))).
% 0.31/1.50 thf(fact_66_sumZeroRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ ((sum @ P) @ piNil)))))).
% 0.31/1.50 thf(fact_67_sumZeroLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ piNil)) @ Rel) @ P))))).
% 0.31/1.50 thf(fact_68_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ late_subject) @ Y2) @ A2) => ((Y2 != X2) => ((late_transitions @ ((res @ Y2) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y2) @ P3))))))))).
% 0.31/1.50 thf(fact_69_inputIneqTrans, axiom, (! [A2:name,X2:name,P:pi,B2:late_subject,Y2:name,P3:pi]: ((((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ B2) @ Y2) @ P3)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 0.31/1.50 thf(fact_70_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 0.31/1.50 thf(fact_71_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 0.31/1.50 thf(fact_72_residual_Odistinct_I1_J, axiom, (! [Subject2:late_subject,Name4:name,Pi3:pi,FreeRes2:late_freeRes,Pi:pi]: (((((late_BoundR @ Subject2) @ Name4) @ Pi3) != ((late_FreeR @ FreeRes2) @ Pi))))).
% 0.31/1.50 thf(fact_73_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject:late_subject,Name3:name,Pi4:pi]: ((P @ (((late_BoundR @ Subject) @ Name3) @ Pi4)))) => ((! [FreeRes:late_freeRes,Pi4:pi]: ((P @ ((late_FreeR @ FreeRes) @ Pi4)))) => (P @ Residual)))))).
% 0.31/1.50 thf(fact_74_pi_Odistinct_I79_J, axiom, (! [Pi1:pi,Pi2:pi,Pi12:pi,Pi22:pi]: ((((sum @ Pi1) @ Pi2) != ((par @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_75_pi_Odistinct_I55_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_76_sumResLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),X2:name,P:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((eqvt @ pi) @ Rel) => (((strong743114133lation @ ((sum @ ((res @ X2) @ P)) @ ((res @ X2) @ Q))) @ Rel) @ ((res @ X2) @ ((sum @ P) @ Q)))))))).
% 0.31/1.50 thf(fact_77_pi_Odistinct_I13_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((par @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_78_outputTauTrans, axiom, (! [A2:name,B2:name,P:pi,P3:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ late_TauR) @ P3))))))).
% 0.31/1.50 thf(fact_79_pi_Odistinct_I31_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((output @ Name12) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 0.31/1.50 thf(fact_80_pi_Odistinct_I27_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name22) @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_81_pi_Odistinct_I21_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Name1:name,Name2:name,Pi:pi]: (((((output @ Name12) @ Name22) @ Pi3) != (((input @ Name1) @ Name2) @ Pi))))).
% 0.31/1.50 thf(fact_82_pi_Odistinct_I1_J, axiom, (! [Name1:name,Name2:name,Pi:pi]: ((piNil != (((output @ Name1) @ Name2) @ Pi))))).
% 0.31/1.50 thf(fact_83_nilSimRight, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: ((((strong743114133lation @ P) @ Rel) @ piNil)))).
% 0.31/1.50 thf(fact_84_resOutputTauTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ ((late_FreeR @ late_TauR) @ P3))))))).
% 0.31/1.50 thf(fact_85_Par1F, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Q:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P3) @ Q))))))).
% 0.31/1.50 thf(fact_86_Strong__Late__Sim_Oreflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ P))))).
% 0.31/1.50 thf(fact_87_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A3) => (A3 = B3)))))).
% 0.31/1.50 thf(fact_88_subsetI, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((! [X5:A]: (((((member @ A) @ X5) @ A3) => (((member @ A) @ X5) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B3))))).
% 0.31/1.50 thf(fact_89_monotonic, axiom, (! [P:pi,A3:(set @ ((product_prod @ pi) @ pi)),P3:pi,B3:(set @ ((product_prod @ pi) @ pi))]: (((((strong743114133lation @ P) @ A3) @ P3) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A3) @ B3) => (((strong743114133lation @ P) @ B3) @ P3)))))).
% 0.31/1.50 thf(fact_90_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 0.31/1.50 thf(fact_91_resOutputInputTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,C2:name,Y2:name,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ (((late_BoundR @ (late_InputS @ C2)) @ Y2) @ P3))))))).
% 0.31/1.50 thf(fact_92_resInputBoundOutputTrans, axiom, (! [X2:name,A2:name,Y2:name,P:pi,B2:name,Z:name,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y2) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z) @ P3))))))).
% 0.31/1.50 thf(fact_93_freeRes_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F2:T]: (((! [X12:name,X23:name]: ((P @ ((F1 @ X12) @ X23)))) => ((P @ F2) => (((((late_freeRes_rec @ T) @ F1) @ F2) @ late_TauR) = F2)))))).
% 0.31/1.50 thf(fact_94_resOutputOutputTrans, axiom, (! [X2:name,A2:name,P:pi,B2:name,Y2:name,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ X2) @ P))) @ ((late_FreeR @ ((late_OutputR @ B2) @ Y2)) @ P3))))))).
% 0.31/1.50 thf(fact_95_Late__Semantics_OfreeRes_Oinject, axiom, (! [X22:name,X1:name,Y22:name,Y1:name]: (((((late_OutputR @ X22) @ X1) = ((late_OutputR @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 0.31/1.50 thf(fact_96_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 0.31/1.50 thf(fact_97_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A5:name,B4:name]: ((A5 != B4))))).
% 0.31/1.50 thf(fact_98_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 0.31/1.50 thf(fact_99_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 0.31/1.50 thf(fact_100_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X22:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 0.31/1.50 thf(fact_101_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject2:late_subject]: (((! [Name3:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject2)))))).
% 0.31/1.50 thf(fact_102_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject2:late_subject]: (((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject2)))))).
% 0.31/1.50 thf(fact_103_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject2:late_subject]: (((! [Name3:name]: ((P @ (late_InputS @ Name3)))) => ((! [Name3:name]: ((P @ (late_BoundOutputS @ Name3)))) => (P @ Subject2)))))).
% 0.31/1.50 thf(fact_104_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name4:name,Name:name]: (((late_InputS @ Name4) != (late_BoundOutputS @ Name))))).
% 0.31/1.50 thf(fact_105_freeRes_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F2:T,Name12:name,Name22:name]: (((! [X12:name,X23:name]: ((P @ ((F1 @ X12) @ X23)))) => ((P @ F2) => (((((late_freeRes_rec @ T) @ F1) @ F2) @ ((late_OutputR @ Name12) @ Name22)) = ((F1 @ Name12) @ Name22))))))).
% 0.31/1.50 thf(fact_106_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name13) @ Name23)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 0.31/1.50 thf(fact_107_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name13) @ Name23)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 0.31/1.50 thf(fact_108_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name]: ((P @ ((late_OutputR @ Name13) @ Name23)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 0.31/1.50 thf(fact_109_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name12:name,Name22:name]: ((((late_OutputR @ Name12) @ Name22) != late_TauR)))).
% 0.31/1.50 thf(fact_110_Open, axiom, (! [P:pi,A2:name,B2:name,P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P3))))))).
% 0.31/1.50 thf(fact_111_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F3:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F3) @ G) => (((ord_less_eq @ B) @ (F3 @ X2)) @ (G @ X2))))))))).
% 0.31/1.50 thf(fact_112_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F3:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F3) @ G) => (((ord_less_eq @ B) @ (F3 @ X2)) @ (G @ X2))))))))).
% 0.31/1.50 thf(fact_113_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F3:(A > B),G:(A > B)]: (((! [X5:A]: ((((ord_less_eq @ B) @ (F3 @ X5)) @ (G @ X5)))) => (((ord_less_eq @ (A > B)) @ F3) @ G)))))))).
% 0.31/1.50 thf(fact_114_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F4:(A > B),G2:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F4 @ X4)) @ (G2 @ X4))))))))))).
% 0.31/1.50 thf(fact_115_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F3:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F3 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X5:B,Y:B]: (((((ord_less_eq @ B) @ X5) @ Y) => (((ord_less_eq @ A) @ (F3 @ X5)) @ (F3 @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F3 @ C2))))))))))).
% 0.31/1.50 thf(fact_116_order__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B2:A,F3:(A > C3),C2:C3]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C3) @ (F3 @ B2)) @ C2) => ((! [X5:A,Y:A]: (((((ord_less_eq @ A) @ X5) @ Y) => (((ord_less_eq @ C3) @ (F3 @ X5)) @ (F3 @ Y))))) => (((ord_less_eq @ C3) @ (F3 @ A2)) @ C2)))))))))).
% 0.31/1.50 thf(fact_117_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F3:(B > A),B2:B,C2:B]: (((A2 = (F3 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X5:B,Y:B]: (((((ord_less_eq @ B) @ X5) @ Y) => (((ord_less_eq @ A) @ (F3 @ X5)) @ (F3 @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F3 @ C2))))))))))).
% 0.31/1.50 thf(fact_118_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F3:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F3 @ B2) = C2) => ((! [X5:A,Y:A]: (((((ord_less_eq @ A) @ X5) @ Y) => (((ord_less_eq @ B) @ (F3 @ X5)) @ (F3 @ Y))))) => (((ord_less_eq @ B) @ (F3 @ A2)) @ C2)))))))))).
% 0.31/1.50 thf(fact_119_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X4))))))))).
% 0.31/1.50 thf(fact_120_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X2) => (X2 = Y2))))))))).
% 0.31/1.50 thf(fact_121_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 0.31/1.50 thf(fact_122_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((X2 = Y2) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 0.31/1.50 thf(fact_123_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 0.31/1.50 thf(fact_124_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 0.31/1.50 thf(fact_125_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A,Z:A]: ((((((ord_less_eq @ A) @ X2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z)))) => (((((ord_less_eq @ A) @ Y2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z)))) => (((((ord_less_eq @ A) @ X2) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y2)))) => (((((ord_less_eq @ A) @ Z) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X2)))) => (((((ord_less_eq @ A) @ Y2) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y2))))))))))))))))).
% 0.31/1.50 thf(fact_126_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X2:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y2) = (X2 = Y2))))))))).
% 0.31/1.50 thf(fact_127_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) & (((ord_less_eq @ A) @ B4) @ A5))))))))).
% 0.31/1.50 thf(fact_128_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 0.31/1.50 thf(fact_129_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 0.31/1.50 thf(fact_130_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 0.31/1.50 thf(fact_131_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z) => (((ord_less_eq @ A) @ X2) @ Z))))))))).
% 0.31/1.50 thf(fact_132_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 0.31/1.50 thf(fact_133_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B5:A]: (((((ord_less_eq @ A) @ A4) @ B5) => ((P @ A4) @ B5)))) => ((! [A4:A,B5:A]: ((((P @ B5) @ A4) => ((P @ A4) @ B5)))) => ((P @ A2) @ B2))))))))).
% 0.31/1.50 thf(fact_134_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 0.31/1.50 thf(fact_135_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A5) & (((ord_less_eq @ A) @ A5) @ B4))))))))).
% 0.31/1.50 thf(fact_136_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 0.31/1.50 thf(fact_137_in__mono, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B3)))))).
% 0.31/1.50 thf(fact_138_subsetD, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B3)))))).
% 0.31/1.50 thf(fact_139_equalityE, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A3)))))))))).
% 0.31/1.50 thf(fact_140_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ A6) => (((member @ A) @ X4) @ B6)))))))))).
% 0.31/1.50 thf(fact_141_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (((ord_less_eq @ (set @ A)) @ A3) @ B3))))).
% 0.31/1.50 thf(fact_142_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (((ord_less_eq @ (set @ A)) @ B3) @ A3))))).
% 0.31/1.50 thf(fact_143_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A6) => (((member @ A) @ T2) @ B6)))))))))).
% 0.31/1.50 thf(fact_144_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 0.31/1.50 thf(fact_145_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) => (Q @ X5)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 0.31/1.50 thf(fact_146_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ C4) => (((ord_less_eq @ (set @ A)) @ A3) @ C4)))))).
% 0.31/1.50 thf(fact_147_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z3:(set @ A)]: ((Y4 = Z3))) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))).
% 0.31/1.50 thf(fact_148_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X4:A]: (((P @ X4) => (Q @ X4)))))))).
% 0.31/1.50 thf(fact_149_resCasesB_H, axiom, (! [X6:name,P:pi,A2:late_subject,Y6:name,P3:pi]: ((((late_transitions @ ((res @ X6) @ P)) @ (((late_BoundR @ A2) @ Y6) @ P3)) => ((! [P4:pi,A4:name,B5:name]: (((((res @ X6) @ P) = ((res @ B5) @ P4)) => (! [P2:pi]: ((((((late_BoundR @ A2) @ Y6) @ P3) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B5) @ P2)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B5)) @ P2)) => (A4 = B5)))))))) => (~ ((! [P4:pi,A4:late_subject,X5:name,P2:pi,Y:name]: (((((res @ X6) @ P) = ((res @ Y) @ P4)) => (((((late_BoundR @ A2) @ Y6) @ P3) = (((late_BoundR @ A4) @ X5) @ ((res @ Y) @ P2))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X5) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A4) => ((Y != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))))))))))).
% 0.31/1.50 thf(fact_150_Output, axiom, (! [A2:name,B2:name,P:pi]: (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P))))).
% 0.31/1.50 thf(fact_151_outputIneqTrans, axiom, (! [A2:name,B2:name,P:pi,C2:name,D:name,P3:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ C2) @ D)) @ P3)) => (~ (((A2 != C2) | (B2 != D)))))))).
% 0.31/1.50 thf(fact_152_outputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ Rs) => (~ ((! [A4:name,B5:name,P4:pi]: ((((A2 = A4) & ((B2 = B5) & (P = P4))) => (Rs != ((late_FreeR @ ((late_OutputR @ A4) @ B5)) @ P4))))))))))).
% 0.31/1.50 thf(fact_153_outputCases, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P3:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P3)) => (((Alpha = ((late_OutputR @ A2) @ B2)) => ((P = P3) => ((Prop @ ((late_OutputR @ A2) @ B2)) @ P))) => ((Prop @ Alpha) @ P3)))))).
% 0.31/1.50 thf(fact_154_Late__Semantics_OInput, axiom, (! [A2:name,X2:name,P:pi]: (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P))))).
% 0.31/1.50 thf(fact_155_transitions_OInput, axiom, (! [X2:name,A2:name,P:pi]: (((X2 != A2) => ((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P)))))).
% 0.31/1.50 thf(fact_156_inputBoundOutputTrans, axiom, (! [A2:name,X2:name,P:pi,B2:name,Y2:name,P3:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y2) @ P3))))))).
% 0.31/1.50 thf(fact_157_resCases_H, axiom, (! [X2:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X2) @ P)) @ Rs) => ((! [P4:pi,A4:name,B5:name]: (((((res @ X2) @ P) = ((res @ B5) @ P4)) => (! [P2:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B5) @ P2)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B5)) @ P2)) => (A4 = B5)))))))) => ((! [P4:pi,A4:late_subject,X5:name,P2:pi,Y:name]: (((((res @ X2) @ P) = ((res @ Y) @ P4)) => ((Rs = (((late_BoundR @ A4) @ X5) @ ((res @ Y) @ P2))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X5) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A4) => ((Y != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P2:pi,Y:name]: (((((res @ X2) @ P) = ((res @ Y) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y) @ P2))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P2)) => (~ (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha2)))))))))))))))).
% 0.31/1.50 thf(fact_158_transitions_OClose2, axiom, (! [P:pi,A2:name,Y2:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y2) @ P) => (((((fresh @ name) @ pi) @ Y2) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ P3) => ((Y2 != A2) => (((((fresh @ name) @ pi) @ Y2) @ Q2) => ((X2 != Y2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ Y2))))))))))))))))))).
% 0.31/1.50 thf(fact_159_transitions_OClose1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,Y2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y2) @ P) => (((((fresh @ name) @ pi) @ Y2) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((Y2 != A2) => (((((fresh @ name) @ pi) @ Y2) @ P3) => ((X2 != Y2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ (((subs @ P3) @ X2) @ Y2)) @ Q2)))))))))))))))))).
% 0.31/1.50 thf(fact_160_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y2:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ Y2) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ Y2))))))))))).
% 0.31/1.50 thf(fact_161_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,Y2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ Q2)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ (((subs @ P3) @ X2) @ Y2)) @ Q2)))))))))).
% 0.31/1.50 thf(fact_162_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y22:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y22)) = (X22 = Y22))))).
% 0.31/1.50 thf(fact_163_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 0.31/1.50 thf(fact_164_Late__Semantics1_OfreeRes_Oinject, axiom, (! [X11:name,X122:name,Y11:name,Y12:name]: (((((late_OutputR @ X11) @ X122) = ((late_OutputR @ Y11) @ Y12)) = ((X11 = Y11) & (X122 = Y12)))))).
% 0.31/1.50 thf(fact_165_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 0.31/1.50 thf(fact_166_simps_I9_J, axiom, (! [X2:name,C2:name,D:name,P:pi]: (((X2 != C2) => ((X2 != D) => ((((subs @ ((res @ X2) @ P)) @ C2) @ D) = ((res @ X2) @ (((subs @ P) @ C2) @ D)))))))).
% 0.31/1.50 thf(fact_167_simps_I8_J, axiom, (! [P:pi,Q:pi,C2:name,D:name]: (((((subs @ ((par @ P) @ Q)) @ C2) @ D) = ((par @ (((subs @ P) @ C2) @ D)) @ (((subs @ Q) @ C2) @ D)))))).
% 0.31/1.50 thf(fact_168_substTrans, axiom, (! [B2:name,P:pi,A2:name,C2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ (((subs @ P) @ A2) @ B2)) @ B2) @ C2) = (((subs @ P) @ A2) @ C2)))))).
% 0.31/1.50 thf(fact_169_simps_I7_J, axiom, (! [P:pi,Q:pi,C2:name,D:name]: (((((subs @ ((sum @ P) @ Q)) @ C2) @ D) = ((sum @ (((subs @ P) @ C2) @ D)) @ (((subs @ Q) @ C2) @ D)))))).
% 0.31/1.50 thf(fact_170_simps_I1_J, axiom, (! [C2:name,D:name]: (((((subs @ piNil) @ C2) @ D) = piNil)))).
% 0.31/1.50 thf(fact_171_forget, axiom, (! [A2:name,P:pi,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B2) = P))))).
% 0.31/1.50 thf(fact_172_fresh__fact1, axiom, (! [A2:name,P:pi,C2:name,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B2) @ C2))))))).
% 0.31/1.50 thf(fact_173_fresh__fact2, axiom, (! [A2:name,B2:name,P:pi]: (((A2 != B2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B2)))))).
% 0.31/1.50 thf(fact_174_substRes3, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B2) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 0.31/1.50 thf(fact_175_substRes2, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((res @ A2) @ P) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 0.31/1.50 thf(fact_176_freeRes_Oexhaust, axiom, (! [Y2:late_freeRes]: (((! [X112:name,X123:name]: ((Y2 != ((late_OutputR @ X112) @ X123)))) => (Y2 = late_TauR))))).
% 0.31/1.50 thf(fact_177_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X122:name]: ((((late_OutputR @ X11) @ X122) != late_TauR)))).
% 0.31/1.50 thf(fact_178_subject_Oexhaust, axiom, (! [Y2:late_subject]: (((! [X12:name]: ((Y2 != (late_InputS @ X12)))) => (~ ((! [X23:name]: ((Y2 != (late_BoundOutputS @ X23)))))))))).
% 0.31/1.50 thf(fact_179_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X22:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X22))))).
% 0.31/1.50 thf(fact_180_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P3) @ X2) @ B2)) @ Q2)))))))).
% 0.31/1.50 thf(fact_181_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B2:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ B2))))))))).
% 0.31/1.50 thf(fact_182_transitions_OComm1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P3) @ X2) @ B2)) @ Q2))))))))))))).
% 0.31/1.50 thf(fact_183_transitions_OComm2, axiom, (! [P:pi,A2:name,B2:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ P3) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ B2)))))))))))))).
% 0.31/1.50 thf(fact_184_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X2:name,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [Q3:pi,A4:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A4) @ X2)) @ Q3)) => ((A4 != X2) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A4)) @ X2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q3)) @ Rel)))))))) => ((! [Q3:pi,A4:late_subject,Y:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y) @ Q3)) => (((((fresh @ name) @ late_subject) @ X2) @ A4) => ((X2 != Y) => (((((fresh @ name) @ A) @ Y) @ C4) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y) @ P5)) & (((((strong2129052853vative @ P5) @ ((res @ X2) @ Q3)) @ A4) @ Y) @ Rel)))))))))) => ((! [Q3:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha2) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ ((res @ X2) @ Q3))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X2) @ Q)))))))))))).
% 0.31/1.50 thf(fact_185_simE_I1_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X2:name,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (? [P2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) & (((((strong2129052853vative @ P2) @ Q2) @ A2) @ X2) @ Rel)))))))))).
% 0.31/1.50 thf(fact_186_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [A4:late_subject,X5:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P) => (((((fresh @ name) @ pi) @ X5) @ Q) => (((((fresh @ name) @ late_subject) @ X5) @ A4) => (((((fresh @ name) @ A) @ X5) @ C4) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ X5) @ P5)) & (((((strong2129052853vative @ P5) @ Q3) @ A4) @ X5) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 0.31/1.50 thf(fact_187_derivativeMonotonic, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,A3:(set @ ((product_prod @ pi) @ pi)),B3:(set @ ((product_prod @ pi) @ pi))]: (((((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ A3) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A3) @ B3) => (((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ B3)))))).
% 0.31/1.50 thf(fact_188_simulation__def, axiom, (strong743114133lation = (^ [P6:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A5:late_subject,X4:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A5) @ X4) @ Q6)) & ((((fresh @ name) @ pi) @ X4) @ P6)) => (? [P7:pi]: ((((late_transitions @ P6) @ (((late_BoundR @ A5) @ X4) @ P7)) & (((((strong2129052853vative @ P7) @ Q6) @ A5) @ X4) @ Rel2))))))) & (! [Alpha3:late_freeRes,Q6:pi]: ((((late_transitions @ Q5) @ ((late_FreeR @ Alpha3) @ Q6)) => (? [P7:pi]: ((((late_transitions @ P6) @ ((late_FreeR @ Alpha3) @ P7)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P7) @ Q6)) @ Rel2)))))))))))).
% 0.31/1.50 thf(fact_189_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A4:late_subject,Y:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y) @ Q3)) => (((((fresh @ name) @ pi) @ Y) @ P) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y) @ P5)) & (((((strong2129052853vative @ P5) @ Q3) @ A4) @ Y) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 0.31/1.50 thf(fact_190_simE_I2_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Alpha:late_freeRes,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => (? [P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P2) @ Q2)) @ Rel))))))))).
% 0.31/1.50 thf(fact_191_derivativeReflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,A2:late_subject,X2:name]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((((strong2129052853vative @ P) @ P) @ A2) @ X2) @ Rel))))).
% 0.31/1.50 thf(fact_192_pair__in__Id__conv, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) = (A2 = B2))))).
% 0.31/1.50 thf(fact_193_IdI, axiom, (! [A:$tType,A2:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ (id @ A))))).
% 0.31/1.50 thf(fact_194_subrelI, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((! [X5:A,Y:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y)) @ R2) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y)) @ S)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R2) @ S))))).
% 0.31/1.50 thf(fact_195_IdE, axiom, (! [A:$tType,P8:((product_prod @ A) @ A)]: (((((member @ ((product_prod @ A) @ A)) @ P8) @ (id @ A)) => (~ ((! [X5:A]: ((P8 != ((((product_Pair @ A) @ A) @ X5) @ X5)))))))))).
% 0.31/1.50 thf(fact_196_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X2:A,Y2:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X2) @ Y2)) = (((((fresh @ X) @ A) @ A2) @ X2) & ((((fresh @ X) @ B) @ A2) @ Y2)))))).
% 0.31/1.50 thf(fact_197_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B7:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B7)) = ((A2 = A7) & (B2 = B7)))))).
% 0.31/1.50 thf(fact_198_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X1 = Y1) & (X22 = Y22)))))).
% 0.31/1.50 thf(fact_199_surj__pair, axiom, (! [A:$tType,B:$tType,P8:((product_prod @ A) @ B)]: ((? [X5:A,Y:B]: ((P8 = ((((product_Pair @ A) @ B) @ X5) @ Y))))))).
% 0.31/1.50 thf(fact_200_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P8:((product_prod @ A) @ B)]: (((! [A4:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B5)))) => (P @ P8))))).
% 0.31/1.50 thf(fact_201_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B7:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B7)) => (~ (((A2 = A7) => (B2 != B7)))))))).
% 0.31/1.50 thf(fact_202_prod__cases3, axiom, (! [A:$tType,B:$tType,C3:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ C3))]: ((~ ((! [A4:A,B5:B,C:C3]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A4) @ ((((product_Pair @ B) @ C3) @ B5) @ C)))))))))).
% 0.31/1.50 thf(fact_203_prod__cases4, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2)))]: ((~ ((! [A4:A,B5:B,C:C3,D3:D2]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D2)) @ B5) @ ((((product_Pair @ C3) @ D2) @ C) @ D3))))))))))).
% 0.31/1.50 thf(fact_204_prod__cases5, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,E:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))))]: ((~ ((! [A4:A,B5:B,C:C3,D3:D2,E2:E]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))) @ B5) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ E)) @ C) @ ((((product_Pair @ D2) @ E) @ D3) @ E2)))))))))))).
% 0.31/1.50 thf(fact_205_prod__cases6, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,E:$tType,F5:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5)))))]: ((~ ((! [A4:A,B5:B,C:C3,D3:D2,E2:E,F6:F5]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5)))) @ B5) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5))) @ C) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F5)) @ D3) @ ((((product_Pair @ E) @ F5) @ E2) @ F6))))))))))))).
% 0.31/1.50 thf(fact_206_prod__cases7, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,E:$tType,F5:$tType,G3:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))))]: ((~ ((! [A4:A,B5:B,C:C3,D3:D2,E2:E,F6:F5,G4:G3]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))) @ B5) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))) @ C) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G3)) @ E2) @ ((((product_Pair @ F5) @ G3) @ F6) @ G4)))))))))))))).
% 0.31/1.50 thf(fact_207_prod__induct3, axiom, (! [C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C3)) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ C3))]: (((! [A4:A,B5:B,C:C3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A4) @ ((((product_Pair @ B) @ C3) @ B5) @ C))))) => (P @ X2))))).
% 0.31/1.50 thf(fact_208_prod__induct4, axiom, (! [D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2)))]: (((! [A4:A,B5:B,C:C3,D3:D2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D2)) @ B5) @ ((((product_Pair @ C3) @ D2) @ C) @ D3)))))) => (P @ X2))))).
% 0.31/1.50 thf(fact_209_prod__induct5, axiom, (! [E:$tType,D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E)))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))))]: (((! [A4:A,B5:B,C:C3,D3:D2,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))) @ B5) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ E)) @ C) @ ((((product_Pair @ D2) @ E) @ D3) @ E2))))))) => (P @ X2))))).
% 0.31/1.50 thf(fact_210_prod__induct6, axiom, (! [F5:$tType,E:$tType,D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5)))))]: (((! [A4:A,B5:B,C:C3,D3:D2,E2:E,F6:F5]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5)))) @ B5) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F5))) @ C) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F5)) @ D3) @ ((((product_Pair @ E) @ F5) @ E2) @ F6)))))))) => (P @ X2))))).
% 0.31/1.50 thf(fact_211_prod__induct7, axiom, (! [G3:$tType,F5:$tType,E:$tType,D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))))]: (((! [A4:A,B5:B,C:C3,D3:D2,E2:E,F6:F5,G4:G3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))) @ B5) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))) @ C) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G3)) @ E2) @ ((((product_Pair @ F5) @ G3) @ F6) @ G4))))))))) => (P @ X2))))).
% 0.31/1.50 thf(fact_212_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y2:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B5:B]: ((Y2 != ((((product_Pair @ A) @ B) @ A4) @ B5))))))))).
% 0.31/1.50 thf(fact_213_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B5)))) => (P @ Prod))))).
% 0.31/1.50 thf(fact_214_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C3:$tType,A2:A,X2:B,Y2:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X2) @ Y2)) => ((((fresh @ A) @ C3) @ A2) @ Y2))))).
% 0.31/1.50 thf(fact_215_fresh__prodD_I1_J, axiom, (! [C3:$tType,A:$tType,B:$tType,A2:A,X2:B,Y2:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X2) @ Y2)) => ((((fresh @ A) @ B) @ A2) @ X2))))).
% 0.31/1.50 thf(fact_216_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 0.31/1.50 thf(fact_217_IdD, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) => (A2 = B2))))).
% 0.31/1.50 thf(fact_218_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F2:(name > T),Name4:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F2 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F2) @ (late_BoundOutputS @ Name4)) = (F2 @ Name4))))))).
% 0.31/1.50 thf(fact_219_subject_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F2:(name > T),Name4:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F2 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F2) @ (late_InputS @ Name4)) = (F1 @ Name4))))))).
% 0.31/1.50 thf(fact_220_resTauOutputTrans, axiom, (! [X2:name,P:pi,A2:name,B2:name,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3))))))).
% 0.31/1.50 thf(fact_221_residual_Ofresh_I1_J, axiom, (! [A2:name,X3:late_subject,X1:name,X22:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ (((late_BoundR @ X3) @ X1) @ X22)) = (((((fresh @ name) @ late_subject) @ A2) @ X3) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 0.31/1.50 thf(fact_222_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 0.31/1.50 thf(fact_223_simps_I2_J, axiom, (! [P:pi,C2:name,D:name]: (((((subs @ (tau @ P)) @ C2) @ D) = (tau @ (((subs @ P) @ C2) @ D)))))).
% 0.31/1.50 thf(fact_224_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X22)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22)))))).
% 0.31/1.50 thf(fact_225_pi_Ofresh_I4_J, axiom, (! [A2:name,X3:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((input @ X3) @ X1) @ X22)) = (((((fresh @ name) @ name) @ A2) @ X3) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 0.31/1.50 thf(fact_226_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B2:name,A2:name,X2:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B2) @ ((((abs_fun @ name) @ A) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ A) @ B2) @ X2))))))))).
% 0.31/1.50 thf(fact_227_abs__fresh_I1_J, axiom, (! [X7:$tType]: (((fs_name @ X7) => (! [B2:name,A2:name,X2:X7]: ((((((fresh @ name) @ (name > (noption @ X7))) @ B2) @ ((((abs_fun @ name) @ X7) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ X7) @ B2) @ X2))))))))).
% 0.31/1.50 thf(fact_228_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 0.31/1.50 thf(fact_229_pi_Odistinct_I3_J, axiom, (! [Pi:pi]: ((piNil != (tau @ Pi))))).
% 0.31/1.50 thf(fact_230_pi_Odistinct_I19_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi:pi]: (((((output @ Name12) @ Name22) @ Pi3) != (tau @ Pi))))).
% 0.31/1.50 thf(fact_231_pi_Odistinct_I35_J, axiom, (! [Pi3:pi,Name1:name,Name2:name,Pi:pi]: (((tau @ Pi3) != (((input @ Name1) @ Name2) @ Pi))))).
% 0.31/1.50 thf(fact_232_pi_Odistinct_I41_J, axiom, (! [Pi3:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_233_pi_Odistinct_I43_J, axiom, (! [Pi3:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(fact_234_pi_Odistinct_I45_J, axiom, (! [Pi3:pi,Name:name,Pi:pi]: (((tau @ Pi3) != ((res @ Name) @ Pi))))).
% 0.31/1.50 thf(fact_235_pi_Oinject_I3_J, axiom, (! [X3:name,X1:name,X22:pi,Y3:name,Y1:name,Y22:pi]: ((((((input @ X3) @ X1) @ X22) = (((input @ Y3) @ Y1) @ Y22)) = ((X3 = Y3) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22))))))).
% 0.31/1.50 thf(fact_236_residual_Oinject_I1_J, axiom, (! [X3:late_subject,X1:name,X22:pi,Y3:late_subject,Y1:name,Y22:pi]: ((((((late_BoundR @ X3) @ X1) @ X22) = (((late_BoundR @ Y3) @ Y1) @ Y22)) = ((X3 = Y3) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22))))))).
% 0.31/1.50 thf(fact_237_pi_Oinject_I8_J, axiom, (! [X1:name,X22:pi,Y1:name,Y22:pi]: (((((res @ X1) @ X22) = ((res @ Y1) @ Y22)) = (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22)))))).
% 0.31/1.50 thf(fact_238_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X2) @ P3))))))).
% 0.31/1.50 thf(fact_239_nilSim_I1_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (tau @ P))))))).
% 0.31/1.50 thf(fact_240_resTauBoundTrans, axiom, (! [X2:name,P:pi,A2:late_subject,Y2:name,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y2) @ P3))))))).
% 0.31/1.50 thf(fact_241_tauOutputTrans, axiom, (! [P:pi,A2:name,B2:name,P3:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3))))))).
% 0.31/1.50 thf(fact_242_tauCases, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (tau @ P)) @ ((late_FreeR @ Alpha) @ P3)) => (((Alpha = late_TauR) => ((P = P3) => ((Prop @ late_TauR) @ P))) => ((Prop @ Alpha) @ P3)))))).
% 0.31/1.50 thf(fact_243_tauCases_H, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ (tau @ P)) @ Rs) => (~ ((! [P4:pi]: ((((tau @ P) = (tau @ P4)) => (Rs != ((late_FreeR @ late_TauR) @ P4))))))))))).
% 0.31/1.50 thf(fact_244_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 0.31/1.50 thf(fact_245_inputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B2) @ P)) @ Rs) => (~ ((! [X5:name,A4:name,P4:pi]: ((((A2 = A4) & (((((abs_fun @ name) @ pi) @ B2) @ P) = ((((abs_fun @ name) @ pi) @ X5) @ P4))) => ((Rs = (((late_BoundR @ (late_InputS @ A4)) @ X5) @ P4)) => (X5 = A4))))))))))).
% 0.31/1.50 thf(fact_246_mismatchIdRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => ((A2 != B2) => (((strong743114133lation @ P) @ Rel) @ (((mismatch @ A2) @ B2) @ P))))))).
% 0.31/1.50 thf(fact_247_mismatchIdLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => ((A2 != B2) => (((strong743114133lation @ (((mismatch @ A2) @ B2) @ P)) @ Rel) @ P)))))).
% 0.31/1.50 thf(fact_248_pi_Ofresh_I6_J, axiom, (! [A2:name,X3:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((mismatch @ X3) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X3) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 0.31/1.50 thf(fact_249_pi_Odistinct_I39_J, axiom, (! [Pi3:pi,Name1:name,Name2:name,Pi:pi]: (((tau @ Pi3) != (((mismatch @ Name1) @ Name2) @ Pi))))).
% 0.31/1.50 thf(fact_250_mismatchCases, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual,F:(name > (name > $o))]: ((((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 != B2) => ((F @ A2) @ B2))) => ((F @ A2) @ B2)))))).
% 0.31/1.50 thf(fact_251_mismatchTrans, axiom, (! [A2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ (((mismatch @ A2) @ A2) @ P)) @ Rs)))))).
% 0.31/1.50 thf(fact_252_mismatchCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs) => (~ ((! [P4:pi,A4:name,B5:name]: ((((A2 = A4) & ((B2 = B5) & (P = P4))) => (((late_transitions @ P4) @ Rs) => (A4 = B5))))))))))).
% 0.31/1.50 thf(fact_253_Mismatch, axiom, (! [P:pi,Rs:late_residual,A2:name,B2:name]: ((((late_transitions @ P) @ Rs) => ((A2 != B2) => ((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs)))))).
% 0.31/1.50 thf(fact_254_pi_Odistinct_I75_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((mismatch @ Name12) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 0.31/1.50 thf(fact_255_pi_Odistinct_I73_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name12) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_1, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 0.31/1.50 thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 0.31/1.50 thf(tcon_Set_Oset___Orderings_Oord_3, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 0.31/1.50 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, (preorder @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_5, axiom, (order @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Oord_6, axiom, (ord @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Agent_Ofs__name_7, axiom, (fs_name @ $o)).
% 0.31/1.50 thf(tcon_Agent_Oname___Agent_Ofs__name_8, axiom, (fs_name @ name)).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9, axiom, (! [A8:$tType,A9:$tType]: ((((fs_name @ A8) & (fs_name @ A9)) => (fs_name @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10, axiom, (fs_name @ late_freeRes)).
% 0.31/1.50 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11, axiom, (fs_name @ late_subject)).
% 0.31/1.50 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12, axiom, (fs_name @ late_residual)).
% 0.31/1.50 thf(conj_0, conjecture, ((late_transitions @ ((res @ x) @ ((sum @ p) @ q))) @ ((late_FreeR @ alpha) @ ((res @ x) @ q2)))).
% 0.31/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.pF5X09mbQh/DTF2DTF1767.p
% 0.31/1.50 ------------------------
% 0.31/1.55 ---- Cleaned THF ---
% 0.31/1.55 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.31/1.55 late_residual: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Late__Semantics_Osubject,type,
% 0.31/1.55 late_subject: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.31/1.55 late_freeRes: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Product__Type_Oprod,type,
% 0.31/1.55 product_prod: $tType > $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Nominal_Onoption,type,
% 0.31/1.55 noption: $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Agent_Oname,type,
% 0.31/1.55 name: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Agent_Opi,type,
% 0.31/1.55 pi: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Set_Oset,type,
% 0.31/1.55 set: $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_HOL_Otype,type,
% 0.31/1.55 type:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Agent_Ofs__name,type,
% 0.31/1.55 fs_name:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Oord,type,
% 0.31/1.55 ord:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Oorder,type,
% 0.31/1.55 order:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/1.55 linorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/1.55 preorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_OInput,type,
% 0.31/1.55 input: name > name > pi > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.31/1.55 mismatch: name > name > pi > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_OOutput,type,
% 0.31/1.55 output: name > name > pi > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_OPar,type,
% 0.31/1.55 par: pi > pi > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.31/1.55 piNil: pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_ORes,type,
% 0.31/1.55 res: name > pi > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_OSum,type,
% 0.31/1.55 sum: pi > pi > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Opi_OTau,type,
% 0.31/1.55 tau: pi > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Agent_Osubs,type,
% 0.31/1.55 subs: pi > name > name > pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.31/1.55 late_OutputR: name > name > late_freeRes ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.31/1.55 late_TauR: late_freeRes ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.31/1.55 late_freeRes_rec:
% 0.31/1.55 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.31/1.55 late_BoundR: late_subject > name > pi > late_residual ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.31/1.55 late_FreeR: late_freeRes > pi > late_residual ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.31/1.55 late_BoundOutputS: name > late_subject ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.31/1.55 late_InputS: name > late_subject ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.31/1.55 late_subject_rec:
% 0.31/1.55 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.31/1.55 late_transitions: pi > late_residual > $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Nominal_Oabs__fun,type,
% 0.31/1.55 abs_fun:
% 0.31/1.55 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Nominal_Ofresh,type,
% 0.31/1.55 fresh:
% 0.31/1.55 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/1.55 ord_less_eq:
% 0.31/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Product__Type_OPair,type,
% 0.31/1.55 product_Pair:
% 0.31/1.55 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.31/1.55 product_rec_prod:
% 0.31/1.55 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Rel_Oeqvt,type,
% 0.31/1.55 eqvt:
% 0.31/1.55 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Relation_OId,type,
% 0.31/1.55 id:
% 0.31/1.55 !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Set_OCollect,type,
% 0.31/1.55 collect:
% 0.31/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.31/1.55 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.31/1.55 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_member,type,
% 0.31/1.55 member:
% 0.31/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_P,type,
% 0.31/1.55 p: pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_PQ____,type,
% 0.31/1.55 pq: pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_Q,type,
% 0.31/1.55 q: pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_Q_H____,type,
% 0.31/1.55 q2: pi ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_Rel,type,
% 0.31/1.55 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v__092_060alpha_062____,type,
% 0.31/1.55 alpha: late_freeRes ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_x,type,
% 0.31/1.55 x: name ).
% 0.31/1.55
% 0.31/1.55 thf(fact_0_cRes_Ohyps_I2_J,axiom,
% 0.31/1.55 fresh @ name @ late_freeRes @ x @ alpha ).
% 0.31/1.55
% 0.31/1.55 thf(fact_1_Eqvt,axiom,
% 0.31/1.55 eqvt @ pi @ rel ).
% 0.31/1.55
% 0.31/1.55 thf(fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062,axiom,
% 0.31/1.55 late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_3_cRes_Ohyps_I1_J,axiom,
% 0.31/1.55 late_transitions @ q @ ( late_FreeR @ alpha @ q2 ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_4_cSum2_Ohyps,axiom,
% 0.31/1.55 late_transitions @ ( res @ x @ q ) @ ( late_FreeR @ alpha @ pq ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_5_Free_Ohyps,axiom,
% 0.31/1.55 late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pq ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_6_pi_Odistinct_I81_J,axiom,
% 0.31/1.55 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.31/1.55 ( ( sum @ Pi1 @ Pi2 )
% 0.31/1.55 != ( res @ Name @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_7_sumCases,axiom,
% 0.31/1.55 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.31/1.55 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.31/1.55 => ( ~ ( late_transitions @ P @ Rs )
% 0.31/1.55 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_8_sumCases_H,axiom,
% 0.31/1.55 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.31/1.55 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.31/1.55 => ( ~ ( late_transitions @ P @ Rs )
% 0.31/1.55 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_9_Sum1,axiom,
% 0.31/1.55 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ Rs )
% 0.31/1.55 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_10_Sum2,axiom,
% 0.31/1.55 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ Rs )
% 0.31/1.55 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_11_resCasesF,axiom,
% 0.31/1.55 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.31/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.31/1.55 => ( ! [P2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 0.31/1.55 => ( F @ ( res @ X2 @ P2 ) ) ) )
% 0.31/1.55 => ( F @ XP ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_12_resCasesF_H,axiom,
% 0.31/1.55 ! [X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.31/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 0.31/1.55 ( ( ( res @ X2 @ P )
% 0.31/1.55 = ( res @ Y @ P4 ) )
% 0.31/1.55 => ( ( ( late_FreeR @ Alpha @ P3 )
% 0.31/1.55 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 0.31/1.55 => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_13_ResF,axiom,
% 0.31/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_freeRes @ Y2 @ Alpha )
% 0.31/1.55 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y2 @ P3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_14_pi_Oinject_I6_J,axiom,
% 0.31/1.55 ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.31/1.55 ( ( ( sum @ X22 @ X1 )
% 0.31/1.55 = ( sum @ Y22 @ Y1 ) )
% 0.31/1.55 = ( ( X22 = Y22 )
% 0.31/1.55 & ( X1 = Y1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_15_residual_Oinject_I2_J,axiom,
% 0.31/1.55 ! [X22: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 0.31/1.55 ( ( ( late_FreeR @ X22 @ X1 )
% 0.31/1.55 = ( late_FreeR @ Y22 @ Y1 ) )
% 0.31/1.55 = ( ( X22 = Y22 )
% 0.31/1.55 & ( X1 = Y1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_16_resInputFreeTrans,axiom,
% 0.31/1.55 ! [X2: name,A2: name,Y2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_17_resZeroTrans,axiom,
% 0.31/1.55 ! [X2: name,Rs: late_residual] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_18_pi_Odistinct_I5_J,axiom,
% 0.31/1.55 ! [Name1: name,Name2: name,Pi: pi] :
% 0.31/1.55 ( piNil
% 0.31/1.55 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_19_name__exists__fresh,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( fs_name @ A )
% 0.31/1.55 => ! [X2: A] :
% 0.31/1.55 ~ ! [C: name] :
% 0.31/1.55 ~ ( fresh @ name @ A @ C @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_20_pi_Odistinct_I57_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.31/1.55 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( res @ Name @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_21_zeroTrans,axiom,
% 0.31/1.55 ! [Rs: late_residual] :
% 0.31/1.55 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_22_nilCases_H,axiom,
% 0.31/1.55 ! [Rs: late_residual] :
% 0.31/1.55 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_23_pi_Odistinct_I53_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_24_pi_Odistinct_I15_J,axiom,
% 0.31/1.55 ! [Name: name,Pi: pi] :
% 0.31/1.55 ( piNil
% 0.31/1.55 != ( res @ Name @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_25_pi_Odistinct_I11_J,axiom,
% 0.31/1.55 ! [Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( piNil
% 0.31/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_26_resTrans_I2_J,axiom,
% 0.31/1.55 ! [X2: name,Y2: name,P: pi,Rs: late_residual] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y2 @ P ) ) @ Rs ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_27_inputFreeTrans,axiom,
% 0.31/1.55 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_28_Id,axiom,
% 0.31/1.55 ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 0.31/1.55
% 0.31/1.55 thf(fact_29_outputFreshTrans,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.31/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.31/1.55 | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_30_freshFreeDerivative_I1_J,axiom,
% 0.31/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.31/1.55 => ( fresh @ name @ late_freeRes @ Y2 @ Alpha ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_31_nilSim_I2_J,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 0.31/1.55 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_32_resTrans_I1_J,axiom,
% 0.31/1.55 ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_33_freeRes_Ofresh_I2_J,axiom,
% 0.31/1.55 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_34_freshFreeDerivative_I2_J,axiom,
% 0.31/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.31/1.55 => ( fresh @ name @ pi @ Y2 @ P3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_35_residual_Ostrong__induct,axiom,
% 0.31/1.55 ! [N: $tType] :
% 0.31/1.55 ( ( fs_name @ N )
% 0.31/1.55 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.31/1.55 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: N] :
% 0.31/1.55 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ Name3 @ Subject )
% 0.31/1.55 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.31/1.55 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.31/1.55 => ( P @ Z @ Residual ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_36_residual_Ostrong__inducts,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( fs_name @ A )
% 0.31/1.55 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.31/1.55 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: A] :
% 0.31/1.55 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ Name3 @ Subject )
% 0.31/1.55 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.31/1.55 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.31/1.55 => ( P @ Z @ Residual ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_37_Par2F,axiom,
% 0.31/1.55 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_38_pi_Ofresh_I8_J,axiom,
% 0.31/1.55 ! [A2: name,X22: pi,X1: pi] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.31/1.55 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.31/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_39_pi_Ofresh_I7_J,axiom,
% 0.31/1.55 ! [A2: name,X22: pi,X1: pi] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 0.31/1.55 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.31/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_40_pi_Ofresh_I2_J,axiom,
% 0.31/1.55 ! [A2: name,X3: name,X22: name,X1: pi] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ ( output @ X3 @ X22 @ X1 ) )
% 0.31/1.55 = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.31/1.55 & ( fresh @ name @ name @ A2 @ X22 )
% 0.31/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_41_pi_Ofresh_I1_J,axiom,
% 0.31/1.55 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_42_residual_Ofresh_I2_J,axiom,
% 0.31/1.55 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.31/1.55 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.31/1.55 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.31/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_43_pi_Oinject_I7_J,axiom,
% 0.31/1.55 ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.31/1.55 ( ( ( par @ X22 @ X1 )
% 0.31/1.55 = ( par @ Y22 @ Y1 ) )
% 0.31/1.55 = ( ( X22 = Y22 )
% 0.31/1.55 & ( X1 = Y1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_44_pi_Oinject_I1_J,axiom,
% 0.31/1.55 ! [X3: name,X22: name,X1: pi,Y3: name,Y22: name,Y1: pi] :
% 0.31/1.55 ( ( ( output @ X3 @ X22 @ X1 )
% 0.31/1.55 = ( output @ Y3 @ Y22 @ Y1 ) )
% 0.31/1.55 = ( ( X3 = Y3 )
% 0.31/1.55 & ( X22 = Y22 )
% 0.31/1.55 & ( X1 = Y1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 0.31/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.31/1.55 = ( P @ A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A] :
% 0.31/1.55 ( ( collect @ A
% 0.31/1.55 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.31/1.55 = A3 ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_47_Collect__cong,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.55 ( ! [X5: A] :
% 0.31/1.55 ( ( P @ X5 )
% 0.31/1.55 = ( Q @ X5 ) )
% 0.31/1.55 => ( ( collect @ A @ P )
% 0.31/1.55 = ( collect @ A @ Q ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_48_pi_Odistinct_I29_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_49_freshBoundDerivative_I2_J,axiom,
% 0.31/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.31/1.55 => ( ( Y2 != X2 )
% 0.31/1.55 => ( fresh @ name @ pi @ Y2 @ P3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_50_freshBoundDerivative_I1_J,axiom,
% 0.31/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.31/1.55 => ( fresh @ name @ late_subject @ Y2 @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_51_Late__Semantics_OPar1B,axiom,
% 0.31/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_52_Late__Semantics_OPar2B,axiom,
% 0.31/1.55 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_53_parCasesB,axiom,
% 0.31/1.55 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 0.31/1.55 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( ! [P2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.31/1.55 => ( Prop @ ( par @ P2 @ Q ) ) )
% 0.31/1.55 => ( ! [Q3: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q3 ) )
% 0.31/1.55 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.31/1.55 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_54_parCasesB_H,axiom,
% 0.31/1.55 ! [P: pi,Q: pi,B2: late_subject,Y2: name,P3: pi] :
% 0.31/1.55 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y2 @ P3 ) )
% 0.31/1.55 => ( ! [P4: pi,A4: late_subject,X5: name,P2: pi,Q4: pi] :
% 0.31/1.55 ( ( ( par @ P @ Q )
% 0.31/1.55 = ( par @ P4 @ Q4 ) )
% 0.31/1.55 => ( ( ( late_BoundR @ B2 @ Y2 @ P3 )
% 0.31/1.55 = ( late_BoundR @ A4 @ X5 @ ( par @ P2 @ Q4 ) ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.31/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 0.31/1.55 => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.31/1.55 ( ( ( par @ P @ Q )
% 0.31/1.55 = ( par @ P4 @ Q4 ) )
% 0.31/1.55 => ( ( ( late_BoundR @ B2 @ Y2 @ P3 )
% 0.31/1.55 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.31/1.55 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.31/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_55_freshResidual,axiom,
% 0.31/1.55 ! [P: pi,Rs: late_residual,X2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ Rs )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_56_transitions_OPar1B,axiom,
% 0.31/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_57_transitions_OPar2B,axiom,
% 0.31/1.55 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_58_sumIdempRight,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_59_sumAssocRight,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_60_sumIdempLeft,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_61_sumAssocLeft,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R ) @ Rel @ ( sum @ P @ ( sum @ Q @ R ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_62_sumSym,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_63_outputBoundTrans,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,C2: late_subject,X2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X2 @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_64_transitions_OResB,axiom,
% 0.31/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 0.31/1.55 => ( ( Y2 != X2 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.31/1.55 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P3 ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_65_nilSim_I3_J,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.31/1.55 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_66_sumZeroRight,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_67_sumZeroLeft,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_68_Late__Semantics_OResB,axiom,
% 0.31/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 0.31/1.55 => ( ( Y2 != X2 )
% 0.31/1.55 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_69_inputIneqTrans,axiom,
% 0.31/1.55 ! [A2: name,X2: name,P: pi,B2: late_subject,Y2: name,P3: pi] :
% 0.31/1.55 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y2 @ P3 ) )
% 0.31/1.55 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_70_pi_Odistinct_I85_J,axiom,
% 0.31/1.55 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.31/1.55 ( ( par @ Pi1 @ Pi2 )
% 0.31/1.55 != ( res @ Name @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_71_freshRes,axiom,
% 0.31/1.55 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_72_residual_Odistinct_I1_J,axiom,
% 0.31/1.55 ! [Subject2: late_subject,Name4: name,Pi3: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.31/1.55 ( ( late_BoundR @ Subject2 @ Name4 @ Pi3 )
% 0.31/1.55 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_73_residual_Oinducts,axiom,
% 0.31/1.55 ! [P: late_residual > $o,Residual: late_residual] :
% 0.31/1.55 ( ! [Subject: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) )
% 0.31/1.55 => ( ! [FreeRes: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.31/1.55 => ( P @ Residual ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_74_pi_Odistinct_I79_J,axiom,
% 0.31/1.55 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( sum @ Pi1 @ Pi2 )
% 0.31/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_75_pi_Odistinct_I55_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_76_sumResLeft,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),X2: name,P: pi,Q: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( ( eqvt @ pi @ Rel )
% 0.31/1.55 => ( strong743114133lation @ ( sum @ ( res @ X2 @ P ) @ ( res @ X2 @ Q ) ) @ Rel @ ( res @ X2 @ ( sum @ P @ Q ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_77_pi_Odistinct_I13_J,axiom,
% 0.31/1.55 ! [Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( piNil
% 0.31/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_78_outputTauTrans,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_79_pi_Odistinct_I31_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.31/1.55 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( res @ Name @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_80_pi_Odistinct_I27_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_81_pi_Odistinct_I21_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.31/1.55 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_82_pi_Odistinct_I1_J,axiom,
% 0.31/1.55 ! [Name1: name,Name2: name,Pi: pi] :
% 0.31/1.55 ( piNil
% 0.31/1.55 != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_83_nilSimRight,axiom,
% 0.31/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_84_resOutputTauTrans,axiom,
% 0.31/1.55 ! [X2: name,A2: name,B2: name,P: pi,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_85_Par1F,axiom,
% 0.31/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_86_Strong__Late__Sim_Oreflexive,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_87_subset__antisym,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 0.31/1.55 => ( A3 = B3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_88_subsetI,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.31/1.55 ( ! [X5: A] :
% 0.31/1.55 ( ( member @ A @ X5 @ A3 )
% 0.31/1.55 => ( member @ A @ X5 @ B3 ) )
% 0.31/1.55 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_89_monotonic,axiom,
% 0.31/1.55 ! [P: pi,A3: set @ ( product_prod @ pi @ pi ),P3: pi,B3: set @ ( product_prod @ pi @ pi )] :
% 0.31/1.55 ( ( strong743114133lation @ P @ A3 @ P3 )
% 0.31/1.55 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 0.31/1.55 => ( strong743114133lation @ P @ B3 @ P3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_90_order__refl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_91_resOutputInputTrans,axiom,
% 0.31/1.55 ! [X2: name,A2: name,B2: name,P: pi,C2: name,Y2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y2 @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_92_resInputBoundOutputTrans,axiom,
% 0.31/1.55 ! [X2: name,A2: name,Y2: name,P: pi,B2: name,Z: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_93_freeRes_Orecs_I2_J,axiom,
% 0.31/1.55 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T] :
% 0.31/1.55 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.31/1.55 => ( ( P @ F2 )
% 0.31/1.55 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ late_TauR )
% 0.31/1.55 = F2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_94_resOutputOutputTrans,axiom,
% 0.31/1.55 ! [X2: name,A2: name,P: pi,B2: name,Y2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y2 ) @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_95_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.31/1.55 ! [X22: name,X1: name,Y22: name,Y1: name] :
% 0.31/1.55 ( ( ( late_OutputR @ X22 @ X1 )
% 0.31/1.55 = ( late_OutputR @ Y22 @ Y1 ) )
% 0.31/1.55 = ( ( X22 = Y22 )
% 0.31/1.55 & ( X1 = Y1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_96_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.31/1.55 ! [X1: name,Y1: name] :
% 0.31/1.55 ( ( ( late_BoundOutputS @ X1 )
% 0.31/1.55 = ( late_BoundOutputS @ Y1 ) )
% 0.31/1.55 = ( X1 = Y1 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_97_name__fresh,axiom,
% 0.31/1.55 ( ( fresh @ name @ name )
% 0.31/1.55 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_98_subject_Ofresh_I1_J,axiom,
% 0.31/1.55 ! [A2: name,X1: name] :
% 0.31/1.55 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.31/1.55 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_99_subject_Ofresh_I2_J,axiom,
% 0.31/1.55 ! [A2: name,X1: name] :
% 0.31/1.55 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.31/1.55 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_100_freeRes_Ofresh_I1_J,axiom,
% 0.31/1.55 ! [A2: name,X22: name,X1: name] :
% 0.31/1.55 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.31/1.55 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.31/1.55 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_101_subject_Ostrong__inducts,axiom,
% 0.31/1.55 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 0.31/1.55 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.31/1.55 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.31/1.55 => ( P @ Z @ Subject2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_102_subject_Ostrong__induct_H,axiom,
% 0.31/1.55 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 0.31/1.55 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.31/1.55 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.31/1.55 => ( P @ Z @ Subject2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_103_subject_Oinducts,axiom,
% 0.31/1.55 ! [P: late_subject > $o,Subject2: late_subject] :
% 0.31/1.55 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.31/1.55 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.31/1.55 => ( P @ Subject2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_104_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.31/1.55 ! [Name4: name,Name: name] :
% 0.31/1.55 ( ( late_InputS @ Name4 )
% 0.31/1.55 != ( late_BoundOutputS @ Name ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_105_freeRes_Orecs_I1_J,axiom,
% 0.31/1.55 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T,Name12: name,Name22: name] :
% 0.31/1.55 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.31/1.55 => ( ( P @ F2 )
% 0.31/1.55 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ ( late_OutputR @ Name12 @ Name22 ) )
% 0.31/1.55 = ( F1 @ Name12 @ Name22 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_106_freeRes_Ostrong__inducts,axiom,
% 0.31/1.55 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.31/1.55 ( ! [Name13: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.31/1.55 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.31/1.55 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_107_freeRes_Ostrong__induct_H,axiom,
% 0.31/1.55 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.31/1.55 ( ! [Name13: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.31/1.55 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.31/1.55 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_108_freeRes_Oinducts,axiom,
% 0.31/1.55 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.31/1.55 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.31/1.55 => ( ( P @ late_TauR )
% 0.31/1.55 => ( P @ FreeRes3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_109_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name] :
% 0.31/1.55 ( ( late_OutputR @ Name12 @ Name22 )
% 0.31/1.55 != late_TauR ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_110_Open,axiom,
% 0.31/1.55 ! [P: pi,A2: name,B2: name,P3: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.31/1.55 => ( ( A2 != B2 )
% 0.31/1.55 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_111_le__funD,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ! [F3: A > B,G: A > B,X2: A] :
% 0.31/1.55 ( ( ord_less_eq @ ( A > B ) @ F3 @ G )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_112_le__funE,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ! [F3: A > B,G: A > B,X2: A] :
% 0.31/1.55 ( ( ord_less_eq @ ( A > B ) @ F3 @ G )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_113_le__funI,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ! [F3: A > B,G: A > B] :
% 0.31/1.55 ( ! [X5: A] : ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( G @ X5 ) )
% 0.31/1.55 => ( ord_less_eq @ ( A > B ) @ F3 @ G ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_114_le__fun__def,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/1.55 = ( ^ [F4: A > B,G2: A > B] :
% 0.31/1.55 ! [X4: A] : ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_115_order__subst1,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( order @ B )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ ( F3 @ B2 ) )
% 0.31/1.55 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.31/1.55 => ( ! [X5: B,Y: B] :
% 0.31/1.55 ( ( ord_less_eq @ B @ X5 @ Y )
% 0.31/1.55 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_116_order__subst2,axiom,
% 0.31/1.55 ! [A: $tType,C3: $tType] :
% 0.31/1.55 ( ( ( order @ C3 )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F3: A > C3,C2: C3] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ C3 @ ( F3 @ B2 ) @ C2 )
% 0.31/1.55 => ( ! [X5: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X5 @ Y )
% 0.31/1.55 => ( ord_less_eq @ C3 @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.31/1.55 => ( ord_less_eq @ C3 @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_117_ord__eq__le__subst,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( ord @ B )
% 0.31/1.55 & ( ord @ A ) )
% 0.31/1.55 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 0.31/1.55 ( ( A2
% 0.31/1.55 = ( F3 @ B2 ) )
% 0.31/1.55 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.31/1.55 => ( ! [X5: B,Y: B] :
% 0.31/1.55 ( ( ord_less_eq @ B @ X5 @ Y )
% 0.31/1.55 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_118_ord__le__eq__subst,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( ord @ B )
% 0.31/1.55 & ( ord @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F3: A > B,C2: B] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ( F3 @ B2 )
% 0.31/1.55 = C2 )
% 0.31/1.55 => ( ! [X5: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X5 @ Y )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( F3 @ Y ) ) )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_119_eq__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.31/1.55 = ( ^ [X4: A,Y5: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.31/1.55 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_120_antisym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X2: A,Y2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.31/1.55 => ( X2 = Y2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_121_linear,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X2: A,Y2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.55 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_122_eq__refl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X2: A,Y2: A] :
% 0.31/1.55 ( ( X2 = Y2 )
% 0.31/1.55 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_123_le__cases,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X2: A,Y2: A] :
% 0.31/1.55 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.55 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_124_order_Otrans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_125_le__cases3,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X2: A,Y2: A,Z: A] :
% 0.31/1.55 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Y2 @ Z ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Z @ Y2 ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ Z @ Y2 )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ Y2 @ Z )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 0.31/1.55 => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_126_antisym__conv,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [Y2: A,X2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.55 = ( X2 = Y2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_127_order__class_Oorder_Oeq__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.31/1.55 = ( ^ [A5: A,B4: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.31/1.55 & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_128_ord__eq__le__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C2: A] :
% 0.31/1.55 ( ( A2 = B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_129_ord__le__eq__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( B2 = C2 )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_130_order__class_Oorder_Oantisym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( A2 = B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_131_order__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X2: A,Y2: A,Z: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ Y2 @ Z )
% 0.31/1.55 => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_132_dual__order_Orefl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_133_linorder__wlog,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.31/1.55 ( ! [A4: A,B5: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A4 @ B5 )
% 0.31/1.55 => ( P @ A4 @ B5 ) )
% 0.31/1.55 => ( ! [A4: A,B5: A] :
% 0.31/1.55 ( ( P @ B5 @ A4 )
% 0.31/1.55 => ( P @ A4 @ B5 ) )
% 0.31/1.55 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_134_dual__order_Otrans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_135_dual__order_Oeq__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.31/1.55 = ( ^ [A5: A,B4: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.31/1.55 & ( ord_less_eq @ A @ A5 @ B4 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_136_dual__order_Oantisym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( A2 = B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_137_in__mono,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A,X2: A] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.55 => ( ( member @ A @ X2 @ A3 )
% 0.31/1.55 => ( member @ A @ X2 @ B3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_138_subsetD,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A,C2: A] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.55 => ( ( member @ A @ C2 @ A3 )
% 0.31/1.55 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_139_equalityE,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.31/1.55 ( ( A3 = B3 )
% 0.31/1.55 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.55 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_140_subset__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.55 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.31/1.55 ! [X4: A] :
% 0.31/1.55 ( ( member @ A @ X4 @ A6 )
% 0.31/1.55 => ( member @ A @ X4 @ B6 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_141_equalityD1,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.31/1.55 ( ( A3 = B3 )
% 0.31/1.55 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_142_equalityD2,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.31/1.55 ( ( A3 = B3 )
% 0.31/1.55 => ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_143_subset__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.55 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.31/1.55 ! [T2: A] :
% 0.31/1.55 ( ( member @ A @ T2 @ A6 )
% 0.31/1.55 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_144_subset__refl,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_145_Collect__mono,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.55 ( ! [X5: A] :
% 0.31/1.55 ( ( P @ X5 )
% 0.31/1.55 => ( Q @ X5 ) )
% 0.31/1.55 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_146_subset__trans,axiom,
% 0.31/1.55 ! [A: $tType,A3: set @ A,B3: set @ A,C4: set @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C4 )
% 0.31/1.55 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_147_set__eq__subset,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 0.31/1.55 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.31/1.55 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_148_Collect__mono__iff,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.31/1.55 = ( ! [X4: A] :
% 0.31/1.55 ( ( P @ X4 )
% 0.31/1.55 => ( Q @ X4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_149_resCasesB_H,axiom,
% 0.31/1.55 ! [X6: name,P: pi,A2: late_subject,Y6: name,P3: pi] :
% 0.31/1.55 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y6 @ P3 ) )
% 0.31/1.55 => ( ! [P4: pi,A4: name,B5: name] :
% 0.31/1.55 ( ( ( res @ X6 @ P )
% 0.31/1.55 = ( res @ B5 @ P4 ) )
% 0.31/1.55 => ! [P2: pi] :
% 0.31/1.55 ( ( ( late_BoundR @ A2 @ Y6 @ P3 )
% 0.31/1.55 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B5 @ P2 ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B5 ) @ P2 ) )
% 0.31/1.55 => ( A4 = B5 ) ) ) )
% 0.31/1.55 => ~ ! [P4: pi,A4: late_subject,X5: name,P2: pi,Y: name] :
% 0.31/1.55 ( ( ( res @ X6 @ P )
% 0.31/1.55 = ( res @ Y @ P4 ) )
% 0.31/1.55 => ( ( ( late_BoundR @ A2 @ Y6 @ P3 )
% 0.31/1.55 = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P2 ) ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P2 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 0.31/1.55 => ( ( Y != X5 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.31/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_150_Output,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_151_outputIneqTrans,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,C2: name,D: name,P3: pi] :
% 0.31/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D ) @ P3 ) )
% 0.31/1.55 => ~ ( ( A2 != C2 )
% 0.31/1.55 | ( B2 != D ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_152_outputCases_H,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.31/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 0.31/1.55 => ~ ! [A4: name,B5: name,P4: pi] :
% 0.31/1.55 ( ( ( A2 = A4 )
% 0.31/1.55 & ( B2 = B5 )
% 0.31/1.55 & ( P = P4 ) )
% 0.31/1.55 => ( Rs
% 0.31/1.55 != ( late_FreeR @ ( late_OutputR @ A4 @ B5 ) @ P4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_153_outputCases,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.31/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ( ( ( Alpha
% 0.31/1.55 = ( late_OutputR @ A2 @ B2 ) )
% 0.31/1.55 => ( ( P = P3 )
% 0.31/1.55 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 0.31/1.55 => ( Prop @ Alpha @ P3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_154_Late__Semantics_OInput,axiom,
% 0.31/1.55 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_155_transitions_OInput,axiom,
% 0.31/1.55 ! [X2: name,A2: name,P: pi] :
% 0.31/1.55 ( ( X2 != A2 )
% 0.31/1.55 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_156_inputBoundOutputTrans,axiom,
% 0.31/1.55 ! [A2: name,X2: name,P: pi,B2: name,Y2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y2 @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_157_resCases_H,axiom,
% 0.31/1.55 ! [X2: name,P: pi,Rs: late_residual] :
% 0.31/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 0.31/1.55 => ( ! [P4: pi,A4: name,B5: name] :
% 0.31/1.55 ( ( ( res @ X2 @ P )
% 0.31/1.55 = ( res @ B5 @ P4 ) )
% 0.31/1.55 => ! [P2: pi] :
% 0.31/1.55 ( ( Rs
% 0.31/1.55 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B5 @ P2 ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B5 ) @ P2 ) )
% 0.31/1.55 => ( A4 = B5 ) ) ) )
% 0.31/1.55 => ( ! [P4: pi,A4: late_subject,X5: name,P2: pi,Y: name] :
% 0.31/1.55 ( ( ( res @ X2 @ P )
% 0.31/1.55 = ( res @ Y @ P4 ) )
% 0.31/1.55 => ( ( Rs
% 0.31/1.55 = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P2 ) ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P2 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 0.31/1.55 => ( ( Y != X5 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.31/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 0.31/1.55 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 0.31/1.55 ( ( ( res @ X2 @ P )
% 0.31/1.55 = ( res @ Y @ P4 ) )
% 0.31/1.55 => ( ( Rs
% 0.31/1.55 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 0.31/1.55 => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_158_transitions_OClose2,axiom,
% 0.31/1.55 ! [P: pi,A2: name,Y2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.31/1.55 => ( ( X2 != A2 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 0.31/1.55 => ( ( Y2 != A2 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ Q2 )
% 0.31/1.55 => ( ( X2 != Y2 )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_159_transitions_OClose1,axiom,
% 0.31/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.31/1.55 => ( ( X2 != A2 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.31/1.55 => ( ( Y2 != A2 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P3 )
% 0.31/1.55 => ( ( X2 != Y2 )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_160_Late__Semantics_OClose2,axiom,
% 0.31/1.55 ! [P: pi,A2: name,Y2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_161_Late__Semantics_OClose1,axiom,
% 0.31/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_162_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.31/1.55 ! [X22: name,Y22: name] :
% 0.31/1.55 ( ( ( late_BoundOutputS @ X22 )
% 0.31/1.55 = ( late_BoundOutputS @ Y22 ) )
% 0.31/1.55 = ( X22 = Y22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_163_subst__identity,axiom,
% 0.31/1.55 ! [P: pi,A2: name] :
% 0.31/1.55 ( ( subs @ P @ A2 @ A2 )
% 0.31/1.55 = P ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_164_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.31/1.55 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.31/1.55 ( ( ( late_OutputR @ X11 @ X122 )
% 0.31/1.55 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.31/1.55 = ( ( X11 = Y11 )
% 0.31/1.55 & ( X122 = Y12 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_165_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.31/1.55 ! [X1: name,Y1: name] :
% 0.31/1.55 ( ( ( late_InputS @ X1 )
% 0.31/1.55 = ( late_InputS @ Y1 ) )
% 0.31/1.55 = ( X1 = Y1 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_166_simps_I9_J,axiom,
% 0.31/1.55 ! [X2: name,C2: name,D: name,P: pi] :
% 0.31/1.55 ( ( X2 != C2 )
% 0.31/1.55 => ( ( X2 != D )
% 0.31/1.55 => ( ( subs @ ( res @ X2 @ P ) @ C2 @ D )
% 0.31/1.55 = ( res @ X2 @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_167_simps_I8_J,axiom,
% 0.31/1.55 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.31/1.55 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 0.31/1.55 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_168_substTrans,axiom,
% 0.31/1.55 ! [B2: name,P: pi,A2: name,C2: name] :
% 0.31/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 0.31/1.55 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 0.31/1.55 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_169_simps_I7_J,axiom,
% 0.31/1.55 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.31/1.55 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D )
% 0.31/1.55 = ( sum @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_170_simps_I1_J,axiom,
% 0.31/1.55 ! [C2: name,D: name] :
% 0.31/1.55 ( ( subs @ piNil @ C2 @ D )
% 0.31/1.55 = piNil ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_171_forget,axiom,
% 0.31/1.55 ! [A2: name,P: pi,B2: name] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ P )
% 0.31/1.55 => ( ( subs @ P @ A2 @ B2 )
% 0.31/1.55 = P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_172_fresh__fact1,axiom,
% 0.31/1.55 ! [A2: name,P: pi,C2: name,B2: name] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ P )
% 0.31/1.55 => ( ( A2 != C2 )
% 0.31/1.55 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_173_fresh__fact2,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi] :
% 0.31/1.55 ( ( A2 != B2 )
% 0.31/1.55 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_174_substRes3,axiom,
% 0.31/1.55 ! [B2: name,P: pi,A2: name] :
% 0.31/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 0.31/1.55 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.31/1.55 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_175_substRes2,axiom,
% 0.31/1.55 ! [B2: name,P: pi,A2: name] :
% 0.31/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 0.31/1.55 => ( ( res @ A2 @ P )
% 0.31/1.55 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_176_freeRes_Oexhaust,axiom,
% 0.31/1.55 ! [Y2: late_freeRes] :
% 0.31/1.55 ( ! [X112: name,X123: name] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( late_OutputR @ X112 @ X123 ) )
% 0.31/1.55 => ( Y2 = late_TauR ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_177_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.31/1.55 ! [X11: name,X122: name] :
% 0.31/1.55 ( ( late_OutputR @ X11 @ X122 )
% 0.31/1.55 != late_TauR ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_178_subject_Oexhaust,axiom,
% 0.31/1.55 ! [Y2: late_subject] :
% 0.31/1.55 ( ! [X12: name] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( late_InputS @ X12 ) )
% 0.31/1.55 => ~ ! [X23: name] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_179_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.31/1.55 ! [X1: name,X22: name] :
% 0.31/1.55 ( ( late_InputS @ X1 )
% 0.31/1.55 != ( late_BoundOutputS @ X22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_180_Late__Semantics_OComm1,axiom,
% 0.31/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_181_Late__Semantics_OComm2,axiom,
% 0.31/1.55 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_182_transitions_OComm1,axiom,
% 0.31/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( ( X2 != A2 )
% 0.31/1.55 => ( ( X2 != B2 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_183_transitions_OComm2,axiom,
% 0.31/1.55 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.31/1.55 => ( ( X2 != A2 )
% 0.31/1.55 => ( ( X2 != B2 )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 0.31/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_184_resSimCases,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( fs_name @ A )
% 0.31/1.55 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C4: A] :
% 0.31/1.55 ( ( eqvt @ pi @ Rel )
% 0.31/1.55 => ( ! [Q3: pi,A4: name] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q3 ) )
% 0.31/1.55 => ( ( A4 != X2 )
% 0.31/1.55 => ? [P5: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P5 ) )
% 0.31/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 0.31/1.55 => ( ! [Q3: pi,A4: late_subject,Y: name] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 0.31/1.55 => ( ( X2 != Y )
% 0.31/1.55 => ( ( fresh @ name @ A @ Y @ C4 )
% 0.31/1.55 => ? [P5: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 0.31/1.55 & ( strong2129052853vative @ P5 @ ( res @ X2 @ Q3 ) @ A4 @ Y @ Rel ) ) ) ) ) )
% 0.31/1.55 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.31/1.55 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 0.31/1.55 => ? [P5: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.31/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ ( res @ X2 @ Q3 ) ) @ Rel ) ) ) )
% 0.31/1.55 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_185_simE_I1_J,axiom,
% 0.31/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 0.31/1.55 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.31/1.55 => ? [P2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.31/1.55 & ( strong2129052853vative @ P2 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_186_simCasesCont,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( fs_name @ A )
% 0.31/1.55 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.31/1.55 ( ( eqvt @ pi @ Rel )
% 0.31/1.55 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.31/1.55 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.31/1.55 => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 0.31/1.55 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.31/1.55 => ? [P5: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 0.31/1.55 & ( strong2129052853vative @ P5 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.31/1.55 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.31/1.55 => ? [P5: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.31/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.31/1.55 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_187_derivativeMonotonic,axiom,
% 0.31/1.55 ! [P: pi,Q: pi,A2: late_subject,X2: name,A3: set @ ( product_prod @ pi @ pi ),B3: set @ ( product_prod @ pi @ pi )] :
% 0.31/1.55 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ A3 )
% 0.31/1.55 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 0.31/1.55 => ( strong2129052853vative @ P @ Q @ A2 @ X2 @ B3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_188_simulation__def,axiom,
% 0.31/1.55 ( strong743114133lation
% 0.31/1.55 = ( ^ [P6: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.31/1.55 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.31/1.55 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.31/1.55 & ( fresh @ name @ pi @ X4 @ P6 ) )
% 0.31/1.55 => ? [P7: pi] :
% 0.31/1.55 ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X4 @ P7 ) )
% 0.31/1.55 & ( strong2129052853vative @ P7 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.31/1.55 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.31/1.55 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.31/1.55 => ? [P7: pi] :
% 0.31/1.55 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 0.31/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_189_simCases,axiom,
% 0.31/1.55 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.31/1.55 ( ! [A4: late_subject,Y: name,Q3: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 0.31/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/1.55 => ? [P5: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 0.31/1.55 & ( strong2129052853vative @ P5 @ Q3 @ A4 @ Y @ Rel ) ) ) )
% 0.31/1.55 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.31/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.31/1.55 => ? [P5: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.31/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.31/1.55 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_190_simE_I2_J,axiom,
% 0.31/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.31/1.55 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.31/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.31/1.55 => ? [P2: pi] :
% 0.31/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P2 @ Q2 ) @ Rel ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_191_derivativeReflexive,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,A2: late_subject,X2: name] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( strong2129052853vative @ P @ P @ A2 @ X2 @ Rel ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_192_pair__in__Id__conv,axiom,
% 0.31/1.55 ! [A: $tType,A2: A,B2: A] :
% 0.31/1.55 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.31/1.55 = ( A2 = B2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_193_IdI,axiom,
% 0.31/1.55 ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_194_subrelI,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.31/1.55 ( ! [X5: A,Y: B] :
% 0.31/1.55 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ R2 )
% 0.31/1.55 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ S ) )
% 0.31/1.55 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_195_IdE,axiom,
% 0.31/1.55 ! [A: $tType,P8: product_prod @ A @ A] :
% 0.31/1.55 ( ( member @ ( product_prod @ A @ A ) @ P8 @ ( id @ A ) )
% 0.31/1.55 => ~ ! [X5: A] :
% 0.31/1.55 ( P8
% 0.31/1.55 != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_196_fresh__prod,axiom,
% 0.31/1.55 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y2: B] :
% 0.31/1.55 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y2 ) )
% 0.31/1.55 = ( ( fresh @ X @ A @ A2 @ X2 )
% 0.31/1.55 & ( fresh @ X @ B @ A2 @ Y2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_197_old_Oprod_Oinject,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.31/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/1.55 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.31/1.55 = ( ( A2 = A7 )
% 0.31/1.55 & ( B2 = B7 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_198_prod_Oinject,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 0.31/1.55 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.31/1.55 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.31/1.55 = ( ( X1 = Y1 )
% 0.31/1.55 & ( X22 = Y22 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_199_surj__pair,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,P8: product_prod @ A @ B] :
% 0.31/1.55 ? [X5: A,Y: B] :
% 0.31/1.55 ( P8
% 0.31/1.55 = ( product_Pair @ A @ B @ X5 @ Y ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_200_prod__cases,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P8: product_prod @ A @ B] :
% 0.31/1.55 ( ! [A4: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B5 ) )
% 0.31/1.55 => ( P @ P8 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_201_Pair__inject,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.31/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/1.55 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.31/1.55 => ~ ( ( A2 = A7 )
% 0.31/1.55 => ( B2 != B7 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_202_prod__cases3,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,C3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.31/1.55 ~ ! [A4: A,B5: B,C: C3] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B5 @ C ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_203_prod__cases4,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 0.31/1.55 ~ ! [A4: A,B5: B,C: C3,D3: D2] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B5 @ ( product_Pair @ C3 @ D2 @ C @ D3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_204_prod__cases5,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 0.31/1.55 ~ ! [A4: A,B5: B,C: C3,D3: D2,E2: E] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_205_prod__cases6,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F5: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.31/1.55 ~ ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ F5 ) @ D3 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_206_prod__cases7,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F5: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 0.31/1.55 ~ ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5,G4: G3] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_207_prod__induct3,axiom,
% 0.31/1.55 ! [C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.31/1.55 ( ! [A4: A,B5: B,C: C3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B5 @ C ) ) )
% 0.31/1.55 => ( P @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_208_prod__induct4,axiom,
% 0.31/1.55 ! [D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 0.31/1.55 ( ! [A4: A,B5: B,C: C3,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B5 @ ( product_Pair @ C3 @ D2 @ C @ D3 ) ) ) )
% 0.31/1.55 => ( P @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_209_prod__induct5,axiom,
% 0.31/1.55 ! [E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 0.31/1.55 ( ! [A4: A,B5: B,C: C3,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 0.31/1.55 => ( P @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_210_prod__induct6,axiom,
% 0.31/1.55 ! [F5: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.31/1.55 ( ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F5 ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ F5 ) @ D3 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 0.31/1.55 => ( P @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_211_prod__induct7,axiom,
% 0.31/1.55 ! [G3: $tType,F5: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 0.31/1.55 ( ! [A4: A,B5: B,C: C3,D3: D2,E2: E,F6: F5,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) )
% 0.31/1.55 => ( P @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_212_old_Oprod_Oexhaust,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 0.31/1.55 ~ ! [A4: A,B5: B] :
% 0.31/1.55 ( Y2
% 0.31/1.55 != ( product_Pair @ A @ B @ A4 @ B5 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_213_old_Oprod_Oinducts,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.31/1.55 ( ! [A4: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B5 ) )
% 0.31/1.55 => ( P @ Prod ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_214_fresh__prodD_I2_J,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType,C3: $tType,A2: A,X2: B,Y2: C3] :
% 0.31/1.55 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y2 ) )
% 0.31/1.55 => ( fresh @ A @ C3 @ A2 @ Y2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_215_fresh__prodD_I1_J,axiom,
% 0.31/1.55 ! [C3: $tType,A: $tType,B: $tType,A2: A,X2: B,Y2: C3] :
% 0.31/1.55 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y2 ) )
% 0.31/1.55 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_216_old_Oprod_Orec,axiom,
% 0.31/1.55 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.31/1.55 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/1.55 = ( F1 @ A2 @ B2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_217_IdD,axiom,
% 0.31/1.55 ! [A: $tType,A2: A,B2: A] :
% 0.31/1.55 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.31/1.55 => ( A2 = B2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_218_subject_Orecs_I2_J,axiom,
% 0.31/1.55 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name4: name] :
% 0.31/1.55 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.31/1.55 => ( ! [X12: name] : ( P @ ( F2 @ X12 ) )
% 0.31/1.55 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_BoundOutputS @ Name4 ) )
% 0.31/1.55 = ( F2 @ Name4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_219_subject_Orecs_I1_J,axiom,
% 0.31/1.55 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name4: name] :
% 0.31/1.55 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.31/1.55 => ( ! [X12: name] : ( P @ ( F2 @ X12 ) )
% 0.31/1.55 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_InputS @ Name4 ) )
% 0.31/1.55 = ( F1 @ Name4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_220_resTauOutputTrans,axiom,
% 0.31/1.55 ! [X2: name,P: pi,A2: name,B2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_221_residual_Ofresh_I1_J,axiom,
% 0.31/1.55 ! [A2: name,X3: late_subject,X1: name,X22: pi] :
% 0.31/1.55 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X3 @ X1 @ X22 ) )
% 0.31/1.55 = ( ( fresh @ name @ late_subject @ A2 @ X3 )
% 0.31/1.55 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_222_pi_Ofresh_I3_J,axiom,
% 0.31/1.55 ! [A2: name,X1: pi] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.31/1.55 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_223_simps_I2_J,axiom,
% 0.31/1.55 ! [P: pi,C2: name,D: name] :
% 0.31/1.55 ( ( subs @ ( tau @ P ) @ C2 @ D )
% 0.31/1.55 = ( tau @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_224_pi_Ofresh_I9_J,axiom,
% 0.31/1.55 ! [A2: name,X1: name,X22: pi] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.31/1.55 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_225_pi_Ofresh_I4_J,axiom,
% 0.31/1.55 ! [A2: name,X3: name,X1: name,X22: pi] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ ( input @ X3 @ X1 @ X22 ) )
% 0.31/1.55 = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.31/1.55 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_226_name__fresh__abs,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( fs_name @ A )
% 0.31/1.55 => ! [B2: name,A2: name,X2: A] :
% 0.31/1.55 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 0.31/1.55 = ( ( B2 = A2 )
% 0.31/1.55 | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_227_abs__fresh_I1_J,axiom,
% 0.31/1.55 ! [X7: $tType] :
% 0.31/1.55 ( ( fs_name @ X7 )
% 0.31/1.55 => ! [B2: name,A2: name,X2: X7] :
% 0.31/1.55 ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B2 @ ( abs_fun @ name @ X7 @ A2 @ X2 ) )
% 0.31/1.55 = ( ( B2 = A2 )
% 0.31/1.55 | ( fresh @ name @ X7 @ B2 @ X2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_228_pi_Oinject_I2_J,axiom,
% 0.31/1.55 ! [X1: pi,Y1: pi] :
% 0.31/1.55 ( ( ( tau @ X1 )
% 0.31/1.55 = ( tau @ Y1 ) )
% 0.31/1.55 = ( X1 = Y1 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_229_pi_Odistinct_I3_J,axiom,
% 0.31/1.55 ! [Pi: pi] :
% 0.31/1.55 ( piNil
% 0.31/1.55 != ( tau @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_230_pi_Odistinct_I19_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.31/1.55 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( tau @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_231_pi_Odistinct_I35_J,axiom,
% 0.31/1.55 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.31/1.55 ( ( tau @ Pi3 )
% 0.31/1.55 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_232_pi_Odistinct_I41_J,axiom,
% 0.31/1.55 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( tau @ Pi3 )
% 0.31/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_233_pi_Odistinct_I43_J,axiom,
% 0.31/1.55 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( tau @ Pi3 )
% 0.31/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_234_pi_Odistinct_I45_J,axiom,
% 0.31/1.55 ! [Pi3: pi,Name: name,Pi: pi] :
% 0.31/1.55 ( ( tau @ Pi3 )
% 0.31/1.55 != ( res @ Name @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_235_pi_Oinject_I3_J,axiom,
% 0.31/1.55 ! [X3: name,X1: name,X22: pi,Y3: name,Y1: name,Y22: pi] :
% 0.31/1.55 ( ( ( input @ X3 @ X1 @ X22 )
% 0.31/1.55 = ( input @ Y3 @ Y1 @ Y22 ) )
% 0.31/1.55 = ( ( X3 = Y3 )
% 0.31/1.55 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.31/1.55 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_236_residual_Oinject_I1_J,axiom,
% 0.31/1.55 ! [X3: late_subject,X1: name,X22: pi,Y3: late_subject,Y1: name,Y22: pi] :
% 0.31/1.55 ( ( ( late_BoundR @ X3 @ X1 @ X22 )
% 0.31/1.55 = ( late_BoundR @ Y3 @ Y1 @ Y22 ) )
% 0.31/1.55 = ( ( X3 = Y3 )
% 0.31/1.55 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.31/1.55 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_237_pi_Oinject_I8_J,axiom,
% 0.31/1.55 ! [X1: name,X22: pi,Y1: name,Y22: pi] :
% 0.31/1.55 ( ( ( res @ X1 @ X22 )
% 0.31/1.55 = ( res @ Y1 @ Y22 ) )
% 0.31/1.55 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.31/1.55 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_238_tauBoundTrans,axiom,
% 0.31/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_239_nilSim_I1_J,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.31/1.55 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_240_resTauBoundTrans,axiom,
% 0.31/1.55 ! [X2: name,P: pi,A2: late_subject,Y2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y2 @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_241_tauOutputTrans,axiom,
% 0.31/1.55 ! [P: pi,A2: name,B2: name,P3: pi] :
% 0.31/1.55 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_242_tauCases,axiom,
% 0.31/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.31/1.55 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.31/1.55 => ( ( ( Alpha = late_TauR )
% 0.31/1.55 => ( ( P = P3 )
% 0.31/1.55 => ( Prop @ late_TauR @ P ) ) )
% 0.31/1.55 => ( Prop @ Alpha @ P3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_243_tauCases_H,axiom,
% 0.31/1.55 ! [P: pi,Rs: late_residual] :
% 0.31/1.55 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.31/1.55 => ~ ! [P4: pi] :
% 0.31/1.55 ( ( ( tau @ P )
% 0.31/1.55 = ( tau @ P4 ) )
% 0.31/1.55 => ( Rs
% 0.31/1.55 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_244_Tau,axiom,
% 0.31/1.55 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_245_inputCases_H,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.31/1.55 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 0.31/1.55 => ~ ! [X5: name,A4: name,P4: pi] :
% 0.31/1.55 ( ( ( A2 = A4 )
% 0.31/1.55 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 0.31/1.55 = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 0.31/1.55 => ( ( Rs
% 0.31/1.55 = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P4 ) )
% 0.31/1.55 => ( X5 = A4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_246_mismatchIdRight,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( ( A2 != B2 )
% 0.31/1.55 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A2 @ B2 @ P ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_247_mismatchIdLeft,axiom,
% 0.31/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.31/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.31/1.55 => ( ( A2 != B2 )
% 0.31/1.55 => ( strong743114133lation @ ( mismatch @ A2 @ B2 @ P ) @ Rel @ P ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_248_pi_Ofresh_I6_J,axiom,
% 0.31/1.55 ! [A2: name,X3: name,X22: name,X1: pi] :
% 0.31/1.55 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X3 @ X22 @ X1 ) )
% 0.31/1.55 = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.31/1.55 & ( fresh @ name @ name @ A2 @ X22 )
% 0.31/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_249_pi_Odistinct_I39_J,axiom,
% 0.31/1.55 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.31/1.55 ( ( tau @ Pi3 )
% 0.31/1.55 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_250_mismatchCases,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.31/1.55 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.31/1.55 => ( ( ( late_transitions @ P @ Rs )
% 0.31/1.55 => ( ( A2 != B2 )
% 0.31/1.55 => ( F @ A2 @ B2 ) ) )
% 0.31/1.55 => ( F @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_251_mismatchTrans,axiom,
% 0.31/1.55 ! [A2: name,P: pi,Rs: late_residual] :
% 0.31/1.55 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_252_mismatchCases_H,axiom,
% 0.31/1.55 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.31/1.55 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.31/1.55 => ~ ! [P4: pi,A4: name,B5: name] :
% 0.31/1.55 ( ( ( A2 = A4 )
% 0.31/1.55 & ( B2 = B5 )
% 0.31/1.55 & ( P = P4 ) )
% 0.31/1.55 => ( ( late_transitions @ P4 @ Rs )
% 0.31/1.55 => ( A4 = B5 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_253_Mismatch,axiom,
% 0.31/1.55 ! [P: pi,Rs: late_residual,A2: name,B2: name] :
% 0.31/1.55 ( ( late_transitions @ P @ Rs )
% 0.31/1.55 => ( ( A2 != B2 )
% 0.31/1.55 => ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_254_pi_Odistinct_I75_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.31/1.55 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( res @ Name @ Pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_255_pi_Odistinct_I73_J,axiom,
% 0.31/1.55 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.31/1.55 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.31/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/1.55 ! [A8: $tType,A9: $tType] :
% 0.31/1.55 ( ( preorder @ A9 )
% 0.31/1.55 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/1.55 ! [A8: $tType,A9: $tType] :
% 0.31/1.55 ( ( order @ A9 )
% 0.31/1.55 => ( order @ ( A8 > A9 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/1.55 ! [A8: $tType,A9: $tType] :
% 0.31/1.55 ( ( ord @ A9 )
% 0.31/1.55 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 0.31/1.55 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.31/1.55 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 0.31/1.55 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.31/1.55 fs_name @ pi ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.31/1.55 preorder @ $o ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.31/1.55 linorder @ $o ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 0.31/1.55 order @ $o ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 0.31/1.55 ord @ $o ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_HOL_Obool___Agent_Ofs__name_7,axiom,
% 0.31/1.55 fs_name @ $o ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Agent_Oname___Agent_Ofs__name_8,axiom,
% 0.31/1.55 fs_name @ name ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9,axiom,
% 0.31/1.55 ! [A8: $tType,A9: $tType] :
% 0.31/1.55 ( ( ( fs_name @ A8 )
% 0.31/1.55 & ( fs_name @ A9 ) )
% 0.31/1.55 => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10,axiom,
% 0.31/1.55 fs_name @ late_freeRes ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 0.31/1.55 fs_name @ late_subject ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12,axiom,
% 0.31/1.55 fs_name @ late_residual ).
% 0.31/1.55
% 0.31/1.55 thf(conj_0,conjecture,
% 0.31/1.55 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ).
% 0.31/1.55 ------------------------
% 0.31/1.59 % (2063)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_1767 for (2999ds/4Mi)
% 0.31/1.59 % (2063)Instruction limit reached!
% 0.31/1.59 % (2063)------------------------------
% 0.31/1.59 % (2063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (2063)Termination reason: Unknown
% 0.31/1.59 % (2063)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (2063)Memory used [KB]: 1407
% 0.31/1.59 % (2063)Time elapsed: 0.003 s
% 0.31/1.59 % (2063)Instructions burned: 4 (million)
% 0.31/1.59 % (2063)------------------------------
% 0.31/1.59 % (2063)------------------------------
% 0.31/1.59 % (2062)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1767 for (2999ds/183Mi)
% 0.31/1.59 % (2064)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_1767 for (2999ds/27Mi)
% 0.31/1.59 % (2065)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1767 for (2999ds/2Mi)
% 0.31/1.59 % (2066)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_1767 for (2999ds/2Mi)
% 0.31/1.60 % (2067)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_1767 for (2999ds/275Mi)
% 0.31/1.60 % (2068)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1767 for (2999ds/18Mi)
% 2.71/1.60 % (2065)Instruction limit reached!
% 2.71/1.60 % (2065)------------------------------
% 2.71/1.60 % (2065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (2065)Termination reason: Unknown
% 2.71/1.60 % (2065)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (2065)Memory used [KB]: 1407
% 2.71/1.60 % (2065)Time elapsed: 0.004 s
% 2.71/1.60 % (2065)Instructions burned: 3 (million)
% 2.71/1.60 % (2065)------------------------------
% 2.71/1.60 % (2065)------------------------------
% 2.71/1.60 % (2066)Instruction limit reached!
% 2.71/1.60 % (2066)------------------------------
% 2.71/1.60 % (2066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (2066)Termination reason: Unknown
% 2.71/1.60 % (2066)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (2066)Memory used [KB]: 1407
% 2.71/1.60 % (2066)Time elapsed: 0.004 s
% 2.71/1.60 % (2066)Instructions burned: 3 (million)
% 2.71/1.60 % (2066)------------------------------
% 2.71/1.60 % (2066)------------------------------
% 2.71/1.60 % (2069)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1767 for (2999ds/3Mi)
% 2.71/1.60 % (2069)Instruction limit reached!
% 2.71/1.60 % (2069)------------------------------
% 2.71/1.60 % (2069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (2069)Termination reason: Unknown
% 2.71/1.60 % (2069)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (2069)Memory used [KB]: 1407
% 2.71/1.60 % (2069)Time elapsed: 0.002 s
% 2.71/1.60 % (2069)Instructions burned: 3 (million)
% 2.71/1.60 % (2069)------------------------------
% 2.71/1.60 % (2069)------------------------------
% 2.71/1.61 % (2068)Instruction limit reached!
% 2.71/1.61 % (2068)------------------------------
% 2.71/1.61 % (2068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.61 % (2068)Termination reason: Unknown
% 2.71/1.61 % (2068)Termination phase: shuffling
% 2.71/1.61
% 2.71/1.61 % (2068)Memory used [KB]: 1791
% 2.71/1.61 % (2068)Time elapsed: 0.013 s
% 2.71/1.61 % (2068)Instructions burned: 18 (million)
% 2.71/1.61 % (2068)------------------------------
% 2.71/1.61 % (2068)------------------------------
% 2.71/1.61 % (2072)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_1767 for (2999ds/3Mi)
% 2.71/1.61 % (2072)Instruction limit reached!
% 2.71/1.61 % (2072)------------------------------
% 2.71/1.61 % (2072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.61 % (2072)Termination reason: Unknown
% 2.71/1.61 % (2072)Termination phase: shuffling
% 2.71/1.61
% 2.71/1.61 % (2072)Memory used [KB]: 1407
% 2.71/1.61 % (2072)Time elapsed: 0.002 s
% 2.71/1.61 % (2072)Instructions burned: 3 (million)
% 2.71/1.61 % (2072)------------------------------
% 2.71/1.61 % (2072)------------------------------
% 2.71/1.61 % (2064)Instruction limit reached!
% 2.71/1.61 % (2064)------------------------------
% 2.71/1.61 % (2064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.61 % (2064)Termination reason: Unknown
% 2.71/1.61 % (2064)Termination phase: shuffling
% 2.71/1.61
% 2.71/1.61 % (2064)Memory used [KB]: 1918
% 2.71/1.61 % (2064)Time elapsed: 0.019 s
% 2.71/1.61 % (2064)Instructions burned: 27 (million)
% 2.71/1.61 % (2064)------------------------------
% 2.71/1.61 % (2064)------------------------------
% 2.71/1.61 % (2070)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_1767 for (2999ds/37Mi)
% 2.71/1.61 % (2071)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_1767 for (2999ds/15Mi)
% 2.71/1.62 % (2073)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_1767 for (2999ds/1041Mi)
% 2.71/1.62 % (2074)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1767 for (2999ds/7Mi)
% 2.71/1.62 % (2074)Instruction limit reached!
% 2.71/1.62 % (2074)------------------------------
% 2.71/1.62 % (2074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (2074)Termination reason: Unknown
% 2.71/1.62 % (2074)Termination phase: shuffling
% 2.71/1.62
% 2.71/1.62 % (2074)Memory used [KB]: 1535
% 2.71/1.62 % (2074)Time elapsed: 0.004 s
% 2.71/1.62 % (2074)Instructions burned: 9 (million)
% 2.71/1.62 % (2074)------------------------------
% 2.71/1.62 % (2074)------------------------------
% 2.71/1.62 % (2071)Instruction limit reached!
% 2.71/1.62 % (2071)------------------------------
% 2.71/1.62 % (2071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (2071)Termination reason: Unknown
% 2.71/1.62 % (2071)Termination phase: shuffling
% 2.71/1.62
% 2.71/1.62 % (2071)Memory used [KB]: 1791
% 2.71/1.62 % (2071)Time elapsed: 0.012 s
% 2.71/1.62 % (2071)Instructions burned: 16 (million)
% 2.71/1.62 % (2071)------------------------------
% 2.71/1.62 % (2071)------------------------------
% 2.71/1.63 % (2075)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1767 for (2999ds/16Mi)
% 2.71/1.63 % (2076)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_1767 for (2999ds/3Mi)
% 2.71/1.63 % (2076)Instruction limit reached!
% 2.71/1.63 % (2076)------------------------------
% 2.71/1.63 % (2076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.63 % (2076)Termination reason: Unknown
% 2.71/1.63 % (2076)Termination phase: shuffling
% 2.71/1.63
% 2.71/1.63 % (2076)Memory used [KB]: 1407
% 2.71/1.63 % (2076)Time elapsed: 0.002 s
% 2.71/1.63 % (2076)Instructions burned: 3 (million)
% 2.71/1.63 % (2076)------------------------------
% 2.71/1.63 % (2076)------------------------------
% 2.71/1.63 % (2070)Instruction limit reached!
% 2.71/1.63 % (2070)------------------------------
% 2.71/1.63 % (2070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.63 % (2070)Termination reason: Unknown
% 2.71/1.63 % (2070)Termination phase: shuffling
% 2.71/1.63
% 2.71/1.63 % (2070)Memory used [KB]: 2174
% 2.71/1.63 % (2070)Time elapsed: 0.021 s
% 2.71/1.63 % (2070)Instructions burned: 37 (million)
% 2.71/1.63 % (2070)------------------------------
% 2.71/1.63 % (2070)------------------------------
% 2.71/1.63 % (2067)First to succeed.
% 2.71/1.64 % (2067)Refutation found. Thanks to Tanya!
% 2.71/1.64 % SZS status Theorem for DTF2THF_1767
% 2.71/1.64 % SZS output start Proof for DTF2THF_1767
% 2.71/1.64 thf(type_def_5, type, name: $tType).
% 2.71/1.64 thf(type_def_6, type, pi: $tType).
% 2.71/1.64 thf(type_def_8, type, late_freeRes: $tType).
% 2.71/1.64 thf(type_def_9, type, late_subject: $tType).
% 2.71/1.64 thf(type_def_10, type, late_residual: $tType).
% 2.71/1.64 thf(type_def_11, type, noption: ($tType) > $tType).
% 2.71/1.64 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 2.71/1.64 thf(type_def_13, type, set: ($tType) > $tType).
% 2.71/1.64 thf(func_def_0, type, late_residual: $tType).
% 2.71/1.64 thf(func_def_1, type, late_subject: $tType).
% 2.71/1.64 thf(func_def_2, type, late_freeRes: $tType).
% 2.71/1.64 thf(func_def_3, type, product_prod: ($tType * $tType) > $tType).
% 2.71/1.64 thf(func_def_4, type, noption: ($tType) > $tType).
% 2.71/1.64 thf(func_def_5, type, name: $tType).
% 2.71/1.64 thf(func_def_6, type, pi: $tType).
% 2.71/1.64 thf(func_def_7, type, set: ($tType) > $tType).
% 2.71/1.64 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 2.71/1.64 thf(func_def_9, type, fs_name: !>[X0: $tType]:($o)).
% 2.71/1.64 thf(func_def_10, type, ord: !>[X0: $tType]:($o)).
% 2.71/1.64 thf(func_def_11, type, order: !>[X0: $tType]:($o)).
% 2.71/1.64 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 2.71/1.64 thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 2.71/1.64 thf(func_def_14, type, input: name > name > pi > pi).
% 2.71/1.64 thf(func_def_15, type, mismatch: name > name > pi > pi).
% 2.71/1.64 thf(func_def_16, type, output: name > name > pi > pi).
% 2.71/1.64 thf(func_def_17, type, par: pi > pi > pi).
% 2.71/1.64 thf(func_def_18, type, piNil: pi).
% 2.71/1.64 thf(func_def_19, type, res: name > pi > pi).
% 2.71/1.64 thf(func_def_20, type, sum: pi > pi > pi).
% 2.71/1.64 thf(func_def_21, type, tau: pi > pi).
% 2.71/1.64 thf(func_def_22, type, subs: pi > name > name > pi).
% 2.71/1.64 thf(func_def_23, type, late_OutputR: name > name > late_freeRes).
% 2.71/1.64 thf(func_def_24, type, late_TauR: late_freeRes).
% 2.71/1.64 thf(func_def_25, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 2.71/1.64 thf(func_def_26, type, late_BoundR: late_subject > name > pi > late_residual).
% 2.71/1.64 thf(func_def_27, type, late_FreeR: late_freeRes > pi > late_residual).
% 2.71/1.64 thf(func_def_28, type, late_BoundOutputS: name > late_subject).
% 2.71/1.64 thf(func_def_29, type, late_InputS: name > late_subject).
% 2.71/1.64 thf(func_def_30, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 2.71/1.64 thf(func_def_31, type, late_transitions: pi > late_residual > $o).
% 2.71/1.64 thf(func_def_32, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 2.71/1.64 thf(func_def_33, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 2.71/1.64 thf(func_def_34, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.71/1.64 thf(func_def_35, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.71/1.64 thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 2.71/1.64 thf(func_def_37, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 2.71/1.64 thf(func_def_38, type, id: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 2.71/1.64 thf(func_def_39, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.71/1.64 thf(func_def_40, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 2.71/1.64 thf(func_def_41, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 2.71/1.64 thf(func_def_42, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.71/1.64 thf(func_def_43, type, p: pi).
% 2.71/1.64 thf(func_def_44, type, pq: pi).
% 2.71/1.64 thf(func_def_45, type, q: pi).
% 2.71/1.64 thf(func_def_46, type, q2: pi).
% 2.71/1.64 thf(func_def_47, type, rel: set @ product_prod @ pi @ pi).
% 2.71/1.64 thf(func_def_48, type, alpha: late_freeRes).
% 2.71/1.64 thf(func_def_49, type, x: name).
% 2.71/1.64 thf(func_def_67, type, sP0: late_subject > name > pi > pi > pi > $o).
% 2.71/1.64 thf(func_def_68, type, sK1: (pi > $o) > late_freeRes > pi > name > pi).
% 2.71/1.64 thf(func_def_69, type, sK2: (late_residual > $o) > late_subject).
% 2.71/1.64 thf(func_def_70, type, sK3: (late_residual > $o) > name).
% 2.71/1.64 thf(func_def_71, type, sK4: (late_residual > $o) > pi).
% 2.71/1.64 thf(func_def_72, type, sK5: (late_residual > $o) > late_freeRes).
% 2.71/1.64 thf(func_def_73, type, sK6: (late_residual > $o) > pi).
% 2.71/1.64 thf(func_def_74, type, sK7: pi > late_freeRes > pi > name > pi).
% 2.71/1.64 thf(func_def_75, type, sK8: pi > late_freeRes > pi > name > late_freeRes).
% 2.71/1.64 thf(func_def_76, type, sK9: pi > late_freeRes > pi > name > pi).
% 2.71/1.64 thf(func_def_77, type, sK10: pi > late_freeRes > pi > name > name).
% 2.71/1.64 thf(func_def_78, type, sK11: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.71/1.64 thf(func_def_79, type, sK12: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.71/1.64 thf(func_def_80, type, sK13: late_subject > name > pi > pi > pi > pi).
% 2.71/1.64 thf(func_def_81, type, sK14: late_subject > name > pi > pi > pi > late_subject).
% 2.71/1.64 thf(func_def_82, type, sK15: late_subject > name > pi > pi > pi > name).
% 2.71/1.64 thf(func_def_83, type, sK16: late_subject > name > pi > pi > pi > pi).
% 2.71/1.64 thf(func_def_84, type, sK17: late_subject > name > pi > pi > pi > pi).
% 2.71/1.64 thf(func_def_85, type, sK18: pi > name > late_subject > pi > pi > pi).
% 2.71/1.64 thf(func_def_86, type, sK19: pi > name > late_subject > pi > pi > late_subject).
% 2.71/1.64 thf(func_def_87, type, sK20: pi > name > late_subject > pi > pi > name).
% 2.71/1.64 thf(func_def_88, type, sK21: pi > name > late_subject > pi > pi > pi).
% 2.71/1.64 thf(func_def_89, type, sK22: pi > name > late_subject > pi > pi > pi).
% 2.71/1.64 thf(func_def_91, type, ph24: !>[X0: $tType]:(X0)).
% 2.71/1.64 thf(f880,plain,(
% 2.71/1.64 $false),
% 2.71/1.64 inference(subsumption_resolution,[status(thm)],[f879,f810])).
% 2.71/1.64 thf(f810,plain,(
% 2.71/1.64 ((fresh @ name @ late_freeRes @ x @ alpha) = $true)),
% 2.71/1.64 inference(cnf_transformation,[status(thm)],[f672])).
% 2.71/1.64 thf(f672,plain,(
% 2.71/1.64 ((fresh @ name @ late_freeRes @ x @ alpha) = $true)),
% 2.71/1.64 inference(fool_elimination,[status(thm)],[f671])).
% 2.71/1.64 thf(f671,plain,(
% 2.71/1.64 (fresh @ name @ late_freeRes @ x @ alpha)),
% 2.71/1.64 inference(rectify,[status(thm)],[f1])).
% 2.71/1.64 thf(f1,axiom,(
% 2.71/1.64 (fresh @ name @ late_freeRes @ x @ alpha)),
% 2.71/1.64 file('/export/starexec/sandbox/tmp/tmp.pF5X09mbQh/DTF2THF_1767.p',fact_0_cRes_Ohyps_I2_J)).
% 2.71/1.64 thf(f879,plain,(
% 2.71/1.64 ((fresh @ name @ late_freeRes @ x @ alpha) != $true)),
% 2.71/1.64 inference(subsumption_resolution,[status(thm)],[f878,f831])).
% 2.71/1.64 thf(f831,plain,(
% 2.71/1.64 ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) = $true)),
% 2.71/1.64 inference(cnf_transformation,[status(thm)],[f388])).
% 2.71/1.64 thf(f388,plain,(
% 2.71/1.64 ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) = $true)),
% 2.71/1.64 inference(fool_elimination,[status(thm)],[f387])).
% 2.71/1.64 thf(f387,plain,(
% 2.71/1.64 (late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))),
% 2.71/1.64 inference(rectify,[status(thm)],[f3])).
% 2.71/1.64 thf(f3,axiom,(
% 2.71/1.64 (late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))),
% 2.71/1.64 file('/export/starexec/sandbox/tmp/tmp.pF5X09mbQh/DTF2THF_1767.p',fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062)).
% 2.71/1.64 thf(f878,plain,(
% 2.71/1.64 ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) != $true) | ((fresh @ name @ late_freeRes @ x @ alpha) != $true)),
% 2.71/1.64 inference(trivial_inequality_removal,[status(thm)],[f877])).
% 2.71/1.64 thf(f877,plain,(
% 2.71/1.64 ((fresh @ name @ late_freeRes @ x @ alpha) != $true) | ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) != $true) | ($true != $true)),
% 2.71/1.64 inference(superposition,[status(thm)],[f823,f817])).
% 2.71/1.64 thf(f817,plain,(
% 2.71/1.64 ( ! [X2 : pi,X3 : name,X0 : pi,X1 : late_freeRes] : (($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))) | ($true != (late_transitions @ X0 @ (late_FreeR @ X1 @ X2))) | ((fresh @ name @ late_freeRes @ X3 @ X1) != $true)) )),
% 2.71/1.64 inference(cnf_transformation,[status(thm)],[f731])).
% 2.71/1.64 thf(f731,plain,(
% 2.71/1.64 ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : (((fresh @ name @ late_freeRes @ X3 @ X1) != $true) | ($true != (late_transitions @ X0 @ (late_FreeR @ X1 @ X2))) | ($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))))),
% 2.71/1.64 inference(flattening,[status(thm)],[f730])).
% 2.71/1.64 thf(f730,plain,(
% 2.71/1.64 ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : ((($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))) | ((fresh @ name @ late_freeRes @ X3 @ X1) != $true)) | ($true != (late_transitions @ X0 @ (late_FreeR @ X1 @ X2))))),
% 2.71/1.64 inference(ennf_transformation,[status(thm)],[f608])).
% 2.71/1.64 thf(f608,plain,(
% 2.71/1.64 ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : (($true = (late_transitions @ X0 @ (late_FreeR @ X1 @ X2))) => (((fresh @ name @ late_freeRes @ X3 @ X1) = $true) => ($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2))))))),
% 2.71/1.64 inference(fool_elimination,[status(thm)],[f607])).
% 2.71/1.64 thf(f607,plain,(
% 2.71/1.64 ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : ((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) => ((fresh @ name @ late_freeRes @ X3 @ X1) => (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))))),
% 2.71/1.64 inference(rectify,[status(thm)],[f14])).
% 2.71/1.64 thf(f14,axiom,(
% 2.71/1.64 ! [X8 : pi,X12 : late_freeRes,X16 : pi,X20 : name] : ((late_transitions @ X8 @ (late_FreeR @ X12 @ X16)) => ((fresh @ name @ late_freeRes @ X20 @ X12) => (late_transitions @ (res @ X20 @ X8) @ (late_FreeR @ X12 @ (res @ X20 @ X16)))))),
% 2.71/1.64 file('/export/starexec/sandbox/tmp/tmp.pF5X09mbQh/DTF2THF_1767.p',fact_13_ResF)).
% 2.71/1.64 thf(f823,plain,(
% 2.71/1.64 ((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2))) != $true)),
% 2.71/1.64 inference(cnf_transformation,[status(thm)],[f721])).
% 2.71/1.64 thf(f721,plain,(
% 2.71/1.64 ((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2))) != $true)),
% 2.71/1.64 inference(flattening,[status(thm)],[f616])).
% 2.71/1.64 thf(f616,plain,(
% 2.71/1.64 ~((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2))) = $true)),
% 2.71/1.64 inference(fool_elimination,[status(thm)],[f615])).
% 2.71/1.64 thf(f615,plain,(
% 2.71/1.64 ~(late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 2.71/1.64 inference(rectify,[status(thm)],[f275])).
% 2.71/1.64 thf(f275,negated_conjecture,(
% 2.71/1.64 ~(late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 2.71/1.64 inference(negated_conjecture,[status(cth)],[f274])).
% 2.71/1.64 thf(f274,conjecture,(
% 2.71/1.64 (late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 2.71/1.64 file('/export/starexec/sandbox/tmp/tmp.pF5X09mbQh/DTF2THF_1767.p',conj_0)).
% 2.71/1.64 % SZS output end Proof for DTF2THF_1767
% 2.71/1.64 % (2067)------------------------------
% 2.71/1.64 % (2067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.64 % (2067)Termination reason: Refutation
% 2.71/1.64
% 2.71/1.64 % (2067)Memory used [KB]: 6652
% 2.71/1.64 % (2067)Time elapsed: 0.042 s
% 2.71/1.64 % (2067)Instructions burned: 66 (million)
% 2.71/1.64 % (2067)------------------------------
% 2.71/1.64 % (2067)------------------------------
% 2.71/1.64 % (2061)Success in time 0.073 s
%------------------------------------------------------------------------------