%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP184^2 : 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 : n031.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 3.67s 1.86s
% Output : Refutation 3.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP184^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n031.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:30:03 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ITP184^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.47 % Domain : Interactive Theorem Proving
% 0.30/0.47 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_470__3413054_1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Des21]
% 0.30/0.47 % Names : Strong_Late_Sim_SC/prob_470__3413054_1 [Des21]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.33 v9.1.0, 0.00 v8.2.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 318 ( 163 unt; 51 typ; 0 def)
% 0.30/0.47 % Number of atoms : 637 ( 268 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 17 ( 2 avg)
% 0.30/0.47 % Number of connectives : 3995 ( 151 ~; 5 |; 49 &;3429 @)
% 0.30/0.47 % ( 0 <=>; 361 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 28 ( 9 avg)
% 0.30/0.47 % Number of types : 6 ( 5 usr)
% 0.30/0.47 % Number of type conns : 154 ( 154 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 49 ( 46 usr; 13 con; 0-5 aty)
% 0.30/0.47 % Number of variables : 1332 ( 9 ^;1289 !; 14 ?;1332 :)
% 0.30/0.47 % ( 20 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:36.935
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % Could-be-implicit typings (8)
% 0.30/0.47 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.30/0.47 late_residual: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Late__Semantics_Osubject,type,
% 0.30/0.47 late_subject: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.30/0.47 late_freeRes: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.47 product_prod: $tType > $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Nominal_Onoption,type,
% 0.30/0.47 noption: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Agent_Oname,type,
% 0.30/0.47 name: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Agent_Opi,type,
% 0.30/0.47 pi: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Set_Oset,type,
% 0.30/0.47 set: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 % Explicit typings (43)
% 0.30/0.47 thf(sy_cl_Agent_Ofs__name,type,
% 0.30/0.47 fs_name:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OBang,type,
% 0.30/0.47 bang: pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OInput,type,
% 0.30/0.47 input: name > name > pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OMatch,type,
% 0.30/0.47 match: name > name > pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.30/0.47 mismatch: name > name > pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OOutput,type,
% 0.30/0.47 output: name > name > pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OPar,type,
% 0.30/0.47 par: pi > pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.30/0.47 piNil: pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_ORes,type,
% 0.30/0.47 res: name > pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OSum,type,
% 0.30/0.47 sum: pi > pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Opi_OTau,type,
% 0.30/0.47 tau: pi > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Osubs,type,
% 0.30/0.47 subs: pi > name > name > pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Agent_Osubst__name,type,
% 0.30/0.47 subst_name: name > name > name > name ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_If,type,
% 0.30/0.47 if:
% 0.30/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 0.30/0.47 late_case_freeRes:
% 0.30/0.47 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.30/0.47 late_OutputR: name > name > late_freeRes ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.30/0.47 late_TauR: late_freeRes ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.30/0.47 late_freeRes_rec:
% 0.30/0.47 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.30/0.47 late_BoundR: late_subject > name > pi > late_residual ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.30/0.47 late_FreeR: late_freeRes > pi > late_residual ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.30/0.47 late_BoundOutputS: name > late_subject ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.30/0.47 late_InputS: name > late_subject ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.30/0.47 late_subject_rec:
% 0.30/0.47 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.30/0.47 late_transitions: pi > late_residual > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Nominal_Oabs__fun,type,
% 0.30/0.47 abs_fun:
% 0.30/0.47 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Nominal_Ofresh,type,
% 0.30/0.47 fresh:
% 0.30/0.47 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.47 product_Pair:
% 0.30/0.47 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.30/0.47 produc2004651681e_prod:
% 0.30/0.47 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.47 product_rec_prod:
% 0.30/0.47 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Rel_Oeqvt,type,
% 0.30/0.47 eqvt:
% 0.30/0.47 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect,type,
% 0.30/0.47 collect:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.30/0.47 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.30/0.47 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member,type,
% 0.30/0.47 member:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_P,type,
% 0.30/0.47 p: pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_PQR____,type,
% 0.30/0.47 pqr: pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_Q,type,
% 0.30/0.47 q: pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_QR____,type,
% 0.30/0.47 qr: pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_Q_H____,type,
% 0.30/0.47 q2: pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_R,type,
% 0.30/0.47 r: pi ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_Rel,type,
% 0.30/0.47 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_a____,type,
% 0.30/0.47 a: late_subject ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_x____,type,
% 0.30/0.47 x: name ).
% 0.30/0.47
% 0.30/0.47 % Relevant facts (256)
% 0.30/0.47 thf(fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062,axiom,
% 0.30/0.47 strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ).
% 0.30/0.47
% 0.30/0.47 % \<open>derivative ((P \<parallel> Q') \<parallel> R) (P \<parallel> Q' \<parallel> R) a x Rel\<close>
% 0.30/0.47 thf(fact_1_cPar1_Ohyps,axiom,
% 0.30/0.47 late_transitions @ q @ ( late_BoundR @ a @ x @ q2 ) ).
% 0.30/0.47
% 0.30/0.47 % cPar1.hyps
% 0.30/0.47 thf(fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.30/0.47 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>(P \<parallel> Q) \<parallel> R \<longmapsto> a\<guillemotleft>x\<guillemotright> \<prec> (P \<parallel> Q') \<parallel> R\<close>
% 0.30/0.47 thf(fact_3_cPar2_Ohyps,axiom,
% 0.30/0.47 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ a @ x @ qr ) ).
% 0.30/0.47
% 0.30/0.47 % cPar2.hyps
% 0.30/0.47 thf(fact_4_Bound_Ohyps_I1_J,axiom,
% 0.30/0.47 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_BoundR @ a @ x @ pqr ) ).
% 0.30/0.47
% 0.30/0.47 % Bound.hyps(1)
% 0.30/0.47 thf(fact_5__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 0.30/0.47 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ a @ x @ ( par @ p @ q2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>P \<parallel> Q \<longmapsto> a\<guillemotleft>x\<guillemotright> \<prec> P \<parallel> Q'\<close>
% 0.30/0.47 thf(fact_6_Bound_Ohyps_I2_J,axiom,
% 0.30/0.47 fresh @ name @ pi @ x @ ( par @ ( par @ p @ q ) @ r ) ).
% 0.30/0.47
% 0.30/0.47 % Bound.hyps(2)
% 0.30/0.47 thf(fact_7__092_060open_062x_A_092_060sharp_062_AQ_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.30/0.47 fresh @ name @ pi @ x @ ( par @ q @ r ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>x \<sharp> Q \<parallel> R\<close>
% 0.30/0.47 thf(fact_8__092_060open_062x_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.30/0.47 fresh @ name @ pi @ x @ q ).
% 0.30/0.47
% 0.30/0.47 % \<open>x \<sharp> Q\<close>
% 0.30/0.47 thf(fact_9__092_060open_062x_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.30/0.47 fresh @ name @ pi @ x @ p ).
% 0.30/0.47
% 0.30/0.47 % \<open>x \<sharp> P\<close>
% 0.30/0.47 thf(fact_10__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.30/0.47 fresh @ name @ pi @ x @ r ).
% 0.30/0.47
% 0.30/0.47 % \<open>x \<sharp> R\<close>
% 0.30/0.47 thf(fact_11_Ass,axiom,
% 0.30/0.47 ! [S: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S @ T2 ) @ U ) @ ( par @ S @ ( par @ T2 @ U ) ) ) @ rel ) ).
% 0.30/0.47
% 0.30/0.47 % Ass
% 0.30/0.47 thf(fact_12_pi_Oinject_I7_J,axiom,
% 0.30/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.30/0.47 ( ( ( par @ X2 @ X1 )
% 0.30/0.47 = ( par @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X2 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(7)
% 0.30/0.47 thf(fact_13_Late__Semantics_OPar1B,axiom,
% 0.30/0.47 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.Par1B
% 0.30/0.47 thf(fact_14_Late__Semantics_OPar2B,axiom,
% 0.30/0.47 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.Par2B
% 0.30/0.47 thf(fact_15_parCasesB,axiom,
% 0.30/0.47 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 0.30/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( ! [P3: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.30/0.47 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.30/0.47 => ( ! [Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 0.30/0.47 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.30/0.47 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % parCasesB
% 0.30/0.47 thf(fact_16_tauBoundTrans,axiom,
% 0.30/0.47 ! [P: pi,A2: late_subject,X3: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X3 @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % tauBoundTrans
% 0.30/0.47 thf(fact_17_outputBoundTrans,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,C2: late_subject,X3: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X3 @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % outputBoundTrans
% 0.30/0.47 thf(fact_18_Res,axiom,
% 0.30/0.47 ! [S: pi,T2: pi,X3: name] :
% 0.30/0.47 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S @ T2 ) @ rel )
% 0.30/0.47 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X3 @ S ) @ ( res @ X3 @ T2 ) ) @ rel ) ) ).
% 0.30/0.47
% 0.30/0.47 % Res
% 0.30/0.47 thf(fact_19_FreshExt_H,axiom,
% 0.30/0.47 ! [X3: name,U: pi,S: pi,T2: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ X3 @ U )
% 0.30/0.47 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X3 @ ( par @ S @ T2 ) ) @ U ) @ ( res @ X3 @ ( par @ S @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 0.30/0.47
% 0.30/0.47 % FreshExt'
% 0.30/0.47 thf(fact_20_FreshExt,axiom,
% 0.30/0.47 ! [X3: name,S: pi,T2: pi,U: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ X3 @ S )
% 0.30/0.47 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X3 @ ( par @ ( par @ S @ T2 ) @ U ) ) @ ( par @ S @ ( res @ X3 @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 0.30/0.47
% 0.30/0.47 % FreshExt
% 0.30/0.47 thf(fact_21_pi_Ofresh_I8_J,axiom,
% 0.30/0.47 ! [A2: name,X2: pi,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( par @ X2 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.30/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(8)
% 0.30/0.47 thf(fact_22_pi_Ofresh_I3_J,axiom,
% 0.30/0.47 ! [A2: name,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.30/0.47 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(3)
% 0.30/0.47 thf(fact_23_pi_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X1: pi,Y1: pi] :
% 0.30/0.47 ( ( ( tau @ X1 )
% 0.30/0.47 = ( tau @ Y1 ) )
% 0.30/0.47 = ( X1 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(2)
% 0.30/0.47 thf(fact_24_pi_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X32: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.30/0.47 ( ( ( output @ X32 @ X2 @ X1 )
% 0.30/0.47 = ( output @ Y3 @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X32 = Y3 )
% 0.30/0.47 & ( X2 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(1)
% 0.30/0.47 thf(fact_25_pi_Odistinct_I45_J,axiom,
% 0.30/0.47 ! [Pi: pi,Name: name,Pi2: pi] :
% 0.30/0.47 ( ( tau @ Pi )
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(45)
% 0.30/0.47 thf(fact_26_pi_Odistinct_I31_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(31)
% 0.30/0.47 thf(fact_27_pi_Odistinct_I19_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( tau @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(19)
% 0.30/0.47 thf(fact_28_resTrans_I1_J,axiom,
% 0.30/0.47 ! [X3: name,B2: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( output @ X3 @ B2 @ P ) ) @ Rs ) ).
% 0.30/0.47
% 0.30/0.47 % resTrans(1)
% 0.30/0.47 thf(fact_29_freshRes,axiom,
% 0.30/0.47 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshRes
% 0.30/0.47 thf(fact_30_name__exists__fresh,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [X3: A] :
% 0.30/0.47 ~ ! [C3: name] :
% 0.30/0.47 ~ ( fresh @ name @ A @ C3 @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % name_exists_fresh
% 0.30/0.47 thf(fact_31_pi_Odistinct_I85_J,axiom,
% 0.30/0.47 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 0.30/0.47 ( ( par @ Pi1 @ Pi22 )
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(85)
% 0.30/0.47 thf(fact_32_pi_Odistinct_I29_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(29)
% 0.30/0.47 thf(fact_33_pi_Odistinct_I43_J,axiom,
% 0.30/0.47 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( tau @ Pi )
% 0.30/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(43)
% 0.30/0.47 thf(fact_34_resTauBoundTrans,axiom,
% 0.30/0.47 ! [X3: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resTauBoundTrans
% 0.30/0.47 thf(fact_35_freshBoundDerivative_I2_J,axiom,
% 0.30/0.47 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.30/0.47 => ( ( Y != X3 )
% 0.30/0.47 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshBoundDerivative(2)
% 0.30/0.47 thf(fact_36_fresh__prod,axiom,
% 0.30/0.47 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y: B] :
% 0.30/0.47 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.30/0.47 = ( ( fresh @ X @ A @ A2 @ X3 )
% 0.30/0.47 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fresh_prod
% 0.30/0.47 thf(fact_37_prod_Oinject,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.30/0.47 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.30/0.47 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.30/0.47 = ( ( X1 = Y1 )
% 0.30/0.47 & ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.inject
% 0.30/0.47 thf(fact_38_old_Oprod_Oinject,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.30/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.47 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.30/0.47 = ( ( A2 = A3 )
% 0.30/0.47 & ( B2 = B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % old.prod.inject
% 0.30/0.47 thf(fact_39_fresh__prodD_I2_J,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,C: $tType,A2: A,X3: B,Y: C] :
% 0.30/0.47 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 0.30/0.47 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % fresh_prodD(2)
% 0.30/0.47 thf(fact_40_fresh__prodD_I1_J,axiom,
% 0.30/0.47 ! [C: $tType,A: $tType,B: $tType,A2: A,X3: B,Y: C] :
% 0.30/0.47 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 0.30/0.47 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % fresh_prodD(1)
% 0.30/0.47 thf(fact_41_resOutputInputTrans,axiom,
% 0.30/0.47 ! [X3: name,A2: name,B2: name,P: pi,C2: name,Y: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resOutputInputTrans
% 0.30/0.47 thf(fact_42_transitions_OResB,axiom,
% 0.30/0.47 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.30/0.47 => ( ( Y != X3 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.30/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.ResB
% 0.30/0.47 thf(fact_43_transitions_OPar2B,axiom,
% 0.30/0.47 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.Par2B
% 0.30/0.47 thf(fact_44_transitions_OPar1B,axiom,
% 0.30/0.47 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.Par1B
% 0.30/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_47_Collect__cong,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.47 ( ! [X5: A] :
% 0.30/0.47 ( ( P @ X5 )
% 0.30/0.47 = ( Q @ X5 ) )
% 0.30/0.47 => ( ( collect @ A @ P )
% 0.30/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_48_ext,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.47 ( ! [X5: A] :
% 0.30/0.47 ( ( F @ X5 )
% 0.30/0.47 = ( G @ X5 ) )
% 0.30/0.47 => ( F = G ) ) ).
% 0.30/0.47
% 0.30/0.47 % ext
% 0.30/0.47 thf(fact_49_parCasesB_H,axiom,
% 0.30/0.47 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.30/0.47 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Q4: pi] :
% 0.30/0.47 ( ( ( par @ P @ Q )
% 0.30/0.47 = ( par @ P4 @ Q4 ) )
% 0.30/0.47 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.30/0.47 = ( late_BoundR @ A5 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) )
% 0.30/0.47 => ~ ! [Q4: pi,A5: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.30/0.47 ( ( ( par @ P @ Q )
% 0.30/0.47 = ( par @ P4 @ Q4 ) )
% 0.30/0.47 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.30/0.47 = ( late_BoundR @ A5 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.30/0.47 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A5 @ X5 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % parCasesB'
% 0.30/0.47 thf(fact_50_pi_Ofresh_I2_J,axiom,
% 0.30/0.47 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X2 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.30/0.47 & ( fresh @ name @ name @ A2 @ X2 )
% 0.30/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(2)
% 0.30/0.47 thf(fact_51_subject_Ofresh_I1_J,axiom,
% 0.30/0.47 ! [A2: name,X1: name] :
% 0.30/0.47 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.30/0.47 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.fresh(1)
% 0.30/0.47 thf(fact_52_freshResidual,axiom,
% 0.30/0.47 ! [P: pi,Rs: late_residual,X3: name] :
% 0.30/0.47 ( ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshResidual
% 0.30/0.47 thf(fact_53_Late__Semantics_OResB,axiom,
% 0.30/0.47 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.30/0.47 => ( ( Y != X3 )
% 0.30/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.ResB
% 0.30/0.47 thf(fact_54_freshBoundDerivative_I1_J,axiom,
% 0.30/0.47 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.30/0.47 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshBoundDerivative(1)
% 0.30/0.47 thf(fact_55_old_Oprod_Oinducts,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.47 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.30/0.47 => ( P @ Prod ) ) ).
% 0.30/0.47
% 0.30/0.47 % old.prod.inducts
% 0.30/0.47 thf(fact_56_old_Oprod_Oexhaust,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.30/0.47 ~ ! [A5: A,B4: B] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ B @ A5 @ B4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % old.prod.exhaust
% 0.30/0.47 thf(fact_57_prod__induct7,axiom,
% 0.30/0.47 ! [G2: $tType,F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 0.30/0.47 => ( P @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct7
% 0.30/0.47 thf(fact_58_prod__induct6,axiom,
% 0.30/0.47 ! [F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 0.30/0.47 => ( P @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct6
% 0.30/0.47 thf(fact_59_prod__induct5,axiom,
% 0.30/0.47 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.30/0.47 => ( P @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct5
% 0.30/0.47 thf(fact_60_prod__induct4,axiom,
% 0.30/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 0.30/0.47 => ( P @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct4
% 0.30/0.47 thf(fact_61_prod__induct3,axiom,
% 0.30/0.47 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 0.30/0.47 => ( P @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct3
% 0.30/0.47 thf(fact_62_prod__cases7,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases7
% 0.30/0.47 thf(fact_63_prod__cases6,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases6
% 0.30/0.47 thf(fact_64_prod__cases5,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases5
% 0.30/0.47 thf(fact_65_prod__cases4,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases4
% 0.30/0.47 thf(fact_66_prod__cases3,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases3
% 0.30/0.47 thf(fact_67_Pair__inject,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.30/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.47 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.30/0.47 => ~ ( ( A2 = A3 )
% 0.30/0.47 => ( B2 != B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Pair_inject
% 0.30/0.47 thf(fact_68_prod__cases,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P5: product_prod @ A @ B] :
% 0.30/0.47 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.30/0.47 => ( P @ P5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases
% 0.30/0.47 thf(fact_69_surj__pair,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,P5: product_prod @ A @ B] :
% 0.30/0.47 ? [X5: A,Y4: B] :
% 0.30/0.47 ( P5
% 0.30/0.47 = ( product_Pair @ A @ B @ X5 @ Y4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % surj_pair
% 0.30/0.47 thf(fact_70_old_Oprod_Orec,axiom,
% 0.30/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.47 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.47 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % old.prod.rec
% 0.30/0.47 thf(fact_71_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X1: name,Y1: name] :
% 0.30/0.47 ( ( ( late_InputS @ X1 )
% 0.30/0.47 = ( late_InputS @ Y1 ) )
% 0.30/0.47 = ( X1 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics1.subject.inject(1)
% 0.30/0.47 thf(fact_72_subject_Orecs_I1_J,axiom,
% 0.30/0.47 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.30/0.47 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.30/0.47 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.30/0.47 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 0.30/0.47 = ( F1 @ Name3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.recs(1)
% 0.30/0.47 thf(fact_73_internal__case__prod__conv,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.30/0.47 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.30/0.47 = ( C2 @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % internal_case_prod_conv
% 0.30/0.47 thf(fact_74_parSym,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.30/0.47 ( ! [R: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 0.30/0.47 => ( ! [R: pi,S2: pi,X5: name] :
% 0.30/0.47 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R @ S2 ) @ Rel )
% 0.30/0.47 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 0.30/0.47 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % parSym
% 0.30/0.47 thf(fact_75_inputIneqTrans,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputIneqTrans
% 0.30/0.47 thf(fact_76_Late__Semantics_OInput,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.Input
% 0.30/0.47 thf(fact_77_transitions_OInput,axiom,
% 0.30/0.47 ! [X3: name,A2: name,P: pi] :
% 0.30/0.47 ( ( X3 != A2 )
% 0.30/0.47 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.Input
% 0.30/0.47 thf(fact_78_name__fresh,axiom,
% 0.30/0.47 ( ( fresh @ name @ name )
% 0.30/0.47 = ( ^ [A6: name,B5: name] : ( A6 != B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % name_fresh
% 0.30/0.47 thf(fact_79_pi_Odistinct_I55_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(55)
% 0.30/0.47 thf(fact_80_pi_Odistinct_I57_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(57)
% 0.30/0.47 thf(fact_81_pi_Odistinct_I21_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(21)
% 0.30/0.47 thf(fact_82_pi_Odistinct_I35_J,axiom,
% 0.30/0.47 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( tau @ Pi )
% 0.30/0.47 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(35)
% 0.30/0.47 thf(fact_83_resTrans_I2_J,axiom,
% 0.30/0.47 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 0.30/0.47
% 0.30/0.47 % resTrans(2)
% 0.30/0.47 thf(fact_84_simE_I1_J,axiom,
% 0.30/0.47 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 0.30/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ? [P3: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.30/0.47 & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simE(1)
% 0.30/0.47 thf(fact_85_resInputBoundOutputTrans,axiom,
% 0.30/0.47 ! [X3: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resInputBoundOutputTrans
% 0.30/0.47 thf(fact_86_simulation__def,axiom,
% 0.30/0.47 ( strong743114133lation
% 0.30/0.47 = ( ^ [P6: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.30/0.47 ( ! [A6: late_subject,X4: name,Q6: pi] :
% 0.30/0.47 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A6 @ X4 @ Q6 ) )
% 0.30/0.47 & ( fresh @ name @ pi @ X4 @ P6 ) )
% 0.30/0.47 => ? [P7: pi] :
% 0.30/0.47 ( ( late_transitions @ P6 @ ( late_BoundR @ A6 @ X4 @ P7 ) )
% 0.30/0.47 & ( strong2129052853vative @ P7 @ Q6 @ A6 @ X4 @ Rel2 ) ) )
% 0.30/0.47 & ! [Alpha: late_freeRes,Q6: pi] :
% 0.30/0.47 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha @ Q6 ) )
% 0.30/0.47 => ? [P7: pi] :
% 0.30/0.47 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha @ P7 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simulation_def
% 0.30/0.47 thf(fact_87_simCases,axiom,
% 0.30/0.47 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.30/0.47 ( ! [A5: late_subject,Y4: name,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y4 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y4 @ P )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y4 @ P8 ) )
% 0.30/0.47 & ( strong2129052853vative @ P8 @ Q3 @ A5 @ Y4 @ Rel ) ) ) )
% 0.30/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.30/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simCases
% 0.30/0.47 thf(fact_88_residual_Ofresh_I1_J,axiom,
% 0.30/0.47 ! [A2: name,X32: late_subject,X1: name,X2: pi] :
% 0.30/0.47 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.30/0.47 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 0.30/0.47 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.fresh(1)
% 0.30/0.47 thf(fact_89_inputCases_H,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 0.30/0.47 => ~ ! [X5: name,A5: name,P4: pi] :
% 0.30/0.47 ( ( ( A2 = A5 )
% 0.30/0.47 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 0.30/0.47 = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 0.30/0.47 => ( ( Rs
% 0.30/0.47 = ( late_BoundR @ ( late_InputS @ A5 ) @ X5 @ P4 ) )
% 0.30/0.47 => ( X5 = A5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputCases'
% 0.30/0.47 thf(fact_90_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X2: name,Y2: name] :
% 0.30/0.47 ( ( ( late_BoundOutputS @ X2 )
% 0.30/0.47 = ( late_BoundOutputS @ Y2 ) )
% 0.30/0.47 = ( X2 = Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics1.subject.inject(2)
% 0.30/0.47 thf(fact_91_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X1: name,Y1: name] :
% 0.30/0.47 ( ( ( late_BoundOutputS @ X1 )
% 0.30/0.47 = ( late_BoundOutputS @ Y1 ) )
% 0.30/0.47 = ( X1 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.subject.inject(2)
% 0.30/0.47 thf(fact_92_subject_Ofresh_I2_J,axiom,
% 0.30/0.47 ! [A2: name,X1: name] :
% 0.30/0.47 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.30/0.47 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.fresh(2)
% 0.30/0.47 thf(fact_93_residual_Ofresh_I2_J,axiom,
% 0.30/0.47 ! [A2: name,X2: late_freeRes,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X2 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ late_freeRes @ A2 @ X2 )
% 0.30/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.fresh(2)
% 0.30/0.47 thf(fact_94_pi_Ofresh_I9_J,axiom,
% 0.30/0.47 ! [A2: name,X1: name,X2: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X2 ) )
% 0.30/0.47 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(9)
% 0.30/0.47 thf(fact_95_pi_Ofresh_I4_J,axiom,
% 0.30/0.47 ! [A2: name,X32: name,X1: name,X2: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X2 ) )
% 0.30/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.30/0.47 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(4)
% 0.30/0.47 thf(fact_96_residual_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.30/0.47 ( ( ( late_FreeR @ X2 @ X1 )
% 0.30/0.47 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X2 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.inject(2)
% 0.30/0.47 thf(fact_97_abs__fun__eq1,axiom,
% 0.30/0.47 ! [X: $tType,A: $tType,A2: X,X3: A,Y: A] :
% 0.30/0.47 ( ( ( abs_fun @ X @ A @ A2 @ X3 )
% 0.30/0.47 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 0.30/0.47 = ( X3 = Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % abs_fun_eq1
% 0.30/0.47 thf(fact_98_pi_Oinject_I8_J,axiom,
% 0.30/0.47 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.30/0.47 ( ( ( res @ X1 @ X2 )
% 0.30/0.47 = ( res @ Y1 @ Y2 ) )
% 0.30/0.47 = ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.30/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(8)
% 0.30/0.47 thf(fact_99_residual_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X32: late_subject,X1: name,X2: pi,Y3: late_subject,Y1: name,Y2: pi] :
% 0.30/0.47 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.30/0.47 = ( late_BoundR @ Y3 @ Y1 @ Y2 ) )
% 0.30/0.47 = ( ( X32 = Y3 )
% 0.30/0.47 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.30/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.inject(1)
% 0.30/0.47 thf(fact_100_residual_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [Subject: late_subject,Name3: name,Pi: pi,FreeRes: late_freeRes,Pi2: pi] :
% 0.30/0.47 ( ( late_BoundR @ Subject @ Name3 @ Pi )
% 0.30/0.47 != ( late_FreeR @ FreeRes @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.distinct(1)
% 0.30/0.47 thf(fact_101_residual_Oinducts,axiom,
% 0.30/0.47 ! [P: late_residual > $o,Residual: late_residual] :
% 0.30/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) )
% 0.30/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.30/0.47 => ( P @ Residual ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.inducts
% 0.30/0.47 thf(fact_102_name__fresh__abs,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [B2: name,A2: name,X3: A] :
% 0.30/0.47 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X3 ) )
% 0.30/0.47 = ( ( B2 = A2 )
% 0.30/0.47 | ( fresh @ name @ A @ B2 @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % name_fresh_abs
% 0.30/0.47 thf(fact_103_abs__fresh_I1_J,axiom,
% 0.30/0.47 ! [X6: $tType] :
% 0.30/0.47 ( ( fs_name @ X6 )
% 0.30/0.47 => ! [B2: name,A2: name,X3: X6] :
% 0.30/0.47 ( ( fresh @ name @ ( name > ( noption @ X6 ) ) @ B2 @ ( abs_fun @ name @ X6 @ A2 @ X3 ) )
% 0.30/0.47 = ( ( B2 = A2 )
% 0.30/0.47 | ( fresh @ name @ X6 @ B2 @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % abs_fresh(1)
% 0.30/0.47 thf(fact_104_pi_Oinject_I3_J,axiom,
% 0.30/0.47 ! [X32: name,X1: name,X2: pi,Y3: name,Y1: name,Y2: pi] :
% 0.30/0.47 ( ( ( input @ X32 @ X1 @ X2 )
% 0.30/0.47 = ( input @ Y3 @ Y1 @ Y2 ) )
% 0.30/0.47 = ( ( X32 = Y3 )
% 0.30/0.47 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.30/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(3)
% 0.30/0.47 thf(fact_105_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [Name3: name,Name: name] :
% 0.30/0.47 ( ( late_InputS @ Name3 )
% 0.30/0.47 != ( late_BoundOutputS @ Name ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.subject.distinct(1)
% 0.30/0.47 thf(fact_106_subject_Oinducts,axiom,
% 0.30/0.47 ! [P: late_subject > $o,Subject: late_subject] :
% 0.30/0.47 ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 0.30/0.47 => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 0.30/0.47 => ( P @ Subject ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.inducts
% 0.30/0.47 thf(fact_107_subject_Ostrong__induct_H,axiom,
% 0.30/0.47 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 0.30/0.47 ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 0.30/0.47 => ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 0.30/0.47 => ( P @ Z @ Subject ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.strong_induct'
% 0.30/0.47 thf(fact_108_subject_Ostrong__inducts,axiom,
% 0.30/0.47 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 0.30/0.47 ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 0.30/0.47 => ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 0.30/0.47 => ( P @ Z @ Subject ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.strong_inducts
% 0.30/0.47 thf(fact_109_subject_Oexhaust,axiom,
% 0.30/0.47 ! [Y: late_subject] :
% 0.30/0.47 ( ! [X12: name] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( late_InputS @ X12 ) )
% 0.30/0.47 => ~ ! [X22: name] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.exhaust
% 0.30/0.47 thf(fact_110_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [X1: name,X2: name] :
% 0.30/0.47 ( ( late_InputS @ X1 )
% 0.30/0.47 != ( late_BoundOutputS @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics1.subject.distinct(1)
% 0.30/0.47 thf(fact_111_Par1F,axiom,
% 0.30/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Q: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P2 @ Q ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Par1F
% 0.30/0.47 thf(fact_112_Par2F,axiom,
% 0.30/0.47 ! [Q: pi,Alpha3: late_freeRes,Q2: pi,P: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P @ Q2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Par2F
% 0.30/0.47 thf(fact_113_ResF,axiom,
% 0.30/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha3 )
% 0.30/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha3 @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ResF
% 0.30/0.47 thf(fact_114_resCasesF_H,axiom,
% 0.30/0.47 ! [X3: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P )
% 0.30/0.47 = ( res @ Y4 @ P4 ) )
% 0.30/0.47 => ( ( ( late_FreeR @ Alpha3 @ P2 )
% 0.30/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.30/0.47 => ~ ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCasesF'
% 0.30/0.47 thf(fact_115_resCasesF,axiom,
% 0.30/0.47 ! [X3: name,P: pi,Alpha3: late_freeRes,XP: pi,F4: pi > $o] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha3 @ XP ) )
% 0.30/0.47 => ( ! [P3: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha3 )
% 0.30/0.47 => ( F4 @ ( res @ X3 @ P3 ) ) ) )
% 0.30/0.47 => ( F4 @ XP ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCasesF
% 0.30/0.47 thf(fact_116_freshFreeDerivative_I1_J,axiom,
% 0.30/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.30/0.47 => ( fresh @ name @ late_freeRes @ Y @ Alpha3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshFreeDerivative(1)
% 0.30/0.47 thf(fact_117_freshFreeDerivative_I2_J,axiom,
% 0.30/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.30/0.47 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshFreeDerivative(2)
% 0.30/0.47 thf(fact_118_inputFreeTrans,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputFreeTrans
% 0.30/0.47 thf(fact_119_outputFreshTrans,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha3 )
% 0.30/0.47 | ( fresh @ name @ late_freeRes @ B2 @ Alpha3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % outputFreshTrans
% 0.30/0.47 thf(fact_120_simE_I2_J,axiom,
% 0.30/0.47 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha3: late_freeRes,Q2: pi] :
% 0.30/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 0.30/0.47 => ? [P3: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simE(2)
% 0.30/0.47 thf(fact_121_subject_Orecs_I2_J,axiom,
% 0.30/0.47 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.30/0.47 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.30/0.47 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.30/0.47 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 0.30/0.47 = ( F22 @ Name3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.recs(2)
% 0.30/0.47 thf(fact_122_resInputFreeTrans,axiom,
% 0.30/0.47 ! [X3: name,A2: name,Y: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resInputFreeTrans
% 0.30/0.47 thf(fact_123_residual_Ostrong__inducts,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.30/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: A] :
% 0.30/0.47 ( ( fresh @ name @ A @ Name4 @ Z2 )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 0.30/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.30/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.30/0.47 => ( P @ Z @ Residual ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.strong_inducts
% 0.30/0.47 thf(fact_124_residual_Ostrong__induct,axiom,
% 0.30/0.47 ! [N: $tType] :
% 0.30/0.47 ( ( fs_name @ N )
% 0.30/0.47 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.30/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: N] :
% 0.30/0.47 ( ( fresh @ name @ N @ Name4 @ Z2 )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 0.30/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.30/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.30/0.47 => ( P @ Z @ Residual ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.strong_induct
% 0.30/0.47 thf(fact_125_inputBoundOutputTrans,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputBoundOutputTrans
% 0.30/0.47 thf(fact_126_simCasesCont,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.30/0.47 ( ( eqvt @ pi @ Rel )
% 0.30/0.47 => ( ! [A5: late_subject,X5: name,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ X5 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X5 @ A5 )
% 0.30/0.47 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ X5 @ P8 ) )
% 0.30/0.47 & ( strong2129052853vative @ P8 @ Q3 @ A5 @ X5 @ Rel ) ) ) ) ) ) )
% 0.30/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.30/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simCasesCont
% 0.30/0.47 thf(fact_127_resCases_H,axiom,
% 0.30/0.47 ! [X3: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 0.30/0.47 => ( ! [P4: pi,A5: name,B4: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P )
% 0.30/0.47 = ( res @ B4 @ P4 ) )
% 0.30/0.47 => ! [P3: pi] :
% 0.30/0.47 ( ( Rs
% 0.30/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 0.30/0.47 => ( A5 = B4 ) ) ) )
% 0.30/0.47 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y4: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P )
% 0.30/0.47 = ( res @ Y4 @ P4 ) )
% 0.30/0.47 => ( ( Rs
% 0.30/0.47 = ( late_BoundR @ A5 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y4 @ A5 )
% 0.30/0.47 => ( ( Y4 != X5 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) ) )
% 0.30/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P )
% 0.30/0.47 = ( res @ Y4 @ P4 ) )
% 0.30/0.47 => ( ( Rs
% 0.30/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.30/0.47 => ~ ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCases'
% 0.30/0.47 thf(fact_128_resCasesB_H,axiom,
% 0.30/0.47 ! [X7: name,P: pi,A2: late_subject,Y5: name,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X7 @ P ) @ ( late_BoundR @ A2 @ Y5 @ P2 ) )
% 0.30/0.47 => ( ! [P4: pi,A5: name,B4: name] :
% 0.30/0.47 ( ( ( res @ X7 @ P )
% 0.30/0.47 = ( res @ B4 @ P4 ) )
% 0.30/0.47 => ! [P3: pi] :
% 0.30/0.47 ( ( ( late_BoundR @ A2 @ Y5 @ P2 )
% 0.30/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 0.30/0.47 => ( A5 = B4 ) ) ) )
% 0.30/0.47 => ~ ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y4: name] :
% 0.30/0.47 ( ( ( res @ X7 @ P )
% 0.30/0.47 = ( res @ Y4 @ P4 ) )
% 0.30/0.47 => ( ( ( late_BoundR @ A2 @ Y5 @ P2 )
% 0.30/0.47 = ( late_BoundR @ A5 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y4 @ A5 )
% 0.30/0.47 => ( ( Y4 != X5 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCasesB'
% 0.30/0.47 thf(fact_129_resSimCases,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P: pi,C4: A] :
% 0.30/0.47 ( ( eqvt @ pi @ Rel )
% 0.30/0.47 => ( ! [Q3: pi,A5: name] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A5 @ X3 ) @ Q3 ) )
% 0.30/0.47 => ( ( A5 != X3 )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ X3 @ P8 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 0.30/0.47 => ( ! [Q3: pi,A5: late_subject,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y4 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X3 @ A5 )
% 0.30/0.47 => ( ( X3 != Y4 )
% 0.30/0.47 => ( ( fresh @ name @ A @ Y4 @ C4 )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y4 @ P8 ) )
% 0.30/0.47 & ( strong2129052853vative @ P8 @ ( res @ X3 @ Q3 ) @ A5 @ Y4 @ Rel ) ) ) ) ) )
% 0.30/0.47 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 0.30/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resSimCases
% 0.30/0.47 thf(fact_130_Open,axiom,
% 0.30/0.47 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.30/0.47 => ( ( A2 != B2 )
% 0.30/0.47 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Open
% 0.30/0.47 thf(fact_131_resOutputTauTrans,axiom,
% 0.30/0.47 ! [X3: name,A2: name,B2: name,P: pi,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resOutputTauTrans
% 0.30/0.47 thf(fact_132_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.30/0.47 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.30/0.47 ( ( ( late_OutputR @ X2 @ X1 )
% 0.30/0.47 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X2 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.freeRes.inject
% 0.30/0.47 thf(fact_133_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.30/0.47 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.30/0.47 ( ( ( late_OutputR @ X11 @ X122 )
% 0.30/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.30/0.47 = ( ( X11 = Y11 )
% 0.30/0.47 & ( X122 = Y12 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics1.freeRes.inject
% 0.30/0.47 thf(fact_134_freeRes_Ofresh_I2_J,axiom,
% 0.30/0.47 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.fresh(2)
% 0.30/0.47 thf(fact_135_freeRes_Ofresh_I1_J,axiom,
% 0.30/0.47 ! [A2: name,X2: name,X1: name] :
% 0.30/0.47 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X2 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ name @ A2 @ X2 )
% 0.30/0.47 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.fresh(1)
% 0.30/0.47 thf(fact_136_freeRes_Ostrong__inducts,axiom,
% 0.30/0.47 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.30/0.47 ( ! [Name13: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.30/0.47 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.30/0.47 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.strong_inducts
% 0.30/0.47 thf(fact_137_freeRes_Ostrong__induct_H,axiom,
% 0.30/0.47 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.30/0.47 ( ! [Name13: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.30/0.47 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.30/0.47 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.strong_induct'
% 0.30/0.47 thf(fact_138_freeRes_Oinducts,axiom,
% 0.30/0.47 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.30/0.47 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.30/0.47 => ( ( P @ late_TauR )
% 0.30/0.47 => ( P @ FreeRes3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.inducts
% 0.30/0.47 thf(fact_139_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name] :
% 0.30/0.47 ( ( late_OutputR @ Name1 @ Name2 )
% 0.30/0.47 != late_TauR ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.freeRes.distinct(1)
% 0.30/0.47 thf(fact_140_freeRes_Oexhaust,axiom,
% 0.30/0.47 ! [Y: late_freeRes] :
% 0.30/0.47 ( ! [X112: name,X123: name] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( late_OutputR @ X112 @ X123 ) )
% 0.30/0.47 => ( Y = late_TauR ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.exhaust
% 0.30/0.47 thf(fact_141_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [X11: name,X122: name] :
% 0.30/0.47 ( ( late_OutputR @ X11 @ X122 )
% 0.30/0.47 != late_TauR ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics1.freeRes.distinct(1)
% 0.30/0.47 thf(fact_142_outputCases,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.30/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ( ( ( Alpha3
% 0.30/0.47 = ( late_OutputR @ A2 @ B2 ) )
% 0.30/0.47 => ( ( P = P2 )
% 0.30/0.47 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 0.30/0.47 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % outputCases
% 0.30/0.47 thf(fact_143_outputCases_H,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 0.30/0.47 => ~ ! [A5: name,B4: name,P4: pi] :
% 0.30/0.47 ( ( ( A2 = A5 )
% 0.30/0.47 & ( B2 = B4 )
% 0.30/0.47 & ( P = P4 ) )
% 0.30/0.47 => ( Rs
% 0.30/0.47 != ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % outputCases'
% 0.30/0.47 thf(fact_144_outputIneqTrans,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,C2: name,D3: name,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D3 ) @ P2 ) )
% 0.30/0.47 => ~ ( ( A2 != C2 )
% 0.30/0.47 | ( B2 != D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % outputIneqTrans
% 0.30/0.47 thf(fact_145_Output,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % Output
% 0.30/0.47 thf(fact_146_tauOutputTrans,axiom,
% 0.30/0.47 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % tauOutputTrans
% 0.30/0.47 thf(fact_147_outputTauTrans,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % outputTauTrans
% 0.30/0.47 thf(fact_148_tauCases,axiom,
% 0.30/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.30/0.47 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.30/0.47 => ( ( ( Alpha3 = late_TauR )
% 0.30/0.47 => ( ( P = P2 )
% 0.30/0.47 => ( Prop @ late_TauR @ P ) ) )
% 0.30/0.47 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % tauCases
% 0.30/0.47 thf(fact_149_tauCases_H,axiom,
% 0.30/0.47 ! [P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.30/0.47 => ~ ! [P4: pi] :
% 0.30/0.47 ( ( ( tau @ P )
% 0.30/0.47 = ( tau @ P4 ) )
% 0.30/0.47 => ( Rs
% 0.30/0.47 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % tauCases'
% 0.30/0.47 thf(fact_150_Tau,axiom,
% 0.30/0.47 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tau
% 0.30/0.47 thf(fact_151_resOutputOutputTrans,axiom,
% 0.30/0.47 ! [X3: name,A2: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ X3 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resOutputOutputTrans
% 0.30/0.47 thf(fact_152_resTauOutputTrans,axiom,
% 0.30/0.47 ! [X3: name,P: pi,A2: name,B2: name,P2: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resTauOutputTrans
% 0.30/0.47 thf(fact_153_Late__Semantics_OClose1,axiom,
% 0.30/0.47 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.Close1
% 0.30/0.47 thf(fact_154_Late__Semantics_OClose2,axiom,
% 0.30/0.47 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.Close2
% 0.30/0.47 thf(fact_155_transitions_OClose1,axiom,
% 0.30/0.47 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.30/0.47 => ( ( X3 != A2 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.30/0.47 => ( ( Y != A2 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.30/0.47 => ( ( X3 != Y )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.Close1
% 0.30/0.47 thf(fact_156_transitions_OClose2,axiom,
% 0.30/0.47 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.30/0.47 => ( ( X3 != A2 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.30/0.47 => ( ( Y != A2 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.30/0.47 => ( ( X3 != Y )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.Close2
% 0.30/0.47 thf(fact_157_subst__identity,axiom,
% 0.30/0.47 ! [P: pi,A2: name] :
% 0.30/0.47 ( ( subs @ P @ A2 @ A2 )
% 0.30/0.47 = P ) ).
% 0.30/0.47
% 0.30/0.47 % subst_identity
% 0.30/0.47 thf(fact_158_simps_I8_J,axiom,
% 0.30/0.47 ! [P: pi,Q: pi,C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ ( par @ P @ Q ) @ C2 @ D3 )
% 0.30/0.47 = ( par @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(8)
% 0.30/0.47 thf(fact_159_simps_I9_J,axiom,
% 0.30/0.47 ! [X3: name,C2: name,D3: name,P: pi] :
% 0.30/0.47 ( ( X3 != C2 )
% 0.30/0.47 => ( ( X3 != D3 )
% 0.30/0.47 => ( ( subs @ ( res @ X3 @ P ) @ C2 @ D3 )
% 0.30/0.47 = ( res @ X3 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(9)
% 0.30/0.47 thf(fact_160_substTrans,axiom,
% 0.30/0.47 ! [B2: name,P: pi,A2: name,C2: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ B2 @ P )
% 0.30/0.47 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 0.30/0.47 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substTrans
% 0.30/0.47 thf(fact_161_simps_I2_J,axiom,
% 0.30/0.47 ! [P: pi,C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ ( tau @ P ) @ C2 @ D3 )
% 0.30/0.47 = ( tau @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(2)
% 0.30/0.47 thf(fact_162_forget,axiom,
% 0.30/0.47 ! [A2: name,P: pi,B2: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ P )
% 0.30/0.47 => ( ( subs @ P @ A2 @ B2 )
% 0.30/0.47 = P ) ) ).
% 0.30/0.47
% 0.30/0.47 % forget
% 0.30/0.47 thf(fact_163_fresh__fact1,axiom,
% 0.30/0.47 ! [A2: name,P: pi,C2: name,B2: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ P )
% 0.30/0.47 => ( ( A2 != C2 )
% 0.30/0.47 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fresh_fact1
% 0.30/0.47 thf(fact_164_fresh__fact2,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi] :
% 0.30/0.47 ( ( A2 != B2 )
% 0.30/0.47 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fresh_fact2
% 0.30/0.47 thf(fact_165_substRes3,axiom,
% 0.30/0.47 ! [B2: name,P: pi,A2: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ B2 @ P )
% 0.30/0.47 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.30/0.47 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substRes3
% 0.30/0.47 thf(fact_166_substRes2,axiom,
% 0.30/0.47 ! [B2: name,P: pi,A2: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ B2 @ P )
% 0.30/0.47 => ( ( res @ A2 @ P )
% 0.30/0.47 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substRes2
% 0.30/0.47 thf(fact_167_Late__Semantics_OComm1,axiom,
% 0.30/0.47 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.Comm1
% 0.30/0.47 thf(fact_168_Late__Semantics_OComm2,axiom,
% 0.30/0.47 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.Comm2
% 0.30/0.47 thf(fact_169_transitions_OComm2,axiom,
% 0.30/0.47 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( ( X3 != A2 )
% 0.30/0.47 => ( ( X3 != B2 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.Comm2
% 0.30/0.47 thf(fact_170_transitions_OComm1,axiom,
% 0.30/0.47 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.30/0.47 => ( ( X3 != A2 )
% 0.30/0.47 => ( ( X3 != B2 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.30/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.Comm1
% 0.30/0.47 thf(fact_171_freeRes_Orecs_I2_J,axiom,
% 0.30/0.47 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 0.30/0.47 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 0.30/0.47 => ( ( P @ F22 )
% 0.30/0.47 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 0.30/0.47 = F22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.recs(2)
% 0.30/0.47 thf(fact_172_freeRes_Orecs_I1_J,axiom,
% 0.30/0.47 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name1: name,Name2: name] :
% 0.30/0.47 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 0.30/0.47 => ( ( P @ F22 )
% 0.30/0.47 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name1 @ Name2 ) )
% 0.30/0.47 = ( F1 @ Name1 @ Name2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.recs(1)
% 0.30/0.47 thf(fact_173_simps_I3_J,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ ( output @ A2 @ B2 @ P ) @ C2 @ D3 )
% 0.30/0.47 = ( output @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(3)
% 0.30/0.47 thf(fact_174_simps_I4_J,axiom,
% 0.30/0.47 ! [X3: name,A2: name,C2: name,D3: name,P: pi] :
% 0.30/0.47 ( ( X3 != A2 )
% 0.30/0.47 => ( ( X3 != C2 )
% 0.30/0.47 => ( ( X3 != D3 )
% 0.30/0.47 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ C2 @ D3 )
% 0.30/0.47 = ( input @ ( subst_name @ A2 @ C2 @ D3 ) @ X3 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(4)
% 0.30/0.47 thf(fact_175_substInput,axiom,
% 0.30/0.47 ! [X3: name,B2: name,C2: name,A2: name,P: pi] :
% 0.30/0.47 ( ( X3 != B2 )
% 0.30/0.47 => ( ( X3 != C2 )
% 0.30/0.47 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ B2 @ C2 )
% 0.30/0.47 = ( input @ ( subst_name @ A2 @ B2 @ C2 ) @ X3 @ ( subs @ P @ B2 @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substInput
% 0.30/0.47 thf(fact_176_subst__name__def,axiom,
% 0.30/0.47 ( subst_name
% 0.30/0.47 = ( ^ [A6: name,B5: name,C5: name] : ( if @ name @ ( A6 = B5 ) @ C5 @ A6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subst_name_def
% 0.30/0.47 thf(fact_177_parZeroLeft,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.30/0.47 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % parZeroLeft
% 0.30/0.47 thf(fact_178_parZeroRight,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.30/0.47 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % parZeroRight
% 0.30/0.47 thf(fact_179_simps_I6_J,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ ( mismatch @ A2 @ B2 @ P ) @ C2 @ D3 )
% 0.30/0.47 = ( mismatch @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(6)
% 0.30/0.47 thf(fact_180_pi_Ofresh_I1_J,axiom,
% 0.30/0.47 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(1)
% 0.30/0.47 thf(fact_181_simps_I1_J,axiom,
% 0.30/0.47 ! [C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ piNil @ C2 @ D3 )
% 0.30/0.47 = piNil ) ).
% 0.30/0.47
% 0.30/0.47 % simps(1)
% 0.30/0.47 thf(fact_182_pi_Ofresh_I6_J,axiom,
% 0.30/0.47 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.30/0.47 & ( fresh @ name @ name @ A2 @ X2 )
% 0.30/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(6)
% 0.30/0.47 thf(fact_183_mismatchNilLeft,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A2 @ A2 @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % mismatchNilLeft
% 0.30/0.47 thf(fact_184_pi_Oinject_I5_J,axiom,
% 0.30/0.47 ! [X32: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.30/0.47 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.30/0.47 = ( mismatch @ Y3 @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X32 = Y3 )
% 0.30/0.47 & ( X2 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(5)
% 0.30/0.47 thf(fact_185_pi_Odistinct_I9_J,axiom,
% 0.30/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(9)
% 0.30/0.47 thf(fact_186_nilSimRight,axiom,
% 0.30/0.47 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.30/0.47
% 0.30/0.47 % nilSimRight
% 0.30/0.47 thf(fact_187_pi_Odistinct_I3_J,axiom,
% 0.30/0.47 ! [Pi2: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( tau @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(3)
% 0.30/0.47 thf(fact_188_pi_Odistinct_I39_J,axiom,
% 0.30/0.47 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( tau @ Pi )
% 0.30/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(39)
% 0.30/0.47 thf(fact_189_pi_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( output @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(1)
% 0.30/0.47 thf(fact_190_pi_Odistinct_I25_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(25)
% 0.30/0.47 thf(fact_191_pi_Odistinct_I5_J,axiom,
% 0.30/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(5)
% 0.30/0.47 thf(fact_192_pi_Odistinct_I51_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(51)
% 0.30/0.47 thf(fact_193_pi_Odistinct_I15_J,axiom,
% 0.30/0.47 ! [Name: name,Pi2: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(15)
% 0.30/0.47 thf(fact_194_pi_Odistinct_I75_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.30/0.47 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(75)
% 0.30/0.47 thf(fact_195_pi_Odistinct_I13_J,axiom,
% 0.30/0.47 ! [Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(13)
% 0.30/0.47 thf(fact_196_pi_Odistinct_I73_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(73)
% 0.30/0.47 thf(fact_197_zeroTrans,axiom,
% 0.30/0.47 ! [Rs: late_residual] :
% 0.30/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.30/0.47
% 0.30/0.47 % zeroTrans
% 0.30/0.47 thf(fact_198_nilCases_H,axiom,
% 0.30/0.47 ! [Rs: late_residual] :
% 0.30/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.30/0.47
% 0.30/0.47 % nilCases'
% 0.30/0.47 thf(fact_199_Mismatch,axiom,
% 0.30/0.47 ! [P: pi,Rs: late_residual,A2: name,B2: name] :
% 0.30/0.47 ( ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( ( A2 != B2 )
% 0.30/0.47 => ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Mismatch
% 0.30/0.47 thf(fact_200_mismatchCases_H,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.30/0.47 => ~ ! [P4: pi,A5: name,B4: name] :
% 0.30/0.47 ( ( ( A2 = A5 )
% 0.30/0.47 & ( B2 = B4 )
% 0.30/0.47 & ( P = P4 ) )
% 0.30/0.47 => ( ( late_transitions @ P4 @ Rs )
% 0.30/0.47 => ( A5 = B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mismatchCases'
% 0.30/0.47 thf(fact_201_mismatchTrans,axiom,
% 0.30/0.47 ! [A2: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.30/0.47
% 0.30/0.47 % mismatchTrans
% 0.30/0.47 thf(fact_202_mismatchCases,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual,F4: name > name > $o] :
% 0.30/0.47 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.30/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( ( A2 != B2 )
% 0.30/0.47 => ( F4 @ A2 @ B2 ) ) )
% 0.30/0.47 => ( F4 @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mismatchCases
% 0.30/0.47 thf(fact_203_resZeroTrans,axiom,
% 0.30/0.47 ! [X3: name,Rs: late_residual] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ piNil ) @ Rs ) ).
% 0.30/0.47
% 0.30/0.47 % resZeroTrans
% 0.30/0.47 thf(fact_204_nilSim_I2_J,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X3: name,P: pi] :
% 0.30/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X3 @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % nilSim(2)
% 0.30/0.47 thf(fact_205_nilSim_I3_J,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.30/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % nilSim(3)
% 0.30/0.47 thf(fact_206_nilSim_I1_J,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.30/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % nilSim(1)
% 0.30/0.47 thf(fact_207_simps_I5_J,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ ( match @ A2 @ B2 @ P ) @ C2 @ D3 )
% 0.30/0.47 = ( match @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(5)
% 0.30/0.47 thf(fact_208_pi_Ofresh_I5_J,axiom,
% 0.30/0.47 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X2 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.30/0.47 & ( fresh @ name @ name @ A2 @ X2 )
% 0.30/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(5)
% 0.30/0.47 thf(fact_209_freeRes_Ocase_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,F1: name > name > A,F22: A] :
% 0.30/0.47 ( ( late_case_freeRes @ A @ F1 @ F22 @ late_TauR )
% 0.30/0.47 = F22 ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.case(2)
% 0.30/0.47 thf(fact_210_pi_Odistinct_I61_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(61)
% 0.30/0.47 thf(fact_211_pi_Odistinct_I7_J,axiom,
% 0.30/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(7)
% 0.30/0.47 thf(fact_212_matchCases,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual,F4: name > name > $o] :
% 0.30/0.47 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.30/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( ( A2 = B2 )
% 0.30/0.47 => ( F4 @ A2 @ A2 ) ) )
% 0.30/0.47 => ( F4 @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % matchCases
% 0.30/0.47 thf(fact_213_matchTrans,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.30/0.47 => ( A2 = B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % matchTrans
% 0.30/0.47 thf(fact_214_matchCases_H,axiom,
% 0.30/0.47 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.30/0.47 => ~ ! [P4: pi] :
% 0.30/0.47 ( ( ( B2 = A2 )
% 0.30/0.47 & ( P = P4 ) )
% 0.30/0.47 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % matchCases'
% 0.30/0.47 thf(fact_215_Match,axiom,
% 0.30/0.47 ! [P: pi,Rs: late_residual,B2: name] :
% 0.30/0.47 ( ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( late_transitions @ ( match @ B2 @ B2 @ P ) @ Rs ) ) ).
% 0.30/0.47
% 0.30/0.47 % Match
% 0.30/0.47 thf(fact_216_pi_Odistinct_I65_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(65)
% 0.30/0.47 thf(fact_217_pi_Odistinct_I67_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.30/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(67)
% 0.30/0.47 thf(fact_218_pi_Odistinct_I49_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(49)
% 0.30/0.47 thf(fact_219_pi_Odistinct_I23_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(23)
% 0.30/0.47 thf(fact_220_pi_Odistinct_I37_J,axiom,
% 0.30/0.47 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.30/0.47 ( ( tau @ Pi )
% 0.30/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(37)
% 0.30/0.47 thf(fact_221_pi_Oinject_I4_J,axiom,
% 0.30/0.47 ! [X32: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.30/0.47 ( ( ( match @ X32 @ X2 @ X1 )
% 0.30/0.47 = ( match @ Y3 @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X32 = Y3 )
% 0.30/0.47 & ( X2 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(4)
% 0.30/0.47 thf(fact_222_matchNilLeft,axiom,
% 0.30/0.47 ! [A2: name,B2: name,Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.30/0.47 ( ( A2 != B2 )
% 0.30/0.47 => ( strong743114133lation @ piNil @ Rel @ ( match @ A2 @ B2 @ P ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % matchNilLeft
% 0.30/0.47 thf(fact_223_freeRes_Ocase_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,F1: name > name > A,F22: A,X11: name,X122: name] :
% 0.30/0.47 ( ( late_case_freeRes @ A @ F1 @ F22 @ ( late_OutputR @ X11 @ X122 ) )
% 0.30/0.47 = ( F1 @ X11 @ X122 ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.case(1)
% 0.30/0.47 thf(fact_224_pi_Ostrong__inducts,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [P: A > pi > $o,Z: A,Pi: pi] :
% 0.30/0.47 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.30/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Pi3: pi,Z2: A] :
% 0.30/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.30/0.47 ( ( fresh @ name @ A @ Name23 @ Z2 )
% 0.30/0.47 => ( ( fresh @ name @ name @ Name23 @ Name13 )
% 0.30/0.47 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.30/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.30/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 0.30/0.47 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.30/0.47 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 0.30/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.30/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 0.30/0.47 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.30/0.47 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 0.30/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.30/0.47 => ( ! [Name4: name,Pi3: pi,Z2: A] :
% 0.30/0.47 ( ( fresh @ name @ A @ Name4 @ Z2 )
% 0.30/0.47 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.30/0.47 => ( ! [Pi3: pi,Z2: A] :
% 0.30/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.30/0.47 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.strong_inducts
% 0.30/0.47 thf(fact_225_pi_Ostrong__induct,axiom,
% 0.30/0.47 ! [N: $tType] :
% 0.30/0.47 ( ( fs_name @ N )
% 0.30/0.47 => ! [P: N > pi > $o,Z: N,Pi: pi] :
% 0.30/0.47 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.30/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Pi3: pi,Z2: N] :
% 0.30/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.30/0.47 ( ( fresh @ name @ N @ Name23 @ Z2 )
% 0.30/0.47 => ( ( fresh @ name @ name @ Name23 @ Name13 )
% 0.30/0.47 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.30/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.30/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.30/0.47 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.30/0.47 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.30/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.30/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.30/0.47 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.30/0.47 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.30/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.30/0.47 => ( ! [Name4: name,Pi3: pi,Z2: N] :
% 0.30/0.47 ( ( fresh @ name @ N @ Name4 @ Z2 )
% 0.30/0.47 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.30/0.47 => ( ! [Pi3: pi,Z2: N] :
% 0.30/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.30/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.30/0.47 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.strong_induct
% 0.30/0.47 thf(fact_226_pi_Ofresh_I10_J,axiom,
% 0.30/0.47 ! [A2: name,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 0.30/0.47 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(10)
% 0.30/0.47 thf(fact_227_pi_Ofresh_I7_J,axiom,
% 0.30/0.47 ! [A2: name,X2: pi,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ pi @ A2 @ ( sum @ X2 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.30/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.fresh(7)
% 0.30/0.47 thf(fact_228_simps_I10_J,axiom,
% 0.30/0.47 ! [P: pi,C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ ( bang @ P ) @ C2 @ D3 )
% 0.30/0.47 = ( bang @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(10)
% 0.30/0.47 thf(fact_229_simps_I7_J,axiom,
% 0.30/0.47 ! [P: pi,Q: pi,C2: name,D3: name] :
% 0.30/0.47 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D3 )
% 0.30/0.47 = ( sum @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simps(7)
% 0.30/0.47 thf(fact_230_pi_Odistinct_I63_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(63)
% 0.30/0.47 thf(fact_231_pi_Odistinct_I69_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.30/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(69)
% 0.30/0.47 thf(fact_232_Bang,axiom,
% 0.30/0.47 ! [P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 0.30/0.47 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 0.30/0.47
% 0.30/0.47 % Bang
% 0.30/0.47 thf(fact_233_bangCases,axiom,
% 0.30/0.47 ! [P: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 0.30/0.47 => ~ ! [P4: pi] :
% 0.30/0.47 ( ( ( bang @ P )
% 0.30/0.47 = ( bang @ P4 ) )
% 0.30/0.47 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bangCases
% 0.30/0.47 thf(fact_234_pi_Odistinct_I87_J,axiom,
% 0.30/0.47 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 0.30/0.47 ( ( par @ Pi1 @ Pi22 )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(87)
% 0.30/0.47 thf(fact_235_pi_Odistinct_I89_J,axiom,
% 0.30/0.47 ! [Name3: name,Pi: pi,Pi2: pi] :
% 0.30/0.47 ( ( res @ Name3 @ Pi )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(89)
% 0.30/0.47 thf(fact_236_pi_Odistinct_I59_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(59)
% 0.30/0.47 thf(fact_237_pi_Odistinct_I33_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(33)
% 0.30/0.47 thf(fact_238_Sum2,axiom,
% 0.30/0.47 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ Rs )
% 0.30/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.30/0.47
% 0.30/0.47 % Sum2
% 0.30/0.47 thf(fact_239_Sum1,axiom,
% 0.30/0.47 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.30/0.47 ( ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.30/0.47
% 0.30/0.47 % Sum1
% 0.30/0.47 thf(fact_240_sumCases_H,axiom,
% 0.30/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.30/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumCases'
% 0.30/0.47 thf(fact_241_sumCases,axiom,
% 0.30/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.30/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.30/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumCases
% 0.30/0.47 thf(fact_242_pi_Odistinct_I47_J,axiom,
% 0.30/0.47 ! [Pi: pi,Pi2: pi] :
% 0.30/0.47 ( ( tau @ Pi )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(47)
% 0.30/0.47 thf(fact_243_pi_Odistinct_I79_J,axiom,
% 0.30/0.47 ! [Pi1: pi,Pi22: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( sum @ Pi1 @ Pi22 )
% 0.30/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(79)
% 0.30/0.47 thf(fact_244_pi_Odistinct_I81_J,axiom,
% 0.30/0.47 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 0.30/0.47 ( ( sum @ Pi1 @ Pi22 )
% 0.30/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(81)
% 0.30/0.47 thf(fact_245_pi_Odistinct_I53_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(53)
% 0.30/0.47 thf(fact_246_pi_Odistinct_I27_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(27)
% 0.30/0.47 thf(fact_247_pi_Odistinct_I41_J,axiom,
% 0.30/0.47 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( tau @ Pi )
% 0.30/0.47 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(41)
% 0.30/0.47 thf(fact_248_pi_Oinject_I9_J,axiom,
% 0.30/0.47 ! [X1: pi,Y1: pi] :
% 0.30/0.47 ( ( ( bang @ X1 )
% 0.30/0.47 = ( bang @ Y1 ) )
% 0.30/0.47 = ( X1 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(9)
% 0.30/0.47 thf(fact_249_pi_Oinject_I6_J,axiom,
% 0.30/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.30/0.47 ( ( ( sum @ X2 @ X1 )
% 0.30/0.47 = ( sum @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X2 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inject(6)
% 0.30/0.47 thf(fact_250_pi_Odistinct_I83_J,axiom,
% 0.30/0.47 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 0.30/0.47 ( ( sum @ Pi1 @ Pi22 )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(83)
% 0.30/0.47 thf(fact_251_pi_Odistinct_I11_J,axiom,
% 0.30/0.47 ! [Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(11)
% 0.30/0.47 thf(fact_252_pi_Odistinct_I17_J,axiom,
% 0.30/0.47 ! [Pi2: pi] :
% 0.30/0.47 ( piNil
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(17)
% 0.30/0.47 thf(fact_253_pi_Odistinct_I71_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.30/0.47 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(71)
% 0.30/0.47 thf(fact_254_pi_Odistinct_I77_J,axiom,
% 0.30/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.30/0.47 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.30/0.47 != ( bang @ Pi2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(77)
% 0.30/0.47 thf(fact_255_pi_Oinducts,axiom,
% 0.30/0.47 ! [P: pi > $o,Pi: pi] :
% 0.30/0.47 ( ( P @ piNil )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.30/0.47 ( ( P @ Pi3 )
% 0.30/0.47 => ( P @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Pi3: pi] :
% 0.30/0.47 ( ( P @ Pi3 )
% 0.30/0.47 => ( P @ ( tau @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.30/0.47 ( ( P @ Pi3 )
% 0.30/0.47 => ( P @ ( input @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.30/0.47 ( ( P @ Pi3 )
% 0.30/0.47 => ( P @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.30/0.47 ( ( P @ Pi3 )
% 0.30/0.47 => ( P @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Pi13: pi,Pi24: pi] :
% 0.30/0.47 ( ( P @ Pi13 )
% 0.30/0.47 => ( ( P @ Pi24 )
% 0.30/0.47 => ( P @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.30/0.47 => ( ! [Pi13: pi,Pi24: pi] :
% 0.30/0.47 ( ( P @ Pi13 )
% 0.30/0.47 => ( ( P @ Pi24 )
% 0.30/0.47 => ( P @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.30/0.47 => ( ! [Name4: name,Pi3: pi] :
% 0.30/0.47 ( ( P @ Pi3 )
% 0.30/0.47 => ( P @ ( res @ Name4 @ Pi3 ) ) )
% 0.30/0.47 => ( ! [Pi3: pi] :
% 0.30/0.47 ( ( P @ Pi3 )
% 0.30/0.47 => ( P @ ( bang @ Pi3 ) ) )
% 0.30/0.47 => ( P @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.inducts
% 0.30/0.47
% 0.30/0.47 % Type constructors (7)
% 0.30/0.47 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.30/0.47 fs_name @ pi ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Agent_Ofs__name_1,axiom,
% 0.30/0.47 fs_name @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Oname___Agent_Ofs__name_2,axiom,
% 0.30/0.47 fs_name @ name ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( ( fs_name @ A7 )
% 0.30/0.47 & ( fs_name @ A8 ) )
% 0.30/0.47 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4,axiom,
% 0.30/0.47 fs_name @ late_freeRes ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5,axiom,
% 0.30/0.47 fs_name @ late_subject ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6,axiom,
% 0.30/0.47 fs_name @ late_residual ).
% 0.30/0.47
% 0.30/0.47 % Helper facts (3)
% 0.30/0.47 thf(help_If_3_1_T,axiom,
% 0.30/0.47 ! [P: $o] :
% 0.30/0.47 ( ( P = $true )
% 0.30/0.47 | ( P = $false ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_2_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,Y: A] :
% 0.30/0.47 ( ( if @ A @ $false @ X3 @ Y )
% 0.30/0.47 = Y ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,Y: A] :
% 0.30/0.47 ( ( if @ A @ $true @ X3 @ Y )
% 0.30/0.47 = X3 ) ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ P8 ) )
% 0.30/0.47 & ( strong2129052853vative @ P8 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 0.32/1.70 ---- Embedded in THF ---
% 0.32/1.70 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.70 %%% Generated on Tue Feb 24 08:30:04 EST 2026
% 0.32/1.70 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.70 %%% Logic specification used:
% 0.32/1.70 %%% thf(spec, logic, $$dhol).
% 0.32/1.70
% 0.32/1.70 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aNTp5qWQTa/DTF2DTF2445.p
% 0.32/1.70 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 0.32/1.70 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 0.32/1.70 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 0.32/1.70 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.32/1.70 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 0.32/1.70 thf(ty_t_Agent_Oname, type, name: $tType).
% 0.32/1.70 thf(ty_t_Agent_Opi, type, pi: $tType).
% 0.32/1.70 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.32/1.70 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OBang, type, bang: (pi > pi)).
% 0.32/1.70 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OMatch, type, match: (name > (name > (pi > pi)))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OMismatch, type, mismatch: (name > (name > (pi > pi)))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 0.32/1.70 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 0.32/1.70 thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 0.32/1.70 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 0.32/1.70 thf(sy_c_Agent_Osubst__name, type, subst_name: (name > (name > (name > name)))).
% 0.32/1.70 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.32/1.70 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes, type, late_case_freeRes: (!> [A:$tType]: (((name > (name > A)) > (A > (late_freeRes > A)))))).
% 0.32/1.70 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 0.32/1.70 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 0.32/1.70 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 0.32/1.70 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 0.32/1.70 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 0.32/1.70 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 0.32/1.70 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 0.32/1.70 thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 0.32/1.70 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 0.32/1.70 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 0.32/1.70 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 0.32/1.70 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 0.32/1.70 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 0.32/1.70 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 0.32/1.70 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 0.32/1.70 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.32/1.70 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 0.32/1.70 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 0.32/1.70 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.32/1.70 thf(sy_v_P, type, p: pi).
% 0.32/1.70 thf(sy_v_PQR____, type, pqr: pi).
% 0.32/1.70 thf(sy_v_Q, type, q: pi).
% 0.32/1.70 thf(sy_v_QR____, type, qr: pi).
% 0.32/1.70 thf(sy_v_Q_H____, type, q2: pi).
% 0.32/1.70 thf(sy_v_R, type, r: pi).
% 0.32/1.70 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 0.32/1.70 thf(sy_v_a____, type, a: late_subject).
% 0.32/1.70 thf(sy_v_x____, type, x: name).
% 0.32/1.70 thf(fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062, axiom, (((((strong2129052853vative @ ((par @ ((par @ p) @ q2)) @ r)) @ ((par @ p) @ ((par @ q2) @ r))) @ a) @ x) @ rel)).
% 0.32/1.70 thf(fact_1_cPar1_Ohyps, axiom, ((late_transitions @ q) @ (((late_BoundR @ a) @ x) @ q2))).
% 0.32/1.70 thf(fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062, axiom, ((late_transitions @ ((par @ ((par @ p) @ q)) @ r)) @ (((late_BoundR @ a) @ x) @ ((par @ ((par @ p) @ q2)) @ r)))).
% 0.32/1.70 thf(fact_3_cPar2_Ohyps, axiom, ((late_transitions @ ((par @ q) @ r)) @ (((late_BoundR @ a) @ x) @ qr))).
% 0.32/1.70 thf(fact_4_Bound_Ohyps_I1_J, axiom, ((late_transitions @ ((par @ p) @ ((par @ q) @ r))) @ (((late_BoundR @ a) @ x) @ pqr))).
% 0.32/1.70 thf(fact_5__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062, axiom, ((late_transitions @ ((par @ p) @ q)) @ (((late_BoundR @ a) @ x) @ ((par @ p) @ q2)))).
% 0.32/1.70 thf(fact_6_Bound_Ohyps_I2_J, axiom, ((((fresh @ name) @ pi) @ x) @ ((par @ ((par @ p) @ q)) @ r))).
% 0.32/1.70 thf(fact_7__092_060open_062x_A_092_060sharp_062_AQ_A_092_060parallel_062_AR_092_060close_062, axiom, ((((fresh @ name) @ pi) @ x) @ ((par @ q) @ r))).
% 0.32/1.70 thf(fact_8__092_060open_062x_A_092_060sharp_062_AQ_092_060close_062, axiom, ((((fresh @ name) @ pi) @ x) @ q)).
% 0.32/1.70 thf(fact_9__092_060open_062x_A_092_060sharp_062_AP_092_060close_062, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 0.32/1.70 thf(fact_10__092_060open_062x_A_092_060sharp_062_AR_092_060close_062, axiom, ((((fresh @ name) @ pi) @ x) @ r)).
% 0.32/1.70 thf(fact_11_Ass, axiom, (! [S:pi,T2:pi,U:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((par @ S) @ T2)) @ U)) @ ((par @ S) @ ((par @ T2) @ U)))) @ rel)))).
% 0.32/1.70 thf(fact_12_pi_Oinject_I7_J, axiom, (! [X2:pi,X1:pi,Y2:pi,Y1:pi]: (((((par @ X2) @ X1) = ((par @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 0.32/1.70 thf(fact_13_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P2) @ Q)))))))).
% 0.32/1.70 thf(fact_14_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X3:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P) @ Q2)))))))).
% 0.32/1.70 thf(fact_15_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X3:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ PQ)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((! [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P3)) => (Prop @ ((par @ P3) @ Q))))) => ((! [Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q3)) => (Prop @ ((par @ P) @ Q3))))) => (Prop @ PQ))))))))).
% 0.32/1.70 thf(fact_16_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X3) @ P2))))))).
% 0.32/1.70 thf(fact_17_outputBoundTrans, axiom, (! [A2:name,B2:name,P:pi,C2:late_subject,X3:name,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ (((late_BoundR @ C2) @ X3) @ P2))))))).
% 0.32/1.70 thf(fact_18_Res, axiom, (! [S:pi,T2:pi,X3:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ S) @ T2)) @ rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X3) @ S)) @ ((res @ X3) @ T2))) @ rel))))).
% 0.32/1.70 thf(fact_19_FreshExt_H, axiom, (! [X3:name,U:pi,S:pi,T2:pi]: ((((((fresh @ name) @ pi) @ X3) @ U) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ X3) @ ((par @ S) @ T2))) @ U)) @ ((res @ X3) @ ((par @ S) @ ((par @ T2) @ U))))) @ rel))))).
% 0.32/1.70 thf(fact_20_FreshExt, axiom, (! [X3:name,S:pi,T2:pi,U:pi]: ((((((fresh @ name) @ pi) @ X3) @ S) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X3) @ ((par @ ((par @ S) @ T2)) @ U))) @ ((par @ S) @ ((res @ X3) @ ((par @ T2) @ U))))) @ rel))))).
% 0.32/1.70 thf(fact_21_pi_Ofresh_I8_J, axiom, (! [A2:name,X2:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X2) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 0.32/1.70 thf(fact_22_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 0.32/1.70 thf(fact_23_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 0.32/1.70 thf(fact_24_pi_Oinject_I1_J, axiom, (! [X32:name,X2:name,X1:pi,Y3:name,Y2:name,Y1:pi]: ((((((output @ X32) @ X2) @ X1) = (((output @ Y3) @ Y2) @ Y1)) = ((X32 = Y3) & ((X2 = Y2) & (X1 = Y1))))))).
% 0.32/1.70 thf(fact_25_pi_Odistinct_I45_J, axiom, (! [Pi:pi,Name:name,Pi2:pi]: (((tau @ Pi) != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_26_pi_Odistinct_I31_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name:name,Pi2:pi]: (((((output @ Name1) @ Name2) @ Pi) != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_27_pi_Odistinct_I19_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi2:pi]: (((((output @ Name1) @ Name2) @ Pi) != (tau @ Pi2))))).
% 0.32/1.70 thf(fact_28_resTrans_I1_J, axiom, (! [X3:name,B2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ X3) @ B2) @ P))) @ Rs)))))).
% 0.32/1.70 thf(fact_29_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 0.32/1.70 thf(fact_30_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X3:A]: ((~ ((! [C3:name]: ((~ (((((fresh @ name) @ A) @ C3) @ X3))))))))))))).
% 0.32/1.70 thf(fact_31_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi22:pi,Name:name,Pi2:pi]: ((((par @ Pi1) @ Pi22) != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_32_pi_Odistinct_I29_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((output @ Name1) @ Name2) @ Pi) != ((par @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_33_pi_Odistinct_I43_J, axiom, (! [Pi:pi,Pi12:pi,Pi23:pi]: (((tau @ Pi) != ((par @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_34_resTauBoundTrans, axiom, (! [X3:name,P:pi,A2:late_subject,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y) @ P2))))))).
% 0.32/1.70 thf(fact_35_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((Y != X3) => ((((fresh @ name) @ pi) @ Y) @ P2))))))).
% 0.32/1.70 thf(fact_36_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X3:A,Y:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) = (((((fresh @ X) @ A) @ A2) @ X3) & ((((fresh @ X) @ B) @ A2) @ Y)))))).
% 0.32/1.70 thf(fact_37_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 0.32/1.70 thf(fact_38_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 0.32/1.70 thf(fact_39_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C:$tType,A2:A,X3:B,Y:C]: ((((((fresh @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ X3) @ Y)) => ((((fresh @ A) @ C) @ A2) @ Y))))).
% 0.32/1.70 thf(fact_40_fresh__prodD_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,A2:A,X3:B,Y:C]: ((((((fresh @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ X3) @ Y)) => ((((fresh @ A) @ B) @ A2) @ X3))))).
% 0.32/1.70 thf(fact_41_resOutputInputTrans, axiom, (! [X3:name,A2:name,B2:name,P:pi,C2:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ B2) @ P))) @ (((late_BoundR @ (late_InputS @ C2)) @ Y) @ P2))))))).
% 0.32/1.70 thf(fact_42_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X3) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y) @ P2))))))))))).
% 0.32/1.70 thf(fact_43_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X3:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P) @ Q2)))))))))).
% 0.32/1.70 thf(fact_44_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P2) @ Q)))))))))).
% 0.32/1.70 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.32/1.70 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A4)))) = A4)))).
% 0.32/1.70 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.32/1.70 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 0.32/1.70 thf(fact_49_parCasesB_H, axiom, (! [P:pi,Q:pi,B2:late_subject,Y:name,P2:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B2) @ Y) @ P2)) => ((! [P4:pi,A5:late_subject,X5:name,P3:pi,Q4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A5) @ X5) @ ((par @ P3) @ Q4))) => (((late_transitions @ P4) @ (((late_BoundR @ A5) @ X5) @ P3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A5)))))))))) => (~ ((! [Q4:pi,A5:late_subject,X5:name,Q3:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A5) @ X5) @ ((par @ P4) @ Q3))) => (((late_transitions @ Q4) @ (((late_BoundR @ A5) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A5))))))))))))))))).
% 0.32/1.70 thf(fact_50_pi_Ofresh_I2_J, axiom, (! [A2:name,X32:name,X2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((output @ X32) @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 0.32/1.70 thf(fact_51_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 0.32/1.70 thf(fact_52_freshResidual, axiom, (! [P:pi,Rs:late_residual,X3:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X3) @ P) => ((((fresh @ name) @ late_residual) @ X3) @ Rs)))))).
% 0.32/1.70 thf(fact_53_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X3) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y) @ P2))))))))).
% 0.32/1.70 thf(fact_54_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_subject) @ Y) @ A2)))))).
% 0.32/1.70 thf(fact_55_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A5:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B4)))) => (P @ Prod))))).
% 0.32/1.70 thf(fact_56_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A5:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A5) @ B4))))))))).
% 0.32/1.70 thf(fact_57_prod__induct7, axiom, (! [G2:$tType,F2:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))))]: (((! [A5:A,B4:B,C3:C,D2:D,E2:E,F3:F2,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G2)) @ E2) @ ((((product_Pair @ F2) @ G2) @ F3) @ G3))))))))) => (P @ X3))))).
% 0.32/1.70 thf(fact_58_prod__induct6, axiom, (! [F2:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: (((! [A5:A,B4:B,C3:C,D2:D,E2:E,F3:F2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F3)))))))) => (P @ X3))))).
% 0.32/1.70 thf(fact_59_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A5:A,B4:B,C3:C,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X3))))).
% 0.32/1.70 thf(fact_60_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A5:A,B4:B,C3:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2)))))) => (P @ X3))))).
% 0.32/1.70 thf(fact_61_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A5:A,B4:B,C3:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B4) @ C3))))) => (P @ X3))))).
% 0.32/1.70 thf(fact_62_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F2:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D,E2:E,F3:F2,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G2)) @ E2) @ ((((product_Pair @ F2) @ G2) @ F3) @ G3)))))))))))))).
% 0.32/1.70 thf(fact_63_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D,E2:E,F3:F2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F3))))))))))))).
% 0.32/1.70 thf(fact_64_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 0.32/1.70 thf(fact_65_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2))))))))))).
% 0.32/1.70 thf(fact_66_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A5:A,B4:B,C3:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B4) @ C3)))))))))).
% 0.32/1.70 thf(fact_67_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 0.32/1.70 thf(fact_68_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P5:((product_prod @ A) @ B)]: (((! [A5:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B4)))) => (P @ P5))))).
% 0.32/1.70 thf(fact_69_surj__pair, axiom, (! [A:$tType,B:$tType,P5:((product_prod @ A) @ B)]: ((? [X5:A,Y4:B]: ((P5 = ((((product_Pair @ A) @ B) @ X5) @ Y4))))))).
% 0.32/1.70 thf(fact_70_old_Oprod_Orec, axiom, (! [A:$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))))).
% 0.32/1.70 thf(fact_71_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 0.32/1.70 thf(fact_72_subject_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F22 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_InputS @ Name3)) = (F1 @ Name3))))))).
% 0.32/1.70 thf(fact_73_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C2 @ A2) @ B2))))).
% 0.32/1.70 thf(fact_74_parSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((! [R:pi,S2:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R) @ S2)) @ ((par @ S2) @ R))) @ Rel))) => ((! [R:pi,S2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ R) @ S2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ R)) @ ((res @ X5) @ S2))) @ Rel)))) => (((strong743114133lation @ ((par @ P) @ Q)) @ Rel) @ ((par @ Q) @ P))))))).
% 0.32/1.70 thf(fact_75_inputIneqTrans, axiom, (! [A2:name,X3:name,P:pi,B2:late_subject,Y:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ B2) @ Y) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 0.32/1.70 thf(fact_76_Late__Semantics_OInput, axiom, (! [A2:name,X3:name,P:pi]: (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P))))).
% 0.32/1.70 thf(fact_77_transitions_OInput, axiom, (! [X3:name,A2:name,P:pi]: (((X3 != A2) => ((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P)))))).
% 0.32/1.70 thf(fact_78_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A6:name,B5:name]: ((A6 != B5))))).
% 0.32/1.70 thf(fact_79_pi_Odistinct_I55_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((input @ Name1) @ Name2) @ Pi) != ((par @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_80_pi_Odistinct_I57_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name:name,Pi2:pi]: (((((input @ Name1) @ Name2) @ Pi) != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_81_pi_Odistinct_I21_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((((output @ Name1) @ Name2) @ Pi) != (((input @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_82_pi_Odistinct_I35_J, axiom, (! [Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((tau @ Pi) != (((input @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_83_resTrans_I2_J, axiom, (! [X3:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ X3) @ Y) @ P))) @ Rs)))))).
% 0.32/1.70 thf(fact_84_simE_I1_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X3:name,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (? [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P3)) & (((((strong2129052853vative @ P3) @ Q2) @ A2) @ X3) @ Rel)))))))))).
% 0.32/1.70 thf(fact_85_resInputBoundOutputTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,B2:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z) @ P2))))))).
% 0.32/1.70 thf(fact_86_simulation__def, axiom, (strong743114133lation = (^ [P6:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A6:late_subject,X4:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A6) @ X4) @ Q6)) & ((((fresh @ name) @ pi) @ X4) @ P6)) => (? [P7:pi]: ((((late_transitions @ P6) @ (((late_BoundR @ A6) @ X4) @ P7)) & (((((strong2129052853vative @ P7) @ Q6) @ A6) @ X4) @ Rel2))))))) & (! [Alpha:late_freeRes,Q6:pi]: ((((late_transitions @ Q5) @ ((late_FreeR @ Alpha) @ Q6)) => (? [P7:pi]: ((((late_transitions @ P6) @ ((late_FreeR @ Alpha) @ P7)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P7) @ Q6)) @ Rel2)))))))))))).
% 0.32/1.70 thf(fact_87_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A5:late_subject,Y4:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A5) @ Y4) @ Q3)) => (((((fresh @ name) @ pi) @ Y4) @ P) => (? [P8:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A5) @ Y4) @ P8)) & (((((strong2129052853vative @ P8) @ Q3) @ A5) @ Y4) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P8:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P8)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P8) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 0.32/1.70 thf(fact_88_residual_Ofresh_I1_J, axiom, (! [A2:name,X32:late_subject,X1:name,X2:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ (((late_BoundR @ X32) @ X1) @ X2)) = (((((fresh @ name) @ late_subject) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X2))))))).
% 0.32/1.70 thf(fact_89_inputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B2) @ P)) @ Rs) => (~ ((! [X5:name,A5:name,P4:pi]: ((((A2 = A5) & (((((abs_fun @ name) @ pi) @ B2) @ P) = ((((abs_fun @ name) @ pi) @ X5) @ P4))) => ((Rs = (((late_BoundR @ (late_InputS @ A5)) @ X5) @ P4)) => (X5 = A5))))))))))).
% 0.32/1.70 thf(fact_90_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X2:name,Y2:name]: ((((late_BoundOutputS @ X2) = (late_BoundOutputS @ Y2)) = (X2 = Y2))))).
% 0.32/1.70 thf(fact_91_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 0.32/1.70 thf(fact_92_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 0.32/1.70 thf(fact_93_residual_Ofresh_I2_J, axiom, (! [A2:name,X2:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X2) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 0.32/1.70 thf(fact_94_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X2:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X2)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X2)))))).
% 0.32/1.70 thf(fact_95_pi_Ofresh_I4_J, axiom, (! [A2:name,X32:name,X1:name,X2:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((input @ X32) @ X1) @ X2)) = (((((fresh @ name) @ name) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X2))))))).
% 0.32/1.70 thf(fact_96_residual_Oinject_I2_J, axiom, (! [X2:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X2) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 0.32/1.70 thf(fact_97_abs__fun__eq1, axiom, (! [X:$tType,A:$tType,A2:X,X3:A,Y:A]: (((((((abs_fun @ X) @ A) @ A2) @ X3) = ((((abs_fun @ X) @ A) @ A2) @ Y)) = (X3 = Y))))).
% 0.32/1.70 thf(fact_98_pi_Oinject_I8_J, axiom, (! [X1:name,X2:pi,Y1:name,Y2:pi]: (((((res @ X1) @ X2) = ((res @ Y1) @ Y2)) = (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2)))))).
% 0.32/1.70 thf(fact_99_residual_Oinject_I1_J, axiom, (! [X32:late_subject,X1:name,X2:pi,Y3:late_subject,Y1:name,Y2:pi]: ((((((late_BoundR @ X32) @ X1) @ X2) = (((late_BoundR @ Y3) @ Y1) @ Y2)) = ((X32 = Y3) & (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 0.32/1.70 thf(fact_100_residual_Odistinct_I1_J, axiom, (! [Subject:late_subject,Name3:name,Pi:pi,FreeRes:late_freeRes,Pi2:pi]: (((((late_BoundR @ Subject) @ Name3) @ Pi) != ((late_FreeR @ FreeRes) @ Pi2))))).
% 0.32/1.70 thf(fact_101_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject2:late_subject,Name4:name,Pi3:pi]: ((P @ (((late_BoundR @ Subject2) @ Name4) @ Pi3)))) => ((! [FreeRes2:late_freeRes,Pi3:pi]: ((P @ ((late_FreeR @ FreeRes2) @ Pi3)))) => (P @ Residual)))))).
% 0.32/1.70 thf(fact_102_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B2:name,A2:name,X3:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B2) @ ((((abs_fun @ name) @ A) @ A2) @ X3)) = ((B2 = A2) | ((((fresh @ name) @ A) @ B2) @ X3))))))))).
% 0.32/1.70 thf(fact_103_abs__fresh_I1_J, axiom, (! [X6:$tType]: (((fs_name @ X6) => (! [B2:name,A2:name,X3:X6]: ((((((fresh @ name) @ (name > (noption @ X6))) @ B2) @ ((((abs_fun @ name) @ X6) @ A2) @ X3)) = ((B2 = A2) | ((((fresh @ name) @ X6) @ B2) @ X3))))))))).
% 0.32/1.70 thf(fact_104_pi_Oinject_I3_J, axiom, (! [X32:name,X1:name,X2:pi,Y3:name,Y1:name,Y2:pi]: ((((((input @ X32) @ X1) @ X2) = (((input @ Y3) @ Y1) @ Y2)) = ((X32 = Y3) & (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 0.32/1.70 thf(fact_105_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name3:name,Name:name]: (((late_InputS @ Name3) != (late_BoundOutputS @ Name))))).
% 0.32/1.70 thf(fact_106_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject:late_subject]: (((! [Name4:name]: ((P @ (late_InputS @ Name4)))) => ((! [Name4:name]: ((P @ (late_BoundOutputS @ Name4)))) => (P @ Subject)))))).
% 0.32/1.70 thf(fact_107_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject:late_subject]: (((! [Name4:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name4)))) => ((! [Name4:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name4)))) => ((P @ Z) @ Subject)))))).
% 0.32/1.70 thf(fact_108_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject:late_subject]: (((! [Name4:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name4)))) => ((! [Name4:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name4)))) => ((P @ Z) @ Subject)))))).
% 0.32/1.70 thf(fact_109_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X12:name]: ((Y != (late_InputS @ X12)))) => (~ ((! [X22:name]: ((Y != (late_BoundOutputS @ X22)))))))))).
% 0.32/1.70 thf(fact_110_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X2:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X2))))).
% 0.32/1.70 thf(fact_111_Par1F, axiom, (! [P:pi,Alpha3:late_freeRes,P2:pi,Q:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha3) @ P2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha3) @ ((par @ P2) @ Q))))))).
% 0.32/1.70 thf(fact_112_Par2F, axiom, (! [Q:pi,Alpha3:late_freeRes,Q2:pi,P:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha3) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha3) @ ((par @ P) @ Q2))))))).
% 0.32/1.70 thf(fact_113_ResF, axiom, (! [P:pi,Alpha3:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha3) @ P2)) => (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha3) => ((late_transitions @ ((res @ Y) @ P)) @ ((late_FreeR @ Alpha3) @ ((res @ Y) @ P2)))))))).
% 0.32/1.70 thf(fact_114_resCasesF_H, axiom, (! [X3:name,P:pi,Alpha3:late_freeRes,P2:pi]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha3) @ P2)) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y4:name]: (((((res @ X3) @ P) = ((res @ Y4) @ P4)) => ((((late_FreeR @ Alpha3) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y4) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y4) @ Alpha2)))))))))))))).
% 0.32/1.70 thf(fact_115_resCasesF, axiom, (! [X3:name,P:pi,Alpha3:late_freeRes,XP:pi,F4:(pi > $o)]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha3) @ XP)) => ((! [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha3) @ P3)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha3) => (F4 @ ((res @ X3) @ P3)))))) => (F4 @ XP)))))).
% 0.32/1.70 thf(fact_116_freshFreeDerivative_I1_J, axiom, (! [P:pi,Alpha3:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_freeRes) @ Y) @ Alpha3)))))).
% 0.32/1.70 thf(fact_117_freshFreeDerivative_I2_J, axiom, (! [P:pi,Alpha3:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ pi) @ Y) @ P2)))))).
% 0.32/1.70 thf(fact_118_inputFreeTrans, axiom, (! [A2:name,X3:name,P:pi,Alpha3:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ ((late_FreeR @ Alpha3) @ P2))))))).
% 0.32/1.70 thf(fact_119_outputFreshTrans, axiom, (! [A2:name,B2:name,P:pi,Alpha3:late_freeRes,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha3) @ P2)) => (~ ((((((fresh @ name) @ late_freeRes) @ A2) @ Alpha3) | ((((fresh @ name) @ late_freeRes) @ B2) @ Alpha3)))))))).
% 0.32/1.70 thf(fact_120_simE_I2_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Alpha3:late_freeRes,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ ((late_FreeR @ Alpha3) @ Q2)) => (? [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha3) @ P3)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P3) @ Q2)) @ Rel))))))))).
% 0.32/1.70 thf(fact_121_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F22 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_BoundOutputS @ Name3)) = (F22 @ Name3))))))).
% 0.32/1.70 thf(fact_122_resInputFreeTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,Alpha3:late_freeRes,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ ((late_FreeR @ Alpha3) @ P2))))))).
% 0.32/1.70 thf(fact_123_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject2:late_subject,Name4:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name4) @ Z2) => (((((fresh @ name) @ late_subject) @ Name4) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name4) @ Pi3)))))) => ((! [FreeRes2:late_freeRes,Pi3:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi3)))) => ((P @ Z) @ Residual))))))))).
% 0.32/1.70 thf(fact_124_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject2:late_subject,Name4:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name4) @ Z2) => (((((fresh @ name) @ late_subject) @ Name4) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name4) @ Pi3)))))) => ((! [FreeRes2:late_freeRes,Pi3:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi3)))) => ((P @ Z) @ Residual))))))))).
% 0.32/1.70 thf(fact_125_inputBoundOutputTrans, axiom, (! [A2:name,X3:name,P:pi,B2:name,Y:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y) @ P2))))))).
% 0.32/1.70 thf(fact_126_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [A5:late_subject,X5:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A5) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P) => (((((fresh @ name) @ pi) @ X5) @ Q) => (((((fresh @ name) @ late_subject) @ X5) @ A5) => (((((fresh @ name) @ A) @ X5) @ C4) => (? [P8:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A5) @ X5) @ P8)) & (((((strong2129052853vative @ P8) @ Q3) @ A5) @ X5) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P8:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P8)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P8) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 0.32/1.70 thf(fact_127_resCases_H, axiom, (! [X3:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X3) @ P)) @ Rs) => ((! [P4:pi,A5:name,B4:name]: (((((res @ X3) @ P) = ((res @ B4) @ P4)) => (! [P3:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A5)) @ B4) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A5) @ B4)) @ P3)) => (A5 = B4)))))))) => ((! [P4:pi,A5:late_subject,X5:name,P3:pi,Y4:name]: (((((res @ X3) @ P) = ((res @ Y4) @ P4)) => ((Rs = (((late_BoundR @ A5) @ X5) @ ((res @ Y4) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A5) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y4) @ A5) => ((Y4 != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A5))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y4:name]: (((((res @ X3) @ P) = ((res @ Y4) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y4) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y4) @ Alpha2)))))))))))))))).
% 0.32/1.70 thf(fact_128_resCasesB_H, axiom, (! [X7:name,P:pi,A2:late_subject,Y5:name,P2:pi]: ((((late_transitions @ ((res @ X7) @ P)) @ (((late_BoundR @ A2) @ Y5) @ P2)) => ((! [P4:pi,A5:name,B4:name]: (((((res @ X7) @ P) = ((res @ B4) @ P4)) => (! [P3:pi]: ((((((late_BoundR @ A2) @ Y5) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A5)) @ B4) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A5) @ B4)) @ P3)) => (A5 = B4)))))))) => (~ ((! [P4:pi,A5:late_subject,X5:name,P3:pi,Y4:name]: (((((res @ X7) @ P) = ((res @ Y4) @ P4)) => (((((late_BoundR @ A2) @ Y5) @ P2) = (((late_BoundR @ A5) @ X5) @ ((res @ Y4) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A5) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y4) @ A5) => ((Y4 != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A5)))))))))))))))))).
% 0.32/1.70 thf(fact_129_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X3:name,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [Q3:pi,A5:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A5) @ X3)) @ Q3)) => ((A5 != X3) => (? [P8:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A5)) @ X3) @ P8)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P8) @ Q3)) @ Rel)))))))) => ((! [Q3:pi,A5:late_subject,Y4:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A5) @ Y4) @ Q3)) => (((((fresh @ name) @ late_subject) @ X3) @ A5) => ((X3 != Y4) => (((((fresh @ name) @ A) @ Y4) @ C4) => (? [P8:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A5) @ Y4) @ P8)) & (((((strong2129052853vative @ P8) @ ((res @ X3) @ Q3)) @ A5) @ Y4) @ Rel)))))))))) => ((! [Q3:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha2) => (? [P8:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P8)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P8) @ ((res @ X3) @ Q3))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X3) @ Q)))))))))))).
% 0.32/1.70 thf(fact_130_Open, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P2))))))).
% 0.32/1.70 thf(fact_131_resOutputTauTrans, axiom, (! [X3:name,A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ B2) @ P))) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 0.32/1.70 thf(fact_132_Late__Semantics_OfreeRes_Oinject, axiom, (! [X2:name,X1:name,Y2:name,Y1:name]: (((((late_OutputR @ X2) @ X1) = ((late_OutputR @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 0.32/1.70 thf(fact_133_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)))))).
% 0.32/1.70 thf(fact_134_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 0.32/1.70 thf(fact_135_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X2:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 0.32/1.70 thf(fact_136_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name13) @ Name23)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 0.32/1.70 thf(fact_137_freeRes_Ostrong__induct_H, axiom, (! [N:$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)))))).
% 0.32/1.70 thf(fact_138_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name]: ((P @ ((late_OutputR @ Name13) @ Name23)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 0.32/1.70 thf(fact_139_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name1:name,Name2:name]: ((((late_OutputR @ Name1) @ Name2) != late_TauR)))).
% 0.32/1.70 thf(fact_140_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X123:name]: ((Y != ((late_OutputR @ X112) @ X123)))) => (Y = late_TauR))))).
% 0.32/1.70 thf(fact_141_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X122:name]: ((((late_OutputR @ X11) @ X122) != late_TauR)))).
% 0.32/1.70 thf(fact_142_outputCases, axiom, (! [A2:name,B2:name,P:pi,Alpha3:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha3) @ P2)) => (((Alpha3 = ((late_OutputR @ A2) @ B2)) => ((P = P2) => ((Prop @ ((late_OutputR @ A2) @ B2)) @ P))) => ((Prop @ Alpha3) @ P2)))))).
% 0.32/1.70 thf(fact_143_outputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ Rs) => (~ ((! [A5:name,B4:name,P4:pi]: ((((A2 = A5) & ((B2 = B4) & (P = P4))) => (Rs != ((late_FreeR @ ((late_OutputR @ A5) @ B4)) @ P4))))))))))).
% 0.32/1.70 thf(fact_144_outputIneqTrans, axiom, (! [A2:name,B2:name,P:pi,C2:name,D3:name,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ C2) @ D3)) @ P2)) => (~ (((A2 != C2) | (B2 != D3)))))))).
% 0.32/1.70 thf(fact_145_Output, axiom, (! [A2:name,B2:name,P:pi]: (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P))))).
% 0.32/1.70 thf(fact_146_tauOutputTrans, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 0.32/1.70 thf(fact_147_outputTauTrans, axiom, (! [A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 0.32/1.70 thf(fact_148_tauCases, axiom, (! [P:pi,Alpha3:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (tau @ P)) @ ((late_FreeR @ Alpha3) @ P2)) => (((Alpha3 = late_TauR) => ((P = P2) => ((Prop @ late_TauR) @ P))) => ((Prop @ Alpha3) @ P2)))))).
% 0.32/1.70 thf(fact_149_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))))))))))).
% 0.32/1.70 thf(fact_150_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 0.32/1.70 thf(fact_151_resOutputOutputTrans, axiom, (! [X3:name,A2:name,P:pi,B2:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ X3) @ P))) @ ((late_FreeR @ ((late_OutputR @ B2) @ Y)) @ P2))))))).
% 0.32/1.70 thf(fact_152_resTauOutputTrans, axiom, (! [X3:name,P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 0.32/1.70 thf(fact_153_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X3) @ Y)) @ Q2)))))))))).
% 0.32/1.70 thf(fact_154_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ Y))))))))))).
% 0.32/1.70 thf(fact_155_transitions_OClose1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X3 != A2) => (((((fresh @ name) @ pi) @ X3) @ Q2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ P2) => ((X3 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X3) @ Y)) @ Q2)))))))))))))))))).
% 0.32/1.70 thf(fact_156_transitions_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X3 != A2) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ Q2) => ((X3 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ Y))))))))))))))))))).
% 0.32/1.70 thf(fact_157_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 0.32/1.70 thf(fact_158_simps_I8_J, axiom, (! [P:pi,Q:pi,C2:name,D3:name]: (((((subs @ ((par @ P) @ Q)) @ C2) @ D3) = ((par @ (((subs @ P) @ C2) @ D3)) @ (((subs @ Q) @ C2) @ D3)))))).
% 0.32/1.70 thf(fact_159_simps_I9_J, axiom, (! [X3:name,C2:name,D3:name,P:pi]: (((X3 != C2) => ((X3 != D3) => ((((subs @ ((res @ X3) @ P)) @ C2) @ D3) = ((res @ X3) @ (((subs @ P) @ C2) @ D3)))))))).
% 0.32/1.70 thf(fact_160_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)))))).
% 0.32/1.70 thf(fact_161_simps_I2_J, axiom, (! [P:pi,C2:name,D3:name]: (((((subs @ (tau @ P)) @ C2) @ D3) = (tau @ (((subs @ P) @ C2) @ D3)))))).
% 0.32/1.70 thf(fact_162_forget, axiom, (! [A2:name,P:pi,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B2) = P))))).
% 0.32/1.70 thf(fact_163_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))))))).
% 0.32/1.70 thf(fact_164_fresh__fact2, axiom, (! [A2:name,B2:name,P:pi]: (((A2 != B2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B2)))))).
% 0.32/1.70 thf(fact_165_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))))))).
% 0.32/1.70 thf(fact_166_substRes2, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((res @ A2) @ P) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 0.32/1.70 thf(fact_167_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B2)) @ Q2)))))))).
% 0.32/1.70 thf(fact_168_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ B2))))))))).
% 0.32/1.70 thf(fact_169_transitions_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B2) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ B2)))))))))))))).
% 0.32/1.70 thf(fact_170_transitions_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B2) => (((((fresh @ name) @ pi) @ X3) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B2)) @ Q2))))))))))))).
% 0.32/1.70 thf(fact_171_freeRes_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T]: (((! [X12:name,X22:name]: ((P @ ((F1 @ X12) @ X22)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ late_TauR) = F22)))))).
% 0.32/1.70 thf(fact_172_freeRes_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T,Name1:name,Name2:name]: (((! [X12:name,X22:name]: ((P @ ((F1 @ X12) @ X22)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ ((late_OutputR @ Name1) @ Name2)) = ((F1 @ Name1) @ Name2))))))).
% 0.32/1.70 thf(fact_173_simps_I3_J, axiom, (! [A2:name,B2:name,P:pi,C2:name,D3:name]: (((((subs @ (((output @ A2) @ B2) @ P)) @ C2) @ D3) = (((output @ (((subst_name @ A2) @ C2) @ D3)) @ (((subst_name @ B2) @ C2) @ D3)) @ (((subs @ P) @ C2) @ D3)))))).
% 0.32/1.70 thf(fact_174_simps_I4_J, axiom, (! [X3:name,A2:name,C2:name,D3:name,P:pi]: (((X3 != A2) => ((X3 != C2) => ((X3 != D3) => ((((subs @ (((input @ A2) @ X3) @ P)) @ C2) @ D3) = (((input @ (((subst_name @ A2) @ C2) @ D3)) @ X3) @ (((subs @ P) @ C2) @ D3))))))))).
% 0.32/1.70 thf(fact_175_substInput, axiom, (! [X3:name,B2:name,C2:name,A2:name,P:pi]: (((X3 != B2) => ((X3 != C2) => ((((subs @ (((input @ A2) @ X3) @ P)) @ B2) @ C2) = (((input @ (((subst_name @ A2) @ B2) @ C2)) @ X3) @ (((subs @ P) @ B2) @ C2)))))))).
% 0.32/1.70 thf(fact_176_subst__name__def, axiom, (subst_name = (^ [A6:name,B5:name,C5:name]: (((((if @ name) @ (A6 = B5)) @ C5) @ A6))))).
% 0.32/1.70 thf(fact_177_parZeroLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((! [Q4:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ Q4) @ piNil)) @ Q4)) @ Rel))) => (((strong743114133lation @ ((par @ P) @ piNil)) @ Rel) @ P))))).
% 0.32/1.70 thf(fact_178_parZeroRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((! [Q4:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ Q4) @ ((par @ Q4) @ piNil))) @ Rel))) => (((strong743114133lation @ P) @ Rel) @ ((par @ P) @ piNil)))))).
% 0.32/1.70 thf(fact_179_simps_I6_J, axiom, (! [A2:name,B2:name,P:pi,C2:name,D3:name]: (((((subs @ (((mismatch @ A2) @ B2) @ P)) @ C2) @ D3) = (((mismatch @ (((subst_name @ A2) @ C2) @ D3)) @ (((subst_name @ B2) @ C2) @ D3)) @ (((subs @ P) @ C2) @ D3)))))).
% 0.32/1.70 thf(fact_180_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 0.32/1.70 thf(fact_181_simps_I1_J, axiom, (! [C2:name,D3:name]: (((((subs @ piNil) @ C2) @ D3) = piNil)))).
% 0.32/1.70 thf(fact_182_pi_Ofresh_I6_J, axiom, (! [A2:name,X32:name,X2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((mismatch @ X32) @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 0.32/1.70 thf(fact_183_mismatchNilLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,P:pi]: ((((strong743114133lation @ piNil) @ Rel) @ (((mismatch @ A2) @ A2) @ P))))).
% 0.32/1.70 thf(fact_184_pi_Oinject_I5_J, axiom, (! [X32:name,X2:name,X1:pi,Y3:name,Y2:name,Y1:pi]: ((((((mismatch @ X32) @ X2) @ X1) = (((mismatch @ Y3) @ Y2) @ Y1)) = ((X32 = Y3) & ((X2 = Y2) & (X1 = Y1))))))).
% 0.32/1.70 thf(fact_185_pi_Odistinct_I9_J, axiom, (! [Name12:name,Name22:name,Pi2:pi]: ((piNil != (((mismatch @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_186_nilSimRight, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: ((((strong743114133lation @ P) @ Rel) @ piNil)))).
% 0.32/1.70 thf(fact_187_pi_Odistinct_I3_J, axiom, (! [Pi2:pi]: ((piNil != (tau @ Pi2))))).
% 0.32/1.70 thf(fact_188_pi_Odistinct_I39_J, axiom, (! [Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((tau @ Pi) != (((mismatch @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_189_pi_Odistinct_I1_J, axiom, (! [Name12:name,Name22:name,Pi2:pi]: ((piNil != (((output @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_190_pi_Odistinct_I25_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((((output @ Name1) @ Name2) @ Pi) != (((mismatch @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_191_pi_Odistinct_I5_J, axiom, (! [Name12:name,Name22:name,Pi2:pi]: ((piNil != (((input @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_192_pi_Odistinct_I51_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((((input @ Name1) @ Name2) @ Pi) != (((mismatch @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_193_pi_Odistinct_I15_J, axiom, (! [Name:name,Pi2:pi]: ((piNil != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_194_pi_Odistinct_I75_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name:name,Pi2:pi]: (((((mismatch @ Name1) @ Name2) @ Pi) != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_195_pi_Odistinct_I13_J, axiom, (! [Pi12:pi,Pi23:pi]: ((piNil != ((par @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_196_pi_Odistinct_I73_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((mismatch @ Name1) @ Name2) @ Pi) != ((par @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_197_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 0.32/1.70 thf(fact_198_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 0.32/1.70 thf(fact_199_Mismatch, axiom, (! [P:pi,Rs:late_residual,A2:name,B2:name]: ((((late_transitions @ P) @ Rs) => ((A2 != B2) => ((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs)))))).
% 0.32/1.70 thf(fact_200_mismatchCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs) => (~ ((! [P4:pi,A5:name,B4:name]: ((((A2 = A5) & ((B2 = B4) & (P = P4))) => (((late_transitions @ P4) @ Rs) => (A5 = B4))))))))))).
% 0.32/1.70 thf(fact_201_mismatchTrans, axiom, (! [A2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ (((mismatch @ A2) @ A2) @ P)) @ Rs)))))).
% 0.32/1.70 thf(fact_202_mismatchCases, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual,F4:(name > (name > $o))]: ((((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 != B2) => ((F4 @ A2) @ B2))) => ((F4 @ A2) @ B2)))))).
% 0.32/1.70 thf(fact_203_resZeroTrans, axiom, (! [X3:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ piNil)) @ Rs)))))).
% 0.32/1.70 thf(fact_204_nilSim_I2_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,X3:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((input @ A2) @ X3) @ P))))))).
% 0.32/1.70 thf(fact_205_nilSim_I3_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((output @ A2) @ B2) @ P))))))).
% 0.32/1.70 thf(fact_206_nilSim_I1_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (tau @ P))))))).
% 0.32/1.70 thf(fact_207_simps_I5_J, axiom, (! [A2:name,B2:name,P:pi,C2:name,D3:name]: (((((subs @ (((match @ A2) @ B2) @ P)) @ C2) @ D3) = (((match @ (((subst_name @ A2) @ C2) @ D3)) @ (((subst_name @ B2) @ C2) @ D3)) @ (((subs @ P) @ C2) @ D3)))))).
% 0.32/1.70 thf(fact_208_pi_Ofresh_I5_J, axiom, (! [A2:name,X32:name,X2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((match @ X32) @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 0.32/1.70 thf(fact_209_freeRes_Ocase_I2_J, axiom, (! [A:$tType,F1:(name > (name > A)),F22:A]: ((((((late_case_freeRes @ A) @ F1) @ F22) @ late_TauR) = F22)))).
% 0.32/1.70 thf(fact_210_pi_Odistinct_I61_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((((match @ Name1) @ Name2) @ Pi) != (((mismatch @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_211_pi_Odistinct_I7_J, axiom, (! [Name12:name,Name22:name,Pi2:pi]: ((piNil != (((match @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_212_matchCases, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual,F4:(name > (name > $o))]: ((((late_transitions @ (((match @ A2) @ B2) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 = B2) => ((F4 @ A2) @ A2))) => ((F4 @ A2) @ B2)))))).
% 0.32/1.70 thf(fact_213_matchTrans, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B2) @ P)) @ Rs) => (A2 = B2))))).
% 0.32/1.70 thf(fact_214_matchCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B2) @ P)) @ Rs) => (~ ((! [P4:pi]: ((((B2 = A2) & (P = P4)) => (~ (((late_transitions @ P4) @ Rs)))))))))))).
% 0.32/1.70 thf(fact_215_Match, axiom, (! [P:pi,Rs:late_residual,B2:name]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ (((match @ B2) @ B2) @ P)) @ Rs))))).
% 0.32/1.70 thf(fact_216_pi_Odistinct_I65_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((match @ Name1) @ Name2) @ Pi) != ((par @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_217_pi_Odistinct_I67_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name:name,Pi2:pi]: (((((match @ Name1) @ Name2) @ Pi) != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_218_pi_Odistinct_I49_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((((input @ Name1) @ Name2) @ Pi) != (((match @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_219_pi_Odistinct_I23_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((((output @ Name1) @ Name2) @ Pi) != (((match @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_220_pi_Odistinct_I37_J, axiom, (! [Pi:pi,Name12:name,Name22:name,Pi2:pi]: (((tau @ Pi) != (((match @ Name12) @ Name22) @ Pi2))))).
% 0.32/1.70 thf(fact_221_pi_Oinject_I4_J, axiom, (! [X32:name,X2:name,X1:pi,Y3:name,Y2:name,Y1:pi]: ((((((match @ X32) @ X2) @ X1) = (((match @ Y3) @ Y2) @ Y1)) = ((X32 = Y3) & ((X2 = Y2) & (X1 = Y1))))))).
% 0.32/1.70 thf(fact_222_matchNilLeft, axiom, (! [A2:name,B2:name,Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((A2 != B2) => (((strong743114133lation @ piNil) @ Rel) @ (((match @ A2) @ B2) @ P)))))).
% 0.32/1.70 thf(fact_223_freeRes_Ocase_I1_J, axiom, (! [A:$tType,F1:(name > (name > A)),F22:A,X11:name,X122:name]: ((((((late_case_freeRes @ A) @ F1) @ F22) @ ((late_OutputR @ X11) @ X122)) = ((F1 @ X11) @ X122))))).
% 0.32/1.70 thf(fact_224_pi_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (pi > $o)),Z:A,Pi:pi]: (((! [Z2:A]: (((P @ Z2) @ piNil))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((output @ Name13) @ Name23) @ Pi3))))) => ((! [Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (tau @ Pi3))))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name23) @ Z2) => (((((fresh @ name) @ name) @ Name23) @ Name13) => ((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((input @ Name13) @ Name23) @ Pi3))))))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((match @ Name13) @ Name23) @ Pi3))))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((mismatch @ Name13) @ Name23) @ Pi3))))) => ((! [Pi13:pi,Pi24:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi24)))))) => ((! [Pi13:pi,Pi24:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((par @ Pi13) @ Pi24)))))) => ((! [Name4:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name4) @ Z2) => ((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ ((res @ Name4) @ Pi3)))))) => ((! [Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (bang @ Pi3))))) => ((P @ Z) @ Pi))))))))))))))))).
% 0.32/1.70 thf(fact_225_pi_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (pi > $o)),Z:N,Pi:pi]: (((! [Z2:N]: (((P @ Z2) @ piNil))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((output @ Name13) @ Name23) @ Pi3))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (tau @ Pi3))))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name23) @ Z2) => (((((fresh @ name) @ name) @ Name23) @ Name13) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((input @ Name13) @ Name23) @ Pi3))))))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((match @ Name13) @ Name23) @ Pi3))))) => ((! [Name13:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((mismatch @ Name13) @ Name23) @ Pi3))))) => ((! [Pi13:pi,Pi24:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi24)))))) => ((! [Pi13:pi,Pi24:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((par @ Pi13) @ Pi24)))))) => ((! [Name4:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name4) @ Z2) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ ((res @ Name4) @ Pi3)))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (bang @ Pi3))))) => ((P @ Z) @ Pi))))))))))))))))).
% 0.32/1.70 thf(fact_226_pi_Ofresh_I10_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (bang @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 0.32/1.70 thf(fact_227_pi_Ofresh_I7_J, axiom, (! [A2:name,X2:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((sum @ X2) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 0.32/1.70 thf(fact_228_simps_I10_J, axiom, (! [P:pi,C2:name,D3:name]: (((((subs @ (bang @ P)) @ C2) @ D3) = (bang @ (((subs @ P) @ C2) @ D3)))))).
% 0.32/1.70 thf(fact_229_simps_I7_J, axiom, (! [P:pi,Q:pi,C2:name,D3:name]: (((((subs @ ((sum @ P) @ Q)) @ C2) @ D3) = ((sum @ (((subs @ P) @ C2) @ D3)) @ (((subs @ Q) @ C2) @ D3)))))).
% 0.32/1.70 thf(fact_230_pi_Odistinct_I63_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((match @ Name1) @ Name2) @ Pi) != ((sum @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_231_pi_Odistinct_I69_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi2:pi]: (((((match @ Name1) @ Name2) @ Pi) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_232_Bang, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ ((par @ P) @ (bang @ P))) @ Rs) => ((late_transitions @ (bang @ P)) @ Rs))))).
% 0.32/1.70 thf(fact_233_bangCases, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ (bang @ P)) @ Rs) => (~ ((! [P4:pi]: ((((bang @ P) = (bang @ P4)) => (~ (((late_transitions @ ((par @ P4) @ (bang @ P4))) @ Rs)))))))))))).
% 0.32/1.70 thf(fact_234_pi_Odistinct_I87_J, axiom, (! [Pi1:pi,Pi22:pi,Pi2:pi]: ((((par @ Pi1) @ Pi22) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_235_pi_Odistinct_I89_J, axiom, (! [Name3:name,Pi:pi,Pi2:pi]: ((((res @ Name3) @ Pi) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_236_pi_Odistinct_I59_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi2:pi]: (((((input @ Name1) @ Name2) @ Pi) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_237_pi_Odistinct_I33_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi2:pi]: (((((output @ Name1) @ Name2) @ Pi) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_238_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 0.32/1.70 thf(fact_239_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 0.32/1.70 thf(fact_240_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 0.32/1.70 thf(fact_241_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 0.32/1.70 thf(fact_242_pi_Odistinct_I47_J, axiom, (! [Pi:pi,Pi2:pi]: (((tau @ Pi) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_243_pi_Odistinct_I79_J, axiom, (! [Pi1:pi,Pi22:pi,Pi12:pi,Pi23:pi]: ((((sum @ Pi1) @ Pi22) != ((par @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_244_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi22:pi,Name:name,Pi2:pi]: ((((sum @ Pi1) @ Pi22) != ((res @ Name) @ Pi2))))).
% 0.32/1.70 thf(fact_245_pi_Odistinct_I53_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((input @ Name1) @ Name2) @ Pi) != ((sum @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_246_pi_Odistinct_I27_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((output @ Name1) @ Name2) @ Pi) != ((sum @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_247_pi_Odistinct_I41_J, axiom, (! [Pi:pi,Pi12:pi,Pi23:pi]: (((tau @ Pi) != ((sum @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_248_pi_Oinject_I9_J, axiom, (! [X1:pi,Y1:pi]: ((((bang @ X1) = (bang @ Y1)) = (X1 = Y1))))).
% 0.32/1.70 thf(fact_249_pi_Oinject_I6_J, axiom, (! [X2:pi,X1:pi,Y2:pi,Y1:pi]: (((((sum @ X2) @ X1) = ((sum @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 0.32/1.70 thf(fact_250_pi_Odistinct_I83_J, axiom, (! [Pi1:pi,Pi22:pi,Pi2:pi]: ((((sum @ Pi1) @ Pi22) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_251_pi_Odistinct_I11_J, axiom, (! [Pi12:pi,Pi23:pi]: ((piNil != ((sum @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_252_pi_Odistinct_I17_J, axiom, (! [Pi2:pi]: ((piNil != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_253_pi_Odistinct_I71_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi12:pi,Pi23:pi]: (((((mismatch @ Name1) @ Name2) @ Pi) != ((sum @ Pi12) @ Pi23))))).
% 0.32/1.70 thf(fact_254_pi_Odistinct_I77_J, axiom, (! [Name1:name,Name2:name,Pi:pi,Pi2:pi]: (((((mismatch @ Name1) @ Name2) @ Pi) != (bang @ Pi2))))).
% 0.32/1.70 thf(fact_255_pi_Oinducts, axiom, (! [P:(pi > $o),Pi:pi]: (((P @ piNil) => ((! [Name13:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((output @ Name13) @ Name23) @ Pi3))))) => ((! [Pi3:pi]: (((P @ Pi3) => (P @ (tau @ Pi3))))) => ((! [Name13:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((input @ Name13) @ Name23) @ Pi3))))) => ((! [Name13:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((match @ Name13) @ Name23) @ Pi3))))) => ((! [Name13:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((mismatch @ Name13) @ Name23) @ Pi3))))) => ((! [Pi13:pi,Pi24:pi]: (((P @ Pi13) => ((P @ Pi24) => (P @ ((sum @ Pi13) @ Pi24)))))) => ((! [Pi13:pi,Pi24:pi]: (((P @ Pi13) => ((P @ Pi24) => (P @ ((par @ Pi13) @ Pi24)))))) => ((! [Name4:name,Pi3:pi]: (((P @ Pi3) => (P @ ((res @ Name4) @ Pi3))))) => ((! [Pi3:pi]: (((P @ Pi3) => (P @ (bang @ Pi3))))) => (P @ Pi)))))))))))))).
% 0.32/1.70 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 0.32/1.70 thf(tcon_HOL_Obool___Agent_Ofs__name_1, axiom, (fs_name @ $o)).
% 0.32/1.70 thf(tcon_Agent_Oname___Agent_Ofs__name_2, axiom, (fs_name @ name)).
% 0.32/1.70 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3, axiom, (! [A7:$tType,A8:$tType]: ((((fs_name @ A7) & (fs_name @ A8)) => (fs_name @ ((product_prod @ A7) @ A8)))))).
% 0.32/1.70 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4, axiom, (fs_name @ late_freeRes)).
% 0.32/1.70 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5, axiom, (fs_name @ late_subject)).
% 0.32/1.70 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6, axiom, (fs_name @ late_residual)).
% 0.32/1.70 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.32/1.70 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 0.32/1.70 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 0.32/1.70 thf(conj_0, conjecture, (? [P8:pi]: ((((late_transitions @ ((par @ ((par @ p) @ q)) @ r)) @ (((late_BoundR @ a) @ x) @ P8)) & (((((strong2129052853vative @ P8) @ ((par @ p) @ ((par @ q2) @ r))) @ a) @ x) @ rel))))).
% 0.32/1.70 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.aNTp5qWQTa/DTF2DTF2445.p
% 0.32/1.70 ------------------------
% 0.32/1.76 ---- Cleaned THF ---
% 0.32/1.76 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.32/1.76 late_residual: $tType ).
% 0.32/1.76
% 0.32/1.76 thf(ty_t_Late__Semantics_Osubject,type,
% 0.32/1.76 late_subject: $tType ).
% 0.32/1.76
% 0.32/1.76 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.32/1.76 late_freeRes: $tType ).
% 0.32/1.76
% 0.32/1.76 thf(ty_t_Product__Type_Oprod,type,
% 0.32/1.76 product_prod: $tType > $tType > $tType ).
% 0.32/1.76
% 0.32/1.76 thf(ty_t_Nominal_Onoption,type,
% 0.32/1.76 noption: $tType > $tType ).
% 0.32/1.76
% 0.32/1.76 thf(ty_t_Agent_Oname,type,
% 0.32/1.76 name: $tType ).
% 0.32/1.76
% 0.32/1.76 thf(ty_t_Agent_Opi,type,
% 0.32/1.76 pi: $tType ).
% 0.32/1.76
% 0.32/1.76 thf(ty_t_Set_Oset,type,
% 0.32/1.76 set: $tType > $tType ).
% 0.32/1.76
% 0.32/1.76 thf(sy_cl_Agent_Ofs__name,type,
% 0.32/1.76 fs_name:
% 0.32/1.76 !>[A: $tType] : $o ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OBang,type,
% 0.32/1.76 bang: pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OInput,type,
% 0.32/1.76 input: name > name > pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OMatch,type,
% 0.32/1.76 match: name > name > pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.32/1.76 mismatch: name > name > pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OOutput,type,
% 0.32/1.76 output: name > name > pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OPar,type,
% 0.32/1.76 par: pi > pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.32/1.76 piNil: pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_ORes,type,
% 0.32/1.76 res: name > pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OSum,type,
% 0.32/1.76 sum: pi > pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Opi_OTau,type,
% 0.32/1.76 tau: pi > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Osubs,type,
% 0.32/1.76 subs: pi > name > name > pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Agent_Osubst__name,type,
% 0.32/1.76 subst_name: name > name > name > name ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_If,type,
% 0.32/1.76 if:
% 0.32/1.76 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 0.32/1.76 late_case_freeRes:
% 0.32/1.76 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.32/1.76 late_OutputR: name > name > late_freeRes ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.32/1.76 late_TauR: late_freeRes ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.32/1.76 late_freeRes_rec:
% 0.32/1.76 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.32/1.76 late_BoundR: late_subject > name > pi > late_residual ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.32/1.76 late_FreeR: late_freeRes > pi > late_residual ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.32/1.76 late_BoundOutputS: name > late_subject ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.32/1.76 late_InputS: name > late_subject ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.32/1.76 late_subject_rec:
% 0.32/1.76 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.32/1.76 late_transitions: pi > late_residual > $o ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Nominal_Oabs__fun,type,
% 0.32/1.76 abs_fun:
% 0.32/1.76 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Nominal_Ofresh,type,
% 0.32/1.76 fresh:
% 0.32/1.76 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Product__Type_OPair,type,
% 0.32/1.76 product_Pair:
% 0.32/1.76 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.32/1.76 produc2004651681e_prod:
% 0.32/1.76 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.32/1.76 product_rec_prod:
% 0.32/1.76 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Rel_Oeqvt,type,
% 0.32/1.76 eqvt:
% 0.32/1.76 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Set_OCollect,type,
% 0.32/1.76 collect:
% 0.32/1.76 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.32/1.76 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.32/1.76 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.32/1.76
% 0.32/1.76 thf(sy_c_member,type,
% 0.32/1.76 member:
% 0.32/1.76 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_P,type,
% 0.32/1.76 p: pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_PQR____,type,
% 0.32/1.76 pqr: pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_Q,type,
% 0.32/1.76 q: pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_QR____,type,
% 0.32/1.76 qr: pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_Q_H____,type,
% 0.32/1.76 q2: pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_R,type,
% 0.32/1.76 r: pi ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_Rel,type,
% 0.32/1.76 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_a____,type,
% 0.32/1.76 a: late_subject ).
% 0.32/1.76
% 0.32/1.76 thf(sy_v_x____,type,
% 0.32/1.76 x: name ).
% 0.32/1.76
% 0.32/1.76 thf(fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062,axiom,
% 0.32/1.76 strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ).
% 0.32/1.76
% 0.32/1.76 thf(fact_1_cPar1_Ohyps,axiom,
% 0.32/1.76 late_transitions @ q @ ( late_BoundR @ a @ x @ q2 ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.32/1.76 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_3_cPar2_Ohyps,axiom,
% 0.32/1.76 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ a @ x @ qr ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_4_Bound_Ohyps_I1_J,axiom,
% 0.32/1.76 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_BoundR @ a @ x @ pqr ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_5__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 0.32/1.76 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ a @ x @ ( par @ p @ q2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_6_Bound_Ohyps_I2_J,axiom,
% 0.32/1.76 fresh @ name @ pi @ x @ ( par @ ( par @ p @ q ) @ r ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_7__092_060open_062x_A_092_060sharp_062_AQ_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.32/1.76 fresh @ name @ pi @ x @ ( par @ q @ r ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_8__092_060open_062x_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.32/1.76 fresh @ name @ pi @ x @ q ).
% 0.32/1.76
% 0.32/1.76 thf(fact_9__092_060open_062x_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.32/1.76 fresh @ name @ pi @ x @ p ).
% 0.32/1.76
% 0.32/1.76 thf(fact_10__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.32/1.76 fresh @ name @ pi @ x @ r ).
% 0.32/1.76
% 0.32/1.76 thf(fact_11_Ass,axiom,
% 0.32/1.76 ! [S: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S @ T2 ) @ U ) @ ( par @ S @ ( par @ T2 @ U ) ) ) @ rel ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_12_pi_Oinject_I7_J,axiom,
% 0.32/1.76 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.32/1.76 ( ( ( par @ X2 @ X1 )
% 0.32/1.76 = ( par @ Y2 @ Y1 ) )
% 0.32/1.76 = ( ( X2 = Y2 )
% 0.32/1.76 & ( X1 = Y1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_13_Late__Semantics_OPar1B,axiom,
% 0.32/1.76 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_14_Late__Semantics_OPar2B,axiom,
% 0.32/1.76 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_15_parCasesB,axiom,
% 0.32/1.76 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 0.32/1.76 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( ! [P3: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.32/1.76 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.32/1.76 => ( ! [Q3: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 0.32/1.76 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.32/1.76 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_16_tauBoundTrans,axiom,
% 0.32/1.76 ! [P: pi,A2: late_subject,X3: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X3 @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_17_outputBoundTrans,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,C2: late_subject,X3: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X3 @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_18_Res,axiom,
% 0.32/1.76 ! [S: pi,T2: pi,X3: name] :
% 0.32/1.76 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S @ T2 ) @ rel )
% 0.32/1.76 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X3 @ S ) @ ( res @ X3 @ T2 ) ) @ rel ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_19_FreshExt_H,axiom,
% 0.32/1.76 ! [X3: name,U: pi,S: pi,T2: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ X3 @ U )
% 0.32/1.76 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X3 @ ( par @ S @ T2 ) ) @ U ) @ ( res @ X3 @ ( par @ S @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_20_FreshExt,axiom,
% 0.32/1.76 ! [X3: name,S: pi,T2: pi,U: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ X3 @ S )
% 0.32/1.76 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X3 @ ( par @ ( par @ S @ T2 ) @ U ) ) @ ( par @ S @ ( res @ X3 @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_21_pi_Ofresh_I8_J,axiom,
% 0.32/1.76 ! [A2: name,X2: pi,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( par @ X2 @ X1 ) )
% 0.32/1.76 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.32/1.76 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_22_pi_Ofresh_I3_J,axiom,
% 0.32/1.76 ! [A2: name,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.32/1.76 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_23_pi_Oinject_I2_J,axiom,
% 0.32/1.76 ! [X1: pi,Y1: pi] :
% 0.32/1.76 ( ( ( tau @ X1 )
% 0.32/1.76 = ( tau @ Y1 ) )
% 0.32/1.76 = ( X1 = Y1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_24_pi_Oinject_I1_J,axiom,
% 0.32/1.76 ! [X32: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.32/1.76 ( ( ( output @ X32 @ X2 @ X1 )
% 0.32/1.76 = ( output @ Y3 @ Y2 @ Y1 ) )
% 0.32/1.76 = ( ( X32 = Y3 )
% 0.32/1.76 & ( X2 = Y2 )
% 0.32/1.76 & ( X1 = Y1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_25_pi_Odistinct_I45_J,axiom,
% 0.32/1.76 ! [Pi: pi,Name: name,Pi2: pi] :
% 0.32/1.76 ( ( tau @ Pi )
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_26_pi_Odistinct_I31_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_27_pi_Odistinct_I19_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( tau @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_28_resTrans_I1_J,axiom,
% 0.32/1.76 ! [X3: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( output @ X3 @ B2 @ P ) ) @ Rs ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_29_freshRes,axiom,
% 0.32/1.76 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_30_name__exists__fresh,axiom,
% 0.32/1.76 ! [A: $tType] :
% 0.32/1.76 ( ( fs_name @ A )
% 0.32/1.76 => ! [X3: A] :
% 0.32/1.76 ~ ! [C3: name] :
% 0.32/1.76 ~ ( fresh @ name @ A @ C3 @ X3 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_31_pi_Odistinct_I85_J,axiom,
% 0.32/1.76 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 0.32/1.76 ( ( par @ Pi1 @ Pi22 )
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_32_pi_Odistinct_I29_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_33_pi_Odistinct_I43_J,axiom,
% 0.32/1.76 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( tau @ Pi )
% 0.32/1.76 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_34_resTauBoundTrans,axiom,
% 0.32/1.76 ! [X3: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_35_freshBoundDerivative_I2_J,axiom,
% 0.32/1.76 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/1.76 => ( ( Y != X3 )
% 0.32/1.76 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_36_fresh__prod,axiom,
% 0.32/1.76 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y: B] :
% 0.32/1.76 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.32/1.76 = ( ( fresh @ X @ A @ A2 @ X3 )
% 0.32/1.76 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_37_prod_Oinject,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.32/1.76 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.32/1.76 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.32/1.76 = ( ( X1 = Y1 )
% 0.32/1.76 & ( X2 = Y2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_38_old_Oprod_Oinject,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.32/1.76 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.32/1.76 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.32/1.76 = ( ( A2 = A3 )
% 0.32/1.76 & ( B2 = B3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_39_fresh__prodD_I2_J,axiom,
% 0.32/1.76 ! [B: $tType,A: $tType,C: $tType,A2: A,X3: B,Y: C] :
% 0.32/1.76 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 0.32/1.76 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_40_fresh__prodD_I1_J,axiom,
% 0.32/1.76 ! [C: $tType,A: $tType,B: $tType,A2: A,X3: B,Y: C] :
% 0.32/1.76 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 0.32/1.76 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_41_resOutputInputTrans,axiom,
% 0.32/1.76 ! [X3: name,A2: name,B2: name,P: pi,C2: name,Y: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_42_transitions_OResB,axiom,
% 0.32/1.76 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.32/1.76 => ( ( Y != X3 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.32/1.76 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_43_transitions_OPar2B,axiom,
% 0.32/1.76 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_44_transitions_OPar1B,axiom,
% 0.32/1.76 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_45_mem__Collect__eq,axiom,
% 0.32/1.76 ! [A: $tType,A2: A,P: A > $o] :
% 0.32/1.76 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.32/1.76 = ( P @ A2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_46_Collect__mem__eq,axiom,
% 0.32/1.76 ! [A: $tType,A4: set @ A] :
% 0.32/1.76 ( ( collect @ A
% 0.32/1.76 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.32/1.76 = A4 ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_47_Collect__cong,axiom,
% 0.32/1.76 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/1.76 ( ! [X5: A] :
% 0.32/1.76 ( ( P @ X5 )
% 0.32/1.76 = ( Q @ X5 ) )
% 0.32/1.76 => ( ( collect @ A @ P )
% 0.32/1.76 = ( collect @ A @ Q ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_48_ext,axiom,
% 0.32/1.76 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.32/1.76 ( ! [X5: A] :
% 0.32/1.76 ( ( F @ X5 )
% 0.32/1.76 = ( G @ X5 ) )
% 0.32/1.76 => ( F = G ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_49_parCasesB_H,axiom,
% 0.32/1.76 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 0.32/1.76 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.32/1.76 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Q4: pi] :
% 0.32/1.76 ( ( ( par @ P @ Q )
% 0.32/1.76 = ( par @ P4 @ Q4 ) )
% 0.32/1.76 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.32/1.76 = ( late_BoundR @ A5 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.32/1.76 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) )
% 0.32/1.76 => ~ ! [Q4: pi,A5: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.32/1.76 ( ( ( par @ P @ Q )
% 0.32/1.76 = ( par @ P4 @ Q4 ) )
% 0.32/1.76 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.32/1.76 = ( late_BoundR @ A5 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.32/1.76 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A5 @ X5 @ Q3 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.32/1.76 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_50_pi_Ofresh_I2_J,axiom,
% 0.32/1.76 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X2 @ X1 ) )
% 0.32/1.76 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.32/1.76 & ( fresh @ name @ name @ A2 @ X2 )
% 0.32/1.76 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_51_subject_Ofresh_I1_J,axiom,
% 0.32/1.76 ! [A2: name,X1: name] :
% 0.32/1.76 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.32/1.76 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_52_freshResidual,axiom,
% 0.32/1.76 ! [P: pi,Rs: late_residual,X3: name] :
% 0.32/1.76 ( ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_53_Late__Semantics_OResB,axiom,
% 0.32/1.76 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.32/1.76 => ( ( Y != X3 )
% 0.32/1.76 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_54_freshBoundDerivative_I1_J,axiom,
% 0.32/1.76 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/1.76 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_55_old_Oprod_Oinducts,axiom,
% 0.32/1.76 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.32/1.76 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.32/1.76 => ( P @ Prod ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_56_old_Oprod_Oexhaust,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.32/1.76 ~ ! [A5: A,B4: B] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( product_Pair @ A @ B @ A5 @ B4 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_57_prod__induct7,axiom,
% 0.32/1.76 ! [G2: $tType,F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.32/1.76 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 0.32/1.76 => ( P @ X3 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_58_prod__induct6,axiom,
% 0.32/1.76 ! [F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.32/1.76 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 0.32/1.76 => ( P @ X3 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_59_prod__induct5,axiom,
% 0.32/1.76 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.32/1.76 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.32/1.76 => ( P @ X3 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_60_prod__induct4,axiom,
% 0.32/1.76 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.32/1.76 ( ! [A5: A,B4: B,C3: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 0.32/1.76 => ( P @ X3 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_61_prod__induct3,axiom,
% 0.32/1.76 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.32/1.76 ( ! [A5: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 0.32/1.76 => ( P @ X3 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_62_prod__cases7,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.32/1.76 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_63_prod__cases6,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.32/1.76 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F3: F2] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_64_prod__cases5,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.32/1.76 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_65_prod__cases4,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.32/1.76 ~ ! [A5: A,B4: B,C3: C,D2: D] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_66_prod__cases3,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.32/1.76 ~ ! [A5: A,B4: B,C3: C] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_67_Pair__inject,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.32/1.76 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.32/1.76 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.32/1.76 => ~ ( ( A2 = A3 )
% 0.32/1.76 => ( B2 != B3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_68_prod__cases,axiom,
% 0.32/1.76 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P5: product_prod @ A @ B] :
% 0.32/1.76 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.32/1.76 => ( P @ P5 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_69_surj__pair,axiom,
% 0.32/1.76 ! [A: $tType,B: $tType,P5: product_prod @ A @ B] :
% 0.32/1.76 ? [X5: A,Y4: B] :
% 0.32/1.76 ( P5
% 0.32/1.76 = ( product_Pair @ A @ B @ X5 @ Y4 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_70_old_Oprod_Orec,axiom,
% 0.32/1.76 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.32/1.76 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.32/1.76 = ( F1 @ A2 @ B2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_71_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.32/1.76 ! [X1: name,Y1: name] :
% 0.32/1.76 ( ( ( late_InputS @ X1 )
% 0.32/1.76 = ( late_InputS @ Y1 ) )
% 0.32/1.76 = ( X1 = Y1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_72_subject_Orecs_I1_J,axiom,
% 0.32/1.76 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.32/1.76 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.32/1.76 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.32/1.76 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 0.32/1.76 = ( F1 @ Name3 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_73_internal__case__prod__conv,axiom,
% 0.32/1.76 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.32/1.76 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.32/1.76 = ( C2 @ A2 @ B2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_74_parSym,axiom,
% 0.32/1.76 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.32/1.76 ( ! [R: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 0.32/1.76 => ( ! [R: pi,S2: pi,X5: name] :
% 0.32/1.76 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R @ S2 ) @ Rel )
% 0.32/1.76 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 0.32/1.76 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_75_inputIneqTrans,axiom,
% 0.32/1.76 ! [A2: name,X3: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 0.32/1.76 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.32/1.76 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_76_Late__Semantics_OInput,axiom,
% 0.32/1.76 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_77_transitions_OInput,axiom,
% 0.32/1.76 ! [X3: name,A2: name,P: pi] :
% 0.32/1.76 ( ( X3 != A2 )
% 0.32/1.76 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_78_name__fresh,axiom,
% 0.32/1.76 ( ( fresh @ name @ name )
% 0.32/1.76 = ( ^ [A6: name,B5: name] : ( A6 != B5 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_79_pi_Odistinct_I55_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( input @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_80_pi_Odistinct_I57_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.32/1.76 ( ( input @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_81_pi_Odistinct_I21_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_82_pi_Odistinct_I35_J,axiom,
% 0.32/1.76 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( tau @ Pi )
% 0.32/1.76 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_83_resTrans_I2_J,axiom,
% 0.32/1.76 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_84_simE_I1_J,axiom,
% 0.32/1.76 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 0.32/1.76 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ? [P3: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.32/1.76 & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_85_resInputBoundOutputTrans,axiom,
% 0.32/1.76 ! [X3: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_86_simulation__def,axiom,
% 0.32/1.76 ( strong743114133lation
% 0.32/1.76 = ( ^ [P6: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.32/1.76 ( ! [A6: late_subject,X4: name,Q6: pi] :
% 0.32/1.76 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A6 @ X4 @ Q6 ) )
% 0.32/1.76 & ( fresh @ name @ pi @ X4 @ P6 ) )
% 0.32/1.76 => ? [P7: pi] :
% 0.32/1.76 ( ( late_transitions @ P6 @ ( late_BoundR @ A6 @ X4 @ P7 ) )
% 0.32/1.76 & ( strong2129052853vative @ P7 @ Q6 @ A6 @ X4 @ Rel2 ) ) )
% 0.32/1.76 & ! [Alpha: late_freeRes,Q6: pi] :
% 0.32/1.76 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha @ Q6 ) )
% 0.32/1.76 => ? [P7: pi] :
% 0.32/1.76 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha @ P7 ) )
% 0.32/1.76 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_87_simCases,axiom,
% 0.32/1.76 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.32/1.76 ( ! [A5: late_subject,Y4: name,Q3: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y4 @ Q3 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y4 @ P )
% 0.32/1.76 => ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y4 @ P8 ) )
% 0.32/1.76 & ( strong2129052853vative @ P8 @ Q3 @ A5 @ Y4 @ Rel ) ) ) )
% 0.32/1.76 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.32/1.76 => ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.32/1.76 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.32/1.76 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_88_residual_Ofresh_I1_J,axiom,
% 0.32/1.76 ! [A2: name,X32: late_subject,X1: name,X2: pi] :
% 0.32/1.76 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.32/1.76 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 0.32/1.76 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_89_inputCases_H,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 0.32/1.76 => ~ ! [X5: name,A5: name,P4: pi] :
% 0.32/1.76 ( ( ( A2 = A5 )
% 0.32/1.76 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 0.32/1.76 = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 0.32/1.76 => ( ( Rs
% 0.32/1.76 = ( late_BoundR @ ( late_InputS @ A5 ) @ X5 @ P4 ) )
% 0.32/1.76 => ( X5 = A5 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_90_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.32/1.76 ! [X2: name,Y2: name] :
% 0.32/1.76 ( ( ( late_BoundOutputS @ X2 )
% 0.32/1.76 = ( late_BoundOutputS @ Y2 ) )
% 0.32/1.76 = ( X2 = Y2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_91_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.32/1.76 ! [X1: name,Y1: name] :
% 0.32/1.76 ( ( ( late_BoundOutputS @ X1 )
% 0.32/1.76 = ( late_BoundOutputS @ Y1 ) )
% 0.32/1.76 = ( X1 = Y1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_92_subject_Ofresh_I2_J,axiom,
% 0.32/1.76 ! [A2: name,X1: name] :
% 0.32/1.76 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.32/1.76 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_93_residual_Ofresh_I2_J,axiom,
% 0.32/1.76 ! [A2: name,X2: late_freeRes,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X2 @ X1 ) )
% 0.32/1.76 = ( ( fresh @ name @ late_freeRes @ A2 @ X2 )
% 0.32/1.76 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_94_pi_Ofresh_I9_J,axiom,
% 0.32/1.76 ! [A2: name,X1: name,X2: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X2 ) )
% 0.32/1.76 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_95_pi_Ofresh_I4_J,axiom,
% 0.32/1.76 ! [A2: name,X32: name,X1: name,X2: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X2 ) )
% 0.32/1.76 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.32/1.76 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_96_residual_Oinject_I2_J,axiom,
% 0.32/1.76 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.32/1.76 ( ( ( late_FreeR @ X2 @ X1 )
% 0.32/1.76 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.32/1.76 = ( ( X2 = Y2 )
% 0.32/1.76 & ( X1 = Y1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_97_abs__fun__eq1,axiom,
% 0.32/1.76 ! [X: $tType,A: $tType,A2: X,X3: A,Y: A] :
% 0.32/1.76 ( ( ( abs_fun @ X @ A @ A2 @ X3 )
% 0.32/1.76 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 0.32/1.76 = ( X3 = Y ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_98_pi_Oinject_I8_J,axiom,
% 0.32/1.76 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.32/1.76 ( ( ( res @ X1 @ X2 )
% 0.32/1.76 = ( res @ Y1 @ Y2 ) )
% 0.32/1.76 = ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.32/1.76 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_99_residual_Oinject_I1_J,axiom,
% 0.32/1.76 ! [X32: late_subject,X1: name,X2: pi,Y3: late_subject,Y1: name,Y2: pi] :
% 0.32/1.76 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.32/1.76 = ( late_BoundR @ Y3 @ Y1 @ Y2 ) )
% 0.32/1.76 = ( ( X32 = Y3 )
% 0.32/1.76 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.32/1.76 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_100_residual_Odistinct_I1_J,axiom,
% 0.32/1.76 ! [Subject: late_subject,Name3: name,Pi: pi,FreeRes: late_freeRes,Pi2: pi] :
% 0.32/1.76 ( ( late_BoundR @ Subject @ Name3 @ Pi )
% 0.32/1.76 != ( late_FreeR @ FreeRes @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_101_residual_Oinducts,axiom,
% 0.32/1.76 ! [P: late_residual > $o,Residual: late_residual] :
% 0.32/1.76 ( ! [Subject2: late_subject,Name4: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) )
% 0.32/1.76 => ( ! [FreeRes2: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.32/1.76 => ( P @ Residual ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_102_name__fresh__abs,axiom,
% 0.32/1.76 ! [A: $tType] :
% 0.32/1.76 ( ( fs_name @ A )
% 0.32/1.76 => ! [B2: name,A2: name,X3: A] :
% 0.32/1.76 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X3 ) )
% 0.32/1.76 = ( ( B2 = A2 )
% 0.32/1.76 | ( fresh @ name @ A @ B2 @ X3 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_103_abs__fresh_I1_J,axiom,
% 0.32/1.76 ! [X6: $tType] :
% 0.32/1.76 ( ( fs_name @ X6 )
% 0.32/1.76 => ! [B2: name,A2: name,X3: X6] :
% 0.32/1.76 ( ( fresh @ name @ ( name > ( noption @ X6 ) ) @ B2 @ ( abs_fun @ name @ X6 @ A2 @ X3 ) )
% 0.32/1.76 = ( ( B2 = A2 )
% 0.32/1.76 | ( fresh @ name @ X6 @ B2 @ X3 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_104_pi_Oinject_I3_J,axiom,
% 0.32/1.76 ! [X32: name,X1: name,X2: pi,Y3: name,Y1: name,Y2: pi] :
% 0.32/1.76 ( ( ( input @ X32 @ X1 @ X2 )
% 0.32/1.76 = ( input @ Y3 @ Y1 @ Y2 ) )
% 0.32/1.76 = ( ( X32 = Y3 )
% 0.32/1.76 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.32/1.76 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_105_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.32/1.76 ! [Name3: name,Name: name] :
% 0.32/1.76 ( ( late_InputS @ Name3 )
% 0.32/1.76 != ( late_BoundOutputS @ Name ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_106_subject_Oinducts,axiom,
% 0.32/1.76 ! [P: late_subject > $o,Subject: late_subject] :
% 0.32/1.76 ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 0.32/1.76 => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 0.32/1.76 => ( P @ Subject ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_107_subject_Ostrong__induct_H,axiom,
% 0.32/1.76 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 0.32/1.76 ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 0.32/1.76 => ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 0.32/1.76 => ( P @ Z @ Subject ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_108_subject_Ostrong__inducts,axiom,
% 0.32/1.76 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 0.32/1.76 ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 0.32/1.76 => ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 0.32/1.76 => ( P @ Z @ Subject ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_109_subject_Oexhaust,axiom,
% 0.32/1.76 ! [Y: late_subject] :
% 0.32/1.76 ( ! [X12: name] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( late_InputS @ X12 ) )
% 0.32/1.76 => ~ ! [X22: name] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_110_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.32/1.76 ! [X1: name,X2: name] :
% 0.32/1.76 ( ( late_InputS @ X1 )
% 0.32/1.76 != ( late_BoundOutputS @ X2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_111_Par1F,axiom,
% 0.32/1.76 ! [P: pi,Alpha3: late_freeRes,P2: pi,Q: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P2 @ Q ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_112_Par2F,axiom,
% 0.32/1.76 ! [Q: pi,Alpha3: late_freeRes,Q2: pi,P: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P @ Q2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_113_ResF,axiom,
% 0.32/1.76 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha3 )
% 0.32/1.76 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha3 @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_114_resCasesF_H,axiom,
% 0.32/1.76 ! [X3: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.32/1.76 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 0.32/1.76 ( ( ( res @ X3 @ P )
% 0.32/1.76 = ( res @ Y4 @ P4 ) )
% 0.32/1.76 => ( ( ( late_FreeR @ Alpha3 @ P2 )
% 0.32/1.76 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.32/1.76 => ~ ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_115_resCasesF,axiom,
% 0.32/1.76 ! [X3: name,P: pi,Alpha3: late_freeRes,XP: pi,F4: pi > $o] :
% 0.32/1.76 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha3 @ XP ) )
% 0.32/1.76 => ( ! [P3: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha3 )
% 0.32/1.76 => ( F4 @ ( res @ X3 @ P3 ) ) ) )
% 0.32/1.76 => ( F4 @ XP ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_116_freshFreeDerivative_I1_J,axiom,
% 0.32/1.76 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/1.76 => ( fresh @ name @ late_freeRes @ Y @ Alpha3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_117_freshFreeDerivative_I2_J,axiom,
% 0.32/1.76 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/1.76 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_118_inputFreeTrans,axiom,
% 0.32/1.76 ! [A2: name,X3: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_119_outputFreshTrans,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.32/1.76 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha3 )
% 0.32/1.76 | ( fresh @ name @ late_freeRes @ B2 @ Alpha3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_120_simE_I2_J,axiom,
% 0.32/1.76 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha3: late_freeRes,Q2: pi] :
% 0.32/1.76 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 0.32/1.76 => ? [P3: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 0.32/1.76 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_121_subject_Orecs_I2_J,axiom,
% 0.32/1.76 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.32/1.76 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.32/1.76 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.32/1.76 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 0.32/1.76 = ( F22 @ Name3 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_122_resInputFreeTrans,axiom,
% 0.32/1.76 ! [X3: name,A2: name,Y: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_123_residual_Ostrong__inducts,axiom,
% 0.32/1.76 ! [A: $tType] :
% 0.32/1.76 ( ( fs_name @ A )
% 0.32/1.76 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.32/1.76 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: A] :
% 0.32/1.76 ( ( fresh @ name @ A @ Name4 @ Z2 )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 0.32/1.76 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.32/1.76 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.32/1.76 => ( P @ Z @ Residual ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_124_residual_Ostrong__induct,axiom,
% 0.32/1.76 ! [N: $tType] :
% 0.32/1.76 ( ( fs_name @ N )
% 0.32/1.76 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.32/1.76 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: N] :
% 0.32/1.76 ( ( fresh @ name @ N @ Name4 @ Z2 )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 0.32/1.76 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.32/1.76 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.32/1.76 => ( P @ Z @ Residual ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_125_inputBoundOutputTrans,axiom,
% 0.32/1.76 ! [A2: name,X3: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_126_simCasesCont,axiom,
% 0.32/1.76 ! [A: $tType] :
% 0.32/1.76 ( ( fs_name @ A )
% 0.32/1.76 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.32/1.76 ( ( eqvt @ pi @ Rel )
% 0.32/1.76 => ( ! [A5: late_subject,X5: name,Q3: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ X5 @ Q3 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ X5 @ A5 )
% 0.32/1.76 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.32/1.76 => ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ X5 @ P8 ) )
% 0.32/1.76 & ( strong2129052853vative @ P8 @ Q3 @ A5 @ X5 @ Rel ) ) ) ) ) ) )
% 0.32/1.76 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.32/1.76 => ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.32/1.76 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.32/1.76 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_127_resCases_H,axiom,
% 0.32/1.76 ! [X3: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 0.32/1.76 => ( ! [P4: pi,A5: name,B4: name] :
% 0.32/1.76 ( ( ( res @ X3 @ P )
% 0.32/1.76 = ( res @ B4 @ P4 ) )
% 0.32/1.76 => ! [P3: pi] :
% 0.32/1.76 ( ( Rs
% 0.32/1.76 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 0.32/1.76 => ( A5 = B4 ) ) ) )
% 0.32/1.76 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y4: name] :
% 0.32/1.76 ( ( ( res @ X3 @ P )
% 0.32/1.76 = ( res @ Y4 @ P4 ) )
% 0.32/1.76 => ( ( Rs
% 0.32/1.76 = ( late_BoundR @ A5 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ Y4 @ A5 )
% 0.32/1.76 => ( ( Y4 != X5 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.32/1.76 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) ) )
% 0.32/1.76 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 0.32/1.76 ( ( ( res @ X3 @ P )
% 0.32/1.76 = ( res @ Y4 @ P4 ) )
% 0.32/1.76 => ( ( Rs
% 0.32/1.76 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.32/1.76 => ~ ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_128_resCasesB_H,axiom,
% 0.32/1.76 ! [X7: name,P: pi,A2: late_subject,Y5: name,P2: pi] :
% 0.32/1.76 ( ( late_transitions @ ( res @ X7 @ P ) @ ( late_BoundR @ A2 @ Y5 @ P2 ) )
% 0.32/1.76 => ( ! [P4: pi,A5: name,B4: name] :
% 0.32/1.76 ( ( ( res @ X7 @ P )
% 0.32/1.76 = ( res @ B4 @ P4 ) )
% 0.32/1.76 => ! [P3: pi] :
% 0.32/1.76 ( ( ( late_BoundR @ A2 @ Y5 @ P2 )
% 0.32/1.76 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 0.32/1.76 => ( A5 = B4 ) ) ) )
% 0.32/1.76 => ~ ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y4: name] :
% 0.32/1.76 ( ( ( res @ X7 @ P )
% 0.32/1.76 = ( res @ Y4 @ P4 ) )
% 0.32/1.76 => ( ( ( late_BoundR @ A2 @ Y5 @ P2 )
% 0.32/1.76 = ( late_BoundR @ A5 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ Y4 @ A5 )
% 0.32/1.76 => ( ( Y4 != X5 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.32/1.76 => ~ ( fresh @ name @ late_subject @ X5 @ A5 ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_129_resSimCases,axiom,
% 0.32/1.76 ! [A: $tType] :
% 0.32/1.76 ( ( fs_name @ A )
% 0.32/1.76 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P: pi,C4: A] :
% 0.32/1.76 ( ( eqvt @ pi @ Rel )
% 0.32/1.76 => ( ! [Q3: pi,A5: name] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A5 @ X3 ) @ Q3 ) )
% 0.32/1.76 => ( ( A5 != X3 )
% 0.32/1.76 => ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ X3 @ P8 ) )
% 0.32/1.76 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 0.32/1.76 => ( ! [Q3: pi,A5: late_subject,Y4: name] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y4 @ Q3 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_subject @ X3 @ A5 )
% 0.32/1.76 => ( ( X3 != Y4 )
% 0.32/1.76 => ( ( fresh @ name @ A @ Y4 @ C4 )
% 0.32/1.76 => ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y4 @ P8 ) )
% 0.32/1.76 & ( strong2129052853vative @ P8 @ ( res @ X3 @ Q3 ) @ A5 @ Y4 @ Rel ) ) ) ) ) )
% 0.32/1.76 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.32/1.76 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.32/1.76 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 0.32/1.76 => ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.32/1.76 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 0.32/1.76 => ( strong743114133lation @ P @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_130_Open,axiom,
% 0.32/1.76 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.32/1.76 => ( ( A2 != B2 )
% 0.32/1.76 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_131_resOutputTauTrans,axiom,
% 0.32/1.76 ! [X3: name,A2: name,B2: name,P: pi,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_132_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.32/1.76 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.32/1.76 ( ( ( late_OutputR @ X2 @ X1 )
% 0.32/1.76 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.32/1.76 = ( ( X2 = Y2 )
% 0.32/1.76 & ( X1 = Y1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_133_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.32/1.76 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.32/1.76 ( ( ( late_OutputR @ X11 @ X122 )
% 0.32/1.76 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.32/1.76 = ( ( X11 = Y11 )
% 0.32/1.76 & ( X122 = Y12 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_134_freeRes_Ofresh_I2_J,axiom,
% 0.32/1.76 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_135_freeRes_Ofresh_I1_J,axiom,
% 0.32/1.76 ! [A2: name,X2: name,X1: name] :
% 0.32/1.76 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X2 @ X1 ) )
% 0.32/1.76 = ( ( fresh @ name @ name @ A2 @ X2 )
% 0.32/1.76 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_136_freeRes_Ostrong__inducts,axiom,
% 0.32/1.76 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.32/1.76 ( ! [Name13: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.32/1.76 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.32/1.76 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_137_freeRes_Ostrong__induct_H,axiom,
% 0.32/1.76 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.32/1.76 ( ! [Name13: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.32/1.76 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.32/1.76 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_138_freeRes_Oinducts,axiom,
% 0.32/1.76 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.32/1.76 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.32/1.76 => ( ( P @ late_TauR )
% 0.32/1.76 => ( P @ FreeRes3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_139_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name] :
% 0.32/1.76 ( ( late_OutputR @ Name1 @ Name2 )
% 0.32/1.76 != late_TauR ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_140_freeRes_Oexhaust,axiom,
% 0.32/1.76 ! [Y: late_freeRes] :
% 0.32/1.76 ( ! [X112: name,X123: name] :
% 0.32/1.76 ( Y
% 0.32/1.76 != ( late_OutputR @ X112 @ X123 ) )
% 0.32/1.76 => ( Y = late_TauR ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_141_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.32/1.76 ! [X11: name,X122: name] :
% 0.32/1.76 ( ( late_OutputR @ X11 @ X122 )
% 0.32/1.76 != late_TauR ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_142_outputCases,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.32/1.76 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ( ( ( Alpha3
% 0.32/1.76 = ( late_OutputR @ A2 @ B2 ) )
% 0.32/1.76 => ( ( P = P2 )
% 0.32/1.76 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 0.32/1.76 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_143_outputCases_H,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 0.32/1.76 => ~ ! [A5: name,B4: name,P4: pi] :
% 0.32/1.76 ( ( ( A2 = A5 )
% 0.32/1.76 & ( B2 = B4 )
% 0.32/1.76 & ( P = P4 ) )
% 0.32/1.76 => ( Rs
% 0.32/1.76 != ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P4 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_144_outputIneqTrans,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,C2: name,D3: name,P2: pi] :
% 0.32/1.76 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D3 ) @ P2 ) )
% 0.32/1.76 => ~ ( ( A2 != C2 )
% 0.32/1.76 | ( B2 != D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_145_Output,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_146_tauOutputTrans,axiom,
% 0.32/1.76 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_147_outputTauTrans,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_148_tauCases,axiom,
% 0.32/1.76 ! [P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.32/1.76 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.32/1.76 => ( ( ( Alpha3 = late_TauR )
% 0.32/1.76 => ( ( P = P2 )
% 0.32/1.76 => ( Prop @ late_TauR @ P ) ) )
% 0.32/1.76 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_149_tauCases_H,axiom,
% 0.32/1.76 ! [P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.32/1.76 => ~ ! [P4: pi] :
% 0.32/1.76 ( ( ( tau @ P )
% 0.32/1.76 = ( tau @ P4 ) )
% 0.32/1.76 => ( Rs
% 0.32/1.76 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_150_Tau,axiom,
% 0.32/1.76 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_151_resOutputOutputTrans,axiom,
% 0.32/1.76 ! [X3: name,A2: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ X3 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_152_resTauOutputTrans,axiom,
% 0.32/1.76 ! [X3: name,P: pi,A2: name,B2: name,P2: pi] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_153_Late__Semantics_OClose1,axiom,
% 0.32/1.76 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_154_Late__Semantics_OClose2,axiom,
% 0.32/1.76 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_155_transitions_OClose1,axiom,
% 0.32/1.76 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.32/1.76 => ( ( X3 != A2 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.32/1.76 => ( ( Y != A2 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.32/1.76 => ( ( X3 != Y )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_156_transitions_OClose2,axiom,
% 0.32/1.76 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.32/1.76 => ( ( X3 != A2 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.32/1.76 => ( ( Y != A2 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.32/1.76 => ( ( X3 != Y )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_157_subst__identity,axiom,
% 0.32/1.76 ! [P: pi,A2: name] :
% 0.32/1.76 ( ( subs @ P @ A2 @ A2 )
% 0.32/1.76 = P ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_158_simps_I8_J,axiom,
% 0.32/1.76 ! [P: pi,Q: pi,C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ ( par @ P @ Q ) @ C2 @ D3 )
% 0.32/1.76 = ( par @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_159_simps_I9_J,axiom,
% 0.32/1.76 ! [X3: name,C2: name,D3: name,P: pi] :
% 0.32/1.76 ( ( X3 != C2 )
% 0.32/1.76 => ( ( X3 != D3 )
% 0.32/1.76 => ( ( subs @ ( res @ X3 @ P ) @ C2 @ D3 )
% 0.32/1.76 = ( res @ X3 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_160_substTrans,axiom,
% 0.32/1.76 ! [B2: name,P: pi,A2: name,C2: name] :
% 0.32/1.76 ( ( fresh @ name @ pi @ B2 @ P )
% 0.32/1.76 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 0.32/1.76 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_161_simps_I2_J,axiom,
% 0.32/1.76 ! [P: pi,C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ ( tau @ P ) @ C2 @ D3 )
% 0.32/1.76 = ( tau @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_162_forget,axiom,
% 0.32/1.76 ! [A2: name,P: pi,B2: name] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ P )
% 0.32/1.76 => ( ( subs @ P @ A2 @ B2 )
% 0.32/1.76 = P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_163_fresh__fact1,axiom,
% 0.32/1.76 ! [A2: name,P: pi,C2: name,B2: name] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ P )
% 0.32/1.76 => ( ( A2 != C2 )
% 0.32/1.76 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_164_fresh__fact2,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi] :
% 0.32/1.76 ( ( A2 != B2 )
% 0.32/1.76 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_165_substRes3,axiom,
% 0.32/1.76 ! [B2: name,P: pi,A2: name] :
% 0.32/1.76 ( ( fresh @ name @ pi @ B2 @ P )
% 0.32/1.76 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.32/1.76 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_166_substRes2,axiom,
% 0.32/1.76 ! [B2: name,P: pi,A2: name] :
% 0.32/1.76 ( ( fresh @ name @ pi @ B2 @ P )
% 0.32/1.76 => ( ( res @ A2 @ P )
% 0.32/1.76 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_167_Late__Semantics_OComm1,axiom,
% 0.32/1.76 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_168_Late__Semantics_OComm2,axiom,
% 0.32/1.76 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_169_transitions_OComm2,axiom,
% 0.32/1.76 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( ( X3 != A2 )
% 0.32/1.76 => ( ( X3 != B2 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_170_transitions_OComm1,axiom,
% 0.32/1.76 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.32/1.76 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/1.76 => ( ( X3 != A2 )
% 0.32/1.76 => ( ( X3 != B2 )
% 0.32/1.76 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.32/1.76 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_171_freeRes_Orecs_I2_J,axiom,
% 0.32/1.76 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 0.32/1.76 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 0.32/1.76 => ( ( P @ F22 )
% 0.32/1.76 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 0.32/1.76 = F22 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_172_freeRes_Orecs_I1_J,axiom,
% 0.32/1.76 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name1: name,Name2: name] :
% 0.32/1.76 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 0.32/1.76 => ( ( P @ F22 )
% 0.32/1.76 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name1 @ Name2 ) )
% 0.32/1.76 = ( F1 @ Name1 @ Name2 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_173_simps_I3_J,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ ( output @ A2 @ B2 @ P ) @ C2 @ D3 )
% 0.32/1.76 = ( output @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_174_simps_I4_J,axiom,
% 0.32/1.76 ! [X3: name,A2: name,C2: name,D3: name,P: pi] :
% 0.32/1.76 ( ( X3 != A2 )
% 0.32/1.76 => ( ( X3 != C2 )
% 0.32/1.76 => ( ( X3 != D3 )
% 0.32/1.76 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ C2 @ D3 )
% 0.32/1.76 = ( input @ ( subst_name @ A2 @ C2 @ D3 ) @ X3 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_175_substInput,axiom,
% 0.32/1.76 ! [X3: name,B2: name,C2: name,A2: name,P: pi] :
% 0.32/1.76 ( ( X3 != B2 )
% 0.32/1.76 => ( ( X3 != C2 )
% 0.32/1.76 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ B2 @ C2 )
% 0.32/1.76 = ( input @ ( subst_name @ A2 @ B2 @ C2 ) @ X3 @ ( subs @ P @ B2 @ C2 ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_176_subst__name__def,axiom,
% 0.32/1.76 ( subst_name
% 0.32/1.76 = ( ^ [A6: name,B5: name,C5: name] : ( if @ name @ ( A6 = B5 ) @ C5 @ A6 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_177_parZeroLeft,axiom,
% 0.32/1.76 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/1.76 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 0.32/1.76 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_178_parZeroRight,axiom,
% 0.32/1.76 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/1.76 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 0.32/1.76 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_179_simps_I6_J,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ ( mismatch @ A2 @ B2 @ P ) @ C2 @ D3 )
% 0.32/1.76 = ( mismatch @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_180_pi_Ofresh_I1_J,axiom,
% 0.32/1.76 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_181_simps_I1_J,axiom,
% 0.32/1.76 ! [C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ piNil @ C2 @ D3 )
% 0.32/1.76 = piNil ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_182_pi_Ofresh_I6_J,axiom,
% 0.32/1.76 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.32/1.76 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.32/1.76 & ( fresh @ name @ name @ A2 @ X2 )
% 0.32/1.76 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_183_mismatchNilLeft,axiom,
% 0.32/1.76 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A2 @ A2 @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_184_pi_Oinject_I5_J,axiom,
% 0.32/1.76 ! [X32: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.32/1.76 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.32/1.76 = ( mismatch @ Y3 @ Y2 @ Y1 ) )
% 0.32/1.76 = ( ( X32 = Y3 )
% 0.32/1.76 & ( X2 = Y2 )
% 0.32/1.76 & ( X1 = Y1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_185_pi_Odistinct_I9_J,axiom,
% 0.32/1.76 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_186_nilSimRight,axiom,
% 0.32/1.76 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_187_pi_Odistinct_I3_J,axiom,
% 0.32/1.76 ! [Pi2: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( tau @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_188_pi_Odistinct_I39_J,axiom,
% 0.32/1.76 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( tau @ Pi )
% 0.32/1.76 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_189_pi_Odistinct_I1_J,axiom,
% 0.32/1.76 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( output @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_190_pi_Odistinct_I25_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_191_pi_Odistinct_I5_J,axiom,
% 0.32/1.76 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_192_pi_Odistinct_I51_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( input @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_193_pi_Odistinct_I15_J,axiom,
% 0.32/1.76 ! [Name: name,Pi2: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_194_pi_Odistinct_I75_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.32/1.76 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_195_pi_Odistinct_I13_J,axiom,
% 0.32/1.76 ! [Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_196_pi_Odistinct_I73_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_197_zeroTrans,axiom,
% 0.32/1.76 ! [Rs: late_residual] :
% 0.32/1.76 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_198_nilCases_H,axiom,
% 0.32/1.76 ! [Rs: late_residual] :
% 0.32/1.76 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_199_Mismatch,axiom,
% 0.32/1.76 ! [P: pi,Rs: late_residual,A2: name,B2: name] :
% 0.32/1.76 ( ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( ( A2 != B2 )
% 0.32/1.76 => ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_200_mismatchCases_H,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.32/1.76 => ~ ! [P4: pi,A5: name,B4: name] :
% 0.32/1.76 ( ( ( A2 = A5 )
% 0.32/1.76 & ( B2 = B4 )
% 0.32/1.76 & ( P = P4 ) )
% 0.32/1.76 => ( ( late_transitions @ P4 @ Rs )
% 0.32/1.76 => ( A5 = B4 ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_201_mismatchTrans,axiom,
% 0.32/1.76 ! [A2: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_202_mismatchCases,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Rs: late_residual,F4: name > name > $o] :
% 0.32/1.76 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.32/1.76 => ( ( ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( ( A2 != B2 )
% 0.32/1.76 => ( F4 @ A2 @ B2 ) ) )
% 0.32/1.76 => ( F4 @ A2 @ B2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_203_resZeroTrans,axiom,
% 0.32/1.76 ! [X3: name,Rs: late_residual] :
% 0.32/1.76 ~ ( late_transitions @ ( res @ X3 @ piNil ) @ Rs ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_204_nilSim_I2_J,axiom,
% 0.32/1.76 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X3: name,P: pi] :
% 0.32/1.76 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X3 @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_205_nilSim_I3_J,axiom,
% 0.32/1.76 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.32/1.76 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_206_nilSim_I1_J,axiom,
% 0.32/1.76 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/1.76 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_207_simps_I5_J,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ ( match @ A2 @ B2 @ P ) @ C2 @ D3 )
% 0.32/1.76 = ( match @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_208_pi_Ofresh_I5_J,axiom,
% 0.32/1.76 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X2 @ X1 ) )
% 0.32/1.76 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.32/1.76 & ( fresh @ name @ name @ A2 @ X2 )
% 0.32/1.76 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_209_freeRes_Ocase_I2_J,axiom,
% 0.32/1.76 ! [A: $tType,F1: name > name > A,F22: A] :
% 0.32/1.76 ( ( late_case_freeRes @ A @ F1 @ F22 @ late_TauR )
% 0.32/1.76 = F22 ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_210_pi_Odistinct_I61_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( match @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_211_pi_Odistinct_I7_J,axiom,
% 0.32/1.76 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_212_matchCases,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Rs: late_residual,F4: name > name > $o] :
% 0.32/1.76 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.32/1.76 => ( ( ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( ( A2 = B2 )
% 0.32/1.76 => ( F4 @ A2 @ A2 ) ) )
% 0.32/1.76 => ( F4 @ A2 @ B2 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_213_matchTrans,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.32/1.76 => ( A2 = B2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_214_matchCases_H,axiom,
% 0.32/1.76 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.32/1.76 => ~ ! [P4: pi] :
% 0.32/1.76 ( ( ( B2 = A2 )
% 0.32/1.76 & ( P = P4 ) )
% 0.32/1.76 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_215_Match,axiom,
% 0.32/1.76 ! [P: pi,Rs: late_residual,B2: name] :
% 0.32/1.76 ( ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( late_transitions @ ( match @ B2 @ B2 @ P ) @ Rs ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_216_pi_Odistinct_I65_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( match @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_217_pi_Odistinct_I67_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.32/1.76 ( ( match @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_218_pi_Odistinct_I49_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( input @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_219_pi_Odistinct_I23_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_220_pi_Odistinct_I37_J,axiom,
% 0.32/1.76 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.32/1.76 ( ( tau @ Pi )
% 0.32/1.76 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_221_pi_Oinject_I4_J,axiom,
% 0.32/1.76 ! [X32: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.32/1.76 ( ( ( match @ X32 @ X2 @ X1 )
% 0.32/1.76 = ( match @ Y3 @ Y2 @ Y1 ) )
% 0.32/1.76 = ( ( X32 = Y3 )
% 0.32/1.76 & ( X2 = Y2 )
% 0.32/1.76 & ( X1 = Y1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_222_matchNilLeft,axiom,
% 0.32/1.76 ! [A2: name,B2: name,Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/1.76 ( ( A2 != B2 )
% 0.32/1.76 => ( strong743114133lation @ piNil @ Rel @ ( match @ A2 @ B2 @ P ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_223_freeRes_Ocase_I1_J,axiom,
% 0.32/1.76 ! [A: $tType,F1: name > name > A,F22: A,X11: name,X122: name] :
% 0.32/1.76 ( ( late_case_freeRes @ A @ F1 @ F22 @ ( late_OutputR @ X11 @ X122 ) )
% 0.32/1.76 = ( F1 @ X11 @ X122 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_224_pi_Ostrong__inducts,axiom,
% 0.32/1.76 ! [A: $tType] :
% 0.32/1.76 ( ( fs_name @ A )
% 0.32/1.76 => ! [P: A > pi > $o,Z: A,Pi: pi] :
% 0.32/1.76 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.32/1.76 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Pi3: pi,Z2: A] :
% 0.32/1.76 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.32/1.76 ( ( fresh @ name @ A @ Name23 @ Z2 )
% 0.32/1.76 => ( ( fresh @ name @ name @ Name23 @ Name13 )
% 0.32/1.76 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.32/1.76 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: A] :
% 0.32/1.76 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 0.32/1.76 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.32/1.76 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 0.32/1.76 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.32/1.76 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 0.32/1.76 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.32/1.76 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 0.32/1.76 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.32/1.76 => ( ! [Name4: name,Pi3: pi,Z2: A] :
% 0.32/1.76 ( ( fresh @ name @ A @ Name4 @ Z2 )
% 0.32/1.76 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.32/1.76 => ( ! [Pi3: pi,Z2: A] :
% 0.32/1.76 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.32/1.76 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_225_pi_Ostrong__induct,axiom,
% 0.32/1.76 ! [N: $tType] :
% 0.32/1.76 ( ( fs_name @ N )
% 0.32/1.76 => ! [P: N > pi > $o,Z: N,Pi: pi] :
% 0.32/1.76 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.32/1.76 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Pi3: pi,Z2: N] :
% 0.32/1.76 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.32/1.76 ( ( fresh @ name @ N @ Name23 @ Z2 )
% 0.32/1.76 => ( ( fresh @ name @ name @ Name23 @ Name13 )
% 0.32/1.76 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.32/1.76 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: N] :
% 0.32/1.76 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.32/1.76 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.32/1.76 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.32/1.76 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.32/1.76 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.32/1.76 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.32/1.76 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.32/1.76 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.32/1.76 => ( ! [Name4: name,Pi3: pi,Z2: N] :
% 0.32/1.76 ( ( fresh @ name @ N @ Name4 @ Z2 )
% 0.32/1.76 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.32/1.76 => ( ! [Pi3: pi,Z2: N] :
% 0.32/1.76 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.32/1.76 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.32/1.76 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_226_pi_Ofresh_I10_J,axiom,
% 0.32/1.76 ! [A2: name,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 0.32/1.76 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_227_pi_Ofresh_I7_J,axiom,
% 0.32/1.76 ! [A2: name,X2: pi,X1: pi] :
% 0.32/1.76 ( ( fresh @ name @ pi @ A2 @ ( sum @ X2 @ X1 ) )
% 0.32/1.76 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.32/1.76 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_228_simps_I10_J,axiom,
% 0.32/1.76 ! [P: pi,C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ ( bang @ P ) @ C2 @ D3 )
% 0.32/1.76 = ( bang @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_229_simps_I7_J,axiom,
% 0.32/1.76 ! [P: pi,Q: pi,C2: name,D3: name] :
% 0.32/1.76 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D3 )
% 0.32/1.76 = ( sum @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_230_pi_Odistinct_I63_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( match @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_231_pi_Odistinct_I69_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.32/1.76 ( ( match @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_232_Bang,axiom,
% 0.32/1.76 ! [P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 0.32/1.76 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_233_bangCases,axiom,
% 0.32/1.76 ! [P: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 0.32/1.76 => ~ ! [P4: pi] :
% 0.32/1.76 ( ( ( bang @ P )
% 0.32/1.76 = ( bang @ P4 ) )
% 0.32/1.76 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_234_pi_Odistinct_I87_J,axiom,
% 0.32/1.76 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 0.32/1.76 ( ( par @ Pi1 @ Pi22 )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_235_pi_Odistinct_I89_J,axiom,
% 0.32/1.76 ! [Name3: name,Pi: pi,Pi2: pi] :
% 0.32/1.76 ( ( res @ Name3 @ Pi )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_236_pi_Odistinct_I59_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.32/1.76 ( ( input @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_237_pi_Odistinct_I33_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_238_Sum2,axiom,
% 0.32/1.76 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.32/1.76 ( ( late_transitions @ Q @ Rs )
% 0.32/1.76 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_239_Sum1,axiom,
% 0.32/1.76 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.32/1.76 ( ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_240_sumCases_H,axiom,
% 0.32/1.76 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.32/1.76 => ( ~ ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_241_sumCases,axiom,
% 0.32/1.76 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.32/1.76 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.32/1.76 => ( ~ ( late_transitions @ P @ Rs )
% 0.32/1.76 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_242_pi_Odistinct_I47_J,axiom,
% 0.32/1.76 ! [Pi: pi,Pi2: pi] :
% 0.32/1.76 ( ( tau @ Pi )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_243_pi_Odistinct_I79_J,axiom,
% 0.32/1.76 ! [Pi1: pi,Pi22: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( sum @ Pi1 @ Pi22 )
% 0.32/1.76 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_244_pi_Odistinct_I81_J,axiom,
% 0.32/1.76 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 0.32/1.76 ( ( sum @ Pi1 @ Pi22 )
% 0.32/1.76 != ( res @ Name @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_245_pi_Odistinct_I53_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( input @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_246_pi_Odistinct_I27_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( output @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_247_pi_Odistinct_I41_J,axiom,
% 0.32/1.76 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( tau @ Pi )
% 0.32/1.76 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_248_pi_Oinject_I9_J,axiom,
% 0.32/1.76 ! [X1: pi,Y1: pi] :
% 0.32/1.76 ( ( ( bang @ X1 )
% 0.32/1.76 = ( bang @ Y1 ) )
% 0.32/1.76 = ( X1 = Y1 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_249_pi_Oinject_I6_J,axiom,
% 0.32/1.76 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.32/1.76 ( ( ( sum @ X2 @ X1 )
% 0.32/1.76 = ( sum @ Y2 @ Y1 ) )
% 0.32/1.76 = ( ( X2 = Y2 )
% 0.32/1.76 & ( X1 = Y1 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_250_pi_Odistinct_I83_J,axiom,
% 0.32/1.76 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 0.32/1.76 ( ( sum @ Pi1 @ Pi22 )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_251_pi_Odistinct_I11_J,axiom,
% 0.32/1.76 ! [Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_252_pi_Odistinct_I17_J,axiom,
% 0.32/1.76 ! [Pi2: pi] :
% 0.32/1.76 ( piNil
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_253_pi_Odistinct_I71_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.32/1.76 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_254_pi_Odistinct_I77_J,axiom,
% 0.32/1.76 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.32/1.76 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.32/1.76 != ( bang @ Pi2 ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(fact_255_pi_Oinducts,axiom,
% 0.32/1.76 ! [P: pi > $o,Pi: pi] :
% 0.32/1.76 ( ( P @ piNil )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.32/1.76 ( ( P @ Pi3 )
% 0.32/1.76 => ( P @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Pi3: pi] :
% 0.32/1.76 ( ( P @ Pi3 )
% 0.32/1.76 => ( P @ ( tau @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.32/1.76 ( ( P @ Pi3 )
% 0.32/1.76 => ( P @ ( input @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.32/1.76 ( ( P @ Pi3 )
% 0.32/1.76 => ( P @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.32/1.76 ( ( P @ Pi3 )
% 0.32/1.76 => ( P @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Pi13: pi,Pi24: pi] :
% 0.32/1.76 ( ( P @ Pi13 )
% 0.32/1.76 => ( ( P @ Pi24 )
% 0.32/1.76 => ( P @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.32/1.76 => ( ! [Pi13: pi,Pi24: pi] :
% 0.32/1.76 ( ( P @ Pi13 )
% 0.32/1.76 => ( ( P @ Pi24 )
% 0.32/1.76 => ( P @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.32/1.76 => ( ! [Name4: name,Pi3: pi] :
% 0.32/1.76 ( ( P @ Pi3 )
% 0.32/1.76 => ( P @ ( res @ Name4 @ Pi3 ) ) )
% 0.32/1.76 => ( ! [Pi3: pi] :
% 0.32/1.76 ( ( P @ Pi3 )
% 0.32/1.76 => ( P @ ( bang @ Pi3 ) ) )
% 0.32/1.76 => ( P @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.32/1.76 fs_name @ pi ).
% 0.32/1.76
% 0.32/1.76 thf(tcon_HOL_Obool___Agent_Ofs__name_1,axiom,
% 0.32/1.76 fs_name @ $o ).
% 0.32/1.76
% 0.32/1.76 thf(tcon_Agent_Oname___Agent_Ofs__name_2,axiom,
% 0.32/1.76 fs_name @ name ).
% 0.32/1.76
% 0.32/1.76 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3,axiom,
% 0.32/1.76 ! [A7: $tType,A8: $tType] :
% 0.32/1.76 ( ( ( fs_name @ A7 )
% 0.32/1.76 & ( fs_name @ A8 ) )
% 0.32/1.76 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4,axiom,
% 0.32/1.76 fs_name @ late_freeRes ).
% 0.32/1.76
% 0.32/1.76 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5,axiom,
% 0.32/1.76 fs_name @ late_subject ).
% 0.32/1.76
% 0.32/1.76 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6,axiom,
% 0.32/1.76 fs_name @ late_residual ).
% 0.32/1.76
% 0.32/1.76 thf(help_If_3_1_T,axiom,
% 0.32/1.76 ! [P: $o] :
% 0.32/1.76 ( ( P = $true )
% 0.32/1.76 | ( P = $false ) ) ).
% 0.32/1.76
% 0.32/1.76 thf(help_If_2_1_T,axiom,
% 0.32/1.76 ! [A: $tType,X3: A,Y: A] :
% 0.32/1.76 ( ( if @ A @ $false @ X3 @ Y )
% 0.32/1.76 = Y ) ).
% 0.32/1.76
% 0.32/1.76 thf(help_If_1_1_T,axiom,
% 0.32/1.76 ! [A: $tType,X3: A,Y: A] :
% 0.32/1.76 ( ( if @ A @ $true @ X3 @ Y )
% 0.32/1.76 = X3 ) ).
% 0.32/1.76
% 0.32/1.76 thf(conj_0,conjecture,
% 0.32/1.76 ? [P8: pi] :
% 0.32/1.76 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ P8 ) )
% 0.32/1.76 & ( strong2129052853vative @ P8 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ) ) ).
% 0.32/1.76 ------------------------
% 3.67/1.80 % (2553)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_2445 for (2999ds/4Mi)
% 3.67/1.80 % (2558)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2445 for (2999ds/18Mi)
% 3.67/1.80 % (2554)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_2445 for (2999ds/27Mi)
% 3.67/1.80 % (2556)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_2445 for (2999ds/2Mi)
% 3.67/1.80 % (2557)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_2445 for (2999ds/275Mi)
% 3.67/1.80 % (2555)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2445 for (2999ds/2Mi)
% 3.67/1.80 % (2552)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2445 for (2999ds/183Mi)
% 3.67/1.80 % (2555)Instruction limit reached!
% 3.67/1.80 % (2555)------------------------------
% 3.67/1.80 % (2555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.80 % (2555)Termination reason: Unknown
% 3.67/1.80 % (2555)Termination phase: shuffling
% 3.67/1.80
% 3.67/1.80 % (2556)Instruction limit reached!
% 3.67/1.80 % (2556)------------------------------
% 3.67/1.80 % (2556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.80 % (2556)Termination reason: Unknown
% 3.67/1.80 % (2556)Termination phase: shuffling
% 3.67/1.80
% 3.67/1.80 % (2556)Memory used [KB]: 1407
% 3.67/1.80 % (2556)Time elapsed: 0.003 s
% 3.67/1.80 % (2556)Instructions burned: 2 (million)
% 3.67/1.80 % (2556)------------------------------
% 3.67/1.80 % (2556)------------------------------
% 3.67/1.80 % (2555)Memory used [KB]: 1407
% 3.67/1.80 % (2555)Time elapsed: 0.003 s
% 3.67/1.80 % (2555)Instructions burned: 2 (million)
% 3.67/1.80 % (2555)------------------------------
% 3.67/1.80 % (2555)------------------------------
% 3.67/1.81 % (2553)Instruction limit reached!
% 3.67/1.81 % (2553)------------------------------
% 3.67/1.81 % (2553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.81 % (2553)Termination reason: Unknown
% 3.67/1.81 % (2553)Termination phase: shuffling
% 3.67/1.81
% 3.67/1.81 % (2553)Memory used [KB]: 1407
% 3.67/1.81 % (2553)Time elapsed: 0.004 s
% 3.67/1.81 % (2553)Instructions burned: 4 (million)
% 3.67/1.81 % (2553)------------------------------
% 3.67/1.81 % (2553)------------------------------
% 3.67/1.81 % (2558)Instruction limit reached!
% 3.67/1.81 % (2558)------------------------------
% 3.67/1.81 % (2558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.81 % (2558)Termination reason: Unknown
% 3.67/1.81 % (2558)Termination phase: shuffling
% 3.67/1.81
% 3.67/1.81 % (2558)Memory used [KB]: 1791
% 3.67/1.81 % (2558)Time elapsed: 0.012 s
% 3.67/1.81 % (2558)Instructions burned: 19 (million)
% 3.67/1.81 % (2558)------------------------------
% 3.67/1.81 % (2558)------------------------------
% 3.67/1.82 % (2554)Instruction limit reached!
% 3.67/1.82 % (2554)------------------------------
% 3.67/1.82 % (2554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.82 % (2554)Termination reason: Unknown
% 3.67/1.82 % (2554)Termination phase: Property scanning
% 3.67/1.82
% 3.67/1.82 % (2554)Memory used [KB]: 1918
% 3.67/1.82 % (2554)Time elapsed: 0.017 s
% 3.67/1.82 % (2554)Instructions burned: 28 (million)
% 3.67/1.82 % (2554)------------------------------
% 3.67/1.82 % (2554)------------------------------
% 3.67/1.82 % (2560)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_2445 for (2999ds/37Mi)
% 3.67/1.82 % (2559)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2445 for (2999ds/3Mi)
% 3.67/1.82 % (2561)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_2445 for (2999ds/15Mi)
% 3.67/1.83 % (2559)Instruction limit reached!
% 3.67/1.83 % (2559)------------------------------
% 3.67/1.83 % (2559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.83 % (2559)Termination reason: Unknown
% 3.67/1.83 % (2559)Termination phase: shuffling
% 3.67/1.83
% 3.67/1.83 % (2559)Memory used [KB]: 1407
% 3.67/1.83 % (2559)Time elapsed: 0.004 s
% 3.67/1.83 % (2559)Instructions burned: 4 (million)
% 3.67/1.83 % (2559)------------------------------
% 3.67/1.83 % (2559)------------------------------
% 3.67/1.83 % (2561)Instruction limit reached!
% 3.67/1.83 % (2561)------------------------------
% 3.67/1.83 % (2561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.83 % (2561)Termination reason: Unknown
% 3.67/1.83 % (2561)Termination phase: shuffling
% 3.67/1.83
% 3.67/1.83 % (2561)Memory used [KB]: 1663
% 3.67/1.83 % (2561)Time elapsed: 0.010 s
% 3.67/1.83 % (2561)Instructions burned: 16 (million)
% 3.67/1.83 % (2561)------------------------------
% 3.67/1.83 % (2561)------------------------------
% 3.67/1.83 % (2562)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_2445 for (2999ds/3Mi)
% 3.67/1.83 % (2562)Instruction limit reached!
% 3.67/1.83 % (2562)------------------------------
% 3.67/1.83 % (2562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.83 % (2562)Termination reason: Unknown
% 3.67/1.83 % (2562)Termination phase: shuffling
% 3.67/1.83
% 3.67/1.83 % (2562)Memory used [KB]: 1407
% 3.67/1.83 % (2562)Time elapsed: 0.004 s
% 3.67/1.83 % (2562)Instructions burned: 4 (million)
% 3.67/1.83 % (2562)------------------------------
% 3.67/1.83 % (2562)------------------------------
% 3.67/1.84 % (2563)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_2445 for (2999ds/1041Mi)
% 3.67/1.84 % (2560)Instruction limit reached!
% 3.67/1.84 % (2560)------------------------------
% 3.67/1.84 % (2560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.84 % (2560)Termination reason: Unknown
% 3.67/1.84 % (2560)Termination phase: shuffling
% 3.67/1.84
% 3.67/1.84 % (2560)Memory used [KB]: 2174
% 3.67/1.84 % (2560)Time elapsed: 0.021 s
% 3.67/1.84 % (2560)Instructions burned: 38 (million)
% 3.67/1.84 % (2560)------------------------------
% 3.67/1.84 % (2560)------------------------------
% 3.67/1.84 % (2564)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2445 for (2999ds/7Mi)
% 3.67/1.85 % (2564)Instruction limit reached!
% 3.67/1.85 % (2564)------------------------------
% 3.67/1.85 % (2564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.85 % (2564)Termination reason: Unknown
% 3.67/1.85 % (2564)Termination phase: shuffling
% 3.67/1.85
% 3.67/1.85 % (2564)Memory used [KB]: 1535
% 3.67/1.85 % (2564)Time elapsed: 0.006 s
% 3.67/1.85 % (2564)Instructions burned: 8 (million)
% 3.67/1.85 % (2564)------------------------------
% 3.67/1.85 % (2564)------------------------------
% 3.67/1.85 % (2565)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2445 for (2999ds/16Mi)
% 3.67/1.85 % (2566)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_2445 for (2999ds/3Mi)
% 3.67/1.85 % (2566)Instruction limit reached!
% 3.67/1.85 % (2566)------------------------------
% 3.67/1.85 % (2566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.85 % (2566)Termination reason: Unknown
% 3.67/1.85 % (2566)Termination phase: shuffling
% 3.67/1.85
% 3.67/1.85 % (2566)Memory used [KB]: 1407
% 3.67/1.85 % (2566)Time elapsed: 0.003 s
% 3.67/1.85 % (2566)Instructions burned: 3 (million)
% 3.67/1.85 % (2566)------------------------------
% 3.67/1.85 % (2566)------------------------------
% 3.67/1.86 % (2557)First to succeed.
% 3.67/1.86 % (2557)Refutation found. Thanks to Tanya!
% 3.67/1.86 % SZS status Theorem for DTF2THF_2445
% 3.67/1.86 % SZS output start Proof for DTF2THF_2445
% 3.67/1.86 thf(type_def_5, type, pi: $tType).
% 3.67/1.86 thf(type_def_7, type, name: $tType).
% 3.67/1.86 thf(type_def_8, type, late_freeRes: $tType).
% 3.67/1.86 thf(type_def_9, type, late_subject: $tType).
% 3.67/1.86 thf(type_def_10, type, late_residual: $tType).
% 3.67/1.86 thf(type_def_11, type, noption: ($tType) > $tType).
% 3.67/1.86 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 3.67/1.86 thf(type_def_13, type, set: ($tType) > $tType).
% 3.67/1.86 thf(func_def_0, type, late_residual: $tType).
% 3.67/1.86 thf(func_def_1, type, late_subject: $tType).
% 3.67/1.86 thf(func_def_2, type, late_freeRes: $tType).
% 3.67/1.86 thf(func_def_3, type, product_prod: ($tType * $tType) > $tType).
% 3.67/1.86 thf(func_def_4, type, noption: ($tType) > $tType).
% 3.67/1.86 thf(func_def_5, type, name: $tType).
% 3.67/1.86 thf(func_def_6, type, pi: $tType).
% 3.67/1.86 thf(func_def_7, type, set: ($tType) > $tType).
% 3.67/1.86 thf(func_def_8, type, fs_name: !>[X0: $tType]:($o)).
% 3.67/1.86 thf(func_def_9, type, bang: pi > pi).
% 3.67/1.86 thf(func_def_10, type, input: name > name > pi > pi).
% 3.67/1.86 thf(func_def_11, type, match: name > name > pi > pi).
% 3.67/1.86 thf(func_def_12, type, mismatch: name > name > pi > pi).
% 3.67/1.86 thf(func_def_13, type, output: name > name > pi > pi).
% 3.67/1.86 thf(func_def_14, type, par: pi > pi > pi).
% 3.67/1.86 thf(func_def_15, type, piNil: pi).
% 3.67/1.86 thf(func_def_16, type, res: name > pi > pi).
% 3.67/1.86 thf(func_def_17, type, sum: pi > pi > pi).
% 3.67/1.86 thf(func_def_18, type, tau: pi > pi).
% 3.67/1.86 thf(func_def_19, type, subs: pi > name > name > pi).
% 3.67/1.86 thf(func_def_20, type, subst_name: name > name > name > name).
% 3.67/1.86 thf(func_def_21, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.67/1.86 thf(func_def_22, type, late_case_freeRes: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 3.67/1.86 thf(func_def_23, type, late_OutputR: name > name > late_freeRes).
% 3.67/1.86 thf(func_def_24, type, late_TauR: late_freeRes).
% 3.67/1.86 thf(func_def_25, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 3.67/1.86 thf(func_def_26, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.67/1.86 thf(func_def_27, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.67/1.86 thf(func_def_28, type, late_BoundOutputS: name > late_subject).
% 3.67/1.86 thf(func_def_29, type, late_InputS: name > late_subject).
% 3.67/1.86 thf(func_def_30, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 3.67/1.86 thf(func_def_31, type, late_transitions: pi > late_residual > $o).
% 3.67/1.86 thf(func_def_32, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 3.67/1.86 thf(func_def_33, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 3.67/1.86 thf(func_def_34, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 3.67/1.86 thf(func_def_35, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.67/1.86 thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.67/1.86 thf(func_def_37, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 3.67/1.86 thf(func_def_38, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.67/1.86 thf(func_def_39, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 3.67/1.86 thf(func_def_40, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 3.67/1.86 thf(func_def_41, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.67/1.86 thf(func_def_42, type, p: pi).
% 3.67/1.86 thf(func_def_43, type, pqr: pi).
% 3.67/1.86 thf(func_def_44, type, q: pi).
% 3.67/1.86 thf(func_def_45, type, qr: pi).
% 3.67/1.86 thf(func_def_46, type, q2: pi).
% 3.67/1.86 thf(func_def_47, type, r: pi).
% 3.67/1.86 thf(func_def_48, type, rel: set @ product_prod @ pi @ pi).
% 3.67/1.86 thf(func_def_49, type, a: late_subject).
% 3.67/1.86 thf(func_def_50, type, x: name).
% 3.67/1.86 thf(func_def_68, type, sP0: pi > pi > late_subject > name > pi > $o).
% 3.67/1.86 thf(func_def_69, type, sK1: (late_residual > $o) > late_freeRes).
% 3.67/1.86 thf(func_def_70, type, sK2: (late_residual > $o) > pi).
% 3.67/1.86 thf(func_def_71, type, sK3: (late_residual > $o) > late_subject).
% 3.67/1.86 thf(func_def_72, type, sK4: (late_residual > $o) > name).
% 3.67/1.86 thf(func_def_73, type, sK5: (late_residual > $o) > pi).
% 3.67/1.86 thf(func_def_74, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 3.67/1.86 thf(func_def_75, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 3.67/1.86 thf(func_def_76, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 3.67/1.86 thf(func_def_77, type, sK9: pi > late_freeRes > set @ product_prod @ pi @ pi > pi > pi).
% 3.67/1.86 thf(func_def_78, type, sK10: (pi > $o) > late_freeRes > pi > name > pi).
% 3.67/1.86 thf(func_def_79, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 3.67/1.86 thf(func_def_80, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 3.67/1.86 thf(func_def_81, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 3.67/1.86 thf(func_def_82, type, sK14: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 3.67/1.86 thf(func_def_83, type, sK15: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 3.67/1.86 thf(func_def_84, type, sK16: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 3.67/1.86 thf(func_def_85, type, sK17: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 3.67/1.86 thf(func_def_86, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 3.67/1.86 thf(func_def_87, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 3.67/1.86 thf(func_def_88, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 3.67/1.86 thf(func_def_89, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 3.67/1.86 thf(func_def_90, type, sK22: pi > pi > late_subject > name > pi > pi).
% 3.67/1.86 thf(func_def_91, type, sK23: pi > pi > late_subject > name > pi > late_subject).
% 3.67/1.86 thf(func_def_92, type, sK24: pi > pi > late_subject > name > pi > name).
% 3.67/1.86 thf(func_def_93, type, sK25: pi > pi > late_subject > name > pi > pi).
% 3.67/1.86 thf(func_def_94, type, sK26: pi > pi > late_subject > name > pi > pi).
% 3.67/1.86 thf(func_def_95, type, sK27: pi > name > late_subject > pi > pi > pi).
% 3.67/1.86 thf(func_def_96, type, sK28: pi > name > late_subject > pi > pi > late_subject).
% 3.67/1.86 thf(func_def_97, type, sK29: pi > name > late_subject > pi > pi > name).
% 3.67/1.86 thf(func_def_98, type, sK30: pi > name > late_subject > pi > pi > pi).
% 3.67/1.86 thf(func_def_99, type, sK31: pi > name > late_subject > pi > pi > pi).
% 3.67/1.86 thf(func_def_100, type, sK32: set @ product_prod @ pi @ pi > pi).
% 3.67/1.86 thf(func_def_101, type, sK33: set @ product_prod @ pi @ pi > pi).
% 3.67/1.86 thf(func_def_102, type, sK34: set @ product_prod @ pi @ pi > name).
% 3.67/1.86 thf(func_def_103, type, sK35: set @ product_prod @ pi @ pi > pi).
% 3.67/1.86 thf(func_def_104, type, sK36: set @ product_prod @ pi @ pi > pi).
% 3.67/1.86 thf(func_def_105, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 3.67/1.86 thf(func_def_106, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 3.67/1.86 thf(func_def_107, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 3.67/1.86 thf(func_def_108, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 3.67/1.86 thf(func_def_109, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 3.67/1.86 thf(func_def_110, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 3.67/1.86 thf(func_def_111, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 3.67/1.86 thf(func_def_112, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 3.67/1.86 thf(func_def_113, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 3.67/1.86 thf(func_def_114, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 3.67/1.86 thf(func_def_115, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 3.67/1.86 thf(func_def_116, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 3.67/1.86 thf(func_def_117, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 3.67/1.86 thf(func_def_118, type, sK50: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 3.67/1.86 thf(func_def_119, type, sK51: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 3.67/1.86 thf(func_def_120, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 3.67/1.86 thf(func_def_121, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 3.67/1.86 thf(func_def_122, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 3.67/1.86 thf(func_def_123, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 3.67/1.86 thf(func_def_124, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 3.67/1.86 thf(func_def_125, type, sK57: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.67/1.86 thf(func_def_126, type, sK58: set @ product_prod @ pi @ pi > pi).
% 3.67/1.86 thf(func_def_127, type, sK59: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 3.67/1.86 thf(func_def_128, type, sK60: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 3.67/1.86 thf(func_def_129, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 3.67/1.86 thf(func_def_130, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 3.67/1.86 thf(func_def_131, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 3.67/1.86 thf(func_def_132, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 3.67/1.86 thf(func_def_133, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 3.67/1.86 thf(func_def_134, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 3.67/1.86 thf(func_def_135, type, sK67: set @ product_prod @ pi @ pi > pi > pi > late_subject).
% 3.67/1.86 thf(func_def_136, type, sK68: set @ product_prod @ pi @ pi > pi > pi > name).
% 3.67/1.86 thf(func_def_137, type, sK69: set @ product_prod @ pi @ pi > pi > pi > pi).
% 3.67/1.86 thf(func_def_138, type, sK70: set @ product_prod @ pi @ pi > pi > pi > late_freeRes).
% 3.67/1.86 thf(func_def_139, type, sK71: set @ product_prod @ pi @ pi > pi > pi > pi).
% 3.67/1.86 thf(func_def_140, type, sK72: (pi > $o) > name > late_subject > pi > pi > pi).
% 3.67/1.86 thf(func_def_141, type, sK73: (pi > $o) > name > late_subject > pi > pi > pi).
% 3.67/1.86 thf(func_def_142, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 3.67/1.86 thf(func_def_143, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 3.67/1.86 thf(func_def_144, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 3.67/1.86 thf(func_def_145, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 3.67/1.86 thf(func_def_146, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 3.67/1.86 thf(func_def_147, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 3.67/1.86 thf(func_def_148, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 3.67/1.86 thf(func_def_149, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 3.67/1.86 thf(func_def_150, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 3.67/1.86 thf(func_def_151, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 3.67/1.86 thf(func_def_152, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 3.67/1.86 thf(func_def_153, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 3.67/1.86 thf(func_def_154, type, sK86: pi > name > late_subject > set @ product_prod @ pi @ pi > pi > pi).
% 3.67/1.86 thf(func_def_155, type, sK87: pi > late_freeRes > pi > name > pi).
% 3.67/1.86 thf(func_def_156, type, sK88: pi > late_freeRes > pi > name > late_freeRes).
% 3.67/1.86 thf(func_def_157, type, sK89: pi > late_freeRes > pi > name > pi).
% 3.67/1.86 thf(func_def_158, type, sK90: pi > late_freeRes > pi > name > name).
% 3.67/1.86 thf(func_def_159, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 3.67/1.86 thf(func_def_160, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 3.67/1.86 thf(func_def_161, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 3.67/1.86 thf(func_def_162, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 3.67/1.86 thf(func_def_163, type, sK95: set @ product_prod @ pi @ pi > pi).
% 3.67/1.86 thf(func_def_165, type, ph97: !>[X0: $tType]:(X0)).
% 3.67/1.86 thf(f931,plain,(
% 3.67/1.86 $false),
% 3.67/1.86 inference(subsumption_resolution,[status(thm)],[f930,f892])).
% 3.67/1.86 thf(f892,plain,(
% 3.67/1.86 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) = $true)),
% 3.67/1.86 inference(cnf_transformation,[status(thm)],[f461])).
% 3.67/1.86 thf(f461,plain,(
% 3.67/1.86 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) = $true)),
% 3.67/1.86 inference(fool_elimination,[status(thm)],[f460])).
% 3.67/1.86 thf(f460,plain,(
% 3.67/1.86 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r)))),
% 3.67/1.86 inference(rectify,[status(thm)],[f3])).
% 3.67/1.86 thf(f3,axiom,(
% 3.67/1.86 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r)))),
% 3.67/1.86 file('/export/starexec/sandbox/tmp/tmp.aNTp5qWQTa/DTF2THF_2445.p',fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062)).
% 3.67/1.86 thf(f930,plain,(
% 3.67/1.86 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) != $true)),
% 3.67/1.86 inference(trivial_inequality_removal,[status(thm)],[f927])).
% 3.67/1.86 thf(f927,plain,(
% 3.67/1.86 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) != $true) | ($true != $true)),
% 3.67/1.86 inference(superposition,[status(thm)],[f882,f802])).
% 3.67/1.86 thf(f802,plain,(
% 3.67/1.86 ((strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) = $true)),
% 3.67/1.86 inference(cnf_transformation,[status(thm)],[f487])).
% 3.67/1.86 thf(f487,plain,(
% 3.67/1.86 ((strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) = $true)),
% 3.67/1.86 inference(fool_elimination,[status(thm)],[f486])).
% 3.67/1.86 thf(f486,plain,(
% 3.67/1.86 (strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel)),
% 3.67/1.86 inference(rectify,[status(thm)],[f1])).
% 3.67/1.86 thf(f1,axiom,(
% 3.67/1.86 (strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel)),
% 3.67/1.86 file('/export/starexec/sandbox/tmp/tmp.aNTp5qWQTa/DTF2THF_2445.p',fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062)).
% 3.67/1.86 thf(f882,plain,(
% 3.67/1.86 ( ! [X0 : pi] : (((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) != $true) | ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)) != $true)) )),
% 3.67/1.86 inference(cnf_transformation,[status(thm)],[f670])).
% 3.67/1.86 thf(f670,plain,(
% 3.67/1.86 ! [X0 : pi] : (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)) != $true) | ((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) != $true))),
% 3.67/1.86 inference(ennf_transformation,[status(thm)],[f609])).
% 3.67/1.86 thf(f609,plain,(
% 3.67/1.86 ~? [X0 : pi] : (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)) = $true) & ((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) = $true))),
% 3.67/1.86 inference(fool_elimination,[status(thm)],[f608])).
% 3.67/1.86 thf(f608,plain,(
% 3.67/1.86 ~? [X0 : pi] : ((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)))),
% 3.67/1.86 inference(rectify,[status(thm)],[f268])).
% 3.67/1.86 thf(f268,negated_conjecture,(
% 3.67/1.86 ~? [X78 : pi] : ((strong2129052853vative @ X78 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X78)))),
% 3.67/1.86 inference(negated_conjecture,[status(cth)],[f267])).
% 3.67/1.86 thf(f267,conjecture,(
% 3.67/1.86 ? [X78 : pi] : ((strong2129052853vative @ X78 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X78)))),
% 3.67/1.86 file('/export/starexec/sandbox/tmp/tmp.aNTp5qWQTa/DTF2THF_2445.p',conj_0)).
% 3.67/1.86 % SZS output end Proof for DTF2THF_2445
% 3.67/1.86 % (2557)------------------------------
% 3.67/1.86 % (2557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/1.86 % (2557)Termination reason: Refutation
% 3.67/1.86
% 3.67/1.86 % (2557)Memory used [KB]: 7164
% 3.67/1.86 % (2557)Time elapsed: 0.055 s
% 3.67/1.86 % (2557)Instructions burned: 93 (million)
% 3.67/1.86 % (2557)------------------------------
% 3.67/1.86 % (2557)------------------------------
% 3.67/1.86 % (2551)Success in time 0.09 s
%------------------------------------------------------------------------------