%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP192^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:18 AM UTC 2026
% Result : Theorem 21.17s 4.84s
% Output : Refutation 21.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP192^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 08:29:42 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : ITP192^2 : TPTP v9.2.1. Released v7.5.0.
% 0.16/0.43 % Domain : Interactive Theorem Proving
% 0.16/0.43 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_997__3418970_1
% 0.16/0.43 % Version : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.16/0.43 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Des21]
% 0.16/0.43 % Names : Strong_Late_Sim_SC/prob_997__3418970_1 [Des21]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.16/0.43 % Syntax : Number of formulae : 321 ( 166 unt; 54 typ; 0 def)
% 0.16/0.43 % Number of atoms : 642 ( 266 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 17 ( 2 avg)
% 0.16/0.43 % Number of connectives : 3947 ( 150 ~; 5 |; 48 &;3399 @)
% 0.16/0.43 % ( 0 <=>; 345 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 28 ( 9 avg)
% 0.16/0.43 % Number of types : 6 ( 5 usr)
% 0.16/0.43 % Number of type conns : 151 ( 151 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 52 ( 49 usr; 16 con; 0-5 aty)
% 0.16/0.43 % Number of variables : 1301 ( 9 ^;1259 !; 13 ?;1301 :)
% 0.16/0.43 % ( 20 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.43 % SPC : TH1_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : This file was generated by Sledgehammer 2021-02-23 16:18:12.399
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % Could-be-implicit typings (8)
% 0.16/0.43 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.16/0.43 late_residual: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Late__Semantics_Osubject,type,
% 0.16/0.43 late_subject: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.16/0.43 late_freeRes: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Product__Type_Oprod,type,
% 0.16/0.43 product_prod: $tType > $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Nominal_Onoption,type,
% 0.16/0.43 noption: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Agent_Oname,type,
% 0.16/0.43 name: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Agent_Opi,type,
% 0.16/0.43 pi: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Set_Oset,type,
% 0.16/0.43 set: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 % Explicit typings (46)
% 0.16/0.43 thf(sy_cl_Agent_Ofs__name,type,
% 0.16/0.43 fs_name:
% 0.16/0.43 !>[A: $tType] : $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OBang,type,
% 0.16/0.43 bang: pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OInput,type,
% 0.16/0.43 input: name > name > pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OMatch,type,
% 0.16/0.43 match: name > name > pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.16/0.43 mismatch: name > name > pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OOutput,type,
% 0.16/0.43 output: name > name > pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OPar,type,
% 0.16/0.43 par: pi > pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.16/0.43 piNil: pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_ORes,type,
% 0.16/0.43 res: name > pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OSum,type,
% 0.16/0.43 sum: pi > pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Opi_OTau,type,
% 0.16/0.43 tau: pi > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Osubs,type,
% 0.16/0.43 subs: pi > name > name > pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Agent_Osubst__name,type,
% 0.16/0.43 subst_name: name > name > name > name ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_If,type,
% 0.16/0.43 if:
% 0.16/0.43 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 0.16/0.43 late_case_freeRes:
% 0.16/0.43 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.16/0.43 late_OutputR: name > name > late_freeRes ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.16/0.43 late_TauR: late_freeRes ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.16/0.43 late_freeRes_rec:
% 0.16/0.43 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.16/0.43 late_BoundR: late_subject > name > pi > late_residual ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.16/0.43 late_FreeR: late_freeRes > pi > late_residual ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.16/0.43 late_BoundOutputS: name > late_subject ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.16/0.43 late_InputS: name > late_subject ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.16/0.43 late_subject_rec:
% 0.16/0.43 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.16/0.43 late_transitions: pi > late_residual > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Nominal_Oabs__fun,type,
% 0.16/0.43 abs_fun:
% 0.16/0.43 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Nominal_Ofresh,type,
% 0.16/0.43 fresh:
% 0.16/0.43 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Product__Type_OPair,type,
% 0.16/0.43 product_Pair:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.16/0.43 produc2004651681e_prod:
% 0.16/0.43 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.16/0.43 product_rec_prod:
% 0.16/0.43 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Rel_Oeqvt,type,
% 0.16/0.43 eqvt:
% 0.16/0.43 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set_OCollect,type,
% 0.16/0.43 collect:
% 0.16/0.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.16/0.43 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.16/0.43 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_member,type,
% 0.16/0.43 member:
% 0.16/0.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_P,type,
% 0.16/0.43 p: pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_PQ____,type,
% 0.16/0.43 pq: pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_P_H____,type,
% 0.16/0.43 p2: pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_Q,type,
% 0.16/0.43 q: pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_Q_H____,type,
% 0.16/0.43 q2: pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_Rel,type,
% 0.16/0.43 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v__092_060alpha_062____,type,
% 0.16/0.43 alpha: late_freeRes ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_aa____,type,
% 0.16/0.43 aa: name ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_x,type,
% 0.16/0.43 x: name ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_xPQ____,type,
% 0.16/0.43 xPQ: pi ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_y____,type,
% 0.16/0.43 y: name ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_z____,type,
% 0.16/0.43 z: name ).
% 0.16/0.43
% 0.16/0.43 % Relevant facts (256)
% 0.16/0.43 thf(fact_0_cClose1_Ohyps_I3_J,axiom,
% 0.16/0.43 fresh @ name @ pi @ y @ p ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(3)
% 0.16/0.43 thf(fact_1_cClose1_Ohyps_I7_J,axiom,
% 0.16/0.43 fresh @ name @ pi @ y @ q2 ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(7)
% 0.16/0.43 thf(fact_2_cClose1_Ohyps_I6_J,axiom,
% 0.16/0.43 y != z ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(6)
% 0.16/0.43 thf(fact_3_assms_I1_J,axiom,
% 0.16/0.43 fresh @ name @ pi @ x @ p ).
% 0.16/0.43
% 0.16/0.43 % assms(1)
% 0.16/0.43 thf(fact_4_cClose1_Ohyps_I12_J,axiom,
% 0.16/0.43 fresh @ name @ name @ y @ x ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(12)
% 0.16/0.43 thf(fact_5_cClose1_Ohyps_I5_J,axiom,
% 0.16/0.43 y != aa ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(5)
% 0.16/0.43 thf(fact_6_cClose1_Ohyps_I4_J,axiom,
% 0.16/0.43 fresh @ name @ pi @ y @ q ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(4)
% 0.16/0.43 thf(fact_7_cClose1_Ohyps_I11_J,axiom,
% 0.16/0.43 fresh @ name @ pi @ z @ p2 ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(11)
% 0.16/0.43 thf(fact_8_cClose1_Ohyps_I1_J,axiom,
% 0.16/0.43 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ) ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(1)
% 0.16/0.43 thf(fact_9_cClose1_Ohyps_I10_J,axiom,
% 0.16/0.43 z != aa ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(10)
% 0.16/0.43 thf(fact_10_cClose1_Ohyps_I13_J,axiom,
% 0.16/0.43 fresh @ name @ name @ z @ x ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(13)
% 0.16/0.43 thf(fact_11_cClose1_Ohyps_I8_J,axiom,
% 0.16/0.43 fresh @ name @ pi @ z @ p ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(8)
% 0.16/0.43 thf(fact_12_cRes_Ohyps_I2_J,axiom,
% 0.16/0.43 fresh @ name @ late_freeRes @ x @ alpha ).
% 0.16/0.43
% 0.16/0.43 % cRes.hyps(2)
% 0.16/0.43 thf(fact_13_assms_I3_J,axiom,
% 0.16/0.43 eqvt @ pi @ rel ).
% 0.16/0.43
% 0.16/0.43 % assms(3)
% 0.16/0.43 thf(fact_14_cClose1_Ohyps_I14_J,axiom,
% 0.16/0.43 alpha = late_TauR ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(14)
% 0.16/0.43 thf(fact_15_cClose1_Ohyps_I2_J,axiom,
% 0.16/0.43 late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ) ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(2)
% 0.16/0.43 thf(fact_16_cClose1_Ohyps_I9_J,axiom,
% 0.16/0.43 fresh @ name @ pi @ z @ q ).
% 0.16/0.43
% 0.16/0.43 % cClose1.hyps(9)
% 0.16/0.43 thf(fact_17_Free_Ohyps,axiom,
% 0.16/0.43 late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ xPQ ) ).
% 0.16/0.43
% 0.16/0.43 % Free.hyps
% 0.16/0.43 thf(fact_18_cRes_Ohyps_I1_J,axiom,
% 0.16/0.43 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ pq ) ).
% 0.16/0.43
% 0.16/0.43 % cRes.hyps(1)
% 0.16/0.43 thf(fact_19_freeRes_Ofresh_I2_J,axiom,
% 0.16/0.43 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.fresh(2)
% 0.16/0.43 thf(fact_20_pi_Ofresh_I8_J,axiom,
% 0.16/0.43 ! [A2: name,X2: pi,X1: pi] :
% 0.16/0.43 ( ( fresh @ name @ pi @ A2 @ ( par @ X2 @ X1 ) )
% 0.16/0.43 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.16/0.43 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.fresh(8)
% 0.16/0.43 thf(fact_21_freshFreeDerivative_I1_J,axiom,
% 0.16/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.16/0.43 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freshFreeDerivative(1)
% 0.16/0.43 thf(fact_22_resCasesF,axiom,
% 0.16/0.43 ! [X3: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.16/0.43 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.16/0.43 => ( ! [P3: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 0.16/0.43 => ( F @ ( res @ X3 @ P3 ) ) ) )
% 0.16/0.43 => ( F @ XP ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % resCasesF
% 0.16/0.43 thf(fact_23_resCasesF_H,axiom,
% 0.16/0.43 ! [X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.43 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y2: name] :
% 0.16/0.43 ( ( ( res @ X3 @ P )
% 0.16/0.43 = ( res @ Y2 @ P4 ) )
% 0.16/0.43 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.16/0.43 = ( late_FreeR @ Alpha2 @ ( res @ Y2 @ P3 ) ) )
% 0.16/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.16/0.43 => ~ ( fresh @ name @ late_freeRes @ Y2 @ Alpha2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % resCasesF'
% 0.16/0.43 thf(fact_24_ResF,axiom,
% 0.16/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 0.16/0.43 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ResF
% 0.16/0.43 thf(fact_25_Res,axiom,
% 0.16/0.43 ! [Y: name,R: pi,S: pi] :
% 0.16/0.43 ( ( fresh @ name @ pi @ Y @ R )
% 0.16/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ ( res @ Y @ S ) ) @ ( res @ Y @ ( par @ R @ S ) ) ) @ rel ) ) ).
% 0.16/0.43
% 0.16/0.43 % Res
% 0.16/0.43 thf(fact_26_ScopeExt,axiom,
% 0.16/0.43 ! [Y: name,R: pi,Z: name,S: pi] :
% 0.16/0.43 ( ( fresh @ name @ pi @ Y @ R )
% 0.16/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) ) @ rel ) ) ).
% 0.16/0.43
% 0.16/0.43 % ScopeExt
% 0.16/0.43 thf(fact_27_Late__Semantics_OPar1B,axiom,
% 0.16/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.Par1B
% 0.16/0.43 thf(fact_28_Late__Semantics_OPar2B,axiom,
% 0.16/0.43 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.Par2B
% 0.16/0.43 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.16/0.43 ! [X1: name,Y1: name] :
% 0.16/0.43 ( ( ( late_BoundOutputS @ X1 )
% 0.16/0.43 = ( late_BoundOutputS @ Y1 ) )
% 0.16/0.43 = ( X1 = Y1 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.subject.inject(2)
% 0.16/0.43 thf(fact_30_name__fresh,axiom,
% 0.16/0.43 ( ( fresh @ name @ name )
% 0.16/0.43 = ( ^ [A3: name,B2: name] : ( A3 != B2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % name_fresh
% 0.16/0.43 thf(fact_31_name__exists__fresh,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( fs_name @ A )
% 0.16/0.43 => ! [X3: A] :
% 0.16/0.43 ~ ! [C2: name] :
% 0.16/0.43 ~ ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % name_exists_fresh
% 0.16/0.43 thf(fact_32_pi_Oinject_I7_J,axiom,
% 0.16/0.43 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.16/0.43 ( ( ( par @ X2 @ X1 )
% 0.16/0.43 = ( par @ Y22 @ Y1 ) )
% 0.16/0.43 = ( ( X2 = Y22 )
% 0.16/0.43 & ( X1 = Y1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.inject(7)
% 0.16/0.43 thf(fact_33_residual_Oinject_I2_J,axiom,
% 0.16/0.43 ! [X2: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 0.16/0.43 ( ( ( late_FreeR @ X2 @ X1 )
% 0.16/0.43 = ( late_FreeR @ Y22 @ Y1 ) )
% 0.16/0.43 = ( ( X2 = Y22 )
% 0.16/0.43 & ( X1 = Y1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.inject(2)
% 0.16/0.43 thf(fact_34_pi_Odistinct_I85_J,axiom,
% 0.16/0.43 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.16/0.43 ( ( par @ Pi1 @ Pi2 )
% 0.16/0.43 != ( res @ Name @ Pi ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(85)
% 0.16/0.43 thf(fact_35_freshRes,axiom,
% 0.16/0.43 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.16/0.43
% 0.16/0.43 % freshRes
% 0.16/0.43 thf(fact_36_residual_Oinducts,axiom,
% 0.16/0.43 ! [P: late_residual > $o,Residual: late_residual] :
% 0.16/0.43 ( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
% 0.16/0.43 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.16/0.43 => ( P @ Residual ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.inducts
% 0.16/0.43 thf(fact_37_residual_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.16/0.43 ( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
% 0.16/0.43 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.distinct(1)
% 0.16/0.43 thf(fact_38_subject_Ostrong__inducts,axiom,
% 0.16/0.43 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 0.16/0.43 ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 0.16/0.43 => ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 0.16/0.43 => ( P @ Z @ Subject2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.strong_inducts
% 0.16/0.43 thf(fact_39_subject_Ostrong__induct_H,axiom,
% 0.16/0.43 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 0.16/0.43 ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 0.16/0.43 => ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 0.16/0.43 => ( P @ Z @ Subject2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.strong_induct'
% 0.16/0.43 thf(fact_40_subject_Oinducts,axiom,
% 0.16/0.43 ! [P: late_subject > $o,Subject2: late_subject] :
% 0.16/0.43 ( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
% 0.16/0.43 => ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
% 0.16/0.43 => ( P @ Subject2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.inducts
% 0.16/0.43 thf(fact_41_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [Name3: name,Name: name] :
% 0.16/0.43 ( ( late_InputS @ Name3 )
% 0.16/0.43 != ( late_BoundOutputS @ Name ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.subject.distinct(1)
% 0.16/0.43 thf(fact_42_Par2F,axiom,
% 0.16/0.43 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Par2F
% 0.16/0.43 thf(fact_43_Par1F,axiom,
% 0.16/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Par1F
% 0.16/0.43 thf(fact_44_freshBoundDerivative_I2_J,axiom,
% 0.16/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.16/0.43 => ( ( Y != X3 )
% 0.16/0.43 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freshBoundDerivative(2)
% 0.16/0.43 thf(fact_45_mem__Collect__eq,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,P: A > $o] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.16/0.43 = ( P @ A2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % mem_Collect_eq
% 0.16/0.43 thf(fact_46_Collect__mem__eq,axiom,
% 0.16/0.43 ! [A: $tType,A4: set @ A] :
% 0.16/0.43 ( ( collect @ A
% 0.16/0.43 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.16/0.43 = A4 ) ).
% 0.16/0.43
% 0.16/0.43 % Collect_mem_eq
% 0.16/0.43 thf(fact_47_Collect__cong,axiom,
% 0.16/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.43 ( ! [X5: A] :
% 0.16/0.43 ( ( P @ X5 )
% 0.16/0.43 = ( Q @ X5 ) )
% 0.16/0.43 => ( ( collect @ A @ P )
% 0.16/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Collect_cong
% 0.16/0.43 thf(fact_48_residual_Ostrong__inducts,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( fs_name @ A )
% 0.16/0.43 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.16/0.43 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: A] :
% 0.16/0.43 ( ( fresh @ name @ A @ Name2 @ Z2 )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 0.16/0.43 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.16/0.43 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.16/0.43 => ( P @ Z @ Residual ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.strong_inducts
% 0.16/0.43 thf(fact_49_residual_Ostrong__induct,axiom,
% 0.16/0.43 ! [N: $tType] :
% 0.16/0.43 ( ( fs_name @ N )
% 0.16/0.43 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.16/0.43 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: N] :
% 0.16/0.43 ( ( fresh @ name @ N @ Name2 @ Z2 )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 0.16/0.43 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.16/0.43 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.16/0.43 => ( P @ Z @ Residual ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.strong_induct
% 0.16/0.43 thf(fact_50_freshFreeDerivative_I2_J,axiom,
% 0.16/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.16/0.43 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freshFreeDerivative(2)
% 0.16/0.43 thf(fact_51_parCasesB,axiom,
% 0.16/0.43 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 0.16/0.43 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( ! [P3: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.16/0.43 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.16/0.43 => ( ! [Q3: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 0.16/0.43 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.16/0.43 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % parCasesB
% 0.16/0.43 thf(fact_52_fresh__prod,axiom,
% 0.16/0.43 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y: B] :
% 0.16/0.43 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.16/0.43 = ( ( fresh @ X @ A @ A2 @ X3 )
% 0.16/0.43 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % fresh_prod
% 0.16/0.43 thf(fact_53_transitions_OClose2,axiom,
% 0.16/0.43 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.16/0.43 => ( ( X3 != A2 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.16/0.43 => ( ( Y != A2 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.16/0.43 => ( ( X3 != Y )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transitions.Close2
% 0.16/0.43 thf(fact_54_transitions_OClose1,axiom,
% 0.16/0.43 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.16/0.43 => ( ( X3 != A2 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.16/0.43 => ( ( Y != A2 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.16/0.43 => ( ( X3 != Y )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transitions.Close1
% 0.16/0.43 thf(fact_55_Late__Semantics_OClose2,axiom,
% 0.16/0.43 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.Close2
% 0.16/0.43 thf(fact_56_Late__Semantics_OClose1,axiom,
% 0.16/0.43 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.Close1
% 0.16/0.43 thf(fact_57_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.16/0.43 ! [X1: name,Y1: name] :
% 0.16/0.43 ( ( ( late_InputS @ X1 )
% 0.16/0.43 = ( late_InputS @ Y1 ) )
% 0.16/0.43 = ( X1 = Y1 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics1.subject.inject(1)
% 0.16/0.43 thf(fact_58_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.16/0.43 ! [X2: name,Y22: name] :
% 0.16/0.43 ( ( ( late_BoundOutputS @ X2 )
% 0.16/0.43 = ( late_BoundOutputS @ Y22 ) )
% 0.16/0.43 = ( X2 = Y22 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics1.subject.inject(2)
% 0.16/0.43 thf(fact_59_old_Oprod_Oinject,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A2: A,B3: B,A5: A,B4: B] :
% 0.16/0.43 ( ( ( product_Pair @ A @ B @ A2 @ B3 )
% 0.16/0.43 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.16/0.43 = ( ( A2 = A5 )
% 0.16/0.43 & ( B3 = B4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.prod.inject
% 0.16/0.43 thf(fact_60_prod_Oinject,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y22: B] :
% 0.16/0.43 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.16/0.43 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.16/0.43 = ( ( X1 = Y1 )
% 0.16/0.43 & ( X2 = Y22 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod.inject
% 0.16/0.43 thf(fact_61_subst__identity,axiom,
% 0.16/0.43 ! [P: pi,A2: name] :
% 0.16/0.43 ( ( subs @ P @ A2 @ A2 )
% 0.16/0.43 = P ) ).
% 0.16/0.43
% 0.16/0.43 % subst_identity
% 0.16/0.43 thf(fact_62_simps_I9_J,axiom,
% 0.16/0.43 ! [X3: name,C3: name,D: name,P: pi] :
% 0.16/0.43 ( ( X3 != C3 )
% 0.16/0.43 => ( ( X3 != D )
% 0.16/0.43 => ( ( subs @ ( res @ X3 @ P ) @ C3 @ D )
% 0.16/0.43 = ( res @ X3 @ ( subs @ P @ C3 @ D ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simps(9)
% 0.16/0.43 thf(fact_63_simps_I8_J,axiom,
% 0.16/0.43 ! [P: pi,Q: pi,C3: name,D: name] :
% 0.16/0.43 ( ( subs @ ( par @ P @ Q ) @ C3 @ D )
% 0.16/0.43 = ( par @ ( subs @ P @ C3 @ D ) @ ( subs @ Q @ C3 @ D ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simps(8)
% 0.16/0.43 thf(fact_64_substTrans,axiom,
% 0.16/0.43 ! [B3: name,P: pi,A2: name,C3: name] :
% 0.16/0.43 ( ( fresh @ name @ pi @ B3 @ P )
% 0.16/0.43 => ( ( subs @ ( subs @ P @ A2 @ B3 ) @ B3 @ C3 )
% 0.16/0.43 = ( subs @ P @ A2 @ C3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % substTrans
% 0.16/0.43 thf(fact_65_residual_Ofresh_I2_J,axiom,
% 0.16/0.43 ! [A2: name,X2: late_freeRes,X1: pi] :
% 0.16/0.43 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X2 @ X1 ) )
% 0.16/0.43 = ( ( fresh @ name @ late_freeRes @ A2 @ X2 )
% 0.16/0.43 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.fresh(2)
% 0.16/0.43 thf(fact_66_subject_Ofresh_I2_J,axiom,
% 0.16/0.43 ! [A2: name,X1: name] :
% 0.16/0.43 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.16/0.43 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.fresh(2)
% 0.16/0.43 thf(fact_67_subject_Ofresh_I1_J,axiom,
% 0.16/0.43 ! [A2: name,X1: name] :
% 0.16/0.43 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.16/0.43 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.fresh(1)
% 0.16/0.43 thf(fact_68_forget,axiom,
% 0.16/0.43 ! [A2: name,P: pi,B3: name] :
% 0.16/0.43 ( ( fresh @ name @ pi @ A2 @ P )
% 0.16/0.43 => ( ( subs @ P @ A2 @ B3 )
% 0.16/0.43 = P ) ) ).
% 0.16/0.43
% 0.16/0.43 % forget
% 0.16/0.43 thf(fact_69_fresh__fact1,axiom,
% 0.16/0.43 ! [A2: name,P: pi,C3: name,B3: name] :
% 0.16/0.43 ( ( fresh @ name @ pi @ A2 @ P )
% 0.16/0.43 => ( ( A2 != C3 )
% 0.16/0.43 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B3 @ C3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % fresh_fact1
% 0.16/0.43 thf(fact_70_fresh__fact2,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi] :
% 0.16/0.43 ( ( A2 != B3 )
% 0.16/0.43 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % fresh_fact2
% 0.16/0.43 thf(fact_71_freshResidual,axiom,
% 0.16/0.43 ! [P: pi,Rs: late_residual,X3: name] :
% 0.16/0.43 ( ( late_transitions @ P @ Rs )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freshResidual
% 0.16/0.43 thf(fact_72_substRes2,axiom,
% 0.16/0.43 ! [B3: name,P: pi,A2: name] :
% 0.16/0.43 ( ( fresh @ name @ pi @ B3 @ P )
% 0.16/0.43 => ( ( res @ A2 @ P )
% 0.16/0.43 = ( res @ B3 @ ( subs @ P @ A2 @ B3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % substRes2
% 0.16/0.43 thf(fact_73_Agent_OsubstRes3,axiom,
% 0.16/0.43 ! [B3: name,P: pi,A2: name] :
% 0.16/0.43 ( ( fresh @ name @ pi @ B3 @ P )
% 0.16/0.43 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B3 )
% 0.16/0.43 = ( res @ B3 @ ( subs @ P @ A2 @ B3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Agent.substRes3
% 0.16/0.43 thf(fact_74_Late__Semantics_OResB,axiom,
% 0.16/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.16/0.43 => ( ( Y != X3 )
% 0.16/0.43 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.ResB
% 0.16/0.43 thf(fact_75_freshBoundDerivative_I1_J,axiom,
% 0.16/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.16/0.43 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freshBoundDerivative(1)
% 0.16/0.43 thf(fact_76_surj__pair,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,P5: product_prod @ A @ B] :
% 0.16/0.43 ? [X5: A,Y2: B] :
% 0.16/0.43 ( P5
% 0.16/0.43 = ( product_Pair @ A @ B @ X5 @ Y2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % surj_pair
% 0.16/0.43 thf(fact_77_prod__cases,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P5: product_prod @ A @ B] :
% 0.16/0.43 ( ! [A6: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.16/0.43 => ( P @ P5 ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_cases
% 0.16/0.43 thf(fact_78_Pair__inject,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A2: A,B3: B,A5: A,B4: B] :
% 0.16/0.43 ( ( ( product_Pair @ A @ B @ A2 @ B3 )
% 0.16/0.43 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.16/0.43 => ~ ( ( A2 = A5 )
% 0.16/0.43 => ( B3 != B4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Pair_inject
% 0.16/0.43 thf(fact_79_prod__cases3,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.43 ~ ! [A6: A,B5: B,C2: C] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_cases3
% 0.16/0.43 thf(fact_80_prod__cases4,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,C: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 0.16/0.43 ~ ! [A6: A,B5: B,C2: C,D3: D2] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_cases4
% 0.16/0.43 thf(fact_81_prod__cases5,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 0.16/0.43 ~ ! [A6: A,B5: B,C2: C,D3: D2,E2: E] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_cases5
% 0.16/0.43 thf(fact_82_prod__cases6,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.16/0.43 ~ ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F2 ) @ D3 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_cases6
% 0.16/0.43 thf(fact_83_prod__cases7,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F2: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 0.16/0.43 ~ ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2,G2: G] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_cases7
% 0.16/0.43 thf(fact_84_prod__induct3,axiom,
% 0.16/0.43 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.43 ( ! [A6: A,B5: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 0.16/0.43 => ( P @ X3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_induct3
% 0.16/0.43 thf(fact_85_prod__induct4,axiom,
% 0.16/0.43 ! [D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 0.16/0.43 ( ! [A6: A,B5: B,C2: C,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) )
% 0.16/0.43 => ( P @ X3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_induct4
% 0.16/0.43 thf(fact_86_prod__induct5,axiom,
% 0.16/0.43 ! [E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 0.16/0.43 ( ! [A6: A,B5: B,C2: C,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 0.16/0.43 => ( P @ X3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_induct5
% 0.16/0.43 thf(fact_87_prod__induct6,axiom,
% 0.16/0.43 ! [F2: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.16/0.43 ( ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F2 ) @ D3 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 0.16/0.43 => ( P @ X3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_induct6
% 0.16/0.43 thf(fact_88_prod__induct7,axiom,
% 0.16/0.43 ! [G: $tType,F2: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 0.16/0.43 ( ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) )
% 0.16/0.43 => ( P @ X3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % prod_induct7
% 0.16/0.43 thf(fact_89_old_Oprod_Oexhaust,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.16/0.43 ~ ! [A6: A,B5: B] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( product_Pair @ A @ B @ A6 @ B5 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.prod.exhaust
% 0.16/0.43 thf(fact_90_old_Oprod_Oinducts,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.16/0.43 ( ! [A6: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.16/0.43 => ( P @ Prod ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.prod.inducts
% 0.16/0.43 thf(fact_91_transitions_OResB,axiom,
% 0.16/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.16/0.43 => ( ( Y != X3 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.16/0.43 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transitions.ResB
% 0.16/0.43 thf(fact_92_parCasesB_H,axiom,
% 0.16/0.43 ! [P: pi,Q: pi,B3: late_subject,Y: name,P2: pi] :
% 0.16/0.43 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B3 @ Y @ P2 ) )
% 0.16/0.43 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Q4: pi] :
% 0.16/0.43 ( ( ( par @ P @ Q )
% 0.16/0.43 = ( par @ P4 @ Q4 ) )
% 0.16/0.43 => ( ( ( late_BoundR @ B3 @ Y @ P2 )
% 0.16/0.43 = ( late_BoundR @ A6 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 0.16/0.43 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.16/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) )
% 0.16/0.43 => ~ ! [Q4: pi,A6: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.16/0.43 ( ( ( par @ P @ Q )
% 0.16/0.43 = ( par @ P4 @ Q4 ) )
% 0.16/0.43 => ( ( ( late_BoundR @ B3 @ Y @ P2 )
% 0.16/0.43 = ( late_BoundR @ A6 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.16/0.43 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.16/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % parCasesB'
% 0.16/0.43 thf(fact_93_transitions_OPar1B,axiom,
% 0.16/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transitions.Par1B
% 0.16/0.43 thf(fact_94_transitions_OPar2B,axiom,
% 0.16/0.43 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transitions.Par2B
% 0.16/0.43 thf(fact_95_fresh__prodD_I2_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,C: $tType,A2: A,X3: B,Y: C] :
% 0.16/0.43 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 0.16/0.43 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % fresh_prodD(2)
% 0.16/0.43 thf(fact_96_fresh__prodD_I1_J,axiom,
% 0.16/0.43 ! [C: $tType,A: $tType,B: $tType,A2: A,X3: B,Y: C] :
% 0.16/0.43 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 0.16/0.43 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % fresh_prodD(1)
% 0.16/0.43 thf(fact_97_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [X1: name,X2: name] :
% 0.16/0.43 ( ( late_InputS @ X1 )
% 0.16/0.43 != ( late_BoundOutputS @ X2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics1.subject.distinct(1)
% 0.16/0.43 thf(fact_98_subject_Oexhaust,axiom,
% 0.16/0.43 ! [Y: late_subject] :
% 0.16/0.43 ( ! [X12: name] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( late_InputS @ X12 ) )
% 0.16/0.43 => ~ ! [X22: name] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.exhaust
% 0.16/0.43 thf(fact_99_old_Oprod_Orec,axiom,
% 0.16/0.43 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B3: B] :
% 0.16/0.43 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B3 ) )
% 0.16/0.43 = ( F1 @ A2 @ B3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.prod.rec
% 0.16/0.43 thf(fact_100_resCases_H,axiom,
% 0.16/0.43 ! [X3: name,P: pi,Rs: late_residual] :
% 0.16/0.43 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 0.16/0.43 => ( ! [P4: pi,A6: name,B5: name] :
% 0.16/0.43 ( ( ( res @ X3 @ P )
% 0.16/0.43 = ( res @ B5 @ P4 ) )
% 0.16/0.43 => ! [P3: pi] :
% 0.16/0.43 ( ( Rs
% 0.16/0.43 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B5 @ P3 ) )
% 0.16/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B5 ) @ P3 ) )
% 0.16/0.43 => ( A6 = B5 ) ) ) )
% 0.16/0.43 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y2: name] :
% 0.16/0.43 ( ( ( res @ X3 @ P )
% 0.16/0.43 = ( res @ Y2 @ P4 ) )
% 0.16/0.43 => ( ( Rs
% 0.16/0.43 = ( late_BoundR @ A6 @ X5 @ ( res @ Y2 @ P3 ) ) )
% 0.16/0.43 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ Y2 @ A6 )
% 0.16/0.43 => ( ( Y2 != X5 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.16/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) )
% 0.16/0.43 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y2: name] :
% 0.16/0.43 ( ( ( res @ X3 @ P )
% 0.16/0.43 = ( res @ Y2 @ P4 ) )
% 0.16/0.43 => ( ( Rs
% 0.16/0.43 = ( late_FreeR @ Alpha2 @ ( res @ Y2 @ P3 ) ) )
% 0.16/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.16/0.43 => ~ ( fresh @ name @ late_freeRes @ Y2 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % resCases'
% 0.16/0.43 thf(fact_101_transitions_OComm1,axiom,
% 0.16/0.43 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B3: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( ( X3 != A2 )
% 0.16/0.43 => ( ( X3 != B3 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B3 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transitions.Comm1
% 0.16/0.43 thf(fact_102_transitions_OComm2,axiom,
% 0.16/0.43 ! [P: pi,A2: name,B3: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.16/0.43 => ( ( X3 != A2 )
% 0.16/0.43 => ( ( X3 != B3 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transitions.Comm2
% 0.16/0.43 thf(fact_103_Late__Semantics_OComm1,axiom,
% 0.16/0.43 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B3: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ Q2 ) )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B3 ) @ Q2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.Comm1
% 0.16/0.43 thf(fact_104_Late__Semantics_OComm2,axiom,
% 0.16/0.43 ! [P: pi,A2: name,B3: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.16/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B3 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.Comm2
% 0.16/0.43 thf(fact_105_resCasesB_H,axiom,
% 0.16/0.43 ! [X6: name,P: pi,A2: late_subject,Y3: name,P2: pi] :
% 0.16/0.43 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y3 @ P2 ) )
% 0.16/0.43 => ( ! [P4: pi,A6: name,B5: name] :
% 0.16/0.43 ( ( ( res @ X6 @ P )
% 0.16/0.43 = ( res @ B5 @ P4 ) )
% 0.16/0.43 => ! [P3: pi] :
% 0.16/0.43 ( ( ( late_BoundR @ A2 @ Y3 @ P2 )
% 0.16/0.43 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B5 @ P3 ) )
% 0.16/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B5 ) @ P3 ) )
% 0.16/0.43 => ( A6 = B5 ) ) ) )
% 0.16/0.43 => ~ ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y2: name] :
% 0.16/0.43 ( ( ( res @ X6 @ P )
% 0.16/0.43 = ( res @ Y2 @ P4 ) )
% 0.16/0.43 => ( ( ( late_BoundR @ A2 @ Y3 @ P2 )
% 0.16/0.43 = ( late_BoundR @ A6 @ X5 @ ( res @ Y2 @ P3 ) ) )
% 0.16/0.43 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ Y2 @ A6 )
% 0.16/0.43 => ( ( Y2 != X5 )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.16/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % resCasesB'
% 0.16/0.43 thf(fact_106_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.16/0.43 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.16/0.43 ( ( ( late_OutputR @ X11 @ X122 )
% 0.16/0.43 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.16/0.43 = ( ( X11 = Y11 )
% 0.16/0.43 & ( X122 = Y12 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics1.freeRes.inject
% 0.16/0.43 thf(fact_107_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.16/0.43 ! [X2: name,X1: name,Y22: name,Y1: name] :
% 0.16/0.43 ( ( ( late_OutputR @ X2 @ X1 )
% 0.16/0.43 = ( late_OutputR @ Y22 @ Y1 ) )
% 0.16/0.43 = ( ( X2 = Y22 )
% 0.16/0.43 & ( X1 = Y1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.freeRes.inject
% 0.16/0.43 thf(fact_108_freeRes_Ofresh_I1_J,axiom,
% 0.16/0.43 ! [A2: name,X2: name,X1: name] :
% 0.16/0.43 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X2 @ X1 ) )
% 0.16/0.43 = ( ( fresh @ name @ name @ A2 @ X2 )
% 0.16/0.43 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.fresh(1)
% 0.16/0.43 thf(fact_109_freeRes_Ostrong__inducts,axiom,
% 0.16/0.43 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.16/0.43 ( ! [Name1: name,Name22: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.16/0.43 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.16/0.43 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.strong_inducts
% 0.16/0.43 thf(fact_110_freeRes_Ostrong__induct_H,axiom,
% 0.16/0.43 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.16/0.43 ( ! [Name1: name,Name22: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.16/0.43 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.16/0.43 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.strong_induct'
% 0.16/0.43 thf(fact_111_freeRes_Oinducts,axiom,
% 0.16/0.43 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.16/0.43 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.16/0.43 => ( ( P @ late_TauR )
% 0.16/0.43 => ( P @ FreeRes3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.inducts
% 0.16/0.43 thf(fact_112_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [Name12: name,Name23: name] :
% 0.16/0.43 ( ( late_OutputR @ Name12 @ Name23 )
% 0.16/0.43 != late_TauR ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics.freeRes.distinct(1)
% 0.16/0.43 thf(fact_113_freeRes_Oexhaust,axiom,
% 0.16/0.43 ! [Y: late_freeRes] :
% 0.16/0.43 ( ! [X112: name,X123: name] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( late_OutputR @ X112 @ X123 ) )
% 0.16/0.43 => ( Y = late_TauR ) ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.exhaust
% 0.16/0.43 thf(fact_114_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [X11: name,X122: name] :
% 0.16/0.43 ( ( late_OutputR @ X11 @ X122 )
% 0.16/0.43 != late_TauR ) ).
% 0.16/0.43
% 0.16/0.43 % Late_Semantics1.freeRes.distinct(1)
% 0.16/0.43 thf(fact_115_Open,axiom,
% 0.16/0.43 ! [P: pi,A2: name,B3: name,P2: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) )
% 0.16/0.43 => ( ( A2 != B3 )
% 0.16/0.43 => ( late_transitions @ ( res @ B3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B3 @ P2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Open
% 0.16/0.43 thf(fact_116_resSimCases,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( fs_name @ A )
% 0.16/0.43 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P: pi,C4: A] :
% 0.16/0.43 ( ( eqvt @ pi @ Rel )
% 0.16/0.43 => ( ! [Q3: pi,A6: name] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A6 @ X3 ) @ Q3 ) )
% 0.16/0.43 => ( ( A6 != X3 )
% 0.16/0.43 => ? [P6: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ X3 @ P6 ) )
% 0.16/0.43 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) ) )
% 0.16/0.43 => ( ! [Q3: pi,A6: late_subject,Y2: name] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y2 @ Q3 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ X3 @ A6 )
% 0.16/0.43 => ( ( X3 != Y2 )
% 0.16/0.43 => ( ( fresh @ name @ A @ Y2 @ C4 )
% 0.16/0.43 => ? [P6: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y2 @ P6 ) )
% 0.16/0.43 & ( strong2129052853vative @ P6 @ ( res @ X3 @ Q3 ) @ A6 @ Y2 @ Rel ) ) ) ) ) )
% 0.16/0.43 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.16/0.43 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 0.16/0.43 => ? [P6: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.43 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 0.16/0.43 => ( strong743114133lation @ P @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % resSimCases
% 0.16/0.43 thf(fact_117_freeRes_Orecs_I2_J,axiom,
% 0.16/0.43 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 0.16/0.43 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 0.16/0.43 => ( ( P @ F22 )
% 0.16/0.43 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 0.16/0.43 = F22 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.recs(2)
% 0.16/0.43 thf(fact_118_subject_Orecs_I1_J,axiom,
% 0.16/0.43 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.16/0.43 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.16/0.43 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.16/0.43 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 0.16/0.43 = ( F1 @ Name3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.recs(1)
% 0.16/0.43 thf(fact_119_subject_Orecs_I2_J,axiom,
% 0.16/0.43 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.16/0.43 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.16/0.43 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.16/0.43 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 0.16/0.43 = ( F22 @ Name3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subject.recs(2)
% 0.16/0.43 thf(fact_120_freeRes_Orecs_I1_J,axiom,
% 0.16/0.43 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name12: name,Name23: name] :
% 0.16/0.43 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 0.16/0.43 => ( ( P @ F22 )
% 0.16/0.43 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.16/0.43 = ( F1 @ Name12 @ Name23 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % freeRes.recs(1)
% 0.16/0.43 thf(fact_121_simE_I1_J,axiom,
% 0.16/0.43 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 0.16/0.43 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.16/0.43 => ? [P3: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.16/0.43 & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simE(1)
% 0.16/0.43 thf(fact_122_simE_I2_J,axiom,
% 0.16/0.43 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.16/0.43 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.16/0.43 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.16/0.43 => ? [P3: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.16/0.43 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simE(2)
% 0.16/0.43 thf(fact_123_simCases,axiom,
% 0.16/0.43 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.16/0.43 ( ! [A6: late_subject,Y2: name,Q3: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y2 @ Q3 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.16/0.43 => ? [P6: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y2 @ P6 ) )
% 0.16/0.43 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ Y2 @ Rel ) ) ) )
% 0.16/0.43 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.16/0.43 => ? [P6: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.43 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 0.16/0.43 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simCases
% 0.16/0.43 thf(fact_124_simulation__def,axiom,
% 0.16/0.43 ( strong743114133lation
% 0.16/0.43 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.16/0.43 ( ! [A3: late_subject,X4: name,Q6: pi] :
% 0.16/0.43 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A3 @ X4 @ Q6 ) )
% 0.16/0.43 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 0.16/0.43 => ? [P8: pi] :
% 0.16/0.43 ( ( late_transitions @ P7 @ ( late_BoundR @ A3 @ X4 @ P8 ) )
% 0.16/0.43 & ( strong2129052853vative @ P8 @ Q6 @ A3 @ X4 @ Rel2 ) ) )
% 0.16/0.43 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.16/0.43 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.16/0.43 => ? [P8: pi] :
% 0.16/0.43 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.16/0.43 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simulation_def
% 0.16/0.43 thf(fact_125_parSym,axiom,
% 0.16/0.43 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.16/0.43 ( ! [R2: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 0.16/0.43 => ( ! [R2: pi,S2: pi,X5: name] :
% 0.16/0.43 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S2 ) @ Rel )
% 0.16/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 0.16/0.43 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % parSym
% 0.16/0.43 thf(fact_126_simCasesCont,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( fs_name @ A )
% 0.16/0.43 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.16/0.43 ( ( eqvt @ pi @ Rel )
% 0.16/0.43 => ( ! [A6: late_subject,X5: name,Q3: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.16/0.43 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.16/0.43 => ( ( fresh @ name @ late_subject @ X5 @ A6 )
% 0.16/0.43 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.16/0.43 => ? [P6: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ X5 @ P6 ) )
% 0.16/0.43 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ X5 @ Rel ) ) ) ) ) ) )
% 0.16/0.43 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.16/0.43 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.16/0.43 => ? [P6: pi] :
% 0.16/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.43 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 0.16/0.43 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simCasesCont
% 0.16/0.43 thf(fact_127_parAssocLeft,axiom,
% 0.16/0.43 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.16/0.43 ( ! [S2: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S2 @ T2 ) @ U ) @ ( par @ S2 @ ( par @ T2 @ U ) ) ) @ Rel )
% 0.16/0.43 => ( ! [S2: pi,T2: pi,X5: name] :
% 0.16/0.43 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S2 @ T2 ) @ Rel )
% 0.16/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 0.16/0.43 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 0.16/0.43 ( ( fresh @ name @ pi @ X5 @ S2 )
% 0.16/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T2 ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.16/0.43 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 0.16/0.43 ( ( fresh @ name @ pi @ X5 @ U )
% 0.16/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.16/0.43 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % parAssocLeft
% 0.16/0.43 thf(fact_128_resTauOutputTrans,axiom,
% 0.16/0.43 ! [X3: name,P: pi,A2: name,B3: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % resTauOutputTrans
% 0.16/0.43 thf(fact_129_resOutputTauTrans,axiom,
% 0.16/0.43 ! [X3: name,A2: name,B3: name,P: pi,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B3 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % resOutputTauTrans
% 0.16/0.43 thf(fact_130_resOutputInputTrans,axiom,
% 0.16/0.43 ! [X3: name,A2: name,B3: name,P: pi,C3: name,Y: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B3 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C3 ) @ Y @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % resOutputInputTrans
% 0.16/0.43 thf(fact_131_resOutputOutputTrans,axiom,
% 0.16/0.43 ! [X3: name,A2: name,P: pi,B3: name,Y: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ X3 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B3 @ Y ) @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % resOutputOutputTrans
% 0.16/0.43 thf(fact_132_pi_Ofresh_I3_J,axiom,
% 0.16/0.43 ! [A2: name,X1: pi] :
% 0.16/0.43 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.16/0.43 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.fresh(3)
% 0.16/0.43 thf(fact_133_simps_I2_J,axiom,
% 0.16/0.43 ! [P: pi,C3: name,D: name] :
% 0.16/0.43 ( ( subs @ ( tau @ P ) @ C3 @ D )
% 0.16/0.43 = ( tau @ ( subs @ P @ C3 @ D ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simps(2)
% 0.16/0.43 thf(fact_134_pi_Ofresh_I2_J,axiom,
% 0.16/0.43 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.16/0.43 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X2 @ X1 ) )
% 0.16/0.43 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.16/0.43 & ( fresh @ name @ name @ A2 @ X2 )
% 0.16/0.43 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.fresh(2)
% 0.16/0.43 thf(fact_135_pi_Oinject_I2_J,axiom,
% 0.16/0.43 ! [X1: pi,Y1: pi] :
% 0.16/0.43 ( ( ( tau @ X1 )
% 0.16/0.43 = ( tau @ Y1 ) )
% 0.16/0.43 = ( X1 = Y1 ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.inject(2)
% 0.16/0.43 thf(fact_136_pi_Oinject_I1_J,axiom,
% 0.16/0.43 ! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
% 0.16/0.43 ( ( ( output @ X32 @ X2 @ X1 )
% 0.16/0.43 = ( output @ Y32 @ Y22 @ Y1 ) )
% 0.16/0.43 = ( ( X32 = Y32 )
% 0.16/0.43 & ( X2 = Y22 )
% 0.16/0.43 & ( X1 = Y1 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.inject(1)
% 0.16/0.43 thf(fact_137_pi_Odistinct_I19_J,axiom,
% 0.16/0.43 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 0.16/0.43 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.43 != ( tau @ Pi ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(19)
% 0.16/0.43 thf(fact_138_pi_Odistinct_I31_J,axiom,
% 0.16/0.43 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.16/0.43 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.43 != ( res @ Name @ Pi ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(31)
% 0.16/0.43 thf(fact_139_pi_Odistinct_I29_J,axiom,
% 0.16/0.43 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.43 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.43 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(29)
% 0.16/0.43 thf(fact_140_pi_Odistinct_I45_J,axiom,
% 0.16/0.43 ! [Pi4: pi,Name: name,Pi: pi] :
% 0.16/0.43 ( ( tau @ Pi4 )
% 0.16/0.43 != ( res @ Name @ Pi ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(45)
% 0.16/0.43 thf(fact_141_pi_Odistinct_I43_J,axiom,
% 0.16/0.43 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.43 ( ( tau @ Pi4 )
% 0.16/0.43 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(43)
% 0.16/0.43 thf(fact_142_resTrans_I1_J,axiom,
% 0.16/0.43 ! [X3: name,B3: name,P: pi,Rs: late_residual] :
% 0.16/0.43 ~ ( late_transitions @ ( res @ X3 @ ( output @ X3 @ B3 @ P ) ) @ Rs ) ).
% 0.16/0.43
% 0.16/0.43 % resTrans(1)
% 0.16/0.43 thf(fact_143_outputBoundTrans,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi,C3: late_subject,X3: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_BoundR @ C3 @ X3 @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % outputBoundTrans
% 0.16/0.43 thf(fact_144_tauBoundTrans,axiom,
% 0.16/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X3 @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % tauBoundTrans
% 0.16/0.43 thf(fact_145_resTauBoundTrans,axiom,
% 0.16/0.43 ! [X3: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % resTauBoundTrans
% 0.16/0.43 thf(fact_146_Output,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi] : ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P ) ) ).
% 0.16/0.43
% 0.16/0.43 % Output
% 0.16/0.43 thf(fact_147_outputIneqTrans,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi,C3: name,D: name,P2: pi] :
% 0.16/0.43 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ ( late_OutputR @ C3 @ D ) @ P2 ) )
% 0.16/0.43 => ~ ( ( A2 != C3 )
% 0.16/0.43 | ( B3 != D ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % outputIneqTrans
% 0.16/0.43 thf(fact_148_outputCases_H,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 0.16/0.43 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ Rs )
% 0.16/0.43 => ~ ! [A6: name,B5: name,P4: pi] :
% 0.16/0.43 ( ( ( A2 = A6 )
% 0.16/0.43 & ( B3 = B5 )
% 0.16/0.43 & ( P = P4 ) )
% 0.16/0.43 => ( Rs
% 0.16/0.43 != ( late_FreeR @ ( late_OutputR @ A6 @ B5 ) @ P4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % outputCases'
% 0.16/0.43 thf(fact_149_outputCases,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.16/0.43 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ( ( ( Alpha
% 0.16/0.43 = ( late_OutputR @ A2 @ B3 ) )
% 0.16/0.43 => ( ( P = P2 )
% 0.16/0.43 => ( Prop @ ( late_OutputR @ A2 @ B3 ) @ P ) ) )
% 0.16/0.43 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % outputCases
% 0.16/0.43 thf(fact_150_outputTauTrans,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % outputTauTrans
% 0.16/0.43 thf(fact_151_tauOutputTrans,axiom,
% 0.16/0.43 ! [P: pi,A2: name,B3: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % tauOutputTrans
% 0.16/0.43 thf(fact_152_Tau,axiom,
% 0.16/0.43 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.16/0.43
% 0.16/0.43 % Tau
% 0.16/0.43 thf(fact_153_tauCases_H,axiom,
% 0.16/0.43 ! [P: pi,Rs: late_residual] :
% 0.16/0.43 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.16/0.43 => ~ ! [P4: pi] :
% 0.16/0.43 ( ( ( tau @ P )
% 0.16/0.43 = ( tau @ P4 ) )
% 0.16/0.43 => ( Rs
% 0.16/0.43 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % tauCases'
% 0.16/0.43 thf(fact_154_tauCases,axiom,
% 0.16/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.16/0.43 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ( ( ( Alpha = late_TauR )
% 0.16/0.43 => ( ( P = P2 )
% 0.16/0.43 => ( Prop @ late_TauR @ P ) ) )
% 0.16/0.43 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % tauCases
% 0.16/0.43 thf(fact_155_outputFreshTrans,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.43 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.43 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.16/0.43 | ( fresh @ name @ late_freeRes @ B3 @ Alpha ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % outputFreshTrans
% 0.16/0.43 thf(fact_156_resInputBoundOutputTrans,axiom,
% 0.16/0.43 ! [X3: name,A2: name,Y: name,P: pi,B3: name,Z: name,P2: pi] :
% 0.16/0.43 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B3 ) @ Z @ P2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % resInputBoundOutputTrans
% 0.16/0.43 thf(fact_157_residual_Ofresh_I1_J,axiom,
% 0.16/0.43 ! [A2: name,X32: late_subject,X1: name,X2: pi] :
% 0.16/0.43 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.16/0.43 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 0.16/0.43 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.fresh(1)
% 0.16/0.43 thf(fact_158_simps_I3_J,axiom,
% 0.16/0.43 ! [A2: name,B3: name,P: pi,C3: name,D: name] :
% 0.16/0.43 ( ( subs @ ( output @ A2 @ B3 @ P ) @ C3 @ D )
% 0.16/0.43 = ( output @ ( subst_name @ A2 @ C3 @ D ) @ ( subst_name @ B3 @ C3 @ D ) @ ( subs @ P @ C3 @ D ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simps(3)
% 0.16/0.43 thf(fact_159_internal__case__prod__conv,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B3: C] :
% 0.16/0.43 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B3 ) )
% 0.16/0.43 = ( C3 @ A2 @ B3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % internal_case_prod_conv
% 0.16/0.43 thf(fact_160_simps_I4_J,axiom,
% 0.16/0.43 ! [X3: name,A2: name,C3: name,D: name,P: pi] :
% 0.16/0.43 ( ( X3 != A2 )
% 0.16/0.43 => ( ( X3 != C3 )
% 0.16/0.43 => ( ( X3 != D )
% 0.16/0.43 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ C3 @ D )
% 0.16/0.43 = ( input @ ( subst_name @ A2 @ C3 @ D ) @ X3 @ ( subs @ P @ C3 @ D ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % simps(4)
% 0.16/0.43 thf(fact_161_substInput,axiom,
% 0.16/0.43 ! [X3: name,B3: name,C3: name,A2: name,P: pi] :
% 0.16/0.43 ( ( X3 != B3 )
% 0.16/0.43 => ( ( X3 != C3 )
% 0.16/0.43 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ B3 @ C3 )
% 0.16/0.43 = ( input @ ( subst_name @ A2 @ B3 @ C3 ) @ X3 @ ( subs @ P @ B3 @ C3 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % substInput
% 0.16/0.43 thf(fact_162_pi_Ofresh_I9_J,axiom,
% 0.16/0.43 ! [A2: name,X1: name,X2: pi] :
% 0.16/0.43 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X2 ) )
% 0.16/0.43 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.fresh(9)
% 0.16/0.43 thf(fact_163_pi_Ofresh_I4_J,axiom,
% 0.16/0.43 ! [A2: name,X32: name,X1: name,X2: pi] :
% 0.16/0.43 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X2 ) )
% 0.16/0.43 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.16/0.43 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.fresh(4)
% 0.16/0.43 thf(fact_164_pi_Odistinct_I57_J,axiom,
% 0.16/0.43 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.16/0.43 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.16/0.43 != ( res @ Name @ Pi ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(57)
% 0.16/0.43 thf(fact_165_pi_Odistinct_I55_J,axiom,
% 0.16/0.43 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.43 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.16/0.43 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.distinct(55)
% 0.16/0.43 thf(fact_166_pi_Oinject_I8_J,axiom,
% 0.16/0.43 ! [X1: name,X2: pi,Y1: name,Y22: pi] :
% 0.16/0.43 ( ( ( res @ X1 @ X2 )
% 0.16/0.43 = ( res @ Y1 @ Y22 ) )
% 0.16/0.43 = ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.16/0.43 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.inject(8)
% 0.16/0.43 thf(fact_167_subst__name__def,axiom,
% 0.16/0.43 ( subst_name
% 0.16/0.43 = ( ^ [A3: name,B2: name,C5: name] : ( if @ name @ ( A3 = B2 ) @ C5 @ A3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subst_name_def
% 0.16/0.43 thf(fact_168_pi_Oinject_I3_J,axiom,
% 0.16/0.43 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y22: pi] :
% 0.16/0.43 ( ( ( input @ X32 @ X1 @ X2 )
% 0.16/0.43 = ( input @ Y32 @ Y1 @ Y22 ) )
% 0.16/0.43 = ( ( X32 = Y32 )
% 0.16/0.43 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.16/0.43 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % pi.inject(3)
% 0.16/0.43 thf(fact_169_abs__fun__eq1,axiom,
% 0.16/0.43 ! [X: $tType,A: $tType,A2: X,X3: A,Y: A] :
% 0.16/0.43 ( ( ( abs_fun @ X @ A @ A2 @ X3 )
% 0.16/0.43 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 0.16/0.43 = ( X3 = Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % abs_fun_eq1
% 0.16/0.43 thf(fact_170_name__fresh__abs,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( fs_name @ A )
% 0.16/0.43 => ! [B3: name,A2: name,X3: A] :
% 0.16/0.43 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B3 @ ( abs_fun @ name @ A @ A2 @ X3 ) )
% 0.16/0.43 = ( ( B3 = A2 )
% 0.16/0.43 | ( fresh @ name @ A @ B3 @ X3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % name_fresh_abs
% 0.16/0.43 thf(fact_171_abs__fresh_I1_J,axiom,
% 0.16/0.43 ! [X7: $tType] :
% 0.16/0.43 ( ( fs_name @ X7 )
% 0.16/0.43 => ! [B3: name,A2: name,X3: X7] :
% 0.16/0.43 ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B3 @ ( abs_fun @ name @ X7 @ A2 @ X3 ) )
% 0.16/0.43 = ( ( B3 = A2 )
% 0.16/0.43 | ( fresh @ name @ X7 @ B3 @ X3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % abs_fresh(1)
% 0.16/0.43 thf(fact_172_residual_Oinject_I1_J,axiom,
% 0.16/0.43 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y22: pi] :
% 0.16/0.43 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.16/0.43 = ( late_BoundR @ Y32 @ Y1 @ Y22 ) )
% 0.16/0.43 = ( ( X32 = Y32 )
% 0.16/0.43 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.16/0.43 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % residual.inject(1)
% 0.16/0.44 thf(fact_173_pi_Odistinct_I21_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(21)
% 0.16/0.44 thf(fact_174_pi_Odistinct_I35_J,axiom,
% 0.16/0.44 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( tau @ Pi4 )
% 0.16/0.44 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(35)
% 0.16/0.44 thf(fact_175_inputCases_H,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( input @ A2 @ B3 @ P ) @ Rs )
% 0.16/0.44 => ~ ! [X5: name,A6: name,P4: pi] :
% 0.16/0.44 ( ( ( A2 = A6 )
% 0.16/0.44 & ( ( abs_fun @ name @ pi @ B3 @ P )
% 0.16/0.44 = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 0.16/0.44 => ( ( Rs
% 0.16/0.44 = ( late_BoundR @ ( late_InputS @ A6 ) @ X5 @ P4 ) )
% 0.16/0.44 => ( X5 = A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inputCases'
% 0.16/0.44 thf(fact_176_resTrans_I2_J,axiom,
% 0.16/0.44 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 0.16/0.44 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 0.16/0.44
% 0.16/0.44 % resTrans(2)
% 0.16/0.44 thf(fact_177_inputFreeTrans,axiom,
% 0.16/0.44 ! [A2: name,X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.44 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % inputFreeTrans
% 0.16/0.44 thf(fact_178_resInputFreeTrans,axiom,
% 0.16/0.44 ! [X3: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.44 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % resInputFreeTrans
% 0.16/0.44 thf(fact_179_Late__Semantics_OInput,axiom,
% 0.16/0.44 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % Late_Semantics.Input
% 0.16/0.44 thf(fact_180_transitions_OInput,axiom,
% 0.16/0.44 ! [X3: name,A2: name,P: pi] :
% 0.16/0.44 ( ( X3 != A2 )
% 0.16/0.44 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % transitions.Input
% 0.16/0.44 thf(fact_181_inputBoundOutputTrans,axiom,
% 0.16/0.44 ! [A2: name,X3: name,P: pi,B3: name,Y: name,P2: pi] :
% 0.16/0.44 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B3 ) @ Y @ P2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % inputBoundOutputTrans
% 0.16/0.44 thf(fact_182_inputIneqTrans,axiom,
% 0.16/0.44 ! [A2: name,X3: name,P: pi,B3: late_subject,Y: name,P2: pi] :
% 0.16/0.44 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B3 @ Y @ P2 ) )
% 0.16/0.44 => ~ ( fresh @ name @ late_subject @ A2 @ B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % inputIneqTrans
% 0.16/0.44 thf(fact_183_parZeroRight,axiom,
% 0.16/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.16/0.44 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 0.16/0.44 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % parZeroRight
% 0.16/0.44 thf(fact_184_parZeroLeft,axiom,
% 0.16/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.16/0.44 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 0.16/0.44 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % parZeroLeft
% 0.16/0.44 thf(fact_185_simps_I6_J,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,C3: name,D: name] :
% 0.16/0.44 ( ( subs @ ( mismatch @ A2 @ B3 @ P ) @ C3 @ D )
% 0.16/0.44 = ( mismatch @ ( subst_name @ A2 @ C3 @ D ) @ ( subst_name @ B3 @ C3 @ D ) @ ( subs @ P @ C3 @ D ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % simps(6)
% 0.16/0.44 thf(fact_186_pi_Ofresh_I1_J,axiom,
% 0.16/0.44 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.16/0.44
% 0.16/0.44 % pi.fresh(1)
% 0.16/0.44 thf(fact_187_simps_I1_J,axiom,
% 0.16/0.44 ! [C3: name,D: name] :
% 0.16/0.44 ( ( subs @ piNil @ C3 @ D )
% 0.16/0.44 = piNil ) ).
% 0.16/0.44
% 0.16/0.44 % simps(1)
% 0.16/0.44 thf(fact_188_pi_Ofresh_I6_J,axiom,
% 0.16/0.44 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.16/0.44 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.16/0.44 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.16/0.44 & ( fresh @ name @ name @ A2 @ X2 )
% 0.16/0.44 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.fresh(6)
% 0.16/0.44 thf(fact_189_pi_Odistinct_I5_J,axiom,
% 0.16/0.44 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( piNil
% 0.16/0.44 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(5)
% 0.16/0.44 thf(fact_190_pi_Odistinct_I51_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(51)
% 0.16/0.44 thf(fact_191_pi_Odistinct_I75_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.16/0.44 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( res @ Name @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(75)
% 0.16/0.44 thf(fact_192_pi_Odistinct_I73_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(73)
% 0.16/0.44 thf(fact_193_pi_Odistinct_I15_J,axiom,
% 0.16/0.44 ! [Name: name,Pi: pi] :
% 0.16/0.44 ( piNil
% 0.16/0.44 != ( res @ Name @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(15)
% 0.16/0.44 thf(fact_194_pi_Odistinct_I13_J,axiom,
% 0.16/0.44 ! [Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( piNil
% 0.16/0.44 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(13)
% 0.16/0.44 thf(fact_195_pi_Odistinct_I25_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(25)
% 0.16/0.44 thf(fact_196_nilSimRight,axiom,
% 0.16/0.44 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.16/0.44
% 0.16/0.44 % nilSimRight
% 0.16/0.44 thf(fact_197_pi_Odistinct_I1_J,axiom,
% 0.16/0.44 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( piNil
% 0.16/0.44 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(1)
% 0.16/0.44 thf(fact_198_pi_Odistinct_I39_J,axiom,
% 0.16/0.44 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( tau @ Pi4 )
% 0.16/0.44 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(39)
% 0.16/0.44 thf(fact_199_pi_Odistinct_I3_J,axiom,
% 0.16/0.44 ! [Pi: pi] :
% 0.16/0.44 ( piNil
% 0.16/0.44 != ( tau @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(3)
% 0.16/0.44 thf(fact_200_mismatchNilLeft,axiom,
% 0.16/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A2 @ A2 @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % mismatchNilLeft
% 0.16/0.44 thf(fact_201_pi_Oinject_I5_J,axiom,
% 0.16/0.44 ! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
% 0.16/0.44 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.16/0.44 = ( mismatch @ Y32 @ Y22 @ Y1 ) )
% 0.16/0.44 = ( ( X32 = Y32 )
% 0.16/0.44 & ( X2 = Y22 )
% 0.16/0.44 & ( X1 = Y1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.inject(5)
% 0.16/0.44 thf(fact_202_pi_Odistinct_I9_J,axiom,
% 0.16/0.44 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( piNil
% 0.16/0.44 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(9)
% 0.16/0.44 thf(fact_203_nilCases_H,axiom,
% 0.16/0.44 ! [Rs: late_residual] :
% 0.16/0.44 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.16/0.44
% 0.16/0.44 % nilCases'
% 0.16/0.44 thf(fact_204_zeroTrans,axiom,
% 0.16/0.44 ! [Rs: late_residual] :
% 0.16/0.44 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.16/0.44
% 0.16/0.44 % zeroTrans
% 0.16/0.44 thf(fact_205_mismatchCases,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.16/0.44 ( ( late_transitions @ ( mismatch @ A2 @ B3 @ P ) @ Rs )
% 0.16/0.44 => ( ( ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( ( A2 != B3 )
% 0.16/0.44 => ( F @ A2 @ B3 ) ) )
% 0.16/0.44 => ( F @ A2 @ B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % mismatchCases
% 0.16/0.44 thf(fact_206_mismatchTrans,axiom,
% 0.16/0.44 ! [A2: name,P: pi,Rs: late_residual] :
% 0.16/0.44 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.16/0.44
% 0.16/0.44 % mismatchTrans
% 0.16/0.44 thf(fact_207_mismatchCases_H,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( mismatch @ A2 @ B3 @ P ) @ Rs )
% 0.16/0.44 => ~ ! [P4: pi,A6: name,B5: name] :
% 0.16/0.44 ( ( ( A2 = A6 )
% 0.16/0.44 & ( B3 = B5 )
% 0.16/0.44 & ( P = P4 ) )
% 0.16/0.44 => ( ( late_transitions @ P4 @ Rs )
% 0.16/0.44 => ( A6 = B5 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % mismatchCases'
% 0.16/0.44 thf(fact_208_Mismatch,axiom,
% 0.16/0.44 ! [P: pi,Rs: late_residual,A2: name,B3: name] :
% 0.16/0.44 ( ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( ( A2 != B3 )
% 0.16/0.44 => ( late_transitions @ ( mismatch @ A2 @ B3 @ P ) @ Rs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Mismatch
% 0.16/0.44 thf(fact_209_resZeroTrans,axiom,
% 0.16/0.44 ! [X3: name,Rs: late_residual] :
% 0.16/0.44 ~ ( late_transitions @ ( res @ X3 @ piNil ) @ Rs ) ).
% 0.16/0.44
% 0.16/0.44 % resZeroTrans
% 0.16/0.44 thf(fact_210_nilSim_I2_J,axiom,
% 0.16/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X3: name,P: pi] :
% 0.16/0.44 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X3 @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % nilSim(2)
% 0.16/0.44 thf(fact_211_nilSim_I3_J,axiom,
% 0.16/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B3: name,P: pi] :
% 0.16/0.44 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B3 @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % nilSim(3)
% 0.16/0.44 thf(fact_212_nilSim_I1_J,axiom,
% 0.16/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.16/0.44 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % nilSim(1)
% 0.16/0.44 thf(fact_213_simps_I5_J,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,C3: name,D: name] :
% 0.16/0.44 ( ( subs @ ( match @ A2 @ B3 @ P ) @ C3 @ D )
% 0.16/0.44 = ( match @ ( subst_name @ A2 @ C3 @ D ) @ ( subst_name @ B3 @ C3 @ D ) @ ( subs @ P @ C3 @ D ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % simps(5)
% 0.16/0.44 thf(fact_214_pi_Ofresh_I5_J,axiom,
% 0.16/0.44 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.16/0.44 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X2 @ X1 ) )
% 0.16/0.44 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.16/0.44 & ( fresh @ name @ name @ A2 @ X2 )
% 0.16/0.44 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.fresh(5)
% 0.16/0.44 thf(fact_215_freeRes_Ocase_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,F1: name > name > A,F22: A] :
% 0.16/0.44 ( ( late_case_freeRes @ A @ F1 @ F22 @ late_TauR )
% 0.16/0.44 = F22 ) ).
% 0.16/0.44
% 0.16/0.44 % freeRes.case(2)
% 0.16/0.44 thf(fact_216_pi_Odistinct_I61_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( match @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(61)
% 0.16/0.44 thf(fact_217_pi_Odistinct_I7_J,axiom,
% 0.16/0.44 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( piNil
% 0.16/0.44 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(7)
% 0.16/0.44 thf(fact_218_Match,axiom,
% 0.16/0.44 ! [P: pi,Rs: late_residual,B3: name] :
% 0.16/0.44 ( ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( late_transitions @ ( match @ B3 @ B3 @ P ) @ Rs ) ) ).
% 0.16/0.44
% 0.16/0.44 % Match
% 0.16/0.44 thf(fact_219_matchCases_H,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( match @ A2 @ B3 @ P ) @ Rs )
% 0.16/0.44 => ~ ! [P4: pi] :
% 0.16/0.44 ( ( ( B3 = A2 )
% 0.16/0.44 & ( P = P4 ) )
% 0.16/0.44 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % matchCases'
% 0.16/0.44 thf(fact_220_matchTrans,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( match @ A2 @ B3 @ P ) @ Rs )
% 0.16/0.44 => ( A2 = B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % matchTrans
% 0.16/0.44 thf(fact_221_matchCases,axiom,
% 0.16/0.44 ! [A2: name,B3: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.16/0.44 ( ( late_transitions @ ( match @ A2 @ B3 @ P ) @ Rs )
% 0.16/0.44 => ( ( ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( ( A2 = B3 )
% 0.16/0.44 => ( F @ A2 @ A2 ) ) )
% 0.16/0.44 => ( F @ A2 @ B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % matchCases
% 0.16/0.44 thf(fact_222_pi_Oinject_I4_J,axiom,
% 0.16/0.44 ! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
% 0.16/0.44 ( ( ( match @ X32 @ X2 @ X1 )
% 0.16/0.44 = ( match @ Y32 @ Y22 @ Y1 ) )
% 0.16/0.44 = ( ( X32 = Y32 )
% 0.16/0.44 & ( X2 = Y22 )
% 0.16/0.44 & ( X1 = Y1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.inject(4)
% 0.16/0.44 thf(fact_223_pi_Odistinct_I37_J,axiom,
% 0.16/0.44 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( tau @ Pi4 )
% 0.16/0.44 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(37)
% 0.16/0.44 thf(fact_224_pi_Odistinct_I23_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(23)
% 0.16/0.44 thf(fact_225_pi_Odistinct_I65_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( match @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(65)
% 0.16/0.44 thf(fact_226_pi_Odistinct_I67_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.16/0.44 ( ( match @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( res @ Name @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(67)
% 0.16/0.44 thf(fact_227_pi_Odistinct_I49_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.44 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(49)
% 0.16/0.44 thf(fact_228_matchNilLeft,axiom,
% 0.16/0.44 ! [A2: name,B3: name,Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.16/0.44 ( ( A2 != B3 )
% 0.16/0.44 => ( strong743114133lation @ piNil @ Rel @ ( match @ A2 @ B3 @ P ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % matchNilLeft
% 0.16/0.44 thf(fact_229_freeRes_Ocase_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,F1: name > name > A,F22: A,X11: name,X122: name] :
% 0.16/0.44 ( ( late_case_freeRes @ A @ F1 @ F22 @ ( late_OutputR @ X11 @ X122 ) )
% 0.16/0.44 = ( F1 @ X11 @ X122 ) ) ).
% 0.16/0.44
% 0.16/0.44 % freeRes.case(1)
% 0.16/0.44 thf(fact_230_pi_Ostrong__induct,axiom,
% 0.16/0.44 ! [N: $tType] :
% 0.16/0.44 ( ( fs_name @ N )
% 0.16/0.44 => ! [P: N > pi > $o,Z: N,Pi4: pi] :
% 0.16/0.44 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 0.16/0.44 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Pi3: pi,Z2: N] :
% 0.16/0.44 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 0.16/0.44 ( ( fresh @ name @ N @ Name22 @ Z2 )
% 0.16/0.44 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 0.16/0.44 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 0.16/0.44 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 0.16/0.44 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.16/0.44 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.16/0.44 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.16/0.44 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.44 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.16/0.44 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.16/0.44 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.16/0.44 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.44 => ( ! [Name2: name,Pi3: pi,Z2: N] :
% 0.16/0.44 ( ( fresh @ name @ N @ Name2 @ Z2 )
% 0.16/0.44 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
% 0.16/0.44 => ( ! [Pi3: pi,Z2: N] :
% 0.16/0.44 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.16/0.44 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.strong_induct
% 0.16/0.44 thf(fact_231_pi_Ostrong__inducts,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( fs_name @ A )
% 0.16/0.44 => ! [P: A > pi > $o,Z: A,Pi4: pi] :
% 0.16/0.44 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 0.16/0.44 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Pi3: pi,Z2: A] :
% 0.16/0.44 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 0.16/0.44 ( ( fresh @ name @ A @ Name22 @ Z2 )
% 0.16/0.44 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 0.16/0.44 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 0.16/0.44 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 0.16/0.44 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
% 0.16/0.44 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 0.16/0.44 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.16/0.44 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 0.16/0.44 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.44 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 0.16/0.44 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.16/0.44 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 0.16/0.44 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.44 => ( ! [Name2: name,Pi3: pi,Z2: A] :
% 0.16/0.44 ( ( fresh @ name @ A @ Name2 @ Z2 )
% 0.16/0.44 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
% 0.16/0.44 => ( ! [Pi3: pi,Z2: A] :
% 0.16/0.44 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.16/0.44 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.16/0.44 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.strong_inducts
% 0.16/0.44 thf(fact_232_pi_Ofresh_I10_J,axiom,
% 0.16/0.44 ! [A2: name,X1: pi] :
% 0.16/0.44 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 0.16/0.44 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.fresh(10)
% 0.16/0.44 thf(fact_233_pi_Ofresh_I7_J,axiom,
% 0.16/0.44 ! [A2: name,X2: pi,X1: pi] :
% 0.16/0.44 ( ( fresh @ name @ pi @ A2 @ ( sum @ X2 @ X1 ) )
% 0.16/0.44 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.16/0.44 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.fresh(7)
% 0.16/0.44 thf(fact_234_simps_I10_J,axiom,
% 0.16/0.44 ! [P: pi,C3: name,D: name] :
% 0.16/0.44 ( ( subs @ ( bang @ P ) @ C3 @ D )
% 0.16/0.44 = ( bang @ ( subs @ P @ C3 @ D ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % simps(10)
% 0.16/0.44 thf(fact_235_simps_I7_J,axiom,
% 0.16/0.44 ! [P: pi,Q: pi,C3: name,D: name] :
% 0.16/0.44 ( ( subs @ ( sum @ P @ Q ) @ C3 @ D )
% 0.16/0.44 = ( sum @ ( subs @ P @ C3 @ D ) @ ( subs @ Q @ C3 @ D ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % simps(7)
% 0.16/0.44 thf(fact_236_pi_Odistinct_I63_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( match @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(63)
% 0.16/0.44 thf(fact_237_pi_Odistinct_I69_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 0.16/0.44 ( ( match @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( bang @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(69)
% 0.16/0.44 thf(fact_238_bangCases,axiom,
% 0.16/0.44 ! [P: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 0.16/0.44 => ~ ! [P4: pi] :
% 0.16/0.44 ( ( ( bang @ P )
% 0.16/0.44 = ( bang @ P4 ) )
% 0.16/0.44 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bangCases
% 0.16/0.44 thf(fact_239_Bang,axiom,
% 0.16/0.44 ! [P: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 0.16/0.44 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 0.16/0.44
% 0.16/0.44 % Bang
% 0.16/0.44 thf(fact_240_pi_Odistinct_I53_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(53)
% 0.16/0.44 thf(fact_241_pi_Odistinct_I59_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 0.16/0.44 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( bang @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(59)
% 0.16/0.44 thf(fact_242_pi_Odistinct_I89_J,axiom,
% 0.16/0.44 ! [Name3: name,Pi4: pi,Pi: pi] :
% 0.16/0.44 ( ( res @ Name3 @ Pi4 )
% 0.16/0.44 != ( bang @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(89)
% 0.16/0.44 thf(fact_243_pi_Odistinct_I87_J,axiom,
% 0.16/0.44 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.16/0.44 ( ( par @ Pi1 @ Pi2 )
% 0.16/0.44 != ( bang @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(87)
% 0.16/0.44 thf(fact_244_sumCases,axiom,
% 0.16/0.44 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.16/0.44 => ( ~ ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sumCases
% 0.16/0.44 thf(fact_245_sumCases_H,axiom,
% 0.16/0.44 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.16/0.44 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.16/0.44 => ( ~ ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sumCases'
% 0.16/0.44 thf(fact_246_Sum1,axiom,
% 0.16/0.44 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.16/0.44 ( ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sum1
% 0.16/0.44 thf(fact_247_Sum2,axiom,
% 0.16/0.44 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.16/0.44 ( ( late_transitions @ Q @ Rs )
% 0.16/0.44 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sum2
% 0.16/0.44 thf(fact_248_pi_Odistinct_I81_J,axiom,
% 0.16/0.44 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.16/0.44 ( ( sum @ Pi1 @ Pi2 )
% 0.16/0.44 != ( res @ Name @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(81)
% 0.16/0.44 thf(fact_249_pi_Odistinct_I79_J,axiom,
% 0.16/0.44 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( sum @ Pi1 @ Pi2 )
% 0.16/0.44 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(79)
% 0.16/0.44 thf(fact_250_pi_Oinject_I9_J,axiom,
% 0.16/0.44 ! [X1: pi,Y1: pi] :
% 0.16/0.44 ( ( ( bang @ X1 )
% 0.16/0.44 = ( bang @ Y1 ) )
% 0.16/0.44 = ( X1 = Y1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.inject(9)
% 0.16/0.44 thf(fact_251_pi_Oinject_I6_J,axiom,
% 0.16/0.44 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.16/0.44 ( ( ( sum @ X2 @ X1 )
% 0.16/0.44 = ( sum @ Y22 @ Y1 ) )
% 0.16/0.44 = ( ( X2 = Y22 )
% 0.16/0.44 & ( X1 = Y1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.inject(6)
% 0.16/0.44 thf(fact_252_pi_Odistinct_I83_J,axiom,
% 0.16/0.44 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.16/0.44 ( ( sum @ Pi1 @ Pi2 )
% 0.16/0.44 != ( bang @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(83)
% 0.16/0.44 thf(fact_253_pi_Odistinct_I27_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(27)
% 0.16/0.44 thf(fact_254_pi_Odistinct_I33_J,axiom,
% 0.16/0.44 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 0.16/0.44 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.16/0.44 != ( bang @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(33)
% 0.16/0.44 thf(fact_255_pi_Odistinct_I41_J,axiom,
% 0.16/0.44 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( tau @ Pi4 )
% 0.16/0.44 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(41)
% 0.16/0.44
% 0.16/0.44 % Type constructors (7)
% 0.16/0.44 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.16/0.44 fs_name @ pi ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Agent_Ofs__name_1,axiom,
% 0.16/0.44 fs_name @ $o ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Agent_Oname___Agent_Ofs__name_2,axiom,
% 0.16/0.44 fs_name @ name ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3,axiom,
% 0.16/0.44 ! [A7: $tType,A8: $tType] :
% 0.16/0.44 ( ( ( fs_name @ A7 )
% 0.16/0.44 & ( fs_name @ A8 ) )
% 0.16/0.44 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4,axiom,
% 0.16/0.44 fs_name @ late_freeRes ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5,axiom,
% 0.16/0.44 fs_name @ late_subject ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6,axiom,
% 0.16/0.44 fs_name @ late_residual ).
% 0.16/0.44
% 0.16/0.44 % Helper facts (3)
% 0.16/0.44 thf(help_If_3_1_T,axiom,
% 0.16/0.44 ! [P: $o] :
% 0.16/0.44 ( ( P = $true )
% 0.16/0.44 | ( P = $false ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(help_If_2_1_T,axiom,
% 0.16/0.44 ! [A: $tType,X3: A,Y: A] :
% 0.16/0.44 ( ( if @ A @ $false @ X3 @ Y )
% 0.16/0.44 = Y ) ).
% 0.16/0.44
% 0.16/0.44 thf(help_If_1_1_T,axiom,
% 0.16/0.44 ! [A: $tType,X3: A,Y: A] :
% 0.16/0.44 ( ( if @ A @ $true @ X3 @ Y )
% 0.16/0.44 = X3 ) ).
% 0.16/0.44
% 0.16/0.44 % Conjectures (1)
% 0.16/0.44 thf(conj_0,conjecture,
% 0.16/0.44 x != aa ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 3.64/1.92 ---- Embedded in THF ---
% 3.64/1.92 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.64/1.92 %%% Generated on Tue Feb 24 08:29:43 EST 2026
% 3.64/1.92 %%% using '$$dhol' embedding, version 1.3.0.
% 3.64/1.92 %%% Logic specification used:
% 3.64/1.92 %%% thf(spec, logic, $$dhol).
% 3.64/1.92
% 3.64/1.92 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2DTF641.p
% 3.64/1.92 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 3.64/1.92 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 3.64/1.92 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 3.64/1.92 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.64/1.92 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 3.64/1.92 thf(ty_t_Agent_Oname, type, name: $tType).
% 3.64/1.92 thf(ty_t_Agent_Opi, type, pi: $tType).
% 3.64/1.92 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.64/1.92 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OBang, type, bang: (pi > pi)).
% 3.64/1.92 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OMatch, type, match: (name > (name > (pi > pi)))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OMismatch, type, mismatch: (name > (name > (pi > pi)))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 3.64/1.92 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 3.64/1.92 thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 3.64/1.92 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 3.64/1.92 thf(sy_c_Agent_Osubst__name, type, subst_name: (name > (name > (name > name)))).
% 3.64/1.92 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.64/1.92 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes, type, late_case_freeRes: (!> [A:$tType]: (((name > (name > A)) > (A > (late_freeRes > A)))))).
% 3.64/1.92 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 3.64/1.92 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 3.64/1.92 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 3.64/1.92 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 3.64/1.92 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 3.64/1.92 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 3.64/1.92 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 3.64/1.92 thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 3.64/1.92 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 3.64/1.92 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 3.64/1.92 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 3.64/1.92 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.64/1.92 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 3.64/1.92 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 3.64/1.92 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 3.64/1.92 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.64/1.92 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 3.64/1.92 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 3.64/1.92 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.64/1.92 thf(sy_v_P, type, p: pi).
% 3.64/1.92 thf(sy_v_PQ____, type, pq: pi).
% 3.64/1.92 thf(sy_v_P_H____, type, p2: pi).
% 3.64/1.92 thf(sy_v_Q, type, q: pi).
% 3.64/1.92 thf(sy_v_Q_H____, type, q2: pi).
% 3.64/1.92 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 3.64/1.92 thf(sy_v__092_060alpha_062____, type, alpha: late_freeRes).
% 3.64/1.92 thf(sy_v_aa____, type, aa: name).
% 3.64/1.92 thf(sy_v_x, type, x: name).
% 3.64/1.92 thf(sy_v_xPQ____, type, xPQ: pi).
% 3.64/1.92 thf(sy_v_y____, type, y: name).
% 3.64/1.92 thf(sy_v_z____, type, z: name).
% 3.64/1.92 thf(fact_0_cClose1_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ y) @ p)).
% 3.64/1.92 thf(fact_1_cClose1_Ohyps_I7_J, axiom, ((((fresh @ name) @ pi) @ y) @ q2)).
% 3.64/1.92 thf(fact_2_cClose1_Ohyps_I6_J, axiom, (y != z)).
% 3.64/1.92 thf(fact_3_assms_I1_J, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 3.64/1.92 thf(fact_4_cClose1_Ohyps_I12_J, axiom, ((((fresh @ name) @ name) @ y) @ x)).
% 3.64/1.92 thf(fact_5_cClose1_Ohyps_I5_J, axiom, (y != aa)).
% 3.64/1.92 thf(fact_6_cClose1_Ohyps_I4_J, axiom, ((((fresh @ name) @ pi) @ y) @ q)).
% 3.64/1.92 thf(fact_7_cClose1_Ohyps_I11_J, axiom, ((((fresh @ name) @ pi) @ z) @ p2)).
% 3.64/1.92 thf(fact_8_cClose1_Ohyps_I1_J, axiom, ((late_transitions @ p) @ (((late_BoundR @ (late_InputS @ aa)) @ y) @ p2))).
% 3.64/1.92 thf(fact_9_cClose1_Ohyps_I10_J, axiom, (z != aa)).
% 3.64/1.92 thf(fact_10_cClose1_Ohyps_I13_J, axiom, ((((fresh @ name) @ name) @ z) @ x)).
% 3.64/1.92 thf(fact_11_cClose1_Ohyps_I8_J, axiom, ((((fresh @ name) @ pi) @ z) @ p)).
% 3.64/1.92 thf(fact_12_cRes_Ohyps_I2_J, axiom, ((((fresh @ name) @ late_freeRes) @ x) @ alpha)).
% 3.64/1.92 thf(fact_13_assms_I3_J, axiom, ((eqvt @ pi) @ rel)).
% 3.64/1.92 thf(fact_14_cClose1_Ohyps_I14_J, axiom, (alpha = late_TauR)).
% 3.64/1.92 thf(fact_15_cClose1_Ohyps_I2_J, axiom, ((late_transitions @ q) @ (((late_BoundR @ (late_BoundOutputS @ aa)) @ z) @ q2))).
% 3.64/1.92 thf(fact_16_cClose1_Ohyps_I9_J, axiom, ((((fresh @ name) @ pi) @ z) @ q)).
% 3.64/1.92 thf(fact_17_Free_Ohyps, axiom, ((late_transitions @ ((res @ x) @ ((par @ p) @ q))) @ ((late_FreeR @ alpha) @ xPQ))).
% 3.64/1.92 thf(fact_18_cRes_Ohyps_I1_J, axiom, ((late_transitions @ ((par @ p) @ q)) @ ((late_FreeR @ alpha) @ pq))).
% 3.64/1.92 thf(fact_19_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 3.64/1.92 thf(fact_20_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)))))).
% 3.64/1.92 thf(fact_21_freshFreeDerivative_I1_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_freeRes) @ Y) @ Alpha)))))).
% 3.64/1.92 thf(fact_22_resCasesF, axiom, (! [X3:name,P:pi,Alpha:late_freeRes,XP:pi,F:(pi > $o)]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha) => (F @ ((res @ X3) @ P3)))))) => (F @ XP)))))).
% 3.64/1.92 thf(fact_23_resCasesF_H, axiom, (! [X3:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y2:name]: (((((res @ X3) @ P) = ((res @ Y2) @ P4)) => ((((late_FreeR @ Alpha) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y2) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y2) @ Alpha2)))))))))))))).
% 3.64/1.92 thf(fact_24_ResF, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha) => ((late_transitions @ ((res @ Y) @ P)) @ ((late_FreeR @ Alpha) @ ((res @ Y) @ P2)))))))).
% 3.64/1.92 thf(fact_25_Res, axiom, (! [Y:name,R:pi,S:pi]: ((((((fresh @ name) @ pi) @ Y) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R) @ ((res @ Y) @ S))) @ ((res @ Y) @ ((par @ R) @ S)))) @ rel))))).
% 3.64/1.92 thf(fact_26_ScopeExt, axiom, (! [Y:name,R:pi,Z:name,S:pi]: ((((((fresh @ name) @ pi) @ Y) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ Z) @ ((par @ R) @ ((res @ Y) @ S)))) @ ((res @ Y) @ ((res @ Z) @ ((par @ R) @ S))))) @ rel))))).
% 3.64/1.92 thf(fact_27_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)))))))).
% 3.64/1.92 thf(fact_28_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)))))))).
% 3.64/1.92 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 3.64/1.92 thf(fact_30_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A3:name,B2:name]: ((A3 != B2))))).
% 3.64/1.92 thf(fact_31_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X3:A]: ((~ ((! [C2:name]: ((~ (((((fresh @ name) @ A) @ C2) @ X3))))))))))))).
% 3.64/1.92 thf(fact_32_pi_Oinject_I7_J, axiom, (! [X2:pi,X1:pi,Y22:pi,Y1:pi]: (((((par @ X2) @ X1) = ((par @ Y22) @ Y1)) = ((X2 = Y22) & (X1 = Y1)))))).
% 3.64/1.92 thf(fact_33_residual_Oinject_I2_J, axiom, (! [X2:late_freeRes,X1:pi,Y22:late_freeRes,Y1:pi]: (((((late_FreeR @ X2) @ X1) = ((late_FreeR @ Y22) @ Y1)) = ((X2 = Y22) & (X1 = Y1)))))).
% 3.64/1.92 thf(fact_34_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_35_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 3.64/1.92 thf(fact_36_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject:late_subject,Name2:name,Pi3:pi]: ((P @ (((late_BoundR @ Subject) @ Name2) @ Pi3)))) => ((! [FreeRes:late_freeRes,Pi3:pi]: ((P @ ((late_FreeR @ FreeRes) @ Pi3)))) => (P @ Residual)))))).
% 3.64/1.92 thf(fact_37_residual_Odistinct_I1_J, axiom, (! [Subject2:late_subject,Name3:name,Pi4:pi,FreeRes2:late_freeRes,Pi:pi]: (((((late_BoundR @ Subject2) @ Name3) @ Pi4) != ((late_FreeR @ FreeRes2) @ Pi))))).
% 3.64/1.92 thf(fact_38_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject2:late_subject]: (((! [Name2:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name2)))) => ((! [Name2:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name2)))) => ((P @ Z) @ Subject2)))))).
% 3.64/1.92 thf(fact_39_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject2:late_subject]: (((! [Name2:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name2)))) => ((! [Name2:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name2)))) => ((P @ Z) @ Subject2)))))).
% 3.64/1.92 thf(fact_40_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject2:late_subject]: (((! [Name2:name]: ((P @ (late_InputS @ Name2)))) => ((! [Name2:name]: ((P @ (late_BoundOutputS @ Name2)))) => (P @ Subject2)))))).
% 3.64/1.92 thf(fact_41_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name3:name,Name:name]: (((late_InputS @ Name3) != (late_BoundOutputS @ Name))))).
% 3.64/1.92 thf(fact_42_Par2F, axiom, (! [Q:pi,Alpha:late_freeRes,Q2:pi,P:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P) @ Q2))))))).
% 3.64/1.92 thf(fact_43_Par1F, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Q:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P2) @ Q))))))).
% 3.64/1.92 thf(fact_44_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((Y != X3) => ((((fresh @ name) @ pi) @ Y) @ P2))))))).
% 3.64/1.92 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.64/1.92 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A4)))) = A4)))).
% 3.64/1.92 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.64/1.92 thf(fact_48_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject:late_subject,Name2:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name2) @ Z2) => (((((fresh @ name) @ late_subject) @ Name2) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name2) @ Pi3)))))) => ((! [FreeRes:late_freeRes,Pi3:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi3)))) => ((P @ Z) @ Residual))))))))).
% 3.64/1.92 thf(fact_49_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject:late_subject,Name2:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name2) @ Z2) => (((((fresh @ name) @ late_subject) @ Name2) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name2) @ Pi3)))))) => ((! [FreeRes:late_freeRes,Pi3:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi3)))) => ((P @ Z) @ Residual))))))))).
% 3.64/1.92 thf(fact_50_freshFreeDerivative_I2_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ pi) @ Y) @ P2)))))).
% 3.64/1.92 thf(fact_51_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X3:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ PQ)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((! [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P3)) => (Prop @ ((par @ P3) @ Q))))) => ((! [Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q3)) => (Prop @ ((par @ P) @ Q3))))) => (Prop @ PQ))))))))).
% 3.64/1.92 thf(fact_52_fresh__prod, axiom, (! [A:$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)))))).
% 3.64/1.92 thf(fact_53_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))))))))))))))))))).
% 3.64/1.92 thf(fact_54_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)))))))))))))))))).
% 3.64/1.92 thf(fact_55_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))))))))))).
% 3.64/1.92 thf(fact_56_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)))))))))).
% 3.64/1.92 thf(fact_57_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 3.64/1.92 thf(fact_58_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X2:name,Y22:name]: ((((late_BoundOutputS @ X2) = (late_BoundOutputS @ Y22)) = (X2 = Y22))))).
% 3.64/1.92 thf(fact_59_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B3:B,A5:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B3) = ((((product_Pair @ A) @ B) @ A5) @ B4)) = ((A2 = A5) & (B3 = B4)))))).
% 3.64/1.92 thf(fact_60_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X1 = Y1) & (X2 = Y22)))))).
% 3.64/1.92 thf(fact_61_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 3.64/1.92 thf(fact_62_simps_I9_J, axiom, (! [X3:name,C3:name,D:name,P:pi]: (((X3 != C3) => ((X3 != D) => ((((subs @ ((res @ X3) @ P)) @ C3) @ D) = ((res @ X3) @ (((subs @ P) @ C3) @ D)))))))).
% 3.64/1.92 thf(fact_63_simps_I8_J, axiom, (! [P:pi,Q:pi,C3:name,D:name]: (((((subs @ ((par @ P) @ Q)) @ C3) @ D) = ((par @ (((subs @ P) @ C3) @ D)) @ (((subs @ Q) @ C3) @ D)))))).
% 3.64/1.92 thf(fact_64_substTrans, axiom, (! [B3:name,P:pi,A2:name,C3:name]: ((((((fresh @ name) @ pi) @ B3) @ P) => ((((subs @ (((subs @ P) @ A2) @ B3)) @ B3) @ C3) = (((subs @ P) @ A2) @ C3)))))).
% 3.64/1.92 thf(fact_65_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)))))).
% 3.64/1.92 thf(fact_66_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.64/1.92 thf(fact_67_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.64/1.92 thf(fact_68_forget, axiom, (! [A2:name,P:pi,B3:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B3) = P))))).
% 3.64/1.92 thf(fact_69_fresh__fact1, axiom, (! [A2:name,P:pi,C3:name,B3:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C3) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B3) @ C3))))))).
% 3.64/1.92 thf(fact_70_fresh__fact2, axiom, (! [A2:name,B3:name,P:pi]: (((A2 != B3) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B3)))))).
% 3.64/1.92 thf(fact_71_freshResidual, axiom, (! [P:pi,Rs:late_residual,X3:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X3) @ P) => ((((fresh @ name) @ late_residual) @ X3) @ Rs)))))).
% 3.64/1.92 thf(fact_72_substRes2, axiom, (! [B3:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B3) @ P) => (((res @ A2) @ P) = ((res @ B3) @ (((subs @ P) @ A2) @ B3))))))).
% 3.64/1.92 thf(fact_73_Agent_OsubstRes3, axiom, (! [B3:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B3) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B3) = ((res @ B3) @ (((subs @ P) @ A2) @ B3))))))).
% 3.64/1.92 thf(fact_74_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))))))))).
% 3.64/1.92 thf(fact_75_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)))))).
% 3.64/1.92 thf(fact_76_surj__pair, axiom, (! [A:$tType,B:$tType,P5:((product_prod @ A) @ B)]: ((? [X5:A,Y2:B]: ((P5 = ((((product_Pair @ A) @ B) @ X5) @ Y2))))))).
% 3.64/1.92 thf(fact_77_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P5:((product_prod @ A) @ B)]: (((! [A6:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B5)))) => (P @ P5))))).
% 3.64/1.92 thf(fact_78_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B3:B,A5:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B3) = ((((product_Pair @ A) @ B) @ A5) @ B4)) => (~ (((A2 = A5) => (B3 != B4)))))))).
% 3.64/1.92 thf(fact_79_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A6:A,B5:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B5) @ C2)))))))))).
% 3.64/1.92 thf(fact_80_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2)))]: ((~ ((! [A6:A,B5:B,C2:C,D3:D2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D2)) @ B5) @ ((((product_Pair @ C) @ D2) @ C2) @ D3))))))))))).
% 3.64/1.92 thf(fact_81_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))))]: ((~ ((! [A6:A,B5:B,C2:C,D3:D2,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ E)) @ C2) @ ((((product_Pair @ D2) @ E) @ D3) @ E2)))))))))))).
% 3.64/1.92 thf(fact_82_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E:$tType,F2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2)))))]: ((~ ((! [A6:A,B5:B,C2:C,D3:D2,E2:E,F3:F2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F2)) @ D3) @ ((((product_Pair @ E) @ F2) @ E2) @ F3))))))))))))).
% 3.64/1.92 thf(fact_83_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E:$tType,F2:$tType,G:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))))]: ((~ ((! [A6:A,B5:B,C2:C,D3:D2,E2:E,F3:F2,G2:G]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G)) @ E2) @ ((((product_Pair @ F2) @ G) @ F3) @ G2)))))))))))))).
% 3.64/1.92 thf(fact_84_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A6:A,B5:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B5) @ C2))))) => (P @ X3))))).
% 3.64/1.92 thf(fact_85_prod__induct4, axiom, (! [D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2)))]: (((! [A6:A,B5:B,C2:C,D3:D2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D2)) @ B5) @ ((((product_Pair @ C) @ D2) @ C2) @ D3)))))) => (P @ X3))))).
% 3.64/1.92 thf(fact_86_prod__induct5, axiom, (! [E:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))))]: (((! [A6:A,B5:B,C2:C,D3:D2,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ E)) @ C2) @ ((((product_Pair @ D2) @ E) @ D3) @ E2))))))) => (P @ X3))))).
% 3.64/1.92 thf(fact_87_prod__induct6, axiom, (! [F2:$tType,E:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2)))))]: (((! [A6:A,B5:B,C2:C,D3:D2,E2:E,F3:F2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F2))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F2)) @ D3) @ ((((product_Pair @ E) @ F2) @ E2) @ F3)))))))) => (P @ X3))))).
% 3.64/1.92 thf(fact_88_prod__induct7, axiom, (! [G:$tType,F2:$tType,E:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))))]: (((! [A6:A,B5:B,C2:C,D3:D2,E2:E,F3:F2,G2:G]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G)) @ E2) @ ((((product_Pair @ F2) @ G) @ F3) @ G2))))))))) => (P @ X3))))).
% 3.64/1.92 thf(fact_89_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A6:A,B5:B]: ((Y != ((((product_Pair @ A) @ B) @ A6) @ B5))))))))).
% 3.64/1.92 thf(fact_90_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A6:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B5)))) => (P @ Prod))))).
% 3.64/1.92 thf(fact_91_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))))))))))).
% 3.64/1.92 thf(fact_92_parCasesB_H, axiom, (! [P:pi,Q:pi,B3:late_subject,Y:name,P2:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B3) @ Y) @ P2)) => ((! [P4:pi,A6:late_subject,X5:name,P3:pi,Q4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B3) @ Y) @ P2) = (((late_BoundR @ A6) @ X5) @ ((par @ P3) @ Q4))) => (((late_transitions @ P4) @ (((late_BoundR @ A6) @ X5) @ P3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6)))))))))) => (~ ((! [Q4:pi,A6:late_subject,X5:name,Q3:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B3) @ Y) @ P2) = (((late_BoundR @ A6) @ X5) @ ((par @ P4) @ Q3))) => (((late_transitions @ Q4) @ (((late_BoundR @ A6) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6))))))))))))))))).
% 3.64/1.92 thf(fact_93_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)))))))))).
% 3.64/1.92 thf(fact_94_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)))))))))).
% 3.64/1.92 thf(fact_95_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))))).
% 3.64/1.92 thf(fact_96_fresh__prodD_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,A2:A,X3:B,Y:C]: ((((((fresh @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ X3) @ Y)) => ((((fresh @ A) @ B) @ A2) @ X3))))).
% 3.64/1.92 thf(fact_97_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X2:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X2))))).
% 3.64/1.92 thf(fact_98_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X12:name]: ((Y != (late_InputS @ X12)))) => (~ ((! [X22:name]: ((Y != (late_BoundOutputS @ X22)))))))))).
% 3.64/1.92 thf(fact_99_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B3:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B3)) = ((F1 @ A2) @ B3))))).
% 3.64/1.92 thf(fact_100_resCases_H, axiom, (! [X3:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X3) @ P)) @ Rs) => ((! [P4:pi,A6:name,B5:name]: (((((res @ X3) @ P) = ((res @ B5) @ P4)) => (! [P3:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A6)) @ B5) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A6) @ B5)) @ P3)) => (A6 = B5)))))))) => ((! [P4:pi,A6:late_subject,X5:name,P3:pi,Y2:name]: (((((res @ X3) @ P) = ((res @ Y2) @ P4)) => ((Rs = (((late_BoundR @ A6) @ X5) @ ((res @ Y2) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A6) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y2) @ A6) => ((Y2 != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y2:name]: (((((res @ X3) @ P) = ((res @ Y2) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y2) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y2) @ Alpha2)))))))))))))))).
% 3.64/1.92 thf(fact_101_transitions_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B3) => (((((fresh @ name) @ pi) @ X3) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B3)) @ Q2))))))))))))).
% 3.64/1.92 thf(fact_102_transitions_OComm2, axiom, (! [P:pi,A2:name,B3:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B3) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ B3)))))))))))))).
% 3.64/1.92 thf(fact_103_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B3)) @ Q2)))))))).
% 3.64/1.92 thf(fact_104_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B3:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ 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) @ B3))))))))).
% 3.64/1.92 thf(fact_105_resCasesB_H, axiom, (! [X6:name,P:pi,A2:late_subject,Y3:name,P2:pi]: ((((late_transitions @ ((res @ X6) @ P)) @ (((late_BoundR @ A2) @ Y3) @ P2)) => ((! [P4:pi,A6:name,B5:name]: (((((res @ X6) @ P) = ((res @ B5) @ P4)) => (! [P3:pi]: ((((((late_BoundR @ A2) @ Y3) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A6)) @ B5) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A6) @ B5)) @ P3)) => (A6 = B5)))))))) => (~ ((! [P4:pi,A6:late_subject,X5:name,P3:pi,Y2:name]: (((((res @ X6) @ P) = ((res @ Y2) @ P4)) => (((((late_BoundR @ A2) @ Y3) @ P2) = (((late_BoundR @ A6) @ X5) @ ((res @ Y2) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A6) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y2) @ A6) => ((Y2 != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6)))))))))))))))))).
% 3.64/1.92 thf(fact_106_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)))))).
% 3.64/1.92 thf(fact_107_Late__Semantics_OfreeRes_Oinject, axiom, (! [X2:name,X1:name,Y22:name,Y1:name]: (((((late_OutputR @ X2) @ X1) = ((late_OutputR @ Y22) @ Y1)) = ((X2 = Y22) & (X1 = Y1)))))).
% 3.64/1.92 thf(fact_108_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)))))).
% 3.64/1.92 thf(fact_109_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name22)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 3.64/1.92 thf(fact_110_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name22)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 3.64/1.92 thf(fact_111_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name]: ((P @ ((late_OutputR @ Name1) @ Name22)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 3.64/1.92 thf(fact_112_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name12:name,Name23:name]: ((((late_OutputR @ Name12) @ Name23) != late_TauR)))).
% 3.64/1.92 thf(fact_113_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X123:name]: ((Y != ((late_OutputR @ X112) @ X123)))) => (Y = late_TauR))))).
% 3.64/1.92 thf(fact_114_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X122:name]: ((((late_OutputR @ X11) @ X122) != late_TauR)))).
% 3.64/1.92 thf(fact_115_Open, axiom, (! [P:pi,A2:name,B3:name,P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ P2)) => ((A2 != B3) => ((late_transitions @ ((res @ B3) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B3) @ P2))))))).
% 3.64/1.92 thf(fact_116_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X3:name,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [Q3:pi,A6:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A6) @ X3)) @ Q3)) => ((A6 != X3) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A6)) @ X3) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel)))))))) => ((! [Q3:pi,A6:late_subject,Y2:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A6) @ Y2) @ Q3)) => (((((fresh @ name) @ late_subject) @ X3) @ A6) => ((X3 != Y2) => (((((fresh @ name) @ A) @ Y2) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A6) @ Y2) @ P6)) & (((((strong2129052853vative @ P6) @ ((res @ X3) @ Q3)) @ A6) @ Y2) @ Rel)))))))))) => ((! [Q3:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha2) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ ((res @ X3) @ Q3))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X3) @ Q)))))))))))).
% 3.64/1.92 thf(fact_117_freeRes_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T]: (((! [X12:name,X22:name]: ((P @ ((F1 @ X12) @ X22)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ late_TauR) = F22)))))).
% 3.64/1.92 thf(fact_118_subject_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F22 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_InputS @ Name3)) = (F1 @ Name3))))))).
% 3.64/1.92 thf(fact_119_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F22 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_BoundOutputS @ Name3)) = (F22 @ Name3))))))).
% 3.64/1.92 thf(fact_120_freeRes_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T,Name12:name,Name23:name]: (((! [X12:name,X22:name]: ((P @ ((F1 @ X12) @ X22)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ ((late_OutputR @ Name12) @ Name23)) = ((F1 @ Name12) @ Name23))))))).
% 3.64/1.92 thf(fact_121_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)))))))))).
% 3.64/1.92 thf(fact_122_simE_I2_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Alpha:late_freeRes,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => (? [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P3) @ Q2)) @ Rel))))))))).
% 3.64/1.92 thf(fact_123_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A6:late_subject,Y2:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A6) @ Y2) @ Q3)) => (((((fresh @ name) @ pi) @ Y2) @ P) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A6) @ Y2) @ P6)) & (((((strong2129052853vative @ P6) @ Q3) @ A6) @ Y2) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 3.64/1.92 thf(fact_124_simulation__def, axiom, (strong743114133lation = (^ [P7:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A3:late_subject,X4:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A3) @ X4) @ Q6)) & ((((fresh @ name) @ pi) @ X4) @ P7)) => (? [P8:pi]: ((((late_transitions @ P7) @ (((late_BoundR @ A3) @ X4) @ P8)) & (((((strong2129052853vative @ P8) @ Q6) @ A3) @ X4) @ Rel2))))))) & (! [Alpha3:late_freeRes,Q6:pi]: ((((late_transitions @ Q5) @ ((late_FreeR @ Alpha3) @ Q6)) => (? [P8:pi]: ((((late_transitions @ P7) @ ((late_FreeR @ Alpha3) @ P8)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P8) @ Q6)) @ Rel2)))))))))))).
% 3.64/1.92 thf(fact_125_parSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((! [R2:pi,S2:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R2) @ S2)) @ ((par @ S2) @ R2))) @ Rel))) => ((! [R2:pi,S2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ R2) @ S2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ R2)) @ ((res @ X5) @ S2))) @ Rel)))) => (((strong743114133lation @ ((par @ P) @ Q)) @ Rel) @ ((par @ Q) @ P))))))).
% 3.64/1.92 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) => ((! [A6:late_subject,X5:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A6) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P) => (((((fresh @ name) @ pi) @ X5) @ Q) => (((((fresh @ name) @ late_subject) @ X5) @ A6) => (((((fresh @ name) @ A) @ X5) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A6) @ X5) @ P6)) & (((((strong2129052853vative @ P6) @ Q3) @ A6) @ X5) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 3.64/1.92 thf(fact_127_parAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((! [S2:pi,T2:pi,U:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((par @ S2) @ T2)) @ U)) @ ((par @ S2) @ ((par @ T2) @ U)))) @ Rel))) => ((! [S2:pi,T2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ S2) @ T2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ S2)) @ ((res @ X5) @ T2))) @ Rel)))) => ((! [S2:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ S2) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ ((par @ ((par @ S2) @ T2)) @ U))) @ ((par @ S2) @ ((res @ X5) @ ((par @ T2) @ U))))) @ Rel)))) => ((! [S2:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ U) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ X5) @ ((par @ S2) @ T2))) @ U)) @ ((res @ X5) @ ((par @ S2) @ ((par @ T2) @ U))))) @ Rel)))) => (((strong743114133lation @ ((par @ ((par @ P) @ Q)) @ R)) @ Rel) @ ((par @ P) @ ((par @ Q) @ R)))))))))).
% 3.64/1.92 thf(fact_128_resTauOutputTrans, axiom, (! [X3:name,P:pi,A2:name,B3:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ P2))))))).
% 3.64/1.92 thf(fact_129_resOutputTauTrans, axiom, (! [X3:name,A2:name,B3:name,P:pi,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ B3) @ P))) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 3.64/1.92 thf(fact_130_resOutputInputTrans, axiom, (! [X3:name,A2:name,B3:name,P:pi,C3:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ B3) @ P))) @ (((late_BoundR @ (late_InputS @ C3)) @ Y) @ P2))))))).
% 3.64/1.92 thf(fact_131_resOutputOutputTrans, axiom, (! [X3:name,A2:name,P:pi,B3:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ X3) @ P))) @ ((late_FreeR @ ((late_OutputR @ B3) @ Y)) @ P2))))))).
% 3.64/1.92 thf(fact_132_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 3.64/1.92 thf(fact_133_simps_I2_J, axiom, (! [P:pi,C3:name,D:name]: (((((subs @ (tau @ P)) @ C3) @ D) = (tau @ (((subs @ P) @ C3) @ D)))))).
% 3.64/1.92 thf(fact_134_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))))))).
% 3.64/1.92 thf(fact_135_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 3.64/1.92 thf(fact_136_pi_Oinject_I1_J, axiom, (! [X32:name,X2:name,X1:pi,Y32:name,Y22:name,Y1:pi]: ((((((output @ X32) @ X2) @ X1) = (((output @ Y32) @ Y22) @ Y1)) = ((X32 = Y32) & ((X2 = Y22) & (X1 = Y1))))))).
% 3.64/1.92 thf(fact_137_pi_Odistinct_I19_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (tau @ Pi))))).
% 3.64/1.92 thf(fact_138_pi_Odistinct_I31_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name:name,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_139_pi_Odistinct_I29_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name23) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_140_pi_Odistinct_I45_J, axiom, (! [Pi4:pi,Name:name,Pi:pi]: (((tau @ Pi4) != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_141_pi_Odistinct_I43_J, axiom, (! [Pi4:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_142_resTrans_I1_J, axiom, (! [X3:name,B3:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ X3) @ B3) @ P))) @ Rs)))))).
% 3.64/1.92 thf(fact_143_outputBoundTrans, axiom, (! [A2:name,B3:name,P:pi,C3:late_subject,X3:name,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B3) @ P)) @ (((late_BoundR @ C3) @ X3) @ P2))))))).
% 3.64/1.92 thf(fact_144_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X3) @ P2))))))).
% 3.64/1.92 thf(fact_145_resTauBoundTrans, axiom, (! [X3:name,P:pi,A2:late_subject,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y) @ P2))))))).
% 3.64/1.92 thf(fact_146_Output, axiom, (! [A2:name,B3:name,P:pi]: (((late_transitions @ (((output @ A2) @ B3) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ P))))).
% 3.64/1.92 thf(fact_147_outputIneqTrans, axiom, (! [A2:name,B3:name,P:pi,C3:name,D:name,P2:pi]: ((((late_transitions @ (((output @ A2) @ B3) @ P)) @ ((late_FreeR @ ((late_OutputR @ C3) @ D)) @ P2)) => (~ (((A2 != C3) | (B3 != D)))))))).
% 3.64/1.92 thf(fact_148_outputCases_H, axiom, (! [A2:name,B3:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B3) @ P)) @ Rs) => (~ ((! [A6:name,B5:name,P4:pi]: ((((A2 = A6) & ((B3 = B5) & (P = P4))) => (Rs != ((late_FreeR @ ((late_OutputR @ A6) @ B5)) @ P4))))))))))).
% 3.64/1.92 thf(fact_149_outputCases, axiom, (! [A2:name,B3:name,P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (((output @ A2) @ B3) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = ((late_OutputR @ A2) @ B3)) => ((P = P2) => ((Prop @ ((late_OutputR @ A2) @ B3)) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 3.64/1.92 thf(fact_150_outputTauTrans, axiom, (! [A2:name,B3:name,P:pi,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B3) @ P)) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 3.64/1.92 thf(fact_151_tauOutputTrans, axiom, (! [P:pi,A2:name,B3:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B3)) @ P2))))))).
% 3.64/1.92 thf(fact_152_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 3.64/1.92 thf(fact_153_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))))))))))).
% 3.64/1.92 thf(fact_154_tauCases, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (tau @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = late_TauR) => ((P = P2) => ((Prop @ late_TauR) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 3.64/1.92 thf(fact_155_outputFreshTrans, axiom, (! [A2:name,B3:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ (((output @ A2) @ B3) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((((((fresh @ name) @ late_freeRes) @ A2) @ Alpha) | ((((fresh @ name) @ late_freeRes) @ B3) @ Alpha)))))))).
% 3.64/1.92 thf(fact_156_resInputBoundOutputTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,B3:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B3)) @ Z) @ P2))))))).
% 3.64/1.92 thf(fact_157_residual_Ofresh_I1_J, axiom, (! [A2:name,X32:late_subject,X1:name,X2:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ (((late_BoundR @ X32) @ X1) @ X2)) = (((((fresh @ name) @ late_subject) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X2))))))).
% 3.64/1.92 thf(fact_158_simps_I3_J, axiom, (! [A2:name,B3:name,P:pi,C3:name,D:name]: (((((subs @ (((output @ A2) @ B3) @ P)) @ C3) @ D) = (((output @ (((subst_name @ A2) @ C3) @ D)) @ (((subst_name @ B3) @ C3) @ D)) @ (((subs @ P) @ C3) @ D)))))).
% 3.64/1.92 thf(fact_159_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B3:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B3)) = ((C3 @ A2) @ B3))))).
% 3.64/1.92 thf(fact_160_simps_I4_J, axiom, (! [X3:name,A2:name,C3:name,D:name,P:pi]: (((X3 != A2) => ((X3 != C3) => ((X3 != D) => ((((subs @ (((input @ A2) @ X3) @ P)) @ C3) @ D) = (((input @ (((subst_name @ A2) @ C3) @ D)) @ X3) @ (((subs @ P) @ C3) @ D))))))))).
% 3.64/1.92 thf(fact_161_substInput, axiom, (! [X3:name,B3:name,C3:name,A2:name,P:pi]: (((X3 != B3) => ((X3 != C3) => ((((subs @ (((input @ A2) @ X3) @ P)) @ B3) @ C3) = (((input @ (((subst_name @ A2) @ B3) @ C3)) @ X3) @ (((subs @ P) @ B3) @ C3)))))))).
% 3.64/1.92 thf(fact_162_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)))))).
% 3.64/1.92 thf(fact_163_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))))))).
% 3.64/1.92 thf(fact_164_pi_Odistinct_I57_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name:name,Pi:pi]: (((((input @ Name12) @ Name23) @ Pi4) != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_165_pi_Odistinct_I55_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name23) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_166_pi_Oinject_I8_J, axiom, (! [X1:name,X2:pi,Y1:name,Y22:pi]: (((((res @ X1) @ X2) = ((res @ Y1) @ Y22)) = (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22)))))).
% 3.64/1.92 thf(fact_167_subst__name__def, axiom, (subst_name = (^ [A3:name,B2:name,C5:name]: (((((if @ name) @ (A3 = B2)) @ C5) @ A3))))).
% 3.64/1.92 thf(fact_168_pi_Oinject_I3_J, axiom, (! [X32:name,X1:name,X2:pi,Y32:name,Y1:name,Y22:pi]: ((((((input @ X32) @ X1) @ X2) = (((input @ Y32) @ Y1) @ Y22)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22))))))).
% 3.64/1.92 thf(fact_169_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))))).
% 3.64/1.92 thf(fact_170_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B3:name,A2:name,X3:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B3) @ ((((abs_fun @ name) @ A) @ A2) @ X3)) = ((B3 = A2) | ((((fresh @ name) @ A) @ B3) @ X3))))))))).
% 3.64/1.92 thf(fact_171_abs__fresh_I1_J, axiom, (! [X7:$tType]: (((fs_name @ X7) => (! [B3:name,A2:name,X3:X7]: ((((((fresh @ name) @ (name > (noption @ X7))) @ B3) @ ((((abs_fun @ name) @ X7) @ A2) @ X3)) = ((B3 = A2) | ((((fresh @ name) @ X7) @ B3) @ X3))))))))).
% 3.64/1.92 thf(fact_172_residual_Oinject_I1_J, axiom, (! [X32:late_subject,X1:name,X2:pi,Y32:late_subject,Y1:name,Y22:pi]: ((((((late_BoundR @ X32) @ X1) @ X2) = (((late_BoundR @ Y32) @ Y1) @ Y22)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22))))))).
% 3.64/1.92 thf(fact_173_pi_Odistinct_I21_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (((input @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_174_pi_Odistinct_I35_J, axiom, (! [Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi4) != (((input @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_175_inputCases_H, axiom, (! [A2:name,B3:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B3) @ P)) @ Rs) => (~ ((! [X5:name,A6:name,P4:pi]: ((((A2 = A6) & (((((abs_fun @ name) @ pi) @ B3) @ P) = ((((abs_fun @ name) @ pi) @ X5) @ P4))) => ((Rs = (((late_BoundR @ (late_InputS @ A6)) @ X5) @ P4)) => (X5 = A6))))))))))).
% 3.64/1.92 thf(fact_176_resTrans_I2_J, axiom, (! [X3:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ X3) @ Y) @ P))) @ Rs)))))).
% 3.64/1.92 thf(fact_177_inputFreeTrans, axiom, (! [A2:name,X3:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ ((late_FreeR @ Alpha) @ P2))))))).
% 3.64/1.92 thf(fact_178_resInputFreeTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ ((late_FreeR @ Alpha) @ P2))))))).
% 3.64/1.92 thf(fact_179_Late__Semantics_OInput, axiom, (! [A2:name,X3:name,P:pi]: (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P))))).
% 3.64/1.92 thf(fact_180_transitions_OInput, axiom, (! [X3:name,A2:name,P:pi]: (((X3 != A2) => ((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P)))))).
% 3.64/1.92 thf(fact_181_inputBoundOutputTrans, axiom, (! [A2:name,X3:name,P:pi,B3:name,Y:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B3)) @ Y) @ P2))))))).
% 3.64/1.92 thf(fact_182_inputIneqTrans, axiom, (! [A2:name,X3:name,P:pi,B3:late_subject,Y:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ B3) @ Y) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B3))))))).
% 3.64/1.92 thf(fact_183_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)))))).
% 3.64/1.92 thf(fact_184_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))))).
% 3.64/1.92 thf(fact_185_simps_I6_J, axiom, (! [A2:name,B3:name,P:pi,C3:name,D:name]: (((((subs @ (((mismatch @ A2) @ B3) @ P)) @ C3) @ D) = (((mismatch @ (((subst_name @ A2) @ C3) @ D)) @ (((subst_name @ B3) @ C3) @ D)) @ (((subs @ P) @ C3) @ D)))))).
% 3.64/1.92 thf(fact_186_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 3.64/1.92 thf(fact_187_simps_I1_J, axiom, (! [C3:name,D:name]: (((((subs @ piNil) @ C3) @ D) = piNil)))).
% 3.64/1.92 thf(fact_188_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))))))).
% 3.64/1.92 thf(fact_189_pi_Odistinct_I5_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((input @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_190_pi_Odistinct_I51_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((input @ Name12) @ Name23) @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_191_pi_Odistinct_I75_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name:name,Pi:pi]: (((((mismatch @ Name12) @ Name23) @ Pi4) != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_192_pi_Odistinct_I73_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name12) @ Name23) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_193_pi_Odistinct_I15_J, axiom, (! [Name:name,Pi:pi]: ((piNil != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_194_pi_Odistinct_I13_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((par @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_195_pi_Odistinct_I25_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_196_nilSimRight, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: ((((strong743114133lation @ P) @ Rel) @ piNil)))).
% 3.64/1.92 thf(fact_197_pi_Odistinct_I1_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((output @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_198_pi_Odistinct_I39_J, axiom, (! [Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_199_pi_Odistinct_I3_J, axiom, (! [Pi:pi]: ((piNil != (tau @ Pi))))).
% 3.64/1.92 thf(fact_200_mismatchNilLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,P:pi]: ((((strong743114133lation @ piNil) @ Rel) @ (((mismatch @ A2) @ A2) @ P))))).
% 3.64/1.92 thf(fact_201_pi_Oinject_I5_J, axiom, (! [X32:name,X2:name,X1:pi,Y32:name,Y22:name,Y1:pi]: ((((((mismatch @ X32) @ X2) @ X1) = (((mismatch @ Y32) @ Y22) @ Y1)) = ((X32 = Y32) & ((X2 = Y22) & (X1 = Y1))))))).
% 3.64/1.92 thf(fact_202_pi_Odistinct_I9_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_203_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 3.64/1.92 thf(fact_204_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 3.64/1.92 thf(fact_205_mismatchCases, axiom, (! [A2:name,B3:name,P:pi,Rs:late_residual,F:(name > (name > $o))]: ((((late_transitions @ (((mismatch @ A2) @ B3) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 != B3) => ((F @ A2) @ B3))) => ((F @ A2) @ B3)))))).
% 3.64/1.92 thf(fact_206_mismatchTrans, axiom, (! [A2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ (((mismatch @ A2) @ A2) @ P)) @ Rs)))))).
% 3.64/1.92 thf(fact_207_mismatchCases_H, axiom, (! [A2:name,B3:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((mismatch @ A2) @ B3) @ P)) @ Rs) => (~ ((! [P4:pi,A6:name,B5:name]: ((((A2 = A6) & ((B3 = B5) & (P = P4))) => (((late_transitions @ P4) @ Rs) => (A6 = B5))))))))))).
% 3.64/1.92 thf(fact_208_Mismatch, axiom, (! [P:pi,Rs:late_residual,A2:name,B3:name]: ((((late_transitions @ P) @ Rs) => ((A2 != B3) => ((late_transitions @ (((mismatch @ A2) @ B3) @ P)) @ Rs)))))).
% 3.64/1.92 thf(fact_209_resZeroTrans, axiom, (! [X3:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ piNil)) @ Rs)))))).
% 3.64/1.92 thf(fact_210_nilSim_I2_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,X3:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((input @ A2) @ X3) @ P))))))).
% 3.64/1.92 thf(fact_211_nilSim_I3_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B3:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((output @ A2) @ B3) @ P))))))).
% 3.64/1.92 thf(fact_212_nilSim_I1_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (tau @ P))))))).
% 3.64/1.92 thf(fact_213_simps_I5_J, axiom, (! [A2:name,B3:name,P:pi,C3:name,D:name]: (((((subs @ (((match @ A2) @ B3) @ P)) @ C3) @ D) = (((match @ (((subst_name @ A2) @ C3) @ D)) @ (((subst_name @ B3) @ C3) @ D)) @ (((subs @ P) @ C3) @ D)))))).
% 3.64/1.92 thf(fact_214_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))))))).
% 3.64/1.92 thf(fact_215_freeRes_Ocase_I2_J, axiom, (! [A:$tType,F1:(name > (name > A)),F22:A]: ((((((late_case_freeRes @ A) @ F1) @ F22) @ late_TauR) = F22)))).
% 3.64/1.92 thf(fact_216_pi_Odistinct_I61_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((match @ Name12) @ Name23) @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_217_pi_Odistinct_I7_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((match @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_218_Match, axiom, (! [P:pi,Rs:late_residual,B3:name]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ (((match @ B3) @ B3) @ P)) @ Rs))))).
% 3.64/1.92 thf(fact_219_matchCases_H, axiom, (! [A2:name,B3:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B3) @ P)) @ Rs) => (~ ((! [P4:pi]: ((((B3 = A2) & (P = P4)) => (~ (((late_transitions @ P4) @ Rs)))))))))))).
% 3.64/1.92 thf(fact_220_matchTrans, axiom, (! [A2:name,B3:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B3) @ P)) @ Rs) => (A2 = B3))))).
% 3.64/1.92 thf(fact_221_matchCases, axiom, (! [A2:name,B3:name,P:pi,Rs:late_residual,F:(name > (name > $o))]: ((((late_transitions @ (((match @ A2) @ B3) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 = B3) => ((F @ A2) @ A2))) => ((F @ A2) @ B3)))))).
% 3.64/1.92 thf(fact_222_pi_Oinject_I4_J, axiom, (! [X32:name,X2:name,X1:pi,Y32:name,Y22:name,Y1:pi]: ((((((match @ X32) @ X2) @ X1) = (((match @ Y32) @ Y22) @ Y1)) = ((X32 = Y32) & ((X2 = Y22) & (X1 = Y1))))))).
% 3.64/1.92 thf(fact_223_pi_Odistinct_I37_J, axiom, (! [Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi4) != (((match @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_224_pi_Odistinct_I23_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (((match @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_225_pi_Odistinct_I65_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((match @ Name12) @ Name23) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_226_pi_Odistinct_I67_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name:name,Pi:pi]: (((((match @ Name12) @ Name23) @ Pi4) != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_227_pi_Odistinct_I49_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((input @ Name12) @ Name23) @ Pi4) != (((match @ Name13) @ Name24) @ Pi))))).
% 3.64/1.92 thf(fact_228_matchNilLeft, axiom, (! [A2:name,B3:name,Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((A2 != B3) => (((strong743114133lation @ piNil) @ Rel) @ (((match @ A2) @ B3) @ P)))))).
% 3.64/1.92 thf(fact_229_freeRes_Ocase_I1_J, axiom, (! [A:$tType,F1:(name > (name > A)),F22:A,X11:name,X122:name]: ((((((late_case_freeRes @ A) @ F1) @ F22) @ ((late_OutputR @ X11) @ X122)) = ((F1 @ X11) @ X122))))).
% 3.64/1.92 thf(fact_230_pi_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (pi > $o)),Z:N,Pi4:pi]: (((! [Z2:N]: (((P @ Z2) @ piNil))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((output @ Name1) @ Name22) @ Pi3))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (tau @ Pi3))))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name22) @ Z2) => (((((fresh @ name) @ name) @ Name22) @ Name1) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((input @ Name1) @ Name22) @ Pi3))))))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((match @ Name1) @ Name22) @ Pi3))))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((mismatch @ Name1) @ Name22) @ Pi3))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi23)))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((par @ Pi13) @ Pi23)))))) => ((! [Name2:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name2) @ Z2) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ ((res @ Name2) @ Pi3)))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (bang @ Pi3))))) => ((P @ Z) @ Pi4))))))))))))))))).
% 3.64/1.92 thf(fact_231_pi_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (pi > $o)),Z:A,Pi4:pi]: (((! [Z2:A]: (((P @ Z2) @ piNil))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((output @ Name1) @ Name22) @ Pi3))))) => ((! [Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (tau @ Pi3))))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name22) @ Z2) => (((((fresh @ name) @ name) @ Name22) @ Name1) => ((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((input @ Name1) @ Name22) @ Pi3))))))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((match @ Name1) @ Name22) @ Pi3))))) => ((! [Name1:name,Name22:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((mismatch @ Name1) @ Name22) @ Pi3))))) => ((! [Pi13:pi,Pi23:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi23)))))) => ((! [Pi13:pi,Pi23:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((par @ Pi13) @ Pi23)))))) => ((! [Name2:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name2) @ Z2) => ((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ ((res @ Name2) @ Pi3)))))) => ((! [Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (bang @ Pi3))))) => ((P @ Z) @ Pi4))))))))))))))))).
% 3.64/1.92 thf(fact_232_pi_Ofresh_I10_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (bang @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 3.64/1.92 thf(fact_233_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)))))).
% 3.64/1.92 thf(fact_234_simps_I10_J, axiom, (! [P:pi,C3:name,D:name]: (((((subs @ (bang @ P)) @ C3) @ D) = (bang @ (((subs @ P) @ C3) @ D)))))).
% 3.64/1.92 thf(fact_235_simps_I7_J, axiom, (! [P:pi,Q:pi,C3:name,D:name]: (((((subs @ ((sum @ P) @ Q)) @ C3) @ D) = ((sum @ (((subs @ P) @ C3) @ D)) @ (((subs @ Q) @ C3) @ D)))))).
% 3.64/1.92 thf(fact_236_pi_Odistinct_I63_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((match @ Name12) @ Name23) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_237_pi_Odistinct_I69_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi:pi]: (((((match @ Name12) @ Name23) @ Pi4) != (bang @ Pi))))).
% 3.64/1.92 thf(fact_238_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)))))))))))).
% 3.64/1.92 thf(fact_239_Bang, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ ((par @ P) @ (bang @ P))) @ Rs) => ((late_transitions @ (bang @ P)) @ Rs))))).
% 3.64/1.92 thf(fact_240_pi_Odistinct_I53_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name23) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_241_pi_Odistinct_I59_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi:pi]: (((((input @ Name12) @ Name23) @ Pi4) != (bang @ Pi))))).
% 3.64/1.92 thf(fact_242_pi_Odistinct_I89_J, axiom, (! [Name3:name,Pi4:pi,Pi:pi]: ((((res @ Name3) @ Pi4) != (bang @ Pi))))).
% 3.64/1.92 thf(fact_243_pi_Odistinct_I87_J, axiom, (! [Pi1:pi,Pi2:pi,Pi:pi]: ((((par @ Pi1) @ Pi2) != (bang @ Pi))))).
% 3.64/1.92 thf(fact_244_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 3.64/1.92 thf(fact_245_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 3.64/1.92 thf(fact_246_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 3.64/1.92 thf(fact_247_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 3.64/1.92 thf(fact_248_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((sum @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 3.64/1.92 thf(fact_249_pi_Odistinct_I79_J, axiom, (! [Pi1:pi,Pi2:pi,Pi12:pi,Pi22:pi]: ((((sum @ Pi1) @ Pi2) != ((par @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_250_pi_Oinject_I9_J, axiom, (! [X1:pi,Y1:pi]: ((((bang @ X1) = (bang @ Y1)) = (X1 = Y1))))).
% 3.64/1.92 thf(fact_251_pi_Oinject_I6_J, axiom, (! [X2:pi,X1:pi,Y22:pi,Y1:pi]: (((((sum @ X2) @ X1) = ((sum @ Y22) @ Y1)) = ((X2 = Y22) & (X1 = Y1)))))).
% 3.64/1.92 thf(fact_252_pi_Odistinct_I83_J, axiom, (! [Pi1:pi,Pi2:pi,Pi:pi]: ((((sum @ Pi1) @ Pi2) != (bang @ Pi))))).
% 3.64/1.92 thf(fact_253_pi_Odistinct_I27_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name23) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(fact_254_pi_Odistinct_I33_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (bang @ Pi))))).
% 3.64/1.92 thf(fact_255_pi_Odistinct_I41_J, axiom, (! [Pi4:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 3.64/1.92 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 3.64/1.92 thf(tcon_HOL_Obool___Agent_Ofs__name_1, axiom, (fs_name @ $o)).
% 3.64/1.92 thf(tcon_Agent_Oname___Agent_Ofs__name_2, axiom, (fs_name @ name)).
% 3.64/1.92 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3, axiom, (! [A7:$tType,A8:$tType]: ((((fs_name @ A7) & (fs_name @ A8)) => (fs_name @ ((product_prod @ A7) @ A8)))))).
% 3.64/1.92 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4, axiom, (fs_name @ late_freeRes)).
% 3.64/1.92 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5, axiom, (fs_name @ late_subject)).
% 3.64/1.92 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6, axiom, (fs_name @ late_residual)).
% 3.64/1.92 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.64/1.92 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 3.64/1.92 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 3.64/1.92 thf(conj_0, conjecture, (x != aa)).
% 3.64/1.92 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2DTF641.p
% 3.64/1.92 ------------------------
% 3.64/1.97 ---- Cleaned THF ---
% 3.64/1.97 thf(ty_t_Late__Semantics_Oresidual,type,
% 3.64/1.97 late_residual: $tType ).
% 3.64/1.97
% 3.64/1.97 thf(ty_t_Late__Semantics_Osubject,type,
% 3.64/1.97 late_subject: $tType ).
% 3.64/1.97
% 3.64/1.97 thf(ty_t_Late__Semantics_OfreeRes,type,
% 3.64/1.97 late_freeRes: $tType ).
% 3.64/1.97
% 3.64/1.97 thf(ty_t_Product__Type_Oprod,type,
% 3.64/1.97 product_prod: $tType > $tType > $tType ).
% 3.64/1.97
% 3.64/1.97 thf(ty_t_Nominal_Onoption,type,
% 3.64/1.97 noption: $tType > $tType ).
% 3.64/1.97
% 3.64/1.97 thf(ty_t_Agent_Oname,type,
% 3.64/1.97 name: $tType ).
% 3.64/1.97
% 3.64/1.97 thf(ty_t_Agent_Opi,type,
% 3.64/1.97 pi: $tType ).
% 3.64/1.97
% 3.64/1.97 thf(ty_t_Set_Oset,type,
% 3.64/1.97 set: $tType > $tType ).
% 3.64/1.97
% 3.64/1.97 thf(sy_cl_Agent_Ofs__name,type,
% 3.64/1.97 fs_name:
% 3.64/1.97 !>[A: $tType] : $o ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OBang,type,
% 3.64/1.97 bang: pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OInput,type,
% 3.64/1.97 input: name > name > pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OMatch,type,
% 3.64/1.97 match: name > name > pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OMismatch,type,
% 3.64/1.97 mismatch: name > name > pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OOutput,type,
% 3.64/1.97 output: name > name > pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OPar,type,
% 3.64/1.97 par: pi > pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OPiNil,type,
% 3.64/1.97 piNil: pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_ORes,type,
% 3.64/1.97 res: name > pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OSum,type,
% 3.64/1.97 sum: pi > pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Opi_OTau,type,
% 3.64/1.97 tau: pi > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Osubs,type,
% 3.64/1.97 subs: pi > name > name > pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Agent_Osubst__name,type,
% 3.64/1.97 subst_name: name > name > name > name ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_If,type,
% 3.64/1.97 if:
% 3.64/1.97 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 3.64/1.97 late_case_freeRes:
% 3.64/1.97 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 3.64/1.97 late_OutputR: name > name > late_freeRes ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 3.64/1.97 late_TauR: late_freeRes ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 3.64/1.97 late_freeRes_rec:
% 3.64/1.97 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 3.64/1.97 late_BoundR: late_subject > name > pi > late_residual ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 3.64/1.97 late_FreeR: late_freeRes > pi > late_residual ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 3.64/1.97 late_BoundOutputS: name > late_subject ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 3.64/1.97 late_InputS: name > late_subject ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 3.64/1.97 late_subject_rec:
% 3.64/1.97 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Late__Semantics_Otransitions,type,
% 3.64/1.97 late_transitions: pi > late_residual > $o ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Nominal_Oabs__fun,type,
% 3.64/1.97 abs_fun:
% 3.64/1.97 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Nominal_Ofresh,type,
% 3.64/1.97 fresh:
% 3.64/1.97 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Product__Type_OPair,type,
% 3.64/1.97 product_Pair:
% 3.64/1.97 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 3.64/1.97 produc2004651681e_prod:
% 3.64/1.97 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.64/1.97 product_rec_prod:
% 3.64/1.97 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Rel_Oeqvt,type,
% 3.64/1.97 eqvt:
% 3.64/1.97 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Set_OCollect,type,
% 3.64/1.97 collect:
% 3.64/1.97 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 3.64/1.97 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 3.64/1.97 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 3.64/1.97
% 3.64/1.97 thf(sy_c_member,type,
% 3.64/1.97 member:
% 3.64/1.97 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_P,type,
% 3.64/1.97 p: pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_PQ____,type,
% 3.64/1.97 pq: pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_P_H____,type,
% 3.64/1.97 p2: pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_Q,type,
% 3.64/1.97 q: pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_Q_H____,type,
% 3.64/1.97 q2: pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_Rel,type,
% 3.64/1.97 rel: set @ ( product_prod @ pi @ pi ) ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v__092_060alpha_062____,type,
% 3.64/1.97 alpha: late_freeRes ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_aa____,type,
% 3.64/1.97 aa: name ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_x,type,
% 3.64/1.97 x: name ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_xPQ____,type,
% 3.64/1.97 xPQ: pi ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_y____,type,
% 3.64/1.97 y: name ).
% 3.64/1.97
% 3.64/1.97 thf(sy_v_z____,type,
% 3.64/1.97 z: name ).
% 3.64/1.97
% 3.64/1.97 thf(fact_0_cClose1_Ohyps_I3_J,axiom,
% 3.64/1.97 fresh @ name @ pi @ y @ p ).
% 3.64/1.97
% 3.64/1.97 thf(fact_1_cClose1_Ohyps_I7_J,axiom,
% 3.64/1.97 fresh @ name @ pi @ y @ q2 ).
% 3.64/1.97
% 3.64/1.97 thf(fact_2_cClose1_Ohyps_I6_J,axiom,
% 3.64/1.97 y != z ).
% 3.64/1.97
% 3.64/1.97 thf(fact_3_assms_I1_J,axiom,
% 3.64/1.97 fresh @ name @ pi @ x @ p ).
% 3.64/1.97
% 3.64/1.97 thf(fact_4_cClose1_Ohyps_I12_J,axiom,
% 3.64/1.97 fresh @ name @ name @ y @ x ).
% 3.64/1.97
% 3.64/1.97 thf(fact_5_cClose1_Ohyps_I5_J,axiom,
% 3.64/1.97 y != aa ).
% 3.64/1.97
% 3.64/1.97 thf(fact_6_cClose1_Ohyps_I4_J,axiom,
% 3.64/1.97 fresh @ name @ pi @ y @ q ).
% 3.64/1.97
% 3.64/1.97 thf(fact_7_cClose1_Ohyps_I11_J,axiom,
% 3.64/1.97 fresh @ name @ pi @ z @ p2 ).
% 3.64/1.97
% 3.64/1.97 thf(fact_8_cClose1_Ohyps_I1_J,axiom,
% 3.64/1.97 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_9_cClose1_Ohyps_I10_J,axiom,
% 3.64/1.97 z != aa ).
% 3.64/1.97
% 3.64/1.97 thf(fact_10_cClose1_Ohyps_I13_J,axiom,
% 3.64/1.97 fresh @ name @ name @ z @ x ).
% 3.64/1.97
% 3.64/1.97 thf(fact_11_cClose1_Ohyps_I8_J,axiom,
% 3.64/1.97 fresh @ name @ pi @ z @ p ).
% 3.64/1.97
% 3.64/1.97 thf(fact_12_cRes_Ohyps_I2_J,axiom,
% 3.64/1.97 fresh @ name @ late_freeRes @ x @ alpha ).
% 3.64/1.97
% 3.64/1.97 thf(fact_13_assms_I3_J,axiom,
% 3.64/1.97 eqvt @ pi @ rel ).
% 3.64/1.97
% 3.64/1.97 thf(fact_14_cClose1_Ohyps_I14_J,axiom,
% 3.64/1.97 alpha = late_TauR ).
% 3.64/1.97
% 3.64/1.97 thf(fact_15_cClose1_Ohyps_I2_J,axiom,
% 3.64/1.97 late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_16_cClose1_Ohyps_I9_J,axiom,
% 3.64/1.97 fresh @ name @ pi @ z @ q ).
% 3.64/1.97
% 3.64/1.97 thf(fact_17_Free_Ohyps,axiom,
% 3.64/1.97 late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ xPQ ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_18_cRes_Ohyps_I1_J,axiom,
% 3.64/1.97 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ pq ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_19_freeRes_Ofresh_I2_J,axiom,
% 3.64/1.97 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_20_pi_Ofresh_I8_J,axiom,
% 3.64/1.97 ! [A2: name,X2: pi,X1: pi] :
% 3.64/1.97 ( ( fresh @ name @ pi @ A2 @ ( par @ X2 @ X1 ) )
% 3.64/1.97 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 3.64/1.97 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_21_freshFreeDerivative_I1_J,axiom,
% 3.64/1.97 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.64/1.97 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.97 => ( ( fresh @ name @ pi @ Y @ P )
% 3.64/1.97 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_22_resCasesF,axiom,
% 3.64/1.97 ! [X3: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 3.64/1.97 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 3.64/1.97 => ( ! [P3: pi] :
% 3.64/1.97 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.64/1.97 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 3.64/1.97 => ( F @ ( res @ X3 @ P3 ) ) ) )
% 3.64/1.97 => ( F @ XP ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_23_resCasesF_H,axiom,
% 3.64/1.97 ! [X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.64/1.97 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.97 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y2: name] :
% 3.64/1.97 ( ( ( res @ X3 @ P )
% 3.64/1.97 = ( res @ Y2 @ P4 ) )
% 3.64/1.97 => ( ( ( late_FreeR @ Alpha @ P2 )
% 3.64/1.97 = ( late_FreeR @ Alpha2 @ ( res @ Y2 @ P3 ) ) )
% 3.64/1.97 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.64/1.97 => ~ ( fresh @ name @ late_freeRes @ Y2 @ Alpha2 ) ) ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_24_ResF,axiom,
% 3.64/1.97 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.64/1.97 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.97 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 3.64/1.97 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_25_Res,axiom,
% 3.64/1.97 ! [Y: name,R: pi,S: pi] :
% 3.64/1.97 ( ( fresh @ name @ pi @ Y @ R )
% 3.64/1.97 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ ( res @ Y @ S ) ) @ ( res @ Y @ ( par @ R @ S ) ) ) @ rel ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_26_ScopeExt,axiom,
% 3.64/1.97 ! [Y: name,R: pi,Z: name,S: pi] :
% 3.64/1.97 ( ( fresh @ name @ pi @ Y @ R )
% 3.64/1.97 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) ) @ rel ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_27_Late__Semantics_OPar1B,axiom,
% 3.64/1.97 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 3.64/1.97 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 3.64/1.97 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.97 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_28_Late__Semantics_OPar2B,axiom,
% 3.64/1.97 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 3.64/1.97 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 3.64/1.97 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.97 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 3.64/1.97 ! [X1: name,Y1: name] :
% 3.64/1.97 ( ( ( late_BoundOutputS @ X1 )
% 3.64/1.97 = ( late_BoundOutputS @ Y1 ) )
% 3.64/1.97 = ( X1 = Y1 ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_30_name__fresh,axiom,
% 3.64/1.97 ( ( fresh @ name @ name )
% 3.64/1.97 = ( ^ [A3: name,B2: name] : ( A3 != B2 ) ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_31_name__exists__fresh,axiom,
% 3.64/1.97 ! [A: $tType] :
% 3.64/1.97 ( ( fs_name @ A )
% 3.64/1.97 => ! [X3: A] :
% 3.64/1.97 ~ ! [C2: name] :
% 3.64/1.97 ~ ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 3.64/1.97
% 3.64/1.97 thf(fact_32_pi_Oinject_I7_J,axiom,
% 3.64/1.98 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 3.64/1.98 ( ( ( par @ X2 @ X1 )
% 3.64/1.98 = ( par @ Y22 @ Y1 ) )
% 3.64/1.98 = ( ( X2 = Y22 )
% 3.64/1.98 & ( X1 = Y1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_33_residual_Oinject_I2_J,axiom,
% 3.64/1.98 ! [X2: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 3.64/1.98 ( ( ( late_FreeR @ X2 @ X1 )
% 3.64/1.98 = ( late_FreeR @ Y22 @ Y1 ) )
% 3.64/1.98 = ( ( X2 = Y22 )
% 3.64/1.98 & ( X1 = Y1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_34_pi_Odistinct_I85_J,axiom,
% 3.64/1.98 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.64/1.98 ( ( par @ Pi1 @ Pi2 )
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_35_freshRes,axiom,
% 3.64/1.98 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_36_residual_Oinducts,axiom,
% 3.64/1.98 ! [P: late_residual > $o,Residual: late_residual] :
% 3.64/1.98 ( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
% 3.64/1.98 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.64/1.98 => ( P @ Residual ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_37_residual_Odistinct_I1_J,axiom,
% 3.64/1.98 ! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 3.64/1.98 ( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
% 3.64/1.98 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_38_subject_Ostrong__inducts,axiom,
% 3.64/1.98 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 3.64/1.98 ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 3.64/1.98 => ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 3.64/1.98 => ( P @ Z @ Subject2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_39_subject_Ostrong__induct_H,axiom,
% 3.64/1.98 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 3.64/1.98 ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 3.64/1.98 => ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 3.64/1.98 => ( P @ Z @ Subject2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_40_subject_Oinducts,axiom,
% 3.64/1.98 ! [P: late_subject > $o,Subject2: late_subject] :
% 3.64/1.98 ( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
% 3.64/1.98 => ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
% 3.64/1.98 => ( P @ Subject2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_41_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 3.64/1.98 ! [Name3: name,Name: name] :
% 3.64/1.98 ( ( late_InputS @ Name3 )
% 3.64/1.98 != ( late_BoundOutputS @ Name ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_42_Par2F,axiom,
% 3.64/1.98 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_43_Par1F,axiom,
% 3.64/1.98 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_44_freshBoundDerivative_I2_J,axiom,
% 3.64/1.98 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ P )
% 3.64/1.98 => ( ( Y != X3 )
% 3.64/1.98 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_45_mem__Collect__eq,axiom,
% 3.64/1.98 ! [A: $tType,A2: A,P: A > $o] :
% 3.64/1.98 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.64/1.98 = ( P @ A2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_46_Collect__mem__eq,axiom,
% 3.64/1.98 ! [A: $tType,A4: set @ A] :
% 3.64/1.98 ( ( collect @ A
% 3.64/1.98 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 3.64/1.98 = A4 ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_47_Collect__cong,axiom,
% 3.64/1.98 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.64/1.98 ( ! [X5: A] :
% 3.64/1.98 ( ( P @ X5 )
% 3.64/1.98 = ( Q @ X5 ) )
% 3.64/1.98 => ( ( collect @ A @ P )
% 3.64/1.98 = ( collect @ A @ Q ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_48_residual_Ostrong__inducts,axiom,
% 3.64/1.98 ! [A: $tType] :
% 3.64/1.98 ( ( fs_name @ A )
% 3.64/1.98 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 3.64/1.98 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: A] :
% 3.64/1.98 ( ( fresh @ name @ A @ Name2 @ Z2 )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 3.64/1.98 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 3.64/1.98 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.64/1.98 => ( P @ Z @ Residual ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_49_residual_Ostrong__induct,axiom,
% 3.64/1.98 ! [N: $tType] :
% 3.64/1.98 ( ( fs_name @ N )
% 3.64/1.98 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 3.64/1.98 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: N] :
% 3.64/1.98 ( ( fresh @ name @ N @ Name2 @ Z2 )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 3.64/1.98 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 3.64/1.98 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.64/1.98 => ( P @ Z @ Residual ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_50_freshFreeDerivative_I2_J,axiom,
% 3.64/1.98 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ P )
% 3.64/1.98 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_51_parCasesB,axiom,
% 3.64/1.98 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 3.64/1.98 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.98 => ( ! [P3: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 3.64/1.98 => ( Prop @ ( par @ P3 @ Q ) ) )
% 3.64/1.98 => ( ! [Q3: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 3.64/1.98 => ( Prop @ ( par @ P @ Q3 ) ) )
% 3.64/1.98 => ( Prop @ PQ ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_52_fresh__prod,axiom,
% 3.64/1.98 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y: B] :
% 3.64/1.98 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 3.64/1.98 = ( ( fresh @ X @ A @ A2 @ X3 )
% 3.64/1.98 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_53_transitions_OClose2,axiom,
% 3.64/1.98 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ Q )
% 3.64/1.98 => ( ( X3 != A2 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 3.64/1.98 => ( ( Y != A2 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 3.64/1.98 => ( ( X3 != Y )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_54_transitions_OClose1,axiom,
% 3.64/1.98 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ Q )
% 3.64/1.98 => ( ( X3 != A2 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 3.64/1.98 => ( ( Y != A2 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ P2 )
% 3.64/1.98 => ( ( X3 != Y )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_55_Late__Semantics_OClose2,axiom,
% 3.64/1.98 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ Q )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_56_Late__Semantics_OClose1,axiom,
% 3.64/1.98 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ P )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_57_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 3.64/1.98 ! [X1: name,Y1: name] :
% 3.64/1.98 ( ( ( late_InputS @ X1 )
% 3.64/1.98 = ( late_InputS @ Y1 ) )
% 3.64/1.98 = ( X1 = Y1 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_58_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 3.64/1.98 ! [X2: name,Y22: name] :
% 3.64/1.98 ( ( ( late_BoundOutputS @ X2 )
% 3.64/1.98 = ( late_BoundOutputS @ Y22 ) )
% 3.64/1.98 = ( X2 = Y22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_59_old_Oprod_Oinject,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,A2: A,B3: B,A5: A,B4: B] :
% 3.64/1.98 ( ( ( product_Pair @ A @ B @ A2 @ B3 )
% 3.64/1.98 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 3.64/1.98 = ( ( A2 = A5 )
% 3.64/1.98 & ( B3 = B4 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_60_prod_Oinject,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y22: B] :
% 3.64/1.98 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 3.64/1.98 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 3.64/1.98 = ( ( X1 = Y1 )
% 3.64/1.98 & ( X2 = Y22 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_61_subst__identity,axiom,
% 3.64/1.98 ! [P: pi,A2: name] :
% 3.64/1.98 ( ( subs @ P @ A2 @ A2 )
% 3.64/1.98 = P ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_62_simps_I9_J,axiom,
% 3.64/1.98 ! [X3: name,C3: name,D: name,P: pi] :
% 3.64/1.98 ( ( X3 != C3 )
% 3.64/1.98 => ( ( X3 != D )
% 3.64/1.98 => ( ( subs @ ( res @ X3 @ P ) @ C3 @ D )
% 3.64/1.98 = ( res @ X3 @ ( subs @ P @ C3 @ D ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_63_simps_I8_J,axiom,
% 3.64/1.98 ! [P: pi,Q: pi,C3: name,D: name] :
% 3.64/1.98 ( ( subs @ ( par @ P @ Q ) @ C3 @ D )
% 3.64/1.98 = ( par @ ( subs @ P @ C3 @ D ) @ ( subs @ Q @ C3 @ D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_64_substTrans,axiom,
% 3.64/1.98 ! [B3: name,P: pi,A2: name,C3: name] :
% 3.64/1.98 ( ( fresh @ name @ pi @ B3 @ P )
% 3.64/1.98 => ( ( subs @ ( subs @ P @ A2 @ B3 ) @ B3 @ C3 )
% 3.64/1.98 = ( subs @ P @ A2 @ C3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_65_residual_Ofresh_I2_J,axiom,
% 3.64/1.98 ! [A2: name,X2: late_freeRes,X1: pi] :
% 3.64/1.98 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X2 @ X1 ) )
% 3.64/1.98 = ( ( fresh @ name @ late_freeRes @ A2 @ X2 )
% 3.64/1.98 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_66_subject_Ofresh_I2_J,axiom,
% 3.64/1.98 ! [A2: name,X1: name] :
% 3.64/1.98 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 3.64/1.98 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_67_subject_Ofresh_I1_J,axiom,
% 3.64/1.98 ! [A2: name,X1: name] :
% 3.64/1.98 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 3.64/1.98 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_68_forget,axiom,
% 3.64/1.98 ! [A2: name,P: pi,B3: name] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ P )
% 3.64/1.98 => ( ( subs @ P @ A2 @ B3 )
% 3.64/1.98 = P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_69_fresh__fact1,axiom,
% 3.64/1.98 ! [A2: name,P: pi,C3: name,B3: name] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ P )
% 3.64/1.98 => ( ( A2 != C3 )
% 3.64/1.98 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B3 @ C3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_70_fresh__fact2,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi] :
% 3.64/1.98 ( ( A2 != B3 )
% 3.64/1.98 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_71_freshResidual,axiom,
% 3.64/1.98 ! [P: pi,Rs: late_residual,X3: name] :
% 3.64/1.98 ( ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_72_substRes2,axiom,
% 3.64/1.98 ! [B3: name,P: pi,A2: name] :
% 3.64/1.98 ( ( fresh @ name @ pi @ B3 @ P )
% 3.64/1.98 => ( ( res @ A2 @ P )
% 3.64/1.98 = ( res @ B3 @ ( subs @ P @ A2 @ B3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_73_Agent_OsubstRes3,axiom,
% 3.64/1.98 ! [B3: name,P: pi,A2: name] :
% 3.64/1.98 ( ( fresh @ name @ pi @ B3 @ P )
% 3.64/1.98 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B3 )
% 3.64/1.98 = ( res @ B3 @ ( subs @ P @ A2 @ B3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_74_Late__Semantics_OResB,axiom,
% 3.64/1.98 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 3.64/1.98 => ( ( Y != X3 )
% 3.64/1.98 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_75_freshBoundDerivative_I1_J,axiom,
% 3.64/1.98 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y @ P )
% 3.64/1.98 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_76_surj__pair,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,P5: product_prod @ A @ B] :
% 3.64/1.98 ? [X5: A,Y2: B] :
% 3.64/1.98 ( P5
% 3.64/1.98 = ( product_Pair @ A @ B @ X5 @ Y2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_77_prod__cases,axiom,
% 3.64/1.98 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P5: product_prod @ A @ B] :
% 3.64/1.98 ( ! [A6: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 3.64/1.98 => ( P @ P5 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_78_Pair__inject,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,A2: A,B3: B,A5: A,B4: B] :
% 3.64/1.98 ( ( ( product_Pair @ A @ B @ A2 @ B3 )
% 3.64/1.98 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 3.64/1.98 => ~ ( ( A2 = A5 )
% 3.64/1.98 => ( B3 != B4 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_79_prod__cases3,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.64/1.98 ~ ! [A6: A,B5: B,C2: C] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_80_prod__cases4,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,C: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 3.64/1.98 ~ ! [A6: A,B5: B,C2: C,D3: D2] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_81_prod__cases5,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 3.64/1.98 ~ ! [A6: A,B5: B,C2: C,D3: D2,E2: E] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_82_prod__cases6,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) )] :
% 3.64/1.98 ~ ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F2 ) @ D3 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_83_prod__cases7,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F2: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 3.64/1.98 ~ ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2,G2: G] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_84_prod__induct3,axiom,
% 3.64/1.98 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.64/1.98 ( ! [A6: A,B5: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 3.64/1.98 => ( P @ X3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_85_prod__induct4,axiom,
% 3.64/1.98 ! [D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 3.64/1.98 ( ! [A6: A,B5: B,C2: C,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) )
% 3.64/1.98 => ( P @ X3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_86_prod__induct5,axiom,
% 3.64/1.98 ! [E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 3.64/1.98 ( ! [A6: A,B5: B,C2: C,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 3.64/1.98 => ( P @ X3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_87_prod__induct6,axiom,
% 3.64/1.98 ! [F2: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) )] :
% 3.64/1.98 ( ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F2 ) @ D3 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 3.64/1.98 => ( P @ X3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_88_prod__induct7,axiom,
% 3.64/1.98 ! [G: $tType,F2: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 3.64/1.98 ( ! [A6: A,B5: B,C2: C,D3: D2,E2: E,F3: F2,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F3 @ G2 ) ) ) ) ) ) )
% 3.64/1.98 => ( P @ X3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_89_old_Oprod_Oexhaust,axiom,
% 3.64/1.98 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 3.64/1.98 ~ ! [A6: A,B5: B] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( product_Pair @ A @ B @ A6 @ B5 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_90_old_Oprod_Oinducts,axiom,
% 3.64/1.98 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.64/1.98 ( ! [A6: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 3.64/1.98 => ( P @ Prod ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_91_transitions_OResB,axiom,
% 3.64/1.98 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 3.64/1.98 => ( ( Y != X3 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 3.64/1.98 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_92_parCasesB_H,axiom,
% 3.64/1.98 ! [P: pi,Q: pi,B3: late_subject,Y: name,P2: pi] :
% 3.64/1.98 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B3 @ Y @ P2 ) )
% 3.64/1.98 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Q4: pi] :
% 3.64/1.98 ( ( ( par @ P @ Q )
% 3.64/1.98 = ( par @ P4 @ Q4 ) )
% 3.64/1.98 => ( ( ( late_BoundR @ B3 @ Y @ P2 )
% 3.64/1.98 = ( late_BoundR @ A6 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 3.64/1.98 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 3.64/1.98 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) )
% 3.64/1.98 => ~ ! [Q4: pi,A6: late_subject,X5: name,Q3: pi,P4: pi] :
% 3.64/1.98 ( ( ( par @ P @ Q )
% 3.64/1.98 = ( par @ P4 @ Q4 ) )
% 3.64/1.98 => ( ( ( late_BoundR @ B3 @ Y @ P2 )
% 3.64/1.98 = ( late_BoundR @ A6 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 3.64/1.98 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 3.64/1.98 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_93_transitions_OPar1B,axiom,
% 3.64/1.98 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_94_transitions_OPar2B,axiom,
% 3.64/1.98 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_95_fresh__prodD_I2_J,axiom,
% 3.64/1.98 ! [B: $tType,A: $tType,C: $tType,A2: A,X3: B,Y: C] :
% 3.64/1.98 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 3.64/1.98 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_96_fresh__prodD_I1_J,axiom,
% 3.64/1.98 ! [C: $tType,A: $tType,B: $tType,A2: A,X3: B,Y: C] :
% 3.64/1.98 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X3 @ Y ) )
% 3.64/1.98 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_97_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 3.64/1.98 ! [X1: name,X2: name] :
% 3.64/1.98 ( ( late_InputS @ X1 )
% 3.64/1.98 != ( late_BoundOutputS @ X2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_98_subject_Oexhaust,axiom,
% 3.64/1.98 ! [Y: late_subject] :
% 3.64/1.98 ( ! [X12: name] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( late_InputS @ X12 ) )
% 3.64/1.98 => ~ ! [X22: name] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( late_BoundOutputS @ X22 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_99_old_Oprod_Orec,axiom,
% 3.64/1.98 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B3: B] :
% 3.64/1.98 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B3 ) )
% 3.64/1.98 = ( F1 @ A2 @ B3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_100_resCases_H,axiom,
% 3.64/1.98 ! [X3: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 3.64/1.98 => ( ! [P4: pi,A6: name,B5: name] :
% 3.64/1.98 ( ( ( res @ X3 @ P )
% 3.64/1.98 = ( res @ B5 @ P4 ) )
% 3.64/1.98 => ! [P3: pi] :
% 3.64/1.98 ( ( Rs
% 3.64/1.98 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B5 @ P3 ) )
% 3.64/1.98 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B5 ) @ P3 ) )
% 3.64/1.98 => ( A6 = B5 ) ) ) )
% 3.64/1.98 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y2: name] :
% 3.64/1.98 ( ( ( res @ X3 @ P )
% 3.64/1.98 = ( res @ Y2 @ P4 ) )
% 3.64/1.98 => ( ( Rs
% 3.64/1.98 = ( late_BoundR @ A6 @ X5 @ ( res @ Y2 @ P3 ) ) )
% 3.64/1.98 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ Y2 @ A6 )
% 3.64/1.98 => ( ( Y2 != X5 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.64/1.98 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) )
% 3.64/1.98 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y2: name] :
% 3.64/1.98 ( ( ( res @ X3 @ P )
% 3.64/1.98 = ( res @ Y2 @ P4 ) )
% 3.64/1.98 => ( ( Rs
% 3.64/1.98 = ( late_FreeR @ Alpha2 @ ( res @ Y2 @ P3 ) ) )
% 3.64/1.98 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.64/1.98 => ~ ( fresh @ name @ late_freeRes @ Y2 @ Alpha2 ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_101_transitions_OComm1,axiom,
% 3.64/1.98 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B3: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.98 => ( ( X3 != A2 )
% 3.64/1.98 => ( ( X3 != B3 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B3 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_102_transitions_OComm2,axiom,
% 3.64/1.98 ! [P: pi,A2: name,B3: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ Q )
% 3.64/1.98 => ( ( X3 != A2 )
% 3.64/1.98 => ( ( X3 != B3 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_103_Late__Semantics_OComm1,axiom,
% 3.64/1.98 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B3: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ Q2 ) )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B3 ) @ Q2 ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_104_Late__Semantics_OComm2,axiom,
% 3.64/1.98 ! [P: pi,A2: name,B3: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 3.64/1.98 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B3 ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_105_resCasesB_H,axiom,
% 3.64/1.98 ! [X6: name,P: pi,A2: late_subject,Y3: name,P2: pi] :
% 3.64/1.98 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y3 @ P2 ) )
% 3.64/1.98 => ( ! [P4: pi,A6: name,B5: name] :
% 3.64/1.98 ( ( ( res @ X6 @ P )
% 3.64/1.98 = ( res @ B5 @ P4 ) )
% 3.64/1.98 => ! [P3: pi] :
% 3.64/1.98 ( ( ( late_BoundR @ A2 @ Y3 @ P2 )
% 3.64/1.98 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B5 @ P3 ) )
% 3.64/1.98 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B5 ) @ P3 ) )
% 3.64/1.98 => ( A6 = B5 ) ) ) )
% 3.64/1.98 => ~ ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y2: name] :
% 3.64/1.98 ( ( ( res @ X6 @ P )
% 3.64/1.98 = ( res @ Y2 @ P4 ) )
% 3.64/1.98 => ( ( ( late_BoundR @ A2 @ Y3 @ P2 )
% 3.64/1.98 = ( late_BoundR @ A6 @ X5 @ ( res @ Y2 @ P3 ) ) )
% 3.64/1.98 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ Y2 @ A6 )
% 3.64/1.98 => ( ( Y2 != X5 )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.64/1.98 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_106_Late__Semantics1_OfreeRes_Oinject,axiom,
% 3.64/1.98 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 3.64/1.98 ( ( ( late_OutputR @ X11 @ X122 )
% 3.64/1.98 = ( late_OutputR @ Y11 @ Y12 ) )
% 3.64/1.98 = ( ( X11 = Y11 )
% 3.64/1.98 & ( X122 = Y12 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_107_Late__Semantics_OfreeRes_Oinject,axiom,
% 3.64/1.98 ! [X2: name,X1: name,Y22: name,Y1: name] :
% 3.64/1.98 ( ( ( late_OutputR @ X2 @ X1 )
% 3.64/1.98 = ( late_OutputR @ Y22 @ Y1 ) )
% 3.64/1.98 = ( ( X2 = Y22 )
% 3.64/1.98 & ( X1 = Y1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_108_freeRes_Ofresh_I1_J,axiom,
% 3.64/1.98 ! [A2: name,X2: name,X1: name] :
% 3.64/1.98 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X2 @ X1 ) )
% 3.64/1.98 = ( ( fresh @ name @ name @ A2 @ X2 )
% 3.64/1.98 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_109_freeRes_Ostrong__inducts,axiom,
% 3.64/1.98 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 3.64/1.98 ( ! [Name1: name,Name22: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 3.64/1.98 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 3.64/1.98 => ( P @ Z @ FreeRes3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_110_freeRes_Ostrong__induct_H,axiom,
% 3.64/1.98 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 3.64/1.98 ( ! [Name1: name,Name22: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 3.64/1.98 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 3.64/1.98 => ( P @ Z @ FreeRes3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_111_freeRes_Oinducts,axiom,
% 3.64/1.98 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 3.64/1.98 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 3.64/1.98 => ( ( P @ late_TauR )
% 3.64/1.98 => ( P @ FreeRes3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_112_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name] :
% 3.64/1.98 ( ( late_OutputR @ Name12 @ Name23 )
% 3.64/1.98 != late_TauR ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_113_freeRes_Oexhaust,axiom,
% 3.64/1.98 ! [Y: late_freeRes] :
% 3.64/1.98 ( ! [X112: name,X123: name] :
% 3.64/1.98 ( Y
% 3.64/1.98 != ( late_OutputR @ X112 @ X123 ) )
% 3.64/1.98 => ( Y = late_TauR ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_114_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 3.64/1.98 ! [X11: name,X122: name] :
% 3.64/1.98 ( ( late_OutputR @ X11 @ X122 )
% 3.64/1.98 != late_TauR ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_115_Open,axiom,
% 3.64/1.98 ! [P: pi,A2: name,B3: name,P2: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) )
% 3.64/1.98 => ( ( A2 != B3 )
% 3.64/1.98 => ( late_transitions @ ( res @ B3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B3 @ P2 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_116_resSimCases,axiom,
% 3.64/1.98 ! [A: $tType] :
% 3.64/1.98 ( ( fs_name @ A )
% 3.64/1.98 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P: pi,C4: A] :
% 3.64/1.98 ( ( eqvt @ pi @ Rel )
% 3.64/1.98 => ( ! [Q3: pi,A6: name] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A6 @ X3 ) @ Q3 ) )
% 3.64/1.98 => ( ( A6 != X3 )
% 3.64/1.98 => ? [P6: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ X3 @ P6 ) )
% 3.64/1.98 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) ) )
% 3.64/1.98 => ( ! [Q3: pi,A6: late_subject,Y2: name] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y2 @ Q3 ) )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ X3 @ A6 )
% 3.64/1.98 => ( ( X3 != Y2 )
% 3.64/1.98 => ( ( fresh @ name @ A @ Y2 @ C4 )
% 3.64/1.98 => ? [P6: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y2 @ P6 ) )
% 3.64/1.98 & ( strong2129052853vative @ P6 @ ( res @ X3 @ Q3 ) @ A6 @ Y2 @ Rel ) ) ) ) ) )
% 3.64/1.98 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.64/1.98 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 3.64/1.98 => ? [P6: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 3.64/1.98 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 3.64/1.98 => ( strong743114133lation @ P @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_117_freeRes_Orecs_I2_J,axiom,
% 3.64/1.98 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 3.64/1.98 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 3.64/1.98 => ( ( P @ F22 )
% 3.64/1.98 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 3.64/1.98 = F22 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_118_subject_Orecs_I1_J,axiom,
% 3.64/1.98 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 3.64/1.98 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 3.64/1.98 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 3.64/1.98 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 3.64/1.98 = ( F1 @ Name3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_119_subject_Orecs_I2_J,axiom,
% 3.64/1.98 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 3.64/1.98 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 3.64/1.98 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 3.64/1.98 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 3.64/1.98 = ( F22 @ Name3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_120_freeRes_Orecs_I1_J,axiom,
% 3.64/1.98 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name12: name,Name23: name] :
% 3.64/1.98 ( ! [X12: name,X22: name] : ( P @ ( F1 @ X12 @ X22 ) )
% 3.64/1.98 => ( ( P @ F22 )
% 3.64/1.98 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name12 @ Name23 ) )
% 3.64/1.98 = ( F1 @ Name12 @ Name23 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_121_simE_I1_J,axiom,
% 3.64/1.98 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 3.64/1.98 ( ( strong743114133lation @ P @ Rel @ Q )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X3 @ P )
% 3.64/1.98 => ? [P3: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 3.64/1.98 & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_122_simE_I2_J,axiom,
% 3.64/1.98 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 3.64/1.98 ( ( strong743114133lation @ P @ Rel @ Q )
% 3.64/1.98 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.64/1.98 => ? [P3: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.64/1.98 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_123_simCases,axiom,
% 3.64/1.98 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 3.64/1.98 ( ! [A6: late_subject,Y2: name,Q3: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y2 @ Q3 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.64/1.98 => ? [P6: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y2 @ P6 ) )
% 3.64/1.98 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ Y2 @ Rel ) ) ) )
% 3.64/1.98 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.64/1.98 => ? [P6: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 3.64/1.98 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 3.64/1.98 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_124_simulation__def,axiom,
% 3.64/1.98 ( strong743114133lation
% 3.64/1.98 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 3.64/1.98 ( ! [A3: late_subject,X4: name,Q6: pi] :
% 3.64/1.98 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A3 @ X4 @ Q6 ) )
% 3.64/1.98 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 3.64/1.98 => ? [P8: pi] :
% 3.64/1.98 ( ( late_transitions @ P7 @ ( late_BoundR @ A3 @ X4 @ P8 ) )
% 3.64/1.98 & ( strong2129052853vative @ P8 @ Q6 @ A3 @ X4 @ Rel2 ) ) )
% 3.64/1.98 & ! [Alpha3: late_freeRes,Q6: pi] :
% 3.64/1.98 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 3.64/1.98 => ? [P8: pi] :
% 3.64/1.98 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 3.64/1.98 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_125_parSym,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 3.64/1.98 ( ! [R2: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 3.64/1.98 => ( ! [R2: pi,S2: pi,X5: name] :
% 3.64/1.98 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S2 ) @ Rel )
% 3.64/1.98 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 3.64/1.98 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_126_simCasesCont,axiom,
% 3.64/1.98 ! [A: $tType] :
% 3.64/1.98 ( ( fs_name @ A )
% 3.64/1.98 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 3.64/1.98 ( ( eqvt @ pi @ Rel )
% 3.64/1.98 => ( ! [A6: late_subject,X5: name,Q3: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ P )
% 3.64/1.98 => ( ( fresh @ name @ pi @ X5 @ Q )
% 3.64/1.98 => ( ( fresh @ name @ late_subject @ X5 @ A6 )
% 3.64/1.98 => ( ( fresh @ name @ A @ X5 @ C4 )
% 3.64/1.98 => ? [P6: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ X5 @ P6 ) )
% 3.64/1.98 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ X5 @ Rel ) ) ) ) ) ) )
% 3.64/1.98 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.64/1.98 => ? [P6: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 3.64/1.98 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 3.64/1.98 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_127_parAssocLeft,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 3.64/1.98 ( ! [S2: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S2 @ T2 ) @ U ) @ ( par @ S2 @ ( par @ T2 @ U ) ) ) @ Rel )
% 3.64/1.98 => ( ! [S2: pi,T2: pi,X5: name] :
% 3.64/1.98 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S2 @ T2 ) @ Rel )
% 3.64/1.98 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 3.64/1.98 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 3.64/1.98 ( ( fresh @ name @ pi @ X5 @ S2 )
% 3.64/1.98 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T2 ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 3.64/1.98 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 3.64/1.98 ( ( fresh @ name @ pi @ X5 @ U )
% 3.64/1.98 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 3.64/1.98 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_128_resTauOutputTrans,axiom,
% 3.64/1.98 ! [X3: name,P: pi,A2: name,B3: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_129_resOutputTauTrans,axiom,
% 3.64/1.98 ! [X3: name,A2: name,B3: name,P: pi,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B3 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_130_resOutputInputTrans,axiom,
% 3.64/1.98 ! [X3: name,A2: name,B3: name,P: pi,C3: name,Y: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B3 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C3 ) @ Y @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_131_resOutputOutputTrans,axiom,
% 3.64/1.98 ! [X3: name,A2: name,P: pi,B3: name,Y: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ X3 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B3 @ Y ) @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_132_pi_Ofresh_I3_J,axiom,
% 3.64/1.98 ! [A2: name,X1: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 3.64/1.98 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_133_simps_I2_J,axiom,
% 3.64/1.98 ! [P: pi,C3: name,D: name] :
% 3.64/1.98 ( ( subs @ ( tau @ P ) @ C3 @ D )
% 3.64/1.98 = ( tau @ ( subs @ P @ C3 @ D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_134_pi_Ofresh_I2_J,axiom,
% 3.64/1.98 ! [A2: name,X32: name,X2: name,X1: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X2 @ X1 ) )
% 3.64/1.98 = ( ( fresh @ name @ name @ A2 @ X32 )
% 3.64/1.98 & ( fresh @ name @ name @ A2 @ X2 )
% 3.64/1.98 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_135_pi_Oinject_I2_J,axiom,
% 3.64/1.98 ! [X1: pi,Y1: pi] :
% 3.64/1.98 ( ( ( tau @ X1 )
% 3.64/1.98 = ( tau @ Y1 ) )
% 3.64/1.98 = ( X1 = Y1 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_136_pi_Oinject_I1_J,axiom,
% 3.64/1.98 ! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
% 3.64/1.98 ( ( ( output @ X32 @ X2 @ X1 )
% 3.64/1.98 = ( output @ Y32 @ Y22 @ Y1 ) )
% 3.64/1.98 = ( ( X32 = Y32 )
% 3.64/1.98 & ( X2 = Y22 )
% 3.64/1.98 & ( X1 = Y1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_137_pi_Odistinct_I19_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( tau @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_138_pi_Odistinct_I31_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_139_pi_Odistinct_I29_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_140_pi_Odistinct_I45_J,axiom,
% 3.64/1.98 ! [Pi4: pi,Name: name,Pi: pi] :
% 3.64/1.98 ( ( tau @ Pi4 )
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_141_pi_Odistinct_I43_J,axiom,
% 3.64/1.98 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( tau @ Pi4 )
% 3.64/1.98 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_142_resTrans_I1_J,axiom,
% 3.64/1.98 ! [X3: name,B3: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( output @ X3 @ B3 @ P ) ) @ Rs ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_143_outputBoundTrans,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,C3: late_subject,X3: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_BoundR @ C3 @ X3 @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_144_tauBoundTrans,axiom,
% 3.64/1.98 ! [P: pi,A2: late_subject,X3: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X3 @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_145_resTauBoundTrans,axiom,
% 3.64/1.98 ! [X3: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_146_Output,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi] : ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_147_outputIneqTrans,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,C3: name,D: name,P2: pi] :
% 3.64/1.98 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ ( late_OutputR @ C3 @ D ) @ P2 ) )
% 3.64/1.98 => ~ ( ( A2 != C3 )
% 3.64/1.98 | ( B3 != D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_148_outputCases_H,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ Rs )
% 3.64/1.98 => ~ ! [A6: name,B5: name,P4: pi] :
% 3.64/1.98 ( ( ( A2 = A6 )
% 3.64/1.98 & ( B3 = B5 )
% 3.64/1.98 & ( P = P4 ) )
% 3.64/1.98 => ( Rs
% 3.64/1.98 != ( late_FreeR @ ( late_OutputR @ A6 @ B5 ) @ P4 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_149_outputCases,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 3.64/1.98 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.98 => ( ( ( Alpha
% 3.64/1.98 = ( late_OutputR @ A2 @ B3 ) )
% 3.64/1.98 => ( ( P = P2 )
% 3.64/1.98 => ( Prop @ ( late_OutputR @ A2 @ B3 ) @ P ) ) )
% 3.64/1.98 => ( Prop @ Alpha @ P2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_150_outputTauTrans,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_151_tauOutputTrans,axiom,
% 3.64/1.98 ! [P: pi,A2: name,B3: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B3 ) @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_152_Tau,axiom,
% 3.64/1.98 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_153_tauCases_H,axiom,
% 3.64/1.98 ! [P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 3.64/1.98 => ~ ! [P4: pi] :
% 3.64/1.98 ( ( ( tau @ P )
% 3.64/1.98 = ( tau @ P4 ) )
% 3.64/1.98 => ( Rs
% 3.64/1.98 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_154_tauCases,axiom,
% 3.64/1.98 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 3.64/1.98 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.98 => ( ( ( Alpha = late_TauR )
% 3.64/1.98 => ( ( P = P2 )
% 3.64/1.98 => ( Prop @ late_TauR @ P ) ) )
% 3.64/1.98 => ( Prop @ Alpha @ P2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_155_outputFreshTrans,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.64/1.98 ( ( late_transitions @ ( output @ A2 @ B3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.64/1.98 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 3.64/1.98 | ( fresh @ name @ late_freeRes @ B3 @ Alpha ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_156_resInputBoundOutputTrans,axiom,
% 3.64/1.98 ! [X3: name,A2: name,Y: name,P: pi,B3: name,Z: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B3 ) @ Z @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_157_residual_Ofresh_I1_J,axiom,
% 3.64/1.98 ! [A2: name,X32: late_subject,X1: name,X2: pi] :
% 3.64/1.98 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 3.64/1.98 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 3.64/1.98 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_158_simps_I3_J,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,C3: name,D: name] :
% 3.64/1.98 ( ( subs @ ( output @ A2 @ B3 @ P ) @ C3 @ D )
% 3.64/1.98 = ( output @ ( subst_name @ A2 @ C3 @ D ) @ ( subst_name @ B3 @ C3 @ D ) @ ( subs @ P @ C3 @ D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_159_internal__case__prod__conv,axiom,
% 3.64/1.98 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B3: C] :
% 3.64/1.98 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B3 ) )
% 3.64/1.98 = ( C3 @ A2 @ B3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_160_simps_I4_J,axiom,
% 3.64/1.98 ! [X3: name,A2: name,C3: name,D: name,P: pi] :
% 3.64/1.98 ( ( X3 != A2 )
% 3.64/1.98 => ( ( X3 != C3 )
% 3.64/1.98 => ( ( X3 != D )
% 3.64/1.98 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ C3 @ D )
% 3.64/1.98 = ( input @ ( subst_name @ A2 @ C3 @ D ) @ X3 @ ( subs @ P @ C3 @ D ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_161_substInput,axiom,
% 3.64/1.98 ! [X3: name,B3: name,C3: name,A2: name,P: pi] :
% 3.64/1.98 ( ( X3 != B3 )
% 3.64/1.98 => ( ( X3 != C3 )
% 3.64/1.98 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ B3 @ C3 )
% 3.64/1.98 = ( input @ ( subst_name @ A2 @ B3 @ C3 ) @ X3 @ ( subs @ P @ B3 @ C3 ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_162_pi_Ofresh_I9_J,axiom,
% 3.64/1.98 ! [A2: name,X1: name,X2: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X2 ) )
% 3.64/1.98 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_163_pi_Ofresh_I4_J,axiom,
% 3.64/1.98 ! [A2: name,X32: name,X1: name,X2: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X2 ) )
% 3.64/1.98 = ( ( fresh @ name @ name @ A2 @ X32 )
% 3.64/1.98 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_164_pi_Odistinct_I57_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 3.64/1.98 ( ( input @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_165_pi_Odistinct_I55_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( input @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_166_pi_Oinject_I8_J,axiom,
% 3.64/1.98 ! [X1: name,X2: pi,Y1: name,Y22: pi] :
% 3.64/1.98 ( ( ( res @ X1 @ X2 )
% 3.64/1.98 = ( res @ Y1 @ Y22 ) )
% 3.64/1.98 = ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 3.64/1.98 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_167_subst__name__def,axiom,
% 3.64/1.98 ( subst_name
% 3.64/1.98 = ( ^ [A3: name,B2: name,C5: name] : ( if @ name @ ( A3 = B2 ) @ C5 @ A3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_168_pi_Oinject_I3_J,axiom,
% 3.64/1.98 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y22: pi] :
% 3.64/1.98 ( ( ( input @ X32 @ X1 @ X2 )
% 3.64/1.98 = ( input @ Y32 @ Y1 @ Y22 ) )
% 3.64/1.98 = ( ( X32 = Y32 )
% 3.64/1.98 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 3.64/1.98 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_169_abs__fun__eq1,axiom,
% 3.64/1.98 ! [X: $tType,A: $tType,A2: X,X3: A,Y: A] :
% 3.64/1.98 ( ( ( abs_fun @ X @ A @ A2 @ X3 )
% 3.64/1.98 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 3.64/1.98 = ( X3 = Y ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_170_name__fresh__abs,axiom,
% 3.64/1.98 ! [A: $tType] :
% 3.64/1.98 ( ( fs_name @ A )
% 3.64/1.98 => ! [B3: name,A2: name,X3: A] :
% 3.64/1.98 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B3 @ ( abs_fun @ name @ A @ A2 @ X3 ) )
% 3.64/1.98 = ( ( B3 = A2 )
% 3.64/1.98 | ( fresh @ name @ A @ B3 @ X3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_171_abs__fresh_I1_J,axiom,
% 3.64/1.98 ! [X7: $tType] :
% 3.64/1.98 ( ( fs_name @ X7 )
% 3.64/1.98 => ! [B3: name,A2: name,X3: X7] :
% 3.64/1.98 ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B3 @ ( abs_fun @ name @ X7 @ A2 @ X3 ) )
% 3.64/1.98 = ( ( B3 = A2 )
% 3.64/1.98 | ( fresh @ name @ X7 @ B3 @ X3 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_172_residual_Oinject_I1_J,axiom,
% 3.64/1.98 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y22: pi] :
% 3.64/1.98 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 3.64/1.98 = ( late_BoundR @ Y32 @ Y1 @ Y22 ) )
% 3.64/1.98 = ( ( X32 = Y32 )
% 3.64/1.98 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 3.64/1.98 = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_173_pi_Odistinct_I21_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_174_pi_Odistinct_I35_J,axiom,
% 3.64/1.98 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( tau @ Pi4 )
% 3.64/1.98 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_175_inputCases_H,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( input @ A2 @ B3 @ P ) @ Rs )
% 3.64/1.98 => ~ ! [X5: name,A6: name,P4: pi] :
% 3.64/1.98 ( ( ( A2 = A6 )
% 3.64/1.98 & ( ( abs_fun @ name @ pi @ B3 @ P )
% 3.64/1.98 = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 3.64/1.98 => ( ( Rs
% 3.64/1.98 = ( late_BoundR @ ( late_InputS @ A6 ) @ X5 @ P4 ) )
% 3.64/1.98 => ( X5 = A6 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_176_resTrans_I2_J,axiom,
% 3.64/1.98 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_177_inputFreeTrans,axiom,
% 3.64/1.98 ! [A2: name,X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_178_resInputFreeTrans,axiom,
% 3.64/1.98 ! [X3: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_179_Late__Semantics_OInput,axiom,
% 3.64/1.98 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_180_transitions_OInput,axiom,
% 3.64/1.98 ! [X3: name,A2: name,P: pi] :
% 3.64/1.98 ( ( X3 != A2 )
% 3.64/1.98 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_181_inputBoundOutputTrans,axiom,
% 3.64/1.98 ! [A2: name,X3: name,P: pi,B3: name,Y: name,P2: pi] :
% 3.64/1.98 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B3 ) @ Y @ P2 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_182_inputIneqTrans,axiom,
% 3.64/1.98 ! [A2: name,X3: name,P: pi,B3: late_subject,Y: name,P2: pi] :
% 3.64/1.98 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B3 @ Y @ P2 ) )
% 3.64/1.98 => ~ ( fresh @ name @ late_subject @ A2 @ B3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_183_parZeroRight,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.64/1.98 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 3.64/1.98 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_184_parZeroLeft,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.64/1.98 ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 3.64/1.98 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_185_simps_I6_J,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,C3: name,D: name] :
% 3.64/1.98 ( ( subs @ ( mismatch @ A2 @ B3 @ P ) @ C3 @ D )
% 3.64/1.98 = ( mismatch @ ( subst_name @ A2 @ C3 @ D ) @ ( subst_name @ B3 @ C3 @ D ) @ ( subs @ P @ C3 @ D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_186_pi_Ofresh_I1_J,axiom,
% 3.64/1.98 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_187_simps_I1_J,axiom,
% 3.64/1.98 ! [C3: name,D: name] :
% 3.64/1.98 ( ( subs @ piNil @ C3 @ D )
% 3.64/1.98 = piNil ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_188_pi_Ofresh_I6_J,axiom,
% 3.64/1.98 ! [A2: name,X32: name,X2: name,X1: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X2 @ X1 ) )
% 3.64/1.98 = ( ( fresh @ name @ name @ A2 @ X32 )
% 3.64/1.98 & ( fresh @ name @ name @ A2 @ X2 )
% 3.64/1.98 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_189_pi_Odistinct_I5_J,axiom,
% 3.64/1.98 ! [Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( piNil
% 3.64/1.98 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_190_pi_Odistinct_I51_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( input @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_191_pi_Odistinct_I75_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 3.64/1.98 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_192_pi_Odistinct_I73_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_193_pi_Odistinct_I15_J,axiom,
% 3.64/1.98 ! [Name: name,Pi: pi] :
% 3.64/1.98 ( piNil
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_194_pi_Odistinct_I13_J,axiom,
% 3.64/1.98 ! [Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( piNil
% 3.64/1.98 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_195_pi_Odistinct_I25_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_196_nilSimRight,axiom,
% 3.64/1.98 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_197_pi_Odistinct_I1_J,axiom,
% 3.64/1.98 ! [Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( piNil
% 3.64/1.98 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_198_pi_Odistinct_I39_J,axiom,
% 3.64/1.98 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( tau @ Pi4 )
% 3.64/1.98 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_199_pi_Odistinct_I3_J,axiom,
% 3.64/1.98 ! [Pi: pi] :
% 3.64/1.98 ( piNil
% 3.64/1.98 != ( tau @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_200_mismatchNilLeft,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A2 @ A2 @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_201_pi_Oinject_I5_J,axiom,
% 3.64/1.98 ! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
% 3.64/1.98 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 3.64/1.98 = ( mismatch @ Y32 @ Y22 @ Y1 ) )
% 3.64/1.98 = ( ( X32 = Y32 )
% 3.64/1.98 & ( X2 = Y22 )
% 3.64/1.98 & ( X1 = Y1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_202_pi_Odistinct_I9_J,axiom,
% 3.64/1.98 ! [Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( piNil
% 3.64/1.98 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_203_nilCases_H,axiom,
% 3.64/1.98 ! [Rs: late_residual] :
% 3.64/1.98 ~ ( late_transitions @ piNil @ Rs ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_204_zeroTrans,axiom,
% 3.64/1.98 ! [Rs: late_residual] :
% 3.64/1.98 ~ ( late_transitions @ piNil @ Rs ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_205_mismatchCases,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 3.64/1.98 ( ( late_transitions @ ( mismatch @ A2 @ B3 @ P ) @ Rs )
% 3.64/1.98 => ( ( ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( ( A2 != B3 )
% 3.64/1.98 => ( F @ A2 @ B3 ) ) )
% 3.64/1.98 => ( F @ A2 @ B3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_206_mismatchTrans,axiom,
% 3.64/1.98 ! [A2: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_207_mismatchCases_H,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( mismatch @ A2 @ B3 @ P ) @ Rs )
% 3.64/1.98 => ~ ! [P4: pi,A6: name,B5: name] :
% 3.64/1.98 ( ( ( A2 = A6 )
% 3.64/1.98 & ( B3 = B5 )
% 3.64/1.98 & ( P = P4 ) )
% 3.64/1.98 => ( ( late_transitions @ P4 @ Rs )
% 3.64/1.98 => ( A6 = B5 ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_208_Mismatch,axiom,
% 3.64/1.98 ! [P: pi,Rs: late_residual,A2: name,B3: name] :
% 3.64/1.98 ( ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( ( A2 != B3 )
% 3.64/1.98 => ( late_transitions @ ( mismatch @ A2 @ B3 @ P ) @ Rs ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_209_resZeroTrans,axiom,
% 3.64/1.98 ! [X3: name,Rs: late_residual] :
% 3.64/1.98 ~ ( late_transitions @ ( res @ X3 @ piNil ) @ Rs ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_210_nilSim_I2_J,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X3: name,P: pi] :
% 3.64/1.98 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X3 @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_211_nilSim_I3_J,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B3: name,P: pi] :
% 3.64/1.98 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B3 @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_212_nilSim_I1_J,axiom,
% 3.64/1.98 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.64/1.98 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_213_simps_I5_J,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,C3: name,D: name] :
% 3.64/1.98 ( ( subs @ ( match @ A2 @ B3 @ P ) @ C3 @ D )
% 3.64/1.98 = ( match @ ( subst_name @ A2 @ C3 @ D ) @ ( subst_name @ B3 @ C3 @ D ) @ ( subs @ P @ C3 @ D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_214_pi_Ofresh_I5_J,axiom,
% 3.64/1.98 ! [A2: name,X32: name,X2: name,X1: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X2 @ X1 ) )
% 3.64/1.98 = ( ( fresh @ name @ name @ A2 @ X32 )
% 3.64/1.98 & ( fresh @ name @ name @ A2 @ X2 )
% 3.64/1.98 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_215_freeRes_Ocase_I2_J,axiom,
% 3.64/1.98 ! [A: $tType,F1: name > name > A,F22: A] :
% 3.64/1.98 ( ( late_case_freeRes @ A @ F1 @ F22 @ late_TauR )
% 3.64/1.98 = F22 ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_216_pi_Odistinct_I61_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( match @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_217_pi_Odistinct_I7_J,axiom,
% 3.64/1.98 ! [Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( piNil
% 3.64/1.98 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_218_Match,axiom,
% 3.64/1.98 ! [P: pi,Rs: late_residual,B3: name] :
% 3.64/1.98 ( ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( late_transitions @ ( match @ B3 @ B3 @ P ) @ Rs ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_219_matchCases_H,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( match @ A2 @ B3 @ P ) @ Rs )
% 3.64/1.98 => ~ ! [P4: pi] :
% 3.64/1.98 ( ( ( B3 = A2 )
% 3.64/1.98 & ( P = P4 ) )
% 3.64/1.98 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_220_matchTrans,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( match @ A2 @ B3 @ P ) @ Rs )
% 3.64/1.98 => ( A2 = B3 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_221_matchCases,axiom,
% 3.64/1.98 ! [A2: name,B3: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 3.64/1.98 ( ( late_transitions @ ( match @ A2 @ B3 @ P ) @ Rs )
% 3.64/1.98 => ( ( ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( ( A2 = B3 )
% 3.64/1.98 => ( F @ A2 @ A2 ) ) )
% 3.64/1.98 => ( F @ A2 @ B3 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_222_pi_Oinject_I4_J,axiom,
% 3.64/1.98 ! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
% 3.64/1.98 ( ( ( match @ X32 @ X2 @ X1 )
% 3.64/1.98 = ( match @ Y32 @ Y22 @ Y1 ) )
% 3.64/1.98 = ( ( X32 = Y32 )
% 3.64/1.98 & ( X2 = Y22 )
% 3.64/1.98 & ( X1 = Y1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_223_pi_Odistinct_I37_J,axiom,
% 3.64/1.98 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( tau @ Pi4 )
% 3.64/1.98 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_224_pi_Odistinct_I23_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_225_pi_Odistinct_I65_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( match @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_226_pi_Odistinct_I67_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 3.64/1.98 ( ( match @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_227_pi_Odistinct_I49_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.64/1.98 ( ( input @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_228_matchNilLeft,axiom,
% 3.64/1.98 ! [A2: name,B3: name,Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.64/1.98 ( ( A2 != B3 )
% 3.64/1.98 => ( strong743114133lation @ piNil @ Rel @ ( match @ A2 @ B3 @ P ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_229_freeRes_Ocase_I1_J,axiom,
% 3.64/1.98 ! [A: $tType,F1: name > name > A,F22: A,X11: name,X122: name] :
% 3.64/1.98 ( ( late_case_freeRes @ A @ F1 @ F22 @ ( late_OutputR @ X11 @ X122 ) )
% 3.64/1.98 = ( F1 @ X11 @ X122 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_230_pi_Ostrong__induct,axiom,
% 3.64/1.98 ! [N: $tType] :
% 3.64/1.98 ( ( fs_name @ N )
% 3.64/1.98 => ! [P: N > pi > $o,Z: N,Pi4: pi] :
% 3.64/1.98 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 3.64/1.98 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Pi3: pi,Z2: N] :
% 3.64/1.98 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 3.64/1.98 ( ( fresh @ name @ N @ Name22 @ Z2 )
% 3.64/1.98 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 3.64/1.98 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 3.64/1.98 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: N] :
% 3.64/1.98 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 3.64/1.98 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 3.64/1.98 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 3.64/1.98 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.64/1.98 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 3.64/1.98 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 3.64/1.98 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 3.64/1.98 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.64/1.98 => ( ! [Name2: name,Pi3: pi,Z2: N] :
% 3.64/1.98 ( ( fresh @ name @ N @ Name2 @ Z2 )
% 3.64/1.98 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
% 3.64/1.98 => ( ! [Pi3: pi,Z2: N] :
% 3.64/1.98 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.64/1.98 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_231_pi_Ostrong__inducts,axiom,
% 3.64/1.98 ! [A: $tType] :
% 3.64/1.98 ( ( fs_name @ A )
% 3.64/1.98 => ! [P: A > pi > $o,Z: A,Pi4: pi] :
% 3.64/1.98 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 3.64/1.98 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Pi3: pi,Z2: A] :
% 3.64/1.98 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 3.64/1.98 ( ( fresh @ name @ A @ Name22 @ Z2 )
% 3.64/1.98 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 3.64/1.98 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 3.64/1.98 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Name1: name,Name22: name,Pi3: pi,Z2: A] :
% 3.64/1.98 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
% 3.64/1.98 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 3.64/1.98 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 3.64/1.98 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 3.64/1.98 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.64/1.98 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 3.64/1.98 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 3.64/1.98 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 3.64/1.98 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.64/1.98 => ( ! [Name2: name,Pi3: pi,Z2: A] :
% 3.64/1.98 ( ( fresh @ name @ A @ Name2 @ Z2 )
% 3.64/1.98 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
% 3.64/1.98 => ( ! [Pi3: pi,Z2: A] :
% 3.64/1.98 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 3.64/1.98 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.64/1.98 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_232_pi_Ofresh_I10_J,axiom,
% 3.64/1.98 ! [A2: name,X1: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 3.64/1.98 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_233_pi_Ofresh_I7_J,axiom,
% 3.64/1.98 ! [A2: name,X2: pi,X1: pi] :
% 3.64/1.98 ( ( fresh @ name @ pi @ A2 @ ( sum @ X2 @ X1 ) )
% 3.64/1.98 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 3.64/1.98 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_234_simps_I10_J,axiom,
% 3.64/1.98 ! [P: pi,C3: name,D: name] :
% 3.64/1.98 ( ( subs @ ( bang @ P ) @ C3 @ D )
% 3.64/1.98 = ( bang @ ( subs @ P @ C3 @ D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_235_simps_I7_J,axiom,
% 3.64/1.98 ! [P: pi,Q: pi,C3: name,D: name] :
% 3.64/1.98 ( ( subs @ ( sum @ P @ Q ) @ C3 @ D )
% 3.64/1.98 = ( sum @ ( subs @ P @ C3 @ D ) @ ( subs @ Q @ C3 @ D ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_236_pi_Odistinct_I63_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( match @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_237_pi_Odistinct_I69_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 3.64/1.98 ( ( match @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( bang @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_238_bangCases,axiom,
% 3.64/1.98 ! [P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 3.64/1.98 => ~ ! [P4: pi] :
% 3.64/1.98 ( ( ( bang @ P )
% 3.64/1.98 = ( bang @ P4 ) )
% 3.64/1.98 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_239_Bang,axiom,
% 3.64/1.98 ! [P: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 3.64/1.98 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_240_pi_Odistinct_I53_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( input @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_241_pi_Odistinct_I59_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 3.64/1.98 ( ( input @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( bang @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_242_pi_Odistinct_I89_J,axiom,
% 3.64/1.98 ! [Name3: name,Pi4: pi,Pi: pi] :
% 3.64/1.98 ( ( res @ Name3 @ Pi4 )
% 3.64/1.98 != ( bang @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_243_pi_Odistinct_I87_J,axiom,
% 3.64/1.98 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 3.64/1.98 ( ( par @ Pi1 @ Pi2 )
% 3.64/1.98 != ( bang @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_244_sumCases,axiom,
% 3.64/1.98 ! [P: pi,Q: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.64/1.98 => ( ~ ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_245_sumCases_H,axiom,
% 3.64/1.98 ! [P: pi,Q: pi,Rs: late_residual] :
% 3.64/1.98 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.64/1.98 => ( ~ ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_246_Sum1,axiom,
% 3.64/1.98 ! [P: pi,Rs: late_residual,Q: pi] :
% 3.64/1.98 ( ( late_transitions @ P @ Rs )
% 3.64/1.98 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_247_Sum2,axiom,
% 3.64/1.98 ! [Q: pi,Rs: late_residual,P: pi] :
% 3.64/1.98 ( ( late_transitions @ Q @ Rs )
% 3.64/1.98 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_248_pi_Odistinct_I81_J,axiom,
% 3.64/1.98 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.64/1.98 ( ( sum @ Pi1 @ Pi2 )
% 3.64/1.98 != ( res @ Name @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_249_pi_Odistinct_I79_J,axiom,
% 3.64/1.98 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( sum @ Pi1 @ Pi2 )
% 3.64/1.98 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_250_pi_Oinject_I9_J,axiom,
% 3.64/1.98 ! [X1: pi,Y1: pi] :
% 3.64/1.98 ( ( ( bang @ X1 )
% 3.64/1.98 = ( bang @ Y1 ) )
% 3.64/1.98 = ( X1 = Y1 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_251_pi_Oinject_I6_J,axiom,
% 3.64/1.98 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 3.64/1.98 ( ( ( sum @ X2 @ X1 )
% 3.64/1.98 = ( sum @ Y22 @ Y1 ) )
% 3.64/1.98 = ( ( X2 = Y22 )
% 3.64/1.98 & ( X1 = Y1 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_252_pi_Odistinct_I83_J,axiom,
% 3.64/1.98 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 3.64/1.98 ( ( sum @ Pi1 @ Pi2 )
% 3.64/1.98 != ( bang @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_253_pi_Odistinct_I27_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_254_pi_Odistinct_I33_J,axiom,
% 3.64/1.98 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 3.64/1.98 ( ( output @ Name12 @ Name23 @ Pi4 )
% 3.64/1.98 != ( bang @ Pi ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(fact_255_pi_Odistinct_I41_J,axiom,
% 3.64/1.98 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.64/1.98 ( ( tau @ Pi4 )
% 3.64/1.98 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 3.64/1.98 fs_name @ pi ).
% 3.64/1.98
% 3.64/1.98 thf(tcon_HOL_Obool___Agent_Ofs__name_1,axiom,
% 3.64/1.98 fs_name @ $o ).
% 3.64/1.98
% 3.64/1.98 thf(tcon_Agent_Oname___Agent_Ofs__name_2,axiom,
% 3.64/1.98 fs_name @ name ).
% 3.64/1.98
% 3.64/1.98 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3,axiom,
% 3.64/1.98 ! [A7: $tType,A8: $tType] :
% 3.64/1.98 ( ( ( fs_name @ A7 )
% 3.64/1.98 & ( fs_name @ A8 ) )
% 3.64/1.98 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4,axiom,
% 3.64/1.98 fs_name @ late_freeRes ).
% 3.64/1.98
% 3.64/1.98 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5,axiom,
% 3.64/1.98 fs_name @ late_subject ).
% 3.64/1.98
% 3.64/1.98 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6,axiom,
% 3.64/1.98 fs_name @ late_residual ).
% 3.64/1.98
% 3.64/1.98 thf(help_If_3_1_T,axiom,
% 3.64/1.98 ! [P: $o] :
% 3.64/1.98 ( ( P = $true )
% 3.64/1.98 | ( P = $false ) ) ).
% 3.64/1.98
% 3.64/1.98 thf(help_If_2_1_T,axiom,
% 3.64/1.98 ! [A: $tType,X3: A,Y: A] :
% 3.64/1.98 ( ( if @ A @ $false @ X3 @ Y )
% 3.64/1.98 = Y ) ).
% 3.64/1.98
% 3.64/1.98 thf(help_If_1_1_T,axiom,
% 3.64/1.98 ! [A: $tType,X3: A,Y: A] :
% 3.64/1.98 ( ( if @ A @ $true @ X3 @ Y )
% 3.64/1.98 = X3 ) ).
% 3.64/1.98
% 3.64/1.98 thf(conj_0,conjecture,
% 3.64/1.98 x != aa ).
% 3.64/1.98 ------------------------
% 3.64/2.02 % (764)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_641 for (2999ds/27Mi)
% 3.64/2.02 % (766)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_641 for (2999ds/2Mi)
% 3.64/2.02 % (767)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_641 for (2999ds/275Mi)
% 3.64/2.02 % (761)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/183Mi)
% 3.64/2.02 % (762)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_641 for (2999ds/4Mi)
% 3.64/2.02 % (765)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/2Mi)
% 3.64/2.02 % (768)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/18Mi)
% 3.64/2.02 % (765)Instruction limit reached!
% 3.64/2.02 % (765)------------------------------
% 3.64/2.02 % (765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.02 % (765)Termination reason: Unknown
% 3.64/2.02 % (766)Instruction limit reached!
% 3.64/2.02 % (766)------------------------------
% 3.64/2.02 % (766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.02 % (765)Termination phase: shuffling
% 3.64/2.02
% 3.64/2.02 % (765)Memory used [KB]: 1407
% 3.64/2.02 % (765)Time elapsed: 0.003 s
% 3.64/2.02 % (765)Instructions burned: 2 (million)
% 3.64/2.02 % (765)------------------------------
% 3.64/2.02 % (765)------------------------------
% 3.64/2.02 % (766)Termination reason: Unknown
% 3.64/2.02 % (766)Termination phase: shuffling
% 3.64/2.02
% 3.64/2.02 % (766)Memory used [KB]: 1407
% 3.64/2.02 % (766)Time elapsed: 0.003 s
% 3.64/2.02 % (766)Instructions burned: 2 (million)
% 3.64/2.02 % (766)------------------------------
% 3.64/2.02 % (766)------------------------------
% 3.64/2.02 % (762)Instruction limit reached!
% 3.64/2.02 % (762)------------------------------
% 3.64/2.02 % (762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.02 % (762)Termination reason: Unknown
% 3.64/2.02 % (762)Termination phase: shuffling
% 3.64/2.02
% 3.64/2.02 % (762)Memory used [KB]: 1407
% 3.64/2.02 % (762)Time elapsed: 0.004 s
% 3.64/2.02 % (762)Instructions burned: 4 (million)
% 3.64/2.02 % (762)------------------------------
% 3.64/2.02 % (762)------------------------------
% 3.75/2.03 % (768)Instruction limit reached!
% 3.75/2.03 % (768)------------------------------
% 3.75/2.03 % (768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.03 % (768)Termination reason: Unknown
% 3.75/2.03 % (768)Termination phase: shuffling
% 3.75/2.03
% 3.75/2.03 % (768)Memory used [KB]: 1791
% 3.75/2.03 % (768)Time elapsed: 0.012 s
% 3.75/2.03 % (768)Instructions burned: 19 (million)
% 3.75/2.03 % (768)------------------------------
% 3.75/2.03 % (768)------------------------------
% 3.75/2.04 % (764)Instruction limit reached!
% 3.75/2.04 % (764)------------------------------
% 3.75/2.04 % (764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.04 % (764)Termination reason: Unknown
% 3.75/2.04 % (764)Termination phase: Property scanning
% 3.75/2.04
% 3.75/2.04 % (764)Memory used [KB]: 1918
% 3.75/2.04 % (764)Time elapsed: 0.017 s
% 3.75/2.04 % (764)Instructions burned: 28 (million)
% 3.75/2.04 % (764)------------------------------
% 3.75/2.04 % (764)------------------------------
% 3.75/2.04 % (771)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_641 for (2999ds/15Mi)
% 3.75/2.04 % (769)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/3Mi)
% 3.75/2.04 % (770)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_641 for (2999ds/37Mi)
% 3.75/2.04 % (769)Instruction limit reached!
% 3.75/2.04 % (769)------------------------------
% 3.75/2.04 % (769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.04 % (769)Termination reason: Unknown
% 3.75/2.04 % (769)Termination phase: shuffling
% 3.75/2.04
% 3.75/2.04 % (769)Memory used [KB]: 1407
% 3.75/2.04 % (769)Time elapsed: 0.003 s
% 3.75/2.04 % (769)Instructions burned: 3 (million)
% 3.75/2.04 % (769)------------------------------
% 3.75/2.04 % (769)------------------------------
% 3.75/2.05 % (767)Refutation not found, incomplete strategy
% 3.75/2.05 % (767)------------------------------
% 3.75/2.05 % (767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.05 % (767)Termination reason: Refutation not found, incomplete strategy
% 3.75/2.05
% 3.75/2.05
% 3.75/2.05 % (767)Memory used [KB]: 6396
% 3.75/2.05 % (767)Time elapsed: 0.026 s
% 3.75/2.05 % (767)Instructions burned: 45 (million)
% 3.75/2.05 % (767)------------------------------
% 3.75/2.05 % (767)------------------------------
% 3.75/2.05 % (771)Instruction limit reached!
% 3.75/2.05 % (771)------------------------------
% 3.75/2.05 % (771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.05 % (771)Termination reason: Unknown
% 3.75/2.05 % (771)Termination phase: shuffling
% 3.75/2.05
% 3.75/2.05 % (771)Memory used [KB]: 1663
% 3.75/2.05 % (771)Time elapsed: 0.010 s
% 3.75/2.05 % (771)Instructions burned: 15 (million)
% 3.75/2.05 % (771)------------------------------
% 3.75/2.05 % (771)------------------------------
% 3.75/2.05 % (773)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_641 for (2999ds/3Mi)
% 3.75/2.05 % (773)Instruction limit reached!
% 3.75/2.05 % (773)------------------------------
% 3.75/2.05 % (773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.05 % (773)Termination reason: Unknown
% 3.75/2.05 % (773)Termination phase: shuffling
% 3.75/2.05
% 3.75/2.05 % (773)Memory used [KB]: 1407
% 3.75/2.05 % (773)Time elapsed: 0.004 s
% 3.75/2.05 % (773)Instructions burned: 4 (million)
% 3.75/2.05 % (773)------------------------------
% 3.75/2.05 % (773)------------------------------
% 3.75/2.06 % (774)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_641 for (2999ds/1041Mi)
% 3.75/2.06 % (770)Instruction limit reached!
% 3.75/2.06 % (770)------------------------------
% 3.75/2.06 % (770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.06 % (770)Termination reason: Unknown
% 3.75/2.06 % (770)Termination phase: shuffling
% 3.75/2.06
% 3.75/2.06 % (770)Memory used [KB]: 2174
% 3.75/2.06 % (770)Time elapsed: 0.021 s
% 3.75/2.06 % (770)Instructions burned: 37 (million)
% 3.75/2.06 % (770)------------------------------
% 3.75/2.06 % (770)------------------------------
% 3.75/2.06 % (775)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/7Mi)
% 3.75/2.07 % (778)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/16Mi)
% 3.75/2.07 % (775)Instruction limit reached!
% 3.75/2.07 % (775)------------------------------
% 3.75/2.07 % (775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.07 % (775)Termination reason: Unknown
% 3.75/2.07 % (775)Termination phase: shuffling
% 3.75/2.07
% 3.75/2.07 % (775)Memory used [KB]: 1535
% 3.75/2.07 % (775)Time elapsed: 0.006 s
% 3.75/2.07 % (775)Instructions burned: 8 (million)
% 3.75/2.07 % (775)------------------------------
% 3.75/2.07 % (775)------------------------------
% 3.75/2.07 % (779)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_641 for (2999ds/3Mi)
% 3.75/2.07 % (779)Instruction limit reached!
% 3.75/2.07 % (779)------------------------------
% 3.75/2.07 % (779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.07 % (779)Termination reason: Unknown
% 3.75/2.07 % (779)Termination phase: shuffling
% 3.75/2.07
% 3.75/2.07 % (779)Memory used [KB]: 1407
% 3.75/2.07 % (779)Time elapsed: 0.004 s
% 3.75/2.07 % (779)Instructions burned: 4 (million)
% 3.75/2.07 % (779)------------------------------
% 3.75/2.07 % (779)------------------------------
% 3.75/2.07 % (780)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/3Mi)
% 3.75/2.07 % (780)Instruction limit reached!
% 3.75/2.07 % (780)------------------------------
% 3.75/2.07 % (780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.07 % (780)Termination reason: Unknown
% 3.75/2.07 % (780)Termination phase: shuffling
% 3.75/2.07
% 3.75/2.07 % (780)Memory used [KB]: 1407
% 3.75/2.07 % (780)Time elapsed: 0.004 s
% 3.75/2.07 % (780)Instructions burned: 4 (million)
% 3.75/2.07 % (780)------------------------------
% 3.75/2.07 % (780)------------------------------
% 3.75/2.07 % (778)Instruction limit reached!
% 3.75/2.07 % (778)------------------------------
% 3.75/2.07 % (778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.07 % (778)Termination reason: Unknown
% 3.75/2.07 % (778)Termination phase: shuffling
% 3.75/2.07
% 3.75/2.07 % (778)Memory used [KB]: 1663
% 3.75/2.07 % (778)Time elapsed: 0.011 s
% 3.75/2.07 % (778)Instructions burned: 17 (million)
% 3.75/2.07 % (778)------------------------------
% 3.75/2.07 % (778)------------------------------
% 3.75/2.08 % (781)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/7Mi)
% 3.75/2.08 % (781)Instruction limit reached!
% 3.75/2.08 % (781)------------------------------
% 3.75/2.08 % (781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.08 % (781)Termination reason: Unknown
% 3.75/2.08 % (781)Termination phase: shuffling
% 3.75/2.08
% 3.75/2.08 % (781)Memory used [KB]: 1535
% 3.75/2.08 % (781)Time elapsed: 0.006 s
% 3.75/2.08 % (781)Instructions burned: 8 (million)
% 3.75/2.08 % (781)------------------------------
% 3.75/2.08 % (781)------------------------------
% 3.75/2.08 % (782)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/3Mi)
% 3.75/2.09 % (782)Instruction limit reached!
% 3.75/2.09 % (782)------------------------------
% 3.75/2.09 % (782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.09 % (782)Termination reason: Unknown
% 3.75/2.09 % (782)Termination phase: shuffling
% 3.75/2.09
% 3.75/2.09 % (782)Memory used [KB]: 1535
% 3.75/2.09 % (782)Time elapsed: 0.004 s
% 3.75/2.09 % (782)Instructions burned: 4 (million)
% 3.75/2.09 % (782)------------------------------
% 3.75/2.09 % (782)------------------------------
% 3.75/2.09 % (783)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/4Mi)
% 3.75/2.09 % (783)Instruction limit reached!
% 3.75/2.09 % (783)------------------------------
% 3.75/2.09 % (783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.09 % (783)Termination reason: Unknown
% 3.75/2.09 % (783)Termination phase: shuffling
% 3.75/2.09
% 3.75/2.09 % (783)Memory used [KB]: 1407
% 3.75/2.09 % (783)Time elapsed: 0.004 s
% 3.75/2.09 % (783)Instructions burned: 4 (million)
% 3.75/2.09 % (783)------------------------------
% 3.75/2.09 % (783)------------------------------
% 3.75/2.09 % (784)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/18Mi)
% 3.75/2.09 % (785)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/710Mi)
% 3.75/2.10 % (784)Instruction limit reached!
% 3.75/2.10 % (784)------------------------------
% 3.75/2.10 % (784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.10 % (784)Termination reason: Unknown
% 3.75/2.10 % (784)Termination phase: shuffling
% 3.75/2.10
% 3.75/2.10 % (784)Memory used [KB]: 1791
% 3.75/2.10 % (784)Time elapsed: 0.012 s
% 3.75/2.10 % (784)Instructions burned: 19 (million)
% 3.75/2.10 % (784)------------------------------
% 3.75/2.10 % (784)------------------------------
% 3.75/2.10 % (786)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/6Mi)
% 3.75/2.11 % (786)Instruction limit reached!
% 3.75/2.11 % (786)------------------------------
% 3.75/2.11 % (786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.11 % (786)Termination reason: Unknown
% 3.75/2.11 % (786)Termination phase: shuffling
% 3.75/2.11
% 3.75/2.11 % (786)Memory used [KB]: 1535
% 3.75/2.11 % (786)Time elapsed: 0.006 s
% 3.75/2.11 % (786)Instructions burned: 7 (million)
% 3.75/2.11 % (786)------------------------------
% 3.75/2.11 % (786)------------------------------
% 3.75/2.11 % (787)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/902Mi)
% 3.75/2.11 % (788)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_641 for (2999ds/21Mi)
% 3.75/2.12 % (761)Instruction limit reached!
% 3.75/2.12 % (761)------------------------------
% 3.75/2.12 % (761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.12 % (761)Termination reason: Unknown
% 3.75/2.12 % (761)Termination phase: Saturation
% 3.75/2.12
% 3.75/2.12 % (761)Memory used [KB]: 7291
% 3.75/2.12 % (761)Time elapsed: 0.097 s
% 3.75/2.12 % (761)Instructions burned: 183 (million)
% 3.75/2.12 % (761)------------------------------
% 3.75/2.12 % (761)------------------------------
% 3.75/2.12 % (785)Refutation not found, incomplete strategy
% 3.75/2.12 % (785)------------------------------
% 3.75/2.12 % (785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.12 % (785)Termination reason: Refutation not found, incomplete strategy
% 3.75/2.12
% 3.75/2.12
% 3.75/2.12 % (785)Memory used [KB]: 6396
% 3.75/2.12 % (785)Time elapsed: 0.026 s
% 3.75/2.12 % (785)Instructions burned: 46 (million)
% 3.75/2.12 % (785)------------------------------
% 3.75/2.12 % (785)------------------------------
% 3.75/2.12 % (788)Instruction limit reached!
% 3.75/2.12 % (788)------------------------------
% 3.75/2.12 % (788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.12 % (788)Termination reason: Unknown
% 3.75/2.12 % (788)Termination phase: shuffling
% 3.75/2.12
% 3.75/2.12 % (788)Memory used [KB]: 1791
% 3.75/2.12 % (788)Time elapsed: 0.013 s
% 3.75/2.12 % (788)Instructions burned: 21 (million)
% 3.75/2.12 % (788)------------------------------
% 3.75/2.12 % (788)------------------------------
% 3.75/2.12 % (789)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/5Mi)
% 3.75/2.12 % (789)Instruction limit reached!
% 3.75/2.12 % (789)------------------------------
% 3.75/2.12 % (789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.12 % (789)Termination reason: Unknown
% 3.75/2.12 % (789)Termination phase: shuffling
% 3.75/2.12
% 3.75/2.12 % (789)Memory used [KB]: 1535
% 3.75/2.12 % (789)Time elapsed: 0.004 s
% 3.75/2.12 % (789)Instructions burned: 5 (million)
% 3.75/2.12 % (789)------------------------------
% 3.75/2.12 % (789)------------------------------
% 3.75/2.12 % (790)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/6Mi)
% 4.43/2.13 % (790)Instruction limit reached!
% 4.43/2.13 % (790)------------------------------
% 4.43/2.13 % (790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.13 % (790)Termination reason: Unknown
% 4.43/2.13 % (790)Termination phase: shuffling
% 4.43/2.13
% 4.43/2.13 % (790)Memory used [KB]: 1535
% 4.43/2.13 % (790)Time elapsed: 0.005 s
% 4.43/2.13 % (790)Instructions burned: 7 (million)
% 4.43/2.13 % (790)------------------------------
% 4.43/2.13 % (790)------------------------------
% 4.43/2.14 % (791)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/377Mi)
% 4.43/2.14 % (792)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/779Mi)
% 4.43/2.14 % (793)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/19Mi)
% 4.43/2.14 % (794)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/879Mi)
% 4.43/2.15 % (795)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/17Mi)
% 4.43/2.15 % (793)Instruction limit reached!
% 4.43/2.15 % (793)------------------------------
% 4.43/2.15 % (793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.15 % (793)Termination reason: Unknown
% 4.43/2.15 % (793)Termination phase: shuffling
% 4.43/2.15
% 4.43/2.15 % (793)Memory used [KB]: 1918
% 4.43/2.15 % (793)Time elapsed: 0.012 s
% 4.43/2.15 % (793)Instructions burned: 20 (million)
% 4.43/2.15 % (793)------------------------------
% 4.43/2.15 % (793)------------------------------
% 4.43/2.16 % (795)Instruction limit reached!
% 4.43/2.16 % (795)------------------------------
% 4.43/2.16 % (795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.16 % (795)Termination reason: Unknown
% 4.43/2.16 % (795)Termination phase: shuffling
% 4.43/2.16
% 4.43/2.16 % (795)Memory used [KB]: 1663
% 4.43/2.16 % (795)Time elapsed: 0.011 s
% 4.43/2.16 % (795)Instructions burned: 17 (million)
% 4.43/2.16 % (795)------------------------------
% 4.43/2.16 % (795)------------------------------
% 4.43/2.17 % (796)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/3Mi)
% 4.43/2.17 % (794)Refutation not found, incomplete strategy
% 4.43/2.17 % (794)------------------------------
% 4.43/2.17 % (794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.17 % (796)Instruction limit reached!
% 4.43/2.17 % (796)------------------------------
% 4.43/2.17 % (796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.17 % (796)Termination reason: Unknown
% 4.43/2.17 % (796)Termination phase: shuffling
% 4.43/2.17
% 4.43/2.17 % (796)Memory used [KB]: 1407
% 4.43/2.17 % (796)Time elapsed: 0.004 s
% 4.43/2.17 % (796)Instructions burned: 4 (million)
% 4.43/2.17 % (796)------------------------------
% 4.43/2.17 % (796)------------------------------
% 4.43/2.17 % (794)Termination reason: Refutation not found, incomplete strategy
% 4.43/2.17
% 4.43/2.17
% 4.43/2.17 % (794)Memory used [KB]: 6396
% 4.43/2.17 % (794)Time elapsed: 0.031 s
% 4.43/2.17 % (794)Instructions burned: 52 (million)
% 4.43/2.17 % (794)------------------------------
% 4.43/2.17 % (794)------------------------------
% 4.43/2.18 % (797)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/30Mi)
% 4.43/2.19 % (798)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/127Mi)
% 4.43/2.19 % (799)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_641 for (2998ds/100Mi)
% 4.43/2.19 % (797)Instruction limit reached!
% 4.43/2.19 % (797)------------------------------
% 4.43/2.19 % (797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.19 % (797)Termination reason: Unknown
% 4.43/2.19 % (797)Termination phase: shuffling
% 4.43/2.19
% 4.43/2.19 % (797)Memory used [KB]: 1918
% 4.43/2.19 % (797)Time elapsed: 0.018 s
% 4.43/2.19 % (797)Instructions burned: 30 (million)
% 4.43/2.19 % (797)------------------------------
% 4.43/2.19 % (797)------------------------------
% 4.62/2.22 % (800)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_641 for (2997ds/3Mi)
% 4.62/2.22 % (800)Instruction limit reached!
% 4.62/2.22 % (800)------------------------------
% 4.62/2.22 % (800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.62/2.22 % (800)Termination reason: Unknown
% 4.62/2.22 % (800)Termination phase: shuffling
% 4.62/2.22
% 4.62/2.22 % (800)Memory used [KB]: 1407
% 4.62/2.22 % (800)Time elapsed: 0.004 s
% 4.62/2.22 % (800)Instructions burned: 4 (million)
% 4.62/2.22 % (800)------------------------------
% 4.62/2.22 % (800)------------------------------
% 4.62/2.24 % (801)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_641 for (2997ds/20Mi)
% 4.62/2.24 % (787)Refutation not found, incomplete strategy
% 4.62/2.24 % (787)------------------------------
% 4.62/2.24 % (787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.62/2.24 % (787)Termination reason: Refutation not found, incomplete strategy
% 4.62/2.24
% 4.62/2.24
% 4.62/2.24 % (787)Memory used [KB]: 8187
% 4.62/2.24 % (787)Time elapsed: 0.137 s
% 4.62/2.24 % (787)Instructions burned: 250 (million)
% 4.62/2.24 % (787)------------------------------
% 4.62/2.24 % (787)------------------------------
% 4.62/2.24 % (799)Instruction limit reached!
% 4.62/2.24 % (799)------------------------------
% 4.62/2.24 % (799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.62/2.24 % (799)Termination reason: Unknown
% 4.62/2.24 % (799)Termination phase: Property scanning
% 4.62/2.24
% 4.62/2.24 % (799)Memory used [KB]: 2686
% 4.62/2.24 % (799)Time elapsed: 0.052 s
% 4.62/2.24 % (799)Instructions burned: 100 (million)
% 4.62/2.24 % (799)------------------------------
% 4.62/2.24 % (799)------------------------------
% 4.62/2.25 % (801)Instruction limit reached!
% 4.62/2.25 % (801)------------------------------
% 4.62/2.25 % (801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.62/2.25 % (801)Termination reason: Unknown
% 4.62/2.25 % (801)Termination phase: shuffling
% 4.62/2.25
% 4.62/2.25 % (801)Memory used [KB]: 1791
% 4.62/2.25 % (801)Time elapsed: 0.014 s
% 4.62/2.25 % (801)Instructions burned: 21 (million)
% 4.62/2.25 % (801)------------------------------
% 4.62/2.25 % (801)------------------------------
% 4.62/2.26 % (798)Instruction limit reached!
% 4.62/2.26 % (798)------------------------------
% 4.62/2.26 % (798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.62/2.26 % (798)Termination reason: Unknown
% 4.62/2.26 % (798)Termination phase: Property scanning
% 4.62/2.26
% 4.62/2.26 % (798)Memory used [KB]: 2558
% 4.62/2.26 % (798)Time elapsed: 0.068 s
% 4.62/2.26 % (798)Instructions burned: 127 (million)
% 4.62/2.26 % (798)------------------------------
% 4.62/2.26 % (798)------------------------------
% 4.62/2.26 % (803)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_641 for (2997ds/107Mi)
% 4.62/2.26 % (802)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_641 for (2997ds/86Mi)
% 4.62/2.27 % (804)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_641 for (2997ds/39Mi)
% 4.62/2.28 % (805)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_641 for (2997ds/448Mi)
% 4.62/2.29 % (804)Instruction limit reached!
% 4.62/2.29 % (804)------------------------------
% 4.62/2.29 % (804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.62/2.29 % (804)Termination reason: Unknown
% 4.62/2.29 % (804)Termination phase: shuffling
% 4.62/2.29
% 4.62/2.29 % (804)Memory used [KB]: 2174
% 4.62/2.29 % (804)Time elapsed: 0.022 s
% 4.62/2.29 % (804)Instructions burned: 40 (million)
% 4.62/2.29 % (804)------------------------------
% 4.62/2.29 % (804)------------------------------
% 5.03/2.31 % (802)Instruction limit reached!
% 5.03/2.31 % (802)------------------------------
% 5.03/2.31 % (802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.31 % (802)Termination reason: Unknown
% 5.03/2.31 % (802)Termination phase: Property scanning
% 5.03/2.31
% 5.03/2.31 % (802)Memory used [KB]: 2558
% 5.03/2.31 % (802)Time elapsed: 0.047 s
% 5.03/2.31 % (802)Instructions burned: 87 (million)
% 5.03/2.31 % (802)------------------------------
% 5.03/2.31 % (802)------------------------------
% 5.03/2.31 % (806)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_641 for (2996ds/46Mi)
% 5.03/2.32 % (803)Instruction limit reached!
% 5.03/2.32 % (803)------------------------------
% 5.03/2.32 % (803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.32 % (803)Termination reason: Unknown
% 5.03/2.32 % (803)Termination phase: Saturation
% 5.03/2.32
% 5.03/2.32 % (803)Memory used [KB]: 6908
% 5.03/2.32 % (803)Time elapsed: 0.059 s
% 5.03/2.32 % (803)Instructions burned: 107 (million)
% 5.03/2.32 % (803)------------------------------
% 5.03/2.32 % (803)------------------------------
% 5.03/2.33 % (807)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_641 for (2996ds/98Mi)
% 5.03/2.33 % (791)Instruction limit reached!
% 5.03/2.33 % (791)------------------------------
% 5.03/2.33 % (791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.33 % (791)Termination reason: Unknown
% 5.03/2.33 % (791)Termination phase: Saturation
% 5.03/2.33
% 5.03/2.33 % (791)Memory used [KB]: 8827
% 5.03/2.33 % (791)Time elapsed: 0.201 s
% 5.03/2.33 % (791)Instructions burned: 378 (million)
% 5.03/2.33 % (791)------------------------------
% 5.03/2.33 % (791)------------------------------
% 5.03/2.34 % (806)Instruction limit reached!
% 5.03/2.34 % (806)------------------------------
% 5.03/2.34 % (806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.34 % (806)Termination reason: Unknown
% 5.03/2.34 % (806)Termination phase: SInE selection
% 5.03/2.34
% 5.03/2.34 % (806)Memory used [KB]: 1918
% 5.03/2.34 % (806)Time elapsed: 0.026 s
% 5.03/2.34 % (806)Instructions burned: 46 (million)
% 5.03/2.34 % (806)------------------------------
% 5.03/2.34 % (806)------------------------------
% 5.03/2.34 % (808)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_641 for (2996ds/507Mi)
% 5.03/2.35 % (809)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_641 for (2996ds/149Mi)
% 5.03/2.36 % (810)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_641 for (2996ds/39Mi)
% 5.03/2.38 % (807)Instruction limit reached!
% 5.03/2.38 % (807)------------------------------
% 5.03/2.38 % (807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.38 % (807)Termination reason: Unknown
% 5.03/2.38 % (807)Termination phase: Preprocessing 3
% 5.03/2.38
% 5.03/2.38 % (807)Memory used [KB]: 2686
% 5.03/2.38 % (807)Time elapsed: 0.050 s
% 5.03/2.38 % (807)Instructions burned: 98 (million)
% 5.03/2.38 % (807)------------------------------
% 5.03/2.38 % (807)------------------------------
% 5.03/2.38 % (810)Instruction limit reached!
% 5.03/2.38 % (810)------------------------------
% 5.03/2.38 % (810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.38 % (810)Termination reason: Unknown
% 5.03/2.38 % (810)Termination phase: Property scanning
% 5.03/2.38
% 5.03/2.38 % (810)Memory used [KB]: 1918
% 5.03/2.38 % (810)Time elapsed: 0.023 s
% 5.03/2.38 % (810)Instructions burned: 40 (million)
% 5.03/2.38 % (810)------------------------------
% 5.03/2.38 % (810)------------------------------
% 5.54/2.40 % (811)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_641 for (2996ds/6Mi)
% 5.54/2.40 % (812)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_641 for (2996ds/1087Mi)
% 5.54/2.40 % (811)Instruction limit reached!
% 5.54/2.40 % (811)------------------------------
% 5.54/2.40 % (811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.40 % (811)Termination reason: Unknown
% 5.54/2.40 % (811)Termination phase: shuffling
% 5.54/2.40
% 5.54/2.40 % (811)Memory used [KB]: 1535
% 5.54/2.40 % (811)Time elapsed: 0.005 s
% 5.54/2.40 % (811)Instructions burned: 6 (million)
% 5.54/2.40 % (811)------------------------------
% 5.54/2.40 % (811)------------------------------
% 5.54/2.42 % (813)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_641 for (2995ds/47Mi)
% 5.54/2.43 % (812)Refutation not found, incomplete strategy
% 5.54/2.43 % (812)------------------------------
% 5.54/2.43 % (812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.43 % (812)Termination reason: Refutation not found, incomplete strategy
% 5.54/2.43
% 5.54/2.43
% 5.54/2.43 % (812)Memory used [KB]: 6396
% 5.54/2.43 % (812)Time elapsed: 0.028 s
% 5.54/2.43 % (812)Instructions burned: 48 (million)
% 5.54/2.43 % (812)------------------------------
% 5.54/2.43 % (812)------------------------------
% 5.54/2.43 % (809)Instruction limit reached!
% 5.54/2.43 % (809)------------------------------
% 5.54/2.43 % (809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.43 % (809)Termination reason: Unknown
% 5.54/2.43 % (809)Termination phase: Property scanning
% 5.54/2.43
% 5.54/2.43 % (809)Memory used [KB]: 4093
% 5.54/2.43 % (809)Time elapsed: 0.075 s
% 5.54/2.43 % (809)Instructions burned: 149 (million)
% 5.54/2.43 % (809)------------------------------
% 5.54/2.43 % (809)------------------------------
% 5.54/2.45 % (814)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_641 for (2995ds/44Mi)
% 5.54/2.45 % (815)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_641 for (2995ds/432Mi)
% 5.54/2.45 % (813)Instruction limit reached!
% 5.54/2.45 % (813)------------------------------
% 5.54/2.45 % (813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.45 % (813)Termination reason: Unknown
% 5.54/2.45 % (813)Termination phase: Naming
% 5.54/2.45
% 5.54/2.45 % (813)Memory used [KB]: 2046
% 5.54/2.45 % (813)Time elapsed: 0.027 s
% 5.54/2.45 % (813)Instructions burned: 47 (million)
% 5.54/2.45 % (813)------------------------------
% 5.54/2.45 % (813)------------------------------
% 5.54/2.47 % (814)Instruction limit reached!
% 5.54/2.47 % (814)------------------------------
% 5.54/2.47 % (814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.47 % (814)Termination reason: Unknown
% 5.54/2.47 % (814)Termination phase: shuffling
% 5.54/2.47
% 5.54/2.47 % (814)Memory used [KB]: 2302
% 5.54/2.47 % (814)Time elapsed: 0.024 s
% 5.54/2.47 % (814)Instructions burned: 44 (million)
% 5.54/2.47 % (814)------------------------------
% 5.54/2.47 % (814)------------------------------
% 5.54/2.47 % (816)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_641 for (2995ds/62Mi)
% 5.54/2.49 % (817)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_641 for (2995ds/31Mi)
% 5.80/2.50 % (816)Instruction limit reached!
% 5.80/2.50 % (816)------------------------------
% 5.80/2.50 % (816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.50 % (816)Termination reason: Unknown
% 5.80/2.50 % (816)Termination phase: Property scanning
% 5.80/2.50
% 5.80/2.50 % (816)Memory used [KB]: 2686
% 5.80/2.50 % (816)Time elapsed: 0.034 s
% 5.80/2.50 % (816)Instructions burned: 63 (million)
% 5.80/2.50 % (816)------------------------------
% 5.80/2.50 % (816)------------------------------
% 5.80/2.51 % (817)Instruction limit reached!
% 5.80/2.51 % (817)------------------------------
% 5.80/2.51 % (817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.51 % (817)Termination reason: Unknown
% 5.80/2.51 % (817)Termination phase: Property scanning
% 5.80/2.51
% 5.80/2.51 % (817)Memory used [KB]: 1918
% 5.80/2.51 % (817)Time elapsed: 0.019 s
% 5.80/2.51 % (817)Instructions burned: 31 (million)
% 5.80/2.51 % (817)------------------------------
% 5.80/2.51 % (817)------------------------------
% 5.80/2.51 % (805)Instruction limit reached!
% 5.80/2.51 % (805)------------------------------
% 5.80/2.51 % (805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.51 % (805)Termination reason: Unknown
% 5.80/2.51 % (805)Termination phase: Saturation
% 5.80/2.51
% 5.80/2.51 % (805)Memory used [KB]: 7803
% 5.80/2.51 % (805)Time elapsed: 0.231 s
% 5.80/2.51 % (805)Instructions burned: 448 (million)
% 5.80/2.51 % (805)------------------------------
% 5.80/2.51 % (805)------------------------------
% 5.80/2.52 % (818)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_641 for (2994ds/96Mi)
% 5.80/2.53 % (819)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_641 for (2994ds/453Mi)
% 5.80/2.53 % (820)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_641 for (2994ds/71Mi)
% 5.80/2.54 % (792)Instruction limit reached!
% 5.80/2.54 % (792)------------------------------
% 5.80/2.54 % (792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.54 % (792)Termination reason: Unknown
% 5.80/2.54 % (792)Termination phase: Saturation
% 5.80/2.54
% 5.80/2.54 % (792)Memory used [KB]: 9083
% 5.80/2.54 % (792)Time elapsed: 0.400 s
% 5.80/2.54 % (792)Instructions burned: 780 (million)
% 5.80/2.54 % (792)------------------------------
% 5.80/2.54 % (792)------------------------------
% 5.80/2.56 % (821)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_641 for (2994ds/83Mi)
% 5.80/2.57 % (820)Instruction limit reached!
% 5.80/2.57 % (820)------------------------------
% 5.80/2.57 % (820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.57 % (820)Termination reason: Unknown
% 5.80/2.57 % (820)Termination phase: Property scanning
% 5.80/2.57
% 5.80/2.57 % (820)Memory used [KB]: 2558
% 5.80/2.57 % (820)Time elapsed: 0.040 s
% 5.80/2.57 % (820)Instructions burned: 72 (million)
% 5.80/2.57 % (820)------------------------------
% 5.80/2.57 % (820)------------------------------
% 5.80/2.57 % (818)Instruction limit reached!
% 5.80/2.57 % (818)------------------------------
% 5.80/2.57 % (818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.57 % (818)Termination reason: Unknown
% 5.80/2.57 % (818)Termination phase: Function definition elimination
% 5.80/2.57
% 5.80/2.57 % (818)Memory used [KB]: 2558
% 5.80/2.57 % (818)Time elapsed: 0.053 s
% 5.80/2.57 % (818)Instructions burned: 97 (million)
% 5.80/2.57 % (818)------------------------------
% 5.80/2.57 % (818)------------------------------
% 5.80/2.59 % (821)Refutation not found, incomplete strategy
% 5.80/2.59 % (821)------------------------------
% 5.80/2.59 % (821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.59 % (821)Termination reason: Refutation not found, incomplete strategy
% 5.80/2.59
% 5.80/2.59
% 5.80/2.59 % (821)Memory used [KB]: 6396
% 5.80/2.59 % (821)Time elapsed: 0.030 s
% 5.80/2.59 % (821)Instructions burned: 52 (million)
% 5.80/2.59 % (821)------------------------------
% 5.80/2.59 % (821)------------------------------
% 5.80/2.59 % (822)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_641 for (2994ds/11Mi)
% 5.80/2.59 % (823)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_641 for (2994ds/41Mi)
% 5.80/2.59 % (822)Instruction limit reached!
% 5.80/2.59 % (822)------------------------------
% 5.80/2.59 % (822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.80/2.59 % (822)Termination reason: Unknown
% 5.80/2.59 % (822)Termination phase: shuffling
% 5.80/2.59
% 5.80/2.59 % (822)Memory used [KB]: 1663
% 5.80/2.59 % (822)Time elapsed: 0.008 s
% 5.80/2.59 % (822)Instructions burned: 11 (million)
% 5.80/2.59 % (822)------------------------------
% 5.80/2.59 % (822)------------------------------
% 6.76/2.61 % (824)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_641 for (2994ds/6Mi)
% 6.76/2.61 % (824)Instruction limit reached!
% 6.76/2.61 % (824)------------------------------
% 6.76/2.61 % (824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.61 % (824)Termination reason: Unknown
% 6.76/2.61 % (824)Termination phase: shuffling
% 6.76/2.61
% 6.76/2.61 % (824)Memory used [KB]: 1535
% 6.76/2.61 % (824)Time elapsed: 0.006 s
% 6.76/2.61 % (824)Instructions burned: 6 (million)
% 6.76/2.61 % (824)------------------------------
% 6.76/2.61 % (824)------------------------------
% 6.76/2.61 % (823)Instruction limit reached!
% 6.76/2.61 % (823)------------------------------
% 6.76/2.61 % (823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.61 % (823)Termination reason: Unknown
% 6.76/2.61 % (823)Termination phase: shuffling
% 6.76/2.61
% 6.76/2.61 % (823)Memory used [KB]: 2174
% 6.76/2.61 % (823)Time elapsed: 0.023 s
% 6.76/2.61 % (823)Instructions burned: 41 (million)
% 6.76/2.61 % (823)------------------------------
% 6.76/2.61 % (823)------------------------------
% 6.76/2.61 % (825)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/150Mi)
% 6.76/2.62 % (808)Instruction limit reached!
% 6.76/2.62 % (808)------------------------------
% 6.76/2.62 % (808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.62 % (808)Termination reason: Unknown
% 6.76/2.62 % (808)Termination phase: Saturation
% 6.76/2.62
% 6.76/2.62 % (808)Memory used [KB]: 9083
% 6.76/2.62 % (808)Time elapsed: 0.278 s
% 6.76/2.62 % (808)Instructions burned: 507 (million)
% 6.76/2.62 % (808)------------------------------
% 6.76/2.62 % (808)------------------------------
% 6.76/2.63 % (826)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/343Mi)
% 6.76/2.63 % (827)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/109Mi)
% 6.76/2.64 % (828)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/253Mi)
% 6.76/2.66 % (828)Refutation not found, incomplete strategy
% 6.76/2.66 % (828)------------------------------
% 6.76/2.66 % (828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.66 % (828)Termination reason: Refutation not found, incomplete strategy
% 6.76/2.66
% 6.76/2.66
% 6.76/2.66 % (828)Memory used [KB]: 6396
% 6.76/2.66 % (828)Time elapsed: 0.027 s
% 6.76/2.66 % (828)Instructions burned: 46 (million)
% 6.76/2.66 % (828)------------------------------
% 6.76/2.66 % (828)------------------------------
% 6.76/2.66 % (774)Instruction limit reached!
% 6.76/2.66 % (774)------------------------------
% 6.76/2.66 % (774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.66 % (774)Termination reason: Unknown
% 6.76/2.66 % (774)Termination phase: Saturation
% 6.76/2.66
% 6.76/2.66 % (774)Memory used [KB]: 10234
% 6.76/2.66 % (774)Time elapsed: 0.612 s
% 6.76/2.66 % (774)Instructions burned: 1042 (million)
% 6.76/2.66 % (774)------------------------------
% 6.76/2.66 % (774)------------------------------
% 6.76/2.68 % (815)Instruction limit reached!
% 6.76/2.68 % (815)------------------------------
% 6.76/2.68 % (815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.68 % (815)Termination reason: Unknown
% 6.76/2.68 % (815)Termination phase: Saturation
% 6.76/2.68
% 6.76/2.68 % (815)Memory used [KB]: 4477
% 6.76/2.68 % (815)Time elapsed: 0.234 s
% 6.76/2.68 % (815)Instructions burned: 433 (million)
% 6.76/2.68 % (815)------------------------------
% 6.76/2.68 % (815)------------------------------
% 6.76/2.68 % (829)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/140Mi)
% 6.76/2.68 % (830)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/614Mi)
% 6.76/2.69 % (825)Instruction limit reached!
% 6.76/2.69 % (825)------------------------------
% 6.76/2.69 % (825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.69 % (825)Termination reason: Unknown
% 6.76/2.69 % (825)Termination phase: Property scanning
% 6.76/2.69
% 6.76/2.69 % (825)Memory used [KB]: 2686
% 6.76/2.69 % (825)Time elapsed: 0.079 s
% 6.76/2.69 % (825)Instructions burned: 151 (million)
% 6.76/2.69 % (825)------------------------------
% 6.76/2.69 % (825)------------------------------
% 6.76/2.69 % (827)Instruction limit reached!
% 6.76/2.69 % (827)------------------------------
% 6.76/2.69 % (827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.69 % (827)Termination reason: Unknown
% 6.76/2.69 % (827)Termination phase: Property scanning
% 6.76/2.69
% 6.76/2.69 % (827)Memory used [KB]: 2558
% 6.76/2.69 % (827)Time elapsed: 0.061 s
% 6.76/2.69 % (827)Instructions burned: 110 (million)
% 6.76/2.69 % (827)------------------------------
% 6.76/2.69 % (827)------------------------------
% 8.23/2.70 % (831)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/202Mi)
% 8.23/2.71 % (832)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/339Mi)
% 8.23/2.71 % (833)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_641 for (2993ds/283Mi)
% 8.23/2.71 % (829)Refutation not found, incomplete strategy
% 8.23/2.71 % (829)------------------------------
% 8.23/2.71 % (829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.71 % (829)Termination reason: Refutation not found, incomplete strategy
% 8.23/2.71
% 8.23/2.71
% 8.23/2.71 % (829)Memory used [KB]: 6524
% 8.23/2.71 % (829)Time elapsed: 0.031 s
% 8.23/2.71 % (829)Instructions burned: 54 (million)
% 8.23/2.71 % (829)------------------------------
% 8.23/2.71 % (829)------------------------------
% 8.23/2.73 % (831)Refutation not found, incomplete strategy
% 8.23/2.73 % (831)------------------------------
% 8.23/2.73 % (831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.73 % (831)Termination reason: Refutation not found, incomplete strategy
% 8.23/2.73
% 8.23/2.73
% 8.23/2.73 % (831)Memory used [KB]: 6396
% 8.23/2.73 % (831)Time elapsed: 0.028 s
% 8.23/2.73 % (831)Instructions burned: 47 (million)
% 8.23/2.73 % (831)------------------------------
% 8.23/2.73 % (831)------------------------------
% 8.23/2.74 % (834)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_641 for (2992ds/134Mi)
% 8.23/2.75 % (835)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_641 for (2992ds/298Mi)
% 8.23/2.77 % (819)Instruction limit reached!
% 8.23/2.77 % (819)------------------------------
% 8.23/2.77 % (819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.77 % (819)Termination reason: Unknown
% 8.23/2.77 % (819)Termination phase: Saturation
% 8.23/2.77
% 8.23/2.77 % (819)Memory used [KB]: 8059
% 8.23/2.77 % (819)Time elapsed: 0.246 s
% 8.23/2.77 % (819)Instructions burned: 453 (million)
% 8.23/2.77 % (819)------------------------------
% 8.23/2.77 % (819)------------------------------
% 8.23/2.79 % (836)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_641 for (2992ds/192Mi)
% 8.60/2.80 % (834)Instruction limit reached!
% 8.60/2.80 % (834)------------------------------
% 8.60/2.80 % (834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.80 % (834)Termination reason: Unknown
% 8.60/2.80 % (834)Termination phase: Property scanning
% 8.60/2.80
% 8.60/2.80 % (834)Memory used [KB]: 2558
% 8.60/2.80 % (834)Time elapsed: 0.071 s
% 8.60/2.80 % (834)Instructions burned: 134 (million)
% 8.60/2.80 % (834)------------------------------
% 8.60/2.80 % (834)------------------------------
% 8.60/2.81 % (826)Instruction limit reached!
% 8.60/2.81 % (826)------------------------------
% 8.60/2.81 % (826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.81 % (826)Termination reason: Unknown
% 8.60/2.81 % (826)Termination phase: Saturation
% 8.60/2.81
% 8.60/2.81 % (826)Memory used [KB]: 8187
% 8.60/2.81 % (826)Time elapsed: 0.186 s
% 8.60/2.81 % (826)Instructions burned: 344 (million)
% 8.60/2.81 % (826)------------------------------
% 8.60/2.81 % (826)------------------------------
% 8.60/2.83 % (837)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_641 for (2991ds/258Mi)
% 8.60/2.83 % (838)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_641 for (2991ds/90Mi)
% 8.60/2.86 % (833)Instruction limit reached!
% 8.60/2.86 % (833)------------------------------
% 8.60/2.86 % (833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.86 % (833)Termination reason: Unknown
% 8.60/2.86 % (833)Termination phase: Saturation
% 8.60/2.86
% 8.60/2.86 % (833)Memory used [KB]: 7675
% 8.60/2.86 % (833)Time elapsed: 0.171 s
% 8.60/2.86 % (833)Instructions burned: 284 (million)
% 8.60/2.86 % (833)------------------------------
% 8.60/2.86 % (833)------------------------------
% 8.60/2.88 % (838)Instruction limit reached!
% 8.60/2.88 % (838)------------------------------
% 8.60/2.88 % (838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.88 % (839)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_641 for (2991ds/231Mi)
% 8.60/2.88 % (838)Termination reason: Unknown
% 8.60/2.88 % (838)Termination phase: Property scanning
% 8.60/2.88
% 8.60/2.88 % (838)Memory used [KB]: 2558
% 8.60/2.88 % (838)Time elapsed: 0.049 s
% 8.60/2.88 % (838)Instructions burned: 90 (million)
% 8.60/2.88 % (838)------------------------------
% 8.60/2.88 % (838)------------------------------
% 8.60/2.89 % (832)Instruction limit reached!
% 8.60/2.89 % (832)------------------------------
% 8.60/2.89 % (832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.89 % (832)Termination reason: Unknown
% 8.60/2.89 % (832)Termination phase: Saturation
% 8.60/2.89
% 8.60/2.89 % (832)Memory used [KB]: 7931
% 8.60/2.89 % (832)Time elapsed: 0.176 s
% 8.60/2.89 % (832)Instructions burned: 339 (million)
% 8.60/2.89 % (832)------------------------------
% 8.60/2.89 % (832)------------------------------
% 8.60/2.89 % (836)Instruction limit reached!
% 8.60/2.89 % (836)------------------------------
% 8.60/2.89 % (836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.89 % (836)Termination reason: Unknown
% 8.60/2.89 % (836)Termination phase: Saturation
% 8.60/2.89
% 8.60/2.89 % (836)Memory used [KB]: 3709
% 8.60/2.89 % (836)Time elapsed: 0.103 s
% 8.60/2.89 % (836)Instructions burned: 192 (million)
% 8.60/2.89 % (836)------------------------------
% 8.60/2.89 % (836)------------------------------
% 9.45/2.90 % (835)Instruction limit reached!
% 9.45/2.90 % (835)------------------------------
% 9.45/2.90 % (835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.90 % (835)Termination reason: Unknown
% 9.45/2.90 % (835)Termination phase: Saturation
% 9.45/2.90
% 9.45/2.90 % (835)Memory used [KB]: 8315
% 9.45/2.90 % (835)Time elapsed: 0.152 s
% 9.45/2.90 % (835)Instructions burned: 299 (million)
% 9.45/2.90 % (835)------------------------------
% 9.45/2.90 % (835)------------------------------
% 9.45/2.90 % (840)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_641 for (2990ds/458Mi)
% 9.45/2.91 % (841)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_641 for (2990ds/31Mi)
% 9.45/2.91 % (842)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_641 for (2990ds/297Mi)
% 9.45/2.92 % (843)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_641 for (2990ds/987Mi)
% 9.45/2.92 % (841)Instruction limit reached!
% 9.45/2.92 % (841)------------------------------
% 9.45/2.92 % (841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.92 % (841)Termination reason: Unknown
% 9.45/2.92 % (841)Termination phase: Property scanning
% 9.45/2.92
% 9.45/2.92 % (841)Memory used [KB]: 1918
% 9.45/2.92 % (841)Time elapsed: 0.018 s
% 9.45/2.92 % (841)Instructions burned: 31 (million)
% 9.45/2.92 % (841)------------------------------
% 9.45/2.92 % (841)------------------------------
% 9.45/2.94 % (844)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_641 for (2990ds/182Mi)
% 9.45/2.96 % (837)Instruction limit reached!
% 9.45/2.96 % (837)------------------------------
% 9.45/2.96 % (837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.96 % (837)Termination reason: Unknown
% 9.45/2.96 % (837)Termination phase: Saturation
% 9.45/2.96
% 9.45/2.96 % (837)Memory used [KB]: 2814
% 9.45/2.96 % (837)Time elapsed: 0.134 s
% 9.45/2.96 % (837)Instructions burned: 258 (million)
% 9.45/2.96 % (837)------------------------------
% 9.45/2.96 % (837)------------------------------
% 9.45/2.98 % (845)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_641 for (2990ds/182Mi)
% 9.45/2.99 % (830)Instruction limit reached!
% 9.45/2.99 % (830)------------------------------
% 9.45/2.99 % (830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.99 % (830)Termination reason: Unknown
% 9.45/2.99 % (830)Termination phase: Saturation
% 9.45/2.99
% 9.45/2.99 % (830)Memory used [KB]: 9466
% 9.45/2.99 % (830)Time elapsed: 0.309 s
% 9.45/2.99 % (830)Instructions burned: 614 (million)
% 9.45/2.99 % (830)------------------------------
% 9.45/2.99 % (830)------------------------------
% 9.45/2.99 % (839)Instruction limit reached!
% 9.45/2.99 % (839)------------------------------
% 9.45/2.99 % (839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.99 % (839)Termination reason: Unknown
% 9.45/2.99 % (839)Termination phase: Saturation
% 9.45/2.99
% 9.45/2.99 % (839)Memory used [KB]: 7291
% 9.45/2.99 % (839)Time elapsed: 0.115 s
% 9.45/2.99 % (839)Instructions burned: 231 (million)
% 9.45/2.99 % (839)------------------------------
% 9.45/2.99 % (839)------------------------------
% 9.45/3.01 % (846)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_641 for (2989ds/154Mi)
% 9.45/3.02 % (847)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_641 for (2989ds/79Mi)
% 10.76/3.03 % (844)Instruction limit reached!
% 10.76/3.03 % (844)------------------------------
% 10.76/3.03 % (844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.76/3.03 % (844)Termination reason: Unknown
% 10.76/3.03 % (844)Termination phase: Property scanning
% 10.76/3.03
% 10.76/3.03 % (844)Memory used [KB]: 4093
% 10.76/3.03 % (844)Time elapsed: 0.091 s
% 10.76/3.03 % (844)Instructions burned: 182 (million)
% 10.76/3.03 % (844)------------------------------
% 10.76/3.03 % (844)------------------------------
% 10.76/3.05 % (848)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_641 for (2989ds/216Mi)
% 10.76/3.06 % (847)Instruction limit reached!
% 10.76/3.06 % (847)------------------------------
% 10.76/3.06 % (847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.76/3.06 % (847)Termination reason: Unknown
% 10.76/3.06 % (847)Termination phase: Property scanning
% 10.76/3.06
% 10.76/3.06 % (847)Memory used [KB]: 2558
% 10.76/3.06 % (847)Time elapsed: 0.043 s
% 10.76/3.06 % (847)Instructions burned: 79 (million)
% 10.76/3.06 % (847)------------------------------
% 10.76/3.06 % (847)------------------------------
% 10.76/3.07 % (842)Instruction limit reached!
% 10.76/3.07 % (842)------------------------------
% 10.76/3.07 % (842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.76/3.07 % (842)Termination reason: Unknown
% 10.76/3.08 % (842)Termination phase: Saturation
% 10.76/3.08
% 10.76/3.08 % (842)Memory used [KB]: 7419
% 10.76/3.08 % (842)Time elapsed: 0.163 s
% 10.76/3.08 % (842)Instructions burned: 297 (million)
% 10.76/3.08 % (842)------------------------------
% 10.76/3.08 % (842)------------------------------
% 10.76/3.08 % (845)Instruction limit reached!
% 10.76/3.08 % (845)------------------------------
% 10.76/3.08 % (845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.76/3.08 % (845)Termination reason: Unknown
% 10.76/3.08 % (845)Termination phase: Saturation
% 10.76/3.08
% 10.76/3.08 % (845)Memory used [KB]: 7419
% 10.76/3.08 % (845)Time elapsed: 0.100 s
% 10.76/3.08 % (845)Instructions burned: 182 (million)
% 10.76/3.08 % (845)------------------------------
% 10.76/3.08 % (845)------------------------------
% 10.76/3.08 % (849)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_641 for (2989ds/114Mi)
% 10.76/3.09 % (846)Instruction limit reached!
% 10.76/3.09 % (846)------------------------------
% 10.76/3.09 % (846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.76/3.09 % (846)Termination reason: Unknown
% 10.76/3.09 % (846)Termination phase: Property scanning
% 10.76/3.09
% 10.76/3.09 % (846)Memory used [KB]: 2686
% 10.76/3.09 % (846)Time elapsed: 0.079 s
% 10.76/3.09 % (846)Instructions burned: 154 (million)
% 10.76/3.09 % (846)------------------------------
% 10.76/3.09 % (846)------------------------------
% 10.76/3.10 % (850)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_641 for (2989ds/922Mi)
% 10.76/3.10 % (851)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_641 for (2989ds/182Mi)
% 10.76/3.11 % (852)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_641 for (2988ds/164Mi)
% 11.29/3.14 % (849)Instruction limit reached!
% 11.29/3.14 % (849)------------------------------
% 11.29/3.14 % (849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.29/3.14 % (849)Termination reason: Unknown
% 11.29/3.14 % (849)Termination phase: Property scanning
% 11.29/3.14
% 11.29/3.14 % (849)Memory used [KB]: 2558
% 11.29/3.14 % (849)Time elapsed: 0.060 s
% 11.29/3.14 % (849)Instructions burned: 114 (million)
% 11.29/3.14 % (849)------------------------------
% 11.29/3.14 % (849)------------------------------
% 11.29/3.15 % (840)Instruction limit reached!
% 11.29/3.15 % (840)------------------------------
% 11.29/3.15 % (840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.29/3.15 % (840)Termination reason: Unknown
% 11.29/3.15 % (840)Termination phase: Saturation
% 11.29/3.15
% 11.29/3.15 % (840)Memory used [KB]: 8827
% 11.29/3.15 % (840)Time elapsed: 0.246 s
% 11.29/3.15 % (840)Instructions burned: 459 (million)
% 11.29/3.15 % (840)------------------------------
% 11.29/3.15 % (840)------------------------------
% 11.29/3.16 % (853)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_641 for (2988ds/50Mi)
% 11.29/3.16 % (848)Instruction limit reached!
% 11.29/3.16 % (848)------------------------------
% 11.29/3.16 % (848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.29/3.16 % (848)Termination reason: Unknown
% 11.29/3.16 % (848)Termination phase: Saturation
% 11.29/3.16
% 11.29/3.16 % (848)Memory used [KB]: 7291
% 11.29/3.17 % (848)Time elapsed: 0.112 s
% 11.29/3.17 % (848)Instructions burned: 217 (million)
% 11.29/3.17 % (848)------------------------------
% 11.29/3.17 % (848)------------------------------
% 11.29/3.17 % (854)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_641 for (2988ds/368Mi)
% 11.29/3.17 % (852)Refutation not found, incomplete strategy
% 11.29/3.17 % (852)------------------------------
% 11.29/3.17 % (852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.29/3.17 % (852)Termination reason: Refutation not found, incomplete strategy
% 11.29/3.17
% 11.29/3.17
% 11.29/3.17 % (852)Memory used [KB]: 2686
% 11.29/3.17 % (852)Time elapsed: 0.063 s
% 11.29/3.17 % (852)Instructions burned: 119 (million)
% 11.29/3.17 % (852)------------------------------
% 11.29/3.17 % (852)------------------------------
% 11.29/3.18 % (853)Instruction limit reached!
% 11.29/3.18 % (853)------------------------------
% 11.29/3.18 % (853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.29/3.18 % (853)Termination reason: Unknown
% 11.29/3.18 % (853)Termination phase: shuffling
% 11.29/3.18
% 11.29/3.18 % (853)Memory used [KB]: 2430
% 11.29/3.18 % (853)Time elapsed: 0.027 s
% 11.29/3.18 % (853)Instructions burned: 51 (million)
% 11.29/3.18 % (853)------------------------------
% 11.29/3.18 % (853)------------------------------
% 11.29/3.19 % (855)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_641 for (2988ds/1021Mi)
% 11.29/3.19 % (851)Instruction limit reached!
% 11.29/3.19 % (851)------------------------------
% 11.29/3.19 % (851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.29/3.19 % (851)Termination reason: Unknown
% 11.29/3.19 % (851)Termination phase: Saturation
% 11.29/3.19
% 11.29/3.19 % (851)Memory used [KB]: 7291
% 11.29/3.19 % (851)Time elapsed: 0.091 s
% 11.29/3.19 % (851)Instructions burned: 182 (million)
% 11.29/3.19 % (851)------------------------------
% 11.29/3.19 % (851)------------------------------
% 11.29/3.19 % (856)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_641 for (2988ds/267Mi)
% 11.83/3.20 % (857)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_641 for (2988ds/204Mi)
% 11.83/3.21 % (858)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_641 for (2988ds/26Mi)
% 11.83/3.22 % (858)Instruction limit reached!
% 11.83/3.22 % (858)------------------------------
% 11.83/3.22 % (858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.83/3.22 % (858)Termination reason: Unknown
% 11.83/3.22 % (858)Termination phase: shuffling
% 11.83/3.22
% 11.83/3.22 % (858)Memory used [KB]: 2046
% 11.83/3.22 % (858)Time elapsed: 0.016 s
% 11.83/3.22 % (858)Instructions burned: 27 (million)
% 11.83/3.22 % (858)------------------------------
% 11.83/3.22 % (858)------------------------------
% 11.83/3.24 % (859)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_641 for (2987ds/53Mi)
% 11.83/3.27 % (859)Instruction limit reached!
% 11.83/3.27 % (859)------------------------------
% 11.83/3.27 % (859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.83/3.27 % (859)Termination reason: Unknown
% 11.83/3.27 % (859)Termination phase: shuffling
% 11.83/3.27
% 11.83/3.27 % (859)Memory used [KB]: 2430
% 11.83/3.27 % (859)Time elapsed: 0.029 s
% 11.83/3.27 % (859)Instructions burned: 54 (million)
% 11.83/3.27 % (859)------------------------------
% 11.83/3.27 % (859)------------------------------
% 11.83/3.29 % (860)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_641 for (2987ds/4436Mi)
% 12.01/3.31 % (857)Instruction limit reached!
% 12.01/3.31 % (857)------------------------------
% 12.01/3.31 % (857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.01/3.31 % (857)Termination reason: Unknown
% 12.01/3.31 % (857)Termination phase: Saturation
% 12.01/3.31
% 12.01/3.31 % (857)Memory used [KB]: 7291
% 12.01/3.31 % (857)Time elapsed: 0.106 s
% 12.01/3.31 % (857)Instructions burned: 205 (million)
% 12.01/3.31 % (857)------------------------------
% 12.01/3.31 % (857)------------------------------
% 12.01/3.32 % (860)Refutation not found, incomplete strategy
% 12.01/3.32 % (860)------------------------------
% 12.01/3.32 % (860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.01/3.32 % (860)Termination reason: Refutation not found, incomplete strategy
% 12.01/3.32
% 12.01/3.32
% 12.01/3.32 % (860)Memory used [KB]: 6396
% 12.01/3.32 % (860)Time elapsed: 0.028 s
% 12.01/3.32 % (860)Instructions burned: 48 (million)
% 12.01/3.32 % (860)------------------------------
% 12.01/3.32 % (860)------------------------------
% 12.01/3.33 % (861)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_641 for (2986ds/1539Mi)
% 12.01/3.33 % (856)Instruction limit reached!
% 12.01/3.33 % (856)------------------------------
% 12.01/3.33 % (856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.01/3.33 % (856)Termination reason: Unknown
% 12.01/3.33 % (856)Termination phase: Saturation
% 12.01/3.33
% 12.01/3.33 % (856)Memory used [KB]: 7675
% 12.01/3.33 % (856)Time elapsed: 0.140 s
% 12.01/3.33 % (856)Instructions burned: 268 (million)
% 12.01/3.33 % (856)------------------------------
% 12.01/3.33 % (856)------------------------------
% 12.01/3.34 % (862)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_641 for (2986ds/408Mi)
% 12.01/3.35 % (863)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_641 for (2986ds/5205Mi)
% 12.01/3.36 % (854)Instruction limit reached!
% 12.01/3.36 % (854)------------------------------
% 12.01/3.36 % (854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.01/3.36 % (854)Termination reason: Unknown
% 12.01/3.36 % (854)Termination phase: Saturation
% 12.01/3.36
% 12.01/3.36 % (854)Memory used [KB]: 8699
% 12.01/3.36 % (854)Time elapsed: 0.198 s
% 12.01/3.36 % (854)Instructions burned: 368 (million)
% 12.01/3.36 % (854)------------------------------
% 12.01/3.36 % (854)------------------------------
% 12.01/3.39 % (864)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_641 for (2986ds/1913Mi)
% 12.67/3.48 % (843)Instruction limit reached!
% 12.67/3.48 % (843)------------------------------
% 12.67/3.48 % (843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.67/3.48 % (843)Termination reason: Unknown
% 12.67/3.48 % (843)Termination phase: Saturation
% 12.67/3.48
% 12.67/3.48 % (843)Memory used [KB]: 10746
% 12.67/3.48 % (843)Time elapsed: 0.564 s
% 12.67/3.48 % (843)Instructions burned: 988 (million)
% 12.67/3.48 % (843)------------------------------
% 12.67/3.48 % (843)------------------------------
% 12.78/3.51 % (865)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_641 for (2985ds/4350Mi)
% 12.78/3.53 % (865)Refutation not found, incomplete strategy
% 12.78/3.53 % (865)------------------------------
% 12.78/3.53 % (865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.78/3.53 % (865)Termination reason: Refutation not found, incomplete strategy
% 12.78/3.53
% 12.78/3.53
% 12.78/3.53 % (865)Memory used [KB]: 6396
% 12.78/3.53 % (865)Time elapsed: 0.028 s
% 12.78/3.53 % (865)Instructions burned: 47 (million)
% 12.78/3.53 % (865)------------------------------
% 12.78/3.53 % (865)------------------------------
% 12.78/3.55 % (866)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_641 for (2984ds/68Mi)
% 12.78/3.56 % (862)Instruction limit reached!
% 12.78/3.56 % (862)------------------------------
% 12.78/3.56 % (862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.78/3.56 % (862)Termination reason: Unknown
% 12.78/3.56 % (862)Termination phase: Saturation
% 12.78/3.56
% 12.78/3.56 % (862)Memory used [KB]: 8827
% 12.78/3.56 % (862)Time elapsed: 0.220 s
% 12.78/3.56 % (862)Instructions burned: 409 (million)
% 12.78/3.56 % (862)------------------------------
% 12.78/3.56 % (862)------------------------------
% 12.78/3.58 % (867)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_641 for (2984ds/358Mi)
% 12.78/3.59 % (866)Instruction limit reached!
% 12.78/3.59 % (866)------------------------------
% 12.78/3.59 % (866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.78/3.59 % (866)Termination reason: Unknown
% 12.78/3.59 % (866)Termination phase: Preprocessing 3
% 12.78/3.59
% 12.78/3.59 % (866)Memory used [KB]: 2430
% 12.78/3.59 % (866)Time elapsed: 0.039 s
% 12.78/3.59 % (866)Instructions burned: 68 (million)
% 12.78/3.59 % (866)------------------------------
% 12.78/3.59 % (866)------------------------------
% 12.78/3.59 % (850)Instruction limit reached!
% 12.78/3.59 % (850)------------------------------
% 12.78/3.59 % (850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.78/3.59 % (850)Termination reason: Unknown
% 12.78/3.59 % (850)Termination phase: Saturation
% 12.78/3.59
% 12.78/3.59 % (850)Memory used [KB]: 7931
% 12.78/3.59 % (850)Time elapsed: 0.499 s
% 12.78/3.59 % (850)Instructions burned: 923 (million)
% 12.78/3.59 % (850)------------------------------
% 12.78/3.59 % (850)------------------------------
% 13.64/3.61 % (869)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_641 for (2984ds/279Mi)
% 13.64/3.61 % (868)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_641 for (2984ds/31Mi)
% 13.64/3.63 % (868)Instruction limit reached!
% 13.64/3.63 % (868)------------------------------
% 13.64/3.63 % (868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.64/3.63 % (868)Termination reason: Unknown
% 13.64/3.63 % (868)Termination phase: Property scanning
% 13.64/3.63
% 13.64/3.63 % (868)Memory used [KB]: 1918
% 13.64/3.63 % (868)Time elapsed: 0.018 s
% 13.64/3.63 % (868)Instructions burned: 31 (million)
% 13.64/3.63 % (868)------------------------------
% 13.64/3.63 % (868)------------------------------
% 13.64/3.65 % (870)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_641 for (2983ds/258Mi)
% 13.67/3.70 % (869)Refutation not found, incomplete strategy
% 13.67/3.70 % (869)------------------------------
% 13.67/3.70 % (869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.67/3.70 % (869)Termination reason: Refutation not found, incomplete strategy
% 13.67/3.70
% 13.67/3.70
% 13.67/3.70 % (869)Memory used [KB]: 7419
% 13.67/3.70 % (869)Time elapsed: 0.111 s
% 13.67/3.70 % (869)Instructions burned: 163 (million)
% 13.67/3.70 % (869)------------------------------
% 13.67/3.70 % (869)------------------------------
% 13.67/3.72 % (871)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_641 for (2982ds/26Mi)
% 13.67/3.73 % (855)Instruction limit reached!
% 13.67/3.73 % (855)------------------------------
% 13.67/3.73 % (855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.67/3.73 % (855)Termination reason: Unknown
% 13.67/3.73 % (855)Termination phase: Saturation
% 13.67/3.73
% 13.67/3.73 % (855)Memory used [KB]: 9466
% 13.67/3.73 % (855)Time elapsed: 0.547 s
% 13.67/3.73 % (855)Instructions burned: 1021 (million)
% 13.67/3.73 % (855)------------------------------
% 13.67/3.73 % (855)------------------------------
% 13.67/3.73 % (871)Instruction limit reached!
% 13.67/3.73 % (871)------------------------------
% 13.67/3.73 % (871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.67/3.73 % (871)Termination reason: Unknown
% 13.67/3.73 % (871)Termination phase: shuffling
% 13.67/3.73
% 13.67/3.73 % (871)Memory used [KB]: 2046
% 13.67/3.73 % (871)Time elapsed: 0.015 s
% 13.67/3.73 % (871)Instructions burned: 26 (million)
% 13.67/3.73 % (871)------------------------------
% 13.67/3.73 % (871)------------------------------
% 13.67/3.75 % (873)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_641 for (2982ds/373Mi)
% 13.67/3.75 % (872)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_641 for (2982ds/995Mi)
% 13.67/3.78 % (867)Instruction limit reached!
% 13.67/3.78 % (867)------------------------------
% 13.67/3.78 % (867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.67/3.78 % (867)Termination reason: Unknown
% 13.67/3.78 % (867)Termination phase: Saturation
% 13.67/3.78
% 13.67/3.78 % (867)Memory used [KB]: 7931
% 13.67/3.78 % (867)Time elapsed: 0.223 s
% 13.67/3.78 % (867)Instructions burned: 359 (million)
% 13.67/3.78 % (867)------------------------------
% 13.67/3.78 % (867)------------------------------
% 13.67/3.79 % (870)Instruction limit reached!
% 13.67/3.79 % (870)------------------------------
% 13.67/3.79 % (870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.67/3.79 % (870)Termination reason: Unknown
% 13.67/3.79 % (870)Termination phase: Saturation
% 13.67/3.79
% 13.67/3.79 % (870)Memory used [KB]: 7931
% 13.67/3.79 % (870)Time elapsed: 0.140 s
% 13.67/3.79 % (870)Instructions burned: 259 (million)
% 13.67/3.79 % (870)------------------------------
% 13.67/3.79 % (870)------------------------------
% 14.75/3.80 % (874)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_641 for (2982ds/253Mi)
% 14.75/3.81 % (875)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_641 for (2981ds/832Mi)
% 14.75/3.93 % (874)Instruction limit reached!
% 14.75/3.93 % (874)------------------------------
% 14.75/3.93 % (874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.75/3.93 % (874)Termination reason: Unknown
% 14.75/3.93 % (874)Termination phase: Saturation
% 14.75/3.93
% 14.75/3.93 % (874)Memory used [KB]: 7675
% 14.75/3.93 % (874)Time elapsed: 0.130 s
% 14.75/3.93 % (874)Instructions burned: 253 (million)
% 14.75/3.93 % (874)------------------------------
% 14.75/3.93 % (874)------------------------------
% 14.75/3.95 % (875)Refutation not found, incomplete strategy
% 14.75/3.95 % (875)------------------------------
% 14.75/3.95 % (875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.75/3.95 % (875)Termination reason: Refutation not found, incomplete strategy
% 14.75/3.95
% 14.75/3.95
% 14.75/3.95 % (875)Memory used [KB]: 8571
% 14.75/3.95 % (875)Time elapsed: 0.138 s
% 14.75/3.95 % (875)Instructions burned: 250 (million)
% 14.75/3.95 % (875)------------------------------
% 14.75/3.95 % (875)------------------------------
% 14.75/3.95 % (876)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_641 for (2980ds/668Mi)
% 14.75/3.96 % (873)Instruction limit reached!
% 14.75/3.96 % (873)------------------------------
% 14.75/3.96 % (873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.75/3.96 % (873)Termination reason: Unknown
% 14.75/3.96 % (873)Termination phase: Saturation
% 14.75/3.96
% 14.75/3.96 % (873)Memory used [KB]: 8827
% 14.75/3.96 % (873)Time elapsed: 0.210 s
% 14.75/3.96 % (873)Instructions burned: 373 (million)
% 14.75/3.96 % (873)------------------------------
% 14.75/3.96 % (873)------------------------------
% 14.75/3.97 % (877)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_641 for (2980ds/40Mi)
% 14.75/3.98 % (878)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_641 for (2980ds/294Mi)
% 14.75/3.99 % (877)Instruction limit reached!
% 14.75/3.99 % (877)------------------------------
% 14.75/3.99 % (877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.75/3.99 % (877)Termination reason: Unknown
% 14.75/3.99 % (877)Termination phase: shuffling
% 14.75/3.99
% 14.75/3.99 % (877)Memory used [KB]: 2174
% 14.75/3.99 % (877)Time elapsed: 0.023 s
% 14.75/3.99 % (877)Instructions burned: 41 (million)
% 14.75/3.99 % (877)------------------------------
% 14.75/3.99 % (877)------------------------------
% 14.75/4.01 % (879)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_641 for (2979ds/187Mi)
% 17.76/4.03 % (878)Refutation not found, incomplete strategy
% 17.76/4.03 % (878)------------------------------
% 17.76/4.03 % (878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/4.03 % (878)Termination reason: Refutation not found, incomplete strategy
% 17.76/4.03
% 17.76/4.03
% 17.76/4.03 % (878)Memory used [KB]: 7164
% 17.76/4.03 % (878)Time elapsed: 0.055 s
% 17.76/4.03 % (878)Instructions burned: 105 (million)
% 17.76/4.03 % (878)------------------------------
% 17.76/4.03 % (878)------------------------------
% 17.76/4.06 % (880)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_641 for (2979ds/371Mi)
% 17.76/4.11 % (879)Instruction limit reached!
% 17.76/4.11 % (879)------------------------------
% 17.76/4.11 % (879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/4.11 % (879)Termination reason: Unknown
% 17.76/4.11 % (879)Termination phase: Saturation
% 17.76/4.11
% 17.76/4.11 % (879)Memory used [KB]: 7291
% 17.76/4.11 % (879)Time elapsed: 0.099 s
% 17.76/4.11 % (879)Instructions burned: 188 (million)
% 17.76/4.11 % (879)------------------------------
% 17.76/4.11 % (879)------------------------------
% 18.46/4.13 % (881)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_641 for (2978ds/1827Mi)
% 18.46/4.18 % (861)Instruction limit reached!
% 18.46/4.18 % (861)------------------------------
% 18.46/4.18 % (861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.46/4.18 % (861)Termination reason: Unknown
% 18.46/4.18 % (861)Termination phase: Saturation
% 18.46/4.18
% 18.46/4.18 % (861)Memory used [KB]: 11257
% 18.46/4.18 % (861)Time elapsed: 0.854 s
% 18.46/4.18 % (861)Instructions burned: 1540 (million)
% 18.46/4.18 % (861)------------------------------
% 18.46/4.18 % (861)------------------------------
% 18.78/4.20 % (882)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_641 for (2978ds/70Mi)
% 18.78/4.24 % (882)Instruction limit reached!
% 18.78/4.24 % (882)------------------------------
% 18.78/4.24 % (882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/4.24 % (882)Termination reason: Unknown
% 18.78/4.24 % (882)Termination phase: Property scanning
% 18.78/4.24
% 18.78/4.24 % (882)Memory used [KB]: 2686
% 18.78/4.24 % (882)Time elapsed: 0.037 s
% 18.78/4.24 % (882)Instructions burned: 70 (million)
% 18.78/4.24 % (882)------------------------------
% 18.78/4.24 % (882)------------------------------
% 18.78/4.26 % (872)Instruction limit reached!
% 18.78/4.26 % (872)------------------------------
% 18.78/4.26 % (872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/4.26 % (872)Termination reason: Unknown
% 18.78/4.26 % (872)Termination phase: Saturation
% 18.78/4.26
% 18.78/4.26 % (872)Memory used [KB]: 9722
% 18.78/4.26 % (872)Time elapsed: 0.507 s
% 18.78/4.26 % (872)Instructions burned: 995 (million)
% 18.78/4.26 % (872)------------------------------
% 18.78/4.26 % (872)------------------------------
% 18.78/4.26 % (884)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_641 for (2977ds/316Mi)
% 18.78/4.26 % (880)Instruction limit reached!
% 18.78/4.26 % (880)------------------------------
% 18.78/4.26 % (880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/4.26 % (880)Termination reason: Unknown
% 18.78/4.26 % (880)Termination phase: Saturation
% 18.78/4.26
% 18.78/4.26 % (880)Memory used [KB]: 7419
% 18.78/4.26 % (880)Time elapsed: 0.208 s
% 18.78/4.26 % (880)Instructions burned: 372 (million)
% 18.78/4.26 % (880)------------------------------
% 18.78/4.26 % (880)------------------------------
% 18.78/4.28 % (885)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_641 for (2977ds/932Mi)
% 18.78/4.28 % (886)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_641 for (2977ds/4714Mi)
% 18.78/4.30 % (876)Instruction limit reached!
% 18.78/4.30 % (876)------------------------------
% 18.78/4.30 % (876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/4.30 % (876)Termination reason: Unknown
% 18.78/4.30 % (876)Termination phase: Saturation
% 18.78/4.30
% 18.78/4.30 % (876)Memory used [KB]: 13944
% 18.78/4.30 % (876)Time elapsed: 0.346 s
% 18.78/4.30 % (876)Instructions burned: 668 (million)
% 18.78/4.30 % (876)------------------------------
% 18.78/4.30 % (876)------------------------------
% 19.09/4.32 % (887)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_641 for (2976ds/8250Mi)
% 19.09/4.37 % (864)Instruction limit reached!
% 19.09/4.37 % (864)------------------------------
% 19.09/4.37 % (864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.09/4.37 % (864)Termination reason: Unknown
% 19.09/4.37 % (864)Termination phase: Saturation
% 19.09/4.37
% 19.09/4.37 % (864)Memory used [KB]: 3837
% 19.09/4.37 % (864)Time elapsed: 1.008 s
% 19.09/4.37 % (864)Instructions burned: 1914 (million)
% 19.09/4.37 % (864)------------------------------
% 19.09/4.37 % (864)------------------------------
% 19.09/4.38 % (884)Refutation not found, incomplete strategy
% 19.09/4.38 % (884)------------------------------
% 19.09/4.38 % (884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.09/4.38 % (884)Termination reason: Refutation not found, incomplete strategy
% 19.09/4.38
% 19.09/4.38
% 19.09/4.38 % (884)Memory used [KB]: 7675
% 19.09/4.38 % (884)Time elapsed: 0.122 s
% 19.09/4.38 % (884)Instructions burned: 240 (million)
% 19.09/4.38 % (884)------------------------------
% 19.09/4.38 % (884)------------------------------
% 19.09/4.39 % (888)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_641 for (2976ds/770Mi)
% 19.79/4.40 % (889)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_641 for (2976ds/794Mi)
% 19.79/4.41 % (886)Refutation not found, incomplete strategy
% 19.79/4.41 % (886)------------------------------
% 19.79/4.41 % (886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.79/4.41 % (886)Termination reason: Refutation not found, incomplete strategy
% 19.79/4.41
% 19.79/4.41
% 19.79/4.41 % (886)Memory used [KB]: 7803
% 19.79/4.41 % (886)Time elapsed: 0.129 s
% 19.79/4.41 % (886)Instructions burned: 250 (million)
% 19.79/4.41 % (886)------------------------------
% 19.79/4.41 % (886)------------------------------
% 19.79/4.42 % (888)Refutation not found, incomplete strategy
% 19.79/4.42 % (888)------------------------------
% 19.79/4.42 % (888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.79/4.42 % (888)Termination reason: Refutation not found, incomplete strategy
% 19.79/4.42
% 19.79/4.42
% 19.79/4.42 % (888)Memory used [KB]: 6524
% 19.79/4.42 % (888)Time elapsed: 0.031 s
% 19.79/4.42 % (888)Instructions burned: 52 (million)
% 19.79/4.42 % (888)------------------------------
% 19.79/4.42 % (888)------------------------------
% 19.79/4.43 % (890)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_641 for (2975ds/464Mi)
% 19.79/4.44 % (891)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_641 for (2975ds/1376Mi)
% 20.18/4.68 % (890)Instruction limit reached!
% 20.18/4.68 % (890)------------------------------
% 20.18/4.68 % (890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.68 % (890)Termination reason: Unknown
% 20.18/4.68 % (890)Termination phase: Saturation
% 20.18/4.68
% 20.18/4.68 % (890)Memory used [KB]: 8187
% 20.18/4.68 % (890)Time elapsed: 0.250 s
% 20.18/4.68 % (890)Instructions burned: 465 (million)
% 20.18/4.68 % (890)------------------------------
% 20.18/4.68 % (890)------------------------------
% 20.56/4.70 % (892)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_641 for (2973ds/906Mi)
% 20.56/4.72 % (885)Instruction limit reached!
% 20.56/4.72 % (885)------------------------------
% 20.56/4.72 % (885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.56/4.72 % (885)Termination reason: Unknown
% 20.56/4.72 % (885)Termination phase: Saturation
% 20.56/4.72
% 20.56/4.72 % (885)Memory used [KB]: 8059
% 20.56/4.72 % (885)Time elapsed: 0.449 s
% 20.56/4.72 % (885)Instructions burned: 934 (million)
% 20.56/4.72 % (885)------------------------------
% 20.56/4.72 % (885)------------------------------
% 20.56/4.75 % (893)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_641 for (2972ds/434Mi)
% 20.56/4.77 % (893)Refutation not found, incomplete strategy
% 20.56/4.77 % (893)------------------------------
% 20.56/4.77 % (893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.56/4.77 % (893)Termination reason: Refutation not found, incomplete strategy
% 20.56/4.77
% 20.56/4.77
% 20.56/4.77 % (893)Memory used [KB]: 6396
% 20.56/4.77 % (893)Time elapsed: 0.027 s
% 20.56/4.77 % (893)Instructions burned: 46 (million)
% 20.56/4.77 % (893)------------------------------
% 20.56/4.77 % (893)------------------------------
% 20.56/4.79 % (894)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_641 for (2972ds/865Mi)
% 21.17/4.83 % (889)Instruction limit reached!
% 21.17/4.83 % (889)------------------------------
% 21.17/4.83 % (889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.83 % (889)Termination reason: Unknown
% 21.17/4.83 % (889)Termination phase: Saturation
% 21.17/4.83
% 21.17/4.83 % (889)Memory used [KB]: 6652
% 21.17/4.83 % (889)Time elapsed: 0.429 s
% 21.17/4.83 % (889)Instructions burned: 794 (million)
% 21.17/4.83 % (889)------------------------------
% 21.17/4.83 % (889)------------------------------
% 21.17/4.84 % (881)First to succeed.
% 21.17/4.84 % (881)Refutation found. Thanks to Tanya!
% 21.17/4.84 % SZS status Theorem for DTF2THF_641
% 21.17/4.84 % SZS output start Proof for DTF2THF_641
% 21.17/4.84 thf(type_def_5, type, pi: $tType).
% 21.17/4.84 thf(type_def_7, type, name: $tType).
% 21.17/4.84 thf(type_def_8, type, late_freeRes: $tType).
% 21.17/4.84 thf(type_def_9, type, late_subject: $tType).
% 21.17/4.84 thf(type_def_10, type, late_residual: $tType).
% 21.17/4.84 thf(type_def_11, type, noption: ($tType) > $tType).
% 21.17/4.84 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 21.17/4.84 thf(type_def_13, type, set: ($tType) > $tType).
% 21.17/4.84 thf(func_def_0, type, late_residual: $tType).
% 21.17/4.84 thf(func_def_1, type, late_subject: $tType).
% 21.17/4.84 thf(func_def_2, type, late_freeRes: $tType).
% 21.17/4.84 thf(func_def_3, type, product_prod: ($tType * $tType) > $tType).
% 21.17/4.84 thf(func_def_4, type, noption: ($tType) > $tType).
% 21.17/4.84 thf(func_def_5, type, name: $tType).
% 21.17/4.84 thf(func_def_6, type, pi: $tType).
% 21.17/4.84 thf(func_def_7, type, set: ($tType) > $tType).
% 21.17/4.84 thf(func_def_8, type, fs_name: !>[X0: $tType]:($o)).
% 21.17/4.84 thf(func_def_9, type, bang: pi > pi).
% 21.17/4.84 thf(func_def_10, type, input: name > name > pi > pi).
% 21.17/4.84 thf(func_def_11, type, match: name > name > pi > pi).
% 21.17/4.84 thf(func_def_12, type, mismatch: name > name > pi > pi).
% 21.17/4.84 thf(func_def_13, type, output: name > name > pi > pi).
% 21.17/4.84 thf(func_def_14, type, par: pi > pi > pi).
% 21.17/4.84 thf(func_def_15, type, piNil: pi).
% 21.17/4.84 thf(func_def_16, type, res: name > pi > pi).
% 21.17/4.84 thf(func_def_17, type, sum: pi > pi > pi).
% 21.17/4.84 thf(func_def_18, type, tau: pi > pi).
% 21.17/4.84 thf(func_def_19, type, subs: pi > name > name > pi).
% 21.17/4.84 thf(func_def_20, type, subst_name: name > name > name > name).
% 21.17/4.84 thf(func_def_21, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 21.17/4.84 thf(func_def_22, type, late_case_freeRes: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 21.17/4.84 thf(func_def_23, type, late_OutputR: name > name > late_freeRes).
% 21.17/4.84 thf(func_def_24, type, late_TauR: late_freeRes).
% 21.17/4.84 thf(func_def_25, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 21.17/4.84 thf(func_def_26, type, late_BoundR: late_subject > name > pi > late_residual).
% 21.17/4.84 thf(func_def_27, type, late_FreeR: late_freeRes > pi > late_residual).
% 21.17/4.84 thf(func_def_28, type, late_BoundOutputS: name > late_subject).
% 21.17/4.84 thf(func_def_29, type, late_InputS: name > late_subject).
% 21.17/4.84 thf(func_def_30, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 21.17/4.84 thf(func_def_31, type, late_transitions: pi > late_residual > $o).
% 21.17/4.84 thf(func_def_32, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 21.17/4.84 thf(func_def_33, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 21.17/4.84 thf(func_def_34, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 21.17/4.84 thf(func_def_35, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 21.17/4.84 thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 21.17/4.84 thf(func_def_37, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 21.17/4.84 thf(func_def_38, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 21.17/4.84 thf(func_def_39, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 21.17/4.84 thf(func_def_40, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 21.17/4.84 thf(func_def_41, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 21.17/4.84 thf(func_def_42, type, p: pi).
% 21.17/4.84 thf(func_def_43, type, pq: pi).
% 21.17/4.84 thf(func_def_44, type, p2: pi).
% 21.17/4.84 thf(func_def_45, type, q: pi).
% 21.17/4.84 thf(func_def_46, type, q2: pi).
% 21.17/4.84 thf(func_def_47, type, rel: set @ product_prod @ pi @ pi).
% 21.17/4.84 thf(func_def_48, type, alpha: late_freeRes).
% 21.17/4.84 thf(func_def_49, type, aa: name).
% 21.17/4.84 thf(func_def_50, type, x: name).
% 21.17/4.84 thf(func_def_51, type, xPQ: pi).
% 21.17/4.84 thf(func_def_52, type, y: name).
% 21.17/4.84 thf(func_def_53, type, z: name).
% 21.17/4.84 thf(func_def_72, type, sP0: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > $o)).
% 21.17/4.84 thf(func_def_73, type, sP1: pi > pi > late_subject > name > pi > $o).
% 21.17/4.84 thf(func_def_74, type, sP2: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_75, type, sP3: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_76, type, sP4: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_77, type, sP5: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_78, type, sP6: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_79, type, sP7: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_80, type, sP8: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_81, type, sP9: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_82, type, sP10: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_83, type, sP11: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_84, type, sP12: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_85, type, sP13: !>[X0: $tType]:((X0 > pi > $o) > $o)).
% 21.17/4.84 thf(func_def_86, type, sP14: late_subject > name > pi > name > pi > $o).
% 21.17/4.84 thf(func_def_87, type, sP15: late_residual > name > pi > $o).
% 21.17/4.84 thf(func_def_88, type, sP16: late_residual > name > pi > $o).
% 21.17/4.84 thf(func_def_89, type, sP17: !>[X0: $tType]:(X0 > pi > pi > set @ product_prod @ pi @ pi > name > $o)).
% 21.17/4.84 thf(func_def_90, type, sP18: pi > set @ product_prod @ pi @ pi > pi > name > $o).
% 21.17/4.84 thf(func_def_91, type, sK19: (late_freeRes > $o) > name).
% 21.17/4.84 thf(func_def_92, type, sK20: (late_freeRes > $o) > name).
% 21.17/4.84 thf(func_def_93, type, sK21: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 21.17/4.84 thf(func_def_94, type, sK22: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 21.17/4.84 thf(func_def_95, type, sK23: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 21.17/4.84 thf(func_def_96, type, sK24: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 21.17/4.84 thf(func_def_97, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 21.17/4.84 thf(func_def_98, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 21.17/4.84 thf(func_def_99, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 21.17/4.84 thf(func_def_100, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 21.17/4.84 thf(func_def_101, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 21.17/4.84 thf(func_def_102, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 21.17/4.84 thf(func_def_103, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 21.17/4.84 thf(func_def_104, type, sK32: pi > name > late_subject > set @ product_prod @ pi @ pi > pi > pi).
% 21.17/4.84 thf(func_def_105, type, sK33: set @ product_prod @ pi @ pi > pi > pi > late_freeRes).
% 21.17/4.84 thf(func_def_106, type, sK34: set @ product_prod @ pi @ pi > pi > pi > pi).
% 21.17/4.84 thf(func_def_107, type, sK35: set @ product_prod @ pi @ pi > pi > pi > late_subject).
% 21.17/4.84 thf(func_def_108, type, sK36: set @ product_prod @ pi @ pi > pi > pi > name).
% 21.17/4.84 thf(func_def_109, type, sK37: set @ product_prod @ pi @ pi > pi > pi > pi).
% 21.17/4.84 thf(func_def_110, type, sK38: !>[X0: $tType]:((name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_111, type, sK39: !>[X0: $tType]:((name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_112, type, sK40: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_113, type, sK41: pi > late_freeRes > pi > name > pi).
% 21.17/4.84 thf(func_def_114, type, sK42: pi > late_freeRes > pi > name > late_freeRes).
% 21.17/4.84 thf(func_def_115, type, sK43: pi > late_freeRes > pi > name > pi).
% 21.17/4.84 thf(func_def_116, type, sK44: pi > late_freeRes > pi > name > name).
% 21.17/4.84 thf(func_def_117, type, sK45: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 21.17/4.84 thf(func_def_118, type, sK46: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > name)).
% 21.17/4.84 thf(func_def_119, type, sK47: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > pi)).
% 21.17/4.84 thf(func_def_120, type, sK48: pi > pi > set @ product_prod @ pi @ pi > late_freeRes).
% 21.17/4.84 thf(func_def_121, type, sK49: pi > pi > set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_122, type, sK50: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 21.17/4.84 thf(func_def_123, type, sK51: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 21.17/4.84 thf(func_def_124, type, sK52: !>[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)).
% 21.17/4.84 thf(func_def_125, type, sK53: !>[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)).
% 21.17/4.84 thf(func_def_126, type, sK54: !>[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)).
% 21.17/4.84 thf(func_def_127, type, sK55: !>[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)).
% 21.17/4.84 thf(func_def_128, type, sK56: !>[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)).
% 21.17/4.84 thf(func_def_129, type, sK57: !>[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)).
% 21.17/4.84 thf(func_def_130, type, sK58: (pi > $o) > late_freeRes > pi > name > pi).
% 21.17/4.84 thf(func_def_131, type, sK59: pi > pi > late_subject > name > pi > pi).
% 21.17/4.84 thf(func_def_132, type, sK60: pi > pi > late_subject > name > pi > late_subject).
% 21.17/4.84 thf(func_def_133, type, sK61: pi > pi > late_subject > name > pi > name).
% 21.17/4.84 thf(func_def_134, type, sK62: pi > pi > late_subject > name > pi > pi).
% 21.17/4.84 thf(func_def_135, type, sK63: pi > pi > late_subject > name > pi > pi).
% 21.17/4.84 thf(func_def_136, type, sK64: pi > name > late_subject > pi > pi > pi).
% 21.17/4.84 thf(func_def_137, type, sK65: pi > name > late_subject > pi > pi > late_subject).
% 21.17/4.84 thf(func_def_138, type, sK66: pi > name > late_subject > pi > pi > name).
% 21.17/4.84 thf(func_def_139, type, sK67: pi > name > late_subject > pi > pi > pi).
% 21.17/4.84 thf(func_def_140, type, sK68: pi > name > late_subject > pi > pi > pi).
% 21.17/4.84 thf(func_def_141, type, sK69: late_residual > pi > name > name > pi).
% 21.17/4.84 thf(func_def_142, type, sK70: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 21.17/4.84 thf(func_def_143, type, sK71: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 21.17/4.84 thf(func_def_144, type, sK72: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 21.17/4.84 thf(func_def_145, type, sK73: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 21.17/4.84 thf(func_def_146, type, sK74: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_147, type, sK75: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_148, type, sK76: set @ product_prod @ pi @ pi > name).
% 21.17/4.84 thf(func_def_149, type, sK77: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_150, type, sK78: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_151, type, sK79: !>[X0: $tType]:((name > name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_152, type, sK80: !>[X0: $tType]:((name > name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_153, type, sK81: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_154, type, sK82: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_155, type, sK83: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_156, type, sK84: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_157, type, sK85: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_158, type, sK86: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_159, type, sK87: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_160, type, sK88: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_161, type, sK89: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_162, type, sK90: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_163, type, sK91: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_164, type, sK92: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_165, type, sK93: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_166, type, sK94: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_167, type, sK95: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_168, type, sK96: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_169, type, sK97: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_170, type, sK98: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_171, type, sK99: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_172, type, sK100: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_173, type, sK101: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_174, type, sK102: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_175, type, sK103: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_176, type, sK104: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_177, type, sK105: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_178, type, sK106: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_179, type, sK107: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_180, type, sK108: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_181, type, sK109: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_182, type, sK110: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_183, type, sK111: !>[X0: $tType]:((name > name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_184, type, sK112: !>[X0: $tType]:((name > name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_185, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.17/4.84 thf(func_def_186, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.17/4.84 thf(func_def_187, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.17/4.84 thf(func_def_188, type, sK116: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 21.17/4.84 thf(func_def_189, type, sK117: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 21.17/4.84 thf(func_def_190, type, sK118: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 21.17/4.84 thf(func_def_191, type, sK119: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 21.17/4.84 thf(func_def_192, type, sK120: !>[X0: $tType]:((X0 > late_residual > $o) > late_subject)).
% 21.17/4.84 thf(func_def_193, type, sK121: !>[X0: $tType]:((X0 > late_residual > $o) > name)).
% 21.17/4.84 thf(func_def_194, type, sK122: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 21.17/4.84 thf(func_def_195, type, sK123: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 21.17/4.84 thf(func_def_196, type, sK124: !>[X0: $tType]:((X0 > late_residual > $o) > late_freeRes)).
% 21.17/4.84 thf(func_def_197, type, sK125: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 21.17/4.84 thf(func_def_198, type, sK126: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 21.17/4.84 thf(func_def_199, type, sK127: !>[X0: $tType]:((X0 > late_residual > $o) > late_freeRes)).
% 21.17/4.84 thf(func_def_200, type, sK128: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 21.17/4.84 thf(func_def_201, type, sK129: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 21.17/4.84 thf(func_def_202, type, sK130: !>[X0: $tType]:((X0 > late_residual > $o) > late_subject)).
% 21.17/4.84 thf(func_def_203, type, sK131: !>[X0: $tType]:((X0 > late_residual > $o) > name)).
% 21.17/4.84 thf(func_def_204, type, sK132: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 21.17/4.84 thf(func_def_205, type, sK133: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 21.17/4.84 thf(func_def_206, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.17/4.84 thf(func_def_207, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.17/4.84 thf(func_def_208, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.17/4.84 thf(func_def_209, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.17/4.84 thf(func_def_210, type, sK138: late_residual > pi > name > name > name).
% 21.17/4.84 thf(func_def_211, type, sK139: late_residual > pi > name > name > name).
% 21.17/4.84 thf(func_def_212, type, sK140: late_residual > pi > name > name > pi).
% 21.17/4.84 thf(func_def_213, type, sK141: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_214, type, sK142: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_215, type, sK143: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_216, type, sK144: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_217, type, sK145: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_218, type, sK146: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_219, type, sK147: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_220, type, sK148: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_221, type, sK149: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_222, type, sK150: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_223, type, sK151: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_224, type, sK152: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_225, type, sK153: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_226, type, sK154: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_227, type, sK155: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_228, type, sK156: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_229, type, sK157: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_230, type, sK158: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_231, type, sK159: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_232, type, sK160: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_233, type, sK161: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_234, type, sK162: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_235, type, sK163: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_236, type, sK164: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_237, type, sK165: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_238, type, sK166: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_239, type, sK167: !>[X0: $tType]:((X0 > pi > $o) > name)).
% 21.17/4.84 thf(func_def_240, type, sK168: !>[X0: $tType]:((X0 > pi > $o) > pi)).
% 21.17/4.84 thf(func_def_241, type, sK169: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_242, type, sK170: !>[X0: $tType]:((X0 > pi > $o) > X0)).
% 21.17/4.84 thf(func_def_243, type, sK171: late_subject > name).
% 21.17/4.84 thf(func_def_244, type, sK172: late_subject > name).
% 21.17/4.84 thf(func_def_245, type, sK173: !>[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)).
% 21.17/4.84 thf(func_def_246, type, sK174: !>[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)).
% 21.17/4.84 thf(func_def_247, type, sK175: !>[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)).
% 21.17/4.84 thf(func_def_248, type, sK176: !>[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)).
% 21.17/4.84 thf(func_def_249, type, sK177: !>[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)).
% 21.17/4.84 thf(func_def_250, type, sK178: !>[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)).
% 21.17/4.84 thf(func_def_251, type, sK179: !>[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)).
% 21.17/4.84 thf(func_def_252, type, sK180: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 21.17/4.84 thf(func_def_253, type, sK181: !>[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)).
% 21.17/4.84 thf(func_def_254, type, sK182: !>[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)).
% 21.17/4.84 thf(func_def_255, type, sK183: !>[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)).
% 21.17/4.84 thf(func_def_256, type, sK184: !>[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)).
% 21.17/4.84 thf(func_def_257, type, sK185: !>[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)).
% 21.17/4.84 thf(func_def_258, type, sK186: !>[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)).
% 21.17/4.84 thf(func_def_259, type, sK187: !>[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)).
% 21.17/4.84 thf(func_def_260, type, sK188: pi > late_freeRes > set @ product_prod @ pi @ pi > pi > pi).
% 21.17/4.84 thf(func_def_261, type, sK189: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_262, type, sK190: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_263, type, sK191: set @ product_prod @ pi @ pi > name).
% 21.17/4.84 thf(func_def_264, type, sK192: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_265, type, sK193: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_266, type, sK194: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_267, type, sK195: set @ product_prod @ pi @ pi > name).
% 21.17/4.84 thf(func_def_268, type, sK196: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_269, type, sK197: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_270, type, sK198: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_271, type, sK199: set @ product_prod @ pi @ pi > name).
% 21.17/4.84 thf(func_def_272, type, sK200: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_273, type, sK201: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_274, type, sK202: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_275, type, sK203: late_residual > pi > name > name > pi).
% 21.17/4.84 thf(func_def_276, type, sK204: late_residual > pi > name > name > name).
% 21.17/4.84 thf(func_def_277, type, sK205: late_residual > pi > name > name > name).
% 21.17/4.84 thf(func_def_278, type, sK206: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 21.17/4.84 thf(func_def_279, type, sK207: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 21.17/4.84 thf(func_def_280, type, sK208: (late_subject > $o) > name).
% 21.17/4.84 thf(func_def_281, type, sK209: (late_subject > $o) > name).
% 21.17/4.84 thf(func_def_282, type, sK210: late_subject > name > pi > name > pi > pi).
% 21.17/4.84 thf(func_def_283, type, sK211: late_subject > name > pi > name > pi > late_subject).
% 21.17/4.84 thf(func_def_284, type, sK212: late_subject > name > pi > name > pi > name).
% 21.17/4.84 thf(func_def_285, type, sK213: late_subject > name > pi > name > pi > pi).
% 21.17/4.84 thf(func_def_286, type, sK214: late_subject > name > pi > name > pi > name).
% 21.17/4.84 thf(func_def_287, type, sK215: pi > name > late_subject > pi > name > pi).
% 21.17/4.84 thf(func_def_288, type, sK216: pi > name > late_subject > pi > name > name).
% 21.17/4.84 thf(func_def_289, type, sK217: pi > name > late_subject > pi > name > name).
% 21.17/4.84 thf(func_def_290, type, sK218: pi > name > late_subject > pi > name > pi).
% 21.17/4.84 thf(func_def_291, type, sK219: !>[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)).
% 21.17/4.84 thf(func_def_292, type, sK220: !>[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)).
% 21.17/4.84 thf(func_def_293, type, sK221: !>[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)).
% 21.17/4.84 thf(func_def_294, type, sK222: !>[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)).
% 21.17/4.84 thf(func_def_295, type, sK223: !>[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)).
% 21.17/4.84 thf(func_def_296, type, sK224: !>[X0: $tType]:(X0 > name)).
% 21.17/4.84 thf(func_def_297, type, sK225: set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_298, type, sK226: late_residual > pi > name > name > name).
% 21.17/4.84 thf(func_def_299, type, sK227: late_residual > pi > name > name > name).
% 21.17/4.84 thf(func_def_300, type, sK228: late_residual > pi > name > name > pi).
% 21.17/4.84 thf(func_def_301, type, sK229: (pi > $o) > name > late_subject > pi > pi > pi).
% 21.17/4.84 thf(func_def_302, type, sK230: (pi > $o) > name > late_subject > pi > pi > pi).
% 21.17/4.84 thf(func_def_303, type, sK231: late_residual > name > pi > pi).
% 21.17/4.84 thf(func_def_304, type, sK232: late_residual > name > pi > late_freeRes).
% 21.17/4.84 thf(func_def_305, type, sK233: late_residual > name > pi > pi).
% 21.17/4.84 thf(func_def_306, type, sK234: late_residual > name > pi > name).
% 21.17/4.84 thf(func_def_307, type, sK235: late_residual > name > pi > pi).
% 21.17/4.84 thf(func_def_308, type, sK236: late_residual > name > pi > late_subject).
% 21.17/4.84 thf(func_def_309, type, sK237: late_residual > name > pi > name).
% 21.17/4.84 thf(func_def_310, type, sK238: late_residual > name > pi > pi).
% 21.17/4.84 thf(func_def_311, type, sK239: late_residual > name > pi > name).
% 21.17/4.84 thf(func_def_312, type, sK240: late_residual > pi > name > pi).
% 21.17/4.84 thf(func_def_313, type, sK241: late_residual > pi > name > name).
% 21.17/4.84 thf(func_def_314, type, sK242: late_residual > pi > name > name).
% 21.17/4.84 thf(func_def_315, type, sK243: late_residual > pi > name > pi).
% 21.17/4.84 thf(func_def_316, type, sK244: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 21.17/4.84 thf(func_def_317, type, sK245: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 21.17/4.84 thf(func_def_318, type, sK246: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 21.17/4.84 thf(func_def_319, type, sK247: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 21.17/4.84 thf(func_def_320, type, sK248: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 21.17/4.84 thf(func_def_321, type, sK249: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 21.17/4.84 thf(func_def_322, type, sK250: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 21.17/4.84 thf(func_def_323, type, sK251: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 21.17/4.84 thf(func_def_324, type, sK252: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 21.17/4.84 thf(func_def_325, type, sK253: late_residual > pi > pi).
% 21.17/4.84 thf(func_def_326, type, sK254: pi > set @ product_prod @ pi @ pi > pi > name > pi).
% 21.17/4.84 thf(func_def_327, type, sK255: pi > set @ product_prod @ pi @ pi > pi > name > name).
% 21.17/4.84 thf(func_def_328, type, sK256: !>[X0: $tType]:(X0 > pi > pi > set @ product_prod @ pi @ pi > name > pi)).
% 21.17/4.84 thf(func_def_329, type, sK257: !>[X0: $tType]:(X0 > pi > pi > set @ product_prod @ pi @ pi > name > late_subject)).
% 21.17/4.84 thf(func_def_330, type, sK258: !>[X0: $tType]:(X0 > pi > pi > set @ product_prod @ pi @ pi > name > name)).
% 21.17/4.84 thf(func_def_331, type, sK259: pi > name > pi > set @ product_prod @ pi @ pi > pi).
% 21.17/4.84 thf(func_def_332, type, sK260: pi > name > pi > set @ product_prod @ pi @ pi > late_freeRes).
% 21.17/4.84 thf(func_def_333, type, sK261: !>[X0: $tType]:((name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_334, type, sK262: !>[X0: $tType]:((name > X0) > (X0 > $o) > name)).
% 21.17/4.84 thf(func_def_335, type, sK263: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 21.17/4.84 thf(func_def_336, type, sK264: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 21.17/4.84 thf(func_def_337, type, sK265: late_freeRes > name).
% 21.17/4.84 thf(func_def_338, type, sK266: late_freeRes > name).
% 21.17/4.84 thf(func_def_339, type, sK267: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 21.17/4.84 thf(func_def_340, type, sK268: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 21.17/4.84 thf(func_def_341, type, sK269: (late_residual > $o) > late_freeRes).
% 21.17/4.84 thf(func_def_342, type, sK270: (late_residual > $o) > pi).
% 21.17/4.84 thf(func_def_343, type, sK271: (late_residual > $o) > late_subject).
% 21.17/4.84 thf(func_def_344, type, sK272: (late_residual > $o) > name).
% 21.17/4.84 thf(func_def_345, type, sK273: (late_residual > $o) > pi).
% 21.17/4.84 thf(func_def_346, type, sK274: !>[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)).
% 21.17/4.84 thf(func_def_347, type, sK275: !>[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)).
% 21.17/4.84 thf(func_def_348, type, sK276: !>[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)).
% 21.17/4.84 thf(func_def_349, type, sK277: !>[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)).
% 21.17/4.84 thf(func_def_350, type, sK278: !>[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)).
% 21.17/4.84 thf(func_def_351, type, sK279: !>[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)).
% 21.17/4.84 thf(func_def_352, type, sK280: late_residual > pi > pi).
% 21.17/4.84 thf(func_def_354, type, ph282: !>[X0: $tType]:(X0)).
% 21.17/4.84 thf(f5080,plain,(
% 21.17/4.84 $false),
% 21.17/4.84 inference(trivial_inequality_removal,[status(thm)],[f5078])).
% 21.17/4.84 thf(f5078,plain,(
% 21.17/4.84 ($true != $true)),
% 21.17/4.84 inference(superposition,[status(thm)],[f4419,f1174])).
% 21.17/4.84 thf(f1174,plain,(
% 21.17/4.84 ( ! [X2 : pi,X0 : name,X1 : name] : (($true = (late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ (late_InputS @ X0) @ X1 @ X2)))) )),
% 21.17/4.84 inference(cnf_transformation,[status(thm)],[f477])).
% 21.17/4.84 thf(f477,plain,(
% 21.17/4.84 ! [X0 : name,X1 : name,X2 : pi] : ($true = (late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ (late_InputS @ X0) @ X1 @ X2)))),
% 21.17/4.84 inference(fool_elimination,[status(thm)],[f476])).
% 21.17/4.84 thf(f476,plain,(
% 21.17/4.84 ! [X0 : name,X1 : name,X2 : pi] : (late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ (late_InputS @ X0) @ X1 @ X2))),
% 21.17/4.84 inference(rectify,[status(thm)],[f180])).
% 21.17/4.84 thf(f180,axiom,(
% 21.17/4.84 ! [X5 : name,X12 : name,X8 : pi] : (late_transitions @ (input @ X5 @ X12 @ X8) @ (late_BoundR @ (late_InputS @ X5) @ X12 @ X8))),
% 21.17/4.84 file('/export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2THF_641.p',fact_179_Late__Semantics_OInput)).
% 21.17/4.84 thf(f4419,plain,(
% 21.17/4.84 ( ! [X2 : name,X3 : pi,X0 : name,X1 : pi] : (($true != (late_transitions @ (input @ aa @ X0 @ X1) @ (late_BoundR @ (late_InputS @ aa) @ X2 @ X3)))) )),
% 21.17/4.84 inference(trivial_inequality_removal,[status(thm)],[f4414])).
% 21.17/4.84 thf(f4414,plain,(
% 21.17/4.84 ( ! [X2 : name,X3 : pi,X0 : name,X1 : pi] : (($true != $true) | ($true != (late_transitions @ (input @ aa @ X0 @ X1) @ (late_BoundR @ (late_InputS @ aa) @ X2 @ X3)))) )),
% 21.17/4.84 inference(superposition,[status(thm)],[f1577,f4172])).
% 21.17/4.84 thf(f4172,plain,(
% 21.17/4.84 ($true = (fresh @ name @ late_subject @ aa @ (late_InputS @ aa)))),
% 21.17/4.84 inference(trivial_inequality_removal,[status(thm)],[f4170])).
% 21.17/4.84 thf(f4170,plain,(
% 21.17/4.84 ($true != $true) | ($true = (fresh @ name @ late_subject @ aa @ (late_InputS @ aa)))),
% 21.17/4.84 inference(superposition,[status(thm)],[f4157,f1495])).
% 21.17/4.84 thf(f1495,plain,(
% 21.17/4.84 ((late_transitions @ p @ (late_BoundR @ (late_InputS @ aa) @ y @ p2)) = $true)),
% 21.17/4.84 inference(cnf_transformation,[status(thm)],[f525])).
% 21.17/4.84 thf(f525,plain,(
% 21.17/4.84 ((late_transitions @ p @ (late_BoundR @ (late_InputS @ aa) @ y @ p2)) = $true)),
% 21.17/4.84 inference(fool_elimination,[status(thm)],[f524])).
% 21.17/4.84 thf(f524,plain,(
% 21.17/4.84 (late_transitions @ p @ (late_BoundR @ (late_InputS @ aa) @ y @ p2))),
% 21.17/4.84 inference(rectify,[status(thm)],[f9])).
% 21.17/4.84 thf(f9,axiom,(
% 21.17/4.84 (late_transitions @ p @ (late_BoundR @ (late_InputS @ aa) @ y @ p2))),
% 21.17/4.84 file('/export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2THF_641.p',fact_8_cClose1_Ohyps_I1_J)).
% 21.17/4.84 thf(f4157,plain,(
% 21.17/4.84 ( ! [X2 : pi,X0 : late_subject,X1 : name] : (($true != (late_transitions @ p @ (late_BoundR @ X0 @ X1 @ X2))) | ($true = (fresh @ name @ late_subject @ aa @ X0))) )),
% 21.17/4.84 inference(trivial_inequality_removal,[status(thm)],[f4143])).
% 21.17/4.84 thf(f4143,plain,(
% 21.17/4.84 ( ! [X2 : pi,X0 : late_subject,X1 : name] : (($true != (late_transitions @ p @ (late_BoundR @ X0 @ X1 @ X2))) | ($true = (fresh @ name @ late_subject @ aa @ X0)) | ($true != $true)) )),
% 21.17/4.84 inference(superposition,[status(thm)],[f1211,f1949])).
% 21.17/4.84 thf(f1949,plain,(
% 21.17/4.84 ($true = (fresh @ name @ pi @ aa @ p))),
% 21.17/4.84 inference(forward_demodulation,[status(thm)],[f1463,f1324])).
% 21.17/4.84 thf(f1324,plain,(
% 21.17/4.84 (x = aa)),
% 21.17/4.84 inference(cnf_transformation,[status(thm)],[f662])).
% 21.17/4.84 thf(f662,plain,(
% 21.17/4.84 (x = aa)),
% 21.17/4.84 inference(flattening,[status(thm)],[f268])).
% 21.17/4.84 thf(f268,negated_conjecture,(
% 21.17/4.84 ~(x != aa)),
% 21.17/4.84 inference(negated_conjecture,[status(cth)],[f267])).
% 21.17/4.84 thf(f267,conjecture,(
% 21.17/4.84 (x != aa)),
% 21.17/4.84 file('/export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2THF_641.p',conj_0)).
% 21.17/4.84 thf(f1463,plain,(
% 21.17/4.84 ((fresh @ name @ pi @ x @ p) = $true)),
% 21.17/4.84 inference(cnf_transformation,[status(thm)],[f583])).
% 21.17/4.84 thf(f583,plain,(
% 21.17/4.84 ((fresh @ name @ pi @ x @ p) = $true)),
% 21.17/4.84 inference(fool_elimination,[status(thm)],[f582])).
% 21.17/4.84 thf(f582,plain,(
% 21.17/4.84 (fresh @ name @ pi @ x @ p)),
% 21.17/4.84 inference(rectify,[status(thm)],[f4])).
% 21.17/4.84 thf(f4,axiom,(
% 21.17/4.84 (fresh @ name @ pi @ x @ p)),
% 21.17/4.84 file('/export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2THF_641.p',fact_3_assms_I1_J)).
% 21.17/4.84 thf(f1211,plain,(
% 21.17/4.84 ( ! [X2 : name,X3 : pi,X0 : pi,X1 : late_subject,X4 : name] : (($true != (fresh @ name @ pi @ X4 @ X0)) | ($true = (fresh @ name @ late_subject @ X4 @ X1)) | ((late_transitions @ X0 @ (late_BoundR @ X1 @ X2 @ X3)) != $true)) )),
% 21.17/4.84 inference(cnf_transformation,[status(thm)],[f914])).
% 21.17/4.84 thf(f914,plain,(
% 21.17/4.84 ! [X0 : pi,X1 : late_subject,X2 : name,X3 : pi,X4 : name] : (($true = (fresh @ name @ late_subject @ X4 @ X1)) | ($true != (fresh @ name @ pi @ X4 @ X0)) | ((late_transitions @ X0 @ (late_BoundR @ X1 @ X2 @ X3)) != $true))),
% 21.17/4.84 inference(flattening,[status(thm)],[f913])).
% 21.17/4.84 thf(f913,plain,(
% 21.17/4.84 ! [X0 : pi,X1 : late_subject,X2 : name,X3 : pi,X4 : name] : ((($true = (fresh @ name @ late_subject @ X4 @ X1)) | ($true != (fresh @ name @ pi @ X4 @ X0))) | ((late_transitions @ X0 @ (late_BoundR @ X1 @ X2 @ X3)) != $true))),
% 21.17/4.84 inference(ennf_transformation,[status(thm)],[f407])).
% 21.17/4.84 thf(f407,plain,(
% 21.17/4.84 ! [X0 : pi,X1 : late_subject,X2 : name,X3 : pi,X4 : name] : (((late_transitions @ X0 @ (late_BoundR @ X1 @ X2 @ X3)) = $true) => (($true = (fresh @ name @ pi @ X4 @ X0)) => ($true = (fresh @ name @ late_subject @ X4 @ X1))))),
% 21.17/4.84 inference(fool_elimination,[status(thm)],[f406])).
% 21.17/4.84 thf(f406,plain,(
% 21.17/4.84 ! [X0 : pi,X1 : late_subject,X2 : name,X3 : pi,X4 : name] : ((late_transitions @ X0 @ (late_BoundR @ X1 @ X2 @ X3)) => ((fresh @ name @ pi @ X4 @ X0) => (fresh @ name @ late_subject @ X4 @ X1)))),
% 21.17/4.84 inference(rectify,[status(thm)],[f76])).
% 21.17/4.84 thf(f76,axiom,(
% 21.17/4.84 ! [X8 : pi,X5 : late_subject,X12 : name,X10 : pi,X11 : name] : ((late_transitions @ X8 @ (late_BoundR @ X5 @ X12 @ X10)) => ((fresh @ name @ pi @ X11 @ X8) => (fresh @ name @ late_subject @ X11 @ X5)))),
% 21.17/4.84 file('/export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2THF_641.p',fact_75_freshBoundDerivative_I1_J)).
% 21.17/4.84 thf(f1577,plain,(
% 21.17/4.84 ( ! [X2 : pi,X3 : late_subject,X0 : name,X1 : name,X4 : name,X5 : pi] : (($true != (fresh @ name @ late_subject @ X0 @ X3)) | ($true != (late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ X3 @ X4 @ X5)))) )),
% 21.17/4.84 inference(cnf_transformation,[status(thm)],[f824])).
% 21.17/4.84 thf(f824,plain,(
% 21.17/4.84 ! [X0 : name,X1 : name,X2 : pi,X3 : late_subject,X4 : name,X5 : pi] : (($true != (fresh @ name @ late_subject @ X0 @ X3)) | ($true != (late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ X3 @ X4 @ X5))))),
% 21.17/4.84 inference(ennf_transformation,[status(thm)],[f676])).
% 21.17/4.84 thf(f676,plain,(
% 21.17/4.84 ! [X0 : name,X1 : name,X2 : pi,X3 : late_subject,X4 : name,X5 : pi] : (($true = (late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ X3 @ X4 @ X5))) => ($true != (fresh @ name @ late_subject @ X0 @ X3)))),
% 21.17/4.84 inference(flattening,[status(thm)],[f405])).
% 21.17/4.84 thf(f405,plain,(
% 21.17/4.84 ! [X0 : name,X1 : name,X2 : pi,X3 : late_subject,X4 : name,X5 : pi] : (($true = (late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ X3 @ X4 @ X5))) => ~($true = (fresh @ name @ late_subject @ X0 @ X3)))),
% 21.17/4.84 inference(fool_elimination,[status(thm)],[f404])).
% 21.17/4.84 thf(f404,plain,(
% 21.17/4.84 ! [X0 : name,X1 : name,X2 : pi,X3 : late_subject,X4 : name,X5 : pi] : ((late_transitions @ (input @ X0 @ X1 @ X2) @ (late_BoundR @ X3 @ X4 @ X5)) => ~(fresh @ name @ late_subject @ X0 @ X3))),
% 21.17/4.84 inference(rectify,[status(thm)],[f183])).
% 21.17/4.84 thf(f183,axiom,(
% 21.17/4.84 ! [X5 : name,X12 : name,X8 : pi,X50 : late_subject,X11 : name,X10 : pi] : ((late_transitions @ (input @ X5 @ X12 @ X8) @ (late_BoundR @ X50 @ X11 @ X10)) => ~(fresh @ name @ late_subject @ X5 @ X50))),
% 21.17/4.84 file('/export/starexec/sandbox2/tmp/tmp.iCqLwW8M5D/DTF2THF_641.p',fact_182_inputIneqTrans)).
% 21.17/4.84 % SZS output end Proof for DTF2THF_641
% 21.17/4.84 % (881)------------------------------
% 21.17/4.84 % (881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.84 % (881)Termination reason: Refutation
% 21.17/4.84
% 21.17/4.84 % (881)Memory used [KB]: 10234
% 21.17/4.84 % (881)Time elapsed: 0.711 s
% 21.17/4.84 % (881)Instructions burned: 1251 (million)
% 21.17/4.84 % (881)------------------------------
% 21.17/4.84 % (881)------------------------------
% 21.17/4.84 % (760)Success in time 2.846 s
%------------------------------------------------------------------------------